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Numerical Instability Resulting from Infrequent Calculation of Radiative Heating

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  • 1 Program in Atmospheres, Oceans, and Climate, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

Owing to its relative expense, radiative heating is often not calculated for every time step in numerical simulations of the atmosphere. This is justified when the radiation field evolves slowly in comparison to the atmospheric flow. However, when the effects of variable water vapor and clouds are taken into account, the radiation field can change rapidly, and the finite time between calls to the radiation scheme can introduce a destabilizing time lag. In the worst case, this lag gives rise to an exponential numerical instability with a growth rate proportional to the time interval between radiative calculations. In less drastic circumstances, in which the radiation would damp oscillations of the real system, numerical instability occurs when the time interval between calls to the radiation scheme exceeds a critical value that depends on the Doppler-shifted natural oscillation frequency and the radiative damping rate. It is shown that this type of instability occurs in a single-column model as well as in an idealized general circulation model. The critical frequency at which the radiative heating rate should be computed is found to depend on several factors, including the large-scale circulation and the model resolution. Several potential remedies are discussed.

Corresponding author address: Olivier Pauluis, NOAA/GFDL, Princeton Forrestal Campus, U.S. Rte. 1, P.O. Box 308, Princeton, NJ 08542-0308. Email: omp@gfdl.gov

* Current affiliation: Atmospheric Oceanic Sciences Program, Princeton University, Princeton, New Jersey

Abstract

Owing to its relative expense, radiative heating is often not calculated for every time step in numerical simulations of the atmosphere. This is justified when the radiation field evolves slowly in comparison to the atmospheric flow. However, when the effects of variable water vapor and clouds are taken into account, the radiation field can change rapidly, and the finite time between calls to the radiation scheme can introduce a destabilizing time lag. In the worst case, this lag gives rise to an exponential numerical instability with a growth rate proportional to the time interval between radiative calculations. In less drastic circumstances, in which the radiation would damp oscillations of the real system, numerical instability occurs when the time interval between calls to the radiation scheme exceeds a critical value that depends on the Doppler-shifted natural oscillation frequency and the radiative damping rate. It is shown that this type of instability occurs in a single-column model as well as in an idealized general circulation model. The critical frequency at which the radiative heating rate should be computed is found to depend on several factors, including the large-scale circulation and the model resolution. Several potential remedies are discussed.

Corresponding author address: Olivier Pauluis, NOAA/GFDL, Princeton Forrestal Campus, U.S. Rte. 1, P.O. Box 308, Princeton, NJ 08542-0308. Email: omp@gfdl.gov

* Current affiliation: Atmospheric Oceanic Sciences Program, Princeton University, Princeton, New Jersey

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