多測站流量時間-空間序率模擬之研究

A Stochastic Spatio-Temporal Simulation Approach for Multi-site Streamflow Generation

謝心怡(Hsin-I Hsieh)

指導教授 ： 蘇明道

共同指導教授 ： 鄭克聲(Ke-Sheng Cheng)

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/博士(2014年)

https://doi.org/10.6342/NTU.2014.01780

摘要

流量資料為區域水資源管理與規劃不可或缺的參考依據，因此模擬流量往往是必要的前置作業。然而流量變數不僅有在時間上的變異還有在空間上的差異，並且往往非常態分布，造成模擬上的困難。故本研究提出結合時間、空間的流量模擬架構，使用臺灣嘉南地區12個流量站26年的歷史流量資料進行分析。此區域流量資料利用各變數平均值與標準差去除長期趨勢後，屬於多元PT3分布。於本研究中分別建立時間、空間半變異元函數，推估各變數間的相關性，並利用非等向性隨機場的概念，結合時間與空間的半變異元函數，建構此地區流量的時間-空間變異結構，導入流量資料時空架構並進行模擬。由於模擬流量變數眾多，且流量變數多為非常態變數，模擬實需考量維持變數間的相關性，造成模擬上的困難。故本研究以頻率因子為基礎，推估多元標準常態隨機變數轉換至多元PT3隨機變數時，相關係數矩陣的變化，以轉換多元常態進行多元非常態分布的模擬，期望改善以往模擬流量的方式。
觀察模擬結果平均而言均能夠呈現研究中所分析的時空變異結構，誤差在5%以下，然而比較模擬結果與實際旬流量相關係數仍有可改善之處。由於本研究所模擬的時空維度裡共有288個不同特性的分布，流量變數眾多，但是所取得流量資料長度僅有26年，較為不足。另一方面嘉南平原資料較完整的流量站僅有12個，在分析空間上的半變異元函數時也會凸顯資料不足的問題。分析過程中，礙於時間或是空間上資料不足的限制，造成建置時空變異架構的不足，均是模擬旬流量相關係數誤差的因素。
本研究亦將模擬流量應用於白河水庫管理處灌區，分析新增17口地下水井後對於此區域灌區缺水率改善情況，結果顯示各灌區於一、二期作期間，缺水率平均約有5-10%的改善。此架構所模擬的多元流量尤其適用於多河川的區域水資源規劃，透過類似的風險分析計算能提供決策所需資訊。
此模擬架構除了可以維持流量本身的機率分布特性，還考量不同時間、不同空間位置的流量相關性，並且透過頻率因子的基礎，解決多元非常態模擬的困難，較以往模擬模式更能掌握流量間的相關性，亦適用於其它具有時間-空間變異結構或者有更高維度的連續變數，如雨量溫度等等。

關鍵字

多元流量 ； 非常態變數 ； 時空架構 ； 頻率因子 ； 聯合分布模擬

並列摘要

Characterizing and simulating streamflow series is an essential task for regional water resources planning and management. It generally involves temporal variation and spatial correlation of streamflow data at different sites. Like many other environmental variables, streamflow data have been found to be asymmetric and non-Gaussian. Such properties exacerbate the difficulties in spatio-temporal modeling of environmental variables. In this study, we developed a stochastic spatio-temporal simulation model which is capable of generating non-Gaussian multi-site ten-day-period (TDP) streamflow data series. Historical streamflow data during 1975 to 2000 from twelve flow stations of an irrigation district in southern Taiwan were used to exemplify application of the proposed model.
TDP streamflow data at different sites in the study area were firstly standardized using site-specific long-term averages and standard deviations. Spatial and temporal variations/ correlations of the standardized streamflow data were analyzed through anisotropic semivariogram modeling, and then the multi-site standardized stremflow data were modeled by a spatio-temporal anisotropic multivariate PT3 distribution. In order to simplify the multivariate non-Gaussian simulation, a frequency-factor-based algorithm was adopted to convert the multivariate PT3 distribution to a corresponding multivariate standard normal distribution with a unique correlation matrix which was derived from the correlation matrix of the multivariate PT3 distribution. Then stochastic simulation of the anisotropic multivariate standard normal distribution was conducted, yielding a large set of multi-site standard normal realizations. Finally, these realizations were converted to realizations of the multi-site PT3 distribution using the general equation of hydrological frequency analysis. Simulated realizations of the spatio-temporal anisotropic multivariate PT3 distribution were validated by comparing different moments of the simulated data and the observed streamflow data. For average, the statistics of simulation results show less than 5% difference with the parameter of raw streamflow data. Short of streamflow stations and streamflow data may cause error of fitting spatial semi-variogram. The simulated data can be separated to 288 distributions, however, the sample size of each distribution is 26. Insufficient sample size and streamflow stations would reduce accuracy and precision for fitting spatio-temporal semivariogram model.
Simulated streamflow data was applied to analyze improvement of water shortage rate after developing 17 ground water well in the case study. The mitigation measure caused 5 to 10% decreasing of water shortage rate of each irrigation command area during culture period. The simulation results is suitable to be applied to regional water resource management which involving multiple streamflows. This simulation model could maintain statistic characteristic of each distribution and correlation between distributions as well. The proposed approach can also be applied for spatio-temporal modeling of other non-Gaussian distributions or even higher dimensions simulation structure.

並列關鍵字

multivariate streamflow ； non-Gaussian variable ； spatio-temporal structure ； frequency factor ； joint-distribution simulation.

參考文獻

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