Booij, Martijn J.

Dohmen-Janssen, Catarine M.

Dong, Xiaohua

English

For the implementation of lumped conceptual models in flood forecasting, point precipitation time series records need to be aggregated into regionally averaged time series. Therefore a question arises: how many rainfall gauges inside a specific river basin are needed to provide sufficient precipitation records for the rainfall-runoff models

University of Twente Research Information

Flood Management and DefenceProceedings NCR days 2003 - 24 -Appropriate spatial sampling resolution of precipitation forflood forecastingX.H. Dong, M.J. Booij & C.M. Dohmen-JanssenFaculty of Engineering Technology, Department of Water Engineering & Management, University of Twente, P.O. Box 217,7500 AE Enschede, The Netherlands; x.h.dong@ctw.utwente.nlIntroductionFor the implementation of lumped conceptualmodels in flood forecasting, point precipitationtime series records need to be aggregated intoregionally averaged time series. Therefore aquestion arises: how many rainfall gaugesinside a specific river basin are needed toprovide sufficient precipitation records for therainfall-runoff models?The variability of rainfall recorded at a singlespot is generally much larger than that of thedischarge recorded at the outlet of the basinconsidered. This is quite understandableconsidering the damping effect of the rainfall-runoff transformation process. For a givenphysics-based hydrological model, the greaterthe diversity between the input (rainfall) andthe output (discharge), the greater difficulty willbe encountered in establishing the mappingfrom the input to the output. Therefore anymeasures, which can help to decrease thevariability of the input, or increase the similaritybetween the input rainfall, time series and theoutput discharge time series will promote theperformance of a calibrated physical model.The operation of aggregating the point-sampled rainfall time series into regional-averaged time series has the expectedsmoothing-out effect. One important aspectthat has to be addressed here is that thepurpose of the appropriate spatial sampling ofrainfall is not to master the regime of therainfall events as detailed as possible, but toserve the practice of flood forecasting.Therefore the appropriate spatial sampling isdefined as that which can possibly lead toaccurate forecasting of discharge in the riverchannel.The problem is attacked in two steps. The firstone is based solely on the statistical analysisof recorded rainfall and discharge data, tryingto identify the appropriate amount of raingages for flood forecasting. The second step isto verify the results obtained in the previousstep by running a physical hydrological model:HBV, which is developed by the SwedishMeteorological and Hydrological Institute(SMHI, 2003). Qingjiang river basin in China isadopted as the case studied in this research,and the area upstream of the Yuxiakou flowstation is considered here, as shown in Fig.1.Figure 1. Qingjiang river basin.Both rainfall and discharge data are measuredat 6 hours time interval.Statistical analysis on rainfall-discharge dataVariances (square of the standard deviation) ofrainfall time series give an indication of thevariability of rainfall at a location or of a region.The recorded rainfall data on the neighbouringrain gages can be treated as mutuallycorrelated random variables if they are notseparated over long distance. The variance ofthe sum of these individual time series (whichis one method of estimating the aerial rainfall)is given by (Osborn & Hulme, 1997):][ )1(122 nrnin sS−+= (1)where 2is is the mean of the station variances;s2n is the variance of the average of thecombination of n station time series; r is themean inter-station correlation between all pairsof stations within the basin which is calculatedfrom Fig. 2; n is the amount of rain gagesincluded in the aggregation.As can be seen from equation 1, the variancewill be reduced with an increasing number ofrain stations n involved in averaging. This isproved by the curves in Fig. 3, from which canbe seen that the variance is reducinghyperbolically as n increases, but after acertain threshold it levels off, which implies thatthe effect of smoothing on the variability(variance reduction) is no longer significantwhen n is greater than about 10.