Publications

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1967
Somerville, RCJ.  1967.  A Nonlinear Spectral Model of Convection in a Fluid Unevenly Heated from Below. Journal of the Atmospheric Sciences. 24:665-676.: American Meteorological Society   10.1175/1520-0469(1967)024<0665:ansmoc>2.0.co;2   AbstractWebsite

A two-dimensional form of the Boussinesq equations is integrated numerically for the case of a rectangular channel with a temperature gradient maintained along the bottom. The side walls are insulating, the top wall has a constant temperature, and the velocity obeys free boundary conditions on all four walls. The fields of stream function and temperature departure are represented by truncated double Fourier series, and integration of the initial-value problem for the spectral amplitudes results in steady states which agree qualitatively with those of previous experimental and theoretical investigations.Calculations are presented at two levels of truncation (wave numbers 2 and 3) for a wide range of Prandtl numbers and a moderate range of horizontal Rayleigh numbers and top temperatures. For sufficiently large gravitational stability, a single asymmetric convection cell develops. Its intensity and asymmetry increase markedly with increasing horizontal Rayleigh number, decrease with increasing top temperature, and respond very slightly to changes in Prandtl number. As the top temperature is decreased below the temperature of the warm side of the bottom, however, the possibility is indicated that the single cell may be modified by a Bénard-like multi-cellular structure.

1971
Lipps, FB, Somervil.Rc.  1971.  Dynamics of Variable Wavelength in Finite-Amplitude Benard Convection. Physics of Fluids. 14:759-&.   10.1063/1.1693502   AbstractWebsite

The finite‐amplitude Bénard convection problem is investigated by numerical integration of the rigid‐boundary Boussinesq equations in two and three space dimensions. Solutions are obtained for a wide range of Prandtl numbers and at moderate Rayleigh numbers for which the flow is observed to approach a two‐dimensional steady state. Detailed quantitative comparisons are made with experimental data in an effort to explain the observed increase of cell wavelength with Rayleigh number and to determine the effect of changing cell size on the heat transport. The three‐dimensional model shows good evidence of being able to yield realistic values of the cell wavelength, while the two‐dimensional models yield wavelengths that are much too short. These results strongly suggest that the increase in wavelength is determined by a three‐dimensional transient process, while the convection tends to a two‐dimensional steady state. The increase in cell size is shown to be responsible for a substantial part of the discrepancy between previous theoretical‐numerical and experimental determinations of Nusselt number. It also provides a plausible explanation for the experimentally observed dependence of heat transport on Prandtl number.

Somerville, RCJ.  1971.  Bénard convection in a rotating fluid. Geophysical Fluid Dynamics. 2:247-262.: Taylor & Francis   10.1080/03091927108236061   AbstractWebsite

Abstract The steady nonlinear regime of Bénard convection in a uniformly rotating fluid is treated using a two-dimensional primitive-equation numerical model with rigid boundaries. Quantitative comparisons with laboratory heat transport data for water are made in the parameter ranges for which the experimental flows are approximately two-dimensional and steady. When an experimentally realistic spatial periodicity is imposed upon the numerical solution, the model simulates the experimental determinations of Nusselt number fairly accurately. In particular, it predicts the observed non-monotonic dependence on Taylor number. When spatial periodicities corresponding to those of the linear stability problem are specified, however, the accuracy of the simulation is less and the Taylor number dependence is monotonic.The steady nonlinear regime of Bénard convection in a uniformly rotating fluid is treated using a two-dimensional primitive-equation numerical model with rigid boundaries. Quantitative comparisons with laboratory heat transport data for water are made in the parameter ranges for which the experimental flows are approximately two-dimensional and steady. When an experimentally realistic spatial periodicity is imposed upon the numerical solution, the model simulates the experimental determinations of Nusselt number fairly accurately. In particular, it predicts the observed non-monotonic dependence on Taylor number. When spatial periodicities corresponding to those of the linear stability problem are specified, however, the accuracy of the simulation is less and the Taylor number dependence is monotonic.

