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Page 1/23 Jul. 27 2011
A new algorithm to automatically determine the boundary of the scatter plot in the triangle
method for evapotranspiration retrieval
Hongbo Su1,2, Jing Tian2, Shaohui Chen2, Renhua Zhang2 Yuan Rong2, Yongmin Yang2, Xinzhai Tang2 and Julio Garcia1
1. Department of Environmental Engineering, Texas A&M University at Kingsville, Kingsville, TX 78363, USA 2. The Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, China
IGARSS2011 Session: WE4.T09 Parameter Estimation
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• Background and Motivation • Methodology
• Findings and Conclusion
Outline
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What is Evapotranspiration? Evapotranspiration (ET) is the combination of water that is evaporated from the surface and transpired by plants as a part of their metabolic processes.
Background and Motivation
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•Water Balance dS
P Qd
Tt
E
n GER H L
•Carbon assimilation & ET process are closely related at
stomatal level
•Surface Energy Balance
Potential Applications:
Draught and flood monitoring and prediction, water resource
management
Weather prediction and climate change detection
Crop yield estimation, optimal irrigation planning
Importance of the Evapotranspiration Study
Background and Motivation
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• Terrestrial Evapotranspiration Measurement from Ground
Bowen Ratio System
Eddy Correlation System
Limitation of the ground measurements:
Spatial scale is about tens or hundreds of meters, dependent on the land surface. Instruments can’t be deployed in remote area.
Advantage: High Accuracy (10-15%)
Background and Motivation
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• Quantifying the land-atmospheric interactions
Opportunity:
Make use of the abundant satellite data observed from Space
Larger scale Global Circulation Model (GCM), regional numerical weather prediction models and Agricultural applications require a globally or regionally distributed ET product to improve the global study and their prediction accuracy.
Challenges:
However, ground (point) based ET measurement can’t meet the challenges because of:
•Limited spatial representativity
•Highly cost to maintain a field network
TerraAqua
Background and Motivation
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• Evapotranspiration Models based on RS
According to the two most recent review papers by Dr. Li and Dr. McCabe and their colleagues, the ET models based on RS can be categoriized
1)Surface Energy balanced models, such as SEBS, SEBAL, ALEXI, partition of H and LE
2)Empirical Regression Models, using minimal inputs, basedon Vegetation Index
3)Physically based process models, in SVAT, LSM, basically P-M and P-T
4)Hybrid Models, such as data assimilation in LSM, Triangle Method
Background and Motivation
Jetse D. Kalma, Tim R. McVicar, Matthew F. McCabe , “Estimating Land Surface Evaporation: A Review of Methods Using Remotely Sensed Surface Temperature Data”, Surveys in Geophysics, 2008 Volume 29, Numbers 4-5, 421-469, DOI: 10.1007/s10712-008-9037-z
Zhao-Liang Li, Ronglin Tang, Zhengming Wan, et. Al. “Review: A Review of Current Methodologies for Regional Evapotranspiration Estimation from Remotely Sensed Data”, Sensors 2009, 9(5), 3801-3853; doi:10.3390/s90503801
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• Triangle Method History: Firstly proposed by Justice in 1980’s. Then developed and improved in the recent 3 decades, by Carlson et al., 1981; Wetzel et al., 1983; Carlson et al., 1984; Nemani and Running, 1989; Kustas, 1990; Stewart et al., 1994; Kustas and Norman, 1996; Bastiaanssen et al., 1998; Mecikalski et al, 1999; Petropoulis et al., 2006
Background and Motivation
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• Triangle Method
Background and Motivation
Mo (Soil Moisture Availability) increasing from 0 on the right side(the warm edge). Curved lines labeled as fractions represent the evapotranspiration fraction, EF.
Simulated by SVAT Model
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• Triangle Method
Revision of the triangle method
The space of Fr and T* can be changed to the space of
1)Ts v.s. VIs, Ts-Ta v.s. VIs,
2)Ts v.s. Albedo
3)Albedo v.s. VIs
VIs can be directly related to Fr using equations similar to:
Background and Motivation
Limitation:•Much uncertainty in how to determine the dry and wet edge/boundary in the scatter plots. Done manually.•The study area has to be big enough
Advantages :
Requiring only 2-3 inputs
Less computation intensive
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Our purpose of this study aims to
•Lower the uncertainty of the determination of the dry and wet edge/boundary in the scatter plots, which is the crucial component in the triangle method.
•Increase the self-consistency of the estimation from Triangle method. (be repeatable)
Not on the validation of the validation of the triangle method. It was previously done by other scholars.
Background and Motivation
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Methodology
A new algorithm to automatically determine the boundary of the triangle shape in the space of the scatter plot is proposed.
