Radar Based Rainfall Estimation for River Catchment Modeling Promotor: ...
Radar based rainfall estimation for river catchment modellingAcknowledgementFirst and foremost, I would like to express my...
Radar based rainfall estimation for river catchment modellingTable of Contents Acknowledgement ---------------------------...
Radar based rainfall estimation for river catchment modelling 2.3.2.1 Model structure --------------------------...
Radar based rainfall estimation for river catchment modelling 3.4.5.2 Basin response ---------------------------...
Radar based rainfall estimation for river catchment modellingA-1: Prior time series processing results -------------------...
Radar based rainfall estimation for river catchment modellingList of FiguresFigure 2-1: Different types of weather radars ...
Radar based rainfall estimation for river catchment modellingFigure 4-11: LAWR-Leuven and RMI-Wideumont daily accumulated ...
Radar based rainfall estimation for river catchment modellingList of TablesTable 2-1: Some characteristics of the Wideumon...
Radar based rainfall estimation for river catchment modellingList of AcronymsAD Average DifferenceBC ...
Radar based rainfall estimation for river catchment modellingAbstractThis paper discusses the first hydro-meteorological p...
Radar based rainfall estimation for river catchment modellingCHAPTER 1: INTRODUCTION1.1 Problem definitionRainfall is the ...
Radar based rainfall estimation for river catchment modellingestimates of rain gauges; from simple merging methods to soph...
Radar based rainfall estimation for river catchment modellingboth the RMI-Wideumont and the LAWR-Leuven for stream flow si...
Radar based rainfall estimation for river catchment modellingCHAPTER 2: LITERATURE REVIEW2.1 RainfallRainfall is one of th...
Radar based rainfall estimation for river catchment modellinglow intensity range up to 0.5 mm/min. He ascribed this phenom...
Radar based rainfall estimation for river catchment modelling Figure 2-1: Different types of weather radars and the...
Radar based rainfall estimation for river catchment modellingTable 2-1: Some characteristics of the Wideumont radar Proper...
Radar based rainfall estimation for river catchment modellingThe rainfall rate (R) can be related to N(D) by the following...
Radar based rainfall estimation for river catchment modellingtotal weight of only 8 kg, which makes it fairly easy to inst...
Radar based rainfall estimation for river catchment modellingbetween ‘counts’ recorded and ground rainfall rate exists. Th...
Radar based rainfall estimation for river catchment modellingFigure 2-3: Influence of choice of Z-R relationship on rainfa...
Radar based rainfall estimation for river catchment modelling Non-uniform vertical profile of reflectivity (VPR): Ev...
Radar based rainfall estimation for river catchment modellingevaluation of these merging methods has been carried out by d...
Radar based rainfall estimation for river catchment modellingones. Spatially distributed models have the potential to repr...
Radar based rainfall estimation for river catchment modellingcalibration. It is an approach with which a lumped conceptual...
Radar based rainfall estimation for river catchment modellingThe step 1 is prior time series processing where a number of ...
Radar based rainfall estimation for river catchment modelling Interflow separation process parameters: aIF,1 I...
Radar based rainfall estimation for river catchment modelling Figure 2-8: The NAM structure...
Radar based rainfall estimation for river catchment modellinga. Surface and root zone parameters Maximum water conte...
Radar based rainfall estimation for river catchment modelling A good overall agreement of the shape of the hydrograp...
Radar based rainfall estimation for river catchment modellingArnaud et al. (2002) conducted a study on catchments ranging ...
Radar based rainfall estimation for river catchment modelling Delobbe et al. (2008) evaluated several radar-gauge me...
Radar based rainfall estimation for river catchment modellingCHAPTER 3: APPLICATION3.1 MethodologyThe methodology mainly c...
Radar based rainfall estimation for river catchment modellingFigure 3-1: Belgium (light green), the RMI-Wideumont radar (b...
Radar based rainfall estimation for river catchment modelling3.3 Radar-gauge comparison and merging3.3.1 The raingauge net...
Radar based rainfall estimation for river catchment modelling3.3.3 Conversion of radar records to rainfall ratesAs already...
Radar based rainfall estimation for river catchment modelling3.3.4 Data periodsOwing to the rainfall pattern in Belgium, t...
Radar based rainfall estimation for river catchment modelling3.3.5 LAWR - gauge comparison and mergingThe first attempt is...
Radar based rainfall estimation for river catchment modellingwas used by Borga (2002). Germann et al. (2006) used 0.3 mm f...
Radar based rainfall estimation for river catchment modellingIt should be noted that the MFB adjustment is applied uniform...
Radar based rainfall estimation for river catchment modelling N ∑ (R i ...
Radar based rainfall estimation for river catchment modelling n ∑ (G i =1 i − Ri ) 2...
Radar based rainfall estimation for river catchment modelling Figure 3-3: Catchment under consideration with position of L...
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]
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Narayan Shrestha [Radar based rainfall estimation for river catchment modelling]

This is my Masters Thesis in partial fulfilment of the requirements for the Degree of Master of Science in Water Resources Engineering. This program is jointly organized by katholieke Universiteit Leuven and Vrije Universiteit Brussel.
