準確而可靠的降雨估算對於各種水文及氣象應用皆扮演重要的角色。在雷達定量降水估計（Quantitative Precipitation Estimation,QPE）上常使用降雨關係式來進行估算，然而，偏極化參數中固有的雜訊與不同事件下雨滴粒徑分布(Drop size distribution)使降雨關係式受到限制。因此，本研究採取變分法進行降雨估算，並與過往所統計出降雨關係式結果進行統計分數比較，希望藉此探討於不同類型的降水事件時，變分法的表現及優缺點分析。
本研究之變分法納入三種雷達參數: 差異反射率（Z_dr）、差異相位差（∅_dp）及比差異相位差（K_dp）。使用RCWF（S波段）與RCMD（C波段）雷達資料，分析台灣2017年梅雨及颱風兩個案，於單一事件中給定8組實驗，分別考慮：1.納入三種雷達變數（Z_dr 、∅_dp 、K_dp）及僅使用兩種參數(Z_dr 、∅_dp) 2.觀測誤差是否固定 3.使用原始及較低解析度進行變分。
RCWF雷達資料於兩個案變分法的8組實驗中，可以得到以下結果：納入三種參數皆優於使用兩種參數；較粗解析度資料優於使用原始解析度資料；在固定及變動觀測誤差方面，於梅雨個案，固定觀測誤差有較好的結果，但於颱風個案，則是隨不同波束變動觀測誤差實驗組較佳。另外在梅雨個案下，進行RCWF與RCMD雷達綜合比較，結果顯示RCMD雷達在降雨關係式表現較差，但若在適當設定下使用變分法，可得到不錯的結果。
後續分析RCWF資料在1.5°仰角平面位置顯示圖（PPI）結果與單一波束上變分場與觀測場差異，在兩個案下皆可以看到變分場之場型與觀測接近，另外變分場結果更加平滑，雜訊也相對較少，且∅_dp 、K_dp皆可修正為正值；最終探討各分數的空間分布，以及針對不同降雨強度進行分析，皆可看到各統計分數與降水強度具有一定相關。

Accurate and reliable Quantitative Precipitation Estimation (QPE) plays important role in hydrological and meteorological applications. QPEs are vastly derived from radar measurements; however, the inherent noise in radar polarization parameters and the variation of drop size distributions (DSD) in different precipitation events limit the accuracy. Therefore, this study utilized the variational technique to estimate the rainfall rate and compared with the radar-based QPE, to evaluate the performance of variational QPE in different precipitation events.
Three radar observed parameters (differential reflectivity (Z_dr), differential phase shift (∅_dp), and specific differential phase (K_dp)) of collocated dual-polarized S- (RCWF) and C-band (RCMD) radars were used. Mei-yu and Typhoon cases in 2017 were selected, and eight different experiments were conducted according to (1) either used three radar observed parameters (Z_dr, ∅_dp, and K_dp) or two radar parameters (Z_dr and ∅_dp); (2) fixed or changed the observation errors; and (3) two different resolutions (raw (R1) and modified-low (R2)).
The observed radar parameters and variational results showed in good agreements. The variational results have the noise reduced and become smoother, variational derived ∅_dp and K_dp are all positive values. Generally, the two cases of variational QPE of RCWF showed that using three parameters are better than two parameters, and resolution R2 are better than resolution R1. However, for the comparison of the fixed and changed observation errors, fixed observation errors in Mei-yu case perform better than Typhoon case. Besides, the variational QPE of RCWF perform better than RCMD in the Mei-yu case, but for the RCMD, the variational QPE are better than the radar-based QPE.

陳如瑜，2017：S 與 C 波段雙偏極化雷達參數定量降雨估計之探討，國立中央大學碩士論文，74頁。
Andsager, K., K. V. Beard, and N. F. Laird, 1999: Laboratory measurements of axis ratios for large raindrops. J. Atmos. Sci., 56, 2673–2683.
Bringi, V. N., and V. Chandrasekar, 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.
——, ——, N. Balakrishnan, and D. S. Zrnić, 1990 : An examination of propagation effects in rainfall on radar measurements at microwave frequencies. J. Atmos. Oceanic Technol., 7, 829-840.
Brandes, E., G. Zhang, and J. Vivekanandan, 2002 : Experiments in rainfall estimation with polarimetric radar in a subtropical environment. J. Appl. Meteor., 41, 674-685.
Chang, W.-Y., J. Vivekanandan, K. Ikeda, and P.-L. Lin, 2016: Quantitative precipitation estimation of the epic 2013 Colorado flood event: Polarization radar-based variational scheme. J. Appl. Meteorol. Climatology, 55(7), 1477–1495.
——, ——, and Wang, T.-C. C., 2014: Estimation of X-band Polarimetric Radar Attenuation and Measurement Uncertainty Using a Variational Method, J. Appl. Meteorol., 53, 1099–1119.
Desroziers, G., L. Berre, B. Chapnik, and P. Poli, 2005: Diagnosis of observation, background and analysis error statistics in observation space. Quart. J. Roy. Meteor. Soc., 131, 3385–3396.
Furness, G., 2005: Using optimal estimation theory for improved rainfall rates from polarization radar. M.Sc. dissertation, Dept. of Mathematics, University of Reading, 66 pp.
Goddard, K. L. Morgan, A. J. Illingworth, and H. Sauvageot, 1995: Dual wavelength polarization measurements in precipitation using the CAMRa and Rabelais radars. Preprints, 27th Int. Conf. on Radar Meteorology, Vail, CO, Amer. Meteor. Soc., 196–198.
Hogan, R. J., 2007: A variational scheme for retrieving rainfall rate and hail intensity from polarization radar. J. Appl. Meteorol. Climatology, 46, 1544-1564.
Huang, H., et al., 2018: Quantitative Precipitation Estimation with Operational Polarimetric Radar Measurements in Southern China: A Differential Phase–Based Variational Approach. J Atmos Ocean Technol, 35, 1253-1271.
Marshall, J. S., and W. M. K. Palmer, 1948: The distribution of raindrops with size. J. Meteor., 5, 165–166.
Melnikov, V. M., 2004: Simultaneous transmission mode for the polarimetric WSR-88D. NOAA/NSSL Rep., 84 pp.
Rodgers, C. D., 2000: Inverse Methods for Atmospheric Sounding: Theory and Practice. World Scientific, 238 pp.
Ryzhkov, S. E. Giangrande, and T. J.Schuur, 2005a: Rainfall estimation with a polarimetric prototype of WSR-88D. J. Appl. Meteor., 44, 502–515.
——, T. J. Schuur, D. W. Burgess, P. L. Heinselman, S. E. Giangrande, and D. S. Zrnić, 2005b: The Joint Polarization Experiment: Polarimetric rainfall measurements and hydrometeor classification. Bull. Amer. Meteor. Soc., 86, 809–824
Seliga, T. A., and V. N. Bringi, 1976: Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation. J. Appl. Meteor., 15, 69–76.
Steiner, M., and J. A. Smith, 2000: Reflectivity, rain rate, and kinetic energy flux relationships based on raindrop spectra. J. Appl. Meteor., 39, 1923–1940.
——, ——, and R. Uijlenhoet, 2004: A microphysical interpretation of radar reflectivity–rain rate relationships. J. Atmos. Sci., 61, 1114–1131
Vivekanandan J., W. M. Adams, and V. N. Bringi, 1991 : Rigorous approach to polarimetric radar modeling of hydrometeor orientation distributions., J. Appl. Meteor., 30, 1053-1063.