Numerical instability resulting from infrequent calculation of radiative heating

Olivier Pauluis, Kerry Emanuel

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)673-686
Number of pages14
JournalMonthly Weather Review
Volume132
Issue number3
StatePublished - Mar 2004

Fingerprint

heating
oscillation
damping
general circulation model
water vapor
calculation
radiation
atmosphere
simulation
rate

ASJC Scopus subject areas

  • Atmospheric Science

Cite this

Numerical instability resulting from infrequent calculation of radiative heating. / Pauluis, Olivier; Emanuel, Kerry.

In: Monthly Weather Review, Vol. 132, No. 3, 03.2004, p. 673-686.

Research output: Contribution to journalArticle

@article{1f0fcb39624349d1b58b310d3cd1a383,
title = "Numerical instability resulting from infrequent calculation of radiative heating",
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.",
author = "Olivier Pauluis and Kerry Emanuel",
year = "2004",
month = "3",
language = "English (US)",
volume = "132",
pages = "673--686",
journal = "Monthly Weather Review",
issn = "0027-0644",
publisher = "American Meteorological Society",
number = "3",

}

TY - JOUR

T1 - Numerical instability resulting from infrequent calculation of radiative heating

AU - Pauluis, Olivier

AU - Emanuel, Kerry

PY - 2004/3

Y1 - 2004/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=1842735952&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842735952&partnerID=8YFLogxK

M3 - Article

VL - 132

SP - 673

EP - 686

JO - Monthly Weather Review

JF - Monthly Weather Review

SN - 0027-0644

IS - 3

ER -