Published on: Mar 3, 2016
Published in: Technology      
Source: www.slideshare.net


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

  • 1. 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
  • 2. Radar based rainfall estimation for river catchment modellingAcknowledgementFirst 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 constantencouragement 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 manyinteresting discussions and made me comfortable during field visits too. He read this thesisfrom beginning to end and offered many valuable comments.From a practical standpoint, the thesis would not have been possible without the collaborationof the Royal Meteorological Institute (RMI) of Belgium who provided the radar data of theWideumont station and the raingauge data as well. I would also like to express gratitude tothe 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 Flemishwater company Aquafin and the Flemish Environment Society for providing the raingaugeseries.Special thanks go to VLIR-UOS for providing the scholarship for this Inter-UniversityProgram in Water Resource Engineering (IUPWARE) 2007-2009 session and KatholiekeUniversiteit, 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 constantsupport 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 afamily, contribute to the success of the thesis to great extent. i
  • 3. Radar based rainfall estimation for river catchment modellingTable of Contents Acknowledgement --------------------------------------------------------------------------------------- i Table of Contents --------------------------------------------------------------------------------------- ii List of Figures ------------------------------------------------------------------------------------------ vi List of Tables ------------------------------------------------------------------------------------------viii List of Acronyms -------------------------------------------------------------------------------------- ix Abstract -------------------------------------------------------------------------------------------------- xCHAPTER 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 ----------------------------------------------------------------------------------- 3CHAPTER 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
  • 4. Radar based rainfall estimation for river catchment modelling 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 ---------------------------------------------22CHAPTER 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 Hydrological modelling ----------------------------------------------------------------------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
  • 5. Radar based rainfall estimation for river catchment modelling 3.4.5.2 Basin response ----------------------------------------------------------------------39CHAPTER 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 ---------------------------------------------------------------------------60CHAPTER 5: CONCLUSIONS ------------------------------------------------- 69 5.1 Comparing and merging of radar − gauge estimates -------------------------------------69 5.2 Hydrological modelling ----------------------------------------------------------------------70 5.3 Limitation and future perspectives----------------------------------------------------------71CHAPTER 6: REFERENCES --------------------------------------------------- 72CHAPTER 7: ANNEXES--------------------------------------------------------- 78 iv
  • 6. Radar based rainfall estimation for river catchment modellingA-1: Prior time series processing results -----------------------------------------------------------78A-2: Model results -------------------------------------------------------------------------------------79A-3: Rainfall series (in terms of Pref) for selected storm events --------------------------------82A-4: Accumulated rainfall over radar pixels for selected storm events -----------------------84A-5: LAWR-Leuven simulated results -------------------------------------------------------------86 v
  • 7. Radar based rainfall estimation for river catchment modellingList of FiguresFigure 2-1: Different types of weather radars and their aspects (Einfalt et al., 2004) --------------------- 6Figure 2-2: Simplified sketch of beam cut-off ------------------------------------------------------------------- 9Figure 2-3: Influence of choice of Z-R relationship on rainfall rates (Einfalt et al., 2004) -------------- 11Figure 2-4: Errors related to height of the measurement (Delobbe, 2007) --------------------------------- 11Figure 2-5: Some typical vertical profile of reflectivity (Delobbe, 2007) ---------------------------------- 12Figure 2-6: General lumped conceptual rainfall-runoff model structure (Willems, 2000)--------------- 14Figure 2-7: Steps in the VHM structure identification and calibration procedure ------------------------ 15Figure 2-8: The NAM structure ----------------------------------------------------------------------------------- 18Figure 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 ------------ 24Figure 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 ----- 24Figure 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 33Figure 3-4: The DEM map of catchment with stream network ---------------------------------------------- 34Figure 4-1: Evolution of RFB with range (using constant CF on the LAWR estimates) ---------------- 41Figure 4-2: Plot of CF as a function of distance to the LAWR, each point representing a TBR (Aquafin &VMM) -------------------------------------------------------------------------------------------- 42Figure 4-3: Evolution of RFB with range (using range dependent CF on the LAWR-Leuven estimates) ------------------------------------------------------------------------------------------------------------------- 43Figure 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 --------- 45Figure 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----------------------------------------- 46Figure 4-6: Frequency distribution of field bias of valid gauge-radar (LAWR) pairs -------------------- 47Figure 4-7: Probability distribution of field bias of valid gauge-radar (LAWR) pairs ------------------- 47Figure 4-8: Evolution of different statistical values with different adjustments on the LAWR-Leuven estimates; [a]-summer period and [b]-winter period ---------------------------------------------------- 49Figure 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 ------------------------------------------ 50Figure 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
  • 8. Radar based rainfall estimation for river catchment modellingFigure 4-11: LAWR-Leuven and RMI-Wideumont daily accumulated estimates comparison plot for summer weeks ------------------------------------------------------------------------------------------------- 53Figure 4-12: LAWR-Leuven and RMI-Wideumont daily accumulated estimates comparison plot for winter weeks --------------------------------------------------------------------------------------------------- 53Figure 4-13: Graphical comparison of nearly independent peak flow maxima ---------------------------- 57Figure 4-14: Graphical comparison of nearly independent slow flow minima ---------------------------- 58Figure 4-15: Graphical comparison of peak flow empirical extreme value distributions ---------------- 58Figure 4-16: Graphical comparison of low flow empirical extreme value distributions ----------------- 59Figure 4-17: Graphical comparison of cumulative flow volumes ------------------------------------------- 59Figure 4-18: NSEobs for different rainfall descriptors and for different storm events ------------------- 61Figure 4-19: Observed and simulated flows derived from different rainfall descriptors ----------------- 65Figure 4-20: Observed and simulated flows derived from different rainfall descriptors ----------------- 66Figure 4-21: Plot of SDIR and NSEref for both the VHM and NAM -------------------------------------- 67Figure A-1: Baseflow filter results ------------------------------------------------------------------------------- 78Figure A-2: Interflow filter results-------------------------------------------------------------------------------- 