Ellingson, R G., J Ellis, and S Fels, 1991: The intercomparison of radiation codes used in climate models: Long wave results. Journal of Geophysical Research, 96(D5), 8929-8953. Abstract PDF
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 plus or minus 2% for fluxes at the atmospheric boundaries, about plus or minus 5% for the flux divergence for the troposphere, and to about plus or minus 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 comparison 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 meaasurement program is recommended for the purpose of obtaining accurate spectral radiance rather than integrated fluxes as a basis for evaluating model performance.
Fels, S, J T Kiehl, A A Lacis, and M Daniel Schwarzkopf, 1991: Infrared cooling rate calculations in operational general circulation models: Comparisons with benchmark computations. Journal of Geophysical Research, 96(D5), 9105-9120. Abstract PDF
As part of the Intercomparison of Radiation Codes in Climate Models (ICRCCM) project, careful comparisons of the performance of a large number of radiation codes were carried out, and the results compared with those of benchmark calculations. In this paper, we document the performance of a number of parameterized models which have been heavily used in climate and numerical prediction research at three institutions: Geophysical Fluid Dynmaics Laboratory (GFDL), National Center for Atmospheric Research (NCAR), and Goddard Institute for Space Studies (GISS).
Schwarzkopf, M D., and S Fels, 1991: The simplified exchange method revisited: An accurate, rapid method for computation of infrared cooling rates and fluxes. Journal of Geophysical Research, 96(D5), 9075-9096. Abstract PDF
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 epsilon-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.
Hou, A Y., S Fels, and R M Goody, 1990: Zonal superrotation above Venus' cloud base induced by the semidiurnal tide and mean meridional circulation. Journal of the Atmospheric Sciences, 47(15), 1894-1901. Abstract PDF
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.
Schwarzkopf, M D., and S Fels, 1989: GFDL radiation codes: The next generation In IRS '88: Current Problems in Atmospheric Radiation, A. Deepak Publishing, 433-435.
Sneider, R K., and S Fels, 1988: The flywheel effect in the middle atmosphere. Journal of the Atmospheric Sciences, 45(24), 3996-4004. Abstract PDF
Because of the requirement of geostrophic balance, mechanical inertia can affect the thermal response of the atmosphere to transient heating. We examine some very simple linear models of this "flywheel effect," and discuss their possible reference to the Antarctic ozone hole.
Fels, S, 1987: Reply. Re: Fels F82 paper. Journal of the Atmospheric Sciences, 44(24), 3829-3832. PDF
Fels, S, 1987: Response of the middle atmosphere to changing response of the middle atmosphere to changing O3 and CO2 - A speculative tutorial In Transport Processes in the Middle Atmosphere, D. Reidel Publishing Co., 371-386.
Crisp, D, S Fels, and M Daniel Schwarzkopf, 1986: Approximate methods for finding CO2 15-µm band transmission in planetary atmospheres. Journal of Geophysical Research, 91(D11), 11,851-11,866. Abstract PDF
The CO2 15-µm band provides an important source of thermal opacity in the atmospheres of Venus, Earth, and Mars. Efficient and accurate methods for finding the transmission in this band are therefore needed before complete, self-consistent physical models of these atmospheres can be developed. In this paper we describe a hierarchy of such methods. The most versatile and accurate of these is an "exact" line-by-line model (Fels and Schwarzkopf, 1981). Other methods described here employ simplifying assumptions about the structure of the 15-µm band which significantly improve their efficiency. Because such approximations can reduce the accuracy of a model, as well as its computational expense, we established the range of validity of these simpler models by comparing their results to those generated by the line-by-line model. Pressures and absorber amounts like those encountered in the atmospheres of Venus, Earth, and Mars were used in these tests. Physical band models based on the Goody (1952) random model compose the first class of approximate methods. These narrow-band models include a general random model and other more efficient techniques that employ the Malkmus (1967) line-strength distribution. Two simple strategies for including Voigt and Doppler line-shape effects are tested. We show that the accuracy of these models at low pressures is very sensitive to the line-strength distribution as well as the line shape. The second class of approximate methods is represented by an exponential wideband model. This physical band model is much more efficient than those described above, since it can be used to find transmission functions for broad sections of the CO2 15-µm band in a single step. When combined with a simple Voigt parameterization, this method produces results almost as accurate as those obtained from the more expensive narrow-band random models. The final class of approximate methods tested here includes the empirical logarithmic wideband models that have been used extensively in climate-modeling studies (Kiehl and Ramanathan, 1983; Pollack, et al., 1981). These methods are very efficient, but their range of validity is more limited than that of the other methods tested here. These methods should therefore be used with caution.
Fels, S, 1986: Analytic representations of standard atmosphere temperature profiles. Journal of the Atmospheric Sciences, 43(2), 219-221. 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.
Fels, S, 1986: An approximate analytical method for calculating tides in the atmosphere of Venus. Journal of the Atmospheric Sciences, 43(23), 2757-2772. 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 w hich 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.
