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

为了将观测或模型预测的低分辨率空间尺度的变量向下映射到地方尺度，有必要缩小大气模型输出的尺度，在这种尺度上，需要将变量用于广泛的应用，包括填补数据缺口、水文或冰川学预测、气候预测、灌溉或能源预测。统计缩减通过寻找作为预测因子的大规模观测指标和/或模型输出与当地尺度预测之间的随机关系来执行。基本变换通常是线性回归，或更一般的非线性变换，例如分位数匹配。在这两种情况下，假设随机变量之间的平稳同方差关系，这正确地映射了变换过程中的条件平均值，但不一定是分布的尾部，这是极端气象事件的特征。在这里，我们提出了一种降水量的概率降尺度方法，实现为贝叶斯条件处理器，它支持带有局部变量的中尺度观测和模式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。该程序允许在一个空间窗口上使用多个预测器，并且可以扩展到包括多个源模型。通过使用多元截断正态分布(MTND)，变换变量之间的异方差相关性结构可以在高斯空间中建模，然后相对于预测值进行解析边界化，并反向变换到原始空间。用非马尔科夫非平稳随机天气产生器将降水量的贝叶斯条件估计从中尺度降至局部尺度。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，对此可以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.