78Figure A-3: Observed and NAM simulated hydrograph for the calibration period (3/1/2006- 2/28/2009) ----------------------------------------------------------------------------------------------------- 79Figure A-4: Cumulative observed and NAM simulated discharge for calibration period (3/1/2006- 2/28/2009) ----------------------------------------------------------------------------------------------------- 79Figure A-5: Observed and NAM simulated hydrograph for the validation period (1/1/2004- 12/31/2005) ---------------------------------------------------------------------------------------------------- 80Figure A-6: Observed and VHM simulated hydrograph for the calibration period (3/1/2006- 2/28/2009) ----------------------------------------------------------------------------------------------------- 80Figure A-7: Cumulative observed and VHM simulated discharge for the calibration period (3/1/2006- 2/28/2009) ----------------------------------------------------------------------------------------------------- 81Figure A-8: Reference rainfall evolution for storm event-1 -------------------------------------------------- 82Figure A-9: Reference rainfall evolution for storm event-2 -------------------------------------------------- 82Figure A-10: Reference rainfall evolution for storm event-3 ------------------------------------------------- 83Figure A-11: Reference rainfall evolution for storm event-4 ------------------------------------------------- 83Figure A-12: Accumulated rainfall for storm event -1 (RMI pixels), north is upward ------------------- 84Figure A-13 : Accumulated rainfall storm event-1 (LAWR pixels), north is upward -------------------- 84Figure A-14: Accumulated rainfall for storm event -3 (RMI pixels), north is upward ------------------- 85Figure A-15: Accumulated rainfall storm event-3 (LAWR pixels), north is upward --------------------- 85Figure A-16: LAWR-Leuven VHM simulated river discharge for the period of 7/2/2008 to 9/30/2008 ------------------------------------------------------------------------------------------------------------------- 86Figure A-17: LAWR-Leuven NAM simulated river discharge for the period of 12/1/2008 to 2/28/2009 ------------------------------------------------------------------------------------------------------ 86 vii
  • 9. Radar based rainfall estimation for river catchment modellingList of TablesTable 2-1: Some characteristics of the Wideumont radar ------------------------------------------------------ 7Table 2-2: Some characteristics of the LAWR-Leuven ------------------------------------------------------- 10Table 3-1: Correction Factors [k] for the Aquafin and VMM raingauges ---------------------------------- 25Table 3-2: Calibration Factor [CF] for Aquafin and VMM raingauges------------------------------------- 26Table 3-3: Data periods of the RMI radar of Wideumont ----------------------------------------------------- 27Table 3-4: Data periods of the LAWR of Leuven -------------------------------------------------------------- 27Table 3-5: Selected storm events; LT means Local Time ---------------------------------------------------- 38Table 4-1: Some statistical parameter values before and after range dependent adjustment on the LAWR estimates. --------------------------------------------------------------------------------------------- 44Table 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) - 48Table 4-3: Some statistical parameter values before and after MFB adjustment on the RMI Wideumont radar estimates, RAW stands for original RMI-Wideumont estimates --------------- 52Table 4-4: The calibrated VHM parameters with their short description ----------------------------------- 54Table 4-5: The calibrated NAM parameters with their short description ----------------------------------- 55Table 4-6: Some goodness-of-fit-statistics ---------------------------------------------------------------------- 56Table 4-7: Rainfall spatial variability measured in terms of SDIR for the different rainfall descriptors and for selected events --------------------------------------------------------------------------------------- 60Table 4-8: Results in terms of NSEobs for the different rainfall descriptors and for different storm events ----------------------------------------------------------------------------------------------------------- 61Table 4-9: Results in terms of NSEref for the different rainfall descriptors------------------------------- 63 viii
  • 10. Radar based rainfall estimation for river catchment modellingList of AcronymsAD Average DifferenceBC Box-Cox TransformationBRA Brandes spatial adjustmentCF Calibration FactorDEM Digital Elevation ModelDHI Danish Hydrological InstituteDMI Danish Meteorological InstituteIUPWARE Inter-University Program in Water Resource EngineeringKMI Koninklijk Meteorologisch InstituutLAWR Local Area Weather RadarMAE Mean Absolute ErrorMFB Mean Field BiasNAM Nedbør-Afstrømnings-Model (Rainfall-Runoff Model)NSE Nash-Sutcliff EfficiencyPOT Peak Over ThresholdRFB Relative Field BiasRMI Royal Meteorological InstituteRMSE Root Mean Square ErrorSDIR Reference Spatial Deviation IndexSWAT Soil & Water Assessment ToolVHM Veralgemeend conceptueel Hydrologisch Model (Generalized lumped conceptual and parsimonious model structure-identification and calibration)VLIR Vlaamse Interuniversitaire RaadVMM Vlaamse Milieumaatschappij (Flemish Environment Agency)VPR Vertical profile of reflectivityWETSPRO Water Engineering Time Series PROcessing tool ix
  • 11. Radar based rainfall estimation for river catchment modellingAbstractThis 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 appliedto raw radar data using gauge readings from a raingauge network of 12 raingauges. The significanceof 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 theNAM, are calibrated with reference rainfall (Pref) − a rainfall representation defined by raingaugeswhich 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 ofthe catchment), the LAWR estimates and the estimates from a C-band weather radar installed by theRoyal Meteorological Institute (RMI) at Wideumont (Belgium). An index, reference spatial deviationindex (SDIR) is defined based on the difference between Pref and the alternative rainfall descriptors. Amodified Nash-Sutcliff Efficiency (NSEref) is used to evaluate the performance of simulated runoffwith respect to reference simulated runoff – runoff derived by reference rainfall.Range dependent adjustment is applied on the LAWR data combining a power and second degreepolynomial function. C-band RMI estimates tend to overestimate summer storms and stronglyunderestimate winter storms. The mean field bias correction followed by Brandes spatial adjustmentimproved the radar estimates to a great extent. After adjustments, the mean absolute error is found todecrease 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 differencesin streamflow simulation capability of the two types of models can be distinguished. Runoffsimulations based on the RG1 rainfall descriptor are almost as accurate as those based on Pref. Usingradar estimated rainfall for runoff simulations showed lower performance compared to both Pref aswell as RG1 indicating that the catchment is less sensitive to spatial rainfall variability and/or theaccuracy of radar based rainfall estimates is low. Runoff peaks for summer and extreme events areunderestimated due to high damping and filtering effects of the catchment or more obviously, due tothe localized summer rainfall events. More uniform storms are simulated with more or less the sameaccuracy for all rainfall descriptors. An inverse correlation between SDIR and NSEref is observed. AnSDIR of more than 10% affected the hydrograph reproduction indicating that the catchment requiresmore robust areal rainfall estimation.Key words: Weather radar; Runoff; Lumped conceptual model; Spatial rainfall variability. x
