本研究的目的在嘗試完成一個四維變分過程，暫時不考慮加入真實的觀測資料，選定一初始場的模式預報為假想觀測軌跡，作為控制組；而另一相較於此初始場12～24小時內不同初始場的模式預報為實驗組，取兩者差值定義目標函數，利用四維變分過程求算最佳的初始場，使其預報結果朝假想觀測軌跡靠近。使用的工具為氣象局全球波譜模式的伴隨模式，以其求算目標函數的梯度，配合極小化程序(minimization)，L-BFGS方法，進行四維變分實驗。在實驗中，嘗試加入不規則的網格分佈成為假想觀測場，也嘗試加入集中某一地區：如臺灣東亞區的觀測資料進行變分工作。整個計算過程，可供氣象局未來四維資料同化工作所需。從三個個案3個比對實驗結果來說，所得之最佳初始場朝假想的觀測初始場逼近，其差距明顯比未經四維變分之原初始場與假想觀測初始場的差距為小。其中，以全部分析網格所做的理想化比對實驗結果必然最佳，可作為理論參考值。對所使用的全球模式預報結果而言，加入全球分佈的不規則觀測場比集中臺灣東亞地區的觀測資料的預報結果為佳。而全球分佈的不規則觀測場加上背景差誤差分析所得的新初始場和預報軌跡相較於未經變分分析的預報軌跡而言，取預報120小時結果比較，約使平均誤差下降12％～29％。以變分極小化作業效率的角度來看，疊代運算30次可使目標函數下降1個數量級，而以其8天期間的預報結果來看，亦與疊代運算100次相仿，所以疊代運算30次可作為實際作業時採行的參考值。

The purpose of this study is the implementation of the 4D-Var processes without adding true observation data. We use one initial condition integrated by numerical model to produce one forecast track to be hypothetical observation track, and use another initial condition within 12~24 h in comparison with previous initial field to produce other forecast track, so obviously the difference between these two forecast tracks can be defined as a cost function. The minimum of this cost function can be solved by the 4D-Var processes; i.e. we can get one optimal initial condition and its forecast will be close to the hypothetical observation track. We use the adjoint model to get the gradient of cost function and use minimization procedure, L-BFGS method, to get the minimum value of the cost function. In this study, we also try to simulate the irregular distributed observational data and somewhere like in Taiwan East Asia having intensive observation data for testing 4D-Var processes. The whole processes mainly follow the current Meteorological operation centers or foreign research units procedures, and they can be the foundation of thefuture 4D-Var operation at Central Weather Bureau.From the 3 cases and 3 twin experiments, the optimal initial fields tend toward the hypothetical initial fields. More specifically, the differences between the optimal initial fields and the hypothetical initial fields are far less than the differences between the original initial fields and the hypothetical initial fields. The ideal twin experiment on entire analytical grids can get the smallest differences between optimal initial fields and the hypothetical initial fields, and this best results could be a reference theoretical value. Comparing global model forecasts, the results of twin experiment on global irregular observation data are better than the results using Taiwan East Asia intensive observation data. The 120 h forecast mean errors of the new initial fields by using global irregular observation data are smaller 12%~29% than the 120 h forecast mean errors of the initial fields which were not accommodated by 4D-Var processes. For the efficiency, the 30 iterations in minimization procedure can reduce the cost function about one order. Furthermore, if we check the 8 days forecasts, the 30 iterations results are similar to 100 iterations results. So, the 30 iterations can be the reference value for future Central Weather Bureau 4D-Var operation.