Numerical weather forecasts can exhibit systematic errors due to simplifying model assumptions and computational approximations. Statistical postprocessing is a statistical approach to correcting such biases. A statistical postprocessing model takes input data from a numerical forecast model, and outputs a parametric predictive distribution of a real-world observation, with model parameters learned from past forecast-observation pairs. In this paper we develop and discuss methods for postprocessing of gridded data. We show that estimates of postprocessing parameters on a spatial grid can be improved by Bayesian hierarchical modelling with spatial priors. We use the "Max-and-Smooth" approach [Hrafnkelsson et al., 2021] to approximate a fully Bayesian inference in two steps. First we calculate maximum-likelihood estimates (MLEs) of postprocessing parameters at individual grid points. Second we smooth the MLEs using a measurement error model with a spatial prior. Our approach provides the theoretical basis for the parameter smoothing approach by Kharin et al. [2017], and simplifies and generalises the Bayesian hierarchical modelling approach by Moeller et al. [2015]. A new derivation of Max-and-Smooth is presented. The method is applicable to arbitrary postprocessing models, as illustrated on Model Output Statistics, Logistic Regression, and Nonhomogeneous Gaussian Regression. We report consistent improvements in forecast accuracy, calibration, and probabilistic skill in postprocessing of temperature and precipitation forecasts.
翻译:数字天气预测可能由于简化模型假设和计算近似而出现系统性错误。统计后处理是一种纠正这种偏差的统计方法。统计后处理模式从数字预测模型中收集输入数据,而输出出一种真实世界观测的参数的参数分布,从过去的预测-观察对配对中学习模型参数。在本文中,我们制定并讨论电网数据后处理方法。我们表明,通过用空间前科对巴伊西亚级处理方法进行模拟,可以改进空间网格中后处理参数的估计数。我们使用“最大和微缩”方法(Hrafnkelsson等人,20211),以两步为基准全面推断。我们首先在单个电网点计算后处理参数的最大相似性估计数(MLEs)。我们用一个空间前期的测量错误模型来平滑动MLEs。我们的方法为Kharin等人的平滑动参数提供了理论依据。我们采用的方法,并且简化和概括了Moelleral 和Aliversal 后期预测中的BS-S-Servicial Reqal Revial Revial模型方法,我们可以对最新和Arvial Revial Ad Red Reds Redation 做了进行。