Satellite based Regional-scale Evapotranspiration in …...Satellite based Regional-scale Evapotranspiration in the Hebei Plain, Northeastern China by Wenjing Lin Thesis submitted

Satellite based Regional-scale Evapotranspiration in the Hebei Plain,

Northeastern China

Wenjing Lin March, 2006

Satellite based Regional-scale Evapotranspiration in the Hebei Plain, Northeastern China

by

Wenjing Lin Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfilment of the requirements for the degree of Master of Science in Geo-information Science and Earth Observation, Specialisation: Advanced use of Remote Sensing in Water Resource Management, Irrigation and Drainage. Thesis Assessment Board Chairman Prof. Dr. Ir. Z. Su Head-WRS Department, ITC, Enschede External Examiner Dr. L. Jia Wageningen University and Research-ALTERRA First Supervisor Prof. Dr. Ir. Z. Su WRS Department, ITC, Enschede Second Supervisor R. van der Velde WRS Department, ITC, Enschede

INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION ENSCHEDE, THE NETHERLANDS

I certify that although I may have conferred with others in preparing for this assignment, and drawn upon a range of sources cited in this work, the content of this thesis report is my original work. Signed……………………

Disclaimer This document describes work undertaken as part of a programme of study at the International Institute for Geo-information Science and Earth Observation. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the institute.

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Abstract

Evapotranspiration is one of the most significant components of the hydrologic budget. Conventional techniques that based on the point measurements are representative only of local scales and will fail for large scales. Satellite sensors that observe the earth from the space give a chance to estimate evapotranspiration in a big scale. The Surface Energy Balance System (SEBS) model was developed to estimate land surface fluxes using remotely sensed data and available meteorological observations. It has the most important advantage of its inclusion of a physical model for the estimation of the roughness height for heat transfer which is the most critical parameter in the parameterization of the heat fluxes of land surface. In this study, SEBS has been utilized to estimate the surface fluxes over Hebei Plain in Northeastern China by using MODIS/TERRA images, in combination of meteorological data collected in meteorological stations distributed over the study area. In order to get the daily evapotranspiration as accurate as possible, a thorough literature research about the various methods to calculate different surface bio-physical parameters and the sensitivity analysis of these parameters to SEBS result were conducted. The estimated daily evapotranspiration by SEBS in cloud free days are first compared with measurements by large weighing lysimeter in Luancheng Agro-Ecosystem Station (LAES) located near Shijiazhuang city. The comparisons show that the estimated evapotranspiration from SEBS have a good agreement with the ground truth data. Based on the validation of the model, a modified model of SEBS has utilized to analysis the soil moisture status on cloud free days over the study area and the spatial-temporal distributions of actual evapotranspiration were analyzed by combination of the up-to-date land cover map in Hebei Plain. Finally, limitations and recommendation for further study were addressed. Key words: actual evapotranspiration, SEBS, MODIS/TERRA, Hebei Plain

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Acknowledgements

When the eighteen months M.Sc study is coming to the end, my wonderful life in the beautiful Netherlands is replayed slowly like an old movie and a lot of stories that are worthy of memory and persons that are worthy of acknowledgement float in my mind.

First of all, I would like to express my deep appreciation to my supervisor, Prof. Dr. Z. (Bob) Su. Throughout this period, I have been fortunate to receive constructive criticism and guidance from him. His rich knowledge in the field of Spatial Hydrology and his experience in the domain of numerical modelling of land surface processes, and advanced remote sensing in water management have had a great contribution to this thesis. My sincere thanks also go to my second supervisor, Rogier van der Velde, who promptly reviewed many of my chapters and guided me through out the structuring of my thesis. His comments and suggestions on the structure and contents of the thesis have considerably improved its quality and readability. I learned a lot from his style of supervision and I really appreciated his patience and friendship.

I would like to give great thanks to the Ministry of Land and Resources (MLR) of China and my organization Institute of Hydrogeology and Environmental Geology, CAGS, who open the door for me to start the exciting life that was full of adventure and freshness. Special appreciation is extended to Prof. Dr. Guiling Wang, for his fully support of my study aboard and much convenience he gave to me not only for the preparation of school entrance application but also for the M.Sc study in the Netherlands. Special thanks also go to my dear colleague, Fan Qi, for her warm hospitality and help each time I had to deal with some urgent affairs of our institute when I am in Netherlands.

There are also many ITC staffs that help me to increase the experiences in doing academic researches. Special thanks go to the Department of Water Resources and Environmental Management. Especially, I like to extend my appreciation to the program director ir. Arno Van Lieshout for his kindness and understanding about every student in the programme. I thank him also for allowing me to spend some times to do the research in my country and be able to see my family on the way.

Further thanks to my dear Chinese group friends at ITC: Shan Xing, Zhou Yuhong, Ai Ping, Li Xia, Wu Xiaoling, Wu Yun, Wang Guoming, Li Xuejie, Chen Zhihong, Zhang Ning, Zhao Daihong, Pan Hui, Zhao Zheng, Bai Lei, Xu Shaona etc, with whom I have shared a rich and colourful life here not only in studies but also for various funs. Especially for my cooking group, who share their cooking skills and delicious food with me and make me full of energy to study. Special appreciation is extended to Wei Junguo for his support at the field data collecting level of my work, his kindness and friendship is highly appreciated.

At the same time, I would like to acknowledge my WREM group classmates, who gave me their kind concern, cooperation and help. I enjoyed the happiness of sharing different cultures and food with them. They are Ambayo Denis, Nguyen Hongquan, Mohammedjemal Mahmmud Abdulwhab, Hailegiorgis Sine Wondimagegn, Ludueña Sebastian, Sikamundenga Florah, Tsagli Joseph, Zongo Gombila, Ngoga Tenge Gislain, Mpusia Peter, etc. Moreover, thanks to many other new foreign friends, from whom I have learned much, especially those friends who still extended their support and bless to me although they are away from ITC already.

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And last but certainly not least, much gratitude to the members of my family for all the moral support they gave me during my study. My heartfelt thanks go to my wife, Dong Lijie, for undertaking the whole burden of our family. Her encouragement and understanding made it possible to bring this dissertation to the world. Loving thanks to my little daughter, Nannan, who has given me so much joy and enjoyed playing with me so much, but had a so long time for miss.

The way ahead is long; I see no ending, yet high and low I’ll search with my will unbending.

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Table of contents

1. Introduction ....................................................................................................................................1

1.1. Background .............................................................................................................................1 1.2. A brief history in remote sensing of evapotranspiration ........................................................2

1.2.1. Analytical approaches ........................................................................................................2 1.2.2. Empirical approaches .........................................................................................................4

1.3. Problem definition ..................................................................................................................4 1.4. Objectives and research questions ..........................................................................................5

2. Study Area and Materials .............................................................................................................6

2.1. Study Area ..............................................................................................................................6 2.2. Meteorological Observations..................................................................................................7 2.3. Satellite Observations .............................................................................................................9

2.3.1. Moderate-resolution Imaging Spectroradiometer (MODIS) ..............................................9 2.3.2. MODIS Products ..............................................................................................................10 2.3.3. Acquirement of MODIS products ....................................................................................12

2.4. Validation data......................................................................................................................13 2.5. Land cover ............................................................................................................................13

3. Surface Energy Balance System (SEBS)....................................................................................16

3.1. Principle of energy balance closure......................................................................................16 3.2. Net radiation .........................................................................................................................17 3.3. Soil heat flux.........................................................................................................................18 3.4. Sensible heat flux..................................................................................................................19 3.5. Evaporative fraction..............................................................................................................19 3.6. Surface roughness length for heat transfer ...........................................................................20 3.7. Turbulent heat fluxes and actual evaporation.......................................................................21

4. Data Processing and Bio-physical Parameters Estimation ......................................................22

4.1. Meteorological data pre-processing......................................................................................22 4.2. Radiation data processing.....................................................................................................25 4.3. Remote sensing data processing ...........................................................................................25 4.4. Surface Biophysical Properties.............................................................................................27

4.4.1. Normalized Difference Vegetation Index (NDVI)...........................................................27 4.4.2. Fractional vegetation cover ..............................................................................................27 4.4.3. Leaf Area Index (LAI)......................................................................................................29 4.4.4. Vegetation height (h)........................................................................................................31

4.5. Surface characteristic parameters .........................................................................................31 4.5.1. Broad-band emissivity......................................................................................................31 4.5.2. Aerodynamic roughness height (z0m) ...............................................................................32 4.5.3. Displacement height (d0) ..................................................................................................35 4.5.4. Albedo ..............................................................................................................................36 4.5.5. Emissivity of the atmosphere ...........................................................................................36

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4.6. Sensitivity analysis ...............................................................................................................37 4.6.1. Sensitivity to displacement height....................................................................................38 4.6.2. Sensitivity to fractional vegetation cover.........................................................................40 4.6.3. Sensitivity to aerodynamic roughness height ...................................................................41 4.6.4. Sensitivity to surface emissivity.......................................................................................43 4.6.5. Summary of sensitivity analysis .......................................................................................44

5. Actual Evapotranspiration and Spatio-temporal Distribution................................................46

5.1. Accuracy Assessment ...........................................................................................................46 5.1.1. Ground truth Actual Evapotranspiration (ETa)................................................................46 5.1.2. Crop Evapotranspiration (ETc) ........................................................................................47 5.1.3. Comparison of SEBS modelled ETa to measured ETa and ETc......................................49

5.2. Spatio-temporal disribution of land surface variables ..........................................................51 5.2.1. Surface reflectance (surface albedo) ................................................................................51 5.2.2. Surface temperature..........................................................................................................52 5.2.3. Relationship between surface reflectance and surface temperature.................................54

5.3. Spatio-temporal disribution of Vegetation Variables..........................................................57 5.3.1. Normalized Difference Vegetation Index (NDVI)...........................................................57 5.3.2. Relationship between NDVI and surface temperature .....................................................58 5.3.3. Fractional Vegetation Cover ............................................................................................60

5.4. Spatial-temporal distribution ETa.........................................................................................62 5.4.1. Spatial distribution of ETa in summer .............................................................................62 5.4.2. Spatial distribution of ETa in autumn ..............................................................................64 5.4.3. Spatial distribution of ETa in winter ................................................................................66 5.4.4. Spatial distribution of ETa in spring ................................................................................67 5.4.5. Temporal distribution of ETa...........................................................................................73

6. Conclusions and Recommendation.............................................................................................80

6.1. General Summary .................................................................................................................80 6.2. Major results and Conclusions .............................................................................................80 6.3. Limitation and challenge ......................................................................................................82 6.4. Recommendations.................................................................................................................82

References .............................................................................................................................................83

Appendices ............................................................................................................................................88

Appendix A: Meteorological Observations .......................................................................................88 Appendix B: Ancillary equations for SEBS algorithms ....................................................................94 Appendix C: The distribution maps of surface variables and vegetation variables over Hebei Plain............................................................................................................................................................97

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List of figures

Figure 1-1: The global water cycle ..........................................................................................................1 Figure 2-1: Location map of the study area .............................................................................................6 Figure 2-2: Distribution of standard meteorological stations in Hebei Plain ..........................................7 Figure 2-3: Mean daily wind speed at 2 meters height in Shijiazhuang Meteorological Station during Jan, 2004 to Mar, 2005.............................................................................................................................8 Figure 2-4: Daily rainfall in Shijiazhuang Meteorological Station during January 01, 2004 to March 31, 2005....................................................................................................................................................8 Figure 2-5: Mean daily air temperature at 2 meters height in Shijiazhuang Meteorological Station during Jan, 2004 to Mar, 2005 .................................................................................................................9 Figure 2-6: Terra (left) and Aqua (right) satellites ..................................................................................9 Figure 2-7: MODIS tile coverage and picking tiles for study area ........................................................12 Figure 2-8: MODIS cloud-free images distribution during August, 2004 to April, 2005 for Hebei Plain................................................................................................................................................................12 Figure 2-9: Large weighing lysimeter in Luancheng Agro-Ecosystem Station, surface and underground ...........................................................................................................................................13 Figure 2-10: Land Cover map of Hebei Plain ........................................................................................14 Figure 2-11: Proportions of different land cover types in Hebei Plain..................................................14 Figure 3-1: Schematic representation of surface energy fluxes .............................................................17 Figure 3-2: Detailed flowchart for net radiation determination by combining RS images and meteorological data in SEBS .................................................................................................................18 Figure 4-1: Interface of MODIS Reprojection Tool (MRT)..................................................................26 Figure 4-2: Images mosaicking by combining two neighbour images to get the whole area of Hebei Plain........................................................................................................................................................26 Figure 4-3: Definition and determination of the soil line combining the near infrared and red reflectance bands....................................................................................................................................28 Figure 4-4: Influence of displacement height (d0) on modeled evaporative fraction for several NDVI values of the study area, SEBS model....................................................................................................39 Figure 4-5: Sensitivity for displacement height of SEBS model ...........................................................39 Figure 4-6: Influence of fractional vegetation cover on SEBS modeled evaporative fraction for several NDVI classes of the study area ..............................................................................................................40 Figure 4-7: Sensitivity for fractional vegetation cover of SEBS model. ...............................................41 Figure 4-8: Influence of aerodynamic roughness height on SEBS modeled evaporative fraction for several NDVI classes of the study area..................................................................................................42 Figure 4-9: Sensitivity for aerodynamic roughness height of SEBS model...........................................42 Figure 4-10: Influence of surface emissivity on SEBS modeled evaporative fraction for several NDVI classes of the study area .........................................................................................................................43 Figure 4-11: Sensitivity for surface emissivity of SEBS model ............................................................44 Figure 4-12: Summary of average sensitivity values to variable SEBS input parameters.....................45 Figure 5-1: Regression model for lysimeter calibration ........................................................................47 Figure 5-2: Comparison of the daily evapotranspiration between estimated by SEBS and obtained from observations...................................................................................................................................50 Figure 5-3: Histogram of surface reflectance over Hebei Plain.............................................................52

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Figure 5-4: Histogram of land surface temperature over Hebei Plain ...................................................53 Figure 5-5: Relations between surface reflectance and surface temperature.........................................55 Figure 5-6: Normalized temperature difference versus albedo over Hebei Plain..................................56 Figure 5-7: Histogram of NDVI over Hebei Plain on selected cloud free days.....................................58 Figure 5-8: Ts and NDVI space .............................................................................................................59 Figure 5-9: Modified “Ts-NDVI” space over Hebei Plain ....................................................................60 Figure 5-10: Histogram of fractional vegetation cover over Hebei Plain on selected cloud free days..61 Figure 5-11: Histogram of evaporative fraction and evapotranspiration in Hebei Plain on 17 August, 2004........................................................................................................................................................62 Figure 5-12: Histogram of daily ETa over different land cover types in Hebei Plain on 17 August, 2004........................................................................................................................................................63 Figure 5-13: Histogram of evaporative fraction and evapotranspiration on 21 September, 2004........65 Figure 5-14: Histogram of daily ETa over different land cover types in Hebei Plain on 21 September, 2004........................................................................................................................................................66 Figure 5-15: Histogram of evaporative fraction and evapotranspiration on 17 November, 2004 ........66 Figure 5-16: Histogram of daily ETa over different land cover types in Hebei Plain on 17 November, 2004........................................................................................................................................................67 Figure 5-17: Histogram of evaporative fraction and evapotranspiration on 4 March, 2005..................68 Figure 5-18: Histogram of daily ETa over different land cover types in Hebei Plain on 4 March, 2004................................................................................................................................................................69 Figure 5-19: Histogram of evaporative fraction and evapotranspiration on 5 March, 2005..................70 Figure 5-20: Histogram of daily ETa over different land cover types in Hebei Plain on 5 March, 2004................................................................................................................................................................71 Figure 5-21: Histogram of evaporative fraction and evapotranspiration on 25 March, 2005................71 Figure 5-22: Histogram of daily ETa over different land cover types in Hebei Plain on 5 March, 2004................................................................................................................................................................72 Figure 5-23: Time series average daily evapotranspiration of different land covers over Hebei Plain.73 Figure 5-24: Map of Evaporative Fraction and daily Evapotranspiration in Hebei Plain, 17 August, 2004........................................................................................................................................................74 Figure 5-25: Map of Evaporative Fraction and daily Evapotranspiration in Hebei Plain, 21 September, 2004........................................................................................................................................................75 Figure 5-26: Map of Evaporative Fraction and daily Evapotranspiration in Hebei Plain, 17 November, 2004........................................................................................................................................................76 Figure 5-27: Map of Evaporative Fraction and daily Evapotranspiration in Hebei Plain, 4 March, 2005................................................................................................................................................................77 Figure 5-28: Map of Evaporative Fraction and daily Evapotranspiration in Hebei Plain, 5 March, 2005................................................................................................................................................................78 Figure 5-29: Map of Evaporative Fraction and daily Evapotranspiration in Hebei Plain, 25 March, 2005........................................................................................................................................................79

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List of tables

Table 2-1: MODIS visible, thermal bands and potential applications...................................................10 Table 2-2: MODIS land products...........................................................................................................10 Table 2-3: MODIS/Terra Surface Reflectance Daily L2G Global 500m SIN Grid V004 products......11 Table 2-4: MODIS/Terra Land Surface Temperature/Emissivity Daily L3 Global 1km SIN Grid V004 product....................................................................................................................................................11 Table 4-1: Average climatic data of study area over satellite passing time...........................................23 Table 4-2: Mean daily air temperatures at different stations on cloud-free days during Aug. 2004 to Mar. 2005 (units: ) .............................................................................................................................23 Table 4-3: Air pressures at meteorological stations over Hebei Plain...................................................24 Table 4-4: Estimated specific humidity at different meteorological stations over Hebei Plain ............24 Table 4-5: Daily sunshine hours over Hebei Plain for cloud-free days .................................................25 Table 4-6: Incoming solar radiation over satellite passing time on selected cloud free days................25 Table 4-7: Parameters requirements for different methods for fc retrieve and availability ...................30 Table 4-8: Empirical constants for Leaf Area Index determination for different crops in the world....31 Table 4-9: Ground emissivity (εg) for the 8-9 µm atmospheric window ...............................................32 Table 4-10: Table land use classes database and associated z0m values ................................................34 Table 4-11: SEBS model parameters and base values used for sensitivity analysis..............................38 Table 4-12: Sensitivities to displacement heights ranging from 0.10mm to 1.00m...............................40 Table 4-13: Sensitivities to fractional vegetation cover ranging from 0.10 to 0.90 [-]..........................41 Table 4-14: Sensitivities to aerodynamic roughness height ranging from 0.02m to 0.30m...................43 Table 4-15: Sensitivities to surface emissivity ranging from 0.92 to 1.00 ............................................44 Table 5-1: Irrigation test scheme and reading observed in lysimeter ....................................................46 Table 5-2: Daily evapotranspiration measured by lysimeter in Luancheng station for cloud free days47 Table 5-3: The average crop coefficient for winter wheat and summer maize in Luancheng Agro-Ecosystem Station during five seasons (1995-2000) .............................................................................48 Table 5-4: Empirical α values for main crops of different months in North China plain....................49 Table 5-5: Comparison of SEBS result ETa to ground truth ETa and Etc ............................................49 Table 5-6: Statistical summaries of surface albedo over Hebei Plain for cloud free days ....................51 Table 5-7: Statistical summaries of surface temperature over Hebei Plain for cloudy free days ..........53 Table 5-8: Statistical summary of NDVI in different season.................................................................57 Table 5-9: Statistical summary of fractional vegetation cover in different season................................61 Table 5-10: The statistics over each land cover classes in study area on 17 August 2004 (mmday-1) ..62 Table 5-11: The statistics over each land cover classes in study area on 21 September 2004 (mmday-1)................................................................................................................................................................65 Table 5-12: The statistics over each land cover classes in study area on 21 September 2004 (mmday-1)................................................................................................................................................................67 Table 5-13: The statistics over each land cover classes in study area on 4 March, 2005 (mmday-1) ....68 Table 5-14: The statistics over each land cover classes in study area on 5 March, 2005 (mmday-1) ....70 Table 5-15: The statistics over each land cover classes in study area on 25 March, 2005 (mmday-1) ..72

SATELLITE BASED REGIONAL-SCALE EVAPOTRANSPIRATION IN THE HEBEI PLAIN, NORTHEASTERN CHINA

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1. Introduction

1.1. Background

Apart from precipitation, the most significant component of the hydrologic budget is evapotranspiration (Figure 1-1). Evapotranspiration varies regionally and seasonally according to ambient environmental conditions, such as climate condition, land cover, land use, soil moisture, and available radiation etc. Because of this variability, research for integrated water resources modelling, dynamic crop-weather modelling and drought monitoring, a thorough understanding of the evapotranspiration process and knowledge about the spatial and temporal rates of evapotranspiration is needed.

