Effect of the Inter-annual Variability of Rainfall Statistics on Stochastically Generated Rainfall Time Series Dongkyun Kim, Seung-Oh Lee, and Kanghee Lee Hydro-Environmental Research Laboratory (HERL), Hongik University, Seoul, Korea

What is stochastic rainfall generator? Provides the hydrologic model with the thousands of years of rainfall input to assess the uncertainty of the risks associated with hydrologic phenomena (e.g., floods, draughts, water availability, water contaminations, etc.)

Poisson Cluster Stochastic Rainfall Generator Olsson and Burlando (2002) “PCM is the most robust and practical approach to simulate rainfall time series” Why robust? Because it is based on physical observation of rainfall processes Matches the important rainfall statistics well Why practical? Because it can generate the “realistic” rainfall at sub-daily time resolution

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Modified Bartlett Lewis Rectangular Pulse Model λ – Storm arrival, Poisson process β – Rain cell arrival, Poisson process γ – Storm duration, Exponential distribution μ – Rain cell intensity, Exponential distribution η – Rain cell duration, Exponential distribution ν, α - Gamma distribution

Parameters of PCM λ, ν, α, μ, φ, κ …………

Parameter Calibration Observed Rainfall Synthetic Rainfall E(Observed Rainfall) = E(Synthetic Rainfall) VAR(Observed Rainfall) = VAR(Synthetic Rainfall) AC(Observed Rainfall) = AC(Synthetic Rainfall) Prob0(Observed Rainfall) = Prob0(Synthetic Rainfall)

Parameter Calibration Rodriguez-Iturbe et al. (1988)

Parameter Calibration n is the number of statistics being matched, Fk is the kth statistic of the simulated rainfall time series, fk is the kth statistics of the observed rainfall time series and wk is a weight factor given to the kth statistic.

What is the Problem? Is this good enough?

What is the Problem? Predicts well the 10 year rainfall but not 100 year rainfall…Why?

What is the Problem? Two types of statistics: E(June 1981 : June 1982 : June 1983 : …. : June 2013) What is the Problem? E(June 1993) Two types of statistics: Long-term rainfall statistics – statistic of a given month for the entire length of the rainfall record. (Used for the calibration of the model parameters) Short-term rainfall statistics - statistics of a given month of a given year

What is the Problem? The parameters of the model are calibrated based on the long-term rainfall statistics. Extreme events cannot be fully explained by the long-term rainfall statistics.

The Hybrid Model (THM) Simulate the short-term rainfall statistics E(June, 2014), Var(June, 2014), AC(June, 2014), Prob0(June, 2014) Parameter calibration for each different month. λ(June, 2014), ν(June, 2014), α(June, 2014), μ(June, 2014), φ(June, 2014), κ(June, 2014) Rainfall time series is generated for each different month. Simulated Rainfall Time Series for June 2014

The Hybrid Model Application and Validation (11 Sites)

The Hybrid Model – Result Observed Rainfall Synthetic Rainfall (Traditional Approach) Synthetic Rainfall (The Hybrid Model)

Result Reproduction of Extreme Rainfall

Result Reproduction of Extreme Flood Flow from observed rainfall Flow from Synthetic Rainfall (Traditional Approach) Flow From Synthetic Rainfall (The Hybrid Model)

Result Reproduction of Extreme Flood

Conclusion THM outperforms the traditional approach of stochastic rainfall generation in reproducing important extreme rainfall and flow values. The model performance can be enhanced by giving more information about the rainfall characteristics especially its inter-annual variability.