Abstract
Automatic interpolation of precipitation maps combining rain gauge and radar data has been done in the past but considering only the data collected at a given time interval. Since radar and rain gauge data are collected at short intervals, a natural extension of previous works is to account for temporal correlations and to include time into the interpolation process. In this work, rainfall is interpolated using data from the current time interval and the previous one. Interpolation is carried out using kriging with external drift, in which the radar rainfall estimate is the drift, and the mean precipitation is set to zero at the locations where the radar estimate is zero. The rainfall covariance is modeled as non-stationary in time, and the space system of reference moves with the storm. This movement serves to maximize the collocated correlation between consecutive time intervals. The proposed approach is analyzed for four episodes that took place in Catalonia (Spain). It is compared with three other approaches: (i) radar estimation, (ii) kriging with external drift using only the data from the same time interval, and (iii) kriging with external drift using data from two consecutive time intervals but not accounting for the displacement of the storm. The comparisons are performed using cross-validation. In all four episodes, the proposed approach outperforms the other three approaches. It is important to account for temporal correlation and use a Lagrangian system of coordinates that tracks the rainfall movement.
Similar content being viewed by others
References
Aran M, Amaro J, Arús J, Bech J, Figuerola F, Gayà M, Vilaclara E (2009) Synoptic and mesoscale diagnosis of a tornado event in Castellcir, Catalonia, on 18th October 2006. Atmos Res 93:147–160
Azimi-Zonooz A, Krajewski W, Bowles D, Seo D (1989) Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data. Stoch Hydrol Hydraul 3:51–67
Bech J, Pascual R, Rigo T, Pineda N, López J, Arús J, Gayá M (2007) An observational study of the 7 September 2005 Barcelona Tornado outbreak. Nat Hazards Earth Syst Sci 7:129–139
Bech J, Pineda N, Rigo T, Aran M, Amaro J, Gayà M, Arús J, Montanyà J, van der Velde O (2011) A mediterranean nocturnal heavy rainfall and tornadic event. Part I: overview, damage survey and radar analysis. Atmos Res 100:621–637
Berenguer M, Sempere-Torres D, Pegram GG (2011) Sbmcast-an ensemble nowcasting technique to assess the uncertainty in rainfall forecasts by Lagrangian extrapolation. J Hydrol 404:226–240
Berenguer M, Sempere-Torres D, Hürlimann M (2015) Debris-flow forecasting at regional scale by combining susceptibility mapping and radar rainfall. Nat Hazards Earth Syst Sci 15:587–602
Bochner S (1949) Fourier transforms. Princeton University Press, London, p 219
Brown PE, Diggle PJ, Lord ME, Young PC (2001) Space–time calibration of radar rainfall data. J R Stat Soc Ser C 50:221–241
Calheiros R, Zawadzki I (1987) Reflectivity-rain rate relationships for radar hydrology in Brazil. J Climate Appl Meteorol 26:118–132
Chumchean S, Seed A, Sharma A (2006) Correcting of real-time radar rainfall bias using a Kalman filtering approach. J Hydrol 317:123–137
Corral C, Velasco D, Forcadell D, Sempere-Torres D, Velasco E (2009) Advances in radar-based flood warning systems. the EHIMI system and the experience in the Besòs flash-flood pilot basin
Creutin J, Delrieu G, Lebel T (1988) Rain measurement by raingage-radar combination: a geostatistical approach. J Atmos Ocean Technol 5:102–115
Delrieu G, Annette W, Brice B, Dominique F, Laurent B, Pierre-Emmanuel K (2014) Geostatistical radar-raingauge merging: a novel method for the quantification of rain estimation accuracy. Adv Water Resour 71:110–124
Deutsch C (1991) The relationship between universal kriging, kriging with an external drift and cokriging. SCRF report 4
Germann U, Turner B, Zawadzki I (2006) Predictability of precipitation from continental radar images. Part IV: limits to prediction. J Atmos Sci 63:2092–2108
Goudenhoofdt E, Delobbe L (2009) Evaluation of radar-gauge merging methods for quantitative precipitation estimates. Hydrol Earth Syst Sci 13:195–203
