The ScaLIng Macroweather Model (SLIMM) and monthly and inter annual regional forecasting.

Abstract:

By exploiting the sensitive dependence on initial conditions, GCM's can generate a statistical ensemble of future states in which the high frequency “weather" is treated as a driving noise. Following Hasselman, 1976, this has lead to stochastic models that directly generate the noise, and model the low frequencies using systems of integer ordered linear ordinary differential equations, the most well known are the linear inverse models (LIM). These have been presented as a benchmark for decadal surface temperature forecast. Using the LIM, hindcast skills comparable to and sometimes even better than the skill of (coupled) Global Circulation Models (GCM's) from phase 5 of the Coupled Model Intercomparison Project (CMIP5). Nevertheless, the short range exponential temporal decorrelations implicit in the LIM models are unrealistic (the true decorrelations are closer to long range power laws), and - as a consequence - the useful limit to the forecast horizon is roughly one year: it enormously underestimates the memory of the system.

In presentation, we make a scaling analogue of the LIM: ScaLIng Macroweather Model (SLIMM) that exploits the power law (scaling) behavior in time of the temperature field and consequently, make use of the long history dependence of the data to improve the skill. The results predicted analytically by the model have been tested by performing actual hindcasts in different 5º x 5º regions on the planet using the Twentieth Century Reanalysis as a reference datasets. As a first step, we removed the anthropogenic component of each time series based on its sensitivity to equivalent CO2 concentration for the last 130 years, the residues are our estimates of the natural variability that SLIMM predicts. This residues were treated as fractional Gaussian noise processes with scaling exponent H between -0.5 and 0. The value of H for each grid-point can be obtained directly from the data. We report maps of theoretical skill predicted by the model and we compare it with actual skill based on hindcasts for monthly, seasonal and annual resolutions. A comparison between our results and previous results using LIM or other GCM's is also shown. The prediction skill obtained for the temperature field have been improved by incorporating some other fields and performing an analogous analysis on the generalized state-vectors.