Precipitation (100%)

Evaporation Transpiration

Surface Runoff

Evapotranspiration (65%)

Subsurface Runoff

35%

InfiltrationHydrosphere

Lithosphere

Biosphere

Atmosphere

Lake

River

Vegetation

Evaporation(100%)

Condensation(65%)

Vapour Transport (35%)

Precipitation (100%)

Evaporation Transpiration

Surface Runoff

Evapotranspiration (65%)

Subsurface Runoff

35%

InfiltrationHydrosphere

Lithosphere

Biosphere

Atmosphere

Lake

River

Vegetation

Evaporation(100%)

Condensation(65%)

Vapour Transport (35%)

Figure 1-1: The global water cycle

In the last few decades the theoretical and applied analysis of evapotranspiration and its components transpiration and evaporation have received much attentions. A physically based equation for potential evapotranspiration (ET0) was derived by Penman by combining energy balance equation with the aerodynamic equation for vapour transfer(Penman 1947; Penman 1956). It was subsequently modified by Monteith to include a canopy resistance for vapour diffusion out of stomata. Apart from above mentioned principles, there are many other methods that have been proposed for estimating ET0. By comparing 20 different methods of estimating ET0, Jensen et al. showed that the Penman-Monteith equation provide the best accurate estimate of evaporation from well-watered grass or alfalfa under varied climate conditions(Jensen and Burman et al., 1990). However, these conventional


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techniques are based on the point measurements and are representative only of local scales and will fail for large scales because of the dynamic nature and regional variation of ET. On the other hands, Penman-Monteith equation provided only an estimation of the potential ET, which limits its use in actual evapotranspiration estimation.

Evaporation of water requires relatively large amounts of energy, either in the form of sensible heat or radiant energy. Therefore the evapotranspiration process is governed by energy exchange at the vegetation surface and is limited by the amount of energy available. Because of this limitation, it is possible to predict the regional actual evapotranspiration by applying the principle of energy conservation. Recently, remote sensing techniques have developed rapidly. From satellite observation, people can obtain consistent and frequent spectral reflectance and emittance of radiation of the land surface in a basin scale, so it is possible to estimate the regional evapotranspiration rate by combining remotely sensing data with the solar radiation observation based on surface energy balance model. In the past decades, considerable efforts have been made to gaining experience and deriving appropriate models to counter this challenge(Norman and Kustas et al., 1995; Bastiaanssen and Menenti et al., 1998; Bastiaanssen and Pelgrum et al., 1998; Su 2002). Several algorithms were developed and they all have been applied and validated in some regions and a brief history will be discussed in the following.

1.2. A brief history in remote sensing of evapotranspiration

Evapotranspiration calculations based on the remote sensing data have been developed rapidly for the last 20 years, and several methods have been adopted by different research groups and used in related study area successfully. Among those methods, some are a little bit simple, only multi-wavebands data were used to calculate the available radiation on the surface, then by applying conventional Priestley-Taylor equation or other model to calculate the evapotranspiration. Some are complicated relatively, such as methods that include the detailed process about sensible heat flux calculation. Some are only use synchronous meteo-satellite data, although images resolution is lower, but almost uninterruptedly observation on the same area can fetch up this limitation to a certain extent. To make a summary of those methods that have been developed for the last few decades, three types of methodology in remote sensing based turbulent heat flux and evapotranspiration estimation can be distinguished generally. They are analytical approaches, semi-empirical approaches and empirical approaches, detailed literature review about research work related to those different approaches are discussed in the following.

1.2.1. Analytical approaches

Analytical approaches about the remote sensing based evapotranspiration estimation include detailed physical process and required various parameters, mainly the surface biophysical attribute, which can be retrieved either through satellite-based remote sensor or through campaign in the field. The forthgoer for this approach can be traced back to Jackson et al. who brought forward and calculated the crop water stress index (CWSI) by combining canopy temperatures, obtained by infrared thermometry, wet- and dry-bulb air temperatures and an estimate of net radiation(Jackson and Idso et al., 1981; Jackson and Kustas et al., 1988). Kalma and Jupp utilized a one-layer resistance model with infrared thermometry to estimate sensible and latent heat flux in pastures near Goulburn, New South


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Wales and the model compares reasonably well with energy balance-Bowen ratio measurements(Kalma and Jupp 1990). Also the two-layer model of Shuttleworth and Wallace(Shuttleworth and Wallace 1985) was used to show that the relationship between the measured infrared surface temperature and the canopy air temperature in their study. Due to the difficulty of measuring foliage temperature of partially vegetated fields when using crop water stress index (CWSI) to detect plant stress, a new index [water deficit index (WDI)] was introduced by Moran et al. for evaluating evapotranspiration rates of both full-cover and partially vegetated sites based on the attempt to combine spectral vegetation indices with composite surface temperature measurements to allow application of the CWSI theory to partially-vegetated fields without knowledge of foliage temperature(Moran and Clarke et al., 1994). And in a further attempt, Menenti and Choudhury extended the CWSI concept to the so-called Surface Energy Balance Index (SEBI) approach(Menenti and Choudhury 1993). These research works have established the base of analytical method to calculate evapotranspiration by using remote sensing data.

Recently, with rapid development of not only the related scientific subjects also the satellite technologies, more work have been done to estimate surface turbulent heat flux and regional evapotranspiration through analytical approaches. An approach based on the combination of dual angle observations of radiative temperature and a two-layer model has been used by Chehbouni et al. to estimate convective surface sensible heat fluxes over sparse grassland site in the San Pedro Basin(Chehbouni and Nouvellon et al., 2001). A composite method was presented by Boegh for the spatial estimation of atmospheric resistance, surface resistance, and evapotranspiration rates using Landsat TM and local data on solar irradiation, air temperature, and air humidity(Boegh and Soegaard et al., 2002). The study that has been done by Chanzy et al. should be also noted here, who analysed the implementation of a simple daily evaporation model on bare soils based on knowledge of the water content and showed that the complementarity between thermal infrared and microwave observations could be used to infer the empirical parameters of the simple evaporation model(Chanzy and Bruchler et al., 1995). One of the important approaches of this stage is the two-layer model of turbulent exchange presented by Norman et al. which includes the view geometry associated with directional radiometric surface temperature(Norman and Kustas et al. 1995). Required inputs for this model are directional brightness temperature and its angle of view, fractional vegetation cover or leaf area index, vegetation height and approximate leaf size, net radiation, and air temperature and wind speed. It was showed that one advantage of this model is directional brightness temperatures were considered so that the model should have wider applicability than single-layer models, and it opened the possibility of a simple solution if directional measurements were available from two substantially different view angles.

More recently, Kustas ans Norman applied actual soil and vegetation component temperatures to the dual-source model of Norman et al. but did not obtain better results than using only composite temperature without changing the applied Priestley and Taylor coefficient to a much high value(Kustas and Norman 1999). Based on the radiometric observations of ground temperature, Castelli estimated the surface heat flux and made an index of the surface control over evaporation using adjoint-state surface energy balance(Castelli and Entekhabi et al., 1999). In order to develop and test methods for interpreting remote sensing data that could lead to a better evaluation of soil and vegetation processes, intensive measurements were performed by Olioso for almost one year over a small agricultural region in the South of France (20 kilometers square)(Olioso and Braud et al., 2002).


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Boni has used a variational land data assimilation system to estimate latent heat flux and surface control on evaporation(Boni and Castelli et al., 2001; Boni and Soegaard et al., 2001). A variational data assimilation scheme is used by Caparrini to infer two key parameters of the surface energy balance that control the partitioning of available energy into latent, sensible, and ground heat fluxes(Caparrini and Castelli et al., 2004).

Compared to all previous remote sensing algorithms for heat fluxes estimation, the Surface Energy Balance System (SEBS) was developed by Su(Su 2002), which has the most important advantage of it’s inclusion of a physical model for the estimation of the roughness height for heat transfer which is the most critical parameter in the parameterization of the heat fluxes of land surface. Based on the SEBS algorithm, some validations have been done successfully in different place with different scale(Su and Jacobs 2001; Su and Jacobs 2001; Su and Wen et al., 2003; Su and Yacob et al., 2003; Su and Mccabe et al., 2005; Timmermans and van der Kwast et al., 2005).

1.2.2. Empirical approaches

As far as the empirical approaches for land surface turbulent heat fluxes estimation were concerned, the work of Nieuwenhuis et al. was among the earliest attempts(Nieuwenhuis and Schmide et al., 1985). Based on the thermal infrared images and relating the actual crop temperatures to the temperature of the same but potentially transpiring arable crop, regional evapotranspiration of that crop was estimated in their study. Later, the development of Surface Energy Balance Algorithm for Land (SEBAL) by Bastiaanssen built up the milestone of this type of approaches(Bastiaanssen and Menenti et al. 1998; Bastiaanssen and Pelgrum et al. 1998). The relationships between visible and thermal infrared spectral radiances of areas with a sufficiently large hydrological contrast (dry and wet land surface types, vegetative cover is not essential) constitute the basis for the formulation of the SEBAL model. After its establishment, a lot of filed validations have been done in different area, especially in arid and semi-arid area. However, due to the difficulty to find exactly right pixels of dry and wet conditions in certain images, its application is limited in a certain degree. To solve related limitation of SEBAL, some correction have been made by Su to make it more practicability, who remedied a theoretical problem of SEBAL model and added a scheme to apply NWP fields with an up-scalling and down-scaling approach(Su and Pelgrum et al., 1999). In another effort, Roerink et al. developed a new method to derive the surface energy fluxes from remote sensing measurements, called the Simplified Surface Energy Balance Index (S-SEBI), which fits dry and wet cases present in the spatial radiometric data and showed reasonable success for application to semiarid areas(Roerink and Su et al., 2000).

1.3. Problem definition

The Hebei plain is situated in the eastern part of China and belongs to Haihe River Basin. It is one of the largest agricultural areas in China and also one of the most densely populated regions in the world. Groundwater resource is one of the most important natural resources in this area, because it provides drinking water to urban and rural communities, supports irrigation and industry, sustains the flow of streams and rivers, and maintains the ecosystems. The amount of water for agricultural as well as industrial use has increased tremendously from 1970s. The water shortage became one of the constraints preventing further development. Investigation has shown that more than 79% of groundwater resources abstracted from aquifer were used for irrigation in this area(Zhang and Shi et


5

al., 2005). Due to the traditional irrigation pattern, a lot of water resources were wasted directly. With the over-exploitation for more than 30 years, a series of environmental problems have occurred, such as decline of regional groundwater level, change of flow field, decrease of water resources and downward movement of saline water body(Zhang and Shi et al., 1997; Zhang and Shi et al., 1997). The hydrogeological environments have changed in the past few decades and the future sustainability of water resources in Hebei Plain is at risk.

In order to make better use of the groundwater resources in the Hebei Plain, many studies have been concentrated on the identification of groundwater net recharge and the identification of agriculture water use(Wang and Lin et al., 2005). Several approaches have been developed to quantify groundwater net recharge. In regional studies, the water balance method is commonly used to estimate areal net recharge, which is mainly controlled by three processes: precipitation, surface runoff and actual evapotranspiration. Due to the little difference of rainfall patterns in semi-arid area and commonly available real time runoff data, main difficulty comes from the estimation of areal evapotranspiration patterns, which have large differences because of land surface diversity. On the other hand, duo to the large proportion of agriculture water use in the Hebei Plain, it is also very important to determine the spatial and temporal evapotranspiration to guide the irrigation water use. Hence, the main problem goes into accurate evapotranspiration estimation spatially and temporally.

This research work focuses on the satellite derived evapotranspiration in order to characterize the spatial and temporal variability of evapotranspiration in the Hebei Plain. The result is believed to be important for water balance studies and water resources management, which will be of great importance for future sustainable water use in study area.

1.4. Objectives and research questions

The main objective of this study is to evaluate the actual evapotranspiration in the Hebei Plain through combination of remotely sensing and meteorological observations. In this study, the following objectives are addressed:

� Estimation of actual evapotranspiration through application of the Surface Energy Balance System (SEBS) and satellite observations.

� To determine the spatial-temporal distribution patterns of the actual evapotranspiration in the study area

After the objectives mentioned above have been achieved, the following research questions of this study will be answered:

� How does the spatial land cover distribution affect the actual evapotranspiration distributions spatially in the Hebei Plain?

� What are the actual evapotranspiration distribution patterns spatially and temporally in the Hebei Plain?


6

2. Study Area and Materials

2.1. Study Area

The study area, Hebei Plain, is located in the northeastern China between the range of 114°15′E-117°45′E and 36°N-39°40′N (figure 2-1). Hebei Plain is one part of the North China Plain, and it covers an area of 62004km2, which is more than 33% of the Hebei Province. The relief is characterized by down step by step surface slope from 2~1 in the west to 1.0~0.5 in the middle plain then to 0.3~0.1 in the east coastal area. The average elevation of study area is 29 meters above the mean sea level, from more then 100m in the Taihang Mountain foot plain in the west to 2~3m in the east.

0 1,250 2,500km

Location of city

N

Capital city

Beijing

Langfang

Tianjin

Shijiazhuang

Bazhou

Baoding

Xingtai

Hengshui

Handan

Cangzhou

BoHai Sea

TaiH

ang

Mou

ntai

n

TaiH

ang

Mou

ntai

n

Figure 2-1: Location map of the study area

Hebei Plain belongs to the semi-arid climate in the monsoon region of the East Asia warm Temperate Zone. The winters are dry and cold, the summer are moist and hot, with low rainfall in the spring and heavy rainfall in the summer.

Average rainfall of the Hebei Plain is about 300~800 mm, which is contributed by the topography mainly. The maximum rainfall is located in the eastern Taihang Mountain foot plain, and yearly total rainfall there can reach 600~700mm. Minimum rainfall appears in the Xingji-Ningjin-Nangong area, annual rainfall there were lower than 400mm. In addition, the rainfall through the year is not evenly


7

distributed. Most of the rainfall comes in the summer, especially in the July and August, which can reach 450mm over almost all area and account for about 65~75% of yearly total amount. In winter, the rainfall is much lower than summer, and most of the area have 5~15mm, only represent 2% of the sum.

Due to the wide range of attitudes and complicated topography in the study, mean yearly air temperature differ much over the whole area, and the average yearly air temperature is between 0~13

, which is up step by step from 4 in the north to 13 in the south. The same as the rainfall patterns, mean monthly air temperatures in Hebei Plain is highly variable. The coldest periods are in the January, which have a mean temperature below -3 , and warmest periods are from June to July,

the temperatures of these days are more or less about 35 , and sometimes more than 40 .

Maximum wind speed appears in spring, which is more than 6.5ms-1. In other season, the wind speed seems smoothly, for most of days, wind speed is less than 2 ms-1. Also due to the big scale of the Hebei Plain, topography plays a very important role to control the near surface wind speed and wind direction. In the eastern seashore area, due to the control by summer monsoon in summer, wind mainly comes from west Pacific Ocean, which is warmer and appear southeaster direction. In winter, since the area is controlled by cold snap came of Siberia, the wind is cold and northwester, and due to the Taihang Mountain located in the west of the study area, the wind become a little bit weak when it reaches to Hebei plain.

2.2. Meteorological Observations

Standard meteorological observations required for SEBS algorithms are: wind speed, air temperature, surface pressure, humidity and radiation.

The Chinese National Meteorological Center (NMC) operates 6 meteorological stations in Hebei Plain on a daily basis. As indicated by figure 2-2, the stations are spatially well-distributed over study area. The dataset available from these stations include a time series starting on 01/01/2004 to 31/05/2005 of the following variables: relative humidity, wind speed, air temperature at 2m height, actual vapour pressure, rainfall, sunshine hours and open water evaporation. Among these meteorological observations, relative humidity, wind speed, air temperature are measured on a hourly basis and are recorded every 6 hours at 2:00, 8:00, 14:00 and 20:00, while rainfall and sunshine hours are stored as daily values.

Figure 2-2: Distribution of standard meteorological

stations in Hebei Plain


8

Mean daily wind speeds, air temperature at reference height (2m) and daily rainfall in Shijiazhuang meteorological station during January 01, 2004 to March 31, 2005 are shown as figures below.

Figure 2-3: Mean daily wind speed at 2 meters height in Shijiazhuang Meteorological Station during Jan, 2004 to Mar, 2005

Figure 2-4: Daily rainfall in Shijiazhuang Meteorological Station during January 01, 2004 to March 31, 2005


9

Figure 2-5: Mean daily air temperature at 2 meters height in Shijiazhuang Meteorological Station during Jan, 2004 to Mar, 2005

2.3. Satellite Observations

2.3.1. Moderate-resolution Imaging Spectroradiometer (MODIS)

Moderate-resolution Imaging Spectroradiometer (MODIS) is one of the primary land observating sensors on-board the Terra (EOS AM) and Aqua (EOS PM) satellites (Fig.2-6). Terra's orbit around the Earth is timed so that it passes from north to south across the equator in the morning, while Aqua passes south to north over the equator in the afternoon. Terra MODIS and Aqua MODIS are viewing the entire Earth's surface every 1 to 2 days, acquiring observations in 36 spectral bands.

Figure 2-6: Terra (left) and Aqua (right) satellites

Table 2-1 lists the pixel resolution and bandwidth of the visible and thermal bands. Bandwidth ranges are in nanometres (nm) for the optical bands and micrometers (µm) for thermal bands. The potential applications indicate key uses considered by the instrument design teams.

Terra Aqua


10

Table 2-1: MODIS visible, thermal bands and potential applications

Band # Pixel

Resolution (m)

Reflected Bandwidth

Range (nm)

Emitted Bandwidth

Range (µm)

Potential Applications

1 250 620-670 Absolute Land Cover Transformation, Vegetation Chlorophyll

2 250 841-876 Cloud Amount, Vegetation Land Cover Transformation

3 500 459-479 Soil/Vegetation Differences 4 500 545-565 Green Vegetation 5 500 1230-1250 Leaf/Canopy Differences 6 500 1628-1652 Snow/Cloud Differences 7 500 2105-2155 Cloud Properties, Land Properties

31 1000 10.780-11.280

Cloud Temperature, Forest Fires & Volcanoes, Surface Temperature

32 1000 11.770-12.270

Cloud Height, Forest Fires & Volcanoes, Surface Temperature

2.3.2. MODIS Products

When using the parameters derived from MODIS images as the input for surface energy balance model, the required parameters should include emissivity, albedo, surface reflectance, and vegetation index (NDVI) as well as surface temperature. Those parameters can all be derived from MODIS standard products of visible bands and the thermal bands, i.e. surface reflectance product and surface temperature/emissivity product. Table 2-2 shows the MODIS land products available.

Table 2-2: MODIS land products

MODIS products MODIS products MOD09 Surface Reflectance MOD15 Leaf Area Index / FPAR MOD11 Land Surface Temp. / Emis. MOD16 Evapotranspiration / SR MOD12 Land Cover / Change MOD17 Primary Production MOD13 Vegetation Indices MOD43 BRDF /Albedo MOD14 Thermal Anomalies / Fire MOD44 Vegetation Continuous Fields

Currently released MODIS Land data products represent provisional and validated Terra and Aqua data sets. Both V003 and V004 are available until 2006. V004 data are validated, meaning that product uncertainties are generally well-defined over a range of surface conditions.

(1) Surface reflectance products

--MODIS/Terra Surface Reflectance Daily L2G Global 500m SIN Grid V004


11

The MODIS Surface Reflectance Daily L2G Global 500m ISIN Grid product, MOD09, is a seven-band product computed from the MODIS Level 1B land bands 1-7 (table 2-3). The product is an estimate of the surface spectral reflectance for each band as it would have been measured at ground level if there were no atmospheric scattering or absorption. The correction scheme includes corrections for the effect of atmospheric gases, aerosols, and thin cirrus clouds.

