Stochastic Storm Rainfall Simulation Prof. Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering National Taiwan University

What is a stochastic model? A model is a physical or mathematical imitation of a reality. Depending on our knowledge about the reality, models can be very sophisticated or relatively rough. Models can be developed based on Physical principles Conceptual perception Empirical association No models are perfect and uncertainties are naturally embedded in modeling and model outputs. 12/31/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

A model consisting of random components is considered a stochastic model. Stochastic modeling is the work of developing and utilizing stochastic models to study of real world problems. 12/31/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Stochastic storm rainfall process Occurrences, duration, event-total depth, and time variation of rainfall rates of individual storms are random in nature and can be considered as a stochastic storm rainfall process. Stochastic modeling of the storm rainfall process have many applications: Frequency analysis for sites with short record lengths Assessing the hydrological impacts of climate change 12/31/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

GCMs and Climate Change General circulation models (GCMs) are widely used to assess the impacts of climate change on temperature and precipitation of projection periods. GCM outputs are in scale of about 250 km in space and month in time. Downscaling to regional, local in space and daily or sub-daily in time Statistical downscaling or dynamic downscaling 12/31/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Stochastic Weather Generator Projected changes in monthly rainfalls of the projection period are provided by GCMs. Monthly rainfalls of the projected period are then calculated with reference to observed monthly rainfalls of the baseline period. The weather generator aims to generate daily temperatures and rainfalls of the projection period. (Downscaling to daily scale from monthly scale) 12/31/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Weather Generator (Richardson and Wright, 1984; Tung and Haith, 1995) Daily temperature generation 12/31/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

May be dependent on daily rainfall amount Daily rainfall generation May be dependent on daily rainfall amount Unif (0,1) 12/31/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

12/31/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

Based on 100 simulated runs. The target data are daily temperatures and daily rainfalls. Thus, why was the validation conducted using data of monthly scale? Based on 100 simulated runs. Historic data represent long-term averages of monthly temperature or precipitation. 12/31/2018 Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.