Over time scales between 10 days and 10–20 years—the macroweather regime—atmospheric fields, including the temperature, respect statistical scale symmetries, such as power-law correlations, that imply the existence of a huge memory in the system that can be exploited for long-term forecasts. The Stochastic Seasonal to Interannual Prediction System (StocSIPS) is a stochastic model that exploits these symmetries to perform long-term forecasts. It models the temperature as the high-frequency limit of the (fractional) energy balance equation, which governs radiative equilibrium processes when the relevant equilibrium relaxation processes are power law, rather than exponential. They are obtained when the order of the relaxation equation is fractional rather than integer and they are solved as past value problems rather than initial value problems. StocSIPS was first developed for monthly and seasonal forecast of globally averaged temperature. In this paper, we extend it to the prediction of the spatially resolved temperature field by treating each grid point as an independent time series. Compared to traditional global circulation models (GCMs), StocSIPS has the advantage of forcing predictions to converge to the real-world climate. It extracts the internal variability (weather noise) directly from past data and does not suffer from model drift. Here we apply StocSIPS to obtain monthly and seasonal predictions of the surface temperature and show some preliminary comparison with multi-model ensemble (MME) GCM results. For 1 month lead time, our simple stochastic model shows similar—but somewhat higher—values of the skill scores than the much more complex deterministic models.

在10天至10-20年的时间尺度上（宏观天气状况），包括温度在内的大气场尊重统计尺度的对称性，例如幂律相关性，这暗示着系统中存在可以利用的巨大内存进行长期预测。随机季节至年际预测系统​​（StocSIPS）是一种随机模型，利用这些对称性进行长期预测。它将温度建模为（分数）能量平衡方程的高频极限，当相关的平衡弛豫过程是幂律而不是指数时，该方程将控制辐射平衡过程。它们是在松弛方程的阶次为分数而不是整数的情况下获得的，它们被解决为过去值问题而不是初始值问题。StocSIPS最初是为全球平均温度的月度和季节预报而开发的。在本文中，我们通过将每个网格点视为一个独立的时间序列，将其扩展到空间分辨温度场的预测。与传统的全球环流模型（GCM）相比，StocSIPS的优势在于可以迫使预测收敛到现实世界的气候。它直接从过去的数据中提取内部可变性（天气噪声），并且不会受到模型漂移的影响。在这里，我们使用StocSIPS来获得月度和季节的表面温度预测，并显示与多模型集合（MME）GCM结果的一些初步比较。在1个月的交货时间中，我们的简单随机模型显示出比更复杂的确定性模型相似（但稍高）的技能得分值。