  • 12. Radar based rainfall estimation for river catchment modellingCHAPTER 1: INTRODUCTION1.1 Problem definitionRainfall is the driving force for the hydrologic cycle, a physical phenomenon which controlsthe terrestrial water supplies. Its nature and characteristics are important to conceptualize andpredict its effect on runoff, infiltration, evapotranspiration and water yield. For most of thesimulation models, it is primary input, often considered spatially uniform over the catchmentwhich 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 andover distances of only a few tens of metres (Austin et al., 2002). Hence the assumption ofuniform rainfall leads to a major uncertainty in simulated events (Willems, 2001). Also, it canbe observed that hydrologists have traditionally paid much more attention to the developmentof more sophisticated rainfall-runoff models or the local models to suit the local conditionsthan to the development of improved techniques for the measurement and prediction of thespace-time variability of rainfall. This is to be deplored, since rainfall is the driving source ofwater behind most of the inland hydrological processes (Berne et al., 2005). So, betterunderstanding on the rainfall input to the hydrological modelling is required to acquire morerobust and accurate hydrological simulation. Hence, it demands a dense rain gaugeobservation 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 areimmediately available, are increasingly being used as an alternative. For the showery rain atleast, 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 passedover 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 radarsite.Also, it is an inherent property of radar measurements that the uncertainty on measurementsincreases as the rainfall intensity increases (Einfalt et al., 2004). These uncertainties shouldbe minimized before using them as input to simulation models by using adjustmenttechniques (Wilson and Brandes, 1979). Hence, merging of both forms of rainfall estimates isadvised. There have been a range of methods to merge the radar and raingauge data for better 1
  • 13. Radar based rainfall estimation for river catchment modellingestimates 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 datacan be greatly enhanced. However, radar-gauge residuals, even after adjustment are notalways 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-orientedhydrological modelling is well-known. However, the application of rainfall radar data toprovide 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 accuratepoint-wise measurements but the spatial representation is limited (Goudenhoofdt andDelobbe, 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 asground truth data and hence serves as validation source as well as basis for correction on theradar 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 theimportance of the spatial variability of rainfall information on the catchment underconsideration. Two lumped conceptual runoff models, the VHM (Veralgemeend conceptueelHydrologisch Model) and the NAM (Nedbør-Afstrømnings-Model), are used for thispropose.1.2 Motivation of the studyThe hydro-meteorological potential of the weather radars has already been explored by manyresearchers and interest in this subject is growing because of their capability of spatialcoverage to finer resolutions which are impossible to obtain with a raingauge network. TheC-band weather radar installed by the RMI at Wideumont has already been used forhydrological modelling. But the LAWR-Leuven, installed by the Flemish water companyAquafin, has rarely been used for such propose. Hence, a research has to be performed toevaluate the performance of the LAWR- Leuven for catchment modelling. In this study, acatchment named Molenbeek/Parkbeek, south of the Leuven is chosen for this propose. Using 2
  • 14. Radar based rainfall estimation for river catchment modellingboth the RMI-Wideumont and the LAWR-Leuven for stream flow simulation would lead toassess the significance of spatial resolution of the two different weather radars.1.3 Thesis aims and objectivesFor 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 outlineChapter 1 gives the general problem definition, motivation for the study, the aims andobjectives of the thesis.Chapter 2 gives the relevant literature review including the different rainfall descriptors, themodels 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 thestudy 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 anddifferent statistical tools used for the study are explained.Chapter 4 discusses the results.Chapter 5 covers the conclusions and recommendations for further researchers and thelimitation of different approaches used in the study as well.Apart from this the thesis also contains an appendix and list of references used. 3
  • 15. Radar based rainfall estimation for river catchment modellingCHAPTER 2: LITERATURE REVIEW2.1 RainfallRainfall is one of the many forms of precipitation and a major component of the hydrologicalcycle. It is the driving force of water for most of the terrestrial hydrological process (Berne etal., 2005). The rainfall must satisfy the intermediate demand of evapotranspiration,infiltration and surface storage before it results in runoff. In hydrological modelling, it is theprimary input (Segond et al., 2007; Velasco-Forero et. al., 2008).Rainfall can be mainly divided into stratiform and convective rainfall. Stratiform rainfallessentially results from stratiform clouds, has small drops and uniform spatial and temporalgradients. Convective storms on other hand are generally more intense and consist of largerdrops. They are characterised by large temporal and spatial gradients.2.2 Rainfall measurementRain gauges and weather radars are the two sensors that are most widely used in rainfallmeasurement (Velasco-Forero et. al., 2008).2.2.1 Rain gaugesThe most common device that is being used for rainfall measurement is a rain gauge. Becauseof its simple working principle, the tipping bucket rain gauges (TBRs) are widely used inrecent time though there are modern techniques coming up as well. The total amount ofrainfall over a given period is expressed as the depth of water which would cover a horizontalarea if there is no runoff, infiltration or evaporation. This depth is generally expressed inmillimetres and is the rainfall depth (FAO irrigation and Drainage Paper 27, 1998).Rain gauge measurements, although representing only point rainfall, are very oftenconsidered the “true” rainfall although there are some errors still associated with it. Duringtipping motion of the bucket, water continues to flow through the funnel which is not takeninto consideration, resulting in an underestimation of the rainfall rate (Goormans andWillems, 2008). Thus a dynamic calibration procedure should be applied. This procedure iswell defined by Luyckx and Berlamont (2001). Vasvari (2007) applied the same procedure onseveral rain gauges in the city of Graz, Austria and found that not all of them areunderestimating. Several rain gauges had a positive relative deviation; some up to 22%, in the 4
  • 16. Radar based rainfall estimation for river catchment modellinglow intensity range up to 0.5 mm/min. He ascribed this phenomenon by the retention of waterin the buckets between tips. But for higher intensities, the study showed a clearunderestimation. Another error associated with rain gauge measurement is due to windeffects. FAO irrigation and Drainage Paper 27, Annex 2 (1998) states that wind errors are amajor error which can be very large, even more than 50%. Hence, local wind shelterinfluences should also be considered. Goormans and Willems (2008) studied severalraingauges around the city of Leuven, Belgium and found that the wind effectsunderestimated the long term rainfall accumulation depth by a factor as high as 1.32. Thesetwo forms of errors that are always associated with rain gauges should be considered becauserain gauge based estimates of rainfall are generally used for validation of radar-based rainfallquantities and will affect final radar performance.2.2.2 Weather radarsRain gauges are reliable instruments for which hydrologists can rely on at least for pointmeasurement (Moreau et al., 2009) but rainfall can vary both in space and time which is notreally captured by the rain gauges. Thus, there have been considerable interests in utilizingthe weather radar, since it provides spatially and temporally continuous measurements thatare 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 butrather the back scattered energy from precipitation particles from elevated volumes and analgorithm should be developed and calibrated against the raingauge network.Wilson and Brandes (1979) and Einfalt et al. (2004) describe the methodology of usingweather radars in quantitative precipitation estimates and the potential error sources. The firststudy also focuses on the methodologies on radar-gauge comparisons and adjustments. Thesecond one gives a clear outline of requirements for weather radars, examples of good andbad 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-bandand the X-band radars. Their relative advantages and disadvantages are given in Figure 2-1. 5
