Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]

Katholieke Universiteit Leuven

Belgium

Radar Based Rainfall Estimationfor River Catchment Modeling

Promotor:Prof. P. Willems

Advisor:T. Goormans

Master dissertation in partial fulfilmentof the requirements for the Degree of

Master of Science in Water Resources Engineering

by: Shrestha Narayan Kumar

September 2009

Radar based rainfall estimation for river catchment modelling

i

Acknowledgement

First and foremost, I would like to express my sincere gratitude to my promoter Prof. dr. ir.

Patrick Willems for valuable suggestions and guidance right from the beginning. His constant

encouragement has been the key for successful completion of this thesis.

I would also like to thank my advisor ir. Toon Goormans; with whom I had so many

interesting discussions and made me comfortable during field visits too. He read this thesis

from beginning to end and offered many valuable comments.

From a practical standpoint, the thesis would not have been possible without the collaboration

of the Royal Meteorological Institute (RMI) of Belgium who provided the radar data of the

Wideumont station and the raingauge data as well. I would also like to express gratitude to

the resource people from the RMI for their technical support and guidance, in particular Dr.

ir. Laurent Delobbe and ir. Edouard Goudenhoofdt. Also, I would like to thank the Flemish

water company Aquafin and the Flemish Environment Society for providing the raingauge

series.

Special thanks go to VLIR-UOS for providing the scholarship for this Inter-University

Program in Water Resource Engineering (IUPWARE) 2007-2009 session and Katholieke

Universiteit, Leuven and Vrije Universiteit Brussel for providing the platform.

On a more personal note, I would like to thank my wife Sabi Shrestha for her constant

support and her love as well as my family for their support for me from day one.

Finally, the author would like to thank all those in IUPWARE 2007-2009 for being like a

family, contribute to the success of the thesis to great extent.


ii

Table of Contents

Acknowledgement --------------------------------------------------------------------------------------- i

Table of Contents --------------------------------------------------------------------------------------- ii

List of Figures ------------------------------------------------------------------------------------------ vi

List of Tables ------------------------------------------------------------------------------------------viii

List of Acronyms -------------------------------------------------------------------------------------- ix

Abstract -------------------------------------------------------------------------------------------------- x

CHAPTER 1: INTRODUCTION ------------------------------------------------- 1

1.1 Problem definition ----------------------------------------------------------------------------- 1

1.2 Motivation of the study ------------------------------------------------------------------------ 2

1.3 Thesis aims and objectives -------------------------------------------------------------------- 3

1.4 Thesis outline ----------------------------------------------------------------------------------- 3

CHAPTER 2: LITERATURE REVIEW ---------------------------------------- 4

2.1 Rainfall ------------------------------------------------------------------------------------------ 4

2.2 Rainfall measurement -------------------------------------------------------------------------- 4

2.2.1 Rain gauges -------------------------------------------------------------------------------- 4

2.2.2 Weather radars ---------------------------------------------------------------------------- 5

2.2.2.1 The RMI weather radar at Wideumont ------------------------------------------- 6

2.2.2.2 Local Area Weather Radar (LAWR) of Leuven -------------------------------- 8

2.2.2.3 Uncertainty associated with radar estimates -----------------------------------10

2.2.2.4 Radar-gauge merging techniques ------------------------------------------------12

2.3 Hydrological modelling ----------------------------------------------------------------------13

2.3.1 The VHM Model ------------------------------------------------------------------------14

2.3.1.1 Model structure ---------------------------------------------------------------------15

2.3.1.2 Model parameters ------------------------------------------------------------------16

2.3.1.3 Model calibration ------------------------------------------------------------------17

2.3.2 The NAM model -------------------------------------------------------------------------17


iii

2.3.2.1 Model structure ---------------------------------------------------------------------17

2.3.2.2 Model parameters ------------------------------------------------------------------18

2.3.2.3 Model calibration ------------------------------------------------------------------19

2.4 Significance of spatial variability of rainfall and basin response ----------------------20

2.5 Similar past studies ---------------------------------------------------------------------------21

2.5.1 Radar-gauge comparison and merging -----------------------------------------------21

2.5.2 Stream flow simulation using radar data ---------------------------------------------22

CHAPTER 3: APPLICATION -------------------------------------------------- 23

3.1 Methodology -----------------------------------------------------------------------------------23

3.2 Study area --------------------------------------------------------------------------------------23

3.3 Radar-gauge comparison and merging -----------------------------------------------------25

3.3.1 The raingauge network ------------------------------------------------------------------25

3.3.2 Correcting raingauge measurements --------------------------------------------------25

3.3.3 Conversion of radar records to rainfall rates -----------------------------------------26

3.3.4 Data periods ------------------------------------------------------------------------------27

3.3.5 LAWR - gauge comparison and merging --------------------------------------------28

3.3.6 RMI Wideumont estimates and gauge comparison and merging -----------------32


3.4.1 The catchment ----------------------------------------------------------------------------32

3.4.1.1 Choice of catchment ---------------------------------------------------------------32

3.4.1.2 Catchment geomorphology -------------------------------------------------------33

3.4.1.3 Input meteorological series -------------------------------------------------------34

3.4.2 Catchment modelling with VHM------------------------------------------------------35

3.4.3 Catchment modelling with NAM------------------------------------------------------36

3.4.4 Performance evaluation of the model results ----------------------------------------36

3.4.5 The significance of spatial data --------------------------------------------------------38

3.4.5.1 Quantifying rainfall variability ---------------------------------------------------38


iv

3.4.5.2 Basin response ----------------------------------------------------------------------39

CHAPTER 4: RESULTS AND DISCUSSION ------------------------------- 41

4.1 LAWR estimates − gauge comparison and merging -------------------------------------41

4.1.1 Using an average value of CF ----------------------------------------------------------41

4.1.2 Range dependent adjustment on CF --------------------------------------------------42

4.1.3 Statistical analysis on range dependent adjustment ---------------------------------43

4.1.4 Mean field bias adjustment -------------------------------------------------------------46

4.1.4.1 Brandes spatial adjustment -------------------------------------------------------48

4.1.4.2 Statistical analysis on the MFB and BRA adjustment ------------------------48

4.2 RMI Wideumont estimates − gauge comparison and merging -------------------------50

4.2.1 MFB adjustment -------------------------------------------------------------------------50

4.2.2 Brandes spatial adjustment -------------------------------------------------------------51

4.2.3 Statistical analysis on the MFB and BRA adjustment ------------------------------51

4.3 Comparison of LAWR-Leuven and RMI-Wideumont estimates ----------------------52

4.4 Catchment modelling -------------------------------------------------------------------------53

4.4.1 Catchment modelling with VHM------------------------------------------------------53

4.4.2 Catchment modelling with NAM------------------------------------------------------54

4.4.3 Model performance evaluation --------------------------------------------------------55

4.5 The significance of spatial data -------------------------------------------------------------60

4.5.1 Rainfall spatial variability --------------------------------------------------------------60

4.5.2 Basin response ---------------------------------------------------------------------------60

CHAPTER 5: CONCLUSIONS ------------------------------------------------- 69

5.1 Comparing and merging of radar − gauge estimates -------------------------------------69


5.3 Limitation and future perspectives ----------------------------------------------------------71

CHAPTER 6: REFERENCES --------------------------------------------------- 72

CHAPTER 7: ANNEXES --------------------------------------------------------- 78


v

A-1: Prior time series processing results -----------------------------------------------------------78

A-2: Model results -------------------------------------------------------------------------------------79

A-3: Rainfall series (in terms of Pref) for selected storm events --------------------------------82

A-4: Accumulated rainfall over radar pixels for selected storm events -----------------------84

A-5: LAWR-Leuven simulated results -------------------------------------------------------------86


vi

List of Figures

Figure 2-1: Different types of weather radars and their aspects (Einfalt et al., 2004) --------------------- 6

Figure 2-2: Simplified sketch of beam cut-off ------------------------------------------------------------------- 9

Figure 2-3: Influence of choice of Z-R relationship on rainfall rates (Einfalt et al., 2004) -------------- 11

Figure 2-4: Errors related to height of the measurement (Delobbe, 2007) --------------------------------- 11

Figure 2-5: Some typical vertical profile of reflectivity (Delobbe, 2007) ---------------------------------- 12

Figure 2-6: General lumped conceptual rainfall-runoff model structure (Willems, 2000) --------------- 14

Figure 2-7: Steps in the VHM structure identification and calibration procedure ------------------------ 15

Figure 2-8: The NAM structure ----------------------------------------------------------------------------------- 18

Figure 3-1: Belgium (light green), the RMI-Wideumont radar (black star), the LAWR-Leuven (red

star) and the catchment (dark green). Black arcs indicate the distance to the RMI-Wideumont,

with an increment of 60 km. The red circle shows 15 distance to the LAWR-Leuven ------------ 24

Figure 3-2: The study area with the location of 12 gauges (red dots: Aquafin &VMM; black triangles:

RMI), the LAWR (yellow star), catchment (dark green polygon) and part of the Walloon region

(light green polygon). Circles indicate the distance to the LAWR, with increment of 5 km ----- 24

Figure 3-3: Catchment under consideration with position of LAWR (star), radar beam blockage sector

(blue shade), rain gauges (dots-the VMM and Aquafin TBRs; triangles-the RMI non-recording

gauges), water courses (blue lines) and circles - distances of 5, 10 and 15 km from the LAWR 33

Figure 3-4: The DEM map of catchment with stream network ---------------------------------------------- 34

Figure 4-1: Evolution of RFB with range (using constant CF on the LAWR estimates) ---------------- 41

Figure 4-2: Plot of CF as a function of distance to the LAWR, each point representing a TBR

(Aquafin &VMM) -------------------------------------------------------------------------------------------- 42

Figure 4-3: Evolution of RFB with range (using range dependent CF on the LAWR-Leuven estimates)

------------------------------------------------------------------------------------------------------------------- 43

Figure 4-4: Scatter plot of daily accumulated radar-gauge valid pairs for summer storm using constant

value of CF and CF after range dependent adjustment on the LAWR-Leuven estimates --------- 45

Figure 4-5: Cumulative rainfall plot of radar and gauge records for the winter and summer periods of

the LAWR estimates after range dependent correction on CF----------------------------------------- 46

Figure 4-6: Frequency distribution of field bias of valid gauge-radar (LAWR) pairs -------------------- 47

Figure 4-7: Probability distribution of field bias of valid gauge-radar (LAWR) pairs ------------------- 47

Figure 4-8: Evolution of different statistical values with different adjustments on the LAWR-Leuven

estimates; [a]-summer period and [b]-winter period ---------------------------------------------------- 49

Figure 4-9: Scatter plot of radar-gauge daily accumulated estimates for week 1 & 2 before [a] and

after [b] MFB correction on the RMI-Wideumont estimates ------------------------------------------ 50


after [b] MFB correction on the RMI Wideumont estimates ------------------------------------------ 51


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Figure 4-11: LAWR-Leuven and RMI-Wideumont daily accumulated estimates comparison plot for

summer weeks ------------------------------------------------------------------------------------------------- 53


winter weeks --------------------------------------------------------------------------------------------------- 53

Figure 4-13: Graphical comparison of nearly independent peak flow maxima ---------------------------- 57

Figure 4-14: Graphical comparison of nearly independent slow flow minima ---------------------------- 58

Figure 4-15: Graphical comparison of peak flow empirical extreme value distributions ---------------- 58

Figure 4-16: Graphical comparison of low flow empirical extreme value distributions ----------------- 59

Figure 4-17: Graphical comparison of cumulative flow volumes ------------------------------------------- 59

Figure 4-18: NSEobs for different rainfall descriptors and for different storm events ------------------- 61

Figure 4-19: Observed and simulated flows derived from different rainfall descriptors ----------------- 65

Figure 4-20: Observed and simulated flows derived from different rainfall descriptors ----------------- 66

Figure 4-21: Plot of SDIR and NSEref for both the VHM and NAM -------------------------------------- 67

Figure A-1: Baseflow filter results ------------------------------------------------------------------------------- 78

Figure A-2: Interflow filter results -------------------------------------------------------------------------------- 78

Figure A-3: Observed and NAM simulated hydrograph for the calibration period (3/1/2006-

2/28/2009) ----------------------------------------------------------------------------------------------------- 79

Figure A-4: Cumulative observed and NAM simulated discharge for calibration period (3/1/2006-

2/28/2009) ----------------------------------------------------------------------------------------------------- 79

Figure A-5: Observed and NAM simulated hydrograph for the validation period (1/1/2004-

12/31/2005) ---------------------------------------------------------------------------------------------------- 80

Figure A-6: Observed and VHM simulated hydrograph for the calibration period (3/1/2006-

2/28/2009) ----------------------------------------------------------------------------------------------------- 80

Figure A-7: Cumulative observed and VHM simulated discharge for the calibration period (3/1/2006-

2/28/2009) ----------------------------------------------------------------------------------------------------- 81

Figure A-8: Reference rainfall evolution for storm event-1 -------------------------------------------------- 82

Figure A-9: Reference rainfall evolution for storm event-2 -------------------------------------------------- 82

Figure A-10: Reference rainfall evolution for storm event-3 ------------------------------------------------- 83

Figure A-11: Reference rainfall evolution for storm event-4 ------------------------------------------------- 83

Figure A-12: Accumulated rainfall for storm event -1 (RMI pixels), north is upward ------------------- 84

Figure A-13 : Accumulated rainfall storm event-1 (LAWR pixels), north is upward -------------------- 84

Figure A-14: Accumulated rainfall for storm event -3 (RMI pixels), north is upward ------------------- 85

Figure A-15: Accumulated rainfall storm event-3 (LAWR pixels), north is upward --------------------- 85

Figure A-16: LAWR-Leuven VHM simulated river discharge for the period of 7/2/2008 to 9/30/2008

------------------------------------------------------------------------------------------------------------------- 86

Figure A-17: LAWR-Leuven NAM simulated river discharge for the period of 12/1/2008 to

2/28/2009 ------------------------------------------------------------------------------------------------------ 86


viii

List of Tables

Table 2-1: Some characteristics of the Wideumont radar ------------------------------------------------------ 7

Table 2-2: Some characteristics of the LAWR-Leuven ------------------------------------------------------- 10

Table 3-1: Correction Factors [k] for the Aquafin and VMM raingauges ---------------------------------- 25

Table 3-2: Calibration Factor [CF] for Aquafin and VMM raingauges ------------------------------------- 26

Table 3-3: Data periods of the RMI radar of Wideumont ----------------------------------------------------- 27

Table 3-4: Data periods of the LAWR of Leuven -------------------------------------------------------------- 27

Table 3-5: Selected storm events; LT means Local Time ---------------------------------------------------- 38

Table 4-1: Some statistical parameter values before and after range dependent adjustment on the

LAWR estimates. --------------------------------------------------------------------------------------------- 44

Table 4-2: Some statistical parameter values before and after MFB and BRA adjustment on the

LAWR estimates for both summer and winter periods; RAW stands for the LAWR estimates

using constant CF values, RDA(LAWR estimates after range dependency adjustment on CF) - 48

Table 4-3: Some statistical parameter values before and after MFB adjustment on the RMI

Wideumont radar estimates, RAW stands for original RMI-Wideumont estimates --------------- 52

Table 4-4: The calibrated VHM parameters with their short description ----------------------------------- 54

Table 4-5: The calibrated NAM parameters with their short description ----------------------------------- 55

Table 4-6: Some goodness-of-fit-statistics ---------------------------------------------------------------------- 56

Table 4-7: Rainfall spatial variability measured in terms of SDIR for the different rainfall descriptors

and for selected events --------------------------------------------------------------------------------------- 60

Table 4-8: Results in terms of NSEobs for the different rainfall descriptors and for different storm

events ----------------------------------------------------------------------------------------------------------- 61

Table 4-9: Results in terms of NSEref for the different rainfall descriptors ------------------------------- 63


ix

List of Acronyms

AD Average Difference

BC Box-Cox Transformation

BRA Brandes spatial adjustment

CF Calibration Factor

DEM Digital Elevation Model

DHI Danish Hydrological Institute

DMI Danish Meteorological Institute

IUPWARE Inter-University Program in Water Resource Engineering

KMI Koninklijk Meteorologisch Instituut

LAWR Local Area Weather Radar

MAE Mean Absolute Error

MFB Mean Field Bias

NAM Nedbør-Afstrømnings-Model (Rainfall-Runoff Model)

NSE Nash-Sutcliff Efficiency

POT Peak Over Threshold

RFB Relative Field Bias

RMI Royal Meteorological Institute

RMSE Root Mean Square Error

SDIR Reference Spatial Deviation Index

SWAT Soil & Water Assessment Tool

VHM Veralgemeend conceptueel Hydrologisch Model (Generalized lumped

conceptual and parsimonious model structure-identification and

calibration)

VLIR Vlaamse Interuniversitaire Raad

VMM Vlaamse Milieumaatschappij (Flemish Environment Agency)

VPR Vertical profile of reflectivity

WETSPRO Water Engineering Time Series PROcessing tool


x

Abstract

This paper discusses the first hydro-meteorological potential of the X-band Local Area Weather Radar

(LAWR), installed in the densely populated city centre of Leuven (Belgium). Adjustments are applied

to raw radar data using gauge readings from a raingauge network of 12 raingauges. The significance

of spatial rainfall information on hydrological responses is investigated in the 48.17 km2

Molenbeek-

Parkbeek catchment, south of Leuven. For this, two lumped conceptual models, the VHM and the

NAM, are calibrated with reference rainfall (Pref) − a rainfall representation defined by raingauges

which are inside the catchment. Three alternative rainfall descriptors are derived, namely the RG1

(single raingauge for the whole catchment taking a gauge which is approximately at the centroid of

the catchment), the LAWR estimates and the estimates from a C-band weather radar installed by the

Royal Meteorological Institute (RMI) at Wideumont (Belgium). An index, reference spatial deviation

index (SDIR) is defined based on the difference between Pref and the alternative rainfall descriptors. A

modified Nash-Sutcliff Efficiency (NSEref) is used to evaluate the performance of simulated runoff

with respect to reference simulated runoff – runoff derived by reference rainfall.

