Applied Hydrology Climate Change and Hydrology Professor Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering National Taiwan University

Global Circulation Models (GCMs) Computer models that are capable of producing a realistic representation of the climate, and can respond to the most obvious quantifiable perturbations. Derived based on weather forecasting models. 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Weather forecasting models The physical state of the atmosphere is updated continually drawing on observations from around the world using surface land stations, ships, buoys, and in the upper atmosphere using instruments on aircraft, balloons and satellites. The model atmosphere is divided into 70 layers and each level is divided up into a network of points about 40 km apart. 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Standard weather forecasts do not predict sudden switches between stable circulation patterns well. At best they get some warning by using statistical methods to check whether or not the atmosphere is in an unpredictable mood. This is done by running the models with slightly different starting conditions and seeing whether the forecasts stick together or diverge rapidly. 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

This ensemble approach provides a useful indication of what modelers are up against when they seek to analyses the response of the global climate to various perturbations and to predict the course it will following in the future. The GCMs cannot represent the global climate in the same details as the numerical weather predictions because they must be run for decades and even centuries ahead in order to consider possible changes. 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Challenges for potential GCMs improvement Typically, most GCMs now have a horizontal resolution of between 125 and 400 km, but retain much of the detailed vertical resolution, having around 20 levels in the atmosphere. Challenges for potential GCMs improvement Modeling clouds formation and distribution Tropical storms (typhoons and hurricanes) Land-surface processes Winds, waves and currents Other greenhouse gases 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

GCMs 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

From GCMs to hydrological process modeling Study of hydrological processes requires spatial and temporal resolutions which are much smaller than GCMs can offer. Downscaling techniques have been developed to downscale GCM outputs to desired scales. Dynamic downscaling Statistical downscaling 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Weather Generator of daily rainfall simulation Markov chain for rain day/no-rain day simulation Exponential distribution for daily rainfall simulation. 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

(童慶斌教授課程講義) 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Effect of climate change on storm characteristics Storm types Convective storms Typhoons MCS (Mei-yu) Frontal systems Assessed based on MRI high-resolution outpots (dynamic downscaling) 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

探討各降雨類型之統計特性且評估氣候變遷下之差異 TCCIP Team 3 蘇元風博士

緣起 過去探討氣候變遷對降雨特性影響之相關研究，多以年降雨量、季節降雨量或月降雨量為研究對象。 許多水資源工程規劃、設計，或是水庫供水調度而言，事件降雨特性至關重要。 逕流演算 入庫流量預報 水利工程設施規劃 動力降尺度 (例MRI) 時雨量資料

降雨事件之門檻與統計參數 門檻 統計參數 時雨量值(例：2mm/hr) 平均次數 降雨延時(例：12 hours) 總降雨量 降雨延時 降雨事件間隔時距

事件降雨特性 序率暴雨模擬模式 後續水文需求： 頻率分析 逕流演算 入庫流量預報 水利工程設計規劃 … 水利署相關計畫之使用 氣候變遷下台灣地區地下水資源補注之影響評估(台大) 強化台灣西北及東北地區因應氣候變遷海岸災害調適能力研究計畫(1/2)(成大) 台灣地區各水資源分區因應氣候變遷水資源管理調適能力綜合研究 (台大) 強化中部水資源分區因應氣候變遷水資源管理調適能力研究(交大) 氣候變遷對中部地區水旱災災害防救衝擊評估及調適策略擬定(1/2)(成大)

MRI-WRF-5km資料是否能重現觀測資料之統計特性？ (基期1979-2003) 測站觀測時雨量 (基期1979-2003) MRI-WRF-5km資料是否能重現觀測資料之統計特性？ 事件降雨特性參數 事件降雨特性參數 降雨門檻 降雨門檻 事件降雨特性參數改變率 (近未來) (世紀末) 比較 MRI-WRF-5km時雨量 (近未來2015-2039) MRI-WRF-5km時雨量 (世紀末2075-2099)

