National Cheng Kung University, Taiwan. downscaling. Speaker: Pao-Shan Yu Co-authors: Dr Shien-Tsung Chen & Mr. Chin-yYuan Lin

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Pao-Shan Yu Co-authors: Dr Shien-Tsung Chen & Mr.

1 Department of Hydraulic & Ocean Engineering, National Cheng Kung University, Taiwan Impact of stochastic weather generator characteristic on daily precipitation downscaling Speaker: Pao-Shan Yu Co-authors: Dr Shien-Tsung Chen & Mr. Chin-yYuan Lin Professor, Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Taiwan Date: May 4-6, 2009

2 Outline Research objective Methods Study area and Data set Results and Discussion 2

Research objective To have daily precipitation

from IPCC DDC To develop a weather generator to produce

3 Research objective To have daily precipitation projection for the study on impacts of climate change on extreme event. Daily GCM projections from 2010~2045 are not available from IPCC DDC To develop a weather generator to produce daily precipitation using monthly output from GCMs. Statistical Downscaling Local precipitation projection 3

GCMs Projections Methods Station rainfall Spatial downscaling Large area Lacal Downscaling methods Model Predictor SVD-based Downscaling Model Model(t+1) Temporal downscaling

4 GCMs Projections Methods Station rainfall Spatial downscaling Large area Lacal Downscaling methods Model Predictor SVD-based Downscaling Model Model(t+1) Temporal downscaling Monthly Daily Weather Generator reconstruction EOF SVDA EOF reconstruction j Z obs( t) vj( t) hj, Zsim( t) u j( t) gj, j Results Z ( t + 1) = h u ( t + 1) j j j Downscaling MME Products 4

5 Methods Downscaling methods GCMs The weather variables in GCMs is rational at large spatial and temporal scales. Delta change Weather generator Using weather generator to produce daily precipitation from monthly GCMs outputs in this work. 5

6 Methods Weather generator developing Markov chain was used to model daily precipitation. Weather generator Transition probability Dry day or Wet day Probability distribution Daily precipitation 6

7 Methods Various probability distributions Exponential distribution Weibull distribution Gamma distribution Pearson type III distribution Which one can well reproduce the daily precipitation in the study area? 7

8 Methods Weather generator projection weather generator Using a delta change of monthly precipitation provided by GCMs to project monthly precipitation in the future. 10 GCMs (CSIRO scenario / GCMs (CSIRO-MK3, GFDL-CM2, GFDL-CM2.1, INM-CM3, IPSL-CM4, NIES-MIROC3.2-MED, MED, MPIM-ECHAM5, MRI- CGCM2.3.2, NCAR-CCSM3, CCSM3, UKMO-HADCM3) and B1 scenario were used. HADCM3) under A2, A1B 8

9 Study area and Data set Tseng-Wen Reservoir basin Reservoir storage capacity : 7800 million m 3 Area of reservoir basin : 481 km 2 Elevation : from 157 to 3,514 m Taiwan Rainfall (mm/m month) Multifunction purposes Reservoir Raingauge 9

10 Study area and Data set precipitations Observed daily yp precipitations p : From 8 raingauges l (mm/month) Rainfall % Rainy Day ys (day) Month Mean annual precipitation is about 2,740 mm Month Approximately 85% occurs during the wet season 10

11 Results and Discussion Transition probability by by Probability P( - ) P( - ) day day day day (day) Rainy days( Month ity Probabili 11

12 Probability density function 2. Generate precipitation amount Exponential distribution: λe f ( x) = 0, λx Weibull distribution: λβ ( λx) f ( x) = 0, Gamma distribution: η λ x f ( x) = Γ( η) 0,, x 0 elsewhere e β - 1 ( λxλ x ) β e η 1 λxλ x, x 0 elsewhere Pearson type III distributions: η λ f ( x) = Γ 0, ( η) ( x A) η 1 e λ ( x A),, x 0 elsewhere x A elsewhere

13 Results and Discussion Statistical Characteristics --Mean Mean Generated mean values in all probability distributions were close to the observed values. 20 Mean of Daily Precipi itation (mm) Overestimation of gamma 10 distribution from June to August Observation Exponential Weibull Gamma PT Month 13

