Filling Gaps in Precipitation Data for Rainfall-Runoff Models

1. Filling Gaps and Daily Disaccumulation of Precipitation Data for Rainfall-runoff model M.F. Villazón K.U.Leuven - Hydraulics Division

2. Introduction Precipitation data is the most important input in hydrological models. In many river basins, records collected in long periods of time contain gaps: • Before applying any hydrological model, data analysis should be executed first, to have complete rather than partial rainfall records • There are two main procedures to fill rainfall gaps: • Stochastic modeling of rainfall sequences (Zuccini te al, 1992; Woolhiser, 1992), used to generate artificial rainfall sequences. Not applicable when the rainfall records are to be used as input to rainfall-runoff models and when the use involves calibration of these models • Interpolation based method, regression (Makhuvha et al, 1997a) • Linear regression and multiple linear regression techniques for the estimation of monthly precipitation in the gaps of 33 stations for the period from 1976 to 1999. • The disaccumulation was done assuming that each station had the same daily distribution as the recording station with the highest correlation.

3. Study area Pirai River basin, which is a tributary of the Amazon River. • It drains a total area of about 2705 km2 till “La Belgica” station

4. Material and Methods The precipitation data is available in 34 stations, of which 22 are located inside the area and 12 in the surroundings 8 have more than 25 years of recorded data; these stations have been called long-term stations. 5 have complete records and 9 have less than 5% gaps

5. Material and Methods Data availability

6. Material and Methods Filling monthly gaps Linear regression approach The methodology begins with the calculation of simple correlation between all pairs of stations for each calendar month, based on at least 10 years of overlapping rainfall records. The correlations are ranked, the missing month is estimated using a linear regression with the station that has the highest correlation and that has a recorded data in the same month April September

7. Material and Methods Filling monthly gaps Multiple linear regression approach The monthly stream simulation tool (HEC4) developed by the U.S. Corps of Engineers (HEC, 1971). Even that the model was developed for streamflow simulation its use in monthly rainfall accumulation is also possible because of the correlated data used. The model applies a logarithmic transformation to the data, where after each value is converted to a normalized standard variate. Correlation coefficients between all pairs of stations for each current and preceding calendar month are calculated and stored in a correlation matrix. K = Monthly logarithmically transformed flow, expressed as a normal standard deviate β = Beta coefficient computed from correlation matrix i = Month number j = Station number n = Number of interrelated stations R = Multiple correlation coefficient z = Random number from standard normal distribution

8. Material and Methods Filling monthly gaps Multiple linear regression approach The manner of grouping stations is extremely important, it is important to include in each successive group as much information as possible

9. Results and Discussion For the evaluation of the techniques applied • 32 months were subtracted from the recorded data: one for every year and every different station.

10. Results and Discussion For the evaluation of the disaccumulation applied • Rainfall distribution curve for daily generated and observed data • Other techniques can estimate small rainfall events on days when there was no rainfall. The latter could cause small effects on the overall RMSE, but could cause more significant effects in modelling rainfall-runoff that uses catchment moisture deficit

11. Results and Discussion • The use of multiple linear regression technique for the monthly rainfall estimation gives us an important reduction (36%) in the STD and RMSE over the linear regression technique. • The EF reaches a value of 0.84 that corroborate the good estimations

12. Thank you for your attention