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

Abstract

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 lowfrequency 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 lowfrequency 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.

Bayesian multiproxy temperature reconstruction with black spruce ring widths and stable isotopes from the northern Quebec taiga

“…Eruption years are vertical lines. Plot b shows a Superimposed Epoch Analysis (median and 60% confidence intervals) based on the data and the eruption years of plot a intra-and inter-site-explicit uncertainty analysis, or (4) taking into account the year to year memory of each component in the model as a fractional Gaussian process (Lovejoy et al 2015) in order to properly integrate the information from different sources (Li et al 2010) and investigate the impact of higher long-term persistence in ring width data compared to instrumental data (Zhang et al 2015). However, concerning this last point, we want to stress out that 3P-STREC is already shown to be well calibrated in the LF domain.…”

Scaling regimes and linear/nonlinear responses of last millennium climate to volcanic and solar forcings

“…Although the difference in β l may not seem so important, the LIM value β l = 0 (white noise) has no low-frequency predictability whereas the actual values 0.2 < β l < 0.8 (depending mostly on the land or ocean location) corresponds to potentially huge predictability (the latter can diverge as β l approaches 1). The new "ScaLIng Macroweather Model" (SLIMM) has been proposed as a set of fractional-order (but still linear) stochastic differential equations with predictive skill for global mean temperatures out to at least 10 years (Lovejoy et al, 2015;Lovejoy, 2015b). However, irrespective of the exact statistical nature of the weather and macroweather regimes, a linear stochastic model may still be a valid approximation over significant ranges.…”

Giant natural fluctuation models and anthropogenic warming

“…The figure shows that although the average temperatures ( μ T ) are roughly constant ( μ T = < T > ≈ < T init > ≈−0.23°C), on the contrary, the standard deviations σ T and σ T init grow nearly linearly with time (the top curve grows at a rate = 0.68 ± 0.01°C/century; see the supporting information). Before discussing this strongly unrealistic behavior, note that the increments of the processes (the first differences of Keenan's series) are on the contrary apparently stationary, with means μ Δ T ≈ 0 and with fairly realistic standard deviations σ Δ T ≈ ±0.11°C/yr corresponding to a “typical” year‐to‐year variation in the globally averaged temperature ( T ( t ) or T init ( t ) that give virtually identical results; NASA's Goddard Institute for Space Studies (GISS) temperature series gives ±0.109°C [ Lovejoy et al ., ]), see Figure .…”

“…An important question is whether the residuals of temperature trends have weak or strong correlation structures; in mathematical terms, power laws versus exponential decorrelations (the latter include autoregressive and kindred processes). This issue is not academic since power law correlations are theoretically predicted as a consequence of the temporal‐scale invariance of the climate equations (see, e.g., the review in Lovejoy and Schertzer []), and they imply that the atmosphere has a huge memory which can be exploited for monthly to decadal forecasts [ Lovejoy , ; Lovejoy et al ., ].…”