Range dependent adjustment is applied on the LAWR data combining a power and second degree

polynomial function. C-band RMI estimates tend to overestimate summer storms and strongly

underestimate winter storms. The mean field bias correction followed by Brandes spatial adjustment

improved the radar estimates to a great extent. After adjustments, the mean absolute error is found to

decrease by 47% and the mean absolute error by 45% compared to the original radar estimates. Still,

the gauge-radar residuals even after adjustments are found to be not negligible. No large differences

in streamflow simulation capability of the two types of models can be distinguished. Runoff

simulations based on the RG1 rainfall descriptor are almost as accurate as those based on Pref. Using

radar estimated rainfall for runoff simulations showed lower performance compared to both Pref as

well as RG1 indicating that the catchment is less sensitive to spatial rainfall variability and/or the

accuracy of radar based rainfall estimates is low. Runoff peaks for summer and extreme events are

underestimated due to high damping and filtering effects of the catchment or more obviously, due to

the localized summer rainfall events. More uniform storms are simulated with more or less the same

accuracy for all rainfall descriptors. An inverse correlation between SDIR and NSEref is observed. An

SDIR of more than 10% affected the hydrograph reproduction indicating that the catchment requires

more robust areal rainfall estimation.

Key words: Weather radar; Runoff; Lumped conceptual model; Spatial rainfall variability.


1

CHAPTER 1: INTRODUCTION

1.1 Problem definition

Rainfall is the driving force for the hydrologic cycle, a physical phenomenon which controls

the terrestrial water supplies. Its nature and characteristics are important to conceptualize and

predict its effect on runoff, infiltration, evapotranspiration and water yield. For most of the

simulation models, it is primary input, often considered spatially uniform over the catchment

which is actually not usually the case. Rather, it is highly variable in both space and time.

During a storm, rainfall may vary by tens of millimetres per hour from minute to minute and

over distances of only a few tens of metres (Austin et al., 2002). Hence the assumption of

uniform rainfall leads to a major uncertainty in simulated events (Willems, 2001). Also, it can

be observed that hydrologists have traditionally paid much more attention to the development

of more sophisticated rainfall-runoff models or the local models to suit the local conditions

than to the development of improved techniques for the measurement and prediction of the

space-time variability of rainfall. This is to be deplored, since rainfall is the driving source of

water behind most of the inland hydrological processes (Berne et al., 2005). So, better

understanding on the rainfall input to the hydrological modelling is required to acquire more

robust and accurate hydrological simulation. Hence, it demands a dense rain gauge

observation network to cover this spatial variability, which is difficult to install and maintain,

making it an undesirable solution (Wilson and Brandes, 1979).

Weather radars, which are capable of providing continuous spatial measurements which are

immediately available, are increasingly being used as an alternative. For the showery rain at

least, the advantage of using radar derived rainfall to raingauge is expected to be obvious.

One particular storm which caused severe flooding at some location might not have passed

over the raingauges and can not be reflected in basin response through a hydrological model.

The weather radar can detect rainfall events to over one hundred kilometres from the radar

site.

Also, it is an inherent property of radar measurements that the uncertainty on measurements

increases as the rainfall intensity increases (Einfalt et al., 2004). These uncertainties should

be minimized before using them as input to simulation models by using adjustment

techniques (Wilson and Brandes, 1979). Hence, merging of both forms of rainfall estimates is

advised. There have been a range of methods to merge the radar and raingauge data for better


2

estimates of rain gauges; from simple merging methods to sophisticated spatial methods.

Many researchers have carried out rigorous study on the evaluation of these merging methods

(e.g. Delobbe et al. (2008); Goudenhoofdt and Delobbe (2009)) and found that raw radar data

can be greatly enhanced. However, radar-gauge residuals, even after adjustment are not

always negligible (Borga, 2002). So, both measurement devices are complementary;

concurrent use of both can provide better estimates of rainfall (Einfalt et al., 2004).

The importance of considering the spatial distribution of rainfall for process-oriented

hydrological modelling is well-known. However, the application of rainfall radar data to

provide such detailed spatial resolution is still under debate (Tetzlaff and Uhlenbrook, 2005)

and is the subject of ongoing research. A network of rain gauges can provide more accurate

point-wise measurements but the spatial representation is limited (Goudenhoofdt and

Delobbe, 2009) but should be supported by quite a dense raingauge network.

In this study, emphasis is made to use the relatively new Local Area Weather Radar (LAWR)

of Leuven, Belgium for its first stream flow modelling. The raingauge network will serve as

ground truth data and hence serves as validation source as well as basis for correction on the

radar estimates. Data from the radar of the Royal Metrological Institute (RMI) − in Dutch:

Koninklijk Meteorologisch Instituut (KMI) − located at Wideumont is also used to check the

importance of the spatial variability of rainfall information on the catchment under

consideration. Two lumped conceptual runoff models, the VHM (Veralgemeend conceptueel

Hydrologisch Model) and the NAM (Nedbør-Afstrømnings-Model), are used for this

propose.

1.2 Motivation of the study

The hydro-meteorological potential of the weather radars has already been explored by many

researchers and interest in this subject is growing because of their capability of spatial

coverage to finer resolutions which are impossible to obtain with a raingauge network. The

C-band weather radar installed by the RMI at Wideumont has already been used for

hydrological modelling. But the LAWR-Leuven, installed by the Flemish water company

Aquafin, has rarely been used for such propose. Hence, a research has to be performed to

evaluate the performance of the LAWR- Leuven for catchment modelling. In this study, a

catchment named Molenbeek/Parkbeek, south of the Leuven is chosen for this propose. Using


3

both the RMI-Wideumont and the LAWR-Leuven for stream flow simulation would lead to

assess the significance of spatial resolution of the two different weather radars.

1.3 Thesis aims and objectives

For this thesis, data are available from a raingauge network and two different types of radars,

all providing rainfall information for the Molenbeek/Parkbeek catchment, south of Leuven,

Belgium, and this leads to the following objectives:

� To compare rainfall information from three sets of data; the raingauges, the C- and X-

band weather radars and hence quantifying the accuracy of radar estimates.

� To test procedures for merging the radar-gauge estimates for better rainfall estimation.

� To investigate the significance of spatial rainfall information by using the above

stated rainfall information on hydrological modelling.

� To provide recommendations on spatial resolution requirements of rainfall

information for the particular catchment.

1.4 Thesis outline

Chapter 1 gives the general problem definition, motivation for the study, the aims and

objectives of the thesis.

Chapter 2 gives the relevant literature review including the different rainfall descriptors, the

models used for simulating the basin response and similar previous studies.

Chapter 3 describes the methodology of the thesis in general and gives a description of the

study area, the rain gauge network and the radars that are used and the data periods. Also,

different comparison as well as adjustment methodologies, modelling methodologies and

different statistical tools used for the study are explained.

Chapter 4 discusses the results.

Chapter 5 covers the conclusions and recommendations for further researchers and the

limitation of different approaches used in the study as well.

Apart from this the thesis also contains an appendix and list of references used.


4

CHAPTER 2: LITERATURE REVIEW

2.1 Rainfall

Rainfall is one of the many forms of precipitation and a major component of the hydrological

cycle. It is the driving force of water for most of the terrestrial hydrological process (Berne et

al., 2005). The rainfall must satisfy the intermediate demand of evapotranspiration,

infiltration and surface storage before it results in runoff. In hydrological modelling, it is the

primary input (Segond et al., 2007; Velasco-Forero et. al., 2008).

Rainfall can be mainly divided into stratiform and convective rainfall. Stratiform rainfall

essentially results from stratiform clouds, has small drops and uniform spatial and temporal

gradients. Convective storms on other hand are generally more intense and consist of larger

drops. They are characterised by large temporal and spatial gradients.

2.2 Rainfall measurement

Rain gauges and weather radars are the two sensors that are most widely used in rainfall

measurement (Velasco-Forero et. al., 2008).

2.2.1 Rain gauges

The most common device that is being used for rainfall measurement is a rain gauge. Because

of its simple working principle, the tipping bucket rain gauges (TBRs) are widely used in

recent time though there are modern techniques coming up as well. The total amount of

rainfall over a given period is expressed as the depth of water which would cover a horizontal

area if there is no runoff, infiltration or evaporation. This depth is generally expressed in

millimetres and is the rainfall depth (FAO irrigation and Drainage Paper 27, 1998).

Rain gauge measurements, although representing only point rainfall, are very often

considered the “true” rainfall although there are some errors still associated with it. During

tipping motion of the bucket, water continues to flow through the funnel which is not taken

into consideration, resulting in an underestimation of the rainfall rate (Goormans and

Willems, 2008). Thus a dynamic calibration procedure should be applied. This procedure is

well defined by Luyckx and Berlamont (2001). Vasvari (2007) applied the same procedure on

several rain gauges in the city of Graz, Austria and found that not all of them are

underestimating. Several rain gauges had a positive relative deviation; some up to 22%, in the


5

low intensity range up to 0.5 mm/min. He ascribed this phenomenon by the retention of water

in the buckets between tips. But for higher intensities, the study showed a clear

underestimation. Another error associated with rain gauge measurement is due to wind

effects. FAO irrigation and Drainage Paper 27, Annex 2 (1998) states that wind errors are a

major error which can be very large, even more than 50%. Hence, local wind shelter

influences should also be considered. Goormans and Willems (2008) studied several

raingauges around the city of Leuven, Belgium and found that the wind effects

underestimated the long term rainfall accumulation depth by a factor as high as 1.32. These

two forms of errors that are always associated with rain gauges should be considered because

rain gauge based estimates of rainfall are generally used for validation of radar-based rainfall

quantities and will affect final radar performance.

2.2.2 Weather radars

Rain gauges are reliable instruments for which hydrologists can rely on at least for point

measurement (Moreau et al., 2009) but rainfall can vary both in space and time which is not

really captured by the rain gauges. Thus, there have been considerable interests in utilizing

the weather radar, since it provides spatially and temporally continuous measurements that

are immediately available at the radar site (Wilson and Brandes, 1979, Einfalt et al., 2004).

But the inherent feature of weather radars are that they did not measure rainfall directly but

rather the back scattered energy from precipitation particles from elevated volumes and an

algorithm should be developed and calibrated against the raingauge network.

Wilson and Brandes (1979) and Einfalt et al. (2004) describe the methodology of using

weather radars in quantitative precipitation estimates and the potential error sources. The first

study also focuses on the methodologies on radar-gauge comparisons and adjustments. The

second one gives a clear outline of requirements for weather radars, examples of good and

bad practices more in terms of online and offline applications of weather radar.

Mostly three types of weather radars are used in hydrometeorology - the S-band, the C-band

and the X-band radars. Their relative advantages and disadvantages are given in Figure 2-1.


6

Figure 2-1: Different types of weather radars and their aspects (Einfalt et al., 2004)

The difference is in the wavelength of the emitted electromagnetic waves. The S-band radars

have the longest wavelength while the X-band radars have the shortest. Using a larger

wavelength for radar measurement would certainly enhance the usable range but problems

arise from radar beam interaction with ground. The shorter wave length radars, although

having fine spatial resolution, suffer from attenuation significantly (Einfalt et al. 2004).

2.2.2.1 The RMI weather radar at Wideumont

The RMI of Belgium operates C-band radar located in Wideumont, in the south of Belgium.

The radar performs a volume scan every 5 minutes with reflectivity measurements up to 240

km. A Doppler scan with radial velocity measurements up to 240 km is performed every 15

minutes (RMI, 2009). The 5 minute radar data are summed up to produce 1h and 24h

precipitation accumulation products. The radar is equipped with a linear receiver and the

reflectivity factors are converted to precipitation rates using the Marshall-Palmer (1948)

relation with ‘a’ and ‘b’ values being 200 and 1.6 respectively.

A time domain Doppler filtering is applied which removes the ground clutter. An additional

treatment is applied to the volume reflectivity file to eliminate residual permanent ground

clutter caused by surrounding hills. Reflectivity data contaminated by permanent ground

clutter are replaced by data collected at higher elevation. A Pseudo-Cappi image at 1500 m is

calculated from the volume data. An advection procedure has also been applied to correct the

effect of time sampling interval on accumulation maps (Delobbe et al. 2006).

Characteristics: Some relevant characteristics of the C-Band Doppler radar located at

Wideumont are presented in Table 2-1 (Berne et al. 2005).


7

Table 2-1: Some characteristics of the Wideumont radar

Property Value

Location Wideumont , Belgium

Operational since October 2001

Type of radar Gematronik pulse Doppler

Frequency/wavelength C-band (5.64GHz/5.32 cm)

Mean transmit power 250 W

Height of tower base 535 m (above mean sea level)

Height of tower 50 m

Height of antenna 585 m (above mean sea level)

Antenna diameter 4.2 m

Radome diameter 6.7 m

Elevations 0.5°, 1.2

°, 1.9

°, 2.6

°, 3.3

°, 4.0

°, 4.9

°, 6.5

°, 9.4

°, 17.5

°

Maximum range reflectivity processing 240 km

Time interval precipitation products 5 min.

Working principle: Radars do not measure rainfall directly but rather the back scattered

energy from precipitation particles from elevated volumes. The received energy from the

precipitation particles is given by:

2

2

r

ZKCPr = (1)

With,

C = radar constant

K = imaginary dielectric constant

r = range of the target

Z = radar reflectivity

The radar reflectivity, Z (mm6/m

3), is proportional to the summation of the sixth power of

particle diameters (Di6) in a unit volume illuminated by the radar beam; and is defined as:

dDDDNDNZ ii

66)(∫∑ == (2)

Where,

Ni= number of drops per unit volume with diameter Di

N(D) = number of drops with diameters between D and D+dD in a unit volume.


8

The rainfall rate (R) can be related to N(D) by the following equation if no vertical air motion

is assumed.

∫= dDDVDDNR t )()(6

3π (3)

Where,

Vt(D)= drop terminal velocity of a drop diameter D which is also a function of D.

But the problem is that both Z and R are functions of the drop size distribution which is

unknown and hence using an empirical Z-R relationship is imminent which is usually in the

exponential form such as:

bRaZ = (4)

with a and b being constants.

It is worth noting that the Equation (4) itself can be regarded as semi-empirical as it has been

derived assuming empirical relationships for Vt(D) and N(D).

Some currently used Z-R relationships as depicted in Einfalt et al. (2004) are as follows;

� 6.1200 RZ = , suitable for stratiform events also known as the Marshall and Palmer

(1948) relationship.

� 2.1250 RZ = , suitable for tropical climates.

� 4.1300 RZ = , suitable for convective events.

Limitation of the above stated relationships should be clear due to the fact that there can not

be null vertical air motion such as the case of a thunderstorm. Also, the drop size distribution

is rarely known and it varies in space and time (Wilson and Brandes, 1979).

2.2.2.2 Local Area Weather Radar (LAWR) of Leuven

Outcome of a project ‘development of a system for short-time prediction of rainfall’, the

Danish Hydrological Institute (DHI) together with the Danish Meteorological Institute (DMI)

developed a cost effective X-band radar called LAWR (DHI Website, 2009). It is based on

X-band marine radar technology and emits only a tenth (25 kW) of the power emitted from

conventional weather radars (250 kW) and is capable to penetrate high intensity rainfall.

From this, DHI also developed a smaller version of the LAWR, the so-called City LAWR.

Important feature of the City LAWR is that it has a compact antenna (diameter of 65 cm) and


9

total weight of only 8 kg, which makes it fairly easy to install. It has a horizontal opening

angle of 3.9° making quantitative precipitation estimation possible up to a distance of 15 km

from the radar site (Goormans et al., 2008). But, the large vertical opening angle of 20° makes

it susceptible to direct ground reflection.

In an ongoing research project of the Hydraulics Laboratory of the Katholieke Universiteit

Leuven for the Flemish water company Aquafin, a City LAWR is installed in the densely

populated city centre of Leuven. Based on quite rigorous clutter tests, the city LAWR is

installed on the roof of the Provinciehuis building – the main office of the province of

Flemish Brabant. This location produced acceptable amounts of clutter, mainly due to a pit

wall which cuts off the lower part of the beam (Goormans et al., 2008). The simplified sketch

of this beam cut-off is shown in Figure 2-2. From here on, the City LAWR will be referred to

as the LAWR.

Figure 2-2: Simplified sketch of beam cut-off

Characteristics: Some relevant characteristics of X-Band LAWR located at Leuven are

presented in Table 2-2.

Working Principle: Contrary to conventional weather radars like C-band weather radars,

which are equipped with a linear receiver, the LAWR has a logarithmic receiver. This

suggests that the conventional transformation from reflectivity to rainfall rate should be

linear. A relationship between the ‘count’ (representation of back scattered energy) and the

rainfall rate recorded at ground level has to be established. According to the manufacturer

and as confirmed by some studies, (e.g. Rollenbeck and Bendix, 2006), a linear relationship


10

between ‘counts’ recorded and ground rainfall rate exists. The conversion factor which

converts radar records to rainfall rate can be termed as Calibration Factor (CF).

Table 2-2: Some characteristics of the LAWR-Leuven

Property Value

Location Leuven, Belgium

Operational since July 2008

Frequency X-band (9410±30GHz)

Peak output power 4 kW

Height of tower (Building) 48 m

Antenna type Hybrid array

Antenna diameter 55cm

Horizontal beam opening 3.9°

Vertical beam opening 20°

Rotation speed 24 rpm

Time interval precipitation products 1 min

2.2.2.3 Uncertainty associated with radar estimates

As the weather radar does not measure rainfall rates directly, it is prone to errors from

different sources. Wilson and Brandes (1979) stated three major sources of errors associated

with radar estimates. These are:

� Variations in the relationship between the backscattered energy and rainfall rates.

� Changes in precipitation forms before reaching the ground.

� Anomalous propagation of beams.

Some other researchers describe similar error sources. Delobbe (2007) mentioned mainly

three sources of errors:

� Erroneous Z-R relationship: It is the basic error source that can greatly affects the

final radar estimates. The plot of reflectivity (Z, in dbZ) and rainfall rate (mm/hr) can

be seen in Figure 2-3. It can be seen that the most important differences exist for

higher rainfall intensities and the higher intensities are of importance while dealing

with flood warnings and urban hydrology applications.


