台灣擁有複雜地形使得預報對流初始、發展、增強及傳遞是更具有挑戰性，本篇研究選擇2014年8月19日北台灣夏季午後對流個案，分析方法分為兩部分。第一部分為地面測站資料分析，第二部分使用最新研發的四維變分都卜勒雷達資料同化系統(IBM_VDRAS)，其運用沉浸邊界法(Immersed Boundary Method)，因此具有解析地形的能力，並且能同化雷達及地面觀測資料，產出每17.5分鐘更新的完整三維高時空解析分析場，本研究共產生8個分析場來分析。
在對流產生降雨前，地面測站資料可分析出水平輻合帶由山區往平地移動，溫度場顯示對流蒸發冷卻效應，降雨觀測可看出被地形隔離的兩個降雨帶。從IBM_VDRAS分析場可以看出，此降雨事件主要是由兩個獨立對流胞成長開始，其中一個對流胞的外流邊界與另一個對流胞合併，使得後者增強，並且往台北市移動，產生80mm的觀測雨量。從近地表輻合和相對溼度場顯示，外流邊界的合併提供動力輻合增強，以及平流潮濕的環境有利對流發展。之後進行移除地形及地面資料同化變數的敏感度實驗，探討地形及同化變數對於定量降水預報的影響。結果顯示，雪山山脈在此事件中扮演的角色為阻礙外流邊界向南傳遞，而陽明山及林口台地增加外流邊界移動速度，此外，同化地面風場可修正地面風速偏差量及地表輻合帶強度並改善地量降水預報結果。

The complex terrain in Taiwan area makes it more challenging to forecast convection initiation, intensification, and propagation. In this research, the heavy rainfall event occurring on 19 August 2014 in northern Taiwan is selected. We use a newly-developed four-dimensional variational Doppler radar assimilation system (IBM_VDRAS), which is capable of simulating the topographic effect by adopting the so-called Immersed Boundary Method, and assimilating radar observations and surface station data. The products of IBM_VDRAS are a series of frequently-updated three-dimensional analysis fields over the complex terrain. In this case study, a total of eight analysis fields times are generated with a temporal interval of 17.5 min over a period of 2.5 h.
From the surface observations and the high temporal/spatial resolution analysis fields generated by IBM_VDRAS, it is found that the rainfall process started with the initiation of individual convective cells. The outflow of one of the convective cells merged with another convective system and helped to intensify the latter. The intensified major convective cell then moved into the Taipei metropolitan area and produced 80 mm of heavy precipitation within 2.5 h. The role played by the topographic forcing on the development of the convective system is investigated. A series of experiments are also designed and conducted by moving out terrain or surface assimilated variables to examine the performance of IBM_VDRAS in short-term rainfall forecasts. The result shows that SMR prevents the outflow from propagating southward, and LKHL and MTYM increase the outflow propagation speed. The surface wind assimilation improves the QPF skill by correcting the wind speed bias and controlling the magnitude of low-level convergence.

陳依涵，2016：發展地面資料同化方法以改善都卜勒雷達變分分析系統之分析
與預報能力。國立中央大學大氣物理所碩士論文，1–95。[Chen, Y.-H., 2016: Development of a surface assimilation scheme in a Variational Doppler Radar Analysis System for improving the model analysis and forecast skill. Master thesis, National Central University].
張少凡，2013：同化策略及冰相微物理對四維變分都卜勒雷達分析系統(VDRAS) 於定量降雨預報之影響研究。國立中央大學大氣物理所博士論文，1–81。[Chang, S.-F., 2013: The influence of assimilation strategies and ice-phase microphysics on the application of a four-dimensional Variational Doppler Radar Analysis System (VDRAS) for quantitative precipitation forecasts. Doctoral Dissertration, National Central University.]
戴聖倫，2010：使用四維變分同化都卜勒雷達資料以改進短期定量降雨預報。國立中央大學大氣物理所碩士論文，1–86。[Tai, S.-L., 2010: Improving short-term quantitaive precipitaion forecast by assimilating doppler radar observations with the four-dimensional variational technique. Master thesis, National Central University.]
周仲島、高聿正、修榮光、鍾吉俊、李宗融、郭鴻基，2016：臺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。大氣科學44(1)，57-82。[Jou, B. J.-D., Y.-C. Kao, R.-G. R. Hsiu, C.-J. U. Jung, J. R. Lee, H. C. Kuo, 2016: Observational Characteristics and Forecast Challenge of Taipei Flash Flood Afternoon Thunderstorm: Case Study of 14 June 2015. Atmospheric Science,44(1),57-82.]
繆炯恩，2017：2015年6月14日台北盆地劇烈午後雷暴個案之高解析度模究。國立臺灣大學大氣科學研究所碩士論文，1–86。[Miao, J.-E., 2017: Cell Merger and Heavy Rainfall of the Severe Afternoon Thunderstorm Event at Taipei on 14 June 2015. Master thesis, National Taiwan University.]
