Browse > Article
http://dx.doi.org/10.3741/JKWRA.2014.47.2.119

Using Extended Kalman Filter for Real-time Decision of Parameters of Z-R Relationship  

Kim, Jungho (School of Civil, Environmental and Architectural Engineering, College of Engineering, Korea Univ.)
Yoo, Chulsang (School of Civil, Environmental and Architectural Engineering, College of Engineering, Korea Univ.)
Publication Information
Journal of Korea Water Resources Association / v.47, no.2, 2014 , pp. 119-133 More about this Journal
Abstract
The study adopted extended Kalman filter technique in an effort to predict Z-R relationship parameter as a stable value in real-time. Toward this end, a parameter estimation model was established based on extended Kalman filter in consideration of non-linearity of Z-R relationship. A state-space model was established based on a study that was conducted by Adamowski and Muir (1989). Two parameters of Z-R relationship were set as state variables of the state-space model. As a result, a stable model where a divergence of Kalman gain and state variables are not generated was established. It is noteworthy that overestimated or underestimated parameters based on a conventional method were filtered and removed. As application of inappropriate parameters might cause physically unrealistic rain rate estimation, it can be more effective in terms of quantitative precipitation estimation. As a result of estimation on radar rainfall based on parameters predicted with the extended Kalman filter, the mean field bias correction factor turned out to be around 1.0 indicating that there was a minor difference from the gauge rain rate without the mean field bias correction. In addition, it turned out that it was possible to conduct more accurate estimation on radar rainfall compared to the conventional method.
Keywords
parameters of Z-R relationship; QPE; radar rain rate; extended Kalman filter;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 Kim, K.H. (1999). Speed sensorless vector control of an induction motor using an extended Kalman filter. Master of Science, dissertation, Korea University.
2 Kotarou T., Takumi, N., and Takaaki, Y. (1995). "Operational calibration of raingauge radar by 10-minute telemeter rainfall." 3rd Int. Sympos. on Wea. Radars, Sao Paulo, Brazil, pp. 75-81.
3 Krajewski, W.F., and Smith, J.A. (2002). "Radar hydrology: rainfall estimation." Advances inWater Resources, Vol. 25, pp. 1387-1394.   DOI   ScienceOn
4 Lee, Y.H., and Singh, V.P. (1998). "Application of the Kalman filter to the Nash model." Hydrological Processes, Vol. 12 pp. 755-767.   DOI
5 Legates, D.R. (2000). "Real-time calibration of radar precipitation estimates." The Professional Geographer, Vol. 52, No. 2, pp. 235-246.   DOI   ScienceOn
6 Lin, D.S and Krajewski, W.F. (1989) "Recursive methods of estimating radar-rainfall field bias. Preprints." 24rd Radar Meteorology conference, AMS, Florida, MA, pp. 648-651.
7 Macias, J.A., and Gomez, A. (2006). "Self-tuning of Kalman filters for harmonic computation." IEEE Trans. Power Del., Vol. 21, No. 1, pp. 501-503.   DOI   ScienceOn
8 Marshall, J.S., and Palmer, W.M. (1948). "The distribution of raindrop with size." Journal ofAtmospheric Sciences, Vol. 5, pp. 165-166.
9 METRI (2002). Development of METRI X-band doppler weather radar operations and radar data analysis technique II. Meteorological Research Institute Korea Meteorological Administration (METRI), pp. 103-104.
10 O'Connell, P.E., and Clarke, R.T. (1981). "Adaptive hydrological forecasting-a review." Hydrological Sciences, Vol. 26, No. 2, pp. 179-205.   DOI   ScienceOn
11 Michelson, D.B., and Koistinen, J. (2000). "Gauge-radar network adjustment for the baltic sea experiment." Physics and Chemistry of the Earth(B), Vol. 25, No. 10-12, pp. 915-920.   DOI   ScienceOn
12 Mohr, C.G., and Vaughan, R.L. (1979). "An economical procedure for cartesian interpolation and display of reflectivity factor data in three-dimensional space." Journal of Applied Meteorology, Vol. 18, No. 5, pp. 661-670.   DOI
13 Murty, Y.V.V.S., and Smolinski, W.J. (1988). "Design and implementation of a digital differential relay for a 3-phase power transformer based on Kalman filtering theory." IEEE Trans. Power Del., Vol. 3, No. 2, pp. 525-533   DOI   ScienceOn
14 Park, S.W(1993). Real-time flood forecasting by transfer function types model and filtering algorithm. Ph. D. dissertation, Dongguk University.