1972
Willis, GE, Deardorff JW, Somerville RCJ.  1972.  Roll-diameter dependence in Rayleigh convection and its effect upon the heat flux. Journal of Fluid Mechanics. 54:351-367.   10.1017/S0022112072000722   Abstract

The average roll diameter in Rayleigh convection for 2000 < R < 31000, where R is the Rayleigh number, has been measured from photographs of three convecting fluids: air, water and a silicone oil with a Prandtl number σ of 450. For air the average dimensionless roll diameter was found to depend uniquely upon R and to increase especially rapidly in the range 2000 < R < 8000. The fluids of larger σ exhibited strong hysteresis but also had average roll diameters tending to increase with R. The increase in average roll diameter with R tended to decrease with σ. Through use of two-dimensional numerical integrations for the case of air it was found that the increase in average roll diameter with R provides an explanation for the usual discrepancy in heat flux observed between experiment and two-dimensional numerical calculations which prescribe a fixed wavelength.

1973
Somerville, RCJ, Lipps FB.  1973.  A Numerical Study in Three Space Dimensions of Bénard Convection in a Rotating Fluid. Journal of the Atmospheric Sciences. 30:590-596.: American Meteorological Society   10.1175/1520-0469(1973)030<0590:ansits>2.0.co;2   AbstractWebsite

The primitive, nonlinear, Boussinesq equations of motion, continuity and thermodynamic energy are integrated numerically in three space dimensions and time to study convection driven by unstable vertical density gradients and subject to Coriolis forces. Parameter values are chosen to permit quantitative comparison with data from laboratory experiments for rotating Bénard convection in water. The model realistically simulates the structure of the convection cells, their horizontal scale, and the mean vertical heat transport. The experimentally observed phenomenon of a non-monotone dependence of heat transport on rotation rate is reproduced and shown to be a consequence of the rotational constraint on the wavelength of the cells.

1974
Stone, PH, Quirk WJ, Somervil.Rc.  1974.  Effect of Small-Scale Vertical Mixing of Horizontal Momentum in a General Circulation Model. Monthly Weather Review. 102:765-771.   10.1175/1520-0493(1974)102<0765:teossv>2.0.co;2   AbstractWebsite

Several experiments are described in which the sub-grid-scale vertical eddy viscosity in the GISS global general circulation model was varied. The results show that large viscosities suppress large-scale eddies in middle and high latitudes, but enhance the circulation in the tropical Hadley cell and increase the extent of the tropical easterlies. Comparison with observations shows that the GISS model requires eddy viscosities 1 m2/s or less to give realistic results for middle and high latitudes, and eddy viscosities 100 m2/s to give realistic results for low latitudes. A plausible mechanism for the implied increase in small-scale mixing in low latitudes is cumulus convection.

Somervil.Rc, Stone PH, Halem M, Hansen JE, Hogan JS, Druyan LM, Russell G, Lacis AA, Quirk WJ, Tenenbau.J.  1974.  GISS Model of Global Atmosphere. Journal of the Atmospheric Sciences. 31:84-117.   10.1175/1520-0469(1974)031<0084:tgmotg>2.0.co;2   AbstractWebsite

A model description and numerical results are presented for a global atmospheric circulation model developed at the Goddard Institute for Space Studies (GISS). The model version described is a 9-level primitive-equation model in sigma coordinates. It includes a realistic distribution of continents, oceans and topography. Detailed calculations of energy transfer by solar and terrestrial radiation make use of cloud and water vapor fields calculated by the model. The model hydrologic cycle includes two precipitation mechanisms: large-scale supersaturation and a parameterization of subgrid-scale cumulus convection.Results are presented both from a comparison of the 13th to the 43rd days (January) of one integration with climatological statistics, and from five short-range forecasting experiments. In the extended integration, the near-equilibrium January-mean model atmosphere exhibits an energy cycle in good agreement with observational estimates, together with generally realistic zonal mean fields of winds, temperature, humidity, transports, diabatic heating, evaporation, precipitation, and cloud cover. In the five forecasting experiments, after 48 hr, the average rms error in temperature is 3.9K, and the average rms error in 500-mb height is 62 m. The model is successful in simulating the 2-day evolution of the major features of the observed sea level pressure and 500-mb height fields in a region surrounding North America.

