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On scales of ≈ 10 days (the lifetimeof planetary-scale structures), there is a drastic transition fromhigh-frequency weather to low-frequency macroweather. This scale is close tothe predictability limits of deterministic atmospheric models; thus, in GCM(general circulation model) macroweather forecasts, theweather is a high-frequency noise. However, neither the GCM noise nor the GCMclimate is fully realistic. In this paper we show how simple stochasticmodels can be developed that use empirical data to force the statistics andclimate to be realistic so that even a two-parameter model can perform aswell as GCMs for annual global temperature forecasts.  The key is to exploit the scaling of the dynamics and the large stochasticmemories that we quantify. Since macroweather temporal (but not spatial)intermittency is low, we propose using the simplest model based on fractionalGaussian noise (fGn): the ScaLIng Macroweather Model (SLIMM). SLIMM is basedon a stochastic ordinary differential equation, differing from usual linearstochastic models (such as the linear inverse modelling – LIM) in that it isof fractional rather than integer order. Whereas LIM implicitly assumes thatthere is no low-frequency memory, SLIMM has a huge memory that can beexploited. Although the basic mathematical forecast problem for fGn has beensolved, we approach the problem in an original manner, notably using themethod of innovations to obtain simpler results on forecast skill and on thesize of the effective system memory.  A key to successful stochastic forecasts of natural macroweather variabilityis to first remove the low-frequency anthropogenic component. A previousattempt to use fGn for forecasts had disappointing results because this wasnot done. We validate our theory using hindcasts of global and NorthernHemisphere temperatures at monthly and annual resolutions. Severalnondimensional measures of forecast skill – with no adjustable parameters –show excellent agreement with hindcasts, and these show some skill even ondecadal scales. We also compare our forecast errors with those of several GCMexperiments (with and without initialization) and with other stochasticforecasts, showing that even this simplest two parameter SLIMM is somewhatsuperior. In future, using a space–time (regionalized) generalization ofSLIMM, we expect to be able to exploit the system memory more extensively andobtain even more realistic forecasts

The ScaLIng Macroweather Model (SLIMM): using scaling to forecast global-scale macroweather from months to decades