11

Figure 2-3: Influence of choice of Z-R relationship on rainfall rates (Einfalt et al., 2004)

� Errors related to the height of the measurements: The errors related to the height of

the measurement might be significant while dealing with areas located at larger

ranges. The height of the radar beam increases with the range increases leading to

following erroneous phenomena:

(1) Evaporation

(2) Growth

(3) Partial beam filling

(4) Overshooting

These four phenomena can be seen schematically in the Figure 2-4 and it is obvious

they can greatly affect the final radar performance.

Figure 2-4: Errors related to height of the measurement (Delobbe, 2007)


12

� Non-uniform vertical profile of reflectivity (VPR): Even at the lowest scan angle, the

radar beam is well above the surface at longer ranges and it has been found that the

reflectivity from all the elevations is non-uniform. It depends on the type of

precipitation as can be seen in Figure 2-5. Presence of a bright band, which leads the

maximum reflectivity, poses another problem. The bright band is a layer of enhanced

radar reflectivity resulting from the difference in the dielectric factor of ice and water

and the aggregation of ice particles as they descend and melt. Gray and Larsen (2004)

observed the need to correct the VPR effect to enhance final radar estimates.

Figure 2-5: Some typical vertical profile of reflectivity (Delobbe, 2007)

Also, radar estimates are based upon a number of working hypotheses and these hypotheses

have to be at least approximately fulfilled to have some reliable estimates on the rainfall rates

(Einfalt et al., 2004). And, because of the inherent hypotheses in radar data measurements,

there is always uncertainty in the final estimates. As far as possible, these uncertainties need

to be quantified. Continued research and use of new technologies might help to reduce these

uncertainties.

2.2.2.4 Radar-gauge merging techniques

It is evident that the strength of radar estimates, to capture spatial information, is the

weakness of gauge records and that the strength of gauge estimates, the ability to capture

rainfall amount at single location, is the radar’s weakness. Hence, merging of both forms of

rainfall information is necessary to obtain better rainfall information. Merging techniques

combine the individual strengths of the two measurement systems. Merging radar and gauge

observations has been a burning topic of research since weather radar is being used in the

early seventies. Different methods have been proposed by different researchers and


13

evaluation of these merging methods has been carried out by different researchers, for

example, Brandes (1975), Wilson and Brandes (1979), Michelson and Koistinen (2000),

Borga (2000), Delobbe et al. (2008) and Goudenhoofdt and Delobbe (2009). Results are more

or less similar. Significant improvements have been observed compared to original radar

estimates. Wilson and Brandes (1979) adjusted radar estimates calculating storm to storm

bias (R/G) and applied it uniformly through out the radar ranges and managed to reduce the

errors up to 30%. They also applied the spatial adjustment (details on Wilson and Brandes,

1979) after utilizing uniform mean field bias correction. Goudenhoofdt and Delobbe (2009)

evaluated a range of merging methods on the data from RMI C-band radar of Wideumont,

Belgium from a simple merging method like mean field bias (MFB) to geospatial merging

methods like kriging, kriging with external drift etc. They concluded that geospatial methods

are better, reducing the mean absolute errors by 40% compared to original radar estimates,

although simple method like MFB reduced the error by 25%. Spatial methods such as

Brandes Spatial Adjustment also performed well reducing the errors as close to the geospatial

methods, which are less tedious and time consuming compared to geospatial methods.

2.3 Hydrological modelling

Hydrological models are simplified, conceptual representations of (a part of) the hydrologic

cycle. They are primarily used for hydrological predictions and for understanding hydrologic

processes. The development and application of hydrological models have evolved greatly

through time. Once the rational method to determine the runoff discharge given rainfall depth

as input is introduced, several concepts to predict and understand the hydrological cycles

have been developed since the 1850’s (Maidment, 1993). The development of the de Saint-

Venant equations for unsteady open channel flow was a boon compounded by the concept of

unit hydrograph to calculate the volume of surface runoff produced by rainfall event. These

inventions led the scope of hydrological modelling to a new height.

Several hydrological models can be found in current time hydrology field as hydrologists try

to develop their new models that suit the local conditions (Berne et al., 2005), which may

operate over different spatial scales and time steps and are developed for various applications.

In literature, the hydrological models are classified in numerous types. It is worth noting that

the classifications based on spatial description (lumped and distributed) and the descriptions

of the physical process (conceptual/empirical and physical) are the most commonly used


14

ones. Spatially distributed models have the potential to represent the effect of spatially

variable inputs while lumped models treat the input in an averaged manner (Arnaud et al.,

2002). The compensation is ease of calibration with expense of detailed information because

calibrating a distributed model is not a straightforward task due to the large number of

parameters involved.

Conceptual models have been widely developed and applied for hydrological modelling because

of the ease on calibrating them. They lump, in a broad sense, the highly complex soil processes

and properties in few macro-scale processes and parameters (Willems, 2000). Most of the

conceptual models have similar structure. The rainfall input (xt) is separated into different

fractions that contribute to the different subflows namely the quick flow (xQF), the slow flow (xSF)

and flow contributing for soil storage (xu). The quick flow can be further separated in the rainfall

portions to overland flow and to interflow. The soil storage plays a role determining the actual

evapotranspiration. After certain routing mechanisms, the total runoff y(t) is sum of the three

runoff components: yOF, yIF and ySF (Willems, 2000). A typical structure of a conceptual model is

shown in Figure 2-6. This is general representation of the processes involved in a typical

conceptual model though the detailed process may vary from one model to another.

Figure 2-6: General lumped conceptual rainfall-runoff model structure (Willems, 2000)

2.3.1 The VHM Model

The VHM (Veralgemeend conceptueel Hydrologisch Model) is a Dutch abbreviation for

generalized lumped conceptual and parsimonious model structure-identification and


15

calibration. It is an approach with which a lumped conceptual rainfall runoff model can be

calibrated in a step wise way. It is developed by Prof. Patrick Willems, Hydraulics

Laboratory, Katholieke Universiteit Leuven, Belgium. The approach aims to derive

parameter values which are as much as possible unique, physical realistic and accurate. It is

data mining based and aims to derive a parsimonious model structure (Willems, 2000).

2.3.1.1 Model structure

The model structure identification and calibration is carried on four distinct ways as can be

seen in Figure 2-7.

Prior time series processing

Step 1a: Reverse river routing

observed river flow series → rainfall-runoff

Step 1b: Subflow separation

→recession constants

→series of overland flow, interflow and slowflow

Step 1c: Split in quick and slow flow events

→event based runoff volumes

Step-wise model-structure identification and calibration

Step 2: Identification and calibration of routing models

→ event-based rainfall fractions to subflows

Step 3: Identification and calibration of soil moisture storage model

→ closing water balance

Step 4: Identification and calibration rainfall fraction to quick and

slow flow events

Figure 2-7: Steps in the VHM structure identification and calibration procedure


16

The step 1 is prior time series processing where a number of prior time series processing

tasks have to be carried out:

� Transformation of the river flow series in a series of lumped rainfall-runoff discharges

(step 1a, Figure 2-7).

� Separation of the rainfall-runoff series in subflow series using a numerical digital

filter. The riverflow series can be either separated into quick flow and the slow flow

(baseflow) or the overland flow, the interflow and the baseflow (step 1b, Figure 2-7).

� Split of the rainfall-runoff series in individual nearly independent peak over threshold

(POT) values. The POTs can be extracted to that of quick flow events and slow flow

events (step 1c, Figure 2-7).

After the prior time series processing, the next step is step-wise model-structure identification and

calibration where lumped representations of different specific rainfall-runoff process equations

are identified and calibrated to related subsets of model parameters. This includes the following

sub-steps:

� Identification and calibration of the routing submodels (step 2, Figure 2-7).

� Identification and calibration of the soil moisture storage submodel where the rain

water fraction fu, the parameter umax (maximum soil moisture content) and uevap (the

threshold moisture content for evapotranspiration is identified (step 3, Figure 2-7).

� Identification and calibration of the submodels describing the rainfall fractions of

quick; fQF (overland and interflow; fOF and fIF) and slow flows; fSF (step 4, Figure 2-

7).

2.3.1.2 Model parameters

The VHM model structure identification and calibration approach deals with the following

parameters related to steps 2 to 4 of the Figure 2-7.

� Recession constant of surface runoff (overland flow): kOF

� Recession constant of interflow: kIF

� Recession constant of baseflow: kBF

� Maximum soil moisture content: umax

� Soil water content at maximum evapotranspiration: uevap

� Surface runoff separation process parameters: aOF,1




17

� Interflow separation process parameters: aIF,1



2.3.1.3 Model calibration

The model parameters are tuned manually as per the information obtained in prior time series

processing. The recession constants of subflows can be adopted as per the values obtained in

step 1b. Optimizing soil storage sub-model parameters can be done by different graphical

plots, for example the plot of fu versus u/umax. The surface and interflow runoff separation

process parameters can be tuned till a good match is observed which can visually be checked

in plots of subflows filter results (overland and interflow) versus model results. This VHM

procedure has clear advantages above an automatic or manual calibration technique, which

most often is based on overall goodness-of-fit statistics optimization. In this approach, when

doing the optimization based on the statistical properties of the model residuals errors for the

different submodels or flow components considered, statistically unbiased sub-model

structures and parameters are derived (Willems, 2000).

2.3.2 The NAM model

NAM is the abbreviation of the Danish "Nedbør-Afstrømnings-Model", meaning

precipitation-runoff-model. This model was originally developed by the Department of

Hydrodynamics and Water Resources at the Technical University of Denmark. The NAM is a

deterministic, lumped and conceptual rainfall-runoff model which simulates the rainfall-

runoff processes occurring at the catchment scale. The NAM is part of the rainfall-runoff

(RR) module of the MIKE 11 River modelling system (DHI, 2004).

2.3.2.1 Model structure

The model structure is shown in Figure 2-8 as adopted from NAM reference manual (DHI,

2004) developed by Danish Hydraulic Institute (DHI). It is an imitation of the land phase of

the hydrological cycle. NAM simulates the rainfall-runoff process by continuously

accounting for the water content in four different and mutually interrelated storages that

represent different physical elements of the catchment. These storages are:

� Snow storage

� Surface storage

� Lower or root zone storage

� Groundwater storage


18

Figure 2-8: The NAM structure

In addition NAM allows treatment of man-made interventions in the hydrological cycle such

as irrigation and groundwater pumping. Based on the meteorological input data NAM

produces catchment runoff as well as information about other elements of the land phase of

the hydrological cycle, such as the temporal variation of the evapotranspiration, soil moisture

content, groundwater recharge, and groundwater levels. The resulting catchment runoff is

split conceptually into overland flow, interflow and baseflow components (DHI, 2004).

2.3.2.2 Model parameters

There are quite a number of model parameters according to the different storage elements

listed below. Detailed information on the parameters can be found in the NAM reference

manual (DHI, 2004). The list of the parameters can be divided in following five subgroups:


19

a. Surface and root zone parameters

� Maximum water content in surface storage [mm]: Umax

� Maximum water content in root zone storage [mm]: Lmax

� Overland flow runoff coefficient [-]: CQOF

� Time constant for interflow [hr]: CKIF

� Time constant for routing interflow and overland flow [hr]: CK12

� Root zone threshold value for overland flow [-]: TOF

� Root zone threshold value for interflow [-]: TIF

b. Ground water parameters

� Baseflow time constant [hr]: CKBF

� Root zone threshold value for groundwater recharge [-]: TG

c. Extended ground water parameters

� Recharge to lower groundwater storage [-]: CQLOW

� Time constant for routing lower baseflow [hr]: CKlow

� Ratio of groundwater catchment to topographical catchment area [-]: Carea

� Maximum groundwater depth causing baseflow [m]: GWLBF0

� Specific yield [-]: SY

� Groundwater depth for unit capillary flux [m]: GWLFL1

d. Snow module parameters

� Degree-day coefficient [mm/ o

C /day]: Csnow

� Base temperature (snow/rain) [oC]: To

� Radiation coefficient [m2/W/mm/day]: Crad

� Rainfall degree-day coefficient [mm/mm/°C/day]: Crain

e. Irrigation module parameters

� Infiltration factor [mm/day]: K0,inf

� Crop coefficients and irrigation losses

2.3.2.3 Model calibration

The process of model calibration is normally done either manually or by using computer-

based automatic procedures including 9 default parameters enlisted above under the

headings; surface, root zone parameters and ground water parameters (DHI, 2004). While

applying the routine for auto-calibration, the following objectives are usually considered:

� A good agreement between the average simulated and observed catchment runoff (i.e.

a good water balance).


20

� A good overall agreement of the shape of the hydrograph.

� A good agreement of the peak flows with respect to timing, rate and volume.

� A good agreement for low flows.

Final tuning is always advised to be done manually which relies on the experience and

knowledge of the modeller, as auto-calibration routines are based on optimizing some

objective function and they are likely to end up in local optimum case rather than global

optimum.

2.4 Significance of spatial variability of rainfall and basin response

The literature on the significance of spatial rainfall for runoff estimation is complex and

sometimes contradictory. Effects can be expected to vary depending on the nature of the

rainfall, the nature of the catchment, the spatial scale of the catchment and the rainfall runoff

model used.

Basin response will obviously vary as rainfall patterns vary. Stratiform and convective

patterns have distinct characteristics on their spatial variability and drop size. In Belgium, the

summer rainfalls are more of convective nature and the winter storms are of stratiform nature.

Many researchers have studied the rainfall-runoff prediction capability of different models

with respect to the type of rainfall. Segond et al. (2007) found a better match between

simulated and observed runoff on winter storm than on summer storms. They concluded that

summer storms have more variability and are less accurate to reproduce flow at the catchment

outlet. Pechlivanidis et al. (2008) reached similar conclusions while testing different rainfall

scenarios on the Upper Lee catchment of UK.

On urbanized catchments, a high proportion of the rainfall becomes effective due to the large

amount of impervious areas. Hence, the effect of spatial rainfall on more urbanised

catchments would obviously be greater. Segond et al. (2007) found that radar estimated

rainfall data are more suitable for stream flow simulation than that from the raingauge

network consisting of one and seven raingauges indicating that the spatial variability of

rainfall is important on urbanised catchments.


21

Arnaud et al. (2002) conducted a study on catchments ranging 20 to 1500 km2 and observed

that the relative error in runoff increases with the size of the catchment while Segond et al.

(2007) showed that as the scale increases, the importance of spatial rainfall decreases because

of the fact that there is a transfer from spatial variability of rainfall to catchment response

time distribution as the dominant factor governing runoff generation which can be regarded

as a dampening effect of the spatial variability of rainfall.

The basin response is essentially dependent on the type of rainfall-runoff model used. Fully

distributed physically based models are believed to better represent the basin characteristics

than the lumped one. But it has always to do with the type of rainfall field used. Radar

rainfall fields, capable of generating more spatial variability, are likely to be more suitable for

distributed models. Shah et al. (1996) conducted a study on a relatively small catchment of

10.55 km2

where they compared the results from a physically distributed SHE (Système

Hydrologique Européen) with the results form a linear transfer function model for spatially

distributed rainfall and found a significant error by using the latter model.

2.5 Similar past studies

Numerous similar past studies can be found in literature and the findings are complex and

sometimes contradictory too.

2.5.1 Radar-gauge comparison and merging

It dates back to the 1980’s that there had already been some study on radar-gauge

comparison. Some notable are:

� Wilson and Brandes (1979) performed a rigorous study on radar-gauge comparison in

an area of over 8000 km2 and found that the R/G ratio varied from 0.41 (radar

underestimate) to 2.41 (radar overestimate). They applied a correction on these data

and managed to reduce the average difference (AD) from 63% to 24%.

� Vieux and Vieux (2005) analysed 60 event samples from Cincinnati, USA for the

purpose of using them in sewer system management and found that for those events,

the agreement between radar and gauge was expected within ± 8% based on the

median average difference between gauge and radar. They also applied a Mean Field

Bias (MFB) correction and found that 60% of the bias factors are expected to fall

between 0.94 and 1.70, where they assume the bias (G/R) would follow a normal

distribution which might not always be the case.


22

� Delobbe et al. (2008) evaluated several radar-gauge merging techniques in the

Walloon region of Belgium using the dense rain gauge network maintained by the

RMI and the RMI-Wideumont radar. The evaluated techniques ranged from simple

MFB adjustment to sophisticated spatial adjustment. They concluded that even simple

adjustment procedures like MFB already improved the original radar estimates

significantly. Results showed that the geo-statistical merging methods sucha as

merging based on kriging are the most effective ones. Similar findings were observed

by Goudenhoofdt and Delobbe (2009) using the same radar data and catchment.

2.5.2 Stream flow simulation using radar data

Accuracy of radar estimated rainfall data for stream flow simulation has been tested by many

researchers. Some notable ones are:

� Berne et al. (2005) tested the hydrological potential of the RMI-Wideumont radar on

the 1597 km2 Ourthe catchment of Belgium using the gauge calibrated HBV-model.

Mean areal average rainfall estimated from the radar was given as input and resulted

in an underestimation of discharge. They ascribed this underestimation to uncertainty

in the final radar estimates and lumped nature of the model.

� Borga (2002) used a conceptual rainfall runoff model to a catchment of 135.3 km2, the

Brue basin in South-West England. He found that model hydrograph predictions

driven by adjusted radar data had similar efficiency (NSE) than the ones obtained

from gauged based rainfall. He got NSE of 0.75 from the former case and 0.83 from

the latter one, meaning a slight underperformance while using the radar estimates.

� Segond et al. (2007) performed an elaborate research on assessing spatial information

requirements of rainfall on the 1400 km2 Lee catchment, UK and found that the gauge

calibrated semi-distributed model called ROBB (details in Laurenson and Mein,

1988) can produce a better match between observed and simulated discharge while

using radar estimated rainfall and they attributed this improvement to the spatial

coverage of rainfall information by the radar.


23

CHAPTER 3: APPLICATION

3.1 Methodology

The methodology mainly consists of two steps. First, the raw radar data of both the LAWR-

Leuven and the RMI-Wideumont are compared with rain gauge data defined by a rain gauge

network of 12 rain gauges as shown in Figure 3-2. Different merging techniques are tested to

increase the accuracy of the final radar estimates. Secondly, the corrected radar data will be

used for modelling of a catchment using two types of lumped conceptual models, namely the

NAM and the VHM. Significance of spatial representation of rainfall is also evaluated

through the basin response.