A hypothesis is advanced that natural dynamical processes might explain much of the observed late winter ozone decreases over Antarctica. For this to be the case, sometime after 1979 there must have been a substantial reduction of the wintertime planetary-scale disturbance activity in the Southern Hemisphere troposphere. The expected stratospheric response to such a natural process is to reduce wintertime polar ozone, prolong the life of the polar vortex, reduce the transport of ozone out of the middle stratosphere, and to increase the possibility of polar rising motion shortly after the return of the sun to high latitudes. All of these effects are in qualitative agreement with the observed ozone changes.
Fels, S, 1985: Radiative-dynamical interactions in the middle atmosphere In Advances in Geophysics, 28A, 277-300.
Schwarzkopf, M D., and S Fels, 1985: Improvements to the algorithm for computing CO2 transmissivities and cooling rates. Journal of Geophysical Research, 90(C10), 10,541-10,550. Abstract PDF
A new interpolation algorithm is derived for obtaining CO2 15-μm transmissivities at any pressure from tables of transmission functions at standard pressures. The new method is a revision of the Fels-Schwarzkopf (1981) technique. Improvements to the standard transmissivity tables are also discussed. An extension of these methods to calculate transmissivities at CO2 concentrations other than those used for the tables is described.
Fels, S, 1984: The radiative damping of short vertical scale waves in the mesosphere. Journal of the Atmospheric Sciences, 41(10), 1755-1764. 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.
Fels, S, J T Schofield, and D Crisp, 1984: Observations and theory of the solar semidiurnal tide in the mesosphere of Venus. Nature, 312(5993), 431-434. Abstract
The Orbiter Infrared Radiometer experiment, aboard the 1978 Pioneer Venus mission, produced strong evidence for the existence of a semidiurnal solar tide in the mesosphere of Venus. At the same time, measurements in situ of radiative fluxes and cloud particle distribution, in other Pioneer Venus experiments, have provided much information about the structure of the solar heating and infrared cooling there, making it possible to calculate the thermal tidal forcing functions with confidence, and also allowing good estimates of the radiative dissipation rates to be made. Because the structure of tidal fields depends sensitively on that of the background zonal mean wind velocity, of radiative fluxes and cloud particle distribution, in other Pioneer Venus experiments, have provided much information about the structure of the solar heating and infrared cooling there, making it possible to calculate the thermal tidal forcing functions with confidence, and also allowing good estimates of the radiative dissipation rates to be made. Because the structure of tidal fields depends sensitively on that of the background zonal mean wind velocity, U(theta, tau), a knowledge of the sources and sinks of tidal energy and of the actual structure of the tide should allow one to infer the behaviour of U. We show here that a physically reasonable mean flow can be found that leads to theoretically predicted tides that are in excellent agreement with those observed. Our zonal mean flow shows a maximum velocity of ~ 130 ms-1 at 70 km, decreasing dramatically to ~ 0 at 88 km, and a jet-like meridional structure that deviates strongly from solid-body rotation.
Fels, S, 1982: A parameterization of scale-dependent radiative damping rates in the middle atmosphere. Journal of the Atmospheric Sciences, 39(5), 1141-1152. Abstract
An analysis of the radiative damping of slowly modulated sinusoidal wave disturbances is presented. It is shown that it is possible to incorporate scale-dependent effects in a manner no more difficult than that used in the usual "Newtonian cooling" approximation. Explicit calculations show that these effects can be very important in the middle atmosphere. Detailed graphs of the scale-dependent relaxation times due to CO2 and O3 are given, as well as simple analytical parameterizations.
Fels, S, and M Daniel Schwarzkopf, 1981: An efficient, accurate algorithm for calculating an efficient, accurate algorithm for calculating CO2 15 um band cooling rates. Journal of Geophysical Research, 86(C2), 1205-1232. Abstract PDF
A fast, accurate method for obtaining atmospheric carbon dioxide transmission functions for the 15-Mum band is presented. Tables of transmissivities for m band is presented. Tables of transmissivities for CO2 mixing ratios of 330 and 660 ppmv on standard pressure grids comprising geopotential heights ranging from 0 to 80 km and using standard temperatures are included. An algorithm for interpolating from these values to any desired temperature profile and to any other pressure grid is detailed.
Fels, S, Jerry D Mahlman, M Daniel Schwarzkopf, and R W Sinclair, 1980: Stratospheric sensitivity to perturbations in ozone and carbon dioxide: Radiative and dynamical response. Journal of the Atmospheric Sciences, 37(10), 2265-2297. Abstract PDF
We have attempted to assess the stratospheric effects of two different perturbations: 1) a uniform 50% reduction in ozone; and 2) a uniform doubling of carbon dioxide. The primary studies employ an annual mean insolation version of the recently developed GFDL 40-level general circulation model (GCM). Supporting the auxiliary calculations using purely radiative models are also presented. One of these, in which the thermal sensitivity is computed using the assumption that heating by dynamical processes is unaffected by changed composition, gives results which generally are in excellent agreement with those from the GCM. Exceptions to this occur in the ozone reduction experiment at the tropical tropopause and the tropical mesosphere.