Table 2-3: MODIS/Terra Surface Reflectance Daily L2G Global 500m SIN Grid V004 products

SDS Units Fill Value Valid Range Scale Factor Band 1 Reflectance -28672 -100 - 16000 10000 Band 2 Reflectance -28672 -100 - 16000 10000 Band 3 Reflectance -28672 -100 - 16000 10000 Band 4 Reflectance -28672 -100 - 16000 10000 Band 5 Reflectance -28672 -100 - 16000 10000 Band 6 Reflectance -28672 -100 - 16000 10000 Band 7 Reflectance -28672 -100 - 16000 10000

QC Flags Bit field 787410671 0 - 4294966019 -- Orbit and Coverage -- 15 0 - 255 --

Number of observations -- -1 0 - 127 --

(2) Land Surface temperature / emissivity products

--MODIS/Terra Land Surface Temperature/Emissivity Daily L3 Global 1km SIN Grid V004

The MODIS Land Surface Temperature and Emissivity (LST/E) products provide per-pixel temperature and emissivity values. Averaged temperatures are extracted in Kelvin with a day/night LST algorithm applied to a pair of MODIS daytime and night time observations. This method yields 1 K accuracy for materials with known emissivities, and view angle information is included in each LST/E product. Emissivities are estimates derived from applying algorithm output to database information. The LST/E algorithms use MODIS data as input, including geo-location, radiance, cloud masking, atmospheric temperature, water vapour, snow, and land cover.

Table 2-4: MODIS/Terra Land Surface Temperature/Emissivity Daily L3 Global 1km SIN Grid V004 product

SDS Units Fill Value Valid Range Scale Factor Daily daytime 1km grid Land-surface Temperature K 0 7500 - 65535 0.0200

Quality control for daytime LST and emissivity -- 0 0 - 255 --

Time of daytime Land-surface Temperature observation Hrs 0 0 - 240 0.1000

View zenith angle of daytime Land-surface Temperature D 255 0 - 130 1.0000

Daily nighttime 1km grid Land-surface Temperature K 0 7500 - 65535 0.0200

Quality control for nighttime LST and emissivity -- 0 0 - 255 --

Time of nighttime Land-surface Temperature observation Hrs 0 1 - 240 0.1000

View zenith angle of nighttime Land-surface Temperature Degree 255 0 - 130 1.0000

Band 31 emissivity -- 0 1 - 255 0.0020 Band 32 emissivity -- 0 1 - 255 0.0020


12

2.3.3. Acquirement of MODIS products

MODIS data or products can be found and downloaded free of charge from Earth Observing System Data Gateway (http://edcimswww.cr.usgs.gov/pub/imswelcome).

MODIS Level 2G, Level 3, and Level 4 products are defined on a global 250 m, 500 m, or 1 km sinusoidal grid (the particular spatial resolution is product-dependent). Because these grids are unmanageably large in their entirety (43200 21600 pixels at 1 km, and 172800 86400 pixels at 250

m), they are divided into fixed tiles approximately 10 10 in size. Each tile is assigned a horizontal (H) and vertical (V) coordinate, ranging from 0 to 35 and 0 to 17, respectively (Figure 2-7).The tile in the upper left (i.e. northernmost and westernmost) corner is numbered (0,0). Below is a map indicating the MODIS tile coverage and labels.

Figure 2-7: MODIS tile coverage and picking tiles for study area

In total, 6 sets cloud free images were found from the period June, 2004 to April, 2005, including surface reflectance products and surface temperature products, which are showing as figure 2-8 below.

Aug-04 Sep-04 Oct-04 Nov-04 Dec-04 Jan-05 Feb-05 Mar-05 Apr-05

date (day)

Figure 2-8: MODIS cloud-free images distribution during August, 2004 to April, 2005 for Hebei Plain


13

2.4. Validation data

The remotely sensed actual evapotranspiration is validated against ground truth ET observations derived from lysimeter observations, which is installed at Luancheng Agro-Ecosystem Station in Hebei Plain.

Luancheng Agro-Ecosystem Station (LAES), one of the 34 agricultural eco-system stations of Chinese Ecological Research Network, is located at Luancheng county of the Hebei Plain (latitude: 37°53′N; longitude: 114°41′E; 50.1 m above sea level). The station is near the Taihang Mountain foot plain, which is representative for the high-yield agriculture in Hebei Plain. Cropping system in this region is corn followed by winter wheat.

The lysimeter measurements are taking by a mechanical scale, which permits an accuracy of 0.02 mm water loss. The weighing lysimeter was installed in 1995 (Figure 2-9) and has a surface area of 3m2(2m×1.5m) and a depth of 2.5m. It was filled with the undisturbed soil (the original soil). The weight of the undisturbed soil in the lysimeter is about 12 ton, and the total weight including the surrounding frame is about 14 ton. On average field capacity of the soil in the lysimeter is about 32-34cm3/cm3, the wilting point varies between10 and 12 cm3/cm3 and the saturated water conductivity range form 0.5 to 1.0 m/day. Inside the lysimeter, neutron access tube was installed to monitor soil water content(Liu and Wang 1999; Liu and Zhang et al., 2002).

(a) (b) Figure 2-9: Large weighing lysimeter in Luancheng Agro-Ecosystem Station, surface and underground

To keep the same plant densities and uniform plant growth inside and outside of the lysimeter, the same agronomic practices were carried out. Crops in the lysimeter were managed according to the local agricultural recommendations, and the irrigation methods were referenced to those used locally.

2.5. Land cover

Over the past several years, researches have increasingly turned to remotely sensed data to describe the geographic distribution of land cover at regional and global scales(Cihlar 2000; Hansen and Defries et al., 2000; Liu and Zhuang et al., 2003). Some of those products are available at internet and can be ordered or downloaded freely. By comparing different source data products, the MOD12Q1 Land Cover Product was selected in this research due to its up-to-date attribute. The MOD12Q1 Land Cover Product can be downloaded free of charge from Earth Observing System Data Gateway (http://edcimswww.cr.usgs.gov/pub/imswelcome).


14

Figure 2-10: Land Cover map of Hebei Plain

barren or sparsely ve

getated

closed shrubland

cropland/natural vegetation mosaic

croplands

evergreen needleleaf forest

grasslands

mixed forests

open shrublands

savannas

urban and built-up

water

woody savannas0

10000

20000

30000

40000

50000

Num

ber

of p

ixel

s

Figure 2-11: Proportions of different land cover types in Hebei Plain


15

The MODIS Land Cover Classification products contain multiple classification schemes describing land cover properties. The primary land cover scheme identifies 17 classes of land cover defined by the International Geosphere-Biosphere Programme (IGBP) which include 11 natural vegetation classes, 3 developed land classes, one of which is a mosaic with natural vegetation, permanent snow or ice, barren or sparsely vegetated, and water. The MOD12 classification schemes are multi-temporal classes describing land cover properties as observed during the year (12 months of input data). Successive production at quarterly intervals of this "annual" product creates new land cover maps with increasing accuracies as both classification techniques and the training site database mature.

Figure 2-10 shows the land cover map of Hebei Plain derived form MODIS Land Cover Classification products. Totally 12 kinds of land cover types were recognized in study area. Among them, the dominant land cover type is crop land, and more than 91.47 % of the area is for agricultural land use (Figure 2-11). Urban and built areas are the second large land cover class in Hebei Plain, which present more than 3 percent of the Hebei Plain according to the map. Grass also play an important role for the land cover of the study area, most of which located in the seashore area of eastern Hebei Plain. In conclusion, the landscape of Hebei Plain is very homogeneous.


16

3. Surface Energy Balance System (SEBS)

Evaportranspiration is not only an important component in the land surface energy balance, but also an important component in water cycle. Conventional methods for ET estimation is based on the using of temperature and solar radiation, therefore, those methods can only to be used to estimate ET at certain location with point measurements, but can not be easily used in large regional scale with a large degree of heterogeneity(Su 2002). Remote sensors are designed to measure energy in specific ranges of the electromagnetic spectrum, which mostly fall within atmospheric windows where atmosphere is almost transparent and atmospheric effect is minimal. The evapotranspiration process of land surface is a consequence of energy change of fluxes between land surface and atmosphere, which can be expressed as the energy balance equation, and the values of the components in the energy balance equation can be determined with remote sensor, so evapotranspiration calculation based on the remote sensing methods comes into truth.

The Surface Energy Balance System (SEBS) model was proposed by Su (Su 2002)to estimate atmosphere turbulent fluxes and the evaporative fraction (the ratio of latent heat flux and the available energy) using satellite data and ancillary surface and meteorological information. SEBS is physically based and has the potential to be used across local, regional, and continental scales with remotely sensed data and standard meteorological observations. SEBS consists of several separate modules to estimate the net radiation and soil heat flux, and to partition the available energy into sensible and latent heat flux, of which a detailed introduction is presented below.

3.1. Principle of energy balance closure

The Surface Energy Balance System (SEBS) model was based on the Conservation of Energy Principle. All the energy involved in the soil-vegetation-atmosphere interface comes from solar radiation, and then expressed as several forms, which can be given as Energy Balance Equation (EBE):

LEHGRn ++= (3.1)

Where, Rn is the net radiation, G is the soil heat flux, H is the sensible heat flux and LE is the latent heat flux, which can be expressed as height of water, i.e. evapotranspiration.


17

All units in this equation are expressed in [Wm-2], and all fluxes are defined positive if directed downwards (Figure 3-1).

Figure 3-1: Schematic representation of surface energy fluxes

Note that the energy required for photosynthesis and heat stored in the vegetation was neglected in this equation.

3.2. Net radiation

Net radiation is the sum of incoming and outgoing short and longwave radiation at the surface, which constitutes a key driver for heating the atmosphere and the ground. Net radiation is given by,

lwulwdswuswdn RRRRR −+−= (3.2)

Where, Rswd, Rswu, Rlwd and Rlwu stand for the incoming shortwave and outgoing shortwave radiation and incoming longwave and outgoing longwave radiation respectively. Due to the truth that some terms required in this equation are always missing, so this equation can also be expressed as,

40)1( TRRR lwdswdn ⋅⋅−⋅+⋅−= σεεα (3.3)

where α is the surface albedo, ε the emissivity of the surface, σ the Stefan-Bolzmann constant, equals to 5.67e10-8 and T0 the surface radiative temperature. α , ε and T0 can be derived from remote sensing data from the visible to the thermal infrared spectral range, and some empirical methods are developed to retrieve those parameters from remotely sensed data, which will be discussed in next chapter.

Figure 3-2 shows the detailed procedure for net radiation determination by combining RS images and meteorological data. Related equations can be found in Appendix B.


18

RS imagesAir temperatureRadiation data

Rlwd

Atomosphereemissivity

Visible bands Thermal bands

Rlwu

SurfacetemperatureNDVIAlbedo

Rswd

point observationGloble radiation

atmospheretransimisivity

fc

Surfaceemissivity

Rswd Rswu

Rn

Figure 3-2: Detailed flowchart for net radiation determination by combining RS images and meteorological data in SEBS

3.3. Soil heat flux

Soil heat flux is determined as an unfixed percentage of the total available energy, which is given as,

( ) ( )[ ]csccn fRG Γ−Γ⋅−+Γ⋅= 10 (3.4)

where �c and �s are empirical coefficient. These values have been determined using experimental observations, but depend also on the soil and vegetation type. For most bare soil conditions a �s value of 0.315 is valid, and for vegetation often �c is assumed to be 0.05. An interpolation is then performed between these limiting cases using the fractional canopy coverage, fc, which can be determined from remote sensing data.


19

3.4. Sensible heat flux

To determine the sensible heat flux, similarity theory is applied. The relationships for the mean wind and temperature profiles are written in integral form as,

*0 0 0

0

ln mm m

m

z d z d zuu

k z L Lψ ψ

� �� − −� � � �= − +� ��

(3.5)

0 0 00 *

0

ln ha h h

p h

z d z d zHku C z L L

θ θ ψ ψρ

� �� − −� � � �− = − +� ��

(3.6)

Where, � is density of air [kg m-3], Cp is the heat capacity of dry air [-], k is the Von Karman constant [= 0.4], z is the height at which the meteorological observations are made [m], u* is the friction velocity [m s-1], �0 and �a are the potential temperature at height zoh and at height z [K], d0 is the displacement height [m], zoh and zom are the surface roughness heights for heat and momentum transport [m], �h and �m are stability correction function for heat and momentum transport and L is the Obukhov stability length [m] given by,

3*p vC u

LkgH

ρ θ= − (3.7)

Where, g is the accerelation due to gravity [m s-2] and �v is the virtual temperature [K].

The actual sensible heat flux (H) is determined by using the friction velocity (u*) and stability length (L) obtained from iterative procedure.

The generation of the sensible heat flux in SEB models is driving by the difference between the aerodynamic temperature (Taero) or �0 and the air temperature (Ta) or �a. The difference between these two temperatures is corrected for stability in the Atmospheric Boundary Layer (ABL) and Atmospheric Surface Layer (ASL) to obtain the sensible heat flux. Detailed discussion for Similarity Stability Correction Functions can be found in Su and Jacobs (2001).

3.5. Evaporative fraction

The surface energy balance computation with the SEBS algorithm is based on the determination of the relative evaporation fraction,

1 wetr

dry wet

H HH H

−Λ = −−

(3.8)

Where, rΛ is the relative evaporation fraction [-], Hwet is the wet-limit of sensible heat flux [Wm-

2] and Hdry is the dry-limit of sensible heat flux [Wm-2].


20

The values for Hdry are simply determined by assuming that latent heat flux become negligible. Energy balance is then represented by,

0dry nH R G= − (3.9)

The sensible heat flux at the wet limit is given by,

( ) ��

��

� ∆+−

⋅−−=γγ

ρ1)(

_0

eer

CGRH s

wetah

pnwet (3.10)

The aerodynamic resistance wetahr _ for wet surface conditions can be derived with,

��

��

��

��

�+��

��

� −−��

��

� −= ∗

wet

hh

weth

hwetah L

zL

dzz

dzku

r 00

0

0_ ln

1 ψψ (3.11)

The stability length suitable for wet conditions (Lwet) is estimated as,

( )3*

00.61wetn

uL

kg R Gρ

λ= −

− (3.12)

3.6. Surface roughness length for heat transfer

The scalar roughness height for heat transfer, z0h, is derived from,

)exp( 10

0 −=kB

zz m

h (3.13)

Where B-1 is the inverse Stanton number, a dimensionless heat transfer coefficient. To estimate the kB-1 value, following model proposed by Su et al. (2001) can be used,

2102

2/

1 /)(/2

)1()(

4ss

t

mscc

nt

d fkBC

hzhuukfff

ehu

uC

kCkB

ec

−∗

∗

−∗

− +⋅⋅+−

= (3.14)

Where fc is the fractional canopy coverage and fs is its compliment. Ct is the heat transfer coefficient of the leaf. For most canopies and environmental conditions, Ct is bounded as 0.005N ≤ sCt ≤ 0.075N (N is number of sides of a leaf to participate in heat exchange). The heat

transfer coefficient of the soil is given by 2/13/2Pr −−∗∗

= et RC , where Pr is the Prandtl number, the

roughness Reynolds number Re*=hsu*/v, where hs the roughness height of the soil. The kinematic


21

viscosity of the air is given by 81.10

5 ))(/0(10327.1 aa TTppv −⋅= − , with p and Ta the ambient

pressure and temperature, and p0=101.3kPa and Tao=273.15K.

3.7. Turbulent heat fluxes and actual evaporation

The actual sensible and latent heat fluxes is expressed as,

)(

)()1(

GRE

GRH

n

n

−⋅∧=−⋅∧−=

λ (3.15)

When the evaporative fraction is known, the daily evaporation can be determined as

W

ndaily

GRE

λρ

_

0

_24

0

71064.8−

×××= ∧ (3.16)

where dailyE is the actual evaporation on daily basis )( 1−⋅ dmm . ∧24

0

is the daily average

evaporative fraction, which can be approximated by the SEBS estimate since the evaporative

fraction is conservative. _

nR and _

0G are the daily net radiation flux and soil heat flux, � is the

latent heat of vaporization ( 1−JKg ), ωρ is the density of water ( 3−Kgm ).

Since the daily soil heat flux is close to zero because of the downward flux in daytime and the upward flux at night balance each other approximately, the daily evaporation only depends on the net radiation flux given by

2424

_

)1( LKRn εα +−= ↓� (3.17)

where ↓24K is the daily incoming global radiation and 24L is daily net longwave radiation. The

daily average albedo, α , and emissivity, �, can be approximated easily with the same values as used previously in the energy balance equation.


22

4. Data Processing and Bio-physical Parameters Estimation

In order to retrieve regional turbulent heat flux, SEBS needs three sets of data as model input. The first set includes land surface albedo, emissivity, land surface temperature (LST), fractional vegetation coverage (fc), leaf area index (LAI) and the height of the vegetation (or roughness height). If the vegetation information is not explicitly available, the Normalized Difference Vegetation Index (NDVI) is used as a surrogate. Those inputs can be derived from remote sensing data, for example, MODIS production (MOD09, MOD11) in this study. The second data set is meteorological data that consists of air pressure, temperature, humidity, and wind speed at a reference height. This data set can also be estimated by using some meteorological model. The third data set includes downward solar radiation and downward long wave radiation that should either be measured or modelled. These three data sets should be prepared before running the SEBS code.

4.1. Meteorological data pre-processing

The time series meteorological data from 01/01/2004 to 31/05/2005 over related meteorological stations have been collected and its elements include Station ID, Station longitude, Station Latitude, Station Altitude, relative humidity, wind speed, air temperature at 2m height, actual vapour pressure, rainfall, sunshine hours and daily evaporation from open free water.

According to frequency of observation, observation items of these meteorological stations can be divided into two groups, daily base and hourly base. Hourly base items include relative humidity, wind speed, air temperature at 2m height, actual vapour pressure, which are observed every 6 hours, i.e., at the time of 2:00, 8:00, 14:00 and 20:00 o’clock in a day, and daily based items include rainfall, sunshine hours and daily evaporation, which are the total amount over the day.

Different meteorological observations at different stations over Hebei Plain can be found in Appendix A.

(1) Meteorological data at satellite passing time

Since the over passing time of the MODIS is about 11:00 AM in Local time, the meteorological data should be interpolated from two times’ observations at 8:00 and 14:00 in local time. Here, a linear interpolation model was used, in addition, due to the relatively little difference of same meteorological items over different stations in Hebei Plain (Appendix A), mean values of those observations will be used to run the SEBS model in this work. The average climatic data over Hebei Plain at satellite passing time is showing as table 4-1 below.


23

Table 4-1: Average climatic data of study area over satellite passing time

RH(%) Wind speed(m/s) Air Temp. ( ) ea(Pa)

2004-08-17 62.15 1.89 24.30 1840.202004-09-21 43.17 1.67 17.64 801.68 2004-11-17 45.84 1.56 5.92 369.87 2005-03-04 29.20 3.86 -1.77 140.27 2005-03-05 34.89 2.93 1.21 210.362005-03-25 27.97 3.58 11.14 312.62

(2) Daily Meteorological data

To calculate the daily net radiation, some mean daily climatic data will be needed, and the mean daily air temperatures at different stations were shown below, which will be interpolated through moving average method over whole study area for later analysis.

Table 4-2: Mean daily air temperatures at different stations on cloud-free days during Aug. 2004 to Mar. 2005 (units: )

53698 53798 54518 54602 54624 54705 2004-08-17 23.4 23.28 24.28 24.18 23.4 24.10 2004-09-21 18.95 18.90 18.88 16.93 18.30 18.85 2004-11-17 10.58 7.18 6.68 6.23 7.98 7.15 2005-03-04 1.55 1.20 0.25 0.78 -0.65 1.80 2005-03-05 4.95 2.75 1.38 2.80 1.08 4.53 2005-03-25 13.15 12.68 12.38 11.48 11.68 12.38

(3) Air pressure

Air pressure at surface and reference height are another parameters required by SEBS algorithms to estimate land surface turbulent heat flux. It depends not only on the local elevations but also the local atmospheric conditions; hence, air pressure is changefully in a certain area. However, to a small and smoothly area, the average value is sufficient in the calculation procedures. In this study, the average values were adopted due to the relatively smooth conditions in the Hebei Plain and little difference of air pressure between different places. Air pressure is calculated by using a simplification of the ideal gas law incorporating the elevation information, and the equation is given as,

)1903.01(

0 443311 �

��

� −= zPPs (4.1)

Where, P0 is the sea level air pressures [Pa], taken 101325 Pa as default value locally, z the elevation of calculation height [m].

