9th International Conference on Hydroinformatics                                                                 HIC 2010,...
1648measurements (Einfalt et al., (2004) [4]). These uncertainties should be minimizedbefore using radar measurements as i...
1649     1. Range Dependent Adjustment: this adjustment on CFs is essential to some extentbecause of ever increasing heigh...
1650The parameter set thus derived is used to simulate the catchment runoff by using adjustedradar estimates. The NSEobs (...
1651LAWR in km), the range dependency problem is addressed which also produced quitegood results reducing overall the RFB ...
1652Table 2. Some goodness-of-fit-statistics                                    Flow                      MSE [m3/s]      ...
1653                                     1.0                                             VHM                              ...
1654of the LAWR estimates. NSEref values less than 0.7 for summer storms indicate that localsummer rain cells played a rol...
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  1. 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. WILLEMSHydraulics 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. GOORMANSHydraulics Laboratory, Department of Civil Engineering, Katholieke Universiteit Leuven, 3000 Leuven, BelgiumThis paper discusses the hydro-meteorological potential of the X-band Local AreaWeather Radar installed in the densely populated city centre of Leuven, Belgium.Different merging techniques are applied to raw radar data using gauge readings from anetwork of 12 rain gauges. The hydrological response is investigated in the 48.17 km2Molenbeek/Parkbeek catchment in Belgium. For this, two lumped conceptual models,VHM and the NAM are used. Range dependent adjustment followed by Mean Field BiasAdjustment and Brandes Spatial Adjustment improved the radar estimates to a greatextent. After adjustments, the mean absolute error is found to decrease by 47% and theroot mean square error by 45% compared to the original radar estimates. No largedifferences in streamflow simulation capability of the two models can be distinguished.More uniform winter storms are simulated with greater accuracy than summer storms.INTRODUCTIONFor most of the simulation models used in water engineering, rainfall is primary inputand often considered spatially uniform over the catchment, or over subregions defined bythe density of the rain gauge network, which is usually not the case. Rather, it is highlyvariable in both space and time. Even in a single storm, rainfall can vary from tens ofmm/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 simulatedevents (Willems, (2001) [8]). Accurate high-resolution – in both space and time –rainfall input to the hydrological modelling is required to acquire more robust andaccurate hydrological simulations. Accurate and short duration rainfall input can beprovided 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 1647
  2. 2. 1648measurements (Einfalt et al., (2004) [4]). These uncertainties should be minimizedbefore using radar measurements as input to simulation models by using adjustmenttechniques (Wilson and Brandes, (1979) [10]). This could be done by merging radar andrain gauge information. The hydro-meteorological potential of weather radars has already been explored bymany researchers. An X-band weather radar is relatively new and it has rarely been usedin hydrological modelling. Owing to its finer resolution, better results are expected thanthose obtained by conventional S and C-band radars if optimal adjustment procedures areapplied. This study focuses on accuracy of LAWR estimates, based on a case in Belgiumwhere an X-band weather radar has been installed.METHODOLOGYThe X-band Local Area Weather Radar (LAWR) of LeuvenAs outcome of a project aiming at the “development of a system for short-time predictionof rainfall”, the Danish Hydrological Institute (DHI) together with the DanishMeteorological 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 wallwhich cuts off the lower part of the beam (Goormans et al., (2008) [5]). The LAWRrecords reflectivity values (representation of back scattered energy) which are convertedto rainfall rates by a linear relationship. The slope of this relationship represents aCalibration Factor (CF), which is a conversion factor that converts radar reflectivityrecords to rainfall rates.Study areaThe study area is within 15 km radius of the LAWR. The rain gauge network comprisesof 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. Theelevation of the catchment ranges from 22 m to 117 m above mean sea level. Agriculturalland and sandy soil is the dominant land-use and soil type of the catchment.Radar-gauge merging techniquesOwing to the rainfall pattern in Belgium, the study is distinguished into two periodsnamely summer storm and winter storm periods. The summer period considered spansfrom July 2, 2008 to September 30, 2008 and the winter period from December 1, 2008to March 31, 2009. Different CFs are obtained for each rain gauge as the result of aregression analysis, based on the storm average rain gauge intensities and the measuredcounts in the corresponding radar pixels. The average value of these CFs is used to obtainrainfall rates. After using a constant CF value for all radar pixels, following mergingtechniques are applied sequentially:
  3. 3. 1649 1. Range Dependent Adjustment: this adjustment on CFs is essential to some extentbecause of ever increasing height of measurement, beam broadening and attenuationeffect. 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 theradar estimates can be corrected by a uniform multiplicative factor and is given by: F 1 (1) R i GiMFB   N N i 3. Brandes Spatial Adjustment (BRA): the main idea is to use a weighted average ofthe correction factors from the rain gauge sites to each radar grid cell, with weights widepending 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 iIn equations (1) and (2), Gi and Ri = gauge and radar valid pair readings; N = totalnumber of valid pairs; d = distance between the gauge and the grid point in km; k = afactor controlling the degree of smoothening, generally given as the inverse of two timesthe 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 thesewere considered as “valid pairs”. For all purposes, the average number of counts over 9radar pixels surrounding the gauge location is used. In order to evaluate theimprovements achieved by each step in the adjustment procedure, comparison on somegoodness-of-fit statistics is made before and after adjustment. The Root Mean SquareError (RMSE), Mean Absolute Error (MAE) and Nash Sutcliff Efficiency (NSE) are usedfor this study.Rainfall-Runoff models and modelling approachTwo different conceptual rainfall-runoff modeling methods (VHM and NAM) have beenused to simulate the effect of the various rainfall input estimations on the catchmentrunoff. VHM is a Dutch abbreviation for generalized lumped conceptual andparsimonious model structure identification and calibration. The VHM modelingapproach 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-runoffprocesses occurring at the catchment scale (DHI, (2004) [3]). The rainfall derived from the rain gauge network was perceived as more robust andhence considered as reference rainfall (Pref) to be used as input for the calibration process.
  4. 4. 1650The parameter set thus derived is used to simulate the catchment runoff by using adjustedradar 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 runoffresults to observed discharges of the river gauging station downstream the catchment:  n     Q (i )  Q (i )  m o 2     MSE  (3)   1  2  i 1NSE  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 = thetotal number of observations; i = the ith number of observation; S2Qo= the variance ofobserved discharge series; Qo = the mean of observed discharge series. The simulated flow driven by the reference rainfall (Pref) is referred to as thereference flow (Qref). The difference between the reference flow and the flow driven byadjusted radar estimates is the error induced due to the tested rainfall input keeping modelparameter uncertainty the same. A modified definition of NSE is introduced to measurethe performance of the simulated runoff in comparison to reference flow defined byequation (3) where Qo is replaced by Qref. Both the NSEobs and NSEref will be defined forthe NAM as well as the VHM. To quantify the effects of using LAWR estimates, 4storms 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 27.2RESULTS AND DISCUSSIONAccuracy of radar estimatesUsing the average value of CF showed significant fluctuation on the radar and gaugevalues 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 radartends to overestimate rainfall in those pixels which are closely located to the LAWR andtends to underestimate rainfall in those pixels which are further away. Combining asecond 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. 5. 1651LAWR in km), the range dependency problem is addressed which also produced quitegood results reducing overall the RFB to nearly 6%. The frequency distribution ofindividual 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 forthe summer and winter period was found to be 1.015 and 0.974 respectively. The radarfield is then subjected to the Brandes Spatial Adjustment. The goodness-of-fit statistics for the subsequent adjustment procedures can beobserved in Figure 1. It can be seen that the adjustment procedures have greatly improvedthe radar estimates for both periods. A decreasing trend of the RMSE as well as MAEvalues and an increasing trend of NSE value can be observed when the raw radar data aresubjected to subsequent adjustment steps. It is calculated that the RMSE values improvedby 25%, the MAE by about 34% for summer weeks. More significant improvements havebeen 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 LAWRestimates. 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 IndicatorsFigure 1. Evolution of different rainfall goodness-of-fit statistical after adjustment step onthe LAWR-Leuven estimates; [a]-summer period and [b]-winter periodHydrological applicationTuning of the model parameters has been done with an heuristic approach. Optimizationof model parameters has been based on good matching on total water balance, shape ofthe hydrograph, peak flows and low flows. Table 2 shows the results of hydrologicalmodel performance evaluation based on the Water Engineering Time Series PROcessingtool (WETSPRO). The model performance statistics shown in that table are the MSE andNSE for “nearly independent” peak and low runoff flows extracted from the hourly timeseries ranging from 9/10/2003 to 2/28/2009. Details about WETSPRO can be found onWillems, (2009) [9].