  • 17. Radar based rainfall estimation for river catchment modelling 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 radarshave the longest wavelength while the X-band radars have the shortest. Using a largerwavelength for radar measurement would certainly enhance the usable range but problemsarise from radar beam interaction with ground. The shorter wave length radars, althoughhaving fine spatial resolution, suffer from attenuation significantly (Einfalt et al. 2004).2.2.2.1 The RMI weather radar at WideumontThe 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 240km. A Doppler scan with radial velocity measurements up to 240 km is performed every 15minutes (RMI, 2009). The 5 minute radar data are summed up to produce 1h and 24hprecipitation accumulation products. The radar is equipped with a linear receiver and thereflectivity 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 additionaltreatment is applied to the volume reflectivity file to eliminate residual permanent groundclutter caused by surrounding hills. Reflectivity data contaminated by permanent groundclutter are replaced by data collected at higher elevation. A Pseudo-Cappi image at 1500 m iscalculated from the volume data. An advection procedure has also been applied to correct theeffect of time sampling interval on accumulation maps (Delobbe et al. 2006).Characteristics: Some relevant characteristics of the C-Band Doppler radar located atWideumont are presented in Table 2-1 (Berne et al. 2005). 6
  • 18. Radar based rainfall estimation for river catchment modellingTable 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 scatteredenergy from precipitation particles from elevated volumes. The received energy from theprecipitation particles is given by: C K2 ZPr = (1) r2With,C = radar constantK = imaginary dielectric constantr = range of the targetZ = radar reflectivityThe radar reflectivity, Z (mm6/m3), is proportional to the summation of the sixth power ofparticle 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 DiN(D) = number of drops with diameters between D and D+dD in a unit volume. 7
  • 19. Radar based rainfall estimation for river catchment modellingThe rainfall rate (R) can be related to N(D) by the following equation if no vertical air motionis 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 isunknown and hence using an empirical Z-R relationship is imminent which is usually in theexponential 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 beenderived 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 notbe null vertical air motion such as the case of a thunderstorm. Also, the drop size distributionis rarely known and it varies in space and time (Wilson and Brandes, 1979).2.2.2.2 Local Area Weather Radar (LAWR) of LeuvenOutcome of a project ‘development of a system for short-time prediction of rainfall’, theDanish 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 onX-band marine radar technology and emits only a tenth (25 kW) of the power emitted fromconventional 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
  • 20. Radar based rainfall estimation for river catchment modellingtotal weight of only 8 kg, which makes it fairly easy to install. It has a horizontal openingangle of 3.9° making quantitative precipitation estimation possible up to a distance of 15 kmfrom the radar site (Goormans et al., 2008). But, the large vertical opening angle of 20° makesit susceptible to direct ground reflection.In an ongoing research project of the Hydraulics Laboratory of the Katholieke UniversiteitLeuven for the Flemish water company Aquafin, a City LAWR is installed in the denselypopulated city centre of Leuven. Based on quite rigorous clutter tests, the city LAWR isinstalled on the roof of the Provinciehuis building – the main office of the province ofFlemish Brabant. This location produced acceptable amounts of clutter, mainly due to a pitwall which cuts off the lower part of the beam (Goormans et al., 2008). The simplified sketchof this beam cut-off is shown in Figure 2-2. From here on, the City LAWR will be referred toas the LAWR. Figure 2-2: Simplified sketch of beam cut-offCharacteristics: Some relevant characteristics of X-Band LAWR located at Leuven arepresented 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. Thissuggests that the conventional transformation from reflectivity to rainfall rate should belinear. A relationship between the ‘count’ (representation of back scattered energy) and therainfall rate recorded at ground level has to be established. According to the manufacturerand as confirmed by some studies, (e.g. Rollenbeck and Bendix, 2006), a linear relationship 9
  • 21. Radar based rainfall estimation for river catchment modellingbetween ‘counts’ recorded and ground rainfall rate exists. The conversion factor whichconverts 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 min2.2.2.3 Uncertainty associated with radar estimatesAs the weather radar does not measure rainfall rates directly, it is prone to errors fromdifferent sources. Wilson and Brandes (1979) stated three major sources of errors associatedwith 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 mainlythree 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
  • 22. Radar based rainfall estimation for river catchment modellingFigure 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) 11
  • 23. Radar based rainfall estimation for river catchment modelling 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 hypotheseshave 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 needto be quantified. Continued research and use of new technologies might help to reduce theseuncertainties.2.2.2.4 Radar-gauge merging techniquesIt is evident that the strength of radar estimates, to capture spatial information, is theweakness of gauge records and that the strength of gauge estimates, the ability to capturerainfall amount at single location, is the radar’s weakness. Hence, merging of both forms ofrainfall information is necessary to obtain better rainfall information. Merging techniquescombine the individual strengths of the two measurement systems. Merging radar and gaugeobservations has been a burning topic of research since weather radar is being used in theearly seventies. Different methods have been proposed by different researchers and 12
  • 24. Radar based rainfall estimation for river catchment modellingevaluation of these merging methods has been carried out by different researchers, forexample, Brandes (1975), Wilson and Brandes (1979), Michelson and Koistinen (2000),Borga (2000), Delobbe et al. (2008) and Goudenhoofdt and Delobbe (2009). Results are moreor less similar. Significant improvements have been observed compared to original radarestimates. Wilson and Brandes (1979) adjusted radar estimates calculating storm to stormbias (R/G) and applied it uniformly through out the radar ranges and managed to reduce theerrors 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 mergingmethods like kriging, kriging with external drift etc. They concluded that geospatial methodsare 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 asBrandes Spatial Adjustment also performed well reducing the errors as close to the geospatialmethods, which are less tedious and time consuming compared to geospatial methods.2.3 Hydrological modellingHydrological models are simplified, conceptual representations of (a part of) the hydrologiccycle. They are primarily used for hydrological predictions and for understanding hydrologicprocesses. The development and application of hydrological models have evolved greatlythrough time. Once the rational method to determine the runoff discharge given rainfall depthas input is introduced, several concepts to predict and understand the hydrological cycleshave 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 ofunit hydrograph to calculate the volume of surface runoff produced by rainfall event. Theseinventions led the scope of hydrological modelling to a new height.Several hydrological models can be found in current time hydrology field as hydrologists tryto develop their new models that suit the local conditions (Berne et al., 2005), which mayoperate 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 thatthe classifications based on spatial description (lumped and distributed) and the descriptionsof the physical process (conceptual/empirical and physical) are the most commonly used 13
