應用觀測系統實驗評估辨識移速場、追蹤雨胞和對流強度變化與外延定量推估降雨之研究

A Study to Evaluate Identifying Velocity Field, Tracking Rain Cells and their Convection, as well as Quantitative Precipitation Nowcast by Designed Observing System Experiments

吳秉澤(Bing-Ze Wu)

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(2019年)

https://doi.org/10.6342/NTU201903264

摘要

利用雷達回波觀測外延定量推估降雨的兩個基本要素：一是降雨系統的水平移速場(advection)；一是辨識雨胞及其垂直對流的時間變化，或回波強度的時間變化(convection)，以及利用大量辨識的雨胞及其強度變化，統計雨胞生命期(life history)的氣候特徵。
利用時間相鄰的數張回波影像，估計降雨系統移速場的兩大類方法，一類是使用Lagrangian架構的影像比對追蹤法，例如TREC (Tracking Radar Echo by Correlation)演算法，估計法是將其中一張影像在兩個主軸方向各平移某水平影像數個網格，和相鄰時間影像比對，找出相關係數最高的平移網格數和距離，除以相鄰影像的時間差，得到兩移速分量。因為比對需要眾數像元，移速場的空間變化率較低；應用於臺灣地區時，近地形降雨系統水平移速場的空間變率大，TREC法的移速場估計的變化彈性不足。另一類是假設移速場中任意位置的兩個速度分量，表示為空間座標(自變數)的函數，利用「迴歸法」估計速度函數的係數，這類方法是用Eulerian架構；若影像時間差之內，移流超出一個網格，無法滿足庫倫條件(CFL, Courant-Friedrichs-Lewy condition)時，迴歸法會失敗，導致係數估計錯誤，移速場估計錯誤。
ABLER (Advection-equation Based Lagrangian-Eulerian Regression)演算法結合了TREC的影像平移和線性速度場函數迴歸，兼具迴歸法的細緻變化，又可以透過平移避免違反庫倫條件。鄭哲榮(2017)利用主成分速度轉換(Principle Velocity Transform, PVT)和分區線性速度場聯合最佳化策略(Piecewise-Linear and Jointly Optimized, PLJO)改進全區線性速度場ABLER (Advection-equation Based Lagrangian-Eulerian Regression)演算法，其結果是：速度場更有彈性，速度估計更正確，計算速度更快，但是該研究不包含雨胞辨識與強度變化辨識。
本研究設計：1.移速場速度分量函數為線性，2.不同的雨胞有不同的對流成長或強度衰退的「觀測系統實驗」(Observing System Experiment, OSE)。利用經鄭哲榮改進的ABLER演算法估計移速場，並做兩項改進：(1)分段線性策略的最佳化方法，改Downhill Simplex Search (DSS)為BFGS法，並改採漸進式參數估計法，大幅加快最佳化係數的計算速度，但雨胞的源滅，仍會導致移速場係數推估的誤差。(2)增加雨胞辨識、強度成長與衰減速率辨識。
雨胞辨識的原理是透過等值線技術，與非零繞數原則辨識出強回波區，再利用數學形態學中的侵蝕(erosion)與膨脹(dilation)辨識出各別雨胞核心區域；另外，利用相鄰時間回波影像對應雨胞的等值線涵蓋區域質量差異，估計成長或衰減，並進行外延估計。
應用OSE評估：A.移速估計誤差；B.雨胞增減率估計誤差；C.雨胞辨識範圍誤差等因素，對於外延定量估計的敏感度。結果發現移速場估計誤差，對於預報準確度有最顯著的影響；增加雨胞辨識和核心區域的強度辨識和強度調整，能夠改善外延定量降雨預報的技術得分。

