BSCALE: Downscaling of precipitation: development, calibration and validation of a probabilisitc Bayesian approach.

• Applicant: Professor Paolo Reggiani, Ph.D.
• Subject Area: Atmospheric Science ; Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 386938837

Downscaling of atmospheric model output is necessary to map variables from low-resolution spatial scales of observation or model prediction down to local scales, at which variables are needed for a wide range of applications, including data gap filling, hydrological or glaciological predictions, climate prognosis, irrigation or energy forecasting. Statistical downscaling is performed by seeking stochastic relationships between large-scale observed indicators and/or model output, serving as predictors, and a local-scale predictand. The underlying transformations are usually linear regressions, or more general non-linear transformations, such as quantile matching. In both cases, stationary homoscedastic relationships between stochastic variables are assumed, which correctly map the conditional mean across the transformation, but not necessarily the tails of the distributions, which characterize extreme meteorological events. Here we propose a probabilistic downscaling approach for precipitation, implemented as a Bayesian conditional processor, which supports non-linear transformations between meso-scale observations and model predictions with local variables, whereby stochastic dependency relationships are modelled in the Gaussian space. The procedure allows using multiple predictors over a spatial window, and can be extended to include multiple source models. By using Multivariate Truncated Normal Distributions (MTND), heteroscedastic dependency structures between transformed variables can be modelled in the Gaussian space, then marginalized analytically with respect to predictors and back-transformed into the original space. The downscaling of the Bayesian conditional estimate of precipitation from the meso-scale to the local scale is performed with a non-Markovian non-stationary stochastic weather generator. The Bayesian processor and weather generator need to be calibrated and validated over a sufficiently long time window, for which continuous predictions and observations are available.

• DFG Programme: Research Grants