We propose a new statistical reduced complexity climate model. The centerpiece of the model consists of a set of physical equations for the global climate system which we show how to cast in non-linear state space form. The parameters in the model are estimated using the method of maximum likelihood with the likelihood function being evaluated by the extended Kalman filter. Our statistical framework is based on well-established methodology and is computationally feasible. In an empirical analysis, we estimate the parameters for a data set comprising the period 1959-2022. A likelihood ratio test sheds light on the most appropriate equation for converting the level of atmospheric concentration of carbon dioxide into radiative forcing. Using the estimated model, and different future paths of greenhouse gas emissions, we project global mean surface temperature until the year 2100. Our results illustrate the potential of combining statistical modelling with physical insights to arrive at rigorous statistical analyses of the climate system.

翻译：我们提出了一种新的统计降维气候模型。该模型的核心由一组描述全球气候系统的物理方程构成，我们展示了如何将其转化为非线性状态空间形式。模型参数采用极大似然法进行估计，其似然函数通过扩展卡尔曼滤波器进行评估。我们的统计框架基于成熟的方法论，并且在计算上是可行的。在一项实证分析中，我们使用涵盖1959年至2022年期间的数据集对参数进行了估计。似然比检验揭示了将大气二氧化碳浓度水平转换为辐射强迫的最合适方程。利用估计的模型以及不同的未来温室气体排放路径，我们预测了直至2100年的全球平均地表温度。我们的结果展示了将统计建模与物理洞察相结合，从而对气候系统进行严格统计分析的可能性。