Surface air pressure, pressure at reference (2m) per station in Hebei Plain and mean values are showing in table 8.


24

Table 4-3: Air pressures at meteorological stations over Hebei Plain

Elevation

(m) Surface Pressure

(Pa) Pressure at reference

height (Pa) 53698 81.2 100368.60 100345.14 53798 18.9 101101.73 101078.13 54518 12.6 101176.11 101152.50 54602 28.6 100987.30 100963.72 54624 7.3 101238.72 101215.09 54705 78.0 100406.16 100382.68

Average ---- 100897.77 100856.21

(4) Specific Humidity

Specific humidity is the mass of water vapour present in a unit mass of air. Where temperatures are high and rainfall is excessive, the specific humidity of the air reaches high proportions. Accurate information is required to determine the surface virtual temperatures in SEBS algorithm, and it can be estimated based on the actual water vapour pressure and surface pressure data:

pe

q a⋅=85

(4.2)

Where, ea is the actual water vapour pressure, p the surface pressure.

Specific humidity in the cloud-free days is shown in table 4-4.

Table 4-4: Estimated specific humidity at different meteorological stations over Hebei Plain

2004-8-17 2004-9-21 2004-11-17 2005-3-4 2005-3-5 2005-3-25

53698 0.012 0.005 0.002 0.001 0.001 0.00253798 0.012 0.006 0.002 0.001 0.001 0.00254518 0.011 0.005 0.003 0.001 0.001 0.00254602 0.012 0.006 0.003 0.001 0.001 0.00254624 0.011 0.006 0.002 0.001 0.001 0.00354705 0.018 0.006 0.003 0.001 0.001 0.003

average 0.013 0.005 0.002 0.001 0.001 0.002

(5) Sunshine Hours

If incoming solar radiation data were missing, another method based on the daily sunshine hours can be used to calculate atmosphere transimitivity, then the daily incoming short wave radiation can be estimated. Daily sunshine hours are a common item measured in related meteorological stations. The sunshine hours on cloud free days over Hebei Plain during August, 2004 to March, 2005 are given below.


25

Table 4-5: Daily sunshine hours over Hebei Plain for cloud-free days

53698 53798 54518 54602 54624 54705 Average 2004-08-17 10.7 11.30 11.60 11.50 11.10 11.90 11.35 2004-08-21 11.4 11.30 11.00 11.70 11.70 11.20 11.38 2004-11-17 8.2 8.20 8.70 8.80 8.80 8.70 8.57 2005-03-04 9.9 9.80 8.30 10.20 9.60 10.60 9.73 2005-03-05 10.1 9.50 9.60 9.80 9.60 10.50 9.85 2005-03-25 11.3 11.20 11.00 10.60 10.90 11.10 11.02

4.2. Radiation data processing

Incoming shortwave radiation (solar radiation) is recorded every one hour in Leting County, Hebei Province. To get the solar radiation at satellite passing time, the linear interpolation model were used to get required data by interpolate two neighbour data sets, mostly at 11:00 o’clock and 12:00 o’clock of local time in study area. Due to the relatively less difference of radiation values in the study area, and to simplify the whole procedure, average solar radiation values were adopted, which is shown in table 4-6.

Table 4-6: Incoming solar radiation over satellite passing time on selected cloud free days

2004-08-17 2004-09-21 2004-11-17 2005-03-04 2005-03-05 2005-03-25

Solar radiation (Wm-2)

1016.82 908.04 510.6 891.0 759.6 863.1

4.3. Remote sensing data processing

The MODIS instrument provides high radiometric sensitivity (12 bit) in 36 spectral bands ranging in wavelength from 0.4 to 14.4, and MODIS productions MOD09, MOD11 will be used in this study, which can provide surface reflectance and surface temperature respectively.

(1) Images re-projection

MODIS imagery, however, is in a new map projection called the Integerized Sinusoidal (ISIN) projection, which is not supported by most existing software packages. So before those images can be used by other software packages, re-projection should be pre-processed. The MODIS Reprojection Tool (MRT) is software designed to help individuals work with MODIS data by reprojecting MODIS images (Level-2G, Level-3, and Level-4 land data products) into more standard map projections (figure 4-1). The software outputs MODIS data in file formats that are supported by existing software packages (raw binary and GeoTIFF) as well as HDF-EOS.

By using this package, MODIS productions were converted to GeoTIFF file format, which can be read by ENVI softwater package directly. The re-projection parameters are showing below:

Resampling type: Nearest Neighbor UTM Zone: 50 Output Projection Type: UTM Output Pixel Size: 1000m Datum: WGS84


26

Figure 4-1: Interface of MODIS Reprojection Tool (MRT)

(2) Images Mosaicking

Since the scale of the study area cover with two neighbour images, which tiles is “h26v05” and “h27vv05” respectively (detail explanations can be found in related MODIS production manuals), so the images downloaded should be put together and the georeferenced subset map should be retrieved to get the study area. This process will be carried out by use “mosaick” function of ENVI software and the tool interface of this images processing is shown as figure 4-2.

Figure 4-2: Images mosaicking by combining two neighbour images to get the whole area of Hebei Plain


27

4.4. Surface Biophysical Properties

Determination of various biophysical parameters is among the most important process in ETa calculation by using remote sensing data. A few experimental and mathematical approaches have been developed for the past few decades, however, due to the difference of the study area of those approaches was derived and the remote sensor of these studies based, the availability and accuracy of those methods should be taken in account carefully when utilize them in a new area. Some of approaches for different surface biophysical parameters estimation and their merits are summarized following.

4.4.1. Normalized Difference Vegetation Index (NDVI)

The normalized difference vegetation index (NDVI) as defined by,

rednir

rednirNDVIρρρρ

+−

= (4.3)

Where, ρ red and ρ nir are reflectance measurements in MODIS channels 1 (0.620-0.670 m) and 2

(0.841-0.876 m).

This is the most commonly used vegetation descriptor from satellite imagery. The difference in reflectance is divided by the sum of the two reflectance bands. This compensates for different amounts of incoming light and produces a number between 0 and 1. The typical range of actual values is about 0.1 for bare soils to 0.9 for dense vegetation.

4.4.2. Fractional vegetation cover

Fractional Vegetation Cover is an important parameter that have key role in the energy exchanges at the land surface. Remote sensing provides a seemingly obvious data source for quantifying f over large areas, and several methods have been developed in the past few decades.

(1) Fractional vegetation cover determined by SAVI (Choudhury and Ahmed et al., 1994)

By using a heat balance and a radiative transfer model, Choudhury et al. have found certain relationship between fractional vegetation cover and Soil Adjusted Vegetation Index (SAVI),

)/()( sds SAVISAVISAVISAVIf −−= (4.4)

Where, SAVI is the SAVI values of the current pixel (SAVI map) SAVIs is the value of SAVI for soils without vegetation selected from the SAVI image SAVId is the value for dense canopies selected from the SAVI SAVI is Soil Adjusted Vegetation Index that resembles the NDVI with some added terms to adjust for different brightness of background soil. It is given by equation,

LL

SAVIrednir

rednir

++−+

=ρρ

ρρ ))(1( (4.5)

Where,


28

L is a soil adjusted factor, which range from 0 for very high vegetation cover to 1 for very low vegetation cover, and it can be calculated by equation. Based on a simplified radiative transfer model, Huete has shown that a value L=0.5 permits the best adjustment, i.e. to minimize the secondary backscattering effect of canopy-transmitted soil background reflected radiation.

WDVINDVIaL ⋅⋅⋅−= 21 (4.6)

Where, coefficient a equal to 1.6, and WDVI is given by:

rednirWDVI ργρ ⋅−= (4.7)

γ is coefficient of soil line:

Figure 4-3: Definition and determination of the soil line combining the near infrared and red reflectance bands

This equation is limited to homogeneous vegetation and soil environment that has a variable canopy density, so the species dependent values of SAVId and soil dependent SAVIs should be known and they can be determined by looking around the target image based on the knowledge about the land cover in the study area. Due to the limited ground truth data about the land cover in the study area, some uncertainty must be happened when applying this method to retrieve fractional vegetation cover.

(2) Fractional vegetation cover determined by NDVI (Baret and Clevers et al., 1995)

Based on the canopy gap fraction analysis by Baret et al., the fractional vegetation cover can be expressed as,

K

NDVINDVINDVINDVI

f ��

��

�

−−

−=minmax

max1 (4.8)

rednir b γρρ +=


29

Where, NDVImin and NDVImax are, respectively, the normalized difference vegetation index values for the soil (LAI=0) and for infinite LAI. Coefficient K depends mostly on canopy architecture, sun and view directions as well leaf optical properties, and can be determined experimentally.

(3) Fractional vegetation cover determined by NDVI (Valor and Caselles 1996)

By considering a mixed pixel with a vegetation cover f and a soil proportion (1-f) and inverting the NDVI expression, Valor et al. (1996) have developed a new algorithm to retrieve fractional vegetation cover, which is given below ,

( )( ) ( )

gg

vv

vv

gg

vg

g

rrrr

KNDVINDVI

KNDVINDVI

K

KKK

Kf

12

12,,

11

1

−−===

−−−−

=

(4.9)

Where, r2 is the reflectance measured in the near infrared and r1 is the reflectance corresponding to the red wavebands, subscript v and g refers to observed vegetation top, ground respectively.

(4) Fractional vegetation cover determined by NDVI (Gutman and Ignatov 1998)

A simple procedure to determine fractional vegetation cover is proposed by Gutman et al. (1998) as,

minmax

max

NDVINDVINDVINDVI

f−

−= (4.10)

Where, NDVImin is the NDVI for bare soil and NDVImax for full vegetation corverage.

As a summary, the parameters required in these equations and available conditions in this study are listed in the table 4-7. The ground truth information of bare land dense canopy is highly required for all those methods. Due to the shortage of ground truth data about land cover over the study area, some uncertainty must be happened when determining the values of these parameters through looking around the target image. Therefore, in order to decrease the uncertainty caused by the uncertain parameters as much as possible, the method that requires minimum parameter is used in this study, namely, method 4.

4.4.3. Leaf Area Index (LAI)

Leaf Area Index (LAI) is the leaf area per unit ground area, which reflects the vertical vegetation amount. Several methods were developed to estimate Leaf Area Index, and some of them are summarized below.


30

Table 4-7: Parameters requirements for different methods for fc retrieve and availability

Parameters required Retrieved information Available conditions SAVI Surface reflectance available SAVIs Bare land Not available SAVI d dense canopies Not available

Method 1

L Surface reflectance Available NDVI Surface reflectance Available NDVImax dense canopies Not available

NDVImin Bare land Not available Method 2

K Vegetation type, soil type etc. Not available NDVI Surface reflectance Available NDVIg Bare land Not available NDVIv Dense canopies Not available r2v Dense canopies Not available r2g Bare land Not available r1v Dense canopies Not available

Method 3

r1v Bare land Not available NDVI Surface reflectance Available

NDVImax dense canopies Not available Method 4

NDVImin Bare land Not available

(1) Leaf Area Index determined by SAVI (Choudhury and Ahmed et al. 1994)

Choudhury et al. (1994) simulated relationships between SAVI and LAI for cotton, maize, and soybean:

��

��

� −⋅−=

2

1

3

ln1

cSAVIc

cLAI (4.10)

The constant c1,c2 and c3 should be determined based on study area, c1 always take the maximum value of the SAVI map, if no information about vegetation available, default values, which adopt the average of many experiences developed by several authors (table 4-8), can be used:

c1=0.69, c2=0.59 and c3=0.91.

For Savannah landscape, equation can be modified to:

2

1

ccSAVI

LAI−

= (4.11)

Where, constant c1 and c2 take the default values, 0.11 and 0.28 respectively.


31

Table 4-8: Empirical constants for Leaf Area Index determination for different crops in the world

crops country c1 c2 c3 R2 Max. LAI Cotton USA 0.82 0.78 0.60 0.98 3.5 Maize Italy 1.27 1.10 1.20 0.79 3.3 Maize USA 0.68 0.50 0.55 0.90 6.0 Soybean USA 0.72 0.61 0.65 0.70 6.0 Wheat Italy 0.73 0.67 0.97 0.94 5.0 Fruit trees Italy 1.34 2.70 2.40 0.39 2.6 Winter vegetables Niger 1.31 2.75 2.20 0.54 4.2 Bush & grassland Niger 0.14 0.30 - 0.95 1.2 Grassland Niger 0.13 0.35 - 0.98 1.3 Millet Niger 0.13 0.47 - 0.83 0.8 Degraded bush Niger 0.11 0.28 - 0.96 1.0 All crops 0.69 0.59 0.91 - 6.0

(2) Leaf Area Index determined by NDVI (Su 1996; Su 2000)

2/1

11

�

��

�

+−+⋅=

NDVINDVINDVI

NDVILAIδ

(4.12)

This formula is strictly only good for low vegetation since NDVI saturates at higher LAI values. However, because of limited information for the study area to support more sophisticated formulations, this equation is adopted in this study.

4.4.4. Vegetation height (h)

When we have limited knowledge about the vegetation structure in the aim area, vegetation height can be estimated by inverting the equation that calculate the zom based on the vegetation height(Richard and Luis et al., 1998), but it required the zom information that is estimated from other method discussed below.

136.0omz

h = (4.13)

4.5. Surface characteristic parameters

4.5.1. Broad-band emissivity

The emissivity is a key factor on temperature measurement. Several methods have been developed to measure ε from satellite. Among those approaches, two of them will be discussed below, which are often used and applied in related study.

(1) Emissivity determined by NDVI (Van de Griend and Owe 1993)

By analysing the relation between surface emmisivity and NDVI, an experimental relationship was obtained by Van de Griend et al. as following,

)ln(047.00094.1 NDVI+=ε (4.14)


32

This equation is restricted to the NDVI values ranging from 0.16~0.74. It is not valid for water bodies with low NDVI and high emissibity (ε =0.99 to 1.0).

(2) Vegetation Cover Method (VCM) (Valor and Caselles 1996)

Every pixel has a fraction cover by vegetation and other fraction cover by soil or rocks, so the pixel emissivity in image should be obtained as a mix of the emissivity of the different surfaces. Taking this consideration into account, the Vegetation Cover Method (VCM) developed by Valor et al. gives the following operational equation:

)1(7372.1)74.11)(1( fffff gv −+−−+= εεε (4.15)

Where, “v” means vegetation and “g” ground, f is the fraction vegetation cover, which could be directly obtained from the NDVI vegetation index derived from satellite measurements.

Table 4-9 shows the ground emissivity (εg) for the 8-9 µm atmospheric window, the average value and the standard deviation are given. εv is usually taken as 0.985.

Table 4-9: Ground emissivity (εg) for the 8-9 µm atmospheric window

Ground type Soil/rock description Ground coefficient

(εg) sandy soil with organic content < 2% 0.88±0.03

Soil

sandy soil with organic content > 2%, clayey soil, and silty soil 0.950±0.018

IGNEOUS aplite, granite, obsidian, rhyolite, granodior, monzonite, qmonzonite, tonalite 0.76±0.03

syenite, andesite, diorite, anorthosite, basalt, diabase, gabbro, ijolite, lamprophyre, norite, dunite, picrite

0.93±0.02

quartzite 0.73±0.03 gneiss, phyllite, schist 0.88±0.04 METAMORPHIC hornfels, marble, slate 0.953±0.011 greywacke, sandstone 0.85±0.04

Rock

SEDIMENTARY limestone, shale, siltstone 0.945±0.017

4.5.2. Aerodynamic roughness height (z0m)

Aerodynamic roughness height is a very important parameter in surface energy balance model, which influence greatly the turbulent characteristics near the surface where the heat fluxes originate. There are several methods to retrieve this parameter currently, including wind profiles method, vegetation height, look up table based on the land use classification etc.

(1) Retrievals from wind profiles

The theory of turbulent mass and heat transport for a land surface into the atmosphere tell us that the wind speed increases logarithmically with height, at a certain distance above the surface, the wind


33

speed becomes zero, and the height where the wind appears to be zero is defined as aerodynamic roughness height. It is clearly that the aerodynamic roughness height can be determined from wind profiles, which seems to be the most accurate methods for the time being. But due to the surface topographic and canopy structure and varies with wind speed and direction, the use of this method is only limited in the local area, and failed when used in a big scale.

(2) Aerodynamic roughness height determined by LAI (Raupach 1994; Verhoef and Mcnaughton et al., 1997)

The Aerodynamic roughness height is inflected by vegetation height, displacement distance, friction velocity and wind speed, etc. So it can be presented as following equation:

]/[ *

)(hh ukuom e

dhz ψ−

−= (4.16)

Where, h is the vegetation height, d the displacement distance, k von karman’s constant (taken 0.41 as

default value), u* friction velocity, h

ψ a vegetation influence function and uh wind speed at the top to

canopy.

The vegetation influence function is given by:

11)ln( −+−= wwh ccψ (4.17)

where constant cw is taken 2.0 as default value.

The ratio of u*/uh is calculated by,

5.0*

2�

��

� += LAIcc

uu

rsh

(4.18)

Note that when the values of u*/uh calculated by above equation is greater than 0.3, take 0.3 as the default value. Constant cr is taken as 0.35, and the cs is given by,

2

2

ln ��

��

�+��

��

� −=

ho

s

zdh

kc

ψ

(4.19)

where constant z0 is default taken as 0.01.

This method thus depends on the displacement height and the LAI information. Due to the shortage of data, use of this method is limited in this study.

(3) Aerodynamic roughness height determined by land use classifications(Hasager and Jensen 1999)


34

By studying on the relationship between zom values and different land use cover, some statistical values were summarized as table 4-10, which can be a resource to determine the Aerodynamic roughness height based on the knowledge about the land cover over the study area.

Table 4-10: Table land use classes database and associated z0m values

Land use classes zom (m) 1 Grass 0.0340 2 Maize 0.4966 3 Potatoes 0.0639 4 Beets 0.0639 5 Cereals 0.4966 6 Other crops 0.0639 7 Greenhouses 0.4066 8 Orchards 0.6065 9 Bulbs 0.0639 10 Deciduous forest 1.2214 11 Coniferous forest 1.2214 12 Heather 0.0408 13 Other open spaces in natural areas 0.0408 14 Bare soil in natural areas 0.0012 15 Freshwater 0.0002 16 Salt water 0.0002 17 Continuous urban area 1.1052 18 Built-up area in rural area 0.5488 19 Deciduous forest in urban area 1.2214 20 Coniferous forest in urban area 1.2214 21 Built-up area with dense forest 1.2214 22 Grass in built-up area 0.0334 23 Bare soil in built-up area 0.0012 24 Main roads and railways 0.0035 25 Buildings in rural areas 0.5488

This method provides a convenient way to estimate the surface roughness height on the assumption that the detailed land use information is available, however, due to seasonal diversity of the different vegetation heights, especially the heights of crops in agricultural land use area, some error must be happened when applying the same z0m values to certain crops for temporal analysis of regional ETa distribution.

(4) Aerodynamic roughness height calculated by vegetation height (Richard and Luis et al. 1998)

Aerodynamic roughness height can be estimated by vegetation height (h), which is given by,

hzom ⋅= 136.0 (4.20)

To apply this equation, detailed information about the vegetation heights should be known first, which limits its use in the big area with heterogeneous land cover.

(5) Aerodynamic roughness height determined by NDVI


35

Using field measurements, a relationship between z0m and NDVI was found by Bastiaanssen as(Bastiaanssen 1995),

)exp( 21 NDVIcczom ⋅+= (4.21)

Where, constant c1, c2 depend on local field conditions, here take the default value -5.5 and 5.8 respectively. Other values for the constants can be found in Morse et al. (Morse and Tasumi et al., 2000).

