This document summarizes the accuracy of rainfall estimates from an X-band Local Area Weather Radar (LAWR) installed in Leuven, Belgium and its application for hydrological modelling of the 48.17 km2 Molenbeek/Parkbeek catchment. Different adjustment techniques including range dependent adjustment, mean field bias adjustment, and Brandes spatial adjustment were applied to raw radar data, improving the mean absolute error by 47% and root mean square error by 45% compared to original radar estimates. Two rainfall-runoff models, VHM and NAM, were used to simulate streamflow in the catchment, showing similar performance and greater accuracy simulating more uniform winter storms than summer storms.

1. 9th International Conference on Hydroinformatics
HIC 2010, Tianjin, CHINA
ACCURACY OF X-BAND LOCAL AREA WEATHER RADAR
(LAWR) OF LEUVEN AND ITS FIRST HYDROLOGICAL
APPLICATION FOR RIVER CATCHMENT MODELLING
N. K. SHRESTHA, P. WILLEMS
Hydraulics Laboratory, Department of Civil Engineering, Katholieke Universiteit Leuven,
3000 Leuven, Belgium
&
Department of Hydrology & Hydraulic Engineering, Vrije Universiteit Brussel
Pleinlaan 2, 1050 Brussels, Belgium
T. GOORMANS
Hydraulics Laboratory, Department of Civil Engineering, Katholieke Universiteit Leuven,
3000 Leuven, Belgium
This paper discusses the hydro-meteorological potential of the X-band Local Area
Weather Radar installed in the densely populated city centre of Leuven, Belgium.
Different merging techniques are applied to raw radar data using gauge readings from a
network of 12 rain gauges. The hydrological response is investigated in the 48.17 km2
Molenbeek/Parkbeek catchment in Belgium. For this, two lumped conceptual models,
VHM and the NAM are used. Range dependent adjustment followed by Mean Field Bias
Adjustment and 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
root mean square error by 45% compared to the original radar estimates. No large
differences in streamflow simulation capability of the two models can be distinguished.
More uniform winter storms are simulated with greater accuracy than summer storms.
INTRODUCTION
For most of the simulation models used in water engineering, rainfall is primary input
and often considered spatially uniform over the catchment, or over subregions defined by
the density of the rain gauge network, which is usually not the case. Rather, it is highly
variable in both space and time. Even in a single storm, rainfall can vary from tens of
mm/hr from minute to minute within distances of few centimeters (Austin et al., (2002)
[1]). Hence the assumption of uniform rainfall leads to a major uncertainty in simulated
events (Willems, (2001) [8]). Accurate high-resolution – in both space and time –
rainfall input to the hydrological modelling is required to acquire more robust and
accurate hydrological simulations. Accurate and short duration rainfall input can be
provided by rain gauges; high spatial resolution data by a dense rain gauge network
(Wilson and Brandes, (1979) [10]) or weather radars. Radar measurements however,
have the disadvantage that they have high uncertainty in rainfall intensity
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2. 1648
measurements (Einfalt et al., (2004) [4]). These uncertainties should be minimized
before using radar measurements as input to simulation models by using adjustment
techniques (Wilson and Brandes, (1979) [10]). This could be done by merging radar and
rain gauge information.
The hydro-meteorological potential of weather radars has already been explored by
many researchers. An X-band weather radar is relatively new and it has rarely been used
in hydrological modelling. Owing to its finer resolution, better results are expected than
those obtained by conventional S and C-band radars if optimal adjustment procedures are
applied. This study focuses on accuracy of LAWR estimates, based on a case in Belgium
where an X-band weather radar has been installed.
METHODOLOGY
The X-band Local Area Weather Radar (LAWR) of Leuven
As outcome of a project aiming at the “development of a system for short-time prediction
of rainfall”, the Danish Hydrological Institute (DHI) together with the Danish
Meteorological Institute (DMI) developed cost effective X-band radar called LAWR.
From this, DHI also developed a smaller version of the LAWR, the so-called City LAWR.
A City LAWR is installed on the roof of the Provinciehuis Building at the city of Leuven,
Belgium as 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) [5]). The LAWR
records reflectivity values (representation of back scattered energy) which are converted
to rainfall rates by a linear relationship. The slope of this relationship represents a
Calibration Factor (CF), which is a conversion factor that converts radar reflectivity
records to rainfall rates.
Study area
The study area is within 15 km radius of the LAWR. The rain gauge network comprises
of 12 rain gauges. A catchment named Molenbeek/Parkbeek, having area of 48.17 km2,
has been selected which is situated south/south-east direction of the LAWR. The
elevation of the catchment ranges from 22 m to 117 m above mean sea level. Agricultural
land and sandy soil is the dominant land-use and soil type of the catchment.
Radar-gauge merging techniques
Owing to the rainfall pattern in Belgium, the study is distinguished into two periods
namely summer storm and winter storm periods. 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. Different CFs are obtained for each rain gauge as the result of a
regression analysis, based on the storm average rain gauge intensities and the measured
counts in the corresponding radar pixels. The average value of these CFs is used to obtain
rainfall rates. After using a constant CF value for all radar pixels, following merging
techniques are applied sequentially:

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1. Range Dependent Adjustment: this adjustment on CFs is essential to some extent
because of ever increasing height of measurement, beam broadening and attenuation
effect. It assumes the CF as a ratio as a function of the distance from the radar site.
2. Mean Field Bias (MFB) Adjustment: in MFB adjustment, it is assumed that the
radar estimates can be corrected by a uniform multiplicative factor and is given by:
F 1 (1)
R
i Gi
MFB  
N N i
3. Brandes Spatial Adjustment (BRA): the main idea is to use a weighted average of
the correction factors from the rain gauge sites to each radar grid cell, with weights wi
depending on the distance from the radar grid cell to gauge i. For a network consisting of
“N” raingauges, it can be given by (Brandes, (1975) [2]):
N
w
i 1
i (G i / R i )  2 
Where, wi  exp  d  and, k  2  1 (2)
C BRA   
k 
N 
w
i 1
i
In equations (1) and (2), Gi and Ri = gauge and radar valid pair readings; N = total
number of valid pairs; d = distance between the gauge and the grid point in km; k = a
factor controlling the degree of smoothening, generally given as the inverse of two times
the mean gauge density (number of gauges divided by total area, denoted by “δ”); CBRA =
Brandes spatial adjustment factor.
If both the daily rain gauge depth and radar depth are greater than 1 mm then these
were considered as “valid pairs”. For all purposes, the average number of counts over 9
radar pixels surrounding the gauge location is used. In order to evaluate the
improvements achieved by each step in the adjustment procedure, comparison on some
goodness-of-fit statistics is made before and after adjustment. The Root Mean Square
Error (RMSE), Mean Absolute Error (MAE) and Nash Sutcliff Efficiency (NSE) are used
for this study.
Rainfall-Runoff models and modelling approach
Two different conceptual rainfall-runoff modeling methods (VHM and NAM) have been
used to simulate the effect of the various rainfall input estimations on the catchment
runoff. VHM is a Dutch abbreviation for generalized lumped conceptual and
parsimonious model structure identification and calibration. The VHM modeling
approach aims to derive parameter values which are as much as possible unique,
physically realistic and accurate (Willems, (2000) [7]). NAM (Nedbør-Afstrømnings-
Model) is the Danish abbreviation for precipitation runoff model. NAM is a deterministic,
lumped and conceptual rainfall-runoff model which simulates the rainfall-runoff
processes occurring at the catchment scale (DHI, (2004) [3]).
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.

4. 1650
The parameter set thus derived is used to simulate the catchment runoff by using adjusted
radar estimates. The NSEobs (Equation 3) is Nash-Sutcliffe efficiency (Nash and Sutcliffe,
(1970) [6]), considered as statistics to validate the goodness-of-fit of the simulated runoff
results to observed discharges of the river gauging station downstream the catchment:
 n 


