| Summary: | The object of this study is to propose a Bayesian hierarchical model for observed monthly precipitation that incorporates predictors based on an output from a meteorological model. The observed data come from forty sites across Iceland. Each month is modeled separately with a Gaussian field with Matérn correlation function and measurement error at the data level. The location and scale parameters at the latent level are also modeled with Gaussian fields with Matérn correlation function. The observed data were collected and corrected for wind, wetting and evaporation loss by the Icelandic Meteorological Office (IMO). The IMO also provided an output from a linear model of orographic precipitation defined on a kilometer by kilometer grid over Iceland. The output from this model is used to construct predictors for the latent parameters on the grid. These predictors are then projected onto each of the observed sites for each month and incorporated into the Bayesian hierarchical model. Markov chain Monte Carlo (MCMC) was used for posterior inference for the parameters. Bayesian kriging is used to predict the latent parameters on the grid. The model developed is quite detailed and accurate in describing the monthly precipitation even though, due to computational difficulties, some parameters had to be estimated outside the MCMC scheme. The results indicate that the output from the meteorological model is well suited to describing the mean monthly precipitation field over Iceland. The meteorological model is not as accurate in describing the variability of the monthly precipitation and generally underestimates it in the North-East part of Iceland and overestimates it in the South-West corner. The results also indicate that no long-term temporal trend is present in the monthly precipitation over the period examined. Rannsóknasjóður Háskóla Íslands
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