1975
Druyan, LM, Somerville RCJ, Quirk WJ.  1975.  Extended-Range Forecasts with GISS Model of Global Atmosphere. Monthly Weather Review. 103:779-795.   10.1175/1520-0493(1975)103<0779:erfwtg>2.0.co;2   AbstractWebsite
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Galchen, T, Somerville RCJ.  1975.  Numerical-Solution of Navier-Stokes Equations with Topography. Journal of Computational Physics. 17:276-310.   10.1016/0021-9991(75)90054-6   AbstractWebsite

A finite difference scheme for solving the equations of fluid motion in a generalized coordinate system has been constructed. The scheme conserves mass and all the first integral moments of the motion. The scheme also advectively “almost conserves” second moments, in that the magnitude of implicit numerical smoothing is typically about an order smaller than explicit viscosity and diffusion. Calculations with the model support the theoretical conjecture that the difference scheme is stable whenever the analogous Cartesian scheme is stable. The scheme has been used to calculate dry atmospheric convection due to differential heating between top and bottom of mountainous terrain. The general small-scale characteristics of mountain up-slope winds have been simulated. In addition, the results have demonstrated the crucial role played by the eddy diffusivities and the environmental stability, in determining both the quantitative and the qualitative features of the circulation.

Galchen, T, Somerville RCJ.  1975.  On the Use of a Coordinate Transformation for Solution of Navier-Stokes Equations. Journal of Computational Physics. 17:209-228.   10.1016/0021-9991(75)90037-6   AbstractWebsite

The equations of fluid motion have been formulated in a generalized noncartesian, non-orthogonal coordinate system. A particular coordinate transformation, which transforms a domain with an irregular lower boundary into a cube, has been constructed. The transformed system, unlike the original one, has flat boundaries and homogeneous boundary conditions. Where the topography is flat, the original and transformed systems are identical, and extra terms do not appear. A finite difference scheme for solving the transformed equations has been constructed and will be described in a subsequent issue of this journal.

1976
Somerville, RCJ, Quirk WJ, Hansen JE, Lacis AA, Stone PH.  1976.  Search for Short-Term Meteorological Effects of Solar Variability in an Atmospheric Circulation Model. Journal of Geophysical Research-Oceans and Atmospheres. 81:1572-1576.   10.1029/JC081i009p01572   AbstractWebsite

A set of numerical experiments is carried out to test the short-range sensitivity of the Giss (Goddard Institute for Space Studies) global atmospheric general circulation model to changes in solar constant and ozone amount. These experiments consist of forecasts initialized with actual atmospheric data. One set of forecasts is made with a standard version of the model, and another set uses the model modified by very different values of the solar constant (two thirds and three halves of the standard value) and of the ozone amount (zero and twice the standard amount). Twelve-day integrations with these very large variations show such small effects that the effects of realistic variations would almost certainly be insignificant meteorologically on this time scale.

1977
Baker, WE, Kung EC, Somerville RCJ.  1977.  Energetics Diagnosis of the NCAR General Circulation Model. Monthly Weather Review. 105:1384-1401.   10.1175/1520-0493(1977)105<1384:edotng>2.0.co;2   AbstractWebsite

A comprehensive energetics analysis has been performed on the NCAR general circulation model. The analysis involves January and July simulation experiments with the 6-layer, 5-degree, second-generation model with two different convective schemes. Spectral analysis of the energy transformations in the wave-number domain was performed separately on a global and hemispheric basis as well as for the tropics and mid-latitudes. Latitudinal distributions of energy variables were also examined.A qualitative agreement with observational estimates is generally recognized in the transformations of eddy energies. Quantitatively, however, the eddy energies, conversions and energy transfer between wavenumbers are weaker than observational estimates. It is noteworthy that substantial differences exist in the energetics of the two versions of the model with different convective schemes.

