Stephen B. Fels

The Simplified Exchange Approximation: A New Method for Radiative Transfer Calculations

Abstract A new scheme for the efficient calculation of longwave radiative heating rates is proposed. Its speed and accuracy make it attractive for use in large atmospheric circulation models. The approximation suggested iswhere q is the heating rate, qe an “emissivity” heating rate calculated using the strong-line approximation and neglecting variation of line intensity with temperature, qeCTS the heating rate calculated using the cool-to-space approximation and the emissivity assumption, and qCTS the heating rate calculated by the cool-to-space approximation. Tests using a variety of soundings indicate that for both clear sky and cloudy cases the new approximation is substantially more accurate than either the emissivity or the cool-to-space approximations alone. Deviations from exact calculations are generally under 0.05 K day−1. Errors in the calculated flux at the surface are also shown to be small especially with the inclusion of a “heat from ground” term in the approximation. Some alternate schemes ...

The intercomparison of radiation codes used in climate models: Long wave results

An international program of intercomparison of radiation codes used in climate models has been initiated because of the central role of radiative processes in many proposed climate change mechanisms. During the past 6 years, results of calculations from such radiation codes have been compared with each other, with results from the most detailed radiation models (line-by-line models) and with observations from within the atmosphere. Line-by-line model results tend to agree with each other to within 1%; however, the intercomparison shows a spread of 10–20% in the calculations of radiation budget components by the less detailed climate model codes. The spread among the results is even larger (30–40%) for the sensitivities of the codes to changes in radiatively important variables, such as carbon dioxide and water vapor. The analysis of the model calculations shows that the outliers to many of the clear-sky calculations appear to be related to those models that have not tested the techniques used to perform the integration over altitude. When those outliers are removed, the agreement between narrow band models and the line-by-line models is about ±2% for fluxes at the atmospheric boundaries, about ±5% for the flux divergence for the troposphere, and to about ±5% for the change of the net flux at the tropopause as CO2 doubles. However, this good agreement does not extend to the majority of the models currently used in climate models. The lack of highly accurate flux observations from within the atmosphere has made it necessary to rely on line-by-line model results for evaluating model accuracy. As the intercomparison project has proceeded, the number of models agreeing more closely with the line-by-line results has increased as the understanding of the various parameterizations has improved and as coding errors have been discovered. The most recent results indicate that several climate model techniques are in the marginal range of (relative) accuracy for longwave flux calculations for many climate programs. However, not all such models will give such accuracy. It is recommended that a code not be accepted to provide such accuracy until it has made comparisons to the line-by-line results of this study. The data necessary to make such comparisons are included herein. However, uncertainties in the physics of line wings and in the proper treatment of the water vapor continuum make it impossible for the line-by-line models to provide an absolute reference for evaluating less-detailed model calculations. A dedicated field measurement program is recommended for the purpose of obtaining accurate spectral radiance rather than integrated fluxes as a basis for evaluating model performance.

The simplified exchange method revisited: An accurate, rapid method for computation of infrared cooling rates and fluxes

The performance and construction of a new algorithm for the calculation of infrared cooling rates and fluxes in terrestrial general circulation models are described in detail. The computational method, which is suitable for use in models of both the troposphere and the middle atmosphere, incorporates effects now known to be important, such as an extended water vapor e-type continuum, careful treatment of water vapor lines, of water-carbon dioxide overlap, and of Voigt line shape. The competing requirements of accuracy and speed are both satisfied by extensive use of a generalization of the simplified exchange approximation of Fels and Schwarzkopf (1975). Cooling rates and fluxes are validated by comparison with benchmark line-by-line calculations on standard atmospheric profiles obtained for the Intercomparison of Radiation Codes Used in Climate Models (ICRCCM). Results indicate that the new algorithm is substantially more accurate than any previously used at the Geophysical Fluid Dynamics Laboratory.

