整合時間尺度之隨機降雨序列模擬機制之發展與應用

Abstract

大多數水利相關工程例如洪水預報、防洪工程，應用於邊坡穩定評估之排水及入滲分析等，降雨資料為必需已知之基本資料。然而常因發生雨量資料不足或其時間尺度不符合要求，而使水利相關工程在分析設計上產生了不確定性進而造成了失敗的風險。由於降雨資料主要由降雨事件年發生次數(Annual Occurrence Number of Rainstorm Events)、降雨延時(Storm Duration)、總降雨量(Rainfall Depth)，事件間隔時間(Inter-event Time)及降雨時間分布(Time Distribution of Rainfall) (即降雨雨型, Storm Pattern) ，等五種特性所組成 (Marien及Vandewiele, 1986)，故本文將以由實測雨量資料所得降雨特性之統計性質為基礎，發展一套隨機降雨序列模擬機制(Stochastic rainfall series generation model, SRSG model)，期使能解決因雨量資料不足所衍生的相關水利工程問題。為了驗證此模式，本文分別比較由模式所得之合成降雨序列與不同紀錄年限的實測雨量資料所推得年最大降雨量-延時-頻率曲線(Rainfall depth-duration-frequency, DDF, Curve)，藉以測試模式在延伸降雨序列之成效。 另為了克服在設計水利相關工程常遇到另一問題，即因自計雨量站不足而造成短時間尺度( )雨量資料短缺，但卻有相當多的普通雨量站可提供長時間尺度雨量(例如日雨量)，故本文亦發展一套可藉由日雨量來推估不同延時(小時)之降雨DDF曲線之時雨量頻率分析模式。依據所採用雨量資料型式，模式可區分為二類型：(1)年最大值事件模式(Annual-maximum-events, AME, Model)：即不同連續日降雨事件總雨量年最大值及其所對應的不同延時最大降雨量；及(2)所有事件模式(All-events, AE, Model)：即採用所有降雨事件之模式。在發展模式過程中，降雨事件依連續降雨天數被區分為不同連續日降雨事件類型，擷取其總雨量及其所對應於不同延時之最大降雨量，建立其分位數之關係，並將其應用於由日雨量機率分布函數所組成之時雨量頻率分析模式之建置。如同驗證隨機降雨序列模擬機制，為了驗證AME及AE模式的正確性，本文亦分別由AME及AE模式推得的降雨DDF曲線與一般常用之年最大降雨序列(Annual Maximum Rainfall Series)配合頻率分析法(本文定義為AMS模式)之推估結果來相互比較，以評估模式可藉由日雨量資訊推估不同延時之降雨DDF曲線之準確性及可靠度。 本文採用香港天文台站1884至1990年之100年時雨量資料 (其中1940至1946因第二次世界大戰而中斷記錄)，驗證所發展之隨機降雨序列模擬機制(SRSG模式)及採用日雨量之時雨量頻率分析模式(AME及AE模式)。由驗證結果可知，SRSG模式確實有能力能製造保存原有統計性質之降雨事件，且可將所有模擬事件等性成降雨序列，藉以延伸降雨資料紀錄，進而改善降雨DDF曲線之準確性，特別是在推估重現期距大於實測時雨量紀錄之年最大降雨量分位數時，其改善程度最為明顯。另對於AME及AE模式而言，在相同現有時雨量紀錄年限下， AME及AE模式因採用不同類型的連續日降雨事件之雨量資料，相對於採用年最大降雨序列之AMS模式而言，AME及AE模式因可採用較多的雨量資訊，而可推得較具有可靠及準確性之降雨DDF曲線。此外由AME及AE模式比較結果可知，AE模式較適用於短實測時雨量資料之不同延時降雨DDF曲線之推估，相對地，AME模式則適用於當具有較長的日雨量資料紀錄年限之降雨DDF曲線之推估。 最後本文將SRSG模式與AME及AE模式整合成一可考量不同時間尺度之隨機降雨序列模擬機制，此整合模式不僅可藉由SRSG模式模擬合成降雨序列，用以增加日雨量及時雨量資料紀錄年限，改善總雨量及其所對應的不同延時最大降雨量分位數關係，藉以提高時雨量頻率分析模式之可靠度，更可由將SRSG模式所衍生大量的降雨序列應用於AME及AE模式所推得降雨DDF曲線之不確定性分析，藉以提供需要降雨DDF曲線之水利相關工程例如洪水預報、防洪工程，及水資源規劃等進行風險分析。