Somerville, RCJ.  1977.  Pattern Recognition Techniques for Weather Forecast Verification. Contributions to Atmospheric Physics [Beitraege zur Physik der Atmosphaere.], Wiesbaden, Germany. 50:403-410. Abstract
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1978
Baker, WE, Kung EC, Somerville RCJ.  1978.  An Energetics Analysis of Forecast Experiments with NCAR General Circulation Model. Monthly Weather Review. 106:311-323.   10.1175/1520-0493(1978)106<0311:aeaofe>2.0.co;2   AbstractWebsite

The energetics in numerical weather forecast experiments with the NCAR general circulation model have been analyzed. The 6-layer, 5-degree, second-generation global model was used to make two 10-day forecasts with the same initial conditions. The two experiments differed primarily in the methods of convective parameterization.Hemispheric integrals of the model energies and energy transformations are presented in the context of their approach to a quasi-equilibrium climatology. Spectral and spatial analyses of the eddy energies and transformations provide further insight into the model response to the initial conditions. After the initial adjustment, the eddy kinetic energy appears to lag the conversion from eddy available potential energy to eddy kinetic energy by at least 48 h in the long waves (wavenumbers 1–4) and by approximately 24 h in the baroclinic waves (wavenumbers 5–7), whereas little or no time lag is apparent in the short waves (wavenumbers 8–12).The sensitivity of the forecast energetics to two different convective parameterizations is also examined. There is little appreciable difference between the two experiments in the eddy kinetic energy integrals during the first 36 h of the forecast, but temporal patterns of the eddy transformations are distinctly different after 12 h.

1979
Gall, R, Blakeslee R, Somerville RCJ.  1979.  Baroclinic Instability and the Selection of the Zonal Scale of the Transient Eddies of Middle Latitudes. Journal of the Atmospheric Sciences. 36:767-784.   10.1175/1520-0469(1979)036<0767:biatso>2.0.co;2   AbstractWebsite

Because the linear growth rates of baroclinic waves on realistic zonal flows are largest at relatively high zonal wavenumbers (e.g., 15), the observed peaks in the transient kinetic energy spectrum cannot be explained simply by peaks in the linear growth-rate spectrum. When the growth-rate spectrum is fairly flat, as suggested by recent studies, then as the waves evolve, the decrease of the instability of the zonal flow and the increase of dissipation in the developing waves become important in determining which wavelength will dominate after the waves are fully developed. In particular, the stabilization of the zonal flow because of northward and upward eddy transport (which is primarily confined to the lower troposphere in all baroclinic waves) causes the instability of the short baroclinic waves (wavenumber > 10) to decrease more rapidly than that of the intermediate-scale waves (wavenumber <10). In addition, as it is usually modeled, dissipation increases with time more rapidly in the short waves. Therefore, the growth of the short waves is terminated by these two processes before the growth of the intermediate-scale waves, which can thus achieve greater equilibrium amplitudes.We have obtained these results in a numerical experiment with a simplified general circulation model, in which waves of all wavelengths are allowed to develop simultaneously from small random perturbations on a flow that is initially zonally symmetric. The kinetic energy spectrum in this experiment does not display a −3 power law in the wavenumber band 10–20, even after the spectrum in this spectral region has been equilibrated for a simulated week or more. This result apparently supports the recent hypothesis of Andrews and Hoskins that atmospheric fronts rather than quasi-geostrophic turbulence are responsible for the observed −3 spectrum at wavenumbers > 10.

Gall, R, Blakeslee R, Somerville RCJ.  1979.  Cyclone-Scale Forcing of Ultralong Waves. Journal of the Atmospheric Sciences. 36:1692-1698.   10.1175/1520-0469(1979)036<1692:csfouw>2.0.co;2   AbstractWebsite

A numerical experiment is carried out with a simplified general circulation model. In this experiment, instabilities of all wavelengths are allowed to develop simultaneously from small perturbations on a zonally symmetric flow. The initial development of the ultralong waves in this experiment is apparently forced by the interaction between the cyclone-scale waves and the basic flow in which they are embedded. Because the spectrum of the developing baroclinic waves is not monochromatic, the interaction between the cyclones and the basic flow varies with longitude, and waves longer than the cyclone scale are forced. The structure of the ultralong waves in the numerical experiment is consistent with this forcing mechanism. One implication for numerical weather prediction is that errors in forecasts of ultralong waves may be due in part to errors in the cyclone scale.

