1. Let-It-Rain: A Web-based Stochastic Rainfall Generator Huidae Cho 1 Dekay Kim 2, Christian Onof 3, Minha Choi 4 April 20, 2016 1 Dewberry, Atlanta, GA 2 Hongik University, Seoul, Korea 3 Imperial College, London, UK 4 Sungkyunkwan University, Suwon, Korea

2. Stochastic Rainfall Generator  Generates synthetic rainfall time series based on the statistics of the past storm events  Let-It-Rain: http://LetItRain.info  Web-based using ArcGIS API for JavaScript  Applications: General Use, Flood, Runoff  Simulation period: January to December  Unlimited number of simulations  Click or enter coordinates  Funded by the Ministry of Science, ICT and Future Planning, Korea  For commercial use, contact Dekay Kim

3. Stochastic Rainfall Generator (cont.)  Uncertainty analysis of hydrologic phenomena such as flood, drought, etc.  Fill data gap for water resources planning and design  Climate change modeling http://www.brisbanetimes.com.au/content/dam/images/1/9/f/e/k/ image.gallery.galleryLandscape.600x400.1pmvn.png/1325987703890.jpg http://s4.firstpost.in/wp-content/uploads/2012/08/Drought_Boy_Afp.jpg

4. Why Does It Matter? 1. Uncertainty Analysis

5. Why Does It Matter? 1. Uncertainty Analysis (cont.) Curve Number Lag Time Prior knowledge about the model and study area Rainfall generator 100-year Floodplain Histogram of the Flooded Area Monte Carlo GLUE Statistical inference

6. Why Does It Matter? 2. Filling Data Gap for Planning and Design Purposes  Statistical generation of rainfall time series for ungaged locations 2554 + 143 NCDC rainfall gages

7. Why Does It Matter? 3. Climate Change Modeling  Future climate projections based on observed data  Estimation of extreme weather events

8. Modified Bartlett-Lewis Rectangular Pulse (MBLRP) Model λ [1/T] – Storm arrival rate, Poisson process β [1/T] – Rain cell arrival rate, Poisson process γ [1/T] – 1/Storm duration, Exponential distribution μ [L/T] – Rain cell intensity, Exponential distribution η [1/T] – 1/Rain cell duration, Exponential distribution ν [T], α [-] - Gamma distribution Normalized φ [-] = γ/η Normalized κ [-] = β/η Time [T] Intensity [L/T]

9. Statistic Measures  Four statistic measures Mean(Synthetic Rainfall) = Mean(Observed Rainfall) Variance(Synthetic Rainfall) = Variance(Observed Rainfall) Autocorrelation(Synthetic Rainfall) = Autocorrelation(Observed Rainfall) Probability of zero rainfall(Synthetic Rainfall) = Probability of zero rainfall(Observed Rainfall)  Four accumulation levels: 1 hour, 3 hours, 12 hours, and 24 hours  Total 4 x 4 = 16 statistic measures for each month

10. Objective Function  θ is the parameter vector (λ, ν, α, μ, φ, κ),  n is the number of statistics being matched,  F k is the k th statistic of the simulated rainfall time series,  f k is the k th statistics of the observed rainfall time series, and  w k is a weight factor given to the k th statistic.  For runoff volume, higher w k for the mean  For flood discharge, higher w k for the mean and variance  For other simulations, equal weights

11. Parameter Calibration  Six-dimensional optimization problem  Highly complicated surface of the objective function  Highly multi-modal  Gradient-based optimization methods cannot solve the problem  Isolated-Speciation-based Particle Swarm Optimization (ISPSO) (Cho et al., 2011) was used  Heuristic approach  Derivative free  Capable of finding not only global optimum but also local optima

12. ISPSO in Action

13. Calibrated Parameters

14. Parameter Regionalization  Estimated the MBLRP parameters at 2,697 NCDC rainfall gages across the United States  Interpolated the parameters using the Ordinary Kriging technique  Cross-validated the parameter maps (12 months x 6 parameters = 72 maps) at all the gages

15. 1 λ ν αμ φ κ

16. Let-It-Rain Architecture ArcGIS Server MBLRP Parameter Maps Web Server MBLRP JavaScript Code 4. MBLRP Modeling Web Client 5. Parameters / Simulated Precipitation 1. Request 2. MBLRP Code 3. MBLRP Parameters

17. Application to Urban Flood Modeling Flood Map of Simulated Rainfall and Design Rainfall (10 minute temporal resolution)

18. Demonstration  http://LetItRain.info http://LetItRain.info

19. Conclusions  Used the mean, variance, autocorrelation, and probability of zero rainfall for calibration of the MBLRP parameters  Used the Ordinary Kriging technique for parameter regionalization  Developed a web-based stochastic rainfall generator  Application results show the validity of simulated rainfall events  Future work includes inter-annual variability

20. References  Huidae Cho, Dongkyun Kim, Francisco Olivera, Seth D. Guikema, August 16, 2011. Enhanced Speciation in Particle Swarm Optimization for Multi-Modal Problems. European Journal of Operational Research 213 (1), 15-23. doi:10.1016/j.ejor.2011.02.026. doi:10.1016/j.ejor.2011.02.026  Dongkyun Kim, Francisco Olivera, Huidae Cho, Scott A. Socolofsky, June 2013. Regionalization of the Modified Bartlett-Lewis Rectangular Pulse Stochastic Rainfall Model. Terrestrial, Atmospheric and Oceanic Sciences 24 (3), 421- 436. doi:10.3319/TAO.2012.11.12.01(Hy).doi:10.3319/TAO.2012.11.12.01(Hy)  Dongkyun Kim, Huidae Cho, Christian Onof, Minha Choi, March 2016. Let-It- Rain: A Web Application for Stochastic Point Rainfall Generation at Ungaged Basins and Its Applicability in Runoff and Flood Modeling. Stochastic Environmental Research and Risk Assessment. doi:10.1007/s00477-016-1234- 6.doi:10.1007/s00477-016-1234- 6