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

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 12/31/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

10. 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.