3.2 Study area

The study area is situated in the Flanders region of Belgium, near the densely populated city

of Leuven. The study area is within 15 km radius of the LAWR-Leuven. The rain gauge

network comprises of 12 rain gauges, most of them towards the north-west direction with

respect to the LAWR-Leuven and within 10 km from the LAWR-Leuven. The entire rain

gauge network lies in between 117 and 128 km from the RMI-Wideumont, in north-west

direction. The catchment is situated south/south-east of the LAWR-Leuven and north/north-

west of the RMI radar of Wideumont as can be seen in Figure 3.1. Two of the twelve

raingauges are located in the catchment. More descriptions on the raingauge network can be

found under the section of 3.3.1. For the catchment, the description is presented under the

section 3.4.1. The study area with the radar location, the catchment and the raingauge

network can be seen in Figure 3.2.


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Figure 3-1: Belgium (light green), the RMI-Wideumont radar (black star), the LAWR-Leuven (red

star) and the catchment (dark green). Black arcs indicate the distance to the RMI-Wideumont, with

an increment of 60 km. The red circle shows 15 distance to the LAWR-Leuven

Figure 3-2: The study area with the location of 12 gauges (red dots: Aquafin &VMM; black

triangles: RMI), the LAWR (yellow star), catchment (dark green polygon) and part of the Walloon

region (light green polygon). Circles indicate the distance to the LAWR, with increment of 5 km


25

3.3 Radar-gauge comparison and merging

3.3.1 The raingauge network

Comparing radar estimated rainfall essentially requires ground “truth” data which is assumed

to be correctly represented by the raingauge network. For our purpose, the network of 12

raingauges is used; 4 of them being operated by Aquafin, 5 by the Flemish Environmental

Agency (VMM) and the other 3 by the RMI of Belgium. The Aquafin raingauges are TBRs

having a gauge resolution of 0.2 mm and a time resolution of 2 minutes. The VMM

raingauges are also TBRs having a gauge resolution of 0.2 mm and a time resolution of 10

minutes. The RMI maintains quite a dense network of non-recording raingauges giving daily

precipitation accumulations between 8 AM and 8 AM Local Time (LT). The network with

the position of the LAWR-Leuven as well as the watershed is shown in Figure 3-2.

3.3.2 Correcting raingauge measurements

As already stated, raingauge data will be used as reference and will be considered as ground

truth data. Goormans and Willems (2008) conducted full dynamic calibration on these

Aquafin and VMM raingauges for the purpose of calibrating the LAWR. Local wind shelter

influences on these TBRs were also investigated and it was found that both sets of TBRs

clearly underestimated rainfall compared to the standard non-recording RMI gauge of Herent.

Long term underestimations up to 24% (corresponding to correction factor of 1.321) were

found. To correct this systematic underestimation, the study proposed a correction factor ‘k’

based on the minimization of the sum of squared differences between cumulative daily RMI

and TBR rainfall series, as presented in Table 3-1.

Table 3-1: Correction Factors [k] for the Aquafin and VMM raingauges

Operator RG Location Correction Factor, k [-]

Aquafin

RWZI Kessel-Lo 1.321

Keulenstraat 1.121

Hoge Beekstraat 1.157

Warotstraat 1.158

VMM

Derijcklaan 1.157

Oudstrijderslaan 1.158

Eenmeilaan 1.143

Brouwersstraat 1.252

Weggevoerdenstraat 1.237


26

3.3.3 Conversion of radar records to rainfall rates

As already depicted, the C-Band radar measures reflectivity (Z) values, as representative for

rain droplets in a certain volume. This Z-value is converted to rainfall rate, R with a Z-R

relationship of the form: Z = aRb. The RMI-Wideumont radar uses values of a and b equal to

200 and 1.6 respectively. The radar is fitted with a linear receiver.

Unlike the C-Band radar, the X-band LAWR-Leuven has a logarithmic receiver and records

the number of counts (a dimensionless measure for the amount of reflected power) as

representative value of rainfall. A relationship between the count and the rainfall rate

recorded at ground level has to be established for conversion. The conversion factor can be

termed as Calibration Factor (CF). As the LAWR is relatively new giving records from July 2

2008 and onwards, and research is ongoing to have optimal CF values, the presented CF

factors in Table 3-2 can be considered as the best estimates currently available. These

calibration factors are the result of a regression analysis, based on the storm average

intensities and measured counts in the corresponding radar pixels of the period 2nd

July- 8th

October 2008 (Block-1, Table 3-4), which can be considered as a summer period. The

intensities are from calibrated raingauge data, and also corrected for the systematic bias due

to local wind effects, the ‘k’ factors as presented in Table 3-1.

Table 3-2: Calibration Factor [CF] for Aquafin and VMM raingauges

Operator RG Location Calibration Factor,

CF [(mm/hr)/(counts/min)]

Aquafin

RWZI Kessel-Lo 0.0600

Keulenstraat 0.1131

Hoge Beekstraat 0.0934

VMM

Derijcklaan 0.0421

Oudstrijderslaan 0.0615

Eenmeilaan 0.0531

Weggevoerdenstraat 0.1601

Average 0.0833


27

3.3.4 Data periods

Owing to the rainfall pattern in Belgium, the comparison study is distinguished into two

periods namely summer storm and winter storm periods. Convective rainfall is encountered

in most of the summer storm cases and stratiform rainfall in both summer and winter periods.

For the data of RMI-Wideumont, a collaboration is reached between the RMI and the

Hydraulics Division of the Katholieke Universiteit Leuven and data of some interesting storm

periods are made available. These periods are named week 1 to week 4 as presented in Table

3-3, weeks 1 and 2 being that of a summer period and weeks 3 and 4 that of a winter period.

The data is hourly accumulation rainfall (mm), the binary file 600x600 with data coded in

single precision float. Matlab algorithms are developed to read, filter and extract the data.

Table 3-3: Data periods of the RMI radar of Wideumont

Week Data Periods

1 July 2, 2008 to July 12, 2008

2 August 3, 2008 to August 13, 2008

3 January 17, 2009 to January 23, 2009

4 February 9, 2009 to February 17, 2009

The data extracted from the LAWR-Leuven are counts with time resolution of one minute in

240x240 grids each measuring 125 m by 125 m. The data can be divided on the three periods

as per the setting of signal processing parameter of the LAWR as presented in Table 3-4. For

block 3, the parameters of signal processing were set to neutral; hence these periods are not

taken into consideration. For the LAWR-gauge comparison, the summer period considered

spans from July 2 2008 to September 30 2008, and the winter period from December 1 2008

to March 31 2009. As the CF values presented on Table 3-2 are the result of analysis made on

block 1 (summer period), the work is sought to see performance of these CFs on block 2

(winter period).

Table 3-4: Data periods of the LAWR of Leuven

Block Data Periods

1 July 2, 2008 to October 8 , 2008

2 October 9 to October 31, 2008 & December 1, 2008 to till now

3 November 1, 2008 to November 30, 2008 (parameters are set to neutral)


28

3.3.5 LAWR - gauge comparison and merging

The first attempt is to use a constant CF value for all radar pixels. This procedure does not

account for the range dependency of the CF values. The results will be compared with the

case where range dependent CF-values are applied. The range dependent adjustment on CF

values is essential to some extent because of ever increasing height of measurement, beam

broadening and attenuation effect. Goudenhoofdt and Delobbe (2009) accounted for a range

dependency of the RMI-Wideumont using a second order polynomial with R/G expressed in

log scale. The same adjustment procedure will be the first trial with R/G (CF) expressed in

linear scale followed by power function as well.

After applying the range dependent CF values (to obtain rainfall rate values), the Mean Field

Bias (MFB) adjustment is applied. In MFB adjustment, it is assumed that the radar estimates

are affected by a uniform multiplicative factor. The factor is determined by gauge-radar

agreement after integration over a space-time window. Although it is a simple adjustment

technique; it can already enhance the quality of rainfall estimate significantly. Goudenhoofdt

and Delobbe (2009) found that the MFB correction reduced the error by 25% compared to

raw radar data. Similar improvements have been observed by Borga (2002). The MFB is

given by:

MFB = ∑∑

=i

ii

R

G

NN

F 1 (5)

With,

N= Number of valid radar-gauge pairs.

Gi, Ri = gauge and radar daily accumulated values associated with gauge i.

The concept of implementing MFB adjustment on the daily accumulated basis rather than

real-time fashion is to avoid additional uncertainty due to time and space mismatching of the

radar and gauge samples at shorter time intervals.

If both daily raingauge accumulation and radar accumulations are greater than 1 mm then

these were considered as “valid pairs”. This ensures that the same data set is used for

comparison. Different authors have used different threshold values for their study.

Goudenhoofdt and Delobbe (2009) used a threshold value of 1 mm; the same threshold value

was taken by Delobbe et al. (2008) on daily time scale basis. A threshold value of 0.5 mm


29

was used by Borga (2002). Germann et al. (2006) used 0.3 mm for the evaluation of radar

precipitation estimates in Swiss mountains. Wilson and Brandes (1979) stated, citing their

previous experiences, that if the gauge rainfall is light (<2 mm), it is best not used in an

adjustment procedure. By this, they advised using a threshold value no less than 2 mm on

daily accumulation. For all purposes, the average counts over 9 radar pixels surrounding the

gauge location is used so as to limit the effect of wind drift which can be very significant

(Lack and Fox, 2007). The number of valid pairs influences the index of statistical

parameters. A low threshold value would result in a significant amplification of some of the

statistical parameters, such as the MFB. For example, for gauge and radar pairs of 2 mm and

0.2 mm respectively, MFB will be 10 and this distorts the mean MFB. Applying a threshold

value will exclude such pairs and will counter the problem to some extent.

Also, arithmetic averaging of individual bias to get the MFB value, as suggested by (5),

requires these individual values to follow a normal distribution which is rather unlikely. After

all, the bias is the ratio of the gauge to radar estimates and can be considered as a product of

two stochastic variables, and this always tends to follow a lognormal distribution. Hence, the

distribution of the bias is checked by fitting theoretical distributions (normal, log-normal,

exponential etc.) over the empirical (observed) distribution. The empirical distribution can be

calculated by using one of the most used formulas, the distribution of Hazen (1930), and is

given by:

Probability of exceedance =n

r )5.0( − (6)

Cumulative probability = 1 - (Probability of exceedance) = n

rn )5.0( +− (7)

With,

r = rank number of current value in the data set.

n = total number of values in the data set.

In case the individual bias follows a lognormal distribution, equation (5) can be modified as:

MFB =

∑

∑

= i

ii

R

G

NN

F

eelog

1)log(

(8)

With,

N= Number of valid radar-gauge pairs.

Gi, Ri = gauge and radar daily accumulated values associated with gauge i.


30

It should be noted that the MFB adjustment is applied uniformly over the entire radar range

using a single factor. The MFB attempts to minimize the bias between the gauge and radar

estimates uniformly. The smoothed radar field is then subjected to an additional adjustment,

the Brandes spatial adjustment, hereafter referred to as BRA. The main idea is to use the

correction factors from rain gauge sites to each radar grid (Brandes, 1975). The rain gauges

which are closer to a grid point take higher weight and those lying further take lower weights.

The weight (wi) applied to each gauge calibrated bias (Gi/Ri) for a particular grid point is

given by:

−=

k

dwi

2

exp (9)

With,

d = distance between the gauge and the grid point in km.

k = a factor controlling the degree of smoothening and is generally given as an inverse of

mean gauge density (number of gauges divided by total area), denoted by ‘δ’. This is

calculated using a formula used by Goudenhoofdt and Delobbe (2009), and is given by:

k = (2 δ)-1

(10)

For a network consisting of ‘N’ raingauges, the Brandes spatial adjustment then can be given

by:

∑

∑

=

==N

i

i

N

i

iii

BRA

w

RGw

C

1

1

)/(

(11)

With,

CBRA = Brandes spatial adjustment factor.

In order to evaluate the improvements achieved by each adjustment procedures, comparison

on some goodness-of-fit statistics is made before and after adjustment. Several of these

parameters are found in literature. However, the Root Mean Square Error, Mean Absolute

Error, Relative Fractional Bias and Nash Criterion are used in this study.

The Root Mean Square Error (RMSE) is one of the most common parameter for verification

studies and is given by:


31

N

GR

RMSE

N

i

ii∑=

−

= 1

2)(

(12)

With,

Ri, Gi = radar and gauge valid pair values.

N = number of valid pairs.

The Mean Absolute Error (MAE) is another parameter used for goodness of fit statistics and

is given by:

N

GR

MAE

N

i

ii∑=

−

= 1

)(

(13)

With,


N = number of valid pairs.

Similarly, the Relative Fractional Bias (RFB) accounts for the bias of radar estimated to

gauge value in a relative manner. It is similar to the term Average Difference (AD) used by

some researchers (e.g. Vieux and Vieux, (2005), Wilson and Brandes (1979) etc.) where they

used absolute values and expressed them in percentage. It is given by:

i

ii

G

GRRFB

−= (14)

With,


However the RFB is sensitive to small values. For example, if the radar estimate for a gauge

value of 0.5 mm is 1.0 mm, then the RFB will be 100% though the absolute difference on the

pair is only 0.5 mm. Hence, the RFB is calculated with cumulative rainfall volumes.

The Nash Criterion evaluated through the Nash-Sutcliff Efficiency (NSE), is usually used to

assess the predictive power of hydrological models (Nash et al., 1970), but adapted for this

case as;


32

∑

∑

−

−

=

−

−

−=n

i

i

n

i

ii

GG

RG

E

1

2

1

2

)(

)(

1 (15)

With,

E = Nash Criterion value.

Gi, Ri = instantaneous gauge and radar values.

The rainfall events can be assumed fairly independent to each-other and hence the Nash

Criterion can be used to evaluate how well radar estimates match with gauge values.

3.3.6 RMI Wideumont estimates and gauge comparison and merging

Regarding the data of the RMI-Wideumont, rainfall volumes can be directly extracted. A

threshold value of 1 mm is taken for this case as well. Similar goodness-of-fit statistics

(Equations 12 to 15) are used to evaluate the accuracy of the radar data. The raw radar

estimates are smoothed by firstly applying the MFB and then the BRA adjustment. While

doing so, weeks 1 and 2 have been merged in to one period, as they are both summer periods,

and same for the weeks 3 and 4, both being winter periods.


3.4.1 The catchment

3.4.1.1 Choice of catchment

Several criteria influence the selection of a suitable watershed for radar hydrology research.

The most obvious requirements are complete areal coverage of the catchment by the radar,

and the availability of stream gauge data. For this case, the choice of the catchment is limited

by the fact that the LAWR of Leuven is capable of giving quantitative estimates up to a

radius of 15 km only. Another fact associated with LAWR is that the Zaventem airport

authorities do not allow transmission in the sector indicated by the light blue sector in Figure

3-3. Due to these constraints the catchment named Molenbeek/Parkbeek, having area of

48.17 km2, has been selected. This choice is also favoured by the absence of heavy clutters as

can be seen from the study of Goormans et al. (2008). The catchment contains two rain

gauges; one is operated by the RMI (Korbeek-Lo) and the other by the VMM (Derijcklaan).

The selected catchment falls within 240 km range of RMI radar of Wideumont. The

catchment, along with raingauges, the LAWR and water courses, is shown in Figure 3-4.


33

Figure 3-3: Catchment under consideration with position of LAWR (star), radar beam blockage

sector (blue shade), rain gauges (dots-the VMM and Aquafin TBRs; triangles-the RMI non-

recording gauges), water courses (blue lines) and circles - distances of 5, 10 and 15 km from the

LAWR

3.4.1.2 Catchment geomorphology

The catchment has a temperate climate, is relatively flat, primarily composed of sandy soils

with high hydraulic conductivity, and hence intensively drained. The Digital Elevation Model

(DEM) of the catchment is shown in Figure 3-4. The elevation ranges from 22 m to 117 m

above mean sea level, with a mean elevation of 59.19 m. Almost 90% of the area has an

elevation less than 78 m. The land use of the catchment is dominated by agricultural land.

Around 53% of the area is used for agricultural activities, 33% of the area has a mixed type

of forest, 13% of the area is urbanised and less than 1% consists of water bodies. Primarily,

the soil types of the catchment can be classified into three groups, namely sand, land-dune

and clay. The sandy soil is the dominant one as it covers almost 70% of the area. Around

28% of the area is covered by land-dune and the remaining 2% by clay.


34

The catchment experiences around 800 mm of yearly precipitation, which is evenly

distributed throughout the winter and summer months. The average daily temperature ranges

from 4 degrees centigrade in winter to 22 degrees centigrade in summer. These data are based

on the data available on the HydroNet (2009) website (www.hydronet.be).

Figure 3-4: The DEM map of catchment with stream network

3.4.1.3 Input meteorological series

Both the VHM and the NAM require rainfall, temperature, potential evapotranspiration and

observed discharge series as input. The rainfall series are obtained through the raingauge

network of the VMM and RMI as one VMM rain gauges. Their weight is calculated using the

Thiessen Polygon method. As the VMM rain gauge’s time resolution is 10 minutes, the data

are aggregated to the hourly aggregation level and corrected with the ‘k’ factor as presented

in Table 3-1. The RMI rain gauge produces only daily rainfall series from 8 AM to 8 AM

local time hence this series is converted to hourly series using its nearest neighbouring station

applying a correction factor for daily accumulated rainfall volume. In doing so, the VMM

rain gauge Derijcklaan is taken as the neighbouring station and its temporal variation is

considered and corrected by a factor. The factor is obtained by dividing the daily

accumulated rainfall volume of the Korbeek-Lo to the Derijcklaan.


35

The daily maximum and minimum temperature series are obtained from HydroNet website

(www.hydronet.be) for station with station number HIS_M08_045, Heverlee/Molenbeek

having X and Y coordinates of 173868 m and 172838 m respectively. The potential

evapotranspiration (ETo) is calculated using the Penman Monteith method. This method

allows calculating ETo even if only maximum and minimum temperature data are available

(Allen et al. 1998). The hourly observed discharge series are also obtained from the

HydroNet website.

