利用貝氏空間模型所做的系集預測

Abstract

氣候和天氣預測是大家所關心的問題。如何做出精確的天氣和氣候預測就變的相當重要。天氣和氣候預測包含了觀測到的真實資料和數值模型預報的結果兩個部分。這些數值預報模型對於起始值的給定和範圍的限定相當的敏感。最近，Krishnamurti (1999) 提出了一個有效的分法叫做超系集，它利用統計中的多項式迴歸方法結合了觀測資料和數值模型預報的資料。在許多篇論文中都顯示了這個方法比用單一的數值預報模型來的精確。而超系集法主要是把每一個地點分開來做多項是迴歸，並沒有把每一個地點的空間相關性放入討論。而這篇論文提出了一個新的方法，利用貝氏空間模型結合觀測資料和數值預報的資料並引入了空間的訊息在此模型當中。在論文的最後比較的地方更可以看出我們所提出的方法勝過超系集法。

Climate and weather forecasting is concerned by everyone. How to make accurate climate and weather forecasting is important and of great challenge. The ingredients for climate and weather forecasting involve both observational data and deterministic numerical model outputs. A numerical model intends to simulate the motion and evolution of the atmosphere via a complex system of nonlinear partial differential equations derived by thermodynamics and fluid mechanics. Nevertheless, these predictions are obtained under a number of approximations and are very sensitive to the initial and boundary conditions. Recently, Krishnamurti \textit{et al}.~(1999) provided an effective method called superensemble by combining observational data with several numerical forecasts using the multiple-regression method. The method has been shown to provide more accurate prediction than what can be obtained from a single numerical model. However, the method is implemented on a location-by-location basis and no attempt has been made to take the information among locations into account. In this study, we provide a new statistical methodology for climate and weather forecasting by combining observational data with several numerical model forecasts using a Bayesian hierarchical spatial model. The proposed method incorporate the information among locations, and is shown to outperform the superensemble method.