Scardovi, Elena
(2015)
Rainfall spatial predictions: a two-part model and its assessment, [Dissertation thesis], Alma Mater Studiorum Università di Bologna.
Dottorato di ricerca in
Metodologia statistica per la ricerca scientifica, 27 Ciclo. DOI 10.6092/unibo/amsdottorato/6744.
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Abstract
Spatial prediction of hourly rainfall via radar calibration is addressed. The change of support problem (COSP), arising when the spatial supports of different data sources do not coincide, is faced in a non-Gaussian setting; in fact, hourly rainfall in Emilia-Romagna region, in Italy, is characterized by abundance of zero values and right-skeweness of the distribution of positive amounts. Rain gauge direct measurements on sparsely distributed locations and hourly cumulated radar grids are provided by the ARPA-SIMC Emilia-Romagna. We propose a three-stage Bayesian hierarchical model for radar calibration, exploiting rain gauges as reference measure. Rain probability and amounts are modeled via linear relationships with radar in the log scale; spatial correlated Gaussian effects capture the residual information. We employ a probit link for rainfall probability and Gamma distribution for rainfall positive amounts; the two steps are joined via a two-part semicontinuous model. Three model specifications differently addressing COSP are presented; in particular, a stochastic weighting of all radar pixels, driven by a latent Gaussian process defined on the grid, is employed. Estimation is performed via MCMC procedures implemented in C, linked to R software.
Communication and evaluation of probabilistic, point and interval predictions is investigated. A non-randomized PIT histogram is proposed for correctly assessing calibration and coverage of two-part semicontinuous models. Predictions obtained with the different model specifications are evaluated via graphical tools (Reliability Plot, Sharpness Histogram, PIT Histogram, Brier Score Plot and Quantile Decomposition Plot), proper scoring rules (Brier Score, Continuous Rank Probability Score) and consistent scoring functions (Root Mean Square Error and Mean Absolute Error addressing the predictive mean and median, respectively). Calibration is reached and the inclusion of neighbouring information slightly improves predictions. All specifications outperform a benchmark model with incorrelated effects, confirming the relevance of spatial correlation for modeling rainfall probability and accumulation.
Abstract
Spatial prediction of hourly rainfall via radar calibration is addressed. The change of support problem (COSP), arising when the spatial supports of different data sources do not coincide, is faced in a non-Gaussian setting; in fact, hourly rainfall in Emilia-Romagna region, in Italy, is characterized by abundance of zero values and right-skeweness of the distribution of positive amounts. Rain gauge direct measurements on sparsely distributed locations and hourly cumulated radar grids are provided by the ARPA-SIMC Emilia-Romagna. We propose a three-stage Bayesian hierarchical model for radar calibration, exploiting rain gauges as reference measure. Rain probability and amounts are modeled via linear relationships with radar in the log scale; spatial correlated Gaussian effects capture the residual information. We employ a probit link for rainfall probability and Gamma distribution for rainfall positive amounts; the two steps are joined via a two-part semicontinuous model. Three model specifications differently addressing COSP are presented; in particular, a stochastic weighting of all radar pixels, driven by a latent Gaussian process defined on the grid, is employed. Estimation is performed via MCMC procedures implemented in C, linked to R software.
Communication and evaluation of probabilistic, point and interval predictions is investigated. A non-randomized PIT histogram is proposed for correctly assessing calibration and coverage of two-part semicontinuous models. Predictions obtained with the different model specifications are evaluated via graphical tools (Reliability Plot, Sharpness Histogram, PIT Histogram, Brier Score Plot and Quantile Decomposition Plot), proper scoring rules (Brier Score, Continuous Rank Probability Score) and consistent scoring functions (Root Mean Square Error and Mean Absolute Error addressing the predictive mean and median, respectively). Calibration is reached and the inclusion of neighbouring information slightly improves predictions. All specifications outperform a benchmark model with incorrelated effects, confirming the relevance of spatial correlation for modeling rainfall probability and accumulation.
Tipologia del documento
Tesi di dottorato
Autore
Scardovi, Elena
Supervisore
Dottorato di ricerca
Scuola di dottorato
Scienze economiche e statistiche
Ciclo
27
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
Hourly rainfall, radar, rain gauge, spatial prediction, Bayesian Hierarchical Model, Change of Support Problem, zero values, Two-part model, semicontinuous, calibration, Gamma distribution, PQPF, evaluation, probabilistic forecasts, coverage, PIT histogram
URN:NBN
DOI
10.6092/unibo/amsdottorato/6744
Data di discussione
2 Febbraio 2015
URI
Altri metadati
Tipologia del documento
Tesi di dottorato
Autore
Scardovi, Elena
Supervisore
Dottorato di ricerca
Scuola di dottorato
Scienze economiche e statistiche
Ciclo
27
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
Hourly rainfall, radar, rain gauge, spatial prediction, Bayesian Hierarchical Model, Change of Support Problem, zero values, Two-part model, semicontinuous, calibration, Gamma distribution, PQPF, evaluation, probabilistic forecasts, coverage, PIT histogram
URN:NBN
DOI
10.6092/unibo/amsdottorato/6744
Data di discussione
2 Febbraio 2015
URI
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