Rainfall data are often required in many water-related engineering studies, such as flood forecast, prevention and mitigation, seepage and infiltration analysis for slope stability assessment. However, engineers frequently face the problem of not having insufficient rainfall data to conduct good the quality and reliable water-related engineering. In general, the occurrence of the rainstorm events can be characterized by the annual occurrence number of events, storm duration, rainfall depth, inter-event time and temporal variation of rainfall (Marien及Vandewiele, 1986). To solve the problem associated with insufficient rainfall data, this thesis presents a stochastic rainfall series generation (SRSG) model based on the statistical properties of correlated rainstorm characteristics calculated from observed rainfall data. To verify the proposed SRSG model, comparisons are made on the derived rainfall depth-duration-frequency (DDF) relationships of the annual maximum rainfall from the simulated rainfall sequences with those solely obtained from observed annual maximum rainfall. Furthermore, due to the fact that short-duration rainfall data (e.g., hour) are insufficiently long compared with relatively long and widely available rainfall data, this thesis also proposed hourly rainfall frequency models that incorporate daily rainfall information to estimate hourly rainfall depth-duration-frequency (DDF) relationships. According to the type of rainfall data used, the proposed hourly rainfall frequency models can be classified two models. One is annual-maximum-events (AME) model incorporated with the annual maximum series of consecutive-rainy-daily events and the other is all-event (AE) model based on all consecutive-rainy-daily events. In the process of deriving the proposed AME and AE models, the rainstorm events are classified according to the number of consecutive-rainy days and their total rainfall amount are extracted. And then, the relationship of quantiles between total rainfall and associated t-hr maximum rainfall are derived for the AME and AE models. Similar to the SRSG model, to verify the proposed the AME and AE models, comparison are made on the rainfall depth-duration-frequency relations of the annual maximum rainfall estimated by the proposed the AME and AE models with those by the conventional frequency analysis by directly using annual maximum series. The frequency analysis based on annual maximum rainfall series is denoted herein as the AMS model. Hourly rainfall data at the Hong Kong Observatory over the period of 1884-1990 are used to demonstrate the development and application of the proposed stochastic rainstorm series generation (SRSG) model and daily-based hourly rainfall frequency model that incorporate daily rainfall information (AME and AE models). From the numerical experiments, the proposed SRSG model is found to be capable of capturing the essential statistical features of rainstorm characteristics and annual extreme rainstorm events calculated from the available data. Since the rainfall series can be synthesized by the proposed SRSG model, it is obvious that the model can be applied to extend the record length of the rainfall data for improving the reliability and accuracy of rainfall quantiles, especially for return period larger than the record length of available rainfall data. For the verification of the AME and AE models, the numerical experiments indicate that AME and AE model are found to produce more accurate and reliable frequency quantiles of annual maximum rainfall than those derived by the AMS model based on the same available hourly rainfall data. Furthermore, the AME and AE models show a promising potential to improve accuracy of rainfall DDF relationships by incorporating extended daily-based rainfall record. It is also found that the AME model is suitable for estimating rainfall DDF curves of various storm durations incorporated with the low record length of hourly rainfall data whereas AE is adequate for the estimation of rainfall DDF curves based on the long-record daily rainfall data. Eventually, in this thesis, the SRSG model, AME and AE models are integrated to be a stochastic rainfall generation model associated with varying time-scale rainfall data. This model can add hourly rainfall data composed of rainstorm characteristics simulated by the SRSG model to modify the quantiles relationship between total daily rainfall and the associated t-hr maximum rainfall. Using the modified quantiles relationship, the AME and AE models can estimate more reliable rainfall DDF relationships of storm durations of interest. Furthermore, the simulated rainfall series by the SRSG model can be applied to risk reliability analysis for the design of hydrosystem infrastructures and water resource planning requiring rainfall DDF relationships.