暴雨事件切割門檻(測站資料) 採用降雨事件間距門檻值，濾除較小的降雨事件 降雨類型切割 降雨延時為1 小時或時雨量低於0.5mm的小事件移除。 降雨類型切割 降雨類型 時期 門檻 第一類 (梅雨) 5月-6月 降雨延時 > 3小時 時雨量 > 0.5 mm/hr 第二類 (颱風) 7月-10月 降雨延時 > 8小時 時雨量 > 2.5 mm/hr 第三類 (對流) 3 小時 > 降雨延時 ≤ 8小時 第四類 (鋒面) 11月~隔年4月 降雨延時 > 4小時

資料說明 測站資料 MRI-WRF-5km 時間：1979-2003時雨量 站數：84站 空間解析度: 5km 1979-2003 2015-2039 2075-2099 時雨量

事件數 第二類 (颱風) 7月-10月 降雨延時 > 8小時 時雨量 > 2.5 mm/hr Gauges MRI-WRF 基期 時期 每年颱風次數(兆尊) 每年事件數 測站(1979-2003) - 3.04 1979-2003 3.52 3.39 2015-2039 3.24 2075-2099 3.28 3.32 Gauges MRI-WRF 基期 近未來 世紀末

平均延時 第二類 (颱風) 7月-10月 降雨延時 > 8小時 時雨量 > 2.5 mm/hr Gauges MRI-WRF 基期 近未來 世紀末

平均總降雨量 第二類 (颱風) 7月-10月 降雨延時 > 8小時 時雨量 > 2.5 mm/hr Gauges MRI-WRF 基期 近未來 世紀末

事件間隔 第二類 (颱風) 7月-10月 降雨延時 > 8小時 時雨量 > 2.5 mm/hr

事件數 第四類 (鋒面) 11月~隔年4月 降雨延時 > 4小時 時雨量 > 0.5 mm/hr Gauges 時期 每年事件數 測站(1979-2003) 7.58 1979-2003 6.94 2015-2039 7.15 2075-2099 8.37 降雨延時>4hrs 時雨量>0.5mm 降雨延時>4hrs 時雨量>2mm Gauges MRI-WRF 基期 近未來 世紀末

平均延時 第四類 (鋒面) 11月~隔年4月 降雨延時 > 4小時 時雨量 > 0.5 mm/hr Gauges 降雨延時>4hrs 時雨量>0.5mm 降雨延時>4hrs 時雨量>2mm Gauges MRI-WRF 基期 近未來 世紀末

平均總降雨量 第四類 (鋒面) 11月~隔年4月 降雨延時 > 4小時 時雨量 > 0.5 mm/hr Gauges 降雨延時>4hrs 時雨量>0.5mm 降雨延時>4hrs 時雨量>2mm Gauges MRI-WRF 基期 近未來 世紀末

事件間隔 第四類 (鋒面) 11月~隔年4月 降雨延時 > 4小時 時雨量 > 0.5 mm/hr 降雨延時>4hrs

事件數 第一類 (梅雨) 5月-6月 降雨延時 > 3小時 時雨量 > 0.5 mm/hr Gauges MRI-WRF 基期 時期 每年事件數 測站(1979-2003) 6.51 1979-2003 7.16 2015-2039 6.89 2075-2099 7.55 降雨延時>3hrs 時雨量>0.5mm 降雨延時>3hrs 時雨量>2mm Gauges MRI-WRF 基期 近未來 世紀末

平均延時 第一類 (梅雨) 5月-6月 降雨延時 > 3小時 時雨量 > 0.5 mm/hr Gauges MRI-WRF 基期 降雨延時>3hrs 時雨量>0.5mm 降雨延時>3hrs 時雨量>2mm Gauges MRI-WRF 基期 近未來 世紀末

平均總降雨量 第一類 (梅雨) 5月-6月 降雨延時 > 3小時 時雨量 > 0.5 mm/hr Gauges 降雨延時>3hrs 時雨量>0.5mm 降雨延時>3hrs 時雨量>2mm Gauges MRI-WRF 基期 近未來 世紀末

