The standard, strong‐constraint formulation of 4D‐Var is designed to correct for random, zero‐mean errors from the model forecast and the observations. However, significant systematic errors are generated by the forecast models used in global numerical weather prediction (NWP), and the Integrated Forecast System (IFS) model of the European Centre for Medium‐Range Weather Forecasts (ECMWF) is no exception. To deal with this type of error, a modification of the standard 4D‐Var algorithm, weak‐constraint 4D‐Var, has long been proposed and was implemented in operations at ECMWF in 2009. In the original implementation, the model error corrections were only active in the upper stratosphere, as a full application of the algorithm would lead to unacceptable degradation of forecast scores. Thus the impact of weak‐constraint 4D‐Var on ECMWF analyses and forecasts has always been small heretofore.

中文翻译：

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迈向无偏平流层分析

标准的4D-Var强约束公式旨在校正模型预测和观测值中的随机零均值误差。但是，全球数值天气预报（NWP）中使用的预报模型会产生重大的系统误差，欧洲中距离天气预报中心（ECMWF）的综合预报系统（IFS）模型也不例外。为了处理这种类型的错误，很久以来就提出了对标准4D-Var算法（弱约束4D-Var）的修改，并于2009年在ECMWF的操作中实施。在原始实现中，仅对模型错误进行校正由于该算法的完整应用将导致平流层上部活动性降低，从而导致预报分数的下降到不可接受的程度。