  6. 6. 1652Table 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 foundin Figure 3 and expresses the errors in reproducing the reference flow introduced by theLAWR 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 eventsFigure 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 andfrom 0.34 to 0.93 for the NAM simulated flows. The storm event of 9-Feb-09 results inthe highest NSEobs value for both models. The storm event of 3-Aug-08 results in thelowest NSEobs value for the VHM and the storm of 5-Dec-08 for the NAM. Degradationof 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 LAWRestimates in winter periods rather than in summer periods. Results indicate that lowerNSEobs values are expected for summer events than for winter events. This may be due tothe rainfall spatial variability in summer events. Summer events are of highly convectivenature and the raingauge may have missed this information. On the other hand, the winterevents have less spatial gradients and the rain gauge network can represent them withconsiderable accuracy. Likewise, the average NSEref values for the LAWR driven flowsare 0.83 and 0.86 and NSEobs values are 0.72 and 0.62 for VHM and NAM simulatedrunoff respectively. The average NSEobs for the Pref driven flow is 0.79 for the VHM and0.70 for the NAM (the difference from 1 can be regarded as model error). Hence thedeviation from NSEref and NSEobs can be considered as the additional error (incomparison with the use of the reference rainfall) introduced by using the LAWRestimates.
  7. 7. 1653 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 eventsFigure 3. Results in terms of NSEref for the different rainfall descriptors Hence from the results, contrary to expectation, underperformance of the LAWRestimated rainfall can be observed. This underperformance can be attributed to thecalibration strategy used, where both models were calibrated against Pref. It is also relatedto the nature of the models used. Both are lumped rainfall runoff models, using averagedareal rainfall rather than using spatially variable input. Hence, for extreme and summerevents where the spatial variability of rainfall is high, the radar estimates are always tendto be dampened due to averaging effects of the large number of pixels covering thecatchment. 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 limitedaccuracy in its rainfall intensities and that the adjustment based on the rain gauges mayhave failed to capture all the spatial variability. Moreover, it can be worthwhile to notethat the importance of spatial rainfall such as the estimates of LAWR depends on howvariable the rainfall is and whether there is enough variability to overcome the dampingand filtering effect of the basins because fast responding catchments are more sensitive tospatial rainfall variability. As the studied catchment is flat and characterized bypredominant sandy soils, a large portion of rainfall infiltrates and local variation of therainfall input is smoothed and delayed within the soil. Hence, rainfall variations aredampened by integrating the response of the catchment.CONCLUSIONS AND RECOMMENDATIONSRange dependent adjustment followed by the MFB adjustment and Brandes SpatialAdjustment improved raw radar estimates quite significantly. In numerical terms, theRoot Mean Square Error was improved by 45% whereby 47% improvement has beenobserved on the Mean Absolute Error. After adjustments, the radar-gauge comparison inthe considered summer period improved more than that in the winter period. In terms ofrunoff simulations, the performance of both the VHM and NAM models could not behighly distinguished. Four storm events were investigated to test the prediction capability
  8. 8. 1654of the LAWR estimates. NSEref values less than 0.7 for summer storms indicate that localsummer rain cells played a role to produce lower peaks. This can also be attributed to thehigh dampening effect of the catchment. Separate analysis on different storm periods (summer and winter) based on longerseries of data is recommended. Use of a model which can use full spatial information ofrainfall is also recommended. Testing the rainfall spatial information on more urbanizedcatchments 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- band radar installation sites, based on on-site clutter tests”, proc. 5th Eur. Conf. on Radar in Meteorology and Hydrology (ERAD 2008), Helsinki, Finland, 30 June – 4 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.[10] Wilson J. W. and Brandes E. A., “Radar Measurement of Rainfall: A Summary”, Bull. Am. Meteor. Soc., 60(9), (1979), pp 1048-1058.