Abstract
The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4×4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.
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References
Abramowitz, M.; Stegun, A. 1970: Handbook of mathematical functions, Dover Publications, New York, N.Y.
Ahnert, P.R.; Krajewski, W.F.; Johnson, E.R. 1986: Kalman filter estimation of radar-rainfall field bias. Preprints of the 23rd conference of radar meteorology and the conference on cloud physics. AMS, Boston, Mass., JP33-JP37
Austin, P.M. 1987: Relation between measured radar reflectivity and surface rainfall, Monthly weather review. 115, 1053–1070
Battan, L.J. 1973: Radar observation of the atmosphere, Univ. Chicago Press, Chicago
Brandes, E.A. 1975: Optimizing rainfall estimates with the aid of radar, J. Appl. Meteorol. 14, 1339–1345
Byers, H.R. 1948: The use of radar in determining the amount of rain falling over a small area. Trans. American Geoph. Union, 29, 187–196
Crawford, K.C. 1979: Considerations for the design of a hydrologic data network using multivariate sensors, Water Resour. Res. 15(6), 1752–1762
Creutin, J.D.; Delrieu G.; Lebel T. 1988: Rain measurement by raingage-radar combination: A geostatistical approach, J. Atm. and Oceanic Tech. 5(1), 102–115
Doviak, R.J.; Zrnic, D.S. 1984: Doppler radar and weather observations. Academic Press, Orlando, FL.
Eddy, A. 1979: Objective analysis of convective scale rainfall using gages and radar, J. Hydrol. 44, 125–134
Greene, D.R.; Flanders A.F. 1976: Radar hydrology—the state of the art. Preprints of the conference on hydrometeorology. AMS, Boston, Mass., 66–71
Greene, D.R.; Hudlow, M.D.; Johnson, E.R. 1980: A test of some objective analysis procedures for merging radar and raingage data. Preprints of the 19th conference on radar meteorology. AMS, Boston, Mass., 470–479
Hiatt, W.E. 1956: Radar in flood hydrology. Publication of 42nd International hydrologic Association, U.G.G.F., 286–290
Hudlow, M.D.; Arkell, R.; Patterson, V.; Pytlowany, P.; Richards, F. 1979: Calibration and intercomparison of the gate C-band radars. NOAA Tech. Rep. EDIS 31, U.S. Dept. of Commer, Washington D.C.
Journel, A.G.; Huijbregts Ch. J. 1978: Mining geostatistics. Academic Press, New York, N.Y.
Kessler, E.; Wilk, K.E. 1968: Radar measurements of precipitation for hydrological purposes. WMO/IHD Report No. 5, Secretariat of the World Meteorological Organization. Geneva, Switzerland
Krajewski, W.F. 1987: Co-kriging radar-rainfall and rain gage data, J. of Geoph. Res. 92(D8), 9571–9580
Krajewski, W.F.; Azimi-Zonooz, A. 1987: Hermite approximation of anamorphosis function, Technical Note, No. 10, Hydrologic Research Laboratory, National Weather Service, Silver Spring, Maryland
Krajewski, W.F.; Georgakakos, K.P. 1985: Synthesis of radar rainfall data, Water Resour. Res., 21(5), 764–768
Krajewski, W.F.; Hudlow, M.D. 1983: Evaluation and application of a real time method to estimate mean areal precipitation from rain gage and radar data. Proceedings of the WMO conference on mitigation of natural hazards, Sacramento, California
Larson, L.W.; Peck, E.L. 1974: Accuracy of precipitation measurements for hydrologic modeling. Water Resour. Res. 10(4), 857–863
Mantolou, A.; Wilson, J.L. 1982: The turning bands method for simulation of random fields using line generation by a spectral method, Water Resour. Res., 18(5), 1379–1394
Matheron, G. 1976: A simple substitute for conditional expectation: the disjunctive kriging, Proceedings, NATO A.S.I. “Geostat 75”, D. Reidel Publishers, Dordrecht, Netherlands
Puente, C.E.; Bras, R.L. 1982: A comparison of linear and nonlinear random field estimators, Ralph. M. Parsons Lab., Technical Report 287, M.I.T., Cambridge, Mass.
Seo, D.J.; Krajewski, W.F.; Bowles, D.S. 1989a: Stochastic interpolation of rainfall data from raingages and radar using co-kriging: 1. Design of experiments. Sumitted to Water Resour. Res.
Seo, D.J.; Krajewski, W.F.; Azimi-Zonooz, A.; Bowles, D.S. 1989b: Stochastic interpolation of rainfall data from raingages and radar using co-kriging: 2. Results. Submitted to Water Resour. Res.
Valdes, J.B.; Rodriguez-Iturbe, I.; Gupta, V.K. 1985: Approximation of temporal rainfall from a multidimensional model. Water Resour. Res. 21(8), 1259–1270
Waymire, E.; Gupta, V.K.; Rodriguez-Iturbe, I. 1984: A spectral theory of rainfall intensity at the Meso-β scale, Water Resour. Res., 20(10), 1453–1465
Wilson, J.W. 1970: Integration of radar and raingage data for improved rainfall measurements, J. Appl. Meteo. 9, 489–497
Wilson, J.W.; Brandes, E.A. 1979: Radar measurement of rainfall—a summary, Bull. Am. Meteorol. Soc., 60(9), 1048–1958
Yates, S.R. 1986: Disjunctive kriging 3. Co-kriging, Water Resour. Res. 22(10), 1371–1376
Zawadzki, I. 1973: Statistical properties of precipitation patterns, J. Appl. Meteorol., 12, 459–472
Zawadzki, I. 1984: Factors affecting the precision of radar measurements of rain, Preprints of the 22nd Conference on radar meteorology. AMS, Boston, Mass., 251–256
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Azimi-Zonooz, A., Krajewski, W.F., Bowles, D.S. et al. Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data. Stochastic Hydrol Hydraul 3, 51–67 (1989). https://doi.org/10.1007/BF01543427
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DOI: https://doi.org/10.1007/BF01543427