Somerville, RCJ, Galchen T.  1979.  A Numerical Simulation of Convection with Mean Vertical Motion. Journal of the Atmospheric Sciences. 36:805-815.   10.1175/1520-0469(1979)036<0805:nsocwm>2.0.co;2   AbstractWebsite

The flow in a convectively unstable layer of fluid may be strongly influenced by large-scale ascent or descent. We consider cellular convection between horizontal surfaces on which vertical velocity is maintained at a constant value. Using an efficient numerical model to simulate the evolution of the convection in three space dimensions and time, we investigate the effect of the imposed vertical velocity on the flow.For moderately supercritical values of the Rayleigh number and for Prandtl numbers near unity, convection is known to occur in the form of steady rolls if the specified mean vertical motion is zero, i.e., in the case of the conventional Bénard problem for a Boussinesq fluid. Our model also produces rolls under these circumstances. For sufficiently large values of the imposed vertical velocity, however, the numerically simulated rolls are replaced by polygonal cells in which the direction of flow depends on whether ascent or descent is prescribed at the boundaries, in accordance with recent theoretical and laboratory results of R. Krishnamurti. We have also investigated the dependence of the convection on the Rayleigh and Prandtl numbers within limited ranges of these parameters, and we discuss several aspects of agreement and disagreement among analytical theory, laboratory experiment and numerical simulation.

Dobosy, RJ, Somerville RCJ.  1979.  Test of Simple Momentum Boundary-Layer Parameterizations in a Numerical Weather Prediction Model. Contributions to Atmospheric Physics [Beitraege zur Physik der Atmosphaere.], Wiesbaden, Germany. 52:190-203. Abstract
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1980
Somerville, RCJ.  1980.  Tropical Influences on the Predictability of Ultralong Waves. Journal of the Atmospheric Sciences. 37:1141-1156.   10.1175/1520-0469(1980)037<1141:tiotpo>2.0.co;2   AbstractWebsite

Some implications of predictability theory for ultralong waves are examined in an ensemble of real-data forecasts carried out with a primitive-equation numerical model in both global and hemispheric configurations. Although the model is adiabatic and almost inviscid, its skill at forecasting the 5-day evolution of ultralong waves in middle latitudes of the Northern Hemisphere is approximately equivalent to that of a physically comprehensive general circulation model. The ultralong wave forecasts produced by a hemispheric version of the model are markedly less skillful than those made by the global version, especially in the latter part of the 5-day period. When the initial state of the hemispheric version is modified by using a smooth field in the tropics in place of analyzed observed data, the skill of the prediction is degraded further, and the effect is apparent early in the 5-day period.These adverse tropical influences on middle-latitude forecast skill are essentially confined to the ultralong waves (zonal wavenumbers 1–3). They appear to be typical of hemispheric integrations with conventional numerical weather prediction models and conventional analysis and initialization techniques. The resulting forecast errors may be associated with the spurious excitation of large-amplitude external modes. These effects of tropical deficiencies in the prediction model and in the initial data provide a partial explanation for the poor skill of typical actual forecasts of ultralong waves, relative to the skill expected on the basis of predictability theory. The results also suggest that improvements in hemispheric analysis and initialization procedures are urgently required. Until such improvements are implemented, the use of global rather than hemispheric models, even for forecasts of only a few days, might be beneficial in operational practice.