3.4.2 Catchment modelling with VHM

The VHM model parameter set for this catchment has already been derived by Prof. P.

Willems of the Hydraulics Laboratory, Katholieke Universiteit Leuven, Belgium. The same

set of parameters with minor adjustments is tested for the studied period of September 2003

to December 2009. The simulated values for the first three months are discarded in order to

eliminate the influence of erroneous initial conditions.

Prior time series processing tasks have been carried out except the step-1a (Figure 2-7) as no

detailed river hydrodynamic model for this catchment is available. Hence, the observed

discharge series is used as the rainfall-runoff series, though this assumption will lead to some

discrepancies. After all, the flow observed at the river flow gauging station is the cumulated

result of the runoff entering the river network upstream of the flow gauging station, which is

further affected by flow attenuation along the river network. By the spatial variability in the

runoff and the river network hydrodynamics, the flow observed at the river gauging station

will probably differ from the rainfall-runoff spatially averaged over the river network

upstream of the gauging station. This effect is often neglected in current rainfall-runoff

modelling. Hence, reverse routing (derivation of rainfall-runoff serries from observed

discharge) should be done (Willems, 2000). But this requires detailed hydrodynamic

modelling. It has been seen in some studies that the flow attenuation could be neglected in

low flows but above the bank-full stage, river flooding strongly affects the runoff series, for

example in the study of the Molenbeek brook subcatchment in the Dender basin in Belgium

(Willems, 2000).

The other two steps (step-1b and step-1c; Figure 2-7) of the prior time series processing tasks

are performed in Water Engineering Time Series Processing Tool (WETSPRO). The

WETSPRO software is developed by Prof. P. Willems of the Hydraulics Laboratory,


36

Katholieke Universiteit Leuven, Belgium. It is a time series processing tool that allows the

users to conduct:

� Sub-flow filtering.

� Peak flow selection and related hydrograph separation; for quick flow and slow flow

periods and related low flow selection.

� Construction of the different model evaluation plots.

The tool makes use of a continuous time series of any hydrological variable as input

(Willems, 2009) and if model performance evaluation is to be carried out, the model results

also form a part of input.

3.4.3 Catchment modelling with NAM

The calibration period is selected from January 1 2006 to February 28 2009. Validation of the

calibrated parameter is made in another independent period from September 10 2003 to

December 31 2005. Calibration is done using both manual and auto-calibration option

available in the NAM software because both the manual and auto-calibration have their own

advantages and disadvantages. Given the advantages and disadvantages of both procedures,

combined use of the two would be most beneficial (Willems, 2009). Good estimation of

routing constant values for sub-flows is made using the WETSPRO tool. Initial conditions are

set according to the guidelines in the reference manual of the NAM software. The simulated

values for the first three months are discarded in order to eliminate the influence of erroneous

initial conditions.

3.4.4 Performance evaluation of the model results

The performance evaluation of the model results is accessed using both the basic goodness-

of-fit statistics supported by graphical tools following the procedure described by Willems

(2009). The use of both goodness-of-fit statistics and graphical goodness-of-fit plots is due to

the fact that these goodness-of-fit statics summarise the performance evaluation information

only in few numbers and values which are difficult and misleading to interpret. The basic

goodness-of-fit statistics used for model performance evaluation are Mean squared error

(MSE) and Nash Sutcliffe efficeinecy (Nash and Sutcliffe., 1970) and are given as:

[ ]

n

iQiQ

MSE

n

i

om∑=

−

= 1

2)()(

(16)


37

[ ]

[ ]

−=

−

−

−=

∑

∑

=

=

2

1

2

1

2

1

)(

)()(

1

oQ

n

i

oo

n

i

om

S

MSE

QiQ

iQiQ

NSE (17)

with,

)(iQo and )(iQm = the observed and modelled river discharge, respectively.

i = the number of observations (1, n) and,

oQ and 2

oQS = the mean and variance of observed discharge series.

The performance evaluation is performed by using a number of sequential time series

processing tasks in the WETSPRO tool. Sub-flows separation, splitting the river flow series

in nearly independent quick and slow flow hydrograph periods, and the extraction of (nearly)

independent peak and low flows are performed to have a more unbiased model performance

evaluation overcoming the problem of serial dependence, which is mostly overlooked in

current rainfall-runoff calibration applications (Willems, 2009). Also, the model residuals

(difference between flow observation and model result) typically increases with higher flows

meaning that model residual variance typically increases with increasing flow, a phenomenon

called heteroscedasticity. This heteroscedasticity has to be addressed by applying any suitable

transformation. The Box-Cox (BC) transformation (Box and Cox, 1964) is very flexible since

it only one parameter. Therefore, it is used in this study. The transformation is given by:

λ

λ 1)(

−=

qqBC (18)

With,

q = the variable taken into consideration (flow series in this case)

λ = parameter of BC-transformation that needs to be calibrated to have homoscedasticity the

model residuals.

The following graphical plots are used to complement the above mentioned goodness-of-fit

statistics (Equations (16) and (17)):

� Scatter-plot for peak flow maxima.

� Scatter-plot for low flow minima.

� Comparison of cumulative volumes

� Extreme value distribution of peak flow maxima

� Extreme value distribution of low flow minima


38

3.4.5 The significance of spatial data

3.4.5.1 Quantifying rainfall variability

In this study, the rainfall derived from the rain gauge network was perceived as more robust

and hence considered as reference rainfall (Pref) to be used as input for the calibration

process. Using Thiessen-polygon method, it was found that 75.94 % of weight can be given

to the rainfall station named Korbeek-Lo and the remaining 24.06% to the rainfall station

named Derijcklaan. With these weights, a weighted average rainfall is calculated. The

following alternative rainfall inputs are tested to quantify the rainfall variability.

� Single rain gauge for the entire catchment and hence uniform rainfall over the

catchment (RG1). For this, the RMI raingauge named Korbeek-Lo is used as it is

almost in the centroid of the catchment.

� Rainfall data derived from the X-band LAWR of Leuven. Accumulated rainfall depth

over one hour is used for this purpose. Altogether 3085 LAWR pixels covered the

catchment and their weight is calculated using the Thiessen-polygon method and the

total weighted average rainfall is used.

� Rainfall data derived from the RMI-Wideumont radar. It was found that 136 RMI-

Wideumont pixels covered the whole catchment. Their weight is calculated using the

Thiessen-polygon method and the total weighted average rainfall is used.

To see the distinct effect of the significance of rainfall spatial variability, 4 storms were

selected in accordance to the available data and the total rainfall volume over the storm

periods as shown in Table 3-5.

Table 3-5: Selected storm events; LT means Local Time

Storm

Events

Start [LT] End [LT] Duration Pref

[mm/dd/yy HH:MM] [mm/dd/yy HH:MM] [h] [mm]

3-Aug-08 8/3/08 19:00 8/4/08 2:00 8 30.7

5-Dec-08 12/5/08 14:00 12/5/08 20:00 7 7.80

22-Jan-09 1/22/09 12:00 1/23/09 19:00 32 30.4

9-Feb-09 2/9/09 16:00 2/10/09 23:00 32 27.2

The Reference Spatial Deviation Index (SDIR) can now be defined for each storm. The SDIR

is an index that compares the rainfall spatial deviation between the areal estimates from the


39

tested rainfall representation to the reference areal precipitation estimates (Segond et al.,

2007) and is given by:

r

ri

P

PPSDIR

−= (19)

With,

Pi = areal precipitation from either radar or subset of the gauges in mm.

Pr = reference areal precipitation in mm.

The use of only one rain gauge located at the centroid of the catchment can be regarded as a

degradation of the spatial representation of rainfall and hence a higher SDIR value is

expected. Radar estimated rainfall improves the spatial representation and a lower SDIR is

expected, compared to the one-gauge situation. However, by definition, the SDIR evaluates

the deviation from Pref and Pref for this study case is defined by only 2 raingauges. So, Pref

itself might not represent actual areal average rainfall adequately, although it is assumed that

it is the most robust estimate of areal rainfall available. Hence, a range of SDIR values can be

expected for the radar estimated rainfall values too, especially when considering the various

errors in radar rainfall measurements. The LAWR-Leuven radar should cover better spatial

coverage as it has a finer resolution than RMI-Wideumont radar. Hence, it is expected that

the LAWR-Leuven should give lower SDIR compared to the RMI-Wideumont.

3.4.5.2 Basin response

After quantifying the rainfall variability for different storms, their basin response is analysed.

The basin response for all the above stated rainfall input is analysed using the same model

parameter sets derived from the calibration using Pref. The NSE value (defined as in Equation

(17)), denoted by NSEobs, can be calculated with reference to the observed discharge series to

see the simulating capability of different rainfall descriptors. It is expected that NSE will

degrade for RG1, and improve for the radar estimated rainfall.

The simulated flow driven by the reference rainfall (Pref) is referred to as the reference flow.

The difference between the reference flow and flow driven by an alternative rainfall

descriptor is the relative error induced due to the tested alternative rainfall keeping model

parameter uncertainty the same. A modified definition of NSE is introduced at this stage to


40

measure the performance of the simulated runoff in comparison to reference flow as used by

(Segond et al., 2007) and is given as:

∑

∑

=

=

−

−

−=N

i

i

N

i

ii

ref

RR

RC

NSE

1

2

1

2

)(

)(

1 (20)

With,

Ci, Ri = calculated and reference discharge at ith

hour

R = mean value of reference discharge

N= number of data set.

Both the NSEobs and NSEref will be defined for the NAM as well as the VHM. These

indicators will lead us to conclude and understand the importance of spatial variability of

rainfall data. The latter indicator enhances the opportunity of testing the rainfall descriptors

making the parameter uncertainty the same for each model.


41

CHAPTER 4: RESULTS AND DISCUSSION

4.1 LAWR estimates − gauge comparison and merging

4.1.1 Using an average value of CF

Using an average value of CF shows a significant fluctuation on the radar and gauge values

for cumulative rainfall volumes for summer periods. The RFB ranges form +1.25 (125%

overestimation) to -0.57 (57% underestimation) as can be depicted from Figure 4-1. A

similar trend can be observed for winter periods (+0.78 to -0.40). As can be seen, the RFB

for the RMI gauges (indicated by circles) − which were not used to derive the CF values −

are systematically under the zero RFB line (dotted horizontal line), meaning a systematic

underestimation by the LAWR which increases as the range increases. A similar trend can

also be observed for other rain gauge stations as well.

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 2.5 5.0 7.5 10.0

RF

B [

-]

Range, r from LAWR [km]

SUMMER [Aquafin+VMM] WINTER [Aquafin+VMM]

SUMMER [KMI] WINTER [KMI]

Figure 4-1: Evolution of RFB with range (using constant CF on the LAWR estimates)

It is therefore easy to understand that there exists some kind of range dependency on CF

values and hence on the radar estimated rainfall values. So, a single averaged value of CF is

not sufficient to convert the “counts” to rainfall estimates. It is clear that the radar tends to

overestimate rainfall in those pixels which are closely located to the LAWR and to

underestimate rainfall in those pixels which are further away.


42

4.1.2 Range dependent adjustment on CF

A second degree polynomial fit (CF = 0.0006 r2 + 0.015r + 0.0159, R

² = 0.6891; r = range

from the LAWR in km) for the CF strongly increses with range, especially for higher ranges,

as depicted by Figure 4-2. This results in a serious overestimation of the radar estimates for

far-away pixels. For example, the RFB was +0.36 (36% overestimation) for the RMI rain

gauge located at Leefdaal (range: 9.5 km) for summer storms. But this fit showed quite a

good match for nearby pixels, with a RFB of 0.0034 (0.34%) on the RMI rain gauge station at

Korbeek-Lo. This shows that using only a second degree polynomial fit for the CF is not

appropriate for the range dependent adjustment on CF.

Hence, a power function [CF = 0.0272 r 0.8226

, R² = 0.8038] is applied which produces quite

good results reducing overall RFB to nearly 6%. The choice of the power function is well

supported by higher R2

value as well. The problem associated with using the power function

for range dependent adjustment is that when range is equal to 0 (at the pixels very close to the

LAWR), the CF will be zero which is unrealistic. But from Figure 4-2, it is clear that for

lower ranges, the second degree polynomial function and the power function are matching

very well. Therefore, the second degree polynomial function is used for ranges less than 1.5

km. Hence, a combination of both functions is used for the range dependent adjustment on

CF.

y = 0.0006x2 + 0.015x + 0.0159R² = 0.6891

y = 0.0272x0.8226

R² = 0.8038

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

1 3 5 7 9 11 13 15

CF

[(m

m/ h

r) /

(co

un

ts /

min

)]

Distance from Radar , r [km]

Figure 4-2: Plot of CF as a function of distance to the LAWR, each point representing a TBR

(Aquafin &VMM)


43

The advantage of a range dependent adjustment on the radar estimates is clear. Prior to this

adjustment, the RFB showed a quite significant variation: overestimation for nearby pixels

and underestimation for far-away ones. After applying the range dependent adjustment on

CF, the fluctuation is limited as can be seen from Figure 4-3. The total RFB for the summer

periods was decreased to -0.06 (-6 %) and mean RFB for the winter storms was about +0.07

(+7%). The interesting thing to be noted is that the RFB shows no trend of either

overestimation or underestimation as the range increases.

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 2.5 5.0 7.5 10.0

RF

B [

-]

Range, r from LAWR [km]

SUMMER [Aquafin+VMM] WINTER [Aquafin+VMM]

SUMMER [KMI] WINTER[KMI]

Figure 4-3: Evolution of RFB with range (using range dependent CF on the LAWR-Leuven

estimates)

4.1.3 Statistical analysis on range dependent adjustment

Some goodness-of-fit statistics are presented in Table 4-1 which validates the idea of using

range dependent adjustment on the CF. Altogether 187 valid pairs for the summer period and

240 pairs for the winter period were analyzed for the constant CF case. And, for the range

adjusted CF case, 197 and 254 valid pairs were analysed respectively for the summer and

winter period.

Using constant CF, the resulted radar estimates are not in accordance to the ground “truth” as

indicated by the low NSE value of 0.47 for the summer period. The case is even below par


44

for the winter period where the Nash Criterion is negative. After the range dependent

adjustment on CF, the statistics improved significantly. The Nash Criterion increases to 0.67

for the summer period. For the winter period, the Nash Criterion increases to 0.42, which is

of course positive compared with the constant CF case but still not promising.

Table 4-1: Some statistical parameter values before and after range dependent adjustment on the

LAWR estimates.

Statistical SUMMER WINTER

Indicators constant CF range adjusted CF constant CF range adjusted CF

Valid Pairs [-] 187 197 240 254

RMSE [mm] 4.12 3.21 5.99 3.86

MAE [mm] 2.76 2.14 3.55 2.63

Nash Criterion [-] 0.47 0.67 -0.53 0.42

Improvement on RMSE and MAE values also favours the adjustment. The RMSE for the

summer period improves from 4.12 mm to 3.21 mm and for the winter period from 5.99 mm

to 3.86 mm. For MAE, a similar trend can be observed.

All the statistics show that the LAWR has low performance in the winter period. This low

performance may be due to precipitation forms, for example snow. For snow-fall, the rain

gauge shows the record after it melts but the radar has already detected it. Hence, there exists

significant time lag for these two records. But it is also to be noted that making use of valid

pairs will solve this problem, at least partially. The low performance could also be explained

because of non-uniform vertical profiles of reflectivity (VPR). For the stratiform storms,

presence of a bright band will lead to higher reflectivity and hence a non-uniform VPR

subsequently, resulting in erroneous precipitation estimates.

Figure 4-4 presents a scatter plot of radar and gauge readings (both TBRs & RMI) for the

summer periods before and after the range dependent adjustment on CF. It can be seen that

the scatter is minimized after the correction, as indicated by the change in slope of the linear

regression lines for each case. The slope improves to from 0.85 to 0.90 after applying the

range dependent adjustment on CF.


45

y = 0.85x

y = 0.90x

0

10

20

30

40

50

60

0 10 20 30 40 50 60

LA

WR

[mm

]

Gauge [mm]

Using constant CF

Using range dependency corrected CF

1:1 Line

Figure 4-4: Scatter plot of daily accumulated radar-gauge valid pairs for summer storm using

constant value of CF and CF after range dependent adjustment on the LAWR-Leuven estimates

Although adjusting the CF with range improves the radar estimated rainfall to a great extent,

there are still some discrepancies on the overall RFB (Figure 4-3) as well as on cumulative

rainfall depths for both periods as can be seen from the Figure 4-5.

As can be seen from Figure 4-5, more scattering can be observed for the winter period than

for the summer period. In the winter period, a quite significant overestimation of the radar

estimated cumulative rainfall volume can be observed for some rain gauges as also seen in

the RFB plot, Figure 4-3. For the summer period, the points are consistently on the 1:1 line

and no serious under − or overestimations are present. The three low cumulative volume plots

for the summer period are due to the fact that three VMM rain gauge stations (Derijcklaan,

Oudstrijderslaan and Weggevoerdenstraat) were out of order for the entire month of July and

August and the cumulative volume plot is for the month of September alone. The scatter

although is expected to be minimised as subsequent merging methods have been incorporated

to the radar estimates.


46

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Rad

ar E

stim

ated

[m

m]

Gauge Recorded [mm]

Summer StormWinter Storm1:1 Line

Figure 4-5: Cumulative rainfall plot of radar and gauge records for the winter and summer periods

of the LAWR estimates after range dependent correction on CF

4.1.4 Mean field bias adjustment

Figure 4-6 shows the frequency distribution of the bias for both summer and winter period.

And, as expected, a high frequency occurs around unit bias. For the summer period, highest

frequency is in between the bias class of 0.75-1, for the winter period the highest frequency is

between the bias class of 0.5-0.75 indicating slight overestimation of the radar estimates.

Overall, more than 75% is in between 0.75-1.25 which is positive as far as radar’s capability

on quantitative precipitation estimation concerns.

Figure 4-7 shows the probability distribution of the field bias calculated for all valid pairs.

The field bias based on the summer period agrees well with the expected lognormal

distribution even for higher biases. The winter period shows a small deviation from the

theoretical distribution. The bias values for the winter period are consistently below the

theoretical lognormal distribution line for low biases and above the theoretical distribution

line for some higher bias values.