Harrold T, Austin P (1974) The structure of precipitation systems—a review. J Rech Atmos 8:41–57
Hevesi JA, Istok JD, Flint AL (1992a) Precipitation estimation in mountainous terrain using multivariate geostatistics. Part I: structural analysis. J Appl Meteorol 31:661–676
Hevesi JA, Istok JD, Flint AL (1992b) Precipitation estimation in mountanious terrain using multivariate geostatistics. Part II: isohyetal maps. J Appl Meteorol 31:677–688
Jewell SA, Gaussiat N (2015) An assessment of kriging-based rain-gauge-radar merging techniques. Q J R Meteorol Soc 141:2300–2313
Journel AG, Rossi M (1989) When do we need a trend model in kriging? Math Geol 21:715–739
Krajewski WF (1987) Cokriging radar-rainfall and rain gage data. J Geophys Res Atmos 92:9571–9580
Mateo J, Ballart D, Brucet C, Aran M, Bech J (2009) A study of a heavy rainfall event and a tornado outbreak during the passage of a squall line over Catalonia. Atmos Res 93:131–146
Pulkkinen S, Koistinen J, Kuitunen T, Harri AM (2016) Probabilistic radar-gauge merging by multivariate spatiotemporal techniques. J Hydrol 542:662–678
Rinehart R, Garvey E (1978) Three-dimensional storm motion detection by conventional weather radar. Nature 273:287
Rosenfeld D, Wolff DB, Atlas D (1993) General probability-matched relations between radar reflectivity and rain rate. J Appl Meteorol 32:50–72
Rosenfeld D, Wolff DB, Amitai E (1994) The window probability matching method for rainfall measurements with radar. J Appl Meteorol 33:682–693
Rosenfeld D, Amitai E, Wolff DB (1995) Improved accuracy of radar WPMM estimated rainfall upon application of objective classification criteria. J Appl Meteorol 34:212–223
Sempere-Torres D, Corral C, Raso J, Malgrat P (1999) Use of weather radar for combined sewer overflows monitoring and control. J Environ Eng 125:372–380
Seo DJ (1998) Real-time estimation of rainfall fields using radar rainfall and rain gage data. J Hydrol 208:37–52
Seo DJ, Krajewski WF, Bowles DS (1990) Stochastic interpolation of rainfall data from rain gages and radar using cokriging: 1. Design of experiments. Water Resour Res 26:469–477
Sideris I, Gabella M, Erdin R, Germann U (2014) Real-time radar-rain-gauge merging using spatio-temporal co-kriging with external drift in the alpine terrain of Switzerland. Q J R Meteorol Soc 140:1097–1111
Sinclair S, Pegram G (2005) Combining radar and rain gauge rainfall estimates using conditional merging. Atmos Sci Lett 6:19–22
Sun X, Mein R, Keenan T, Elliott J (2000) Flood estimation using radar and raingauge data. J Hydrol 239:4–18
Todini E (2001) A bayesian technique for conditioning radar precipitation estimates to rain-gauge measurements. Hydrol Earth Syst Sci Dis 5:187–199
Velasco-Forero CA, Sempere-Torres D, Cassiraga EF, Gómez-Hernández JJ (2009) A non-parametric automatic blending methodology to estimate rainfall fields from rain gauge and radar data. Adv Water Resour 32:986–1002
Wilson JW, Brandes EA (1979) Radar measurement of rainfall—a summary. Bull Am Meteorol Soc 60:1048–1060
Yao T, Journel AG (1998) Automatic modeling of (cross) covariance tables using fast fourier transform. Math Geol 30:589–615
Yoon SS, Bae DH (2013) Optimal rainfall estimation by considering elevation in the Han River Basin, South Korea. J Appl Meteorol Climatol 52:802–818
Zawadzki I (1973) Statistical properties of precipitation patterns. J Appl Meteorol 12:459–472
Acknowledgements
This work has been done in the framework of the Spanish Project FFHazF (CGL2014-60700) and the EC H2020 project ANYWHERE (DRS-1-2015-700099). Thanks are due to the Meteorological Service of Catalonia for providing the radar and rain gauges data used here.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cassiraga, E., Gómez-Hernández, J.J., Berenguer, M. et al. Spatiotemporal Precipitation Estimation from Rain Gauges and Meteorological Radar Using Geostatistics. Math Geosci 53, 499–516 (2021). https://doi.org/10.1007/s11004-020-09882-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11004-020-09882-1