區域化變數理論應用於降雨之時間與空間特性之研究

The Study of Spatial-Temporal Characteristics for Rainfall by Applying Theory of Regionalized Variables

鄭士仁(Shin-Jen Cheng) ； 洪君伯(Chun-Po Hung) ； 謝惠紅(Huey-Hong Hsieh) ； 王育民(Yu-Ming Wang)

《農業工程學報》 51卷4期 (2005/12) Pp. 69-83

https://doi.org/10.29974/JTAE.200512.0006

摘要

過去降雨之時間與空間特性，常常分開單一討論。本研究主要目的為嘗試應用區域化變數理論，以架構並評估降雨之時間與空間關係。研究所採用之基本工具為半變異圖與交叉半變異圖。半變異圖用以推估平均雨量，而交叉半變異圖則用以架構降雨之空間分佈與時間序列特性。
研究中，半變異圖與交叉半變異圖皆採用次冪模式。藉由無因次半變異圖與區塊克利金法快速推估逐時平均雨量。而重覆法則用以評估雨量測站對平均雨量推估之影響程度。為了更進一步瞭解水文變數之時空架構，每個測站觀測資料視為一維時間序列，但測站與測站間關係為二維空間結構。如此便能以有限觀測資料取得具有時空特性之交叉半變異圖。最後應用共克利金法推估觀測漏失之測站，進行雨量補遣工作。
有關於共克利金法推估雨量之精確度，本研究乃以交叉驗證法予以衡量。分析結果顯示其精確度令人滿意，同時亦證實本研究所提出之方法與程序適合用於集水區防洪系統降雨－逕流模式之即時輸入。

關鍵字

半變異圖 ； 區塊克利金 ； 重覆法 ； 交叉半變異圖 ； 共克利金 ； 交叉驗證 ； 時間－空間降雨

並列摘要

This study adopts regionalized variables theory, and describes the rainfall process in terms of its structure in time and space. The basic analytical tools are semivariogram of Kriging and cross semivariogram of co-Kriging. The semivariogram was used to calculate mean rainfall of study watershed for every time period, while cross semivariogram was employed to establish structure of rainfall for distribution of space and time series.
It’s convenient to computing hourly mean rainfall for the dimensionless semivariogram, which is obtained from standardized rainfall depth for a realization of recordings. The power form was selected for the parameters of the semivariogram model using the block Kriging method. The iterative method was utilized for observing the impacts on density of raingauges in a river basin. Any site was subtracted of analysis errors from the raingauge network and the influence of the missing data on estimating average rainfall is evaluated.
To further understand the space-time structure of hydrological variables, the observed values at each measurement site are considered as separate but correlated in the one-dimensional time series. This assumption allows rainfall information to be gathered from limited rainguage readings, to be treated as a set of correlated one-dimensional random variables, and then used to obtain a cross semivariogram. Subsequently, the co-Kriging method may be used to fill in the gaps among rainfall data from the measurement sites. The accuracy of rainfall estimation using the co-Kriging method was analyzed with cross validation to reveal the adequacy of the supplementary data. Analytical results herein are satisfactory, and demonstrate that the procedure is suitable for use as the real-time input of runoff models in a project river basin.

並列關鍵字

Semivariogram ； Block Kriging ； Iterative method ； Cross semivariogram ； Co-Kriging ； Cross validation ； Spatial-temporal rainfall