The predicted response to the ozone reduction is largest at 50 km in the tropics, where the temperature decreases by 25 K; at the tropical tropopause, the decrease is 5 K. The carbon dioxide increase results in a 10 K decrease at 50 km, decreasing to zero at the tropopause. The temperature change in the CO2 experiment is remarkably uniform in latitude.
Rossow, W, S Fels, and P H Stone, 1980: Comments on "A Three-dimensional model of dynamical processes in the Venus atmosphere". Journal of the Atmospheric Sciences, 37(1), 250-252.
Fels, S, 1979: Simple strategies for inclusion of Voigt effects in infrared cooling rate calculations. Applied Optics, 18(15), 2634-2637. Abstract
A line shape with rectangular core and v-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.
Fels, S, 1978: Reply. Journal of the Atmospheric Sciences, 35(5), 925-927.
Fels, S, 1977: Momentum and energy exchanges due to orographically scattered gravity waves. Journal of the Atmospheric Sciences, 34(3), 499-514. Abstract
The scattering of two-dimensional, hydrostatic, Boussinesq, internal gravity waves by orographic features is considered, with special attention paid to energy and momentum fluxes.
A general integral equation for the streamfunction is derived from which a special Fourier representation is shown to hold in a well-defined region of the atmosphere. This leads to simple expressions for the energy and momentum fluxes and to a useful form for the energy conservation law. Scattering efficiency functions are defined.
When the topography satisfies certain conditions, analytic approximations can be used to determine the scattering; it is found that the reflected momentum flux is larger than the incident flux. The manner in which viscosity affects this result is discussed.
In the special case that the maximum topographic slope is less than that of the incident wave fronts, a simple integral equation is derived and used to calculate numerically the scattering from several different orographies. In every case, the flux anomaly mentioned above persists. The numerical results show that there is very little interference between nearby orographic features, and suggest that the vertical scale of the topography must be of the order of one-quarter of the incident vertical wavelength to significantly scatter.
On the basis of these results, it is possible that topographic scattering may significantly affect the tidal momentum flux in the Venusian atmosphere.
Fels, S, and L D Kaplan, 1975: A test of the role of longwave radiative transfer in a general circulation model. Journal of the Atmospheric Sciences, 32(4), 779-789. Abstract
The dynamical consequences of systematic changes in longwave radiative transfer computations have been investigated using the NCAR six-layer General Circulation Model. The experiments were run for a period of 40 days each: the "control" case with an emissivity computation, and the "test" case using a 19-spectral-interval calculation, in which the Curtis-Godson approximation is employed. The two calculations lead to substantially different cooling rates when applied to identical soundings, especially in the tropics.
Significant differences are observed in the thermal structure of the two cases, and in the mean meridional circulations. The total kinetic energy is somewhat higher in the test case, probably due to increased baroclinic activity in mid-latitudes.
Fels, S, and M Daniel Schwarzkopf, 1975: The simplified exchange approximation: a new method for radiative transfer calculations. Journal of the Atmospheric Sciences, 32(7), 1475-1488. 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 isA 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 is q ~ qe - qe CTS + qCTS,CTS, where q is the heating rate, qe an "emissivity" heating rate calculated using the strong-line approximation and neglecting variation of line intensity with temperature, qe CTS 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 using similar approximations are presented and their utility discussed.
Fels, S, 1974: The trapeze instability on an open domain. Journal of the Atmospheric Sciences, 31(2), 434-443. Abstract
The "trapeze instability" of Orlanski is investigated in the absence of a reflecting lid above the fluctuating layer. An expansion of the exact solution as a power series in a parameter representing the ratio of the fluctuating to the mean stability is made, and the first two terms calculated, both of which grow only for a finite length of time, after which they level off. This is quite unlike what occurs in the closed case. On the basis of a plausible conjecture about the behavior of higher order terms, we conclude that only waves whose vertical wavelength is small compared to the depth of the active layer will be amplified by the trapeze instability. When estimates of the effects of eddy viscosity are included, waves of horizontal wavelength of the order of 200-400 km and a period of two days are expected to be most unstable.
Fels, S, and R S Lindzen, 1974: The interaction of thermally excited gravity waves and mean flows. Geophysical Fluid Dynamics, 6, 149-191. Abstract
It is shown that the thermal excitation of internal gravity waves in a semi-infinite atmosphere will lead to mean accelerations of the fluid within the region of excitation. While accelerations both in the direction of and opposite to the wave's phase speed are produced, the mean density weighted acceleration is opposite of the phase speed's direction. The mechanism involved is studied for a wide variety of cases, and explicitly applied to the examination of the mean flows resulting from thermal tides on Venus and the Earth. The procedure for studying the nonlinear evolution of flows is developed for cases with and without damping, and the results are applied to a discussion of the evolution of the observed 4-day circulation on Venus.