  • 25. Radar based rainfall estimation for river catchment modellingones. Spatially distributed models have the potential to represent the effect of spatiallyvariable 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 becausecalibrating a distributed model is not a straightforward task due to the large number ofparameters involved.Conceptual models have been widely developed and applied for hydrological modelling becauseof the ease on calibrating them. They lump, in a broad sense, the highly complex soil processesand properties in few macro-scale processes and parameters (Willems, 2000). Most of theconceptual models have similar structure. The rainfall input (xt) is separated into differentfractions 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 rainfallportions to overland flow and to interflow. The soil storage plays a role determining the actualevapotranspiration. After certain routing mechanisms, the total runoff y(t) is sum of the threerunoff components: yOF, yIF and ySF (Willems, 2000). A typical structure of a conceptual model isshown in Figure 2-6. This is general representation of the processes involved in a typicalconceptual 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 ModelThe VHM (Veralgemeend conceptueel Hydrologisch Model) is a Dutch abbreviation forgeneralized lumped conceptual and parsimonious model structure-identification and 14
  • 26. Radar based rainfall estimation for river catchment modellingcalibration. It is an approach with which a lumped conceptual rainfall runoff model can becalibrated in a step wise way. It is developed by Prof. Patrick Willems, HydraulicsLaboratory, Katholieke Universiteit Leuven, Belgium. The approach aims to deriveparameter values which are as much as possible unique, physical realistic and accurate. It isdata mining based and aims to derive a parsimonious model structure (Willems, 2000).2.3.1.1 Model structureThe model structure identification and calibration is carried on four distinct ways as can beseen 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
  • 27. Radar based rainfall estimation for river catchment modellingThe step 1 is prior time series processing where a number of prior time series processingtasks 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 andcalibration where lumped representations of different specific rainfall-runoff process equationsare identified and calibrated to related subsets of model parameters. This includes the followingsub-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 parametersThe VHM model structure identification and calibration approach deals with the followingparameters 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 Surface runoff separation process parameters: aOF,2 Surface runoff separation process parameters: aOF,3 16
  • 28. Radar based rainfall estimation for river catchment modelling Interflow separation process parameters: aIF,1 Interflow separation process parameters: aIF,2 Interflow separation process parameters: aIF,32.3.1.3 Model calibrationThe model parameters are tuned manually as per the information obtained in prior time seriesprocessing. The recession constants of subflows can be adopted as per the values obtained instep 1b. Optimizing soil storage sub-model parameters can be done by different graphicalplots, for example the plot of fu versus u/umax. The surface and interflow runoff separationprocess parameters can be tuned till a good match is observed which can visually be checkedin plots of subflows filter results (overland and interflow) versus model results. This VHMprocedure has clear advantages above an automatic or manual calibration technique, whichmost often is based on overall goodness-of-fit statistics optimization. In this approach, whendoing the optimization based on the statistical properties of the model residuals errors for thedifferent submodels or flow components considered, statistically unbiased sub-modelstructures and parameters are derived (Willems, 2000).2.3.2 The NAM modelNAM is the abbreviation of the Danish "Nedbør-Afstrømnings-Model", meaningprecipitation-runoff-model. This model was originally developed by the Department ofHydrodynamics and Water Resources at the Technical University of Denmark. The NAM is adeterministic, 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 structureThe 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 ofthe hydrological cycle. NAM simulates the rainfall-runoff process by continuouslyaccounting for the water content in four different and mutually interrelated storages thatrepresent different physical elements of the catchment. These storages are: Snow storage Surface storage Lower or root zone storage Groundwater storage 17
  • 29. Radar based rainfall estimation for river catchment modelling Figure 2-8: The NAM structureIn addition NAM allows treatment of man-made interventions in the hydrological cycle suchas irrigation and groundwater pumping. Based on the meteorological input data NAMproduces catchment runoff as well as information about other elements of the land phase ofthe hydrological cycle, such as the temporal variation of the evapotranspiration, soil moisturecontent, groundwater recharge, and groundwater levels. The resulting catchment runoff issplit conceptually into overland flow, interflow and baseflow components (DHI, 2004).2.3.2.2 Model parametersThere are quite a number of model parameters according to the different storage elementslisted below. Detailed information on the parameters can be found in the NAM referencemanual (DHI, 2004). The list of the parameters can be divided in following five subgroups: 18
  • 30. Radar based rainfall estimation for river catchment modellinga. 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 [-]: TIFb. Ground water parameters Baseflow time constant [hr]: CKBF Root zone threshold value for groundwater recharge [-]: TGc. 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]: GWLFL1d. 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]: Craine. Irrigation module parameters Infiltration factor [mm/day]: K0,inf Crop coefficients and irrigation losses2.3.2.3 Model calibrationThe process of model calibration is normally done either manually or by using computer-based automatic procedures including 9 default parameters enlisted above under theheadings; surface, root zone parameters and ground water parameters (DHI, 2004). Whileapplying 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
  • 31. Radar based rainfall estimation for river catchment modelling 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 andknowledge of the modeller, as auto-calibration routines are based on optimizing someobjective function and they are likely to end up in local optimum case rather than globaloptimum.2.4 Significance of spatial variability of rainfall and basin responseThe literature on the significance of spatial rainfall for runoff estimation is complex andsometimes contradictory. Effects can be expected to vary depending on the nature of therainfall, the nature of the catchment, the spatial scale of the catchment and the rainfall runoffmodel used.Basin response will obviously vary as rainfall patterns vary. Stratiform and convectivepatterns have distinct characteristics on their spatial variability and drop size. In Belgium, thesummer 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 modelswith respect to the type of rainfall. Segond et al. (2007) found a better match betweensimulated and observed runoff on winter storm than on summer storms. They concluded thatsummer storms have more variability and are less accurate to reproduce flow at the catchmentoutlet. Pechlivanidis et al. (2008) reached similar conclusions while testing different rainfallscenarios on the Upper Lee catchment of UK.On urbanized catchments, a high proportion of the rainfall becomes effective due to the largeamount of impervious areas. Hence, the effect of spatial rainfall on more urbanisedcatchments would obviously be greater. Segond et al. (2007) found that radar estimatedrainfall data are more suitable for stream flow simulation than that from the raingaugenetwork consisting of one and seven raingauges indicating that the spatial variability ofrainfall is important on urbanised catchments. 20
