A Comparison of Spatio-Temporal Bayesian Models for Reconstruction of Rainfall Fields in a Cloud Seeding Experiment

Abstract

Abstract:In response to the drought experienced in Southern Italy a rain seeding project has been setup and developed during the years 1989-1994. The initiative was taken with the purpose of applying existing methods of rain enhancement technology to regions of south Italy including Puglia. The aim of this study is to provide statistical support for the evaluation of the experimental part of the project. In particular our aim is to reconstruct rainfall fields by combining two data sources: rainfall intensity as measured by ground raingauges and radar reflectivity. A difficulty in modeling the rainfall data here comes from rounding of many recorded rainguages. The rounding of the rainfall measurements make the data essentially discrete and models based on continuous distributions are not suitable for modeling these discrete data. In this study we extend two recently developed spatio-temporal models for continuous data to accommodate rounded rainfall measurements taking discrete values with positive probabilities. We use MCMC methods to implement the models and obtain forecasts in space and time together with their standard errors. We compare the two models using predictive Bayesian methods. The benefits of our modeling extensions are seen in accurate predictions of dry periods with no positive prediction standard errors.

Comparing spatio‐temporal models for particulate matter in Piemonte

“…Instead, in a Bayesian framework Pollice and Jona Lasinio () and Cocchi and Bruno () adopted the deviance information criterion (DIC). Moreover, to compare prediction capability, Huang et al () used mean squared prediction errors at a fixed time, whereas Sahu et al () applied the predictive model choice criterion (PMCC) that included a penalty term for model complexity. Specifically for fine particulate matter, Pang et al () compared ordinary kriging with Bayesian maximum entropy technique, as implemented in SEKS‐GUI software (Kolovos et al ), in particular through averaged estimation errors and error variances at four validation sites.…”

Advances in the Evaluation of Cloud Seeding: Statistical Evidence for the Enhancement of Precipitation

“…The development of statistical methods would open new horizons for effect test of artificial precipitation enhancement. The Monte Carlo method (e.g., Silverman, ) and the Bayesian method (e.g., Sahu et al, ; Steinschneider & Lall, ) have been successively applied to effect evaluation of weather modification and have been widely accepted. Modern statistical methods, including geostatistics (e.g., Cowley et al, ; Sun et al, ), self‐organizing map method (e.g., Zhou & Jiang, ), generalized additive models (e.g., Wang et al, ; Yang et al, ), Markov model (e.g., Holsclaw et al, ), Bayesian model averaging (e.g., Qu et al, ), and hierarchical Bayesian approach (e.g., Tebaldi & Sansó, ), can overcome the limitation of traditional linear regression analysis and take full advantage of the spatial structure, nonlinear relationship, and prior information of data.…”

“…These techniques include particle observation system that conducts a full coverage observation of particles in clouds (Geerts et al, ), remote sensing measurement of cloud liquid water content (Wang et al, ), and dual‐polarimetric radar (Jing & Geerts, ). In addition, modern statistical methods, such as Monte Carlo method (e.g., Silverman, , ), Bayesian analysis (e.g., Sahu et al, ; Steinschneider & Lall, ), empirical orthogonal function analysis (e.g., Cheng et al, ; Li et al, ), Kriging interpolation (e.g., Bourennane et al, ; Li et al, ), generalized linear model (e.g., Cao et al, ; Chandler & Wheater, ; George et al, ; Liu et al, ; Segond et al, ; Yang et al, ), and neural networks (e.g., Hsu et al, ; Nong & Jin, ), have gradually been applied to quantitative analysis of precipitation. Effect tests of the artificial precipitation enhancement have experienced from the traditional methods that rely on single statistical test and stress randomized experiments to a combination of multiple tests, which emphasize physical evidence, require scientific design of experiments and operations, and establish reasonable evaluation indicators (Changnon, ; Tang et al, ).…”

Mathematical Genesis of the Spatio-Temporal Covariance Functions

“…It is worth citing Jones and Zhang (1997), Cressie and Huang (1999), Christakos (2000);De Cesare et al (2001); Gneiting (2002); Ma (2005), Stein (1999;, Fernandez-Casal et al (2003). Sahu et al, 2005, is also a recommended applied reference from the Bayesian perspective. Most of these contributions deal with stationary spatio-temporal covariances assuming isotropy in space and time.…”