The MFB for the whole summer and winter period was found to be 1.015 and 0.974

respectively and are calculated as per Equation (8) for the lognormal distribution. An upper

and lower limit for the 90%-confidence interval of the bias has been calculated for both


47

periods. It can be stated that the real MFB adjustment factor for the summer period lies in

between 0.953 to 1.076 with high probability, for the winter period the MFB factor lies

between 0.920 to 1.030.

0

0.2

0.4

0.6

0.8

1

1.2

0

10

20

30

40

50

60

70

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00

Cu

mu

lati

ve F

req

uen

cy [

-]

Fre

qu

ency

[-]

Bias, (G/R) [-]

Frequency (Summer Period)

Frequency (Winter Period)

Cumulative Frequency (Summer Period)

Cumulative Frequency (WInter Period)

Figure 4-6: Frequency distribution of field bias of valid gauge-radar (LAWR) pairs

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Bia

s (G

/R) [

-]

Cumulative Probability [-]

Empirical Distribution (Summer)

Empirical Distribution (Winter)

Lognormal Theoretical Distribution

Figure 4-7: Probability distribution of field bias of valid gauge-radar (LAWR) pairs


48

4.1.4.1 Brandes spatial adjustment

As two (the Aquafin rain gauge located at Warotstraat and the VMM raingauge located at

Brouwersstraat) of the 12 rain gauges were in the beam blocking sector, only 10 rain gauges

were used to adjust the radar estimates applying the Brandes spatial adjustment procedure.

The threshold of 1 mm to select valid pair is used for this case as well. Brandes spatial

adjustment factors for each grid and for each valid storm event (defined by valid pairs) were

calculated and applied separately for the summer and winter storms.

4.1.4.2 Statistical analysis on the MFB and BRA adjustment

The MFB adjustment has improved the radar estimates to some. Some statistical parameters

can be seen in Table 4-2. For the summer period, the parameters did not improve

significantly. The NSE value improved from 0.67 to 0.68; the RMSE slightly improved and

no improvement has been observed for the MAE. This is obvious because of the fact that the

MFB correction factor was almost equal to 1. For the winter period, the statistics showed

significant improvement. The RMSE reduced from 3.86 mm to 3.74 mm; the MAE from 2.63

mm to 2.57 and the NSE value improved from 0.43 to 0.46.

Table 4-2: Some statistical parameter values before and after MFB and BRA adjustment on the

LAWR estimates for both summer and winter periods; RAW stands for the LAWR estimates using

constant CF values, RDA(LAWR estimates after range dependency adjustment on CF)

Statistical SUMMER WINTER

Indicators RAW RDA MFB BRA RAW RDA MFB BRA

RMSE [mm] 4.12 3.21 3.19 3.09 5.99 3.86 3.74 3.40

MAE [mm] 2.76 2.14 2.14 2.06 3.55 2.63 2.57 2.42

Nash Criterion [-] 0.47 0.67 0.68 0.70 -0.53 0.42 0.46 0.55

The advantage of using a spatial correction factor is obvious as can be seen in Table 4-2.

Goodness-of-fit-statistics is improved after the Brandes spatial adjustment is applied. For

summer storms, significant improvements can be observed in RMSE and MAE values as well

as in Nash Criterion. For winter storm, improvements are even better.

Figure 4-8 [a] & [b] show how goodness-of-fit statistical values improved when adjustment

procedures have been applied on raw LAWR estimates for the summer and winter periods

respectively. It can be seen that the adjustment procedures have greatly improved the radar

estimates for both periods especially for the winter case where the raw radar estimates had


49

negative NSE value, overcome significant improvement to 0.55. Decreasing trend of the

RMSE and MAE values and increasing trend of NSE values can be observed when the raw

radar data are subjected to subsequent adjustment procedures.

0

1

2

3

4

5

RMSE MAE NSE

RM

SE

an

d M

AE

[mm

], N

SE

[-]

Statistical Indicators

[a] Raw dataRange dependent adjustmentMean field bias adjustmentBrandes spatial adjustment

-1

0

1

2

3

4

5

6

RMSE MAE NSE

RM

SE

an

d M

AE

[mm

], N

SE

[-]

Statistical Indicators

[b] Raw data

Range dependent adjustment

Mean field bias adjustment

Brandes spatial adjustment

Figure 4-8: Evolution of different statistical values with different adjustments on the LAWR-

Leuven estimates; [a]-summer period and [b]-winter period

It appears that gauge-radar residuals even after the spatial adjustment are not negligible but

considerable improvements have been observed compared to raw LAWR estimates. It can be

observed that the RMSE values improved by 25%, the MAE by about 34% for summer

weeks. More significant improvements have been observed in the winter period than the

summer period denoted by about 43% improvement on the RMSE and 47% on the MAE

compared to the original LAWR estimates.


50

4.2 RMI Wideumont estimates − gauge comparison and merging

A threshold value of 1 mm is used to define valid pairs. The same 12 rain gauge network is

utilised. Altogether 99 valid pairs for weeks 1 and 2 and 88 valid pairs for weeks 3 and 4

were analysed.

4.2.1 MFB adjustment

The scatter plot of raw radar-gauge data for the week 1 and 2 shows a complex picture. In

overall, radar estimates tend to overestimate the daily accumulated values as in Figure 4-9

[a]. This might be caused by evaporation, where rain droplets are present on high elevation

and evaporates before reaching ground due to hot and humid conditions.

0

10

20

30

40

0 10 20 30 40

Rad

ar E

stim

ated

[m

m]

Gauge Value [mm]

[a]

Before MFB correction

1:1 Line0

10

20

30

40

0 10 20 30 40

Rad

ar E

stim

ated

[m

m]

Gauge Value [mm]

[b]

After MFB Correction

1:1 Line


after [b] MFB correction on the RMI-Wideumont estimates

For the weeks 3 and 4 the situation is different. As can be seen in Figure 4-10[a], the radar

tends to underestimate the daily accumulated rainfall volumes. This may be because of the

fact that the weeks 3 and 4 are from a winter period and for winter periods, Belgium

experiences mostly stratiform rainfall. This rainfall originates from stratiform clouds which

are low in elevation. Also, as already depicted, the entire raingauge network lies in between

118 to 129 km from the RMI-Wideumont radar. That means the radar beam will be

sufficiently high to miss the raindrops resulting in low radar estimates. This phenomenon is

called ‘overshooting’. Clear underestimation of radar estimates might possibly caused by

another phenomenon called ‘growth’ of rainfall, as it approaches the ground surface. Smaller

droplets at higher elevation, which are measured by the radar, might grow and hence larger

raindrops may be caught by rain gauges at the ground, a process relatively possible in the

stratiform rainfall.


51

0

10

20

30

0 10 20 30

Rad

ar E

stim

ated

[mm

]

Gauge Value [mm]

[b]

After MFB correction

1:1 Line0

10

20

30

0 10 20 30

Rad

ar E

stim

ated

[mm

]

Gauge Value [mm]

[a]

Before MFB correction

1:1 Line


after [b] MFB correction on the RMI Wideumont estimates

By looking at the scatter plots (Figures 4-9 [a] and 4-10 [a]), it is clear that radar data

requires a suitable correction before using it for rainfall-runoff modelling. The MFB is

calculated as the mean of an empirical lognormal distribution as it has already been shown

that the bias of individual valid pairs follows a lognormal distribution (Figure 4-7). The MFB

values for ‘weeks 1 and 2’ and ‘3 and 4’ were calculated as 0.732 and 2.217 respectively. The

90%-confidence limit on the bias is also calculated. The upper and lower confidence limit for

summer weeks (weeks 1 and 2) were found to be 0.808 and 0.662 respectively and we can

say there is high probability that the real MFB will lie in between the limit. For winter weeks

(weeks 3 and 4), the upper and lower limits were found to be 2.414 and 2.036 respectively.

4.2.2 Brandes spatial adjustment

The Brandes spatial adjustment is applied in a similar way as with the LAWR data. All 12

rain gauges have been used to calculate the adjustment factors for both summer and winter

weeks.

4.2.3 Statistical analysis on the MFB and BRA adjustment

The advantage of applying MFB adjustment is obvious as can be seen in Figures 4-9 [b] and

4-10 [b]. The points of radar-gauge valid pairs are somewhat oscillating around the 1:1 line.

This is followed by the Brandes spatial adjustment and some statistical parameters after the

adjustments have been calculated as presented in Table 4-3.

It is clear that the MFB adjustment improves the radar estimates to a great extent. The RMSE

value reduces from 5.70 mm to 4.93 mm for the summer periods. Better adjustment can be

observed for winter periods where RMSE value reduced greatly from 6.79 mm to 3.80 mm.


52

The MAE showed good improvement on the summer periods. The Nash Criterion (NSE)

improved from 0.31 to 0.48 for the summer periods. For the winter periods, the stastical

parameters show quite significant improvements. The NSE value improved from -0.10 to

0.66.

Although the improvements after Brandes spatial adjustment are minimal on summer weeks,

some improvements can be seen on winter weeks.

Table 4-3: Some statistical parameter values before and after MFB adjustment on the RMI

Wideumont radar estimates, RAW stands for original RMI-Wideumont estimates

Statistical SUMMER WEEKS WINTER WEEKS

Indicators RAW MFB BRA RAW MFB BRA

RMSE [mm] 5.70 4.93 4.91 6.79 3.80 3.76

MAE [mm] 4.24 3.06 3.02 5.08 4.52 4.38

NSE [-] 0.31 0.48 0.48 -0.10 0.66 0.66

Hence, it can be seen that the adjustment procedures can improve the raw radar estimates to a

great extent. For summer weeks, around 14% improvement has been observed on the RMSE

value compared to the raw RMI-Wideumont estimates. The MAE improves with about 29%.

In terms of improvement, the winter week’s estimates are better. The RMSE improved with

about 45% and the MAE with about 14%.

4.3 Comparison of LAWR-Leuven and RMI-Wideumont estimates

Figures 4-11 and 4-12 show a comparison plot of LAWR and RMI daily accumulated rainfall

estimates for the summer weeks (week 1 and 2) and the winter weeks (week 3 and 4)

respectively after MFB adjustment. It is observed that the RMI-Wideumont estimates tend to

underestimate higher rainfall accumulation depths though a fair matching can be observed for

lower intensities. This systematic underestimation for higher rainfall depth values might be

an indication of a strong MFB correction for the summer weeks (MFB = 0.732). The plot for

the winter weeks has not followed systematic underestimation or overestimation throughout

the range of rainfall depth values, although a slight underestimation can be observed for

extreme events. Trend of higher scatterings can be observed for higher intensities.


53

0

5

10

15

20

25

30

0 5 10 15 20 25 30

KM

I [m

m]

LAWR [mm]

SUMMER WEEKS


summer weeks

0

5

10

15

20

25

30

0 5 10 15 20 25 30

KM

I [m

m]

LAWR [mm]

WINTER WEEKS


winter weeks

4.4 Catchment modelling

4.4.1 Catchment modelling with VHM

The flow separation using the WETSPRO tool has resulted in time constants of 3500 and 50

hours for baseflow and interflow respectively. The baseflow filter result for the first 32000


54

time steps (hour) can be seen in Figure A-1 (Appendix). Similarly, the interflow filter result

for time step of 2000-4000 hours is shown in Figure A-2. Two linear reservoirs in series have

been applied for routing the overland flow each having a time constant of 5 hours. A linear

model is selected for describing the storage sub-model. Maximum soil water content of 500

mm and soil water content at maximum evapotranspiration of 200 mm is chosen. Similarly,

the surface runoff and interflow separation process parameters are tuned by heuristic

approach and with visual comparison of different sub-model results. Table 4-4 presents the

calibrated VHM parameters.

Table 4-4: The calibrated VHM parameters with their short description

Storage sub-model parameters

Umax (Maximum soil water content) 500 mm

Uevap (Soil water constant for maximum evapotranspiration) 200 mm

Overland flow model

aOF,1 (Surface runoff separation process parameter) 0.0523 -



Inter flow model

aIF,1 (Interflow separation process parameter) 0.0150 -

aIF,2 (Interflow separation process parameter) 2.5 -

aIF,3 (Interflow separation process parameter) 0 -

Flow routing parameters

KBF (Time constant for routing baseflow) 3500 hr

KIF(Time constant for routing interflow) 50 hr

KOF (Time constant for routing overland flow) 5 hr

4.4.2 Catchment modelling with NAM

Altogether 15 parameters have been calibrated to have a better agreement between the

simulated and observed river discharge. The WETSPRO analysis made it easy to fix the

range of the CKBF and CKIF while running the auto-calibration routine. A range of 3000-

4000 hr was fixed for CKBF and 50-150 hour for CKIF. CK1,2 value of 5.5 hours was

selected for routing the overland flow. Extended ground water parameters and a snow module

were also included. The GWLBFO value of 11 m is adopted owing to the flat and low lying

catchment. Similarly, the value of GWLFL1was fixed to 1.5 m as the predominant soil type

is sand. As CKlow is always greater than CKBF, a value of 7500 hours is taken with 0.1 as


55

portioning factor. A Csnow of 2 mm/°C/day together with a base temperature of 0°C have been

fixed for the snow module. The auto-calibration was run to match the overall water balance,

minimize overall RMSE and match low and high flows. The parameter values after auto-

calibration was further tuned manually to obtain better results. This has to be done because of

the fact that auto-calibration routines are made to optimize certain objective function and are

prone to errors due to the presence of local optima. The calibrated values can be seen in Table

4-5:

Table 4-5: The calibrated NAM parameters with their short description

Surface water parameters

Umax (Maximum contents of surface storage) 4.1 mm

Lmax (Maximum contents of root zone storage) 2000 mm

CQOF (Overland flow coefficient) 0.165 -

CKIF (Time constant for interflow) 150 hr

CK1,2 (Time constant for routing overland flow) 5.5 hr

TOF (Root zone threshold value for overland flow) 0 -

TIF (Root zone threshold value for interflow) 0.4 -

Ground water parameter

TG (Root zone threshold value for recharge) 0.24 -

CKBF (Time constant for routing baseflow) 4000 hr

Extended ground water component

GWLBFO (Threshold ground water depth for baseflow) 11 m

GWLFL1 (Capillary flux, depth for unit flux) 1.5 m

CQlow(Lower baseflow, recharge to lower reservoir) 0.1 -

CKlow (Time constant for routing lower baseflow) 7500 hr

Snow Melt Parameter

Csnow (Constant degree day coefficient) 2 mm/°C/day

T0 (Base temperature) 0 °C

The simulated hydrograph for the calibration period of January 1 2006 to December 28 2009

can be seen in Figure A-3. The comparison for cumulated volume for the same period is

shown in Figure A-4. And, the simulated hydrograph for the validation period can be seen in

Figure A-5 (Appendix).

4.4.3 Model performance evaluation

Table 4-6 along with Figures 4-13 to 4-17 show the results of the model performance

evaluation made with the WETSPRO tool. The statistics and graphical plots are the result of a


56

performance evaluation using the observed and modelled rainfall-runoff values for the period

of January 1 2004 to February 28 2009 which includes both calibration and validation periods

allocated for the NAM modelling. Altogether, 273 and 13 POTs are extracted for quick flow

and slow flow periods. The parameter − λ for BC-transformation is taken as 0.25. Statistics

indicate that the VHM simulated the rainfall-runoff more accurately than the NAM. The

VHM simulated rainfall-runoff series has lower MSE values and higher NSE values than the

corresponding NAM results both for quick and slow flow periods especially for quick flow

periods. Performance of both models in slow flow periods can not be highly distinguished.

Table 4-6: Some goodness-of-fit-statistics

Figure 4-13 shows the peak flow comparison after BC-transformation. It is clear that the

NAM simulated discharge shows a higher scatter. The mean deviation line is below the

bisector meaning that the peak flows simulated by the NAM are systematically

underestimated. This is also reflected in the peak flow extreme value plot (Figure 4-15)

where the NAM data points are systematically lower than the observed ones. Nonetheless the

comparison plot of observed and simulated discharge for the calibration period of the NAM

does not indicate that much underestimation (Figure A-3); it is due to the strongly

underestimated peak flows in the validation period (Figure A-5) and as already depicted, the

performance evaluation is made merging both periods. The underperformance in the

validation period is generally expected because of the fact that the calibrated parameters have

been tested to another independent period. Also, the performance of the model is known to be

affected by a significant change in trend of the annual average precipitation (Pipat et. al.,

2005) and the calibration of the parameters was based on a given precipitation trend and we

have a slightly varying trend in the validation period. As can be seen in Figure 4-13, the

VHM modelled peak flows show less scatter and almost no bias (slightly positive biased) as

indicated by the overlap of the bisector and the mean deviation line. Hence, the VHM can

simulate peak discharges with high accuracy. This is also confirmed in the peak flow extreme

value plot (Figure 4-15). But both models have the tendency to underestimate the peak flows

towards the upper tail of the extreme value distribution.

Flow

Periods

Number

of POTs

MSE [m3/s] NSE [-]

VHM NAM VHM NAM

Quick Flow periods 273 1.06 1.14 90% 75%

Slow Flow periods 13 1.01 1.02 92% 89%


57

Figure 4-14 shows the scatter plot for slow flow or base flows. In this regard, the VHM can

be considered as performing quite well, due to the low scatter and almost zero bias. The

NAM simulated results clearly overestimate the low flows which is also reflected in the low

flow extreme value plot (Figure 4-16) where the NAM simulated points are systematically

under the observed minima (the y-axis is plotted taking 1/ discharge). Nevertheless, both

models have a tendency to overestimate the low flows towards the upper tail of the extreme

value distribution.

