Ali Kemal BAKIR, Pınar KIRCI, Engin MAŞAZADE

A Kalman filter application for rainfall estimation using radar reflectivity measurements

The rainfall amount observed at a given location mostly depend on the cloud density, which can be quantifiedwith the reflectivity values observed by meteorology weather radars. In this study, we aim to estimate the rainfall amountusing a Kalman filter with radar reflectivity measurements. We first assume that the amount of rainfall observed atautomatic weather observation stations (AWOSs) are elements of an unknown state vector and consider the Kalmanfilter process model as the true rainfall amounts observed at these AWOSs over time. For the measurement modelof the Kalman filter, we use the radar reflectivity values observed at each AWOS location. For the execution of theKalman filter, a number of rainfall amount and radar reflectivity value pairs are first required to learn the process andmeasurement models of the Kalman filter. The estimation performance of the proposed Kalman filter is then comparedwith empirical reflectivity (Z) - rainfall (R) relationships. Numerical results show that when the Kalman filter is executedwith radar reflectivity measurements observed around a large number of AWOS locations, the mean squared errors ofthe Kalman filter rainfall estimates are smaller than the ones obtained with empirical ZR relationships.

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[1] Fabry F. Radar Meteorology: Principles and Practice. 1st ed. Cambridge, UK, Cambridge University Press; 2015.
[2] Hazer A, Kara N. Meteoroloji radar agında, ZR iliskisindeki a ve b katsayılarının bulunması ve bunların radara uygulanarak sonuclarin yer gozlemiyle karsılastırılması. In: MGM, III. Meteorolojik Uzaktan Algılama Sempozyumu. Antalya, T urkiye; 16 - 19 Ekim 2017.
[3] Battan L. Radar observation of the atmosphere. Chicago, USA, The University of Chicago Press. 1973;3:24.
[4] Dhiram K, Wang Z. Evaluation on radar reflectivity-rainfall rate (ZR) relationships for Guyana. Atmospheric and Climate Sciences. 2016;6(04):489.
[5] Chumchean S, Sharma A, Seed A. Radar rainfall error variance and its impact on radar rainfall calibration. Physics and Chemistry of the Earth, Parts A/B/C. 2003;28(1-3):27–39.
[6] Mapiam PP, Sharma A, Sriwongsitanon N. Defining the Z–R relationship using gauge rainfall with coarse temporal resolution: implications for flood forecasting. Journal of Hydrologic Engineering. 2014;19(8):04014003.
[7] Ruzanski E, Chandrasekar V. Weather radar data interpolation using a Kernel-based Lagrangian nowcasting technique. IEEE Transactions on Geoscience and Remote Sensing. 2015 June;53(6):3073–3083.
[8] Chumchean S, Seed A, Sharma A. Correcting of real-time radar rainfall bias using a Kalman filtering approach. Journal of Hydrology. 2006;317(1):123 – 137.
[9] Chumchean S, Sharma A, Seed A. An integrated approach to error correction for real-time radar-rainfall estimation. Journal of Atmospheric and Oceanic Technology. 2006;23(1):67–79.
[10] Kay SM. Fundamentals of statistical signal processing, Vol. I: Estimation Theory. 1st ed. Upper Saddle River, NJ, USA, Prentice Hall; 1993.
[11] Costa MAS, Monteiro MSV, Manuela Goncalves A. Kalman filtering approach in the calibration of radar rainfall data: a comparative analysis of state space representations. Rainfall: Behavior, Forecasting and Distribution. 2012;p. 167–184.
[12] Yuehong S, Wanchang Z, Yonghe L, Jingying Z. Analysis of quantitative estimation of precipitation using different algorithms with Doppler radar data. In: 2008 International Workshop on Education Technology and Training 2008 International Workshop on Geoscience and Remote Sensing. vol. 2; 2008. p. 372–375.
[13] Hamilton JD. Time series analysis. 1st ed. Princeton, NJ, USA, Princeton University Press; 1994.
[14] Marshall JS, Palmer WMK. The distribution of raindrops with size. Journal of meteorology. 1948;5(4):165–166.
[15] Biggerstaff MI, Listemaa SA. An improved scheme for convective/stratiform echo classification using radar reflectivity. Journal of applied meteorology. 2000;39(12):2129–2150.
[16] Crosson WL, Duchon CE, Raghavan R, Goodman SJ. Assessment of rainfall estimates using a standard ZR relationship and the probability matching method applied to composite radar data in central Florida. Journal of Applied Meteorology. 1996;35(8):1203–1219.
[17] Houze Jr RA. Stratiform precipitation in regions of convection: A meteorological paradox? Bulletin of the American Meteorological Society. 1997;78(10):2179–2196.
[18] Lang S, Tao W, Simpson J, Ferrier B. Modeling of convective–stratiform precipitation processes: sensitivity to partitioning methods. Journal of Applied Meteorology. 2003;42(4):505–527.
[19] Ozturk K, Cubuk A. Orta olcekli konvektif hadiselerde meteoroloji radarlarinin yagis tahminlerinin analizi. In: MGM, III. Meteorolojik Uzaktan Algilama Sempozyumu. Antalya, Turkiye; 16 - 19 Ekim 2017.
[20] Lichtenstern A. Kriging methods in spatial statistics, Bachelor Thesis, Technische Universitat Munchen. 2013.
[21] Cressie N, Wikle CK. Statistics for spatio-temporal data. 1st ed. NY, USA, John Wiley & Sons; 2015.
[22] Tan H, Chandrasekar V, Chen H. A machine learning model for radar rainfall estimation based on gauge observa tions. In: 2017 United States National Committee of URSI National Radio Science Meeting (USNC-URSI NRSM); 2017. p. 1–2.