14 Results and Discussion Statistical Characteristics --Standard deviation Standard deviation Exponential ldi distribution ib ti underestimated. Two-and dth three-parameter t distributions can well capture the data dispersion. SD of Daily Precipita ation (mm) Observation Exponential Weibull Gamma PT Month 14

15 Results and Discussion Statistical Characteristics --Coefficient of skewness One-parameter exponential distribution ib ti also underestimates t CS. Other distributions have a similar pattern as the CS observation. PT3 distribution, which uses the CS to calculate the parameters, had best CS estimation CS of Daily Precip pitation Coefficient of skewness(cs) Observation Exponential Weibull Gamma PT Month 15

16 Results and Discussion Statistical Characteristics -annual maximum daily series ly Precipitation (m mm) Generated Dail Exponential Weibull Gamma PT3 Exponential distribution significantly underestimates. PT3 distribution outperforms other distributions. (less than 400mm/day) Observed Daily Precipitation (mm) Quantile-to-quantile plot for daily precipitation generation For a few very large extreme event, the gamma distribution better fit the observations. 16

17 Results and Discussion Statistical Characteristics -annual daily maximum series 100 ly Precipitation (m mm) Generated Dai Exponential Weibull Gamma PT Observed Daily Precipitation (mm) Generated precipitation by the PT3 distribution were closest to the observation < 100mm/day Overall, the three-parameter PT3 distribution best fit the observed daily precipitation. Quantile-to-quantile plot for daily precipitation less than 100mm 17

18 Results and Discussion 31-year annual maximum daily series is ranked Da aily Precipitat tion (mm) Generated extreme events Heavy rain (daily precipitation > 50mm) Extremely heavy rain (> 130mm) Torrential rain (> 200mm) Extremely torrential rain (> 350mm) Obs Observation Exponential Weibull Gamma PT3 Weibull Gamma 0 Extreme Event Exp PT3 18

Results and Discussion Statistical Characteristics Extreme Events The number and the accuracy of extreme events of different levels regarding the observations and

Accuracy Observation 358-94 - 51-12 - Exponential 314 0.88 7 0.07 2 0.04 0 0.00 Weibull 452 1.26 106 1.13 42 0.82 9 0.75 Gamma 509 1.42 102 1.09 44 0.86 8 0.

19 Results and Discussion Statistical Characteristics Extreme Events The number and the accuracy of extreme events of different levels regarding the observations and the generated precipitation Heavy Rain Extremely Heavy Rain Torrential Rain Extremely Torrential Rain Number Accuracy Number Accuracy Number Accuracy Number Accuracy Observation Exponential Weibull Gamma PT Heavy rain (daily precipitation > 50mm) Extremely heavy rain (> 130mm) Torrential rain (> 200mm) Extremely torrential rain (> 350mm) 19

20 Results and Discussion Daily precipitation projection Projected annual maximum daily precipitations (mm) Annual Maximum m Daily Precipitation Scenario A Scenario A1B Model Mean 1000 Model Mean 1000 Model Mean Obs. Projections by 10 GCMs Obs. Projections by 10 GCMs Obs Projections by 10 GCMs Scenario B1 Observed annual maximum daily precipitation ranges from 100 to 650 mm/day. Projected annual maximum daily precipitations it ti have a wider range and variability 20

21 Conclusions 1 Weather generator is an important tool to produce future daily precipitation, if we only have monthly projection output. But, more sound research on choice of probability distribution may be needed for extreme events. 22 In the future, extremely daily precipitations will possibly occur in the study area under the climate change scenarios. 3 To combine the spatial downscaling with the temporal downscaling may be more reasonable for precipitation projection. 21

22 Department of Hydraulic & Ocean Engineering, National Cheng Kung University, Taiwan

23 Department of Hydraulic & Ocean Engineering, National Cheng Kung University, Taiwan

25 AVG OBS EXP WEI GAM PT STDEV OBS EXP WEI GAM PT SKEW OBS EXP WEI GAM PT

26 1. Deciding a dry or wet day Random number r ( 01, 1) (1) If r P(W ), then the first day is a precipitation day (2) If the previous day is a wet day, then ( ) If r P W, then the current day is a wet day W ( ) If r P W, then the current day is a dry day W (3) If the previous day is a dry day, then ( ) If r P W, then the current day is a wet day D ( ) If r P W, then the current day is a dry day D

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