Radiative-dynamical interactions in the middle atmosphere

Publisher Summary This chapter elaborates the radiative–dynamical interaction in the middle atmosphere. There are several ways of addressing the question of the degree of radiative imbalance that exists in an atmosphere, and the simplest is to compare the observed thermal structure with that, which would exist, were all dynamical heating and cooling processes suppressed. It is found that because radiative processes are essentially local horizontally, one may compute the radiatively determined temperature profile at specified latitude as a function of time and height. The observed temperatures in the summer stratosphere agree well with those calculated by the radiative model. It is suggested that the occurrence of warmings depends on the existence of a suitably preconditioned structure. In the model simulation, the strong radiative control of the polar-night jet means that the ability of the stratosphere to propagate waves should be tightly locked to the annual cycle. It is found that radiative damping is of secondary importance for most planetary waves, basically because of their very large vertical scale.

Intercomparison of Radiation Codes in Climate Models (ICRCCM): Longwave Clear-Sky Results—A Workshop Summary

An international program of intercomparison of radiation models has been initiated because of the central role of radiative processes in many proposed climate change mechanisms. Models ranging from the most detailed (line-by-line) to the most-highly parameterized have been compared with each other and with selected aircraft observations. Although line-by-line-model fluxes tend to agree with each other to within one percent (if the water-vapor–continuum absorption is ignored), the less-detailed models show a spread of 10–20 percent. The spread is even larger (30–40 percent) for the sensitivities of the models to changes in important radiation variables, such as carbon dioxide amounts and water-vapor amounts. These spreads are disturbingly large. Lacking highly accurate flux observations from within the atmosphere, it has been customary to regard line-by-line–model results as “the truth.” However, uncertainties in the physics of line wings and in the proper treatment of the water-vapor continuum make it imp...

Simple strategies for inclusion of Voigt effects in infrared cooling rate calculations

A line shape with rectangular core and nu(-2) wings is shown to be an excellent alias for the Voigt profile when calculating equivalent widths. It leads to closed analytic forms in the commonly employed random models and gives highly accurate ozone cooling rates. An even simpler device for applications where less accurate results are required involves use of the Lorentz profile with a width which does not vanish at zero pressure.

The radiative damping of short vertical scale waves in the mesosphere

Abstract The mesospheric radiative damping rates for temperature perturbations with vertical wavelengths less than 6 km are calculated, based on previous works of Spiegel and Fels. Effects due to the breakdown of local thermodynamic equilibrium are included, and found to be important above 70 km. The damping calculated is considerably weaker than that found recently by Schoeberl, Strobel, and Apruzese.

Analytic representations of standard atmosphere temperature profiles

Abstract Analytic functions which approximate six commonly used standard temperature profiles (the AFGL set, and the 1976 U.S. Standard) are described. These provide a uniform way of rounding off the sharp corners of the original models, and have been used in a recent radiation model intercomparison study.

Zonal superrotation above venus' cloud base induced by the semidiurnal tide and the mean meridional circulation

Abstract We have calculated the equilibrium zonal wind structure resulting from the interaction of the semidiurnal tide and the mean meridional circulation driven by the zonally averaged solar heating above the Venus cloud base. The results show that the tidal mechanism proposed by Fels and Lindzen can account for a substantial fraction—and possibly all—of the increase of the equatorial wind speed above the cloud base. Above the cloud tops, tidal deceleration may be too small to produce the zonal wind decrease with height inferred from thermal data. Tidal forcing does not explain the superrotation below the clouds and additional eddy sources are needed to account for the zonal wind structure at mid and high latitudes.

An approximate analytical method for calculating tides in the atmosphere of Venus

Abstract We describe a semianalytical method for calculating solar tides in an atmosphere whose zonal mean velocity need not be close to solid-body rotation, but which varies slowly in the vertical direction. The scheme is closely related to the asymptotic methods developed earlier by others for use in work on terrestrial equatorial waves, and leads to a simple and intuitively appealing formulation of the nonseparable tidal problem as a set of uncoupled ordinary differential equations. The manner in which the meridional structure of the mean state affects the vertical and horizontal tidal structure is especially transparent. The method has been used recently to explain a number of observed features of the Venus semidiurnal tide. The sensitivity of these tidal fields to the structure of the zonal mean wind is briefly discussed, and the Eliasson-Palm flux divergence calculated.