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- Author or Editor: Martin I. Hoffert x
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Abstract
A similarity model is developed for the vertical profiles of turbulent flow variables in an entraining turbulent boundary layer of arbitrary buoyant stability. In the general formulation the vertical profiles, internal rotation of the velocity vector, discontinuities or jumps at a capping inversion and bulk aerodynamic coefficients of the boundary layer are given by solutions to a system of ordinary differential equations in the similarity variable η = z/h, where h is the physical height or thickness, where the system includes six parameters associated with surface roughness, buoyant stability of the turbulence near the surface, Coriolis effects, baroclinicity and stability of the air mass above the boundary layer. To close the system a new formulation for buoyantly interactive eddy diffusivity in the boundary layer is introduced which recovers Monin-Obukhov similarity near the surface and incorporates a hypothesis accounting for the observed variation of mixing length throughout the boundary layer.
The model is tested in simplified versions which depend only on roughness, surface buoyancy and Coriolis effects by comparison with Clarke's planetary boundary layer wind and temperature profile observations, Arya's measurements of flat-plate boundary layers in a thermally stratified wind tunnel, and Lenschow's observations of profiles of terms in the turbulent kinetic energy budget of convective planetary boundary layers. On balance, the simplified model reproduced the trend of these various observations and experiments reasonably well, suggesting that the full similarity formulation be pursued further.
Abstract
A similarity model is developed for the vertical profiles of turbulent flow variables in an entraining turbulent boundary layer of arbitrary buoyant stability. In the general formulation the vertical profiles, internal rotation of the velocity vector, discontinuities or jumps at a capping inversion and bulk aerodynamic coefficients of the boundary layer are given by solutions to a system of ordinary differential equations in the similarity variable η = z/h, where h is the physical height or thickness, where the system includes six parameters associated with surface roughness, buoyant stability of the turbulence near the surface, Coriolis effects, baroclinicity and stability of the air mass above the boundary layer. To close the system a new formulation for buoyantly interactive eddy diffusivity in the boundary layer is introduced which recovers Monin-Obukhov similarity near the surface and incorporates a hypothesis accounting for the observed variation of mixing length throughout the boundary layer.
The model is tested in simplified versions which depend only on roughness, surface buoyancy and Coriolis effects by comparison with Clarke's planetary boundary layer wind and temperature profile observations, Arya's measurements of flat-plate boundary layers in a thermally stratified wind tunnel, and Lenschow's observations of profiles of terms in the turbulent kinetic energy budget of convective planetary boundary layers. On balance, the simplified model reproduced the trend of these various observations and experiments reasonably well, suggesting that the full similarity formulation be pursued further.
Abstract
A time-dependent, one-dimensional model of the coupled chemistry and vertical mixing of the atmosphere is used to compute the distribution for many atmospheric constituents of the troposphere and stratosphere. The model treats the photochemistry of the carbon-hydrogen-oxygen-nitrogen system and is (with the exception of H2o) self-consistent in the sense of requiring no assumptions regarding minor constituent distributions.
Abstract
A time-dependent, one-dimensional model of the coupled chemistry and vertical mixing of the atmosphere is used to compute the distribution for many atmospheric constituents of the troposphere and stratosