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  1. Abstract

    We present a Bayesian hierarchical space‐time stochastic weather generator (BayGEN) to generate daily precipitation and minimum and maximum temperatures. BayGEN employs a hierarchical framework with data, process, and parameter layers. In the data layer, precipitation occurrence at each site is modeled using probit regression using a spatially distributed latent Gaussian process; precipitation amounts are modeled as gamma random variables; and minimum and maximum temperatures are modeled as realizations from Gaussian processes. The latent Gaussian process that drives the precipitation occurrence process is modeled in the process layer. In the parameter layer, the model parameters of the data and process layers are modeled as spatially distributed Gaussian processes, consequently enabling the simulation of daily weather at arbitrary (unobserved) locations or on a regular grid. All model parameters are endowed with weakly informative prior distributions. The No‐U Turn sampler, an adaptive form of Hamiltonian Monte Carlo, is used to maximize the model likelihood function and obtain posterior samples of each parameter. Posterior samples of the model parameters propagate uncertainty to the weather simulations, an important feature that makes BayGEN unique compared to traditional weather generators. We demonstrate the utility of BayGEN with application to daily weather generation in a basin of the Argentine Pampas. Furthermore, we evaluate the implications of crop yield by driving a crop simulation model with weather simulations from BayGEN and an equivalent non‐Bayesian weather generator.

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    Abstract. Most available verification metrics for ensemble forecasts focus on univariate quantities. That is, they assess whether the ensemble provides anadequate representation of the forecast uncertainty about the quantity of interest at a particular location and time. For spatially indexed ensemble forecasts, however, it is also important that forecast fields reproduce the spatial structure of the observed field and represent the uncertainty about spatial properties such as the size of the area for which heavy precipitation, high winds, critical fire weather conditions, etc., areexpected. In this article we study the properties of the fraction of threshold exceedance (FTE) histogram, a new diagnostic tool designed forspatially indexed ensemble forecast fields. Defined as the fraction of grid points where a prescribed threshold is exceeded, the FTE is calculated for the verification field and separately for each ensemble member. It yields a projection of a – possibly high-dimensional – multivariatequantity onto a univariate quantity that can be studied with standard tools like verification rank histograms. This projection is appealing since itreflects a spatial property that is intuitive and directly relevant in applications, though it is not obvious whether the FTE is sufficientlysensitive to misrepresentation of spatial structure in the ensemble. In a comprehensive simulation study we find that departures from uniformity ofthe FTE histograms can indeed be related to forecast ensembles with biased spatial variability and that these histograms detect shortcomings in the spatial structure of ensemble forecast fields that are not obvious by eye. For demonstration, FTE histograms are applied in the context of spatiallydownscaled ensemble precipitation forecast fields from NOAA's Global Ensemble Forecast System. 
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