1982
Roads, JO, Somerville RCJ.  1982.  Predictability of Ultralong Waves in Global and Hemispheric Quasi-Geostrophic Barotropic Models. Journal of the Atmospheric Sciences. 39:745-755.   10.1175/1520-0469(1982)039<0745:pouwig>2.0.co;2   AbstractWebsite

A global quasi-geostrophic barotropic model, including orography, zonal forcing and frictional dissipation, is compared to two hemispheric models, one with antisymmetric equatorial boundary conditions and one with symmetric boundary conditions. The stationary solutions in the global model and the hemispheric models are found to be different, because the hemispheric models lack either the symmetric or antisymmetric waves, and because the nonlinear feedbacks are much larger in the hemispheric models. Time-dependent calculations show that the hemispheric models can excite anomalous Rossby waves and can produce erroneous short-range forecasts in middle latitudes. We conclude that global models are preferred for making both short-range and long-range forecasts for middle latitudes.

1983
Barnett, TP, Somerville RCJ.  1983.  Advances in Short-Term Climate Prediction. Reviews of Geophysics. 21:1096-1102.   10.1029/RG021i005p01096   AbstractWebsite

Dynamical and several empirical and statistical approaches to short term climate prediction are surveyed. General circulation models have displayed considerable potential for this application. Physical/synoptic and purely statistical methods have been intensively developed and tested in recent years. Important problems have been recognized in areas such as predictability, forecast verification and evaluation, and combining complementary approaches to prediction.

Hathaway, DH, Somerville RCJ.  1983.  Three-Dimensional Simulations of Convection in Layers with Tilted Rotation Vectors. Journal of Fluid Mechanics. 126:75-&.   10.1017/s0022112083000051   AbstractWebsite

Three-dimensional and time-dependent numerical simulations of thermal convection are carried out for rotating layers in which the rotation vector is tilted from the vertical to represent various latitudes. The vertical component of the rotation vector produces narrow convection cells and a reduced heat flux. As this vertical component of the rotation vector diminishes in the lower latitudes, the vertical heat flux increases. The horizontal component of the rotation vector produces striking changes in the convective motions. It elongates the convection cells in a north–south direction. It also tends to turn upward motions to the west and downward motions to the east in a manner that produces a large-scale circulation. This circulation is directed to the west and towards the poles in the upper half of the layer and to the east and towards the equator in the bottom half. Since the layer is warmer on the bottom this circulation also carries an equatorward flux of heat. When the rotation vector is tilted from the vertical, angular momentum is always transported downwards and toward the equator. For rapidly rotating layers, the pressure field changes in a manner that tends to balance the Coriolis force on vertical motions. This results in an increase in the vertical heat flux as the rotation rate increases through a limited range of rotation rates.

1984
Somerville, RCJ, Remer LA.  1984.  Cloud Optical-Thickness Feedbacks in the Co2 Climate Problem. Journal of Geophysical Research-Atmospheres. 89:9668-9672.   10.1029/JD089iD06p09668   AbstractWebsite

A radiative-convective equilibrium model is developed and applied to study cloud optical thickness feedbacks in the CO2 climate problem. The basic hypothesis is that in the warmer and moister CO2-rich atmosphere, cloud liquid water content will generally be larger too. For clouds other than thin cirrus the result is to increase the albedo more than to increase the greenhouse effect. Thus the sign of the feedback is negative: cloud optical properties act as a thermostat and alter in such a way as to reduce the surface and tropospheric warming caused by the addition of CO2. This negative feedback can be substantial. When observational estimates of the temperature dependence of cloud liquid water content are employed in the model, the surface temperature change caused by doubling CO2 is reduced by about one half. This result is obtained for global and annual average conditions, no change in cloud amount or altitude, and constant relative humidity. These idealizations, together with other simplifications typical of one-dimensional radiative-convective climate models, render the result tentative. Further study of cloud optical property feedbacks is warranted, however, because the climate is apparently so sensitive to them.

Roads, JO, Somerville RCJ.  1984.  Linear Predictability: Effects of Stationary Forcing. Aip Conference Proceedings. :557-570. AbstractWebsite
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1985
Engquist, BE, Osher S, Somerville RCJ.  1985.  Large-Scale Computations in Fluid Mechanics. Lectures in Applied Mathematics. :779.: American Mathematical Society AbstractWebsite
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