Barnes, S. L., 1964: A Technique for Maximizing Details in Numerical Weather Map Analysis. J. Appl. Meteor., 3, 396-409.
Byers, H. R., and R. R. Braham, 1948: Thunderstorm Structure and Circulation. J. Meteor., 5, 71-86.
Chang, S.-F., Y.-C. Liou, J. Sun, and S.-L. Tai, 2016: The Implementation of the Ice-Phase Microphysical Process into a Four-Dimensional Variational Doppler Radar Analysis System (VDRAS) and Its Impact on Parameter Retrieval and Quantitative Precipitation Nowcasting. J. Atmos. Sci., 73, 1015-1038.
Chang, S.-F., J. Sun, Y.-C. Liou, S.-L. Tai, and C.-Y. Yang, 2014: The influence of erroneous background, beam-blocking and microphysical non-linearity on the application of a four-dimensional variational Doppler radar data assimilation system for quantitative precipitation forecasts. Meteor. Appl., 21, 444-458.
Chen, X., K. Zhao, J. Sun, B. Zhou, and W.-C. Lee, 2016: Assimilating surface observations in a four-dimensional variational Doppler radar data assimilation system to improve the analysis and forecast of a squall line case. Adv. Atmos. Sci., 33, 1106-1119.
Chung, K.-S., I. Zawadzki, M. K. Yau, and L. Fillion, 2009: Short-Term Forecasting of a Midlatitude Convective Storm by the Assimilation of Single–Doppler Radar Observations. Mon. Wea. Rev., 137, 4115-4135.
Crook, N. A., and J. Sun, 2002: Assimilating Radar, Surface, and Profiler Data for the Sydney 2000 Forecast Demonstration Project. J. Atmos. Oceanic Technol, 19, 888-898.
Crook, N. A., and J. Sun, 2004: Analysis and Forecasting of the Low-Level Wind during the Sydney 2000 Forecast Demonstration Project. Wea. Forecasting, 19, 151-167.
Feng, Z., S. Hagos, A. K. Rowe, C. D. Burleyson, M. N. Martini, and S. P. de Szoeke, 2015: Mechanisms of convective cloud organization by cold pools over tropical warm ocean during the AMIE/DYNAMO field campaign. J. Adv. Model. Earth Syst., 7, 357-381.
Franke, R., 1982: Scattered Data Interpolation: Tests of Some Method. Math. Comput., 38, 181-200.
Friedrich, K., and Coauthors, 2016: Raindrop Size Distribution and Rain Characteristics during the 2013 Great Colorado Flood. J. Hydrometeor., 17, 53-72.
Gao, T., Y.-H. Tseng, and X.-Y. Lu, 2007: An improved hybrid Cartesian/immersed boundary method for fluid–solid flows. Int. J. Numer. Methods Fluids, 55, 1189-1211.
Gochis, D., and Coauthors, 2015: The Great Colorado Flood of September 2013. Bull. Amer. Meteor. Soc., 96, 1461-1487.
Hayden, C. M., and R. J. Purser, 1995: Recursive Filter Objective Analysis of Meteorological Fields: Applications to NESDIS Operational Processing. J. Appl. Meteor., 34, 3-15.
Hsu, S. A., E. A. Meindl, and D. B. Gilhousen, 1994: Determining the Power-Law Wind-Profile Exponent under Near-Neutral Stability Conditions at Sea. J. Appl. Meteor., 33, 757-765.
Kalnay, E., 2002: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press.
Kawabata, J., H. Seko, K. Saito, T. Kuroda, K. Tamiya, T. Tsuyuki, and Wakazuki, 2007: An assimilation and forecasting experiment of the Nerima heavy rainfall with a cloud-resolving nonhydrostatic 4-dimensiojnal variational data assimilation system. J. Meteor. Soc. Japan, 85, 255-276.
Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulations. Meteor. Mongr., Amer. Meteor. Soc., 1-84.
Li, Y., X. Wang, and M. Xue, 2012: Assimilation of Radar Radial Velocity Data with the WRF Hybrid Ensemble–3DVAR System for the Prediction of Hurricane Ike (2008). Mon. Wea. Rev., 140, 3507-3524.
Lin, P.-F., P.-L. Chang, B. J.-D. Jou, J. W. Wilson, and R. D. Roberts, 2011: Warm season afternoon thunderstorm characteristics under weak synoptic-scale forcing over taiwan island. Wea. Forecasting, 26, 44-60.
Malkus, J. S., 1954: Some results of a trade-cumulus cloud investigation. J. Meteor., 11, 220-237.
Malkus, J. S., and H. Riehl, 1964: Cloud structure and distributions over the tropical Pacific Ocean. Tellus, 16, 275-287.
Miller, M. J., and R. P. Pearce, 1974: A three-dimensional primitive equation model of cumulonimbus convection. Q. J. R. Meteor. Soc., 100, 133-154.
Navon, I. M., X. Zou, J. Derber, and J. Sela, 1992: Variational Data Assimilation with an Adiabatic Version of the NMC Spectral Model. Mon. Wea. Rev., 120, 1433-1446.
