The Fractional Energy Balance Equation, macroweather forecasts and climate projections

Shaun Lovejoy

Physics, McGill

Tuesday, Nov 12, 2019, 11:00 am
DSRC Room 1D403


The earth is not quite in thermodynamic equilibrium with the sun and outer space: at any moment the difference between the incoming and outgoing energy fluxes is stored in the soil, ocean and atmosphere. These storage processes occur over a hierarchy of structures from small to large with corresponding short to long time scales, I argue that they are scaling. Scaling storage leads the Fractional Energy Balance Equation (FEBE) which differs from the usual EBE by its fractional order H rather than the integer order H = 1. The FEBE shows that the Earth’s temperature is a response to the combination of random internal “innovations” and external forcings; it unites them both.

The FEBE characterizes the storage and hence memory of the climate system. It predicts two scaling regimes with a very gradual cross over at a scale of about two years. The scaling memory can be exploited for macroweather (monthly, seasonal, annual) forecasts. The result is the Stochastic Seasonal and Interannual Prediction System (StocSIPS), operational at McGill since 2016. Compared to traditional global circulation models (GCM) it has the advantage of forcing predictions to converge to the real-world climate (not the model climate). It extracts the internal variability (weather noise) directly from past data and does not suffer from model drift or poor model seasonality. It can hindcast GCM control runs to nearly their theoretical stochastic predictability limits. It’s relative skill with respect to GCMs increases over land and with lead time. Practical advantages include much lower computational cost, no need for downscaling and no ad hoc postprocessing.

The FEBE memory can also be used to project the climate over the next century. Existing GCM projections suffer from a wide model to model dispersion and hence uncertainty. When compared to the historical record, the multimodel mean of 32 CMIP5 simulations also has a warm bias (about 15%). We show how to make historical based projections with much smaller uncertainties and biases. When these empirically determined Scaling Climate Response Functions (SCRFs) are applied to the CMIP5 models, the method is generally quite accurate but nevertheless has small scenario dependent biases.


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