Regionalizing Stochastic Rainfall Generators

1. American Society Civil Engineers Environmental and Water Resources Institute World Environmental & Water Resources Congress 2010 Providence, Rhode Island – May 17, 2010 Regionalizing StochasticRainfall Generators Dongkyun Kim and Francisco Olivera Zachry Department of Civil Engineering Texas A&M University

2. Why stochastic rainfall generation? • Synthetic rainfall “data” can be used as input to hydrologic models whenever rainfall data are not available: • Basins with rain gages but with missing data • Basins that need thousands of years of rainfall input to assess the risks associated with hydrologic phenomena (e.g. floods, draughts, water availability, water contamination) • Basins with no rain gages

3. Storm components • Image Source: http://www.meteoswiss.admin.ch/web/en/research/projects/rain.html

5. MBLRP model parameters – Storm arrival: Poisson process – Storm duration: Exponential distribution – Rain cell arrival: Poisson process • – Rain cell intensity: Exponential distribution , - Gamma distribution – Rain cell duration: Exponential distribution

6. MBLRP model parameters • λ (1/T): expected number of storms per unit time. • / (T): expected rain cell duration. • : uniformity of the rain cell durations. • (L/T): expected rain cell intensity. • : ratio of the expected rain cell duration to the expected duration of storm activity. • : product of the expected number of rain cells per unit time times the expected rain cell duration. • For the convenience, the parameters are normalized as  = / and  = /. • Therefore, the following six parameters are typically used: , , , ,  and . • The model calibration consists of minimizing the discrepancy between the statistics of observed and simulated precipitation.

7. Rainfall statistics Mean_1 Var_1 AC_1 Prob0_1 Mean_3 Var_3 AC_3 Prob0_3 Mean_12 Var_12 AC_12 Prob0_12 Mean_24 Var_24 AC_24 Prob0_24

8. Rainfall statistics Mean Variance Prob0 Lag-1 autocorrelation

9. Regionalization • Estimate the MBLRP parameters at 3,444 NCDC gages across the contiguous US. • Interpolate the parameters using the Ordinary Kriging technique. • Cross-validate the parameter maps at all 3,444 gages.

10. Regionalization - Interpolation • Ordinary Kriging was used to interpolate the estimated parameters • zi = a1*w1 + a2*w2 + a3*w3 + … + an * wn • The weights wi are determined based on a empirically driven function called “variogram.”

11. Expected Results Expected number of storms per hour in September:  (1/hr)

12. Regionalization - Multimodality 2 2.8 2 2.3 Number of rain cells 6 15 2 2

13. Regionalization - Multimodality

14. Results 72 maps = 6 parameters  12 months

15. (1/hr)  (hr) •  (mm/hr) •   May

16. Rainfall Characteristics • Rainfall characteristics according to the MBLRP model:

17. Average number of rain cells per storm • Average rain cell arrival rate (1/hr) May • Average storm duration (hr) • Average rainfall depth per storm (mm) • Average rain cell duration (hr).

18. Averagerainfall characteristics for the month of May for selected locations with mean monthly rainfall depth of 141 mm

19. Validation Cross-validated parameters were used to simulate the accuracy of interpolated points.

20. Validation

21. Validation

23. Summary and Conclusions • 72 MBLRP parameter maps were developed for the contiguous US (i.e., 6 parameters  12 months). • Overall, the parameters showed a regional and seasonal variability: • Strong : λ , μ • Discernible : φ, κ, α • Weak: ν • Parameter values from the maps were cross-validation and showed that the rainfall statistics could be reproduced reasonably well except for the lag-1 autocorrelation coefficient.

24. Questions?