15 Puente, C.E., and Bras, R.L. (1987). "Application of nonlinear filtering in the real time forecasting of river flows." Water Resources Research, Vol. 23, No. 4, pp. 675-682.   DOI
16 Rendon, S.H., Vieux, B.E., and Pathak, C.S. (2011). "Deriving radar specific Z-R relationships for hydrologic operations." World Environmental and Water Resources Congress.
17 Rendon, S.H., Vieux, B.E., and Pathak, C.S. (2012). "Continuous forecasting and evaluation of derived Z-R relationships in a sparse rain gauge network using NEXRAD." Journal of Hydrologic Engineering, accepted January 6 2012, posted ahead of print.
18 Rosenfeld, D., Wolff, D.B., and Amitai, E. (1994). "The window probability matching method for rainfall measurements with radar." Journal ofApplied Meteorology, Vol. 33, pp. 682-693.
19 Smith, J.A., and Krajewski, W.F. (1991). "Estimation of the mean field bias of radar rainfall estimates." Journal of Applied Meteorology, Vol. 30, pp. 397-412.   DOI
20 Sage, A., and Husa, G.W. (1969). "Adaptive filtering with unknown prior statistics." Joint Automatic Control Conference, pp. 760-769.
21 Schmidt, S.F. (1970). "Computational techniques in Kalman filtering, in theory and applications of Kalman filtering." AGARDograph 139, NATO Advisory Group for Aerospace Research and Development, London.
22 Seo, B.H., and Gang, G.W. (1985). "A hydrologic prediction of streamflows for flood forecasting and warning system." Journal of Korea Water Resources Association, KWRA, Vol. 18, No. 2, pp. 153-161.   과학기술학회마을
23 Steiner M., and Smith J.A, (2000). "Reflectivity, rain rate, and kinetic energy flux relationships based on raindrop spectra." Journal of Applied Meteorology, Vol. 39, pp. 1923-1940.   DOI
24 Twomey, S. (1952). "On the measurement of precipitation intensity by radar." Journal ofMeteorology, Vol. 10, pp. 66-67.
25 Uijlenhoet, R., Steiner, M., and Smith, J.A. (2003). "Variability of raindrop size distributions in a squall line and implications for radar rainfall estimation." Journal of Hydrology, Vol. 4, pp. 43-61.
26 Wang, C.H., and Bai, Y.L. (2008). "Algorithm for real time correction of stream flow concentration based on Kalman filter." Journal of Hydrologic Engineering, Vol. 13, pp. 290-296.   DOI   ScienceOn
27 Wang, G.T., Yu, Y.-S., and Wu, K. (1987). "Improved flood routing by ARMA modelling and the Kalman filter technique." Journal of Hydrology, Vol. 93, pp. 175-190.   DOI   ScienceOn
28 Adamowski, K., and Muir, J. (1989). "A Kalman filter modelling of space-time rainfall using radar and raingauge obervations." Canadian Journal of Civil Engineering, Vol. 16, No. 5, pp. 767-773.   DOI
29 Yoo, C., Ha, E., Kim, B., Kim, K., and Choi, J. (2008). "Sampling error of areal average rainfall due to radar partial coverage." Journal of Korea Water Resources Association, KWRA, Vol. 41, No. 5, pp. 545-558.   과학기술학회마을   DOI   ScienceOn
30 Yoo, C., Kim, J., Chung, J.H., and Yang, D.M. (2011). "Mean field bias correction of the very short range forecast rainfall using the Kalman filter." Korean Society ofHazard Mitigation, Vol. 11, No. 3, pp. 17-28.   과학기술학회마을
31 Alfieri, L., Claps, P., and Laio, F. (2010). "Time-dependent Z-R relationship for estimating rainfall fields from radar measurements." Natural Hazards and Earth System Sciences, Vol. 10, pp. 149-158.   DOI
32 Bolzern, P., Ferrario, M., and Fronza, G. (1980). "Adaptive real-time forecast of river flow-rates from rainfall data." Journal of Hydrology, Vol. 47, pp. 251-267.   DOI   ScienceOn
