Articles | Volume 6, issue 2
Earth Syst. Dynam., 6, 637–658, 2015
Earth Syst. Dynam., 6, 637–658, 2015

Research article 29 Sep 2015

Research article | 29 Sep 2015

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

S. Lovejoy, L. del Rio Amador, and R. Hébert S. Lovejoy et al.
  • Physics, McGill University, 3600 University St., Montreal, Que. H3A 2T8, Canada

Abstract. On 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; thus, in GCM (general circulation model) macroweather forecasts, the weather is a high-frequency noise. However, neither the GCM noise nor the GCM climate is fully realistic. In this paper we show how simple stochastic models can be developed that use empirical data to force the statistics and climate to be realistic so that even a two-parameter model can perform as well as GCMs for annual global temperature forecasts.

The key is to exploit the scaling of the dynamics and the large stochastic memories that we quantify. Since macroweather temporal (but not spatial) intermittency is low, we propose using the simplest model based on fractional Gaussian noise (fGn): the ScaLIng Macroweather Model (SLIMM). SLIMM is based on a stochastic ordinary differential equation, differing from usual linear stochastic models (such as the linear inverse modelling – LIM) in that it is of fractional rather than integer order. Whereas LIM implicitly assumes that there is no low-frequency memory, SLIMM 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 stochastic forecasts of natural macroweather variability is to first remove the low-frequency anthropogenic component. A previous attempt to use fGn for forecasts had disappointing 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 on 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 SLIMM is somewhat superior. In future, using a space–time (regionalized) generalization of SLIMM, we expect to be able to exploit the system memory more extensively and obtain even more realistic forecasts.

Short summary
Numerical climate models forecast the weather well beyond the deterministic limit. In this “macroweather” regime, they are random number generators. Stochastic models can have more realistic noises and can be forced to converge to the real-world climate. Existing stochastic models do not exploit the very long atmospheric and oceanic memories. With skill up to decades, our new ScaLIng Macroweather Model (SLIMM) exploits this to make forecasts more accurate than GCMs.
Final-revised paper