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

BC

(Sim

ula

ted

Max

ima)

BC (observed Maxima)

NAM

VHM

Bisector

Mean Deviation [NAM]

Mean Deviation [VHM]

Standard Deviation [VHM]

Figure 4-13: Graphical comparison of nearly independent peak flow maxima


58

-2

-1.8

-1.6

-1.4

-1.2

-1

-2 -1.8 -1.6 -1.4 -1.2 -1

BC

(Sim

ula

ted

Min

ima)

BC (observed Minima)

NAMVHMBisectorMean Deviation [NAM]Mean Deviation [VHM]Standard Deviation [VHM]

Figure 4-14: Graphical comparison of nearly independent slow flow minima

0

1

2

3

4

5

6

0.01 0.1 1 10

Pea

k F

low

s [m

3/s

]

Return period [years]

observed

NAM

VHM

Figure 4-15: Graphical comparison of peak flow empirical extreme value distributions


59

3

4

5

6

7

8

9

0.1 1 10

1 /

Lo

w fl

ow

s [m

3/s

]

Return period [years]

observed

NAM

VHM

Figure 4-16: Graphical comparison of low flow empirical extreme value distributions

Figure 4-17 shows the graphical comparison of cumulative flow volumes. It is clear that the

VHM simulated discharge values are slightly overestimated (3.8%). The NAM gives better

results in this respect, with a slight underestimation (0.82%).

0

2000

4000

6000

8000

10000

12000

14000

0 10000 20000 30000 40000 50000

Cu

mu

lati

ve v

alu

e [m

3 /s]

Time [number of hours]

observed

NAM

VHM

Figure 4-17: Graphical comparison of cumulative flow volumes


60

4.5 The significance of spatial data

4.5.1 Rainfall spatial variability

Table 4-7 represents the total rainfall volume for each period event as well as the rainfall

characteristics and variability in terms of the SDIR. Across all events and all rainfall

descriptors, the SDIR varies from 0% to 43.2%. As expected, a large discrepancy is

introduced for the event-1, the storm of 3-Aug-08, because of its convective nature. The radar

data lead to higher SDIR-values in areal rainfall than RG1 for all events. Better agreement

has been observed between the Pref and the RG1 for all periods. The storm event-1 has the

highest SDIR even for RG1. The radar estimates have been seen to represent the areal

average rainfall in a better way for the storm event-3 (22-Jan-08), as suggested by low SDIR

values. No RMI Wideumont data was available for storm event-2.

Hence, the results indicate that for this catchment RG1 can capture areal average rainfall in

almost same accuracy as Pref. This may be because of the fact that the catchment is small and

a network of only 2 raingauges forms the Pref. On the other hand, the radar areal average

estimates are poor as compared to the Pref as indicated by higher SDIR values. This may be

due to discrepancies in the sampling mode, an inappropriate conversion equation, a non-

optimal correction/adjustment methodology. Another, more important reason and perhaps

more evident reason may be that the radars represent the true areal rainfall and that rain

gauges may have failed to capture all the spatial variability.

Table 4-7: Rainfall spatial variability measured in terms of SDIR for the different rainfall

descriptors and for selected events

Events Rainfall Record SDIR

Reference RG1 LAWR RMI RG1 LAWR RMI

[d-m-yy] [mm] [mm] [mm] [mm] [%] [%] [%]

3-Aug-08 30.67 33.07 20.11 17.43 7.8 34.4 43.2

4-Dec-08 7.75 7.65 6.95 - 1.4 10.3 -

22-Jan-09 30.36 30.37 26.87 28.86 0.0 11.5 4.9

9-Feb-09 27.22 26.47 17.07 29.95 2.8 37.3 10.0

4.5.2 Basin response

Table 4-8 shows the results in terms of the NSEobs for the different rainfall descriptors.

Across all storm events, the NSEobs for Pref varies from 0.66 to 0.90 for the VHM and from


61

0.34 to 0.93 for the NAM simulated results. The storm event of 9-Feb-09 results in the

highest NSEobs value for both models. The storm event of 3-Aug-08 results in the lowest

NSEobs value for the VHM and the storm of 5-Dec-08 for the NAM. Degradation of the

NSEobs can be observed for other alternative rainfall descriptors in most of the cases. For the

RG1, the NSEobs closely matches with the same derived with the Pref. The radar simulated

discharge results in a lower NSEobs value than that based on Pref except for the event of 5-

Dec-08 where the LAWR-Leuven data driven discharge has the highest NSEobs (0.84 for the

VHM and 0.57 for the NAM). A further mismatching is observed between the RMI-

Wideumont simulated discharge and the observed discharge where NSEobs values are as low

as 0.19. Considerable improvement can be observed in NSEobs values when using radar

estimated rainfall in winter periods rather than in summer periods. Across all events, the

performance of the VHM and NAM can not be highly distinguished except for the event of 4-

Dec-08 where the VHM simulated runoff matches more closely than the NAM simulated

runoff where runoff driven by Pref has NSEobs value of 0.78 for the VHM and 0.34 for the

NAM.

Table 4-8: Results in terms of NSEobs for the different rainfall descriptors and for different storm

events

Storm Pref RG1 LAWR KMI

VHM NAM VHM NAM VHM NAM VHM NAM

3-Aug-08 0.66 0.70 0.63 0.69 0.45 0.45 0.19 0.27

4-Dec-08 0.78 0.34 0.81 0.36 0.84 0.57 - -

22-Jan-09 0.83 0.82 0.84 0.83 0.89 0.78 0.39 0.33

9-Feb-09 0.90 0.93 0.91 0.92 0.68 0.68 0.50 0.58

0.0

0.2

0.4

0.6

0.8

1.0

3-Aug-08 4-Dec-08 22-Jan-09 9-Feb-09

NS

Eo

bs

[-]

Storm events

[NAM] Pref

RG1

LAWR

KMI

0.0

0.2

0.4

0.6

0.8

1.0

3-Aug-08 4-Dec-08 22-Jan-09 9-Feb-09

NS

Eo

bs

[-]

Storm events

[VHM]

Figure 4-18: NSEobs for different rainfall descriptors and for different storm events


62

Figure 4-18 is a graphical representation of the Table 4-8 where the evolution of NSEobs for

alternative rainfall descriptors for both models can be seen. It is clear that NSEobs values are

degrading for alternative rainfall descriptors especially for the radar estimates.

As observed, the Pref and RG1 derived response can not be highly distinguished for all events.

The radar estimates showed low performance compared to that derived from Pref. The

performance was further degraded for RMI-Wideumont derived rainfall. This might be

because of courser spatial resolution of the RMI-Wideumont radar than that of the LAWR-

Leuven. The low performance of radar data against the raingauge data may be due to the fact

that the model has been calibrated against the rain gauge data. Better agreement might be

observed when calibrating it against the radar estimated rainfall. This was not possible in this

study because too few radar data from both the LAWR-Leuven and the RMI-Wideumont

radars was available for calibration.

Results indicate that lower NSEobs values are expected for summer events than for winter

events. This may be due to the rainfall spatial variability in summer events. Summer events

are of highly convective nature and the raingauge may have missed the rainfall information.

On the other hand, the winter events have less spatial gradients and the rain gauge network

can represent them quite well. This fact is reflected in the SDIR values as well as in the

coefficient of variance (CV, defined as standard deviation normalized by mean) which is

calculated by taking storm accumulated rainfall depth over the pixels covering the catchment

as variable. The storm event-1 (3-Aug-08) shows the highest CV of 18% for RMI-

Wideumont data while it is significantly lower for the winter events, for example: 11 % for

event-3 (22-Jan-09) and 8% for event-4 (9-Feb-09). This can also be seen in Figures A-12 to

A-15 where the pixel to pixel distribution of the accumulated rainfall depths for storm event-1

and storm event-3 for both the RMI-Wideumont as well as the LAWR-Leuven pixels are

presented. It is clear that the storm event-1 (3-Aug-08, Figure A-12) shows a higher pixel to

pixel variability where the accumulated rainfall depth varies from 11 to 28 mm across the

RMI-Wideumont pixels covering the catchment. The storm event-3 (22-Jan-09, Figure A-14)

shows less variability as compared to event-1 as the accumulated rainfall depth varies from

23 to 28 mm across all the RMI-Wideumont pixels. The LAWR data show a complex picture

(Storm-1, Figure A-13 and storm-3, Figure A-15). Some pixel values even show total

accumulated rainfall depths equal to zero which is highly unrealistic. This is because of the


63

algorithms set on the LAWR-control to remove permanent clutter where even a maximum

count (255) is subtracted from the reflected counts making those pixels reading always zero.

Also, the difference in simulating capacity of VHM and NAM is not that pronounced. Across

all events, the VHM produced more consistent results which were also indicated by the

model performance evaluation (section 4.4.3). This might indicate a more robust model

structure or at least it might favour the step-wise calibration procedure of the VHM.

Simulated runoff with the different rainfall descriptors is compared to the observed series as

shown in Figure 4-19 and Figure 4-20. The results in terms of NSEref can be found in Table

4-9 and express the errors in reproducing the reference flow introduced by the alternative

rainfall representations, keeping the parameter uncertainty the same.

Table 4-9: Results in terms of NSEref for the different rainfall descriptors

Strom RG1 LAWR RMI

VHM NAM VHM NAM VHM NAM

3-Aug-08 0.98 0.98 0.72 0.72 0.42 0.51

4-Dec-08 1.00 1.00 0.97 0.94 - -

22-Jan-09 1.00 1.00 0.89 0.97 0.80 0.84

9-Feb-09 1.00 1.00 0.74 0.79 0.83 0.82

For all events, the average NSEref values for RG1, LAWR and RMI estimated rainfall driven

flows from the VHM are 0.99, 0.83 and 0.69 and from the NAM 0.99, 0.86 and 0.73

respectively. Looking to the corresponding values of NSEobs, values of 0.79, 0.72 and 0.36

for the VHM could be found, and 0.70, 0.62 and 0.36 for the NAM. The average NSEobs for

the reference rainfall driven flow is 0.79 for the VHM and 0.70 for the NAM (the difference

from 1 can be regarded as model error). Hence the deviation can be considered as the error

introduced by using the other rainfall descriptor. For all events, the value of NSEref for RG1

is close to 1 meaning that RG1 closely matches with Pref as far as basin response concerns.

For radar estimated rainfall driven flows, NSEref decreased to 0.83 (for the VHM) and 0.86

(for the NAM) for the LAWR-Leuven; and 0.69 (for the VHM) and 0.73 (for the NAM) for

the RMI-Wideumont radar estimates, indicating better performance of the LAWR-Leuven

estimates. The better performance of the LAWR-Leuven estimated rainfall could be

attributed to its high resolution (125x125 m) compared to the RMI-Wideumont radar


64

(600x600 m). Results (NSEref for RG1 ≈ 1) indicate that only one raingauge can sufficiently

reproduce the flows with some accuracy as far as this catchment concerns. Also, better

performance can be seen for storm events of winter periods than summer periods, clearly

indicated by the rather low NSEref as well as NSEobs values for summer storm of 3-Aug-08.

Looking at the hydrographs produced by different rainfall descriptors (Figure 4-19 and

Figure 4-20), it is clear that the LAWR-Leuven and the RMI-Wideumont estimated rainfall

tend to give lower peaks especially for extreme and summer events. It might be due to the

dampening effect because of the fact that the weighted average of 3085 LAWR-Leuven

pixels and 136 RMI-Wideumont pixels were used to calculate areal average rainfall. This

trend is clearly seen for the storm event-1 (3-Aug-2008, Figure 4-19 [upper]) both from the

VHM simulated and the NAM simulated. This also has to do with the lumped nature of the

models used because both the VHM and the NAM uses catchment average rainfall meaning

that localized summer events are dampened. The mismatching of hydrograph trend for the

same storm event is possibly due to flood influence (having flatter recession limb) or due to

man made influences or regulation when the discharge is greater than certain threshold. Less

severe trends are observed for uniform winter events where peaks are quite nicely matched

for all rainfall descriptors except for the event-4 (9-Feb-09; Figure 4-20 [lower]), where the

LAWR estimated rainfall driven flow is characterized by slightly earlier responding lower

peaks. On other hand, for the winter storms, the RMI-Wideumont driven flows are

characterised by high peaks with early response (Figure 4-20 [both]) for both the VHM as

well as the NAM. This might be due to the strong MFB in the winter periods (MFB = 2.217)

based on the data period of few weeks although the Brandes spatial adjustment is applied

after the MFB adjustment. Also, higher peaks and quick response might also be attributed to

the lumped nature of the models used. As can be seen in Figure A-13, the pixels having

higher rainfall accumulation are on the very upstream side of the catchment. If a fully

distributed model could have been used, the response from the pixels having higher rainfall

depth would have been sufficiently lagged to have less severe peaks and the response would

have been in time due to routing of the flow along the river.

Figure 4-21 shows a plot of SDIR versus NSEref for both models. As can be depicted from

the figure, a correlation between increase in SDIR and decrease in NSEref is observed. Up to

an SDIR value of around 10%, the NSEref remains close to 1 and then tends to decrease as

SDIR increases. These trends are almost similar for both models.


65

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 12 24 36 48

Dis

char

ge

[m3/s

]

Hours

[VHM] Qobs

Pref

RG 1

LAWR

KMI

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 12 24 36 48

Dis

char

ge

[m3/s

]

Hours

[VHM] Qobs

Pref

RG1

LAWR

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 12 24 36 48

Dis

char

ge

[m3/s

]

Hours

[NAM] Qobs

Pref

RG 1

LAWR

KMI

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 12 24 36 48

Dis

char

ge

[m3/s

]

Hours

[NAM] Qobs

Pref

RG1

LAWR

Figure 4-19: Observed and simulated flows derived from different rainfall descriptors

for storm-1 [upper] and storm-2 [lower]


66

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

0 12 24 36 48 60 72 84 96

Dis

char

ge

[m3/s

]

Hours

[VHM] Qobs

Pref

RG 1

LAWR

KMI

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 12 24 36 48 60 72 84 96 108 120

Dis

char

ge

[m3/s

]

Hours

[VHM] Qobs

Pref

RG 1

LAWR

KMI

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

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2.2

0 12 24 36 48 60 72 84 96

Dis

char

ge

[m3/s

]

Hours

[NAM] Qobs

Pref

RG 1

LAWR

KMI

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 12 24 36 48 60 72 84 96 108 120

Dis

char

ge

[m3/s

]

Hours

[NAM] Qobs

Pref

RG 1

LAWR

KMI

Figure 4-20: Observed and simulated flows derived from different rainfall descriptors

for storm-3 [upper] and storm-4 [lower]


67

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

NS

Ere

f [-

]

SDIR [%]

VHM

NAM

Figure 4-21: Plot of SDIR and NSEref for both the VHM and NAM

Hence from the results, contrary to expectation, the radar estimated rainfall driven flows

underperformed compared to the RG1. The RG1 on the other hand, which was presumed as

the degradation of spatial rainfall representation over the catchment, can reproduce the flow

with an accuracy as good as Pref. The underperformance of radar estimated rainfall is related

to the calibration strategy used, where both the models were calibrated against Pref. It is also

related to the nature of the models used. Both are lumped rainfall runoff models, using

averaged areal rainfall rather than using spatially variable input. Hence, for extreme and

summer events where the spatial variability of rainfall is high, the radar estimates are always

dampened due to averaging effects of large number of pixels covering the catchment.

Analyzing the significance of spatial representation of rainfall through stream flow

simulation revealed that a single raingauge can reproduce the flow with some accuracy for a

small catchment of size around 50 km2. The radar though has better spatial coverage of

rainfall, the spatial resolution of LAWR-Leuven being as fine as 125 m, has resulted lower

NSEobs as well as NSEref values. By this fact, it can be worthwhile to note that the importance

of spatial rainfall depends on how variable the rainfall is and whether there is enough

variability to overcome the damping and filtering effect of the basins because fast responding

catchments are more sensitive to spatial rainfall variability. As the studied catchment is flat

and characterised by predominant sandy soils, hence quite a large portion of rainfall


68

infiltrates and local variation of the rainfall input is smoothed and delayed within the soil.

Hence, rainfall variations are dampened by integrating response of the catchment. As a result,

for this catchment, more precise areal rainfall estimates are required than spatially variable

rainfall information. Similar results have been observed by Smith et al. (2004) where they

tested rainfall spatial variability in two catchments having high and low level of basin

filtering and found that precise estimates of catchment average rainfall are requited rather

than having spatially more variable rainfall information. Also, a deviation of 10% on areal

average rainfall in terms of SDIR merely affects the simulated stream flow but deviations of

more than 10% proved to cause larger variations, because of the small scale of the catchment.

After all, it has to be noted that the effect of rainfall spatial variability is accessed indirectly,

via lumped conceptual models.


69

CHAPTER 5: CONCLUSIONS

In conclusion, this thesis addressed two themes related to the hydrological community. First,

a comparison study is made which allowed validating and merging the gauge and radar

estimates from two different types of radars, namely the X-band and C-band radars. Second,

the significance of spatial representation of rainfall is assessed using two lumped conceptual

models, namely the VHM and the NAM.

5.1 Comparing and merging of radar − gauge estimates

The goal of radar-gauge comparison was to quantify the accuracy of radar precipitation

estimates. For this, a rain gauge network consisting of 12 rain gauges having different time

resolutions was used. Merging of radar-gauge estimates which involved rainfall information

from the X-band LAWR-Leuven and the C-Band RMI-Wideumont radar was done to have

robust final radar estimates. The study period was sub-divided into summer and winter

periods according to data availability. A threshold value of 1 mm for daily rainfall

accumulation was used to define valid pairs.

For the LAWR-Leuven estimates, using constant CF value to convert the “counts” to rainfall

rates was found to be inappropriate as the radar estimates were heavily overestimated in

nearby pixels and heavily underestimates in far-away pixels. A power function (CF = 0.0272

r 0.8226

, r ≥ 1.5 km) and a second degree polynomial function (CF = 0.0006 r2 + 0.015r +

0.0159, r < 1.5 km) were combined to apply a range dependent adjustment on the CF values.

Then, a MFB adjustment was applied to adjust these radar estimates. It was observed that the

individual bias (G/R) followed a lognormal distribution both for summer and winter periods.

The MFB was found to be 1.015 and 0.974 for summer and winter periods respectively. The

90% upper and lower confidence limit for the MFB was found to be 1.076 and 0.95

respectively, for summer periods. For winter periods, the limits were 1.030 to 0.920

respectively. After the MFB adjustment, a Brandes spatial adjustment was applied. Radar

estimates after adjustments improved quite significantly. It was observed that the mean

absolute error as much as high as 47% compared to raw radar estimates.