Pan, X., X. Tian, X. Li, Z. Xie, A. Shao, and C. Lu, 2012: Assimilating Doppler radar radial velocity and reflectivity observations in the weather research and forecasting model by a proper orthogonal-decomposition-based ensemble, three-dimensional variational assimilation method. J. Geophys. Res, 117.
Simpson, J., W. L. Woodley, A. H. Miller, and G. F. Cotton, 1971: Precipitation Results of Two Randomized Pyrotechnic Cumulus Seeding Experiments. J. Appl. Meteor., 10, 526-544.
Simpson, J., T. D. Keenan, B. Ferrier, R. H. Simpson, and G. J. Holland, 1993: Cumulus mergers in the maritime continent region. Meteor Atmos. Phys., 51, 73-99.
Snyder, C., and F. Zhang, 2003: Assimilation of Simulated Doppler Radar Observations with an Ensemble Kalman Filter. Mon. Wea. Rev., 131, 1663-1677.
Sun, J., and N. A. Crook, 1997: Dynamical and Microphysical Retrieval from Doppler Radar Observations Using a Cloud Model and Its Adjoint. Part I: Model Development and Simulated Data Experiments. J. Atmos. Sci., 54, 1642-1611.
——, 1998: Dynamical and Microphysical Retrieval from Doppler Radar Observations Using a Cloud Model and Its Adjoint. Part II: Retrieval Experiments of an Observed Florida Convective Storm. J. Atmos. Sci., 55, 835-852.
——, 2001: Real-Time Low-Level Wind and Temperature Analysis Using Single WSR-88D Data. Wea. Forecasting, 16, 117-132.
Sun, J., and Y. Zhang, 2008: Analysis and Prediction of a Squall Line Observed during IHOP Using Multiple WSR-88D Observations. Mon. Wea. Rev., 136, 2364-2388.
Sun, J., and H. Wang, 2013: Radar Data Assimilation with WRF 4D-Var. Part II: Comparison with 3D-Var for a Squall Line over the U.S. Great Plains. Mon. Wea. Rev., 141, 2245-2264.
Sun, J., M. Chen, and Y. Wang, 2010: A Frequent-Updating Analysis System Based on Radar, Surface, and Mesoscale Model Data for the Beijing 2008 Forecast Demonstration Project. Wea. Forecasting, 25, 1715-1735.
Tai, S.-L., Y.-C. Liou, J. Sun, and S.-F. Chang, 2017: The Development of a Terrain-Resolving Scheme for the Forward Model and Its Adjoint in the Four-Dimensional Variational Doppler Radar Analysis System (VDRAS). Mon. Wea. Rev., 145, 289-306.
Tai, S.-L., Y.-C. Liou, J. Sun, S.-F. Chang, and M.-C. Kuo, 2011: Precipitation Forecasting Using Doppler Radar Data, a Cloud Model with Adjoint, and the Weather Research and Forecasting Model: Real Case Studies during SoWMEX in Taiwan. Wea. Forecasting, 26, 975-992.
Tao, W.-K., and J. Simpson, 1984: Cloud Interactions and Merging: Numerical Simulations. J. Atmos. Sci., 41, 2901-2917.
Tao, W.-K., and J. Simpson, 1989: A Further Study of Cumulus Interactions and Mergers: Three-Dimensional Simulations with Trajectory Analyses. J. Atmos. Sci., 46, 2974-3004.
Tong, M., and M. Xue, 2005: Ensemble Kalman Filter Assimilation of Doppler Radar Data with a Compressible Nonhydrostatic Model: OSS Experiments. Mon. Wea. Rev., 133, 1789-1807.
Tseng, Y.-H., and J. H. Ferziger, 2003: A ghost-cell immersed boundary method for flow in complex geometry. J. Comput. Phys., 192, 593-623.
Watson, A. I., and D. O. Blanchard, 1984: The Relationship between Total Area Divergence and Convective Precipitation in South Florida. Mon. Wea. Rev., 112, 673-685.
Westcott, N., 1984: A Historical Perspective on Cloud Mergers. Bull. Amer. Meteor. Soc., 65, 219-226.
Xiao, Q., and J. Sun, 2007: Multiple-Radar Data Assimilation and Short-Range Quantitative Precipitation Forecasting of a Squall Line Observed during IHOP_2002. Mon. Wea. Rev., 135, 3381-3404.
Xiao, X., J. Sun, M. Chen, X. Qie, Y. Wang, and Z. Ying, 2017: The characteristics of weakly forced mountain-to-plain precipitation systems based on radar observations and high-resolution reanalysis. J. Geophys. Res, 122, 3193-3213.
Xue, M., M. Tong, and K. K. Droegemeier, 2006: An OSSE framework based on the ensemble square root kalman filter for evaluating the impact of data from radar networks on thunderstorm analysis and forecasting. J. Atmos. Oceanic Technol., 23, 46-66.