  • 32. Radar based rainfall estimation for river catchment modellingArnaud et al. (2002) conducted a study on catchments ranging 20 to 1500 km2 and observedthat 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 becauseof the fact that there is a transfer from spatial variability of rainfall to catchment responsetime distribution as the dominant factor governing runoff generation which can be regardedas a dampening effect of the spatial variability of rainfall.The basin response is essentially dependent on the type of rainfall-runoff model used. Fullydistributed physically based models are believed to better represent the basin characteristicsthan the lumped one. But it has always to do with the type of rainfall field used. Radarrainfall fields, capable of generating more spatial variability, are likely to be more suitable fordistributed models. Shah et al. (1996) conducted a study on a relatively small catchment of10.55 km2 where they compared the results from a physically distributed SHE (SystèmeHydrologique Européen) with the results form a linear transfer function model for spatiallydistributed rainfall and found a significant error by using the latter model.2.5 Similar past studiesNumerous similar past studies can be found in literature and the findings are complex andsometimes contradictory too.2.5.1 Radar-gauge comparison and mergingIt dates back to the 1980’s that there had already been some study on radar-gaugecomparison. 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
  • 33. Radar based rainfall estimation for river catchment modelling 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 dataAccuracy of radar estimated rainfall data for stream flow simulation has been tested by manyresearchers. 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
  • 34. Radar based rainfall estimation for river catchment modellingCHAPTER 3: APPLICATION3.1 MethodologyThe 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 gaugenetwork of 12 rain gauges as shown in Figure 3-2. Different merging techniques are tested toincrease the accuracy of the final radar estimates. Secondly, the corrected radar data will beused for modelling of a catchment using two types of lumped conceptual models, namely theNAM and the VHM. Significance of spatial representation of rainfall is also evaluatedthrough the basin response.3.2 Study areaThe study area is situated in the Flanders region of Belgium, near the densely populated cityof Leuven. The study area is within 15 km radius of the LAWR-Leuven. The rain gaugenetwork comprises of 12 rain gauges, most of them towards the north-west direction withrespect to the LAWR-Leuven and within 10 km from the LAWR-Leuven. The entire raingauge network lies in between 117 and 128 km from the RMI-Wideumont, in north-westdirection. 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 twelveraingauges are located in the catchment. More descriptions on the raingauge network can befound under the section of 3.3.1. For the catchment, the description is presented under thesection 3.4.1. The study area with the radar location, the catchment and the raingaugenetwork can be seen in Figure 3.2. 23
  • 35. Radar based rainfall estimation for river catchment modellingFigure 3-1: Belgium (light green), the RMI-Wideumont radar (black star), the LAWR-Leuven (redstar) 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; blacktriangles: 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
  • 36. Radar based rainfall estimation for river catchment modelling3.3 Radar-gauge comparison and merging3.3.1 The raingauge networkComparing radar estimated rainfall essentially requires ground “truth” data which is assumedto be correctly represented by the raingauge network. For our purpose, the network of 12raingauges is used; 4 of them being operated by Aquafin, 5 by the Flemish EnvironmentalAgency (VMM) and the other 3 by the RMI of Belgium. The Aquafin raingauges are TBRshaving a gauge resolution of 0.2 mm and a time resolution of 2 minutes. The VMMraingauges are also TBRs having a gauge resolution of 0.2 mm and a time resolution of 10minutes. The RMI maintains quite a dense network of non-recording raingauges giving dailyprecipitation accumulations between 8 AM and 8 AM Local Time (LT). The network withthe position of the LAWR-Leuven as well as the watershed is shown in Figure 3-2.3.3.2 Correcting raingauge measurementsAs already stated, raingauge data will be used as reference and will be considered as groundtruth data. Goormans and Willems (2008) conducted full dynamic calibration on theseAquafin and VMM raingauges for the purpose of calibrating the LAWR. Local wind shelterinfluences on these TBRs were also investigated and it was found that both sets of TBRsclearly 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) werefound. 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 RMIand 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 25
  • 37. Radar based rainfall estimation for river catchment modelling3.3.3 Conversion of radar records to rainfall ratesAs already depicted, the C-Band radar measures reflectivity (Z) values, as representative forrain droplets in a certain volume. This Z-value is converted to rainfall rate, R with a Z-Rrelationship of the form: Z = aRb. The RMI-Wideumont radar uses values of a and b equal to200 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 recordsthe number of counts (a dimensionless measure for the amount of reflected power) asrepresentative value of rainfall. A relationship between the count and the rainfall raterecorded at ground level has to be established for conversion. The conversion factor can betermed as Calibration Factor (CF). As the LAWR is relatively new giving records from July 22008 and onwards, and research is ongoing to have optimal CF values, the presented CFfactors in Table 3-2 can be considered as the best estimates currently available. Thesecalibration factors are the result of a regression analysis, based on the storm averageintensities and measured counts in the corresponding radar pixels of the period 2nd July- 8thOctober 2008 (Block-1, Table 3-4), which can be considered as a summer period. Theintensities are from calibrated raingauge data, and also corrected for the systematic bias dueto 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 26
  • 38. Radar based rainfall estimation for river catchment modelling3.3.4 Data periodsOwing to the rainfall pattern in Belgium, the comparison study is distinguished into twoperiods namely summer storm and winter storm periods. Convective rainfall is encounteredin 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 theHydraulics Division of the Katholieke Universiteit Leuven and data of some interesting stormperiods are made available. These periods are named week 1 to week 4 as presented in Table3-3, 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 insingle 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, 2009The data extracted from the LAWR-Leuven are counts with time resolution of one minute in240x240 grids each measuring 125 m by 125 m. The data can be divided on the three periodsas per the setting of signal processing parameter of the LAWR as presented in Table 3-4. Forblock 3, the parameters of signal processing were set to neutral; hence these periods are nottaken into consideration. For the LAWR-gauge comparison, the summer period consideredspans from July 2 2008 to September 30 2008, and the winter period from December 1 2008to March 31 2009. As the CF values presented on Table 3-2 are the result of analysis made onblock 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
