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
Outline Research objective Methods Study area and Data set Results and Discussion 2
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 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
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
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
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
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
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
Study area and Data set precipitations Observed daily yp precipitations p : 1975 2006 From 8 raingauges. 800 30 l (mm/month) Rainfall 600 400 200 85% Rainy Day ys (day) 20 10 0 1 2 3 4 5 6 7 8 9 10 11 12 Month Mean annual precipitation is about 2,740 mm 0 1 2 3 4 5 6 7 8 9 10 11 12 Month Approximately 85% occurs during the wet season 10
Results and Discussion Transition probability by by Probability P( - ) P( - ) day day day day 1 242 134 719 608 0.25 0.55 0.85 2 290 194 614 507 0.32 0.67 0.83 3 345 213 616 485 0.36 0.62 0.79 4 451 292 509 354 0.47 0.65 0.70 600 5 662 552 299 180 0.69 0.83 0.60 6 747 642 213 120 0.78 0.86 0.56 7 774 674 187 84 0.81 0.87 0.45 8 852 787 109 40 089 0.89 092 0.92 037 0.37 9 750 620 210 99 0.78 0.83 0.47 10 462 310 499 354 0.47 0.67 0.71 11 235 133 725 608 0.24 0.57 0.84 12 200 111 761 669 0.21 0.56 0.88 (day) Rainy days( 1000 1 800 400 200 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Month 0.8 0.6 0.4 0.2 ity Probabili 11
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
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. 30 0 Observation Exponential Weibull Gamma PT3 1 2 3 4 5 6 7 8 9 10 11 12 Month 13
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) 60 40 20 0 Observation Exponential Weibull Gamma PT3 1 2 3 4 5 6 7 8 9 10 11 12 Month 14
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 16 12 8 4 0 Coefficient of skewness(cs) Observation Exponential Weibull Gamma PT3 1 2 3 4 5 6 7 8 9 10 11 12 Month 15
Results and Discussion Statistical Characteristics -annual maximum daily series ly Precipitation (m mm) Generated Dail 700 600 500 400 300 200 Exponential Weibull Gamma PT3 Exponential distribution significantly underestimates. PT3 distribution outperforms other distributions. (less than 400mm/day) 100 0 0 100 200 300 400 500 600 700 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
Results and Discussion Statistical Characteristics -annual daily maximum series 100 ly Precipitation (m mm) Generated Dai 80 60 40 20 0 Exponential Weibull Gamma PT3 0 20 40 60 80 100 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
Results and Discussion 31-year annual maximum daily series is ranked Da aily Precipitat tion (mm) 700 600 500 400 350 300 200 130 100 50 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 the generated precipitation Heavy Rain Extremely Heavy Rain Torrential Rain Extremely Torrential Rain Number Accuracy Number Accuracy Number Accuracy Number 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 0.67 PT3 414 1.16 108 1.15 46 0.90 12 1.00 Heavy rain (daily precipitation > 50mm) Extremely heavy rain (> 130mm) Torrential rain (> 200mm) Extremely torrential rain (> 350mm) 19
Results and Discussion Daily precipitation projection Projected annual maximum daily precipitations (mm) Annual Maximum m Daily Precipitation 1200 1000 800 600 400 200 Scenario A2 1200 Scenario A1B Model Mean 1000 Model Mean 1000 Model Mean 800 800 600 600 400 400 200 200 Obs. Projections by 10 GCMs Obs. Projections by 10 GCMs Obs. 0 0 0 1200 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
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
Department of Hydraulic & Ocean Engineering, National Cheng Kung University, Taiwan
Department of Hydraulic & Ocean Engineering, National Cheng Kung University, Taiwan
1 2 3 4 5 6 7 8 9 10 11 12 AVG OBS 1.1 2.1 3.4 4.3 11.4 17.3 18.0 20.1 10.3 2.5 0.8 1.2 EXP 1.2 2.1 3.2 3.8 11.7 17.0 18.5 19.7 10.0 2.5 0.9 1.1 WEI 1.1 2.1 3.1 3.7 11.7 17.9 18.0 21.8 11.3 1.9 0.9 1.1 GAM 12 1.2 23 2.3 19 1.9 43 4.3 11.11 18.88 21.4 23.22 11.2 23 2.3 07 0.7 10 1.0 PT3 1.0 2.5 2.5 4.0 11.8 15.4 18.5 21.3 8.6 2.0 0.7 0.8 STDEV OBS 4.4 6.9 14.0 11.5 23.6 35.4 50.2 46.0 30.4 8.1 3.2 7.1 EXP 2.9 5.2 6.8 7.0 15.3 22.5 22.2 22.7 13.0 4.5 2.3 3.1 WEI 3.8 6.8 12.2 10.6 23.0 35.0 49.0 48.2 32.3 5.8 4.0 5.6 GAM 4.8 7.4 10.8 10.8 22.1 38.5 51.0 47.8 27.7 7.2 3.0 6.6 PT3 3.5 7.1 12.9 9.8 24.4 34.5 48.7 47.2 27.5 7.1 2.7 5.0 SKEW OBS 80 8.0 67 6.7 10.2 42 4.2 42 4.2 46 4.6 62 6.2 55 5.5 95 9.5 73 7.3 65 6.5 13.4 EXP 3.8 3.9 3.0 2.6 2.0 2.8 1.9 2.4 2.1 2.5 3.9 3.8 WEI 5.8 5.6 6.6 6.5 3.8 4.3 6.2 5.0 7.2 6.1 8.3 12.4 GAM 8.7 6.4 15.4 4.5 3.4 5.2 5.0 4.5 4.9 5.4 7.5 12.0 PT3 6.3 5.4 10.1 3.9 4.3 5.3 5.3 4.3 8.7 8.2 7.6 11.7
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