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

大气模式输出的降尺度对于将观测或模式预测的低分辨率空间尺度的变量映射到局部尺度是必要的，在局部尺度上，各种应用都需要变量，包括数据缺口填补、水文或冰川学预测、气候预测、灌溉或能源预测。统计降尺度是通过寻找大尺度观测指标和/或模型输出（作为预测因子）与局部尺度预测之间的随机关系来实现的。底层的转换通常是线性回归，或者更一般的非线性转换，比如分位数匹配。在这两种情况下，假设随机变量之间的平稳均方差关系，这正确地映射了整个变换的条件平均值，但不一定映射分布的尾部，这是极端气象事件的特征。在这里，我们提出了一种降水的概率降尺度方法，作为贝叶斯条件处理器实现，它支持中尺度观测和具有局部变量的模型预测之间的非线性转换，从而在高斯空间中模拟随机依赖关系。该过程允许在一个空间窗口上使用多个预测器，并且可以扩展为包括多个源模型。利用多变量截断正态分布（MTND），可以在高斯空间中对变换变量之间的异方差依赖结构进行建模，然后对预测因子进行边缘化分析，并将其反变换到原始空间中。利用非马尔可夫非平稳随机天气发生器将降水贝叶斯条件估计从中尺度降尺度到局地尺度。贝叶斯处理器和天气发生器需要在足够长的时间窗口内进行校准和验证，以便进行连续的预测和观测。

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.