  • 39. Radar based rainfall estimation for river catchment modelling3.3.5 LAWR - gauge comparison and mergingThe first attempt is to use a constant CF value for all radar pixels. This procedure does notaccount for the range dependency of the CF values. The results will be compared with thecase where range dependent CF-values are applied. The range dependent adjustment on CFvalues is essential to some extent because of ever increasing height of measurement, beambroadening and attenuation effect. Goudenhoofdt and Delobbe (2009) accounted for a rangedependency of the RMI-Wideumont using a second order polynomial with R/G expressed inlog scale. The same adjustment procedure will be the first trial with R/G (CF) expressed inlinear scale followed by power function as well.After applying the range dependent CF values (to obtain rainfall rate values), the Mean FieldBias (MFB) adjustment is applied. In MFB adjustment, it is assumed that the radar estimatesare affected by a uniform multiplicative factor. The factor is determined by gauge-radaragreement after integration over a space-time window. Although it is a simple adjustmenttechnique; it can already enhance the quality of rainfall estimate significantly. Goudenhoofdtand Delobbe (2009) found that the MFB correction reduced the error by 25% compared toraw radar data. Similar improvements have been observed by Borga (2002). The MFB isgiven by: ∑F 1 Gi ∑R iMFB = = (5) N N iWith,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 thanreal-time fashion is to avoid additional uncertainty due to time and space mismatching of theradar and gauge samples at shorter time intervals.If both daily raingauge accumulation and radar accumulations are greater than 1 mm thenthese were considered as “valid pairs”. This ensures that the same data set is used forcomparison. Different authors have used different threshold values for their study.Goudenhoofdt and Delobbe (2009) used a threshold value of 1 mm; the same threshold valuewas taken by Delobbe et al. (2008) on daily time scale basis. A threshold value of 0.5 mm 28
  • 40. Radar based rainfall estimation for river catchment modellingwas used by Borga (2002). Germann et al. (2006) used 0.3 mm for the evaluation of radarprecipitation estimates in Swiss mountains. Wilson and Brandes (1979) stated, citing theirprevious experiences, that if the gauge rainfall is light (<2 mm), it is best not used in anadjustment procedure. By this, they advised using a threshold value no less than 2 mm ondaily accumulation. For all purposes, the average counts over 9 radar pixels surrounding thegauge 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 statisticalparameters. A low threshold value would result in a significant amplification of some of thestatistical parameters, such as the MFB. For example, for gauge and radar pairs of 2 mm and0.2 mm respectively, MFB will be 10 and this distorts the mean MFB. Applying a thresholdvalue 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. Afterall, the bias is the ratio of the gauge to radar estimates and can be considered as a product oftwo stochastic variables, and this always tends to follow a lognormal distribution. Hence, thedistribution of the bias is checked by fitting theoretical distributions (normal, log-normal,exponential etc.) over the empirical (observed) distribution. The empirical distribution can becalculated by using one of the most used formulas, the distribution of Hazen (1930), and isgiven by: ( r − 0.5)Probability of exceedance = (6) n ( n − r + 0.5)Cumulative probability = 1 - (Probability of exceedance) = (7) nWith,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
  • 41. Radar based rainfall estimation for river catchment modellingIt should be noted that the MFB adjustment is applied uniformly over the entire radar rangeusing a single factor. The MFB attempts to minimize the bias between the gauge and radarestimates 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 thecorrection factors from rain gauge sites to each radar grid (Brandes, 1975). The rain gaugeswhich 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 isgiven 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 ofmean gauge density (number of gauges divided by total area), denoted by ‘δ’. This iscalculated 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 givenby: N ∑w i =1 i (G i / R i )C BRA = N (11) ∑w i =1 iWith,CBRA = Brandes spatial adjustment factor.In order to evaluate the improvements achieved by each adjustment procedures, comparisonon some goodness-of-fit statistics is made before and after adjustment. Several of theseparameters are found in literature. However, the Root Mean Square Error, Mean AbsoluteError, 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 verificationstudies and is given by: 30
  • 42. Radar based rainfall estimation for river catchment modelling N ∑ (R i =1 i − Gi ) 2RMSE = (12) NWith,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 andis given by: N ∑ (R i =1 i − Gi )MAE = (13) NWith,Ri, Gi = radar and gauge valid pair values.N = number of valid pairs.Similarly, the Relative Fractional Bias (RFB) accounts for the bias of radar estimated togauge value in a relative manner. It is similar to the term Average Difference (AD) used bysome researchers (e.g. Vieux and Vieux, (2005), Wilson and Brandes (1979) etc.) where theyused absolute values and expressed them in percentage. It is given by: Ri − GiRFB = (14) GiWith,Ri, Gi = radar and gauge valid pair values.However the RFB is sensitive to small values. For example, if the radar estimate for a gaugevalue of 0.5 mm is 1.0 mm, then the RFB will be 100% though the absolute difference on thepair 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 toassess the predictive power of hydrological models (Nash et al., 1970), but adapted for thiscase as; 31
  • 43. Radar based rainfall estimation for river catchment modelling n ∑ (G i =1 i − Ri ) 2E =1− n − (15) ∑ (G i −1 i − G) 2With,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 NashCriterion can be used to evaluate how well radar estimates match with gauge values.3.3.6 RMI Wideumont estimates and gauge comparison and mergingRegarding the data of the RMI-Wideumont, rainfall volumes can be directly extracted. Athreshold 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 radarestimates are smoothed by firstly applying the MFB and then the BRA adjustment. Whiledoing 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 modelling3.4.1 The catchment3.4.1.1 Choice of catchmentSeveral 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 limitedby the fact that the LAWR of Leuven is capable of giving quantitative estimates up to aradius of 15 km only. Another fact associated with LAWR is that the Zaventem airportauthorities do not allow transmission in the sector indicated by the light blue sector in Figure3-3. Due to these constraints the catchment named Molenbeek/Parkbeek, having area of48.17 km2, has been selected. This choice is also favoured by the absence of heavy clutters ascan be seen from the study of Goormans et al. (2008). The catchment contains two raingauges; 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. Thecatchment, along with raingauges, the LAWR and water courses, is shown in Figure 3-4. 32
  • 44. Radar based rainfall estimation for river catchment modelling 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 LAWR3.4.1.2 Catchment geomorphologyThe catchment has a temperate climate, is relatively flat, primarily composed of sandy soilswith 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 mabove mean sea level, with a mean elevation of 59.19 m. Almost 90% of the area has anelevation 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 typeof 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-duneand clay. The sandy soil is the dominant one as it covers almost 70% of the area. Around28% of the area is covered by land-dune and the remaining 2% by clay. 33

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