For the RMI-Wideumont estimates, it was observed that the raw radar data were

overestimated in summer period and underestimated in winter periods. Taking that the

individual bias (G/R) followed a lognormal distribution, the MFB for summer and winter


70

periods was found to be 0.732 and 2.217 respectively. The 90% upper and lower confidence

limit for the MFB was found to be 0.808 and 0.662 respectively, for summer periods. For

winter periods, the limits were 2.414 and 2.036 respectively. The advantage of using the

Brandes spatial adjustment on radar estimates has been shown quite well. It was observed

that the root mean square error decreased as much as high as 45% with respect to the original

radar estimates.


Significance of spatial rainfall information was tested using two lumped conceptual models,

the VHM and the NAM. Calibration of the models was done using rain gauges situated in the

catchment. The calibrated parameter set thus derived was tested to alternative rainfall

descriptors namely RG1 (using one rain gauge station located approximately at the centroid),

the LAWR-Leuven estimates and the RMI-Wideumont estimates after applying adjustment

procedures. Four storm events were selected to investigate the effects.

In terms of runoff simulations, the performance of both models could not be highly

distinguished. Contrary to expectation, RG1, which was presumed as rainfall with a

degradation of rainfall representation, was found to reproduce hydrographs with almost the

same accuracy those based on by Pref. Radar estimated rainfall driven flows were less

accurate than those simulated with RG1. The radar estimates from the LAWR-Leuven were

better than the estimates from the RMI-Wideumont for simulating the runoff. Extreme and

summer events could not be well simulated by radar estimates although the winter events

have been simulated with higher accuracy. A trend between increase in SDIR and decrease in

NSEref was observed. It was observed that SDIR values greater than 10% proved to cause

large variations in on hydrograph reproduction for both the models.

Hence, for the studied catchment, a central rain gauge alone can be used to simulate the flows

with good accuracy. This is because of the fact Pref is based on a network consisting of only 2

rain gauges. Lower performance of the radar estimates on stream flow simulation can be

attributed to the dampening and filtering effect of the catchment and/or to non-optimal radar-

gauge adjustments. The flat catchment with predominant sandy soil allows a larger portion of

water to infiltrate and hence the local variation of the rainfall input is smoothed and delayed

within the soil. It is observed that a robust method to estimate the catchment averaged rainfall


71

(SDIR ≈ 10%) is required. These findings are also in accordance to some studies that have

been carried out by some researchers (Chaubey et al., 1999; Smith et al., 2004; Segond et al.,

2007 etc.).

5.3 Limitation and future perspectives

Radar data handling and processing tasks are very time consuming since both spatial and

temporal aspects are taken into consideration. Also, a quite dense network of raingauges is

required to validate the radar estimates. Radar gauge merging techniques also demand many

data. The main limitation of the study is the availability of data. The LAWR-Leuven is

relatively new producing radar estimates from July 2, 2008. Also, data of only a few weeks of

RMI-Wideumont radar could be made available. The availability of a dense rain gauge

situated in another direction of the study area is also a limitation as most rain gauges are

along the north-west side of the LAWR and only a limited number of raingauges is available

in the southern part. Part of the LAWR radar beam blockage towards the Zaventem airport

led to a limitation on choosing the catchment for hydrological modelling. Also, use of lumped

conceptual models might be a limitation to investigate significance of the spatial rainfall

variability. Model parameters resulted by calibrating the models using rain gauge data is a

limitation too because the parameter set might not necessarily be the same if the model would

have been calibrated against the radar data.

Hence, merging the radar – gauge rainfall estimates should be carried out using longer data

period series. Separate analysis on different storm periods (summer and winter) is

recommended because of the difference in drop size distributions as well as spatial rainfall

patterns. Use of a model which can use full spatial information of rainfall is recommended.

Such models might reproduce better hydrographs while using adjusted radar estimated

rainfall. Or, a comparison study between lumped conceptual and fully distributed models

might be interesting. Testing the rainfall spatial information on more urbanized catchments

which are characterised by high imperviousness is recommended as they are fast responding.

It is presumed that these catchments have low filtering and local rainfall variations should be

reflected more clearly in stream flow simulation.


72

CHAPTER 6: REFERENCES

Allen, R., Pereira, L., Raes, D. and Smith, M. (1998): Crop evapotranspiration (guidelines for

computing crop water requirements). FAO Irrigation and Drainage Paper No. 56, Rome,

Italy.

Arnaud, P., Bouvier, C., Cisneros, L. and Dominguez, R. (2002): Influence of rainfall spatial

variability on flood prediction, J. Hydrol, 260, (1), 216-230.

Austin, G. L., Nicol, J., Smith, K., Peace, A. and Stow, D. (2002): The Space Time

Variability of Rainfall Patterns: Implications for Measurement and Prediction. Western

Pacific Geophysics Meeting, AGU, Wellington, New Zealand.

Berne, A. , Heggeler, M. , Uijlenhoet, R. , Delobbe, L. , Dierickx, Ph. and de Wit, M. (2005):

A preliminary investigation of radar rainfall estimation in the Ardennes region and a first

hydrological application for the Ourthe catchment. Nat. Hazards Earth Syst. Sci., 5(2), 267-

274.

Borga, M. (2002): Accuracy of radar rainfall estimates for streamflow simulation. J. Hydr.,

267(1-2), 26-39.

Box, G.E.P. and Cox, D.R. (1964): An analysis of transformations. J. Royal Stat. Soc., 26,

211–243.

Brandes, E. A. (1975): Optimizing rainfall estimates with the aid of radar. J. Appl. Meteor, 14

(7), 1339-1345.

Chaubey, I., Hann, C., Grunwald, S. and Salisbury, J. (1999): Uncertainty in the model

parameters due to spatial variability of rainfall. J. Hydrol., 220 (1-2), 48–61.

Delobbe, L., Dehem, D., Dierickx, P., Roulin, E., Thunus, M. and Tricot, C. (2006):

Combined use of radar and gauge observations for Hydrological applications in the Walloon

Region of Belgium. 4th

Eur. Conf. on Radar in Meteorology and Hydrology (ERAD 2006),

Barcelona, Spain, 18-22 September 2006.


73

Delobbe, L. (2007). Weather radars: applications and research. Presentation held at the 1st

Symposium on Meteorology and Climatology for PhD students in Belgium

(MeteoClim2007), Katholieke Universiteit Leuven, Leuven, Belgium, 10 October 2007.

Delobbe, L., Bastin, G., Dierickx, P., Goudenhoofdt, E., Leclercq, G., Moens, L. and Thunus,

M. (2008): Evaluation of several radar-gauge merging techniques for operational use in the

Walloon region of Belgium. International Symposium on Weather Radar and Hydrology,

Grenoble, France, 10-12 March 2008.

DHI (2004): ‘MIKE 11 User & Reference Manual’, Danish Hydraulic Institute, Denmark.

DHI Website (2009): DHI, Local Area Weather Radar (LAWR) website:

http://radar.dhigroup.com/, visited on March 2, 2009.

Einfalt, T., Nielsen, K.A., Golz, C., Jensen N. E., Quirmbach, M., Vaes, G, and Vieux, B.

(2004): Towards a roadmap for use of radar rainfall data in urban drainage, J. Hydrol.,

299(3-4), 186-202.

FAO irrigation and Drainage Paper 27 (1998): Agrometeorological Field Stations, Chapter 6

Annex II, website: http://www.fao.org/docrep/t7202e/t7202e09.htm, visited on March 5,

2009.

Filho, A. J. P. (2005): Integrating gauge, radar and satellite rainfall, 2nd

Workshop of the

International Precipitation Working Group, Brazil.

Germann, U., Galli, G., Boscacci, M., and Bolliger, M. (2006): Radar precipitation

measurements in a mountainous region, Q. J. R. Meteor. Soc., 132, 1669–1692.

Goormans, T. and Willems, P. (2008): Correcting rain gauge measurements for calibration of

an X-band weather radar. 11th

Int. Conf. on Urban Drainage, Edinburgh, Scotland, UK, 31

August- 5 September 2008.


74

Goormans, T., Willems P. and Jensen, N. E. (2008): Empirical assessment of possible X-band

radar installation sites, based on on-site clutter tests. 5th

Eur. Conf. on Radar in Meteorology

and Hydrology (ERAD 2008), Helsinki, Finland, 30 June – 4 July 2008.

Goudenhoofdt, E. and Delobbe, L. (2009): Evaluation of radar-gauge merging methods for

quantitative precipitation estimates, Hydrol. Earth Syst. Sci., 13 (2), 195–203.

Gray, W. and Larsen, L. (2004): Radar Rainfall Estimation in the New Zealand Context. 6th

Int. Symposium on Hydrological Applications of Weather Radar, Melbourne, Australia, 2 – 4

February 2004.

Hazen, A. (1930): Flood flow, a study of frequencies and magnitudes. John Wiley and Sons,

INC. New York (as cited in unpublished course notes on Statistics for Water Engineering,

Willems, P., 2008).

Heistermann, M., Kneis, D. and Bronstert, A. (2008): Evaluation of radar-based rainfall

estimation by cross validation and runoff simulation, Geophysical Research Abstracts, 10,

EGU2008-A-09702.

HydroNet (2009): Hydronet Databank Oppervlaktewater website: http://www.hydronet.be,

visited on March 5, 2009.

Lack, S. A. and Fox, N. I. (2007): An examination of the effect of wind drift on radar-derived

surface rainfall estimations. Atmos. Res., 85 (2), 217–229.

Laurenson, E., Mein, R. (1988): RORB version 4 Runoff Routing program, User Manual,

Technical Report, Monash University, Department of Civil Engineering (citied on Segond et

al., 2007).

Luyckx G. and Berlamont J. (2001): Simplified method to correct rainfall measurements from

tipping bucket raingauges. In: Brashear R.W. & Maksimovic C. (eds.): Proc. Urban Drainage

Modelling (UDM) Symposium, part of the World Water Resources & Environmental

Resources Congress, Orlando, Florida, USA, 20-24.


75

Maidment, D.R. (1993): Developing a spatially distributed unit hydrograph by using GIS. In:

Kovar, K. and Natchnebel, H.P. (eds) Application of Geographic Information Systems in

Hydrology and Water Resources. Proceedings of Vienna Conference, Vienna, IAHS publ. no

211, 181-192.

Marshall, J.S. and Palmer, W. Mc. K. (1948): The distribution of raindrops with size, J.

Meteor., 5(4), 165-166.

Michelson, D. B. and Koistine, J. (2000): Gauge-Radar Network Adjustment for the Baltic

Sea Experiment. Phys. Chem. Earth (B), 25(10-12), 915-920.

Michelson, D. B., Andersson, T., Koistinen, J., Collier, C. G., Riedl, J., Szturc, J., Gjertsen,

U., Nielsen, A., and Overgaard, S. (2000): BALTEX Radar Data Centre Products and their

methodologies. SMHI Reports Meteorology and Climatology RMK Nr. 90, SMHI, SE-601

76, Norrkoping, Sweden, pp. 76.

Moreau, E., Testud, J., Le Bouar, E. (2009): Rainfall spatial variability observed by X-band

weather radar and its implication for the accuracy of rainfall estimates. Adv Water Resour,

32(7) 1011-1019.

Nash, J. E. and Sutcliffe, J. V. (1970): River flow forecasting through conceptual models part

I — A discussion of principles, J. Hydrol., 10 (3), 282–290.

Pechlivanidis, I.G., McIntyre, N. and Wheater, H.S. (2008): The Significance of Spatial

Variability of Rainfall on Runoff. Int. Congr. on Environmental Modelling and Software

(iEMSs 2008), Barcelona, Spain, 10 July 2008.

Pipat, R., Ramesh, S. K., Manoj, J., Philip, W. G., Khalil, A., and Ali, S. (2005): Calibration

and Validation of SWAT for the Upper Maquoketa River Watershed. Centres for Agricultural

and Rural Development Iowa State University, Working Paper 05-WP 396.

Raes, D. (2007): Reference Manual ETo, Katholieke Universiteit Leuven, Leuven, Belgium,

Version 2.3.


76

RMI (2009): Koninklijk Meteorologisch Instituut, in English: Royal Metrological Institute,

website: http://www.meteo.be/meteo/view/, visited on March 11, 2009.

Rodgers, J. L. and Nicewander W.A. (1988): Thirteen ways to look at the correlation

coefficient. The American Statistician, 42(1) 59–66.

Rollenbeck R. and Bendix J. (2006): Experimental calibration of cost-effective X-band

weather radar for climate ecological studies in southern Ecuador. Atmos. Res., 79(3-4), 296-

316.

Segond, M. L., Wheater, H.S. and Onof, C. (2007): The significance of spatial rainfall

representation for flood runoff estimation. A numerical evaluation based on the Lee

catchment, UK, J. Hydrol., 347(1-2), 116 - 131.

Shah, S., O’Connel, P. and Hosking, J. (1996): Modelling the effects of spatial variability in

rainfall on catchment response. Experiments with distributed and lumped models. J. Hydrol.,

175(1-4), 89–111.

Sinclair, S., and Pegram, G. (2005): Combining radar and rain gauge rainfall estimates using

conditional merging. Atmos. Sci. Let., 6(1), 19–22.

Smith, M., Koren, V., Zhang, Z., Reed, S., Pan, J., and Moreda, F. (2004): Runoff response to

spatial variability in precipitation: an analysis of observed data. J. Hydrol., 298(1-4),267–

286.

Sokol, Z. (2003): The use of radar and gauge measurements to estimate areal precipitation for

several Czech river basins. Stud. Geophy. Geod., 47(3), 587−604.

Tetzlaff, D. and Uhlenbrook, U. (2005): Effects of spatial variability of precipitation for

process-oriented hydrological modelling: results from two nested catchments. Hydrol. Earth

Syst. Sci., 9, 29–41.

Vasvári, V. (2005): Calibration of tipping bucket rain gauges in the Graz urban research area.

Atmos. Res., 77(1-4), 18-28.


77

Velasco-Forero C.A., Sempere-Torres, D., Cassiraga, E.D. and Gómez-Hernández, J.J.

(2008): A non-parametric automatic blending methodology to estimate rainfall fields from

rain gauge and radar data. Adv. Water Res., 32(7), 986-1002.

Vieux, B.E. and Vieux, J.E. (2005): Statistical evaluation of a radar rainfall system for sewer

system management. Atmos. Res., 77(1-4), 322– 336.

Willems, P. (2000): Probabilistic immission modelling of receiving surface waters. PhD

Thesis, Katholieke Universiteit Leuven, Faculty of Engineering, Leuven, Belgium.

Willems, P. (2001): Stochastic description of the rainfall input errors in lumped hydrological

models. Stoch. Env. Res. and Risk Assess., 15(2), 132-152.

Willems, P. (2009): A time series tool to support the multi-criteria performance evaluation of

rainfall-runoff models. Env. Mod. Soft., 24(3), 311-321.

Wilson, J. W. and Brandes, E. A. (1979): Radar Measurement of Rainfall: A Summary. Bull.

Am. Meteor. Soc., 60(9), 1048–1058.


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CHAPTER 7: ANNEXES

A-1: Prior time series processing results

0.1

1

10

0 4000 8000 12000 16000 20000 24000 28000 32000

Dis

char

ge

[m3/s

], lo

g s

cale

Number of time steps [hours]

Time seriesFiltered baseflowSlope recession constant baseflow

Figure A-1: Baseflow filter results

0

0.5

1

1.5

2

2.5

2000 2400 2800 3200 3600 4000

Dis

char

ge

[m3/s

]

Number of time steps [hours]

Time seriesFiltered overland flowFiltered interflowFiltered baseflow

Figure A-2: Interflow filter results


79

A-2: Model results

Figure A-3: Observed and NAM simulated hydrograph for the calibration period (3/1/2006-

2/28/2009)

Figure A-4: Cumulative observed and NAM simulated discharge for calibration period (3/1/2006-

2/28/2009)


80

Figure A-5: Observed and NAM simulated hydrograph for the validation period (1/1/2004-

12/31/2005)

Figure A-6: Observed and VHM simulated hydrograph for the calibration period (3/1/2006-

2/28/2009)


81

Figure A-7: Cumulative observed and VHM simulated discharge for the calibration period

(3/1/2006-2/28/2009)


82

A-3: Rainfall series (in terms of Pref) for selected storm events

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

1 2 3 4 5 6 7 8

Rai

nfa

ll [m

m]

Storm duration [hr]

Pref [3-Aug-08]

Figure A-8: Reference rainfall evolution for storm event-1

0.0

0.5

1.0

1.5

2.0

2.5

1 2 3 4 5 6 7

Rai

nfa

ll [m

m]

Storm duration [hr]

Pref [5-Dec-08]



83

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

Rai

nfa

ll [m

m]

Storm duration [hr]

Pref [22-Jan-09]


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

Rai

nfa

ll [m

m]

Storm duration [hr]

Pref [9-Feb-09]



84

A-4: Accumulated rainfall over radar pixels for selected storm events

Figure A-12: Accumulated rainfall for storm event -1 (RMI pixels), north is upward

Figure A-13 : Accumulated rainfall storm event-1 (LAWR pixels), north is upward


85

Figure A-14: Accumulated rainfall for storm event -3 (RMI pixels), north is upward

Figure A-15: Accumulated rainfall storm event-3 (LAWR pixels), north is upward


86

A-5: LAWR-Leuven simulated results

0

0.4

0.8

1.2

1.6

2

2.4

2.8

7/2/2008 7/17/2008 8/1/2008 8/16/2008 8/31/2008 9/15/2008 9/30/2008

Dis

char

ge

[m3/s

]

Date [mm/dd/YYYY]

Observed

VHM Simulated

Figure A-16: LAWR-Leuven VHM simulated river discharge for the period of 7/2/2008 to

9/30/2008

0

0.4

0.8

1.2

1.6

12/1/2008 12/16/2008 12/31/2008 1/15/2009 1/30/2009 2/14/2009 3/1/2009

Dis

char

ge

[m3/s

]

Date [mm/dd/YYYY]

Observed

NAM Simulalted

Figure A-17: LAWR-Leuven NAM simulated river discharge for the period of 12/1/2008 to

2/28/2009

Technology

Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]