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

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 2

Image Source: Storm components 3

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MBLRP model 5

– Storm arrival: Poisson process  – Rain cell arrival: Poisson process  – Storm duration: Exponential distribution  – Rain cell intensity: Exponential distribution  – Rain cell duration: Exponential distribution,  - Gamma distribution MBLRP model parameters 6

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. 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. 7

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 Rainfall statistics 8

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 z i = a 1 *w 1 + a 2 *w 2 + a 3 *w 3 + … + a n * w n The weights w i 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 Number of rain cells 13

Regionalization - Multimodality Set 1 Set 2 Set 3 Set 4 Set 1 Set 2 Set 3 Set 1 Set 2 Set 3 Set 4 Set 1 Set 2 Set 1 Set 2 Set 3 Set 2 Set 3 Set 1 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

May 18 Average number of rain cells per storm Average storm duration (hr) Average rain cell arrival rate (1/hr) Average rainfall depth per storm (mm) Average rain cell duration (hr).

Average rainfall 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 22

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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? 25