Another simple relationship that was used to derive the roughness length for momentum transfer as follows(Su and Jacobs 2001),

5.2

max0 5.0005.0 ��

��

�⋅+=

NDVINDVI

z m (4.22)

The values derived from the above two expressions are practically the same when NDVI 0.7,

however, when NDVI 1.0, the equation 4.21 gives z0m>1.0m, which is much too big for low vegetation when compared to literature recommendations. The maximum values given by latter are 0.5 for NDVI 1.0, which is more realistic.

In conclusion, equation 4.22 was considered to be suitable for current research.

4.5.3. Displacement height (d0)

Displacement height, same as zero-plane displacement, a height scale in turbulent flow over tall roughness elements associated with the average level of action of momentum transfer between the flow and the roughness elements. It is the height that the surface level is normally displaced to a level just below the vegetation canopy due to tall vegetation canopy, where the wind speed is zero. It can be estimated either from leaf area index (LAI) or from aerodynamic roughness height (zom).

(1) Displacement height determined by LAI (Verhoef and Mcnaughton et al. 1997)

��

�

��

� −−=−

LAIc

ehd

LAIc

10

111 (4.23)

Where, h is vegetation height, taken 1m as default values if no information available, constant c1 is taken as 20.6. Note that when LAI equal to 0.0, the d0 is filtered to adopt values 0.

(2) Displacement height estimated by zom

Displacement height can be derived from the relationship between aerodynamic roughness height, vegetation height as well as displacement height,

omzcd ⋅=0 (4.24)


36

Where, c is constant based on the local conditions, for a grass reference surface, c can be derived as 5.42(Richard and Luis et al. 1998).

4.5.4. Albedo

Albedo is the fraction of the incident sunlight that is reflected. When an object reflects most of the light that hits it, it looks bright and it has a high albedo. When an object absorbs most of the light that hits it, it looks dark. Dark objects have low albedo. Albedo can be measured easily by using special instrument, but it only limited to a small scale with point values. As far as this is concerned, remote sensing is the only practical means for mapping land surface albedo globally. Based on extensive radiative transfer simulations, Shunlin Liang has proposed a series of formulas to convert single band albedo that were recorded in different narrow bands sensors to broad bands albedo(Liang 2001; Liang and Chad et al., 2003). The conversion formula for shortwave bands of MODIS is:

0015.0081.0112.0116.0243.0291.0160.0 754321 −+++++= ααααααα short (4.25)

Where, shortα is simulated total shortwave albedo, iα (i = 1~7) is the narrow bands albedo of

MODIS shortwave bands.

4.5.5. Emissivity of the atmosphere

(1) Emissivity of the atmosphere determined by standard meteorological data

71

27324.1 ��

��

�

+⋅=

a

da T

eε (4.26)

Where, de is the water vapor pressure in millibars and can be calculated from relative humidity and air

temperature.

��

��

�

+⋅

⋅=3.237

27.17exp108.6

a

as T

Te (4.27)

sd eRHe ⋅= 100/ (4.28)

Where, se is the saturated water vapor pressure in millibars, RH the relative humidity.

(2) Emissivity of the atmosphere determined by air temperature (Campbell and Norman 1998)

26 )15.273(102.9 +⋅⋅= −aa Tε (4.29)

In SEBS, the later method was preferred.


37

4.6. Sensitivity analysis

Sensitivity analysis is used to ascertain how a given model depends upon the input parameters. If a small change in a parameter results in relatively large changes in the model outcomes, the model is said to be sensitive to that parameter. This may mean that the parameter has to be determined very accurately or that the model has to be redesigned for low sensitivity. It is an important method for checking the quality of a given model, as well as a powerful tool to ensure which parameters should be emphasized when running the model.

In order to determine the required precision of input parameters used in the SEBS model, it is necessary to determine the sensitivity of the model result to various changes in input values. As discussed before, the basic idea of the SEBS model is to determine evaporative fraction. So, sensitivity tests in this study were conducted on the following: fractional vegetation cover displacement height, aerodynamic roughness height and surface emissivity (Table 4-11) and determine the sensitivity of the modelling evaporative fraction to various changes in those input values. The values of the parameters on September 21, 2004 were selected as the base values, which is grouped into 4 classes according to the NDVI values.

Sensitivity is defined (McCuen and Snyder 1986) as the rate at which one factor changes with respect to the change in another,

i

o

FO

S∂∂

= (4.30)

Factor O often represents a model output or output of one component of a model, whereas F may be any input variable. Analytical differentiation as shown in equation has not been used extensively in hydrological modelling because of limited mathematical framework of sensitivity. The method of “factor perturbation” is commonly used to compute sensitivity(Nearing and Deer-Ascough et al., 1990). The sensitivity is obtained by incrementing or decreasing the F-factor and computing the resulting change in O,

]/)[(]/)[(

1212

1212

IIIOOOS

−−= (4.31)

Where I1 and I2 are the least and greatest values of input used for a certain range, 12I is the average of

I1 and I2. O1 and O2 are the output for the two input values and 12O is the average of the two outputs.

The parameter S represents a relative normalized change in output to a normalized change in input, which allows a means of comparing sensitivities for input parameters which have different orders of magnitude. The parameter S will be a function of the chosen input range for nonlinear response. Due to multi input ranges, more than one S values are given for more than one input range in this study. The ranges of the inputs over which S calculated are reported in table for each of the parameters.

One of the limitations to current method in sensitivity analysis discussed by McCuen and Snyder (1983) was that the linear form of the sensitivity parameter does not reflect sensitivity of the variable over the entire range of the parameter because of the non-linear response of the model. However, as pointed out by McCuen and Snyder, the sensitivity which represents the extremes of the physical conditions is often of


38

primary interest. In addition, the sensitivity of the variable over the entire range of the parameter can be approximately achieved by applying multi input ranges for a single input parameter.

Table 4-11: SEBS model parameters and base values used for sensitivity analysis

Parameters Units Base values Range of test NDVI=0.2 0.699 NDVI=0.4 0.768 NDVI=0.6 0.811

Displacement height

NDVI=0.8

m

0.848

0.00-1.90

NDVI=0.2 0.043 NDVI=0.4 0.343 NDVI=0.6 0.629

Fractional vegetation cover

NDVI=0.8

-

0.914

0.10-0.90

NDVI=0.2 0.016 NDVI=0.4 0.073 NDVI=0.6 0.192

Aerodynamic roughness height

NDVI=0.8

m

0.388

0.005-0.45

NDVI=0.2 0.985 NDVI=0.4 0.989 NDVI=0.6 0.987

Surface emissivity

NDVI=0.8

-

0.985

0.90-1.00

4.6.1. Sensitivity to displacement height

To carry out this analysis, all the other parameters used in the SEBS model were kept as constant for all designed runs in which the values of displacement height vary from 0.10 to 2.0m, and four pixels in the images that represent 4 classes NDVI were selected as target. Selected results from this sensitivity analysis are shown in figure 4-4, 4-5 and table 4-12.

Figure 4-4 shows the changes of modelled evaporative fraction due to variable displacement height values. As seen from it, SEBS modelled evaporative fractions decreased slightly with the increasing displacement heights in the lower range. When the displacement height reaches a certain values, the evaporative fraction begins to decrease drastically with the increasing displacement values. In addition, evaporative fraction is a function not only of displacement height, but also of the NDVI values. The area that has the high green leaf biomass, namely, high NDVI values, normally has relatively lower evaporative fraction, but more sensitive to the displacement height (figure 4-5).


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Figure 4-4: Influence of displacement height (d0) on modeled evaporative fraction for several NDVI values of the study area, SEBS model

Figure 4-5 shows the sensitivity to displacement height of SEBS modelled evaporative fraction. As it is showed, sensitivity is bigger in high ranges of displacement heights, for example, during 0.9m to 1.2 m, and smaller when displacement heights below 0.9m, which is only a little bit more than 0 and negligible. In high ranges of displacement heights, the model is more sensitive in high NDVI area. Due to the base value of displacement heights in this case is between 0.60-0.90m, the average for the ranges 0.10 to 1.10 were adopted as the sensitivity parameter to displacement height, which is 0.55 (table 4-12).

Figure 4-5: Sensitivity for displacement height of SEBS model


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Table 4-12: Sensitivities to displacement heights ranging from 0.10mm to 1.00m

4.6.2. Sensitivity to fractional vegetation cover

To carry out this analysis, all the other parameters used in the SEBS model were kept as constant, which equal to base values listed in table 4-11, for all designed runs in which the values of fractional vegetation cover varies from 0.10 to 1.00 [-], and four pixels in the images that represent 4 classes NDVI were selected again as targets. Selected results from this sensitivity analysis are shown in figure 4-6, 4-7 and table 4-13.

Figure 4-6 shows the changes of modelled evaporative fraction due to variable fractional vegetation cover values. As seen from it, SEBS modelled evaporative fractions increased slightly with the increasing fractional vegetation covers from ten percent to hundred percent with almost the same rate. Taken the case of which NDVI equals to 0.4 as an example, when fractional vegetation cover equals to 0.10, the modelled evaporative fraction is about 0.70, finally, when fractional vegetation cover reaches to 0.9, modelled evaporative fraction increases to 0.77 correspondingly and the sensitivity is only 0.05. Total amount of surface biomass also plays an important role to affect the evaporative fraction. The larger NDVI, the less evapotranspiration it has.

Figure 4-6: Influence of fractional vegetation cover on SEBS modeled evaporative fraction for several NDVI classes of the study area


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Figure 4-7: Sensitivity for fractional vegetation cover of SEBS model.

Figure 4-7 show the sensitivity to fractional vegetation cover of SEBS modelled evaporative fraction. As it is showed, sensitivity to fractional vegetation cover arise gradually with the increasing fractional vegetation cover when which is lower than 0.9. As far as NDVI value is concerned, the SEBS modelled evaporative fraction is more sensitive to high NDVI value area and less sensitive to lower NDVI value area. Table 13 below shows some results from this sensitivity analysis, and average is 0.22.

Table 4-13: Sensitivities to fractional vegetation cover ranging from 0.10 to 0.90 [-]

4.6.3. Sensitivity to aerodynamic roughness height

To carry out this analysis, all the other parameters used in the SEBS model were kept as constant, which equal to base values listed in table 4-11, for all designed runs in which the values of aerodynamic roughness height varies from 0.005 to 0.30m, and four pixels in the images that represent 4 classes NDVI were selected again as targets. Selected results from this sensitivity analysis are shown in figure 4-8, 4-9 and table 4-14.

Figure 4-8 shows the changes of modelled evaporative fraction due to variable aerodynamic roughness height values. As seen from it, SEBS modelled evaporative fractions decreased drasticlly with the increasing aerodynamic roughness height values from 0.005m to 0.30m. Taken the case of which


42

NDVI equals to 0.40 as an example, when aerodynamic roughness height equals to 0.005m, the modelled evaporative fraction is about 0.88, finally, when aerodynamic roughness height reaches to 0.30m, modelled evaporative fraction decreases to 0.29 correspondingly and the average sensitivity of the ranges of 0.005m-0.30m is about 0.63 [-]. Furthermore, total amount of surface biomass also plays an important role to affect the evaporative fraction. The larger NDVI, the more evapotranspiration it has and less sensitive to the aerodynamic roughness height change (figure 4-9).

Figure 4-8: Influence of aerodynamic roughness height on SEBS modeled evaporative fraction for several NDVI classes of the study area

Figure 4-9 show the sensitivity to aerodynamic roughness height of SEBS modelled evaporative fraction. As it is shown, sensitivity arises gradually with the increasing aerodynamic roughness height. As far as NDVI value is concerned, the SEBS modelled evaporative fraction is more sensitive to lower NDVI value area and more sensitive to higher NDVI value area. Table 14 shows some results from this sensitivity analysis, and average is 0.88.

Figure 4-9: Sensitivity for aerodynamic roughness height of SEBS model


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Table 4-14: Sensitivities to aerodynamic roughness height ranging from 0.02m to 0.30m

4.6.4. Sensitivity to surface emissivity

To carry out this analysis, all the other parameters used in the SEBS model were kept as constant, which equal to base values listed in table 4-11, for all designed runs in which the values of surface emissivity varies from 0.92 to 1.00m because the emissivity of vegetation, soils and rocks varies between 0.9 and 1.0 and the emissivity of water is close to 1. Four pixels in the images that represent 4 classes NDVI were selected again as targets. Selected results from this sensitivity analysis are shown in figure 4-10, 4-11 and table 4-15.

Figure 4-10 shows the changes of modelled evaporative fraction due to variable surface emissivity values. As seen from it, SEBS modelled evaporative fractions keep more or less the same with the increasing surface emissivity values from 0.92 to 1.00. Taken the case of which NDVI equals to 0.40 as an example, when surface emissivity equals to 0.92, the modelled evaporative fraction is about 0.728, finally, when surface emissivity reaches to 1.00, modelled evaporative fraction decreases to 0.723 correspondingly and the average sensitivity in the ranges of 0.92-1.00 is only about 0.08.

Figure 4-10: Influence of surface emissivity on SEBS modeled evaporative fraction for several NDVI classes of the study area

Figure 4-11 show the sensitivity to surface emissivity of SEBS modelled evaporative fraction. As it is showed, there isn’t a clear relationship between surface emissivity change and sensitivity. As far as NDVI value is concerned, the SEBS modelled evaporative fraction is not sensitive to surface


44

emissivity changes in lower biomass area, but more sensitive to higher NDVI value area. Table 15 shows some results from this sensitivity analysis, and average is 0.25.

Figure 4-11: Sensitivity for surface emissivity of SEBS model

Table 4-15: Sensitivities to surface emissivity ranging from 0.92 to 1.00

Emissivity [-]

4.6.5. Summary of sensitivity analysis

A summary of the sensitivity analysis for various SEBS input parameters mentioned before are presented as figure 4-12. Aerodynamic roughness height is the major factor in terms of model response and it should be determined with much care when applying different empirical methods. Displacement height falls into the moderately sensitive range of the parameters and care also should be taken when a vegetation map is unavailable and empirical equations have to be applied. Fractional vegetation cover and surface emissivity are not dominant factors; they do have influence on SEBS modelled evaporative fraction, but not as great as other parameters.


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Figure 4-12: Summary of average sensitivity values to variable SEBS input parameters

Other important parameters that affect model output include the vegetation height and leaf area index, especially the leaf area index, which plays an important role when determining the kB-1 values by using the extended model of Su et al. Since the information of those parameters is limited in this study, they are all derived from remote sensing images, and sensitivity of these parameters to the SEBS result is not necessary in this study.


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5. Actual Evapotranspiration and Spatio-temporal Distribution

5.1. Accuracy Assessment

5.1.1. Ground truth Actual Evapotranspiration (ETa)

Weighing lysimeters is the standard tool for evapotranspiration measurements at point scale. Comprehensive reviews of lysimeters can be found in related literatures. One of the main purposes of lysimeters is to measure evapotranspiration or evaporation and transpiration for studying water use by plants and water loss from surface. The basic concept for lysimeter to measure water gains or water losses is to find the weight difference during a certain period. Due to the measurement of mechanical weighing system includes not only the basic load of the soil mass in the lysimeter but also the self weight of instruments involved in it, a relationship should be found between reading weight number of the lysimeter and certain amount of water, namely, the lysimeter should be calibrated before evapotranspiration determination. Following sections we will focus on the irrigation test that was carry out during field campaign in Luancheng Agro-Ecosystem Station to calibrate the lysimeter and actual evapotranspiration calculation by using regression equation.

(1) Lysimeter calibration

To calibrate the lysimeter and get a mathematic relationship between the weight difference and soil water change to calculate the actual water losses or water gains, a irrigation test were carried out during the field work by inputting certain amount of water into the surface soil among the scope of the lysimeter, then observe the change of lysimeter weight. Table 5-1 below shows the sets of water input scheme and the following weight changes.

Table 5-1: Irrigation test scheme and reading observed in lysimeter

Amount of irrigation

water (kg) Reading of lysimeter

Amount of input water (kg)

Reading of lysimeter

(before irrigation) 61560 11 16.5 54814 1 5.5 61487 12 16.5 53893 2 5.5 61178 13 11 53210 3 5.5 60885 14 11 52606 4 5.5 60570 15 11 52030 5 11 60000 16 5.5 51730 6 11 59300 17 5.5 51432 7 11 58720 18 5.5 51110 8 16.5 57804 19 11 50490 9 16.5 56844 20 16.5 49654

10 22 55675 21 5.5 49318


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Figure 5-1: Regression model for lysimeter calibration

By applying a linear relation (figure 5-1) between lysimeter reading changes and soil water change (mm/m2), the equation for lysimeter calibration to calculate evapotranspiration is given below,

( ) 2499.00057.0 21 +−×=∆ DDW (5.1)

Where, W∆ is soil water change in the lysimeter [mmday-1], D1, D2 the lysimeter reading during beginning and ending time of a certain period, commonly one day. By using this equation, we can calculate the daily evapotranspiration on the cloud free days based on the daily observation in the lysimeter of Luancheng Agro-Ecosystem Station to validate SEBS algorithms.

(2) Actual evapotranspiration determined by lysimeter

Based on the regression linear model of lysimeter calibration, actual evapotranspiration of the cloudy free days can be calculated. Daily reading numbers of lysimeter and water loss which presented as evapotranspiration [mmday-1] here for cloud free days are showed in table 5-2 below.

Table 5-2: Daily evapotranspiration measured by lysimeter in Luancheng station for cloud free days

Date D1 D2 ETa (mmday-1) 1 17/08/2004 34321 33077 7.34 2 21/09/2004 44582 53857 4.38 3 17/11/2004 52216 52072 1.07 4 04/03/2005 45548 45300 1.66 5 05/03/2005 45784 45548 1.60 6 25/03/2005 49288 48994 1.91

5.1.2. Crop Evapotranspiration (ETc)

The crop evapotranspiration under standard conditions, denoted as ETc, is the evapotranspiration from disease-free, well-fertilized crops, grown in large fields, under optimum soil water conditions, and achieving full production under the given climatic conditions. As the main crop product area in North


48

China Plain, the crops in study area are under a very good management and irrigation water supply, especially in Taihang Mountain foot plain where Luancheng Agro-Ecosystem Station locates. Therefore, estimated crop evapotranspiration by taking local meteorological condition and crop types into account can be a helpful resource to evaluate the SEBS modelled actual evapotranspiration.

(1) ‘Kc-ET0’ approaches

A ‘Kc-ET0’ approach is introduced in FAO Irrigation and Drainage Paper No.56 to calculate the crop evapotranspiration under standard conditions(Richard and Luis et al. 1998), which is given as,

0ETKET cc = (5.2)

Where Kc is the crop coefficient [-], and ET0 the reference crop evapotranspiration [mm d-1]

Reference crop evapotranspiration ET0 is the maximum possible evapotranspiration of a reference crop (usually clipped grass) according to prevailing atmospheric conditions and constant biophysical properties. The FAO Penman-Monteith method is maintained as the sole standard method for the computation of ET0 from meteorological data, and it is given by,

)34.01(

)(273

900)(408.0

2

2

0 u

eeut

GRnET

as

++∆

−+

+−=

γ

γ (5.3)

Where, t is mean daily air temperature at 2 m height [°C], u2 wind speed at 2 m height [m s-1], es saturation vapour pressure [kPa], ea actual vapour pressure [kPa], (es - ea) saturation vapour pressure deficit [kPa], ∆ slope vapour pressure curve [kPa °C-1],and γ psychrometric constant [kPa °C-1].

The computation of all the required for the calculation of the reference evapotranspiration followed the method and procedure given in Chapter 3 of the FAO paper 56.

The crop coefficient Kc is an adjusted factor that distinguishes the crop from reference grass. Due to variations in the crop characteristics throughout its growing season, Kc for a given crop changes from sowing till harvest. Empirical Kc values for main crops of different seasons in Taihang Mountain foot plain are list in table 5-3(Liu and Zhang et al. 2002).

Table 5-3: The average crop coefficient for winter wheat and summer maize in Luancheng Agro-Ecosystem Station during five seasons (1995-2000)

Crops Winter Wheat Months Oct. Nov. Dec. Jan. Feb. Mar. Apr.