關鍵字

移速場 ； ABLER演算法 ； 雨胞辨識 ； 強度辨識 ； 觀測系統試驗 ； 雷達外延 ； 定量降水預報 ； 技術得分

並列摘要

There are two basic elements of quantitative precipitation nowcasting with radar echo observation: one is the horizontal velocity field of the rainfall system; the other is to identify the time variation of the rain cell and its vertical convection, or the time variation of the echo intensity (Convection), and the use of a large number of identified rain cells and their intensity changes to count the climate characteristics of the rain cell life history.
Two kinds of methods for estimating the velocity field of the rainfall system are estimated by using several echo images adjacent to each other. One is the image matching method for tracking, which is Lagrangian framework, such as the TREC (Tracking Radar Echo by Correlation) algorithm. One of the images is translated grids of a horizontal image in two main axes, and compared with adjacent time images to find the number of translation grids and the distance with the highest correlation coefficient, and divide by the time difference of the adjacent images to obtain two Shifting component. Because the image comparison requires a number of pixels, the spatial variability of the velocity field is low; when the method is applied in Taiwan, the spatial variability of the horizontal velocity field of the near-topographic rainfall system is large, and the variation of the velocity field estimation of the TREC method is insufficient.The other is to assume that two velocity components at any position in the velocity field are expressed as a function of the space coordinate (self-variable), and the coefficient of the velocity function is estimated by the "regression method". This method uses the Eulerian framework. If the flow is beyond a grid in a time difference and the Courant-Friedrichs-Lewy condition is not satisfied, the regression method will fail, resulting in incorrect coefficient estimation and incorrect estimation of the velocity field.
The ABLER (Advection-equation Based Lagrangian-Eulerian Regression) algorithm combines TREC's image translation and the regression of linear velocity field function, which combines the detailed changes of the regression method, and can avoid violation of the Courant condition through image translation. Cheng(2017) proposed the Principle Velocity Transform (PVT) and the Piecewise-Linear and Jointly Optimized (PLJO) strategy to improved the linear velocity field ABLER (Advection-equation Based Lagrangian--Eulerian Regression) algorithm. the result is: the velocity field is more flexible, the speed estimation is more accurate, and the calculation speed is faster, but the study does not include rain cell identification and intensity change identification.
The design of this study: 1. The velocity component function of the velocity field is linear, 2. The different rain cells have different convection growth or decay of the Observing System Experiment (OSE). Using the improved ABLER algorithm improved by Cheng(2017) to estimate the moving velocity field, and make two improvements: (1) Optimizing the piecewise linear strategy, changing the Downhill Simplex Search (DSS) to the BFGS method, and adopting the incremental parameter estimation. The method greatly speeds up the calculation of the optimization coefficient, but the source of the rain cell will still cause the error of the estimation of the velocity field coefficient. (2) Add the identification of rain cells, intensity growth and attenuation rate.
The principle of rain cell identification is to identify the strong echo region by the isoline technique and the non-zero winding number principle, and then use the erosion and dilation in mathematical morphology to identify the core regions of the respective rain cells; In addition, the contours of the rain cells corresponding to the adjacent time echo images are used to cover regional quality differences, estimate growth or attenuation, and perform extrapolation estimation.
Application OSE evaluation: A. velocity field estimation error; B. rain cell increase and decrease rate estimation error; C. rain cell identification range error and other factors, sensitivity to epitaxial quantitative estimation. The results show that the estimation error of the velocity field has the most significant impact on the accuracy of the forecast. Increasing the rain cell identification and the intensity identification and intensity adjustment of the core region can improve the technical score of the extended quantitative rainfall forecast.

並列關鍵字

Velocity Field ； ABLER Algorithm ； Rain Cell Identification ； Intensity Identification ； Observation System Test ； Radar Extrapolation ； Quantitative Precipitation Forecast ； Technical Score

參考文獻

Chen, T.-C., Wang, S.-Y., & Yen, M.-C. (2007). Enhancement of afternoon thunderstorm activity by urbanization in a valley: Taipei. Journal of Applied Meteorology and Climatology, 46(9), 1324-1340.

Han, L., Fu, S., Zhao, L., Zheng, Y., Wang, H., & Lin, Y. (2009). 3D convective storm identification, tracking, and forecasting—An enhanced TITAN algorithm. Journal of Atmospheric and Oceanic Technology, 26(4), 719-732.

Houze Jr, R. A. (1997). Stratiform precipitation in regions of convection: A meteorological paradox? Bulletin of the American Meteorological Society, 78(10), 2179-2196.

Ishihara, M. (2013). Radar echo population of air-mass thunderstorms and nowcasting of thunderstorm-induced local heavy rainfalls Part 1: statistical characteristics.

Jou, B. J.-D. (1994). Mountain-Originated Mesoscale Precipitation System in Northern Taiwan: A Case Study 21 June 1991. Terrestrial(2).