 Q (i )  Q (i ) 
m o
2
 
  MSE
 (3)
  1  2 
i 1
NSE  1 
S Qo 
 Q (i )  Q 
n
 2   
 o o 
 i 1 
with, Qo(i) = the observed river discharge; Qm(i) = the modelled river discharge; n = the
total number of observations; i = the ith number of observation; S2Qo= the variance of
observed discharge series; Qo = the mean of observed discharge series.
The simulated flow driven by the reference rainfall (Pref) is referred to as the
reference flow (Qref). The difference between the reference flow and the flow driven by
adjusted radar estimates is the error induced due to the tested rainfall input keeping model
parameter uncertainty the same. A modified definition of NSE is introduced to measure
the performance of the simulated runoff in comparison to reference flow defined by
equation (3) where Qo is replaced by Qref. Both the NSEobs and NSEref will be defined for
the NAM as well as the VHM. To quantify the effects of using LAWR estimates, 4
storms were selected as shown in Table 1.
Table 1. Selected storm events; LT means Local Time.
Start [LT] End [LT] Duration Pref
Storm
Events [mm/dd/yy
[mm/dd/yy HH:MM] [h] [mm]
HH: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
RESULTS AND DISCUSSION
Accuracy of radar estimates
Using the average value of CF showed significant fluctuation on the radar and gauge
values for cumulative rainfall volumes in the summer period. The Relative Field Bias
(RFB; given by the difference in radar and gauge value normalized by gauge value)
ranges from +1.25 (125% overestimation) to -0.57 (57% underestimation). The radar
tends to overestimate rainfall in those pixels which are closely located to the LAWR and
tends to underestimate rainfall in those pixels which are further away. Combining a
second degree polynomial equation (CF = 0.0006 r2 + 0.015r + 0.0159, for r < 1.5 km)
and a power function (CF = 0.0272 r 0.8226, for r ≥ 1.5; with, r = from the distance to the

5. 1651
LAWR in km), the range dependency problem is addressed which also produced quite
good results reducing overall the RFB to nearly 6%. The frequency distribution of
individual Field Bias showed that the bias followed a near perfect lognormal distribution.
Hence the mean of lognormal distribution was calculated to get the MFB. The MFB for
the summer and winter period was found to be 1.015 and 0.974 respectively. The radar
field is then subjected to the Brandes Spatial Adjustment.
The goodness-of-fit statistics for the subsequent adjustment procedures can be
observed in Figure 1. It can be seen that the adjustment procedures have greatly improved
the radar estimates for both periods. A decreasing trend of the RMSE as well as MAE
values and an increasing trend of NSE value can be observed when the raw radar data are
subjected to subsequent adjustment steps. It is calculated 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 45%
improvement on the RMSE and 47% on the MAE compared to the original LAWR
estimates.
5 7
[a] Raw data [b] Raw data
Range dependent adjustment 6
[mm] for RMSE & MAE, NSE [-]
4 Range dependent adjustment
[mm] for RMSE & MAE, NSE [-]
MFB adjustment 5 MFB adjustment
BRA adjustment BRA adjustment
3 4
3
2
2
1 1
0
0
RMSE MAE NSE
RMSE MAE NSE -1
Statistical Indicators Statistical Indicators
Figure 1. Evolution of different rainfall goodness-of-fit statistical after adjustment step on
the LAWR-Leuven estimates; [a]-summer period and [b]-winter period
Hydrological application
Tuning of the model parameters has been done with an heuristic approach. Optimization
of model parameters has been based on good matching on total water balance, shape of
the hydrograph, peak flows and low flows. Table 2 shows the results of hydrological
model performance evaluation based on the Water Engineering Time Series PROcessing
tool (WETSPRO). The model performance statistics shown in that table are the MSE and
NSE for “nearly independent” peak and low runoff flows extracted from the hourly time
series ranging from 9/10/2003 to 2/28/2009. Details about WETSPRO can be found on
Willems, (2009) [9].

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Table 2. Some goodness-of-fit-statistics
Flow MSE [m3/s] NSE [-]
Periods VHM NAM VHM NAM
Quick Flow 1.06 1.14 90% 75%
Slow Flow 1.01 1.02 92% 89%
Figure 2 shows results in terms of NSEobs.The result in terms of NSEref can be found
in Figure 3 and expresses the errors in reproducing the reference flow introduced by the
LAWR rainfall, keeping the parameter uncertainty the same.
1.0 1.0
[VHM] Pref LAWR [NAM] Pref LAWR
0.8 0.8
NSEobs [-]
0.6 0.6
NSEobs [-]
0.4 0.4
0.2 0.2
0.0 0.0
3-Aug-08 4-Dec-08 22-Jan-09 9-Feb-09 3-Aug-08 4-Dec-08 22-Jan-09 9-Feb-09
Storm events Storm events
Figure 2. NSEobs for different rainfall descriptors and for different storm events
Across all storm events, the NSEobs for Pref varies from 0.66 to 0.90 for the VHM and
from 0.34 to 0.93 for the NAM simulated flows. 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 the LAWR derived flows in most of the cases.
Considerable improvement can be observed in NSEobs values when using LAWR
estimates in winter periods rather than in summer periods. 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 this information. On the other hand, the winter
events have less spatial gradients and the rain gauge network can represent them with
considerable accuracy. Likewise, the average NSEref values for the LAWR driven flows
are 0.83 and 0.86 and NSEobs values are 0.72 and 0.62 for VHM and NAM simulated
runoff respectively. The average NSEobs for the Pref 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 from NSEref and NSEobs can be considered as the additional error (in
comparison with the use of the reference rainfall) introduced by using the LAWR
estimates.