It has to meet the requirement of1) maintaining the self-consistency 2) lowering the subjectivity by minimizing the human interference.
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Methodology
Three different algorithms were developed to automatically determine the boundary of the triangle shape in the scatter plots.
It is assumed that x denotes the variable in the X dimension, y stands for the variable in the Y dimension in the two-dimensional scatter plot, the number of pixel is N and the threshold is α ( 0<α<0.5)
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MethodologyFor the Algorithm I, the procedures are:
a)Linear fitting using all the N pairs of (x, y) and obtaining a line L of y=A+Bx; b)Solving the intercept of the line L with the Line x=1. Assuming that this intercept is at the
point (1, D); c)Drawing a line L1, whose slope is B and the intercept of L1 with the Line x=1 is (1, D).
Obviously, the y-intercept is (0, A); d)Changing (decreasing) the slope of L1, at the same time, keeping (1, D) on the line L1; e)Counting the number of points which is below the line L1; assuming the number is n; f)If the fraction of n to N is less than (1-α), go back to the procedure e); g)The line L1 is assigned to be the upper boundary of the triangle shape; h)Drawing a line L2, whose slope is B and the intercept of L2 with the Line x=1 is (1, D).
Obviously, the y-intercept is (0, A); i)Changing (increasing) the slope of L2, at the same time, keeping (1, D) on the line L2;j)Counting the number of points which is below the line L2; assuming the number is n;k)If the fraction of n to N is larger than α, go back to the procedure j); l)The line L2 is assigned to be the lower boundary of the triangle shape;
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Methodology
For some particular shape of the scatter plot (see Figure on the right, albedo V.S. Vegetation Fraction), the above algorithm couldn’t converge because of the forked shape on the right hand side.
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MethodologyTherefore, Algorithm II was developed. The Algorithm II is actually a
revision based on the Algorithm I. The procedures are
a)Linear fitting using all the N pairs of (x,y) and obtaining a line L of y=A+Bx;
b)Separating the N points in the scatter plot into two groups. The points above the line L will be Group I. The other points will be in Group II.
c)For the points from Group I, apply the Algorithm I. The upper boundary of the whole scatter plot will be determined by that of those points from Group I.
d)For the points from Group II, apply the Algorithm I. The lower boundary of the whole scatter plot will be determined by that of those points from Group II.
The threshold level in I and II is 0.05.
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Methodology
Algorithm III is quite different with the above two.
Firstly, the x-y space is divided equally into n (here n is assigned to be 15) domains according to their x values. For vegetation fraction, it is in the range of 0 and 1.
Secondly, after sorting the y values in each of the 15 sub-domains, the α and (1-α) quintile of the y values is retrieved.
Thirdly, the lower boundary line is fitted using the 15 α quintile y values and the corresponding x values. Similarly, the upper boundary line is fitted using the 15 (1-α) quintile y values and the corresponding x values.
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Methodology
Examples of the determination of the boundary of the scatter plot
Figure 2 Albedo V.S. Vegetation Fraction for (a) date 03/14/2006; (b) date03/28/2006
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0nR G H LE Energy Balance:
Parameterized using fractional vegetation cover
Estimation using:• incoming Rswd
• downward Rlwd
• surface infrared
temperature
• emissivity
• albedo
40(1 )n swd lwdR R R T
0 ( (1 ) )n c c c sG R f f
Heat balance, often used in Hydrology
and Meteorology
Radative balance,
conveniently estimated by
remote sensing
Methodology
After the boundary of the triangle shape is determined, the standard triangle method is applied to calculate the terrestrial evaporation
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Methodology
( )
( )
( )1
( ) ( )
( )1
( )
1
u u u
l l l
u i ii
u i l i
ii i
i
ii
i
DT Fr a b Fr
DT Fr a b Fr
DT Fr DTB
DT Fr DT Fr
BH Rn G
B
Rn GLE
B
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Findings and Conclusion
The study area is the Northern China Plain, which is flat and has a wide range of soil wetness and fractional vegetation cover.
MODIS land data products, including land surface temperature, albedo, vegetation index, together with the necessary meteorological variables (mainly the surface downward and upward radiative fluxes) from the GDAS (Global Data Assimilation System) database developed by NOAA/NCEP, are used to test the proposed algorithm.
Figure 3 Evapotranspiration estimate for the Northern China Plain based on the new algorithm
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Three algorithms were developed and compared in this study. The new algorithms have the capability of automatically determining the boundary of the 2-D scatter plots and the results are repeatable.
It was found that
•Algorithm II is better than I, because it can handle the bi-forked shape of the scatter plots.
•Algorithm III is less computation intensive and has the best overall
Findings and Conclusion
