The Scaling LInear Macroweather model (SLIM): using scaling to forecast global scale macroweather from months to decades.

At scales of ≈10 days (the lifetime of planetary scale structures), there is a drastic transition from high frequency weather to low frequency macroweather. This scale is close to the predictability limits of deterministic atmospheric models; so that in GCM macroweather forecasts, the weather is a high frequency noise. But neither the GCM noise nor the GCM climate is fully realistic. In this paper we show how simple stochastic models can be developped that use empirical data to force the statistics and climate to be realistic so that even a two parameter model can outperform GCM's for annual global temperature forecasts. The key is to exploit the scaling of the dynamics and the enormous stochastic memories that it implies. Since macroweather intermittency is low, we propose using the simplest model based on fractional Gaussian noise (fGn): the Scaling LInear Macroweather model (SLIM). SLIM is based on a stochastic ordinary differential equations, differing from usual linear stochastic models (such as the Linear Inverse Mod15 elling, LIM) in that it is of fractional rather than integer order. Whereas LIM implicitly assumes there is no low frequency memory, SLIM has a huge memory that can be exploited. Although the basic mathematical forecast problem for fGn has been solved, we approach the problem in an original manner notably using the method of innovations to obtain simpler results on forecast skill and on the size of the effective system memory. A key to successful forecasts of natural macroweather variability is to first remove the low frequency anthropogenic component. A previous attempt to use fGn for forecasts had poor results because this was not done. We validate our theory using hindcasts of global and Northern Hemisphere temperatures at monthly and annual resolutions. Several nondimensional measures of forecast skill - with no adjustable parameters - show excellent agreement with hindcasts and these show some skill even at decadal scales. We also compare our forecast errors with those of several GCM experiments (with and without initialization), and with other stochastic forecasts showing that even this simplest two parameter SLIM model is somewhat superior. In future, using a space-time (regionalized) generalization of SLIM we expect to be able to exploiting the system memory more extensively and obtain even more realistic forecasts. [ABSTRACT FROM AUTHOR]