應用分段線性聯合最佳化與主成份速度追蹤改進ABLER法降水系統移速場估計

Enhancing the ABLER algorithm on Rainstorm Velocity-Field Estimation by Jointly Optimized Piecewise-Linear Functions and Tracking with Principle-Velocity Transform

鄭哲榮(Che-Jung Cheng)

指導教授 ： 李天浩

國立臺灣大學/工學院/土木工程學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201702343

摘要

本研究探討ABLER移速估計演算法的偏誤原因，提出兩項策略來改進演算法。分別是：(1)利用主成份速度轉換與追蹤，改進質點追蹤效率；與(2)利用分段線性速度場函數聯合最佳化估計程序，改進估計移速場的表現能力。並且利用線性／非線性移速場觀測系統模擬試驗，定量檢驗此兩項改善策略的效益。最後，使用五分山雷達的CAPPI資料與QPESUMS資料測試改進效益。
ABLER (Advection-equation Based Lagrangian-Eulerian Regression)演算法融合了拉格朗日描述法的TREC（Tracking Radar Echo by Correlation）；以及歐拉描述法－使用離散的移流方程式估計速度場函數係數的Shiiba迴歸法。ABLER法有四個主要估計誤差來源，分別是：(1)離散假設在一個時間間距內降雨胞的移動軌跡是直線，因此估計速度場函數係數先天便存在偏估問題；(2)線性速度場函數自由度(彈性)不足，或是速度場並非線性函數；(3)降雨系統具有源滅項，與ABLER法的單純移流假設不符；(4)雷達觀測影像受到雜訊影響，所導致的估計不確定性。
本研究針對(1)、(2)兩項誤差進行改善。針對問題(1)，PVT的概念為將空間變數投影到主軸上，且代入初始條件，獲得任意時刻的質點位置，最後利用最佳化策略調整速度場係數。最佳化方法利用MATLAB最佳化工具箱求解，其方法為Downhill Simplex Search (DSS)。針對原因(2)，PLJO有三個概念。其一為增加速度場的描述自由度，其二為連結速度場係數的一致性，最後為使質點追蹤之過程中具有合理性。
在OSS試驗，(1)最佳化策略能夠有效改善速度場係數、(2)分區個別估計能提供較多的描述自由度及(3)跨區更換速度場係數使得質點追蹤具有合理性。而在實際案例中，雖最佳化效率欠佳，但PLJO之起始猜值大部分都能夠改善單一區塊的ABLER演算法。但若系統具有強烈的源滅特性以及雨胞相對運動，會致使演算法無法準確地提供降雨系統的估計移速而導致偏估結果。

關鍵字

雷達 ； 外延 ； ABLER ； OSSE ； 降水系統 ； 移速場

並列摘要

This study is based on Advection-Based Lagrangian-Eulerian Regression (ABLER) algorithm from Center Weather Bureau (2014 ) and Liu’s master thesis (2014 ). First, discussing the reasons and features of bias by using ABLER algorithm. In this study, there are two problems which need to improve. One is that Principle-Velocity Transform (PVT). The PVT can improve the efficiency of calculation in the particle tracking. Another is that the procedure of Piecewise-Linear velocity field function with Jointly Optimized (PLJO). The PLJO can improve the capacity of the performance of velocity field. Simultaneously, Evaluating the strategies of improvement quantitatively by using linear and nonlinear Observing Systems Simulations Experiments (OSSE). Finally, focus on forecasting short-duration and applied the PVT and PLJO. And the radar data is used by Constant Altitude Plan Position Indicator (CAPPI) and QPESUMS.
The ABLER algorithm combines two conceptions from TREC method and Shiiba’s regression method. TREC (Tracking Radar Echo by Correlation) method is a Lagrangian framework, and the Shiiba’s regression method is an Eulerian framework which discrete advection equation into regression term by using finite difference method (FDM). There are four main reasons in estimating the velocity field of a rainstorm by using ABLER algorithm. (1) The assumption of the discreteness is that the trajectory for the particle is straight line in a time step. At the beginning, the coefficients of the velocity field function hav the problems of bias. (2) The degree of freedom is not good enough or the velocity field is not linear functions. (3) The rainstorm has sources or sinks term opposition with assumptions. (4) There are observing uncertainty in the radar image.
In this study, we focus on problems (1) and (2). For the problem (1), the conception of PVT is that transforming the spactial variables into principle axis. Obtaining the position of particle in each time-steps by substituting initial conditions. Finally, adjusting the coefficient of velocity field function to obtain the better coefficients by using optimization strategy. The method of optimization strategy is Downhill Simplex Search (DSS) form MATLAB optimization boxes. For the problem (2), there are three conceptions of PLJO. One is that increasing the degrees of greedom in describing velocity field. Another is that giving consistency of the velocity field functions. The final part is that making reasoned particle tracking.
For the verification, there are three mainly results. (1) The stragety of optimization can improve the coefficient of velocity field function. (2) The stragety of piecewise-linear velocity field function has more degrees of freedom than original ABLER algorithm. (3) The stragety of changing coefficient can provide reasoned particle tracking. For the application, PLJO mostly has the better results than original ABLER algorithm. If rainstorm has intense source/sink term or relative motion, the algorithm can not descript velocity good enough.

並列關鍵字

Radar ； Extrapolation ； ABLER ； OSSE ； Rainstorm ； Velocity field

參考文獻

[17] 劉承昕，2014，利用ABLER移流迴歸法估計颱風降水系統移速之研究，國立臺灣大學土木工程學研究所碩士論文。

[15] 周仲島、高聿正、修榮光、鍾吉俊、李宗融、郭鴻基，2016，台北都會區豪雨型午後雷暴的觀測特徵與預報挑戰：2015年6月14日個案研究。大氣研究資料庫大氣科學期刊，第44期第1號，第57-82頁。

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