Kc 0.60 0.82 0.86 0.43 0.38 0.57 1.23

Crops Winter Wheat Maize Months May Jun.(1st-10th) Jun.(11th-30th) Jul. Aug. Sep.(1st-20th)

Kc 1.42 0.72 0.59 1.24 1.38 1.17

(2) Pan evaporation approach

Due to the wide distribution of pan evaporation measure stations, it is common to use pan evaporation that present the water loss from an open water surface under certain climatic condition to retrieve the crop evapotranspiration by applying a ratio factor between crop evapotranspiration and pan


49

evaporation. Since the evapotranspiration from certain land cover and evaporation from open water surface all depend on the weather conditions, so the ratio between crop evapotranspiration and pan evaporation, denotes as coefficient of crop water consumption, should keep more or less stable. Therefore, the crop evapotranspiration can be presented as,

0EETc ⋅= α (5.4)

Where, E0 is the pan evaporation [mm d-1], α the crop water consumption coefficient [-] and empirical α values for main crops of different months in North China plain is summarized in table 5-4(Han and Zhen et al., 2004).

The values of Pan Evaporation used in equation are based on the E601 pan, which is commonly used in China to observe evaporation from open water surface. For E20 pan, which is another commonly used pan in China, a conversional factor should be multiplied before apply this equation.

Table 5-4: Empirical α values for main crops of different months in North China plain

Crops Winter Wheat Months Oct. Nov. Dec. Jan. Feb. Mar. Apr.

α 0.32 0.78 0.65 0.45 0.52 0.80 1.15

Crops Winter Wheat Maize Months May Jun.(1st-10th) Jun.(11th-30th) Jul. Aug. Sep.(1st-20th)

α 1.50 1.05 0.30 0.80 1.25 0.70

5.1.3. Comparison of SEBS modelled ETa to measured ETa and ETc

Figure 5-2 shows the comparison between the daily evapotranspiration values obtained from SEBS and from other approaches mentioned above based on the point measurements. The actual values are given in Table 5-5, together with the standard deviation of the SEBS estimation.

Table 5-5: Comparison of SEBS result ETa to ground truth ETa and Etc


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Figure 5-2: Comparison of the daily evapotranspiration between estimated by SEBS and obtained from observations

Figure 5-2 shows the comparison between SEBS result ETa at the weather station pixel and point measurement based evapotranspiration for cloud free days during August, 2004 to March, 2005. It shows a good agreement with the SEBS modeled ETa and ground truth ETa measured by lysimeter except the day of 17, August 2004. It can be explained by combining the climatic condition for that certain period over study area and pixel based remote sensing techniques. Most of the rainfall over Hebei Plain comes in the summer season, especially in the July and August, which account for about 65~75% of yearly total amount rainfall. In addition, it is also the hottest season over the year. Therefore, a high evapotranspiration value based on the high humidity and high available solar radiation can be reached. On the other hand, by taking crop types into account, dominant crops of August over Hebei Plain are corn, which has a high water requirement in August due to the flowering season with a high leaf area index (LAI), so the high ETa value that measured by lysimeter is possible. The relative lower ETa values estimated by SEBS model can be explained by the pixel by pixel based algorithms. The image used in this study is the MODIS product with 1 km resolution. Due to the high intensity distribution of small villages in Hebei Plain, the land cover types included in one pixel are not only the crop land, but also the rural area that have small potential evapotranspiration, so a lower ETa values that weighting these different land covers in one pixel is reasonable.

For the point measurement based crop evapotranspiration derived from related empirical equations, only part of the results have a perfect match with the SEBS results, for example, on the julian day of 04-265, 05-063 as well as 05-064. This is mainly because that the coefficients those empirical equations used were mostly derived from experiments or statistical analysis under some certain climatic at certain area with given crop types. When they were used in a large area with homogeneous land covers, relatively accurate results can be obtained for the purpose of crop water requirement estimation, irrigation management as well as large scale water resource circulation modeling. However, when used in a small area to compare with other accurate in situ measurements, for instance, 3 m2 that the lysimeter covers in this study, difference must be happened.


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5.2. Spatio-temporal disribution of land surface variables

5.2.1. Surface reflectance (surface albedo)

One of the important parameters required for surface energy balance modelling is the surface reflectance (surface albedo), which can be used to model how many incoming solar radiation were dissipated again into the atmosphere by surface reflection. It depends not only on the surface soil type and mineral that solar radiation hitting but also on the land cover types of given time that reflectance happened. Hebei Plain is one of the biggest Quaternary alluvial plain in the world, and its main land use is agriculture with winter wheat and maize as its dominant crops over the year. The planting season of winter wheat in Hebei Plain is more or less during the first ten days of October each year to the middle ten days of June of following next year, and the growing season of maize is after the harvest of winter wheat and before seedtime of winter wheat, namely, during June to September. Since the land cover type over the whole plain is relatively coherent at a certain time, the surface reflectance at one time should be homogeneous. However, due to the big scale of study area, difference between of crop types of different place and spatial unstable soil moisture, surface reflectance over the area shows a wide range temporally and spatially. A summary of reflectance statistical values is shown as table below.

Table 5-6: Statistical summaries of surface albedo over Hebei Plain for cloud free days

2004-08-17 2004-09-21 2004-11-17 2005-03-04 2005-03-05 2005-03-25 Min. 0.01 0.02 0.03 0.03 0.04 0.02 Max. 0.61 0.21 0.22 0.66 0.23 0.27

Median 0.19 0.13 0.14 0.15 0.13 0.15

It is showed from the statistical summaries that the surface reflectance among the study area is around 0.19 in later summers (August 17, 2004), 0.13 in winters (November 17, 2004) and 0.15 in springs (March 2005), which is coherent with land cover over study area very well. The histograms of albedo are shown as figure 5-3. As we can see from the figures, all of them only have one peak, which indicate the homogeneous land cover in the study area at a certain time.

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Figure 5-3: Histogram of surface reflectance over Hebei Plain

Regional distributions of surface albedo over the Hebei Plain are listed in Appendix C. Take the images of August 17, 2004 as an example, the surface broadband albedo goes from 0.1 t0 0.26 over the study area. Lower values are found at urban area, Shijiazhuang City for instance, and albedo there is more or less about 0.15. Lower albedo values can also be found in seashore area and north-west part of the Hebei Plain. In seashore area, the albedo is about 0.15 to 0.17, and in the north-west part of the study area, the albedo values are round 0.15-0.18. High values are found in some agriculture area, which is located in the south-east part of the Hebei Plain, and albedo there is round 0.25.

5.2.2. Surface temperature

Land surface temperature is the surface response to the energy exchange process in the soil-crop-atmosphere system, which depend not only on the incoming solar radiation, backward reflected radiation, but also on the surface wind speed, surface roughness and soil texture. Under the wet limit case, where the evaporation takes place at potential rate, (i.e., the evaporation is only limited by the available energy under the given surface and atmospheric conditions; see detailed definition by Su, 2002), land surface temperature is mainly controlled by surface evapotranspiration. Basically, there is a positive relationship between surface evapotranspiration and land surface temperature. The higher temperature the place has, the lower evapotranspiration there is.

Histograms and statistic summaries of Land surface temperatures retrieved from MODIS products on cloud free days during August, 2004 to March, 2005 are given in figure 5-4. Surface temperatures in study area show a similar pattern as surface reflectance with one peak, which indicating the relatively homogenises land cover in the Hebei Plain. Higher values were presented in the later summer and

Nov. 17, 2004 Mar. 04, 2005

Mar. 05, 2005 Mar. 25, 2005


53

later spring, which is more or less about 310 K. As a rule of thumb, surface temperature in summer season should have the highest values in study area, but due to the rain season, the evaporation takes place at potential rate, the surface temperature will be affected.

Table 5-7: Statistical summaries of surface temperature over Hebei Plain for cloudy free days

2004-08-17 2004-09-21 2004-11-17 2005-03-04 2005-03-05 2005-03-25 Min. 295.82 292.98 280.56 270.34 274.72 281.34 Max. 309.60 308.04 294.26 288.54 292.38 310.14

Median 300.24 299.70 287.58 280.54 283.60 300.64

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Figure 5-4: Histogram of land surface temperature over Hebei Plain

August 17, 2004 Sep. 21, 2004

Nov. 17, 2004 Mar. 04, 2005

Mar. 25, 2005 Mar. 05, 2005


54

5.2.3. Relationship between surface reflectance and surface temperature

The surface reflectance is a dominant factor to determine the surface available radiative energy. The knowledge on a pixel-by-pixel basis provides a pattern of absorbed incoming down solar energy on the surface. The surface temperature is a specific measurement of the partition of surface available energy, indicating the dynamic equilibrium between surface incoming and outgoing energy flux. It is clear that there must be a relationship between surface reflectance and surface temperature. Recently, several methods have been applied to recognize this relation and try to explain wetness condition of land surface over satellite passing time(Menenti and Bastiaanssen 1991; Jia and Su et al., 2003), two of which will be applied over Hebei Plain in the following.

(1) Regression Model

Based on the assumption that the global radiation and air temperature will not change, Menenti et al. have showed the relations between surface temperature and surface reflectance under different albedo scales(Menenti and Bastiaanssen 1991). Under the lower surface albedo conditions, surface temperature will have a little changes or no change with the rising surface albedo, taking free water surface and irrigating farm lands as examples, all the energy available there are utilizing for evaporation. Under the higher surface albedo conditions, surface temperature will rise with rising surface albedo, and the consume of the energy is not only for evaporation but also the sensible heat flux, as a result, total amount of evaporation will be a little bit depressed relatively. When surface albedo rise to a certain threshold value, surface temperature will decline with the rising surface albedo, and almost no evaporation occurred due to lower soil moisture. Based on the analysis above, we can conclude that the relation between the surface reflectance and surface temperature can be an indicator of the surface soil moisture.

In order to understand the wetness condition over study area, regression relations between surface temperature and surface reflectance were obtained as figure 5-5. In summer season, due to the high available soil moisture, energy is mainly consumed for evaporate soil water; hence, surface temperature change with the rising surface reflectance should be not obvious, this can be verified by the figure on August 17, 2004. In other season, there seems a positive relation between surface temperature and surface reflectance under lower surface albedo, which indicate some energy were transferred downward to heat land surface and soil moisture in these seasons is scarce relatively over study area. However, as we can see, the relation is not strong enough to fit regression line.

Another interesting and meaningful feature of relations is the slope of regression line. The positive slope at low reflectance, which corresponds to vegetated and wet surface, is controlled by evaporation. The negative slope at higher reflectance, corresponding to drier surface with limited evaporation, is controlled by net radiation. However, there isn’t a clearly relations for these case, and the slope of regression line is difficult to be recognized.

In conclusion, it is difficult to use this method to retrieve the relations between surface reflectance and surface temperature in this study.


55

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Figure 5-5: Relations between surface reflectance and surface temperature

(2) Normalized temperature difference model

A modified version of the Surface Energy Balance System (SEBS) was introduced by Jia et al. (2003) to analyse land surface wetness condition based on the comparison between Normalized temperature differences under actual condition and dry, wet condition. The dry and wet boundaries can be defined in the “albedo- Normalized temperature differences” space. Data points clustered closer to the wet (lower) boundary indicate prevailing wetter conditions, while displacement towards the dry boundary indicates drying of the land surface. In other words, the measure of dryness is the position of the data points relative to wet and day boundaries(Jia and Su et al. 2003). Detailed procedures for determination of Normalized temperature differences under actual, dry and wet conditions can be referred to work of Li, J. et al. (2003) or Su et al. (2003).

2004-08-17 2004-09-21

2004-11-17

2005-03-04

2005-03-05 2005-03-25


56

Figure 5-6: Normalized temperature difference versus albedo over Hebei Plain Figure 5-6 shows the time series scatter plots of the normalized temperature difference versus surface albedo over Hebei Plain. It can be seen that it is very easy to analyze the surface wetness condition from these plots. In August and September, since plenty of energy came from solar radiation can be used in this season, soil water can be evaporated rapidly, land surface is always under water tension, so the scatter plot is close to the dry boundary. In winter and early spring, most of the area belongs to


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wet condition due to the frozen. Then, with the thawing of land surface and consciousness of the winter wheat as well as the rainfall scarcity in later spring study area again became dry.

5.3. Spatio-temporal disribution of Vegetation Variables

5.3.1. Normalized Difference Vegetation Index (NDVI)

One of the mostly wide used vegetation index to monitoring the spatial the temporal distribution of the vegetation presented in certain area is the Normalized Difference Vegetation Index (NDVI), which is derived from remotely sensed near infrared and red bands data due to the high spectral reflectance of vegetation in the near infrared bands. Basically, for very dense vegetation land cover, NDVI values are almost equal to 1, and for bare soil, it close to 0. In practical words, due to the presence of water body, NDVI values can be less than 0, and in that case, default value of 0.01 always be taken as default values for the convenience of calculations.

Table 5-8 below shows the statistical summary of NDVI values for the target cloud free images during August, 2004 to April, 2005 in Hebei Plain. Figure 5-7 shows the time series NDVI histograms over the Hebei Plain. Temporal distributions of NDVI are very coherent with crops patterns in study area. In summer season (August 17, 2004), the dominant crops over Hebei Plain are maize, which grows from the early June to later September each year. Since maize has a very densely leaf area over the whole farm lands, the highest NDVI values can be expected in that season, the median of which is more or less about 0.82. In winter season, winter wheat is the main crops in Hebei Plain. It grows from the October to the early June of following year, so the changing trend of NDVI is relevant to the growth of winter wheat. Before the freeze season (December), the relatively high NDVI values (0.30) indicate the growth and health of winter wheat. In spring, winter wheat begins to grow up again, so the NDVI value increases gradually after thawing.

Table 5-8: Statistical summary of NDVI in different season

2004-08-17 2004-09-21 2004-11-17 2005-03-04 2005-03-05 2005-03-25 Min. 0.23 0.19 0.12 0.06 0.06 0.08 Max. 0.93 0.83 0.62 0.31 0.32 0.44

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Figure 5-7: Histogram of NDVI over Hebei Plain on selected cloud free days

5.3.2. Relationship between NDVI and surface temperature

Vegetation index is an indicator not only for surface vegetation fractional cover but also the vegetation growth condition. There is a negative relation between remotely sensed vegetation indices and surface temperature, which have been widely observed for the last few decades. A lot of scholars have studied the relations between surface temperature, NDVI and surface soil moisture, and they found that different surface with different land cover and soil moisture has the different distribution in the Ts-NDVI space. Previous findings (Goward and Hope 1989; Price 1990; Nemani and Pierce et al., 1993) on the Ts-NDVI feature space are summarized in Figure 5-8. Over bare soil, variations in radiant surface temperature are highly correlated with variations in surface water content. Thus, point A and B on figure represent, respectively, dry bare soil (low NDVI, high Ts) and moist bare soil (low NDVI, low Ts). As the fractional vegetation cover increase, surface temperature decrease. Pint C on figure corresponds to continuous vegetation canopies with a high resistance to evapotranspiration (high NDVI, relatively high Ts), e.g., due to a low soil water availability. Point D corresponds to continuous vegetation canopies with low resistance to evapotranspiration (high NDVI, low Ts) e.g. on well-water surface. The upper envelope of observations in that space, A-C, represents the low-evapotranspiration line (i.e. dry condition). The lower envelope B-D represents the line of potential evapotranspiration (wet condition).

Nov. 17, 2004 Mar. 04, 2005

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The concept of “Ts-NDVI” space is easy to understand qualitatively, however, since the boundary of polygon is highly depended on many factors (surface physical variables and atmospheric states), it is difficult to draw some clear and unique lines (low-evapotranspiration line, potential evapotranspiration line, etc.) that would be applicable to different sites. In order to determine the “dry” land and “wet” land in “Ts-NDVI” space, the normalized temperature difference concept introduced by Jia et al. (2003) was used. The time series normalized temperature difference versus NDVI over study area is shown as figure 5-9. It can be seen that the land with different soil moisture is easy to be recognized when the “wet” limit and “dry” dry limit was defined by the modified version of the SEBS model. In addition, the land cover types (bare land, partial cover and full cover) also can be determined through taking NDVI values into account.

Due to the same concept of normalized temperature difference were used in figure 5-9 below and figure 5-6 that illustrate the relations between normalized temperature difference and surface albedo, the same soil moisture conditions over land surface were obtained. Another important feature of the modified “Ts-NDVI” Space is the clear information about the land vegetation health illustrated by NDVI values, which have the same mean of vegetation coverage in figure 5-8. In conclusion, the concept of normalized temperature difference derived from modified SEBS model is a useful tool to explain the qualitative relations present in remote sensing images.


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Figure 5-9: Modified “Ts-NDVI” space over Hebei Plain

5.3.3. Fractional Vegetation Cover

Figure 9-10 shows the time series fractional vegetation cover (fc) over Hebei Plain during august, 2004 to march, 2005. The highest values are found in the august, which range from 0.09 to 0.99 with a mean value about 0.81 (table 5-9). As discussed before, the dominant crops in these days is flowering


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summer maize, a high fc is expected due to the high density leaves. In later September, with the coming harvest season of summer maize, some leaves dried and died, which lead to a relative lower fc value that round 0.69. In winter and early spring, winter wheat growth stopped, low fc values are presented over whole area (table 5-9).

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Table 5-9: Statistical summary of fractional vegetation cover in different season

2004-08-17 2004-09-21 2004-11-17 2005-03-04 2005-03-05 2005-03-25 Min. 0.09 0.09 0.09 0.09 0.08 0.07 Max. 0.99 0.95 0.91 0.85 0.79 0.91 Mean 0.81 0.69 0.49 0.46 0.45 0.42


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5.4. Spatial-temporal distribution ETa

Spatial distribution of ETa over Hebei Plain will be discussed based on the daily actual evapotranspiration on cloudy free days during August, 2004 to March, 2005 by combining the up-to-date land cover map over study area in this section. In addition, temporal distribution of ETa will be analysised by taking seasonal ETa difference into account.

5.4.1. Spatial distribution of ETa in summer

The Spatial distribution of ETa in summer season will be discussed based on the result of 17 August, 2004. The results and the histograms are presented in figures 5-24 and 5-11 respectively. The evaporative fraction ranges from 0.6 for dry riverbed and bare land to 1.0 for grassland and water body. The higher values are mainly located in the south-west part of the plain and the lower value which is about 0.70 is mainly spreading around the crop land area in north-west part of the plain. Spatial daily evapotranspiration has a similar distribution pattern with the evaporative fraction. Lower values, which are more or less about 3 mm day-1, are mainly presented in the north-west part of the plain that corresponds to the lower evaporative fraction values area. Higher values that about 5 mm day-1 are mainly presented in the south-west part of the plain. The statistical characteristics and histograms of ETa over each land cover are shown in table 5-10 and figure 5-12.

Figure 5-11: Histogram of evaporative fraction and evapotranspiration in Hebei Plain on 17 August, 2004

Table 5-10: The statistics over each land cover classes in study area on 17 August 2004 (mmday-1)

Barren or sparsely

vegetated Cropland Forest Grass land Shrub land Urban and

built-up Water

Minimum 4.69 0.83 4.02 2.26 1.85 2.27 3.28 Maximum 6.64 6.61 6.56 6.77 6.59 6.66 7.03 Average 5.79 4.07 5.35 4.54 4.51 4.18 5.4 Median 5.83 4.09 5.32 4.46 4.41 4.15 5.67 St. dev 0.4 1.1 0.6 1.0 0.8 0.9 0.9


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Figure 5-12: Histogram of daily ETa over different land cover types in Hebei Plain on 17 August, 2004

According to the distribution patterns in ETa histogram and daily ETa statistics over each land cover, the land cover types of study area in summer season can be grouped into three classes: the first class is the barren or sparsely vegetated area with high ETa values (the mean value for barren or sparsely vegetated area is 5.79), the second class is the water body and forest, which have high ETa values but with two peaks (the mean ETa values for them are 5.40 mm day-1 and 5.35 mmday-1 respectively), the third class includes grass land, shrub, cropland and urban area with the mean ETa of 4.54, 4.51, 4.07 and 4.18 mm day-1 respectively.

