Abstract
Rainfall is a phenomenon difficult to model and predict, for the strong spatial and temporal heterogeneity and the presence of many zero values. We deal with hourly rainfall data provided by rain gauges, sparsely distributed on the ground, and radar data available on a fine grid of pixels. Radar data overcome the problem of sparseness of the rain gauge network, but are not reliable for the assessment of rain amounts. In this work we investigate how to calibrate radar measurements via rain gauge data and make spatial predictions for hourly rainfall, by means of Monte Carlo Markov Chain algorithms in a Bayesian hierarchical framework. We use zero-inflated distributions for taking zero-measurements into account. Several models are compared both in terms of data fitting and predictive performances on a set of validation sites. Finally, rainfall fields are reconstructed and standard error estimates at each prediction site are shown via easy-to-read spatial maps.
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Adler RF, Huffman GJ, Chang A, Ferraro R, Xie PP, Janowiak J, Rudolf B, Schneider U, Curtis S, Bolvin D, Gruber A, Susskind J, Arkin P, Nelkin E (2003) The version-2 global precipitation climatology project (GPCP) monthly precipitation analysis (1979-present). J Hydrometeorol 4:1147–1167
Berrocal VJ, Raftery AE, Gneiting T (2008) Probabilistic quantitative precipitation field forecasting using a two-stage spatial model. Ann Appl Stat 4:1170–1193. doi:10.1214/08-AOAS203
Brier GW (1950) Verification of forecasts expressed in terms of probability. Mon Weather Rev 78:1–3
Brown PJ (1994) Measurement, regression and calibration. Oxford University Press, Oxford
Brown PE, Diggle PJ, Lord ME, Young PC (2001) Space-time calibration of radar rainfall data. Appl Stat 50:221–241
Chumchean S, Seed A, Sharma A (2006) Correcting of real-time radar rainfall bias using a Kalman filtering approach. J Hydrol 317:123–137
Cooley D, Nychka D, Naveau P (2007) Bayesian spatial modeling of extreme precipitation return levels. J Am Stat Assoc 497:824–840
Costa M, Alpuim T (2011) Adjustment of state space models in view of area rainfall estimation. Environmetrics 22:530–540
Fornasiero A, Amorati R, Alberoni PP, Ferraris L, Taramasso AC (2004) Impact of combined beam blocking and anomalous propagation correction algorithms on radar data quality. In: Proceedings of ERAD 2004, the 3th ERAD conference held in Gotland, Sweden, Copernicus GmbH 2004, pp 216–222
Fuentes M, Reich B, Lee G (2008) Spatial–temporal mesoscale modeling of rainfall intensity using gageand radar data. Ann Appl Stat 4:1148–1169. doi:10.1214/08-AOAS166
Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford Univ. Press, New York
Goudenhoofdt E, Delobbe L (2009) Evaluation of radar-gauge merging methods for quantitative precipitation estimates. Hydroland Earth System Sci 13:195–203
Kim T-W, Ahn H (2009) Spatial rainfall model using a pattern classifier for estimating missing daily rainfall data. Stoch Environ Res Risk Assess 23:367–376. doi:10.1007/s00477-008-0223-9
Li W, Zhang C, Dey DK (2010) Estimating threshold-exceeding probability maps of environmental variables with Markov chain random fields. Stoch Environ Res Risk Assess 24:1113–1126. doi:10.1007/s00477-010-0389-9
Marshall J, Palmer W (1948) The distribution of raindrops with size. J Meteorol 5:165–166
Orasi A, Jona Lasinio G, Ferrari C (2009) Comparison of calibration methods for the reconstruction of space-time rainfall fields during a rain enhancement experiment in Southern Italy. Environmetrics 20:812–834. doi:10.1002/env.956
Pilz J, Spöck G (2008) Why do we need and how should we implement Bayesian kriging methods. Stoch Environ Res Risk Assess 22:621–632. doi:10.1007/s00477-007-0165-7
Sahu SK, Jona Lasinio G, Orasi A, Mardia KV (2005) A comparison of spatio-temporal bayesian models for reconstruction of rainfall fields in a cloud seeding experiment. J Math Stat 1(4):273–281. ISSN 1549-3644
Sahu SK, Gelfand AE, Holland DM (2010) Fusing point and areal level space-time data with application to wet deposition. J R Stat Soc Ser C 59:77–103
Scardovi E, Alberoni PP, Amorati R, Cocchi D, Pavan V (2012a) Uso integrato dei dati di pioggia radar-pluviometro: analisi esplorativa dei dati orari. Quaderno Tecnico ARPA
Scardovi E, Bruno F, Amorati R, Cocchi D (2012b) Rainfall spatial modeling from different data sources. In: Gonçalves AM, Sousa I, Machado L, Pereira P, Menezes R, Faria S (eds) Proceedings of the VI International Workshop on Spatio-Temporal Modelling (METMA6). Guimarães, Portugal, 12–14 September 2012, CMAT—Centro de Matemática da Universidade do Minho, pp 1–4. ISBN: 978-989-97939-0-3
Seo DJ, Smith JA (1991a) Rainfall estimation using raingages and radar—a Bayesian approach: 1. Derivation of estimators. Stoch Hydrol Hydraul 5:17–29
Seo DJ, Smith JA (1991b) Rainfall estimation using raingages and radar—a Bayesian approach: 1. An application. Stoch Hydrol Hydraul 5:31–44
Sloughter J, Raftery AE, Gneiting T, Fraley C (2007) Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Mon Weather Rev 135:3209–3220
Spiegelhalter DJ, Best N, Carlin BP, Van der Linde A (2002) Bayesian measures of model complexity and fit (with discussion). J R Stat Soc Ser B 64:311–324
Stein ML (1999) Interpolation of spatial data. Some theory for kriging. Springer, New York
Stern RD, Coe R (1984) A model fitting analysis of daily rainfall data. J R Stat Soc Ser A 147(Part 1):1–34
Thomas A, O’Hara B, Ligges U, Sturz S (2006) Making BUGS open. R News 6:12–17
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
Yoo C, Ha E (2007) Effect of zero measurements on the spatial correlation structure of rainfall. Stoch Environ Res Risk Assess 21:287–297. doi:10.1007/s00477-006-0064-3
Acknowledgments
We wish to thank ARPA-SIMC Emilia Romagna for introducing us to the problem, providing data and performing data pre-processing. The research work underlying this paper was funded by an ARPA-SIMC/Department of Statistical Sciences agreement (nr.20/2012) and a FIRB 2012 grant (project no. RBFR12URQJ; title: Statistical modelling of environmental phenomena: pollution, meteorology, health and their interactions) for research projects by the Italian Ministry of Education, Universities and Research.
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Bruno, F., Cocchi, D., Greco, F. et al. Spatial reconstruction of rainfall fields from rain gauge and radar data. Stoch Environ Res Risk Assess 28, 1235–1245 (2014). https://doi.org/10.1007/s00477-013-0812-0
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DOI: https://doi.org/10.1007/s00477-013-0812-0