##################### #################$$ $YuxiakouFlood Management and Defence- 25 - Proceedings NCR-days 2003Figure 2. Correlation between pairs of point rainfalltime series versus their separation distance for allpossible combinations of station pairs in Qingjiangriver basin.Figure 3. Variance of rainfall time series obtained byaveraging n station time series together for differentn.With the decreasing variability of the rainfall, itis expected that the similarity between therainfall time series and discharge time serieswill be increased, which will benefit to therainfall-runoff modelling. This similarity ismeasured with the maximum cross correlationbetween rainfall time series (with different n)and discharge time series as shown in Fig. 4.Figure 4. Maximum cross correlation (at time lag 3)versus different values of n.The use of the concept of maximum crosscorrelation stems from the fact that thecorrelation between two time series differsaccording to different time lags. For the areaupstream to Yuxiakou the hydrologicalresponse time can be identified as 3 timeunites (18 hours) (see Fig. 5).It is assumed that with the averaged rainfalltime series becoming more similar to thedischarge time series, as indicated by theincreasing values of correlation coefficients inFig. 4, the performance of a given hydrologicalmodel will be increased. Fig. 4 reveals that,when n is increased to 10, the correlationbetween averaged rainfall time series anddischarge time series hardly increases anymore, therefore 10 will be identified as theappropriate number of rain gages thatdetermines the appropriate spatial resolution ofrainfall sampling for the area upstream toYuxioakou in Qingjiang river. This result isverified by performing real flood forecastingwith HBV model.Figure 5. Cross correlation between averagedrainfall time series (with different n) and dischargetime series for different time lags.Verification with HBV modelThe area upstream to the Yuxiakou flowstation is treated as one sub basin as seen inFig. 1. The one-sub basin HBV model iscalibrated with rainfall, evaporation anddischarge data ranging from 1989 to 1996.Then it is validated with data from 1997 to1999. The effect of the amount of rainfallstations on the forecasting results is shown inFig. 6, where Nash-Sutcliffe efficiencycoefficient R2 and relative accumulateddifference between computed and recordeddischarge are used as the criteria to judge theperformance of forecasting. The validationresults compare favourably to the onesobtained in the preceding step.0 50 100 150 200 25000.20.40.60.81distance (km)correlationcoefficient0 5 10 15 20 2551015202530number of rain gagesvariance(mm2/(6hr)MeanMaximumMinimum0 5 10 15 20 250.40.450.50.550.60.65number of rain gagesmaxlagcrosscorrelationMeanMaximumMinimum0 2 4 6 8 100.30.350.40.450.50.550.60.650.7← 26 gagestime lagcorrelationcoefficient← 9 gages← 3 gages← 1 gageFlood Management and DefenceProceedings NCR days 2003 - 26 -Figure 6. Verification using HBV model.ConclusionsAmong 27 rain gages used in the studied area,10 are found to be the effective amount forflood forecasting. This is deduced first from theobserved rainfall and runoff data, bycalculating the variance reduction effect of allcombinations of rain gages from one to thetotal amount of the cluster, and theircorrelation with discharge time series. Theresult is further verified by running rainfall-runoff model-HBV, with only one combinationfor a certain number of rain gages. Althoughthe latter verification process is not as robustas the preceding statistical method (which isnot practically possible for running hydrologicalmodels), it provides a reasonable prove on thestatistical result from a different point of view.ReferencesSwedish Meteorological and Hydrological Institute(SMHI), 2003. Integrated Hydrological ModellingSystem (IHMS); Manual version 4.5. Norrköping,Sweden.Osborn, T.J. & M. Hulme, 1997. Development of arelationship between station and grid-box raindayfrequencies for climate model evaluation. Journal ofClimate. 10, pp. 1885-1908.0.60.650.70.750.80.850.90.951 3 6 9 12 15 18 21 24 27number of rain gagesR200.050.10.150.20.250.30.350.4relativeaccumulateddifferenceR2 | RelAccDiff |

Appropriate spatial sampling resolution of precipitation for flood forecasting

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Appropriate spatial sampling resolution of precipitation for flood forecasting

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