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Richard C. J. Somerville

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Richard C. J. Somerville

Abstract

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.

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Richard C. J. Somerville

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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.

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David P. Baumhefner and Richard C. J. Somerville

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Sam F. Iacobellis and Richard C. J. Somerville

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A single-column model (SCM) and observational data collected during TOGA COARE were used to investigate the sensitivity of model-produced cloud properties and radiative fluxes to the representation of cloud microphysics in the cloud-radiation parameterizations. Four 78-day SCM numerical experiments were conducted for the atmospheric column overlying the COARE Intensive Flux Array. Each SCM experiment used a different cloud-radiation parameterization with a different representation of cloud microphysics.

All the SCM experiments successfully reproduced most of the observed temporal variability in precipitation, cloud fraction, shortwave and longwave cloud forcing, and downwelling surface shortwave flux. The magnitude and temporal variability of the downward surface longwave flux was overestimated by all the SCM experiments. This bias is probably due to clouds forming too low in the model atmosphere. Time-averaged model results were used to examine the sensitivity of model performance to the differences between the four cloud-radiation parameterization packages. The SCM versions that calculated cloud amount as a function of cloud liquid water, instead of using a relative humidity-based cloud scheme, produced smaller amounts of both low and deep convective clouds. Additionally, larger high (cirrus) cloud emissivities were obtained with interactive cloud liquid water schemes than with the relative humidity-based scheme. Surprisingly, calculating cloud optical properties as a function of cloud liquid water amount, instead of parameterizing them based on temperature, humidity, and pressure, resulted in relatively little change in radiative fluxes. However, model radiative fluxes were sensitive to the specification of the effective cloud droplet radius. Optically thicker low clouds and optically thinner high clouds were produced when an interactive effective cloud droplet radius scheme was used instead of specifying a constant value. Comparison of model results to both surface and satellite observations revealed that model experiments that calculated cloud properties as a function of cloud liquid water produced more realistic cloud amounts and radiative fluxes. The most realistic vertical distribution of clouds was obtained from the SCM experiment that included the most complete representation of cloud microphysics. Due to the limitations of SCMs, the above conclusions are model dependent and need to be tested in a general circulation model.

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John O. Roads and Richard C. J. Somerville

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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.

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Richard C. J. Somerville and Tzvi Gal-Chen

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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.

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Richard C. J. Somerville and Frank B. Lipps

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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.

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Duane E. Waliser and Richard C. J. Somerville

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The latitude preference of the intertropical convergence zone (ITCZ) is examined on the basis of observations, theory, and a modeling analysis. Observations show that convection is enhanced at latitudes of about 4° to 10° relative to the equator, even in regions where the sea surface temperature (SST) is maximum on the equator. Both linear shallow-water theory and a moist primitive equation model suggest a new explanation for the off-equatorial latitude preference of the ITCZ that requires neither the existence of zonally propagating disturbances nor an off-equatorial maximum in SST. The shallow-water theory indicates that a finite-width, zonally oriented, midtropospheric heat source (i.e., an ITCZ) produces the greatest local low-level convergence when placed a finite distance away from the equator. This result suggests that an ITCZ is most likely to be supported via low-level convergence of moist energy when located at these “preferred” latitudes away from the equator. For a plausible range of heating widths and damping parameters, the theoretically predicted latitude is approximately equal to the observed position(s) of the ITCZ(s). Analysis with an axially symmetric, moist, primitive equation model indicates that when the latent heating field is allowed to be determined internally, a positive feedback develops between the midtropospheric latent heating and the low-level convergence, with the effect of enhancing the organization of convection at latitudes of about 4° to 12°. Numerical experiments show that 1) two peaks in convective precipitation develop straddling the equator when the SST maximum is located on the equator; 2) steady ITCZ-like structures form only when the SST maximum is located away from the equator; and 3) peaks in convection can develop away from the maximum in SST, with a particular preference for latitudes of about 4° to 12°, even in the (“cold”) hemisphere without the SST maximum. The relationship between this mechanism and earlier theories is discussed, as are implications for the coupled ocean-atmosphere system and the roles played by midlevel latent heating and SST gradients in forcing the low-level atmospheric circulation in the tropics.

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Karen M. Shell and Richard C. J. Somerville

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Energy balance models have proven useful in understanding mechanisms and feedbacks in the climate system. An original global energy balance model is presented here. The model is solved numerically for equilibrium climate states defined by zonal average temperature as a function of latitude for both a surface and an atmospheric layer. The effects of radiative, latent, and sensible heating are parameterized. The model includes a variable lapse rate and parameterizations of the major dynamical mechanisms responsible for meridional heat transport: the Hadley cell, midlatitude baroclinic eddies, and ocean circulation. The model reproduces both the mean variation of temperature with latitude and the global average heat budget within the uncertainty of observations.

The utility of the model is demonstrated through examination of various climate feedbacks. One important feedback is the effect of the lapse rate on climate. When the planet warms as a result of an increase in the solar constant, the lapse rate acts as a negative feedback, effectively enhancing the longwave emission efficiency of the atmosphere. The lapse rate is also responsible for an increase in global average temperature when the meridional heat transport effectiveness is increased. The water vapor feedback enhances temperature changes, while the latent and sensible heating feedback reduces surface temperature changes.

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