事件間隔 第一類 (梅雨) 5月-6月 降雨延時 > 3小時 時雨量 > 0.5 mm/hr 降雨延時>3hrs

事件數 第三類 (對流) 7月-10月 3小時<降雨延時 ≤ 8小時 時雨量 > 2.5 mm/hr Gauges 時期 每年事件數 測站(1979-2003) 3.10 1979-2003 6.75 2015-2039 6.51 2075-2099 6.36 Gauges MRI-WRF 基期 近未來 世紀末

平均延時 第三類 (對流) 7月-10月 3小時<降雨延時 ≤ 8小時 時雨量 > 2.5 mm/hr Gauges MRI-WRF 基期 近未來 世紀末

平均總降雨量 第三類 (對流) 7月-10月 3小時<降雨延時 ≤ 8小時 時雨量 > 2.5 mm/hr Gauges MRI-WRF 基期 近未來 世紀末

事件間隔

結論 MRI-WRF-5km所得到的降雨參數大致上能夠反映出測站資料所得降雨參數之空間分布特性，尤其是颱風與鋒面兩類降雨類型。

後續工作規劃 將MRI-WRF-5km資料所決定之降雨門檻值應用於MRI-WRF-5km所有網格點。 計算並繪製降雨參數改變率分布圖。

Stochastic storm rainfall simulation model (SSRSM) Occurrences of storm events and time distribution of the event-total rainfalls are random in nature. Physical parameters based # of events in a certain period Duration Event-total depths Time distribution (hyetograph) Rainfall intermittence 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Modeling occuerrences of storms Number of storm events in a certain period Occurrences of rare events like typhoons can be modeled by the Poisson process. Inter-event-time has an exponential distribution. Occurrences of other types of storms which are more frequently occurred may not be well characterized by the Poisson process. 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Duration and total depth Generally speaking, storms of longer durations draw higher amount of total rainfalls. Event-total rainfall (D) and duration (tr) are correlated and can be modeled by a joint distribution. (D, tr) of typhoons are modeled by a bivariate gamma distribution. Bivariate distribution of different families of marginal densities may be possible. 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Conversion of BVG correlation and BVN correlation. Simulation of bivariate gamma distribution – A frequency factor based approach Transforming a bivariate gamma distribution to a corresponding bivariate standard normal distribution. Conversion of BVG correlation and BVN correlation. 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Gamma density

Rationale of BVG simulation using frequency factor From the view point of random number generation, the frequency factor can be considered as a random variable K, and KT is a value of K with exceedence probability 1/T. Frequency factor of the Pearson type III distribution can be approximated by Standard normal deviate [A]

Assume two gamma random variables X and Y are jointly distributed. The two random variables are respectively associated with their frequency factors KX and KY . Equation (A) indicates that the frequency factor KX of a random variable X with gamma density is approximated by a function of the standard normal deviate and the coefficient of skewness of the gamma density.

Flowchart of BVG simulation (1/2)

Flowchart of BVG simulation (2/2)

[B]

Time distribution of event-total rainfall The duration is divided into n intervals of equal length. Each interval is associated with a rainfall percentage. Based on the simple scaling assumption, rainfall percentages of the i-th interval (i = 1, …, n) of all events (of the same storm type) form a random sample of a common distribution. Rainfall percentages of individual intervals form a random process. Gamma-Markov process 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Modeling the dimensionless hyetograph Rainfall percentages can only assume values between 0 and 100. The sum of all rainfall percentages should equal 100%. Constrained gamma-Markov simulation Gamma distribution will generate random numbers exceeding 100%. Truncated gamma distribution (truncated from above) The truncation threshold (cut off value) is significantly lower than 100%. 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU

Determining parameters of the truncated gamma distributions. Observations of rainfall percentages are samples of truncated gamma distributions. Determining parameters of the truncated gamma distributions. Scale parameter, shape parameter and the truncation threshold. Gamma-Markov simulation is based on simulation of a bivariate truncated-gamma distribution. Determing the correlation coefficient of the parent bivariate gamma distribution. 12/2/2018 Lab for Remote Sensing Hydrology and Spatial Modeling Dept of Bioenvironmental Systems Eng, NTU