33 Box, G.E.P., and Jenkins, G.M. (1976). Time series analysis; forecasting and control. revised edition, holden-day.
34 Bae, D.H., Lee, B.J., and Georgakakos, K.P. (2009). "Stochastic continuous storage function model with ensemble Kalman filtering( I ) : model development." Journal ofKoreaWater Resources Association, KWRA, Vol. 42, No. 11, pp. 953-961.   과학기술학회마을   DOI   ScienceOn
35 Battan, L.J. (1973). Radar observation of the atmosphere. The University of Chicago Press. Chicago, p. 324.
36 Blanchard, D.C. (1953). "Raindrop size distribution in Hawaiian rains." Journal ofMeteorology, Vol. 10, pp. 457-473.
37 Bringi, V.N., and Chandrasekar, V. (2001). Polarimetric Doppler weather radar, principles and applications. Cambridge University Press, New York.
38 Brown, P.E., Diggle, P.J., Lord, M.E., and Young, P.C. (2001). "Space-time calibration of radar rainfall data." Applied Statistics, Vol. 50, pp. 221-242.
39 Chou, C.M., and Wang, R.Y. (2004). "Application of wavelet-bsed multi-model Kalman filters to real-time flood forecasting." Hydrological Processes, Vol. 18, pp. 987-1008.   DOI   ScienceOn
40 Costa, M., and Alpuim, T. (2010). "Adjustment of state space models in view of area rainfall estimation." Environmetrics, Vol. 22, pp. 530-540.
41 Dan, S. (2006). Optimal state estimation: Kalman, H infinity, and nonlinear approaches, Wiley.
42 Eigbe, U., Beck, M.B., and Hirano, W.F. (1998). "Kalman filtering in groundwater flow modelling: problems and prospects." Stochastic Hydrology and Hydraulic, Vol. 12, pp. 15-32.   DOI
43 Harter R.M. (1990). An estimation of rainfall amounts using radar-drived Z-R relationships. Master of Science Thesis, Purdue University.
44 Francois, C., Quesney, A., and Ottle, C. (2003). "Sequential assimilation of ERS-1 SAR data into a coupled land surface-hydrological model using an extended Kalman filter." American Meterological Society, Vol. 4, No. 2, pp. 473-487.
45 Gelb, A. (1974). Applied optimal estimation. The MIT Press.
46 Habib, E., Malakpet, C.G., Tokay, A., and Kucera, P.A. (2008). "Sensitivity of streamflow simulation to temporal variability and estimation of Z-R relationships." Journal of Hydrologic Engineering, ASCE, Vol. 13, No. 12, pp. 1177-1186.   DOI   ScienceOn
47 Hebson, C., and Wood, E.F. (1985). "Partitioned state and parameter estimation for real-time flood forecasting." Applied Mathematics and Computation, Vol. 17, pp. 357-374.   DOI   ScienceOn
48 Henschke, A., Habib, E., and Pathak, C.S. (2009). "Adjustment of the Z-R relationship in real-time for use in South Florida." World Environmental and Water Resources Congress 2009, ASCE, pp. 6069-6080.
49 Jang, S.G. (2002). Combining forecast methods of Chungju dam streamflow using Kalman filter. Master of Science, dissertation, Seoul National University.
50 Jung, S.H., Kim, K,E., and Ha, K.J. (2005). "Real-time estimation of improved radar rainfall intensity using rainfall intensity measured by rain gauges." Asia-Pacific Journal of Atmospheric Sciences, Vol. 41, No. 5, pp. 751-762.   과학기술학회마을
51 Kalman, R.E. (1960). "A new approach to linear filtering and prediction problems." Transactions of the ASME -Journal of Basic Engineering, No. 82 (Series D), pp. 35-45.   DOI
52 Leung, H., Zhu, Z., and Ding, Z. (2000). "An aperiodic phenomenon of the extended Kalman filter in filtering noisy chaotic signals." IEEE Trans. Signal Process, Vol. 48, No. 6, pp. 1807-1810.   DOI   ScienceOn
53 Jones, D.M.A. (1956). Rainfall drop-size distribution and radar reflectivity. Research Report 6, Urbana, Meteor. Lab., Illinois State Water Survey.