Radar Rainfall Estimation Boosts River Modelling

Radar Based Rainfall Estimation
for River Catchment Modeling

Promotor:
Prof. P. Willems

Advisor:
T. Goormans

Master dissertation in partial fulfilment
of the requirements for the Degree of
Master of Science in Water Resources Engineering
by: Shrestha Narayan Kumar

September 2009

Katholieke Universiteit Leuven
Belgium

Radar based rainfall estimation for river catchment modelling

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.

i


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

ii


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

iii


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

iv


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

v


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
Figure 4-10: Scatter plot of radar-gauge daily accumulated estimates for week 3 & 4 before [a] and
after [b] MFB correction on the RMI Wideumont estimates ------------------------------------------ 51

vi


Figure 4-11: LAWR-Leuven and RMI-Wideumont daily accumulated estimates comparison plot for
summer weeks ------------------------------------------------------------------------------------------------- 53
Figure 4-12: LAWR-Leuven and RMI-Wideumont daily accumulated estimates comparison plot for
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

vii


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

viii


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

ix


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.

x


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

1


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

2


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.

3


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

4


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.

5


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).

6


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:
C K2 Z
Pr = (1)
r2
With,
C = radar constant
K = imaginary dielectric constant
r = range of the target
Z = radar reflectivity
The radar reflectivity, Z (mm6/m3), 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:

Z = ∑ N i Di = ∫ N ( D) D 6 dD
6
(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.

7


The rainfall rate (R) can be related to N(D) by the following equation if no vertical air motion
is assumed.
π
6∫
R= N ( D ) D 3 Vt ( D ) dD (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:
Z = a Rb (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;
Z = 200 R1.6 , suitable for stratiform events also known as the Marshall and Palmer
(1948) relationship.
Z = 250 R1.2 , suitable for tropical climates.

Z = 300 R1.4 , 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

8


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

9


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.

10


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)

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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

12


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

13


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

14


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

15


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

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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

17


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:

18


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/ oC /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).

19


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.

20


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.

21


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.

22


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

24


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 [-]
RWZI Kessel-Lo 1.321
Keulenstraat 1.121
Aquafin
Hoge Beekstraat 1.157
Warotstraat 1.158
Derijcklaan 1.157
Oudstrijderslaan 1.158
VMM Eenmeilaan 1.143
Brouwersstraat 1.252
Weggevoerdenstraat 1.237

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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
Calibration Factor,
Operator RG Location
CF [(mm/hr)/(counts/min)]
RWZI Kessel-Lo 0.0600
Aquafin Keulenstraat 0.1131
Hoge Beekstraat 0.0934
Derijcklaan 0.0421
Oudstrijderslaan 0.0615
VMM
Eenmeilaan 0.0531
Weggevoerdenstraat 0.1601
Average 0.0833

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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)

27


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:

∑F 1 Gi
∑R
i
MFB = = (5)
N N i

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

28


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:
( r − 0.5)
Probability of exceedance = (6)
n
( n − r + 0.5)
Cumulative probability = 1 - (Probability of exceedance) = (7)
n
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:
 ∑ log( Fi )   1 G 
   ∑ log  i 
N R 
 N    i 
MFB = e =e (8)

With,

N= Number of valid radar-gauge pairs.

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

29


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:

 d2 
wi = exp −
 k  (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

∑w
i =1
i (G i / R i )
C BRA = N
(11)
∑w
i =1
i

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:

30


N

∑ (R
i =1
i − Gi ) 2
RMSE = (12)
N
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

∑ (R
i =1
i − Gi )
MAE = (13)
N
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:
Ri − Gi
RFB = (14)
Gi
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;

31


n

∑ (G
i =1
i − Ri ) 2
E =1− n −
(15)
∑ (G
i −1
i − G) 2

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 Hydrological modelling
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.

32


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.

33


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.
34

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