regionalizing stochastic rainfall generators
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Regionalizing StochasticRainfall Generators
Dongkyun Kim and Francisco OliveraZachry Department of Civil Engineering
Texas A&M University
American Society Civil EngineersEnvironmental and Water Resources Institute
World Environmental & Water Resources Congress 2010Providence, Rhode Island – May 17, 2010
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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 dataBasins 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
3Image Source: http://www.meteoswiss.admin.ch/web/en/research/projects/rain.html
Storm components
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– Storm arrival: Poisson process
– Rain cell arrival: Poisson process
– Storm duration: Exponential distribution
m– Rain cell intensity: Exponential distribution
– Rain cell duration: Exponential distribution , - Gamma distribution
MBLRP model parameters
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MBLRP model parameters
For the convenience, the parameters are normalized as = / and = /.
Therefore, the following six parameters are typically used: , , , m, 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.
m (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.
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Mean_1Var_1AC_1Prob0_1
Mean_3Var_3AC_3Prob0_3
Mean_12Var_12AC_12Prob0_12
Mean_24Var_24AC_24Prob0_24
Rainfall statistics
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Rainfall statistics
MeanVariance
Prob0 Lag-1 autocorrelation
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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.
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Regionalization - InterpolationOrdinary 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.”
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Expected Results
Expected number of storms per hour in September: (1/hr)
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Regionalization - Multimodality
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2.8
2.3 6
22 Number
of rain cells
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Regionalization - Multimodality
Set 1Set 2Set 3Set 4
Set 1Set 2Set 3
Set 1Set 2Set 3Set 4
Set 1Set 2
Set 1Set 2Set 3
Set 2
Set 3
Set 1
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Results
72 maps = 6 parameters 12 months
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(1/hr) (hr)
m (mm/hr)
May
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Rainfall CharacteristicsRainfall characteristics according to the
MBLRP model:
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May
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).
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State Texas Iowa Washingto
n
Florida
Longitude -95.592° -93.591° -123.975° -80.913°
Latitude 30.349° 41.966° 47.862° 27.050°
Rainfall depth per storm
(mm)
22.2 13.5 14.2 19.2
Storm duration (hr) 7.9 8.7 12.1 11.7
Number of rain cells per
storm
4.7 6.0 16.4 4.0
Rain cell arrival rate (1/hr) 0.57 0.61 1.30 0.38
Rain cell Duration (hr) 0.24 0.28 0.21 0.24
Average rainfall characteristics for the month of May for selected locations with mean monthly rainfall depth of 141 mm
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Validation
Cross-validated parameters were used to simulate the accuracy of interpolated points.
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Validation
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Validation
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Summary and Conclusions72 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.
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Questions?
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