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1.0 VHM
NAM
0.8
NSEref [-]
0.6
0.4
0.2
0.0
3-Aug-08 4-Dec-08 22-Jan-09 9-Feb-09
Storm events
Figure 3. Results in terms of NSEref for the different rainfall descriptors
Hence from the results, contrary to expectation, underperformance of the LAWR
estimated rainfall can be observed. This underperformance can be attributed to the
calibration strategy used, where both 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 tend
to be dampened due to averaging effects of the large number of pixels covering the
catchment. The underestimation may also be due to discrepancies in the sampling mode,
an inappropriate conversion equation, a non-optimal adjustment methodology. Another,
more important and perhaps more evident reason may be that the radar has limited
accuracy in its rainfall intensities and that the adjustment based on the rain gauges may
have failed to capture all the spatial variability. Moreover, it can be worthwhile to note
that the importance of spatial rainfall such as the estimates of LAWR 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 characterized by
predominant sandy soils, a large portion of rainfall infiltrates and local variation of the
rainfall input is smoothed and delayed within the soil. Hence, rainfall variations are
dampened by integrating the response of the catchment.
CONCLUSIONS AND RECOMMENDATIONS
Range dependent adjustment followed by the MFB adjustment and Brandes Spatial
Adjustment improved raw radar estimates quite significantly. In numerical terms, the
Root Mean Square Error was improved by 45% whereby 47% improvement has been
observed on the Mean Absolute Error. After adjustments, the radar-gauge comparison in
the considered summer period improved more than that in the winter period. In terms of
runoff simulations, the performance of both the VHM and NAM models could not be
highly distinguished. Four storm events were investigated to test the prediction capability

8. 1654
of the LAWR estimates. NSEref values less than 0.7 for summer storms indicate that local
summer rain cells played a role to produce lower peaks. This can also be attributed to the
high dampening effect of the catchment.
Separate analysis on different storm periods (summer and winter) based on longer
series of data is recommended. Use of a model which can use full spatial information of
rainfall is also recommended. Testing the rainfall spatial information on more urbanized
catchments having a lower dampening effect is also recommended.
REFERENCES
[1] Austin G. L., Nicol J., Smith K., Peace A. and Stow D., “The Space Time
Variability of Rainfall Patterns: Implications for Measurement and Prediction”,
Proc. Western Pacific Geophysics Meeting, AGU, Wellington, New Zealand,
(2002).
[2] Brandes E. A., “Optimizing rainfall estimates with the aid of radar.”, J. Appl.
Meteor., 14(4), (1975), pp 1339-1345.
[3] DHI, “MIKE 11 User & Reference Manual”, Danish Hydraulic Institute, Denmark,
(2004).
[4] Einfalt T., Nielsen K.A., Golz C., Jensen N. E., Quirmbach M., Vaes G. and Vieux
B, “Towards a roadmap for use of radar rainfall data in urban drainage” , J. Hydrol.,
299(3-4), (2004), pp 186-202.
[5] Goormans T., Willems P. and Jensen N. E., “Empirical assessment of possible X-
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July, (2008).
[6] Nash J. E. and Sutcliffe J. V., “River flow forecasting through conceptual models
part I − A discussion of principles”, J. Hydrol., 10 (3), (1970), pp 282-290.
[7] Willems P., “Probabilistic immission modelling of receiving surface waters”, PhD
Thesis, Katholieke Universiteit Leuven, Faculty of Engineering, Leuven, Belgium,
(2000).
[8] Willems P., “Stochastic description of the rainfall input errors in lumped
hydrological models”, Stoch. Env. Res. and Risk Assess., 15(2), (2001), pp 132-152.
[9] Willems P., “A time series tool to support the multi-criteria performance evaluation
of rainfall-runoff models”, Env. Mod. Soft., 24(3), (2009), pp 311-321.
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Bull. Am. Meteor. Soc., 60(9), (1979), pp 1048-1058.