The barren and sparsely vegetated land cover distributed among seashore area (figure 2-10). The spatial ETa distribution over this kind of land is mainly controlled by the soil moistrue presented in the root zone and the total energy available from solar radiation. Either of them is all controlled by climatic condition in a certain degree. In summer season, especially in August, study area is among the most humid periods over the year. Abundant of rainfall and the blazing sun in this season provides a guarantee of soil water and energy, which result in the high ETa values in barren and sparsely vegetated area.

The water body and forest have a two-peak ETa histogram in this season, which hints those land cover types have two different conditions and cause the spatial variety in the ETa and ETa maps. For the


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water body, two kinds of water body can be found in study area, one is the lake that sparsely appeared in Hebei Plain with fresh water, the other one is the seawater among the plage, so the spatial variety difference of ETa over those water bodies is possible if the climatic condition of them being is different, wind speed, for instance. The forest is a very small part over the whole plain, which only distributed sparsely over the plain. The same as the water body, there are also two kinds of forest can be recognized in Hebei Plain, one is the natural forest that no irrigation is needed, the other one is manmade forest, which mainly the fruit trees under irrigation. Therefore, two-peak ETa histogram over forest is reasonable.

Most of the crop land in Hebei Plain is under irrigation. More or less 4-5 times irrigation for the winter wheat during October to June and 2-3 times irrigation for the corn during June to September can totally change the soil moisture in root zone, which induce a relatively high ETa values. In summer season, normally, no irrigation is needed for the corn due to the high frequency rainfall events in this season, especially in early August. However, since the spatial distribution of each rainfall is variable, the spatial difference of ETa over the plain must be happened. From the estimated ETa map on 17 August, 2004, the spatial distribution pattern is that the south-western part has a higher ETa value than in the north-eastern part. By comparing the ETa map with land surface temperature map of the same day (Appendix), we can found that the south-western part is exactly the low land surface temperature area. The most possible explanation for this phenomenon is that there had been a rainfall event before, which brought the richness of the soil moisture and caused the high evapotranspiration and lower land surface temperature.

The statistics reflects that the urban and built-up area also have a certain amount of evapotranspiration. This is contrary to the knowledge that the residential areas should have lower ETa. This can be explained by the pixel based remote sensing techniques. The pixels of urban area includes not only the construction but also the water body, street trees and grass parcels, which all have very high evapotranspiration. Therefore, the estimated ETa in urban area represented the mixed effection of all these things.

5.4.2. Spatial distribution of ETa in autumn

The Spatial distribution of ETa in autumn season will be discussed based on the result of 21 September, 2004. The results and the histograms are presented in figures 5-25 and 5-13 respectively. The evaporative fraction ranges from 0.3 for dry cropland to 0.9 for urban area body. The higher values are mainly located in the north-western part of the plain and the lower value which ranges from 0.4 to 0.5 spreading around almost all the plain. Spatial daily evapotranspiration has a similar distribution pattern with the evaporative fraction. Corresponding to the high evaporative fraction, high ETa values are mainly presented in the north-western part of the plain and other place were dominated by lower evapotranspiration. The statistical characteristics and histograms of ETa over each land cover are shown in table 5-11.

As we can see from the figure 5-14, when taking land cover types into account, the spatial distribution pattern of the ETa in winter season appears very similar to that in summer season. The highest values are found in the barren or sparsely vegetated area, the mean of which is up to 5.4 mm day-1. The second higher values of ETa are mainly appearing in the forest and open water area, which have the


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mean ETa about 4.8 mm day-1 and 4.6 mm day-1 respectively. The grass land, cropland, shrub land as well as the urban area have relatively small ETa values.

Figure 5-13: Histogram of evaporative fraction and evapotranspiration on 21 September, 2004

Table 5-11: The statistics over each land cover classes in study area on 21 September 2004 (mmday-1)

Barren or sparsely


built-up Water



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Figure 5-14: Histogram of daily ETa over different land cover types in Hebei Plain on 21 September, 2004

The most significant change of ETa in autumn season as compare to the summer season is the relatively small ETa values in cropland area, which can be explained by taking the growing periods of crops into account. In autumn, the dominant crop in Hebei Plain is corn, which will be harvested around the end of September. The crop water requirement at this period keeps the smallest values during the whole growing periods, which induce the relative small ETa as compared to the summer season.

5.4.3. Spatial distribution of ETa in winter

The spatial distribution of ETa in winter season will be discussed based on the result of 17 November, 2004. The results and the histograms are presented in figures 5-26 and 5-15 respectively. The evaporative fraction ranges from 0.34 to 0.43. The low values are mainly located in the western Taihang Mountain foot plain in the western of the study area and north-eastern part of the plain. The high value which ranges from 0.40 to 0.43 spread along the central of the plain from north to sorth and the highest evaporative fraction presented in the north part of the plain, which is around 0.42.

As far as spatial ETa was concerned, the highest ETa that range from 0.57 to 0.70 mm day-1 mainly located in the south part of study area and low ETa values are mainly in the north Hebei Plain, which is between 0.40 and 0.48 mm day-1. The statistical characteristics of ETa over each land cover have been analyzed. The statistics and histograms of ETa over each land covers are shown in table 5-12 and figure 5-16.

Figure 5-15: Histogram of evaporative fraction and evapotranspiration on 17 November, 2004


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Table 5-12: The statistics over each land cover classes in study area on 21 September 2004 (mmday-1)

Barren or sparsely


built-up Water


Figure 5-16: Histogram of daily ETa over different land cover types in Hebei Plain on 17 November, 2004

Compared with other seasons, winter has a fairly homogeneous spatial distribution ETa with relatively small values. The highest ETa was found in the open water body, which ranges from 0.48 to 0.94 mm day-1 with mean value 0.71 mm day-1. As expected, winter vegetations, like winter wheat, grass, shrub, etc, all have the relatively lower ETa values as compare to the summer season and autumn season due to the physiological dormancy with almost zero transpiration.

5.4.4. Spatial distribution of ETa in spring

Totally 3 images for cloudy free days have been found for the spring of 2005, 4 March, 5 March and 25 March. The spatial distribution of ETa on those days will be analyzed separately as a start, then, the spatial distribution of ETa over Hebei Plain in spring season will be summarized in this section.


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(1) 04 March, 2005

The estimated evaporative fraction and ETa over study area on 4 March, 2005 are shown as figures 5-27. The range of evaporative fraction is between 0.37 and 0.53. The highest values that about 0.48 to 0.53 can be found in the central plain and other area have the low values ranging from 0.37 to 0.48. The lowest values only distributed sparsely in the south-west and north part of the area. The spatial distributions of ETa have the similar patterns. Central Hebei Plain has the highest ETa ranging form 1.46 mm day-1 to 1.79 mm day-1, but some lower values that below 1.45 mm day-1 can be seen clearly along the dry river bed to the north of Shijiazhuang City. The lower ETa values that below 1.3 mm day-1 are sprinkled on the north part and south part the plain. The statistical characteristics and histogram of ETa over each land cover types are shown as table 5-13 and figure 5-18.

In early March, the highest ETa values that up to 2.34 mm day-1 are found from the open water surface in the eastern seashore area and lakes in the plain. Although a high ETa values for croplands were found in the ETa maps, which mostly situated in the central plain, statistically lower mean values were obtained due to the large area it covers with different climatic conditions and variable actual evapotranspiartion. High ETa values in barren or sparsely vegetated land indicates the abundant soil moisture underground in this season, which verified the conclusion of “Ts-NDVI” space analysis that Hebei Plain is in a “wet land” condition in early spring.

Figure 5-17: Histogram of evaporative fraction and evapotranspiration on 4 March, 2005 Table 5-13: The statistics over each land cover classes in study area on 4 March, 2005 (mmday-1)

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Figure 5-18: Histogram of daily ETa over different land cover types in Hebei Plain on 4 March, 2004

(2) 05 March, 2005

Figure 28 shows the estimated evaporative fraction and ETa over study area on 25 March, 2005, which has the more or less similar spatial distributions with those on 4 March, 2004. The low evaporative fraction values that ranges form 0.36 to 0.40 mainly situated in the south part of the Plain. Some small values can also be found in the dry river bed to the north of Shijiazhuang City. High evaporative fraction that between 0.46 and 0.48 was concentrated in the central plain. As far as daily ETa was concerned, a very comparable spatial distribution can be obtained. High ETa values that correspond to the high evaporative fractions appeared in the central part of plain, which is up to 1.74 mm day-1, and lower ETa values were lying in the south Hebei Plain and dry river bed area. The statistical characteristics and histogram of ETa over each land cover types are shown as table 5-14 and figure 5-20.


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Figure 5-19: Histogram of evaporative fraction and evapotranspiration on 5 March, 2005 Table 5-14: The statistics over each land cover classes in study area on 5 March, 2005 (mmday-1)

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Since the coherence of daily ETa over two continuous days, the statistical results are very similar, so it will be not discussed into detail here.

(3) 25 March, 2005

Figure 29 shows the estimated evaporative fraction and ETa over Hebei Plain on 5 March, 2005 and the histogram of them is showing below. A clearly south-east to north-west gradient in the plain can be found not only for the evaporative fraction but also for the daily evapotranspiration spatial distribution. High evaporative fraction values were located in the south-east boundary of the plain with the mean values more or less about 0.28, then, it declined step by step to 0.19 in the north-west boundary. The spatial ETa shows a contrary changing trend. The lowest ETa values located in the north-western part of the study, which is about 0.85 mm day-1, and the higher ETa values are present in the south-east part of the area, ranging from 1.25 mm day-1 to 1.64 mm per day. The statistical characteristics and histogram of ETa over each land cover types are shown as table 5-15 and figure 5-22.

Figure 5-21: Histogram of evaporative fraction and evapotranspiration on 25 March, 2005

As we can see from the statistical results, open water and barren or sparsely vegetated land among the highest level of the daily ETa, mean of which are 1.86 mm day-1 and 1.67 mm day-1, respectively. Cropland again falls into the lowest level range with a mean value around 1.31 mm day-1. Normally, vegetations that grow in the humidity area with a plenty water supply will have the higher ETa values, but in Hebei Plain, spring season is always the driest season over the year, which can be demonstrated from the annual rainfall events in Fig.5. Due to less rainfall in this season, especially in later March and April, crops are always under water stress, therefore, the lower ETa values are expected.


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Table 5-15: The statistics over each land cover classes in study area on 25 March, 2005 (mmday-1)

Barren or sparsely


built-up Water



In summary, there is an obvious difference of the spatial distribution of evaporative fraction and daily ETa over Hebei Plain between early March and later March. In early March, because of the thawing of the frozen land, the soil were rich of moisture and whole plain is on the “wet land” condition defined by “Ts-NDVI” space. The mean evaporative fraction at this period ranges from 0.18 to 0.60 with a mean value about 0.41; in addition, higher evaporative fraction values are mostly located in the central plain and lower evaporative fraction values are mainly in the dry land, dry river bed, for example, so soil moisture is the dominant factor the control the regional evapotranspiration. In the later March, a relatively small evaporative fraction were found, which ranges from 0.16 to 0.48 with a mean value about 0.32. Spatially, a clearly south-east to north-west gradient in the plain can be found and the evaporative fraction drops step by step from south-east to the north-west part of the plain. From the local meteorological observations, the similar trend surface can also be found not only for


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the air temperature but also the wind speed, so a conclusion can be derived that the evaptranspiration process in later March is more controlled by climatic conditions.

As far as the spatial evapotranspiration was concerned, the similar spatial-temporal distribution patterns can be found accordingly, which will not be explained into detail.

5.4.5. Temporal distribution of ETa

Figure 5-28 shows the time series daily evapotranspiration of different land covers over Hebei Plain for the cloud free days. Due to little difference between the values obtained on March 4, 2005 and March 5, 2005, mean values for these two days were taken to plot, as figure shown. Since the images obtained are limited, so the temporal analysis of daily evapotranspiration is partly representative.

Figure 5-23: Time series average daily evapotranspiration of different land covers over Hebei Plain

As the figure shown, maximum values of all kinds of land cover types are in the summer season (17 August, 2004), the mean values is between 4.0 and 5.8 mm day-1. Then, autumn comes with relatively a little bit small daily evapotranspiration as compared to summer season, the mean of which is about 3.4 to 5.4 mm day-1 (21 September, 2004). The minimum values for all kind of land cover types are appearing in the winter season, with a range of mean values that between 0.5 and 0.8 mm day-1. In spring, with the thawing of the land and the anabiosis of vegetation, the daily evapotranspiration increase slowly to a range about 1.3-1.8 mm day-1 on early March (4 March, 2005 or 5 March, 2005). In later March (25 March, 2005), due to the dry climatic condition and limited soil moisture over Hebei Plain, little change or decrease for the daily evapotranspiration were observed from the figure as compared to the early March.

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80

6. Conclusions and Recommendation

General information about this research and major conclusions will be summarized in this chapter. In addition, some recommendation about the limitation during the work and further work that should be conducted is proposed.

6.1. General Summary

Evapotranspiration is among the most important components of basin-scale water cycle. It is also the most difficult items to be determined, especially in a big area. Remote sensing techniques give people a chance to deal with this challenge from the space. As a freely selected M.Sc research topic, Hebei Plain in North-eastern China is selected as target area to estimate and analyze the regional-scale evapotranspiration based on the Surface Energy Balance System (SEBS). To run SEBS, several datasets were needed, including meteorological observation, remote sensing images as well as surface bio-physical parameters. They were all obtained either from filed campaign or modelling. Among these datasets, the most challenge came from the surface bio-physical parameter determination. In order to get this dataset as accurate as possible, a critical literature research on the various methods and sensitivity analysis of different parameters to SEBS result were conducted. After the determination of evapotranspiration, the accuracy was analyzed by comparing with the lysimeter measurements. Finally, some relations of surface variables and spatial-temporal distribution of surface variables and evapotranspiration were presented.

6.2. Major results and Conclusions

Major contributions of this research are summarized hereafter.

(1) Detailed literature review on the determination of various surface bio-physical parameters and sensitivity analysis to the SEBS result

Critical literature researches on the various methods that have been developed to retrieve surface bio-physical parameters were conducted and discussed into detail in this thesis. Four parameters were selected to do the sensitivities analysis. It showed that the aerodynamic roughness height is the major factor in terms of SEBS response and it should be determined with much care when apply different empirical methods. Displacement height falls into the moderately sensitive range of the parameters and care also should be taken when a vegetation map is unavailable and empirical equations have to be applied. Fractional vegetation cover and surface emissivity are not dominant factors; they do have influence on SEBS modelled evaporative fraction, but not as great as other parameters.

(2) Accuracy of SEBS estimated evapotranspiration


81

The comparisons between the daily evapotranspiration values obtained from SEBS and from other approaches were conducted. A good agreement with the SEBS modeled ETa and ground truth ETa measured by lysimeter were obtained for most of the selected cloudy free days, which verified that the SEBS is a useful and accurate tool to estimate the regional evapotranspiration. Without doubt, due to the pixel by pixel based remote sensing techniques, some error must occur, especially, when the coarse resolution images were used. There have relative big differences between SEBS modeled evapotranspiration and crop evapotranspiration derived from empirical equation with local coefficient. This is mainly because that the coefficients in those empirical equations used were mostly derived from experiments or statistical analysis under some certain climatic at certain area with given crop types. When used in a small area to compare with other accurate in situ measurements, difference must be happened.

(3) Qualitative evaluation of temporal surface moisture status

By combining the surface albedo, NDVI with normalized temperature difference derived from modified SEBS, the soil moisture conditions over Hebei Plain at different season were analyzed qualitatively. In August and September, since plenty of energy came from solar radiation can be used, soil water can be evaporated rapidly, land surface is always under water tension, the evapotranspiration is controlled mainly by available soil moisture in the root zone. In winter and early spring, most of the area belongs to wet land with abundant soil moisture. The dominant factor on the evapotranspiration process is the available energy from solar radiation. Then, with the thawning of land surface and regeneration of the winter wheat as well as the rainfall scarcity in later spring the study area again became dry.

(4) Spatial-temporal distribution of evapotranspiration

Spatial-temporal distribution of ETa over Hebei Plain was discussed based on the daily actual evapotranspiration on cloud free days during August, 2004 to March, 2005 by combining the up-to-date land cover. Maximum ETa values of all kinds of land cover types over Hebei Plain are in the summer season, the mean is between 4.0 and 5.8 mm day-1. In autumn, a relative small ETa values is dominant over study area as compared to summer season, which is about 3.4 to 5.4 mm day-1 (21 September, 2004). The minimum values are appearing in the winter season, with a range of mean values that between 0.5 and 0.8 mm day-1. In spring, with the thaw of the land and the anabiosis of vegetation, the daily evapotranspiration increase slowly to a range about 1.3-1.8 mm day-1 on early March (4 March, 2005 or 5 March, 2005). In later March (25 March, 2005), due to the dry climatic condition and limited soil moisture over Hebei Plain, little change or decrease for the daily evapotranspiration were observed.

Hebei Plain is one of the most important agriculture farm lands in China. The dominant crop types over this area are the winter wheat following by summer maize. Due to the various irrigation performances in difference place and high spatially distribution of rainfall, the soil moisture in the root zone in different site is highly different. Therefore, a spatial distribution pattern of ETa over Hebei Plain is difficult to be obtained. As far as different land cover types were concerned, most of the high ETa values are found in barren or sparely vegetated area and water body. In addition, a certain amount of evapotranspiration can be found in urban area, which can be explained by the water body, street trees and grass parcels that located in urban area.


82

6.3. Limitation and challenge

Surface bio-physical parameters take an important role in the energy change between the land surface and atmosphere. These parameters can be retrieved either from remote sensing images or from field observations. For later one, the advantages of the remote sensing techniques are lost. For remote sensing approaches, all the current empirical method based on the visible band and thermal bands observations from space are obtained from certain area with special land covers. When used in a new area, some modifications are necessary. Due to the limited ground truth data in this research, some deviation must be happened when use these empirical equations directly, and this forms the main limitation of this study.

Due to the high frequency of human activity in study area, most of the pixels in the high resolution MODIS images used in this study include not only the farm land but also many human constructions, for example, building, road, etc. So the ETa that certain pixel reflected is a combining result. When use this ETa derived from highly resolution images to compare with ground truth ETa measured by lysimeter, the bias is inevitable, as a result, accuracy analysis of SEBS algorithms maybe wrong.

6.4. Recommendations

The study could re-establish the fact that, the application of remote sensing brings a significant contribution to estimate the spatial evapotranspiration in regional scale for all types of land covers. However, the ground observation based methods are always very important, especially in verifying the results of different remote sensing based approaches. In this research, the lysimeter data in Luancheng Agro-Ecosystem Station is vital in this regard.

It is acknowledged that evapotranspiration is computed not for its own sake but for other purpose, regional water resources evaluation and management, irrigation performance assessment, as well as global climate change etc. for example. In this regard, further consideration should be addressed according to the fields it applied. Take the regional water balance research as an example, how to get regional scale actual evapotranspiration on cloudy days is challenging.


83

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Appendices

Appendix A: Meteorological Observations

Table A-1: Meteorological Stations in Hebei Plain

Table A-2: Routine Meteorological Observations over Hebei Plain

53698 17-Aug-04 2:00 87 0.0 19.2 19.3 53698 17-Aug-04 8:00 76 1.7 21.2 19.1 53698 17-Aug-04 14:00 47 1.4 28.4 18.2 53698 17-Aug-04 20:00 67 1.2 24.8 21.0 54602 17-Aug-04 2:00 89 1.0 19.9 20.7 54602 17-Aug-04 8:00 77 1.0 22.5 21.0 54602 17-Aug-04 14:00 44 3.0 28.9 17.5 54602 17-Aug-04 20:00 59 0.6 25.4 19.1 54518 17-Aug-04 2:00 87 1.2 20.2 20.6 54518 17-Aug-04 8:00 72 0.9 22.2 19.3 54518 17-Aug-04 14:00 43 2.4 28.8 17.0 54518 17-Aug-04 20:00 58 0.9 25.9 19.4 54705 17-Aug-04 2:00 96 1.7 16.3 17.8 54705 17-Aug-04 8:00 97 1.6 19.8 22.4 54705 17-Aug-04 14:00 48 2.2 28.7 18.9 54705 17-Aug-04 20:00 66 1.6 24.0 19.7 54624 17-Aug-04 2:00 86 1.7 19.0 18.9 54624 17-Aug-04 8:00 79 2.8 21.4 20.1 54624 17-Aug-04 14:00 43 2.4 28.6 16.8 54624 17-Aug-04 20:00 66 1.4 24.6 20.4 53798 17-Aug-04 2:00 93 0.7 19.2 20.7 53798 17-Aug-04 8:00 83 0.7 21.8 21.7 53798 17-Aug-04 14:00 48 1.6 27.3 17.4 53798 17-Aug-04 20:00 65 0.9 24.8 20.3

53698 21-Sep-04 2:00 47 1.5 16.0 8.5 53698 21-Sep-04 8:00 47 0.7 17.0 9.1


89

Table A-2 contd.

53698 21-Sep-04 14:00 25 2.1 24.6 7.7 53698 21-Sep-04 20:00 50 0.6 18.2 10.4 54602 21-Sep-04 2:00 50 0.9 14.5 8.3 54602 21-Sep-04 8:00 56 0.4 17.5 11.2 54602 21-Sep-04 14:00 20 2.4 24.8 6.3 54602 21-Sep-04 20:00 43 1.5 18.8 9.3 54518 21-Sep-04 2:00 46 1.5 14.4 7.5 54518 21-Sep-04 8:00 42 2.2 16.7 8.0 54518 21-Sep-04 14:00 22 1.6 25.0 7.0 54518 21-Sep-04 20:00 36 0.8 19.4 8.1 54705 21-Sep-04 2:00 82 1.1 10.6 10.5 54705 21-Sep-04 8:00 73 2.0 14.3 11.9 54705 21-Sep-04 14:00 18 1.1 25.8 6.0 54705 21-Sep-04 20:00 45 1.3 17.0 8.7 54624 21-Sep-04 2:00 64 1.8 13.6 10.0 54624 21-Sep-04 8:00 58 1.7 16.5 10.9 54624 21-Sep-04 14:00 24 2.7 24.3 7.3 54624 21-Sep-04 20:00 45 2.1 18.8 9.8 53798 21-Sep-04 2:00 65 1.1 14.7 10.9 53798 21-Sep-04 8:00 51 0.9 16.8 9.8 53798 21-Sep-04 14:00 26 2.0 24.4 7.9 53798 21-Sep-04 20:00 36 0.9 19.5 8.2

53698 17-Nov-04 2:00 23 2.0 8.8 2.6 53698 17-Nov-04 8:00 26 1.7 7.3 2.7 53698 17-Nov-04 14:00 15 1.2 16.3 2.8 53698 17-Nov-04 20:00 34 0.9 9.9 4.1 54602 17-Nov-04 2:00 70 0.0 2.7 5.2 54602 17-Nov-04 8:00 53 1.3 3.9 4.3 54602 17-Nov-04 14:00 23 1.1 15.0 3.9 54602 17-Nov-04 20:00 48 0.1 7.1 4.8 54518 17-Nov-04 2:00 43 0.8 4.1 3.5 54518 17-Nov-04 8:00 67 0.9 1.8 4.7 54518 17-Nov-04 14:00 21 1.4 15.0 3.6 54518 17-Nov-04 20:00 50 1.6 5.8 4.6 54705 17-Nov-04 2:00 70 0.9 1.5 4.8 54705 17-Nov-04 8:00 80 0.8 1.8 5.6 54705 17-Nov-04 14:00 22 1.9 16.1 4.0 54705 17-Nov-04 20:00 67 1.6 5.5 6.0 54624 17-Nov-04 2:00 50 1.4 3.7 4.0 54624 17-Nov-04 8:00 39 1.9 5.8 3.6 54624 17-Nov-04 14:00 18 2.7 15.5 3.2 54624 17-Nov-04 20:00 54 1.4 6.9 5.4 53798 17-Nov-04 2:00 59 0.3 3.1 4.5 53798 17-Nov-04 8:00 50 1.0 3.1 3.8 53798 17-Nov-04 14:00 19 2.2 14.9 3.2 53798 17-Nov-04 20:00 46 0.9 7.5 4.8

53698 04-Mar-05 2:00 25 2.1 -0.3 1.5 53698 04-Mar-04 8:00 26 1.7 -0.6 1.5


90

Table A-2 contd.

53698 04-Mar-03 14:00 13 4.5 5.1 1.1 53698 04-Mar-02 20:00 22 1.1 2.0 1.6 54602 04-Mar-01 2:00 21 3.0 -0.2 1.3 54602 04-Mar-00 8:00 24 1.7 -0.5 1.4 54602 04-Mar-99 14:00 15 1.7 3.9 1.2 54602 04-Mar-98 20:00 26 1.6 1.6 1.8 54518 04-Mar-97 2:00 22 5.1 -0.9 1.3 54518 04-Mar-96 8:00 27 3.0 -2.5 1.4 54518 04-Mar-95 14:00 14 3.6 3.5 1.1 54518 04-Mar-94 20:00 21 6.3 0.9 1.4 54705 04-Mar-93 2:00 40 5.8 0.2 2.5 54705 04-Mar-92 8:00 45 2.1 -1.6 2.4 54705 04-Mar-91 14:00 19 6.5 4.0 1.5 54705 04-Mar-90 20:00 37 2.7 0.5 2.3 54624 04-Mar-89 2:00 40 3.9 -1.0 2.3 54624 04-Mar-88 8:00 37 2.3 -2.8 1.8 54624 04-Mar-87 14:00 20 6.0 1.9 1.4 54624 04-Mar-86 20:00 29 2.0 -0.7 1.7 53798 04-Mar-85 2:00 25 2.2 0.7 1.6 53798 04-Mar-84 8:00 24 2.1 -0.6 1.4 53798 04-Mar-83 14:00 14 2.9 4.7 1.2 53798 04-Mar-82 20:00 25 2.2 2.4 1.8

53698 05-Mar-80 2:00 24 1.7 1.3 1.6 53698 05-Mar-80 8:00 32 1.9 0.4 2.0 53698 05-Mar-80 14:00 20 4.3 10.8 2.6 53698 05-Mar-80 20:00 34 2.2 7.3 3.5 54602 05-Mar-80 2:00 46 0.6 -2.6 2.3 54602 05-Mar-80 8:00 37 2.9 -1.0 2.1 54602 05-Mar-80 14:00 22 2.5 9.3 2.6 54602 05-Mar-80 20:00 37 1.7 5.3 3.3 54518 05-Mar-80 2:00 33 0.0 -3.6 1.5 54518 05-Mar-80 8:00 48 2.0 -4.0 2.2 54518 05-Mar-80 14:00 20 3.3 7.8 2.1 54518 05-Mar-80 20:00 32 1.4 5.3 2.8 54705 05-Mar-80 2:00 70 0.0 -4.2 3.1 54705 05-Mar-80 8:00 38 4.2 -1.9 2.0 54705 05-Mar-80 14:00 20 3.1 10.1 2.5 54705 05-Mar-80 20:00 29 3.4 7.2 2.9 54624 05-Mar-80 2:00 39 2.9 -4.4 1.7 54624 05-Mar-80 8:00 39 1.2 -2.4 2.0 54624 05-Mar-80 14:00 19 4.0 7.0 1.9 54624 05-Mar-80 20:00 31 1.8 4.1 2.5 53798 05-Mar-80 2:00 41 1.2 -0.9 2.3 53798 05-Mar-80 8:00 41 1.8 -1.4 2.3 53798 05-Mar-80 14:00 16 3.3 11.8 2.2 53798 05-Mar-80 20:00 27 2.6 8.6 3.0

53698 25-Mar-80 2:00 39 0.7 4.2 3.2 53698 25-Mar-80 8:00 34 1.6 9.7 4.1


91

Table A-2 contd.

53698 25-Mar-80 14:00 12 1.9 22.4 3.2 53698 25-Mar-80 20:00 23 1.6 16.3 4.3 54602 25-Mar-80 2:00 39 2.9 4.7 3.3 54602 25-Mar-80 8:00 41 2.4 5.3 3.6 54602 25-Mar-80 14:00 8 3.4 23.7 2.3 54602 25-Mar-80 20:00 18 2.3 17.0 3.5 54518 25-Mar-80 2:00 39 2.9 5.0 3.4 54518 25-Mar-80 8:00 49 2.4 4.6 4.2 54518 25-Mar-80 14:00 9 4.9 22.9 2.5 54518 25-Mar-80 20:00 16 1.6 17.0 3.1 54705 25-Mar-80 2:00 49 6.4 4.4 4.1 54705 25-Mar-80 8:00 58 5.3 4.8 5.0 54705 25-Mar-80 14:00 13 5.2 21.7 3.4 54705 25-Mar-80 20:00 31 4.4 15.0 5.3 54624 25-Mar-80 2:00 36 6.0 5.1 3.2 54624 25-Mar-80 8:00 52 6.8 5.2 4.6 54624 25-Mar-80 14:00 15 4.8 21.7 3.9 54624 25-Mar-80 20:00 31 3.3 14.7 5.2 53798 25-Mar-80 2:00 45 2.7 4.8 3.9 53798 25-Mar-80 8:00 31 1.8 8.0 3.3 53798 25-Mar-80 14:00 10 2.9 21.8 2.6 53798 25-Mar-80 20:00 41 2.2 14.9 6.9

Table A-3: Sunshine Hours

Table A-4: Incoming shortwave radiation at Leting Station, Hebei Province

Date Time Rswd (MJm-2) Date Time Rswd (MJm-2) 17-Aug-04 1:00 0 17-Aug-04 13:00 2.99 17-Aug-04 2:00 0 17-Aug-04 14:00 2.69 17-Aug-04 3:00 0 17-Aug-04 15:00 2.06 17-Aug-04 4:00 0 17-Aug-04 16:00 1.83 17-Aug-04 5:00 0 17-Aug-04 17:00 1.04 17-Aug-04 6:00 0.06 17-Aug-04 18:00 0.42 17-Aug-04 7:00 0.52 17-Aug-04 19:00 0.05 17-Aug-04 8:00 1.15 17-Aug-04 20:00 0 17-Aug-04 9:00 1.86 17-Aug-04 21:00 0 17-Aug-04 10:00 2.36 17-Aug-04 22:00 0 17-Aug-04 11:00 2.66 17-Aug-04 23:00 0 17-Aug-04 12:00 2.87 17-Aug-04 0:00 0


92

Table A-4 contd. Date Time Rswd (MJm-2) Date Time Rswd (MJm-2)

21-Sep-04 1:00 0 21-Sep-04 13:00 2.77 21-Sep-04 2:00 0 21-Sep-04 14:00 2.48 21-Sep-04 3:00 0 21-Sep-04 15:00 2.05 21-Sep-04 4:00 0 21-Sep-04 16:00 1.42 21-Sep-04 5:00 0 21-Sep-04 17:00 0.71 21-Sep-04 6:00 0 21-Sep-04 18:00 0.11 21-Sep-04 7:00 0.25 21-Sep-04 19:00 0 21-Sep-04 8:00 0.96 21-Sep-04 20:00 0 21-Sep-04 9:00 1.66 21-Sep-04 21:00 0 21-Sep-04 10:00 2.25 21-Sep-04 22:00 0 21-Sep-04 11:00 2.63 21-Sep-04 23:00 0 21-Sep-04 12:00 2.82 21-Sep-04 0:00 0

17-Nov-04 1:00 0 17-Nov-04 13:00 1.64 17-Nov-04 2:00 0 17-Nov-04 14:00 1.33 17-Nov-04 3:00 0 17-Nov-04 15:00 0.92 17-Nov-04 4:00 0 17-Nov-04 16:00 0.42 17-Nov-04 5:00 0 17-Nov-04 17:00 0.03 17-Nov-04 6:00 0 17-Nov-04 18:00 0 17-Nov-04 7:00 0 17-Nov-04 19:00 0 17-Nov-04 8:00 0.2 17-Nov-04 20:00 0 17-Nov-04 9:00 0.69 17-Nov-04 21:00 0 17-Nov-04 10:00 1.22 17-Nov-04 22:00 0 17-Nov-04 11:00 1.56 17-Nov-04 23:00 0 17-Nov-04 12:00 1.74 17-Nov-04 0:00 0

04-Mar-05 1:00 0 04-Mar-93 13:00 2.15 04-Mar-04 2:00 0 04-Mar-92 14:00 1.47 04-Mar-03 3:00 0 04-Mar-91 15:00 1.51 04-Mar-02 4:00 0 04-Mar-90 16:00 1.24 04-Mar-01 5:00 0 04-Mar-89 17:00 0.69 04-Mar-00 6:00 0 04-Mar-88 18:00 0.15 04-Mar-99 7:00 0.02 04-Mar-87 19:00 0 04-Mar-98 8:00 0.37 04-Mar-86 20:00 0 04-Mar-97 9:00 1.26 04-Mar-85 21:00 0 04-Mar-96 10:00 1.87 04-Mar-84 22:00 0 04-Mar-95 11:00 2.09 04-Mar-83 23:00 0 04-Mar-94 12:00 2.51 04-Mar-82 0:00 0



93

Table A-4 contd. Date Time Rswd (MJm-2) Date Time Rswd (MJm-2)



94

Appendix B: Ancillary equations for SEBS algorithms

1. Instantaneous incoming short wave radiation

Normally, incoming short wave radiation can be estimated by multiplying terrestrial short wave radiation with a transmission coefficient, which descript the transmit ability of short wave radiation through the atmosphere,

exoswd KR ↓⋅= τ

Where, τ [-] is the optical thickness (atmosphere transmissivity coefficient), exoK ↓ is the terrestrial short wave radiation [watt m-2].

The terrestrial short wave radiation is a function of the solar zenith angle at certain latitude and time and the distance between sun and earth. The maximum instantaneous shortwave radiation outside the atmosphere, measured at an average sun-earth distance and perpendicular to the solar rays is equal to 1367 watt/m2, which is the solar constant. For a study area at certain moment, instantaneous terrestrial short wave radiation is given by,

)cos(0 θ⋅⋅=↓ ESCK exo

Where, SC is the solar constant (1367 watt/m2), E0 the eccentricity correction factor and θ the solar zenith angle in radians.

Eccentricity correction factor E0 explains the variances of Earth-Sun distance throughout the year due to the circle orbit that Earth around the sun. It is give by,

)2sin(000077.0)2cos(000719.0

)sin(001280.0)cos(034221.0000110.10

dada

dadaE

⋅+⋅+++=

Where the day angle (da) is defined as

3652

)1(π⋅−= ndda

Where dn is the day number of the year, which ranging from 1 on January, to 365 on December 31. Note that on leap years the number of days in the year is 366. Therefore the accuracy of up equation varies

slightly another simple equation can be use,

��

��

�+=365

2cos033.010

ndE

π

Solar zenith angle θ is determined from,

)cos()cos()cos()sin()sin()cos( ωδφδφθ +=


95

Where, φ is the latitude of the target area, ω the hour angle and δ the solar declination.

Hour angle ω is calculated based on the local solar time (LAT),

180)12(15

πω −= LAT

When the Universal Time or (GMT) is given, LAT can be calculated as follows,

60/60/4 tc ELUTCLAT +⋅+=

Where, Lc is the longitude at the point of interest, and Et is the so-called equation of time, which descript the fluctuation of local time due to the earth rotates around its axis when it moves in an elliptical orbit around the sun. Et is given by,

)2sin(04089.0)2cos(014615.0

)sin(032077.0)cos(001868.0000075.0

dada

dadaEt

⋅−⋅−−+=

Solar declination δ is the angle between the ecliptic plane and the earth’s equatorial plane, which describe the position of the sun during different seasons. It can be calculated as,

)3sin(00148.0)3cos(002697.0)2sin(000907.0)2cos(006758.0)sin(070257.0)cos(399912.0006918.0

dadada

dadada

⋅+⋅−⋅+⋅−+−=δ

A much simpler equation for solar declination is,

��

��

� += )284(365360

sin45.23 ndδ

Atmosphere transmissivity coefficient τ can be derived from measurements at the weather station, if no measurements, a simple relation developed by Tasumi et al. can be used, which is expressed as,

h⋅⋅+= −510275.0τ

Where h is the elevation in meters above sea level.

2. Instantaneous incoming long wave radiation

The incoming long wave radiation Rlwd is emitted by atmosphere when it has a certain temperature, so it depends on the temperature of atmosphere and transmittance process in the atmosphere. It can be calculated according to Planck Law:

4)273( +⋅⋅= aalwd TR εσ


96

Where, Ta is the atmosphere temperature in Celsius at reference height, aε the emissivity of the

atmosphere, and a few practical approaches can be selected to derive this parameter. In SEBS, the Swinbank formula given by Campell and Norman was adopted,

26 )15.273(102.9 +⋅⋅= −aa Tε

3. Instantaneous outgoing short wave radiation

Part of the incoming short wave radiation will go back to atmosphere from surface due to the surface reflectance between certain ranges of wavelengths. The ratio of incident solar to reflected solar radiation is called the albedo and the instantaneous outgoing short wave radiation is multiply the incoming shortwave radiation with the surface albedo,

α⋅= swdswu RR

Where, α is surface broadband albedo that can be estimated from single bands reflectance recorded in satellite based sensors.

4. Instantaneous out going long wave radiation

The outgoing long wave radiation is derectly calculated from Stefan-Boltamann’s Law,

400 TRlwu σε=

where, 0ε is the surface broad band emissivity and T0 the surface temperature. They all can be derived

from remote sensing data from the visible to the thermal infrared spectral range.

5. Daily incoming global radiation

Daily incoming global radiation ↓24K is a function of geometric and atmospheric factors and it can be

estimated as

��

��

�⋅�

��

� ⋅+⋅= ↓↓ exoss K

Nn

baK 2424 5741.11

Where, exoK ↓24 is the daily terrestrial solar radiation [megajoules m-2 day-1],

Nn

is the sunshine

fraction [-], sa and sb are constants to be evaluated at ground stations, default values for them are

0.25 and 0.5 respectively.

Daily terrestrial solar radiation exoK ↓24 at the point of consideration is defined as

)tan(sinsin24

0'

24 ssexo wwESCK −⋅⋅⋅⋅⋅=↓ δφ

π


97

Where, 'SC is the solar constant, equals to 0036.01367 × mega joules m-2 hour-1 here, and the

sunrise hour angle sw is given below,

)tan()tan(cos δφ ⋅−=sw

For the sunshine fractionNn

, n is the amount of hours that the sun was actually shining for a certain

day and location and it can be obtained from meteorological observation. N is the total hours of sunshine for a perfect clear day, which is given by

swN ⋅⋅

=π15

360

6. Daily net longwave radiation

Daily net longwave radiation 24L is the energy exchange between the earth’s surface and the

atmosphere in form of radiation at longer wavelengths. It can be measured by appropriate instruments in stations. If the station does not have any net longwave radiometer, the mean daily air temperature can be used to retrieve this term through combination with air emisivity,

4,

' )273( +⋅⋅⋅−= meanaday TfL σε

Where:

''σ is the Stefan constant=5.6697 810−⋅ [ Watt m-2 K-4]

"" 'ε [-] is the net emissivity between the atmosphere and the ground.

Ta, mean is the mean daily air temperature at screen level [ C� ].

Appendix C: The distribution maps of surface variables and vegetation variables over Hebei Plain

Figure B-1: Time series maps of surface albedo over Hebei Plain Figure B-2: Time series maps of surface temperature over Hebei Plain Figure B-3: Time series maps of NDVI over Hebei Plain Figure B-4: Time series maps of fractional vegetation cover over Hebei Plain


98

Figure B-1: Time series maps of surface albedo over Hebei Plain


99

Figure B-2: Time series maps of surface temperature over Hebei Plain


100

Figure B-3: Time series maps of NDVI over Hebei Plain


101

Figure B-4: Time series maps of fractional vegetation cover over Hebei Plain

Documents

Satellite based Regional-scale Evapotranspiration in …...Satellite based Regional-scale Evapotranspiration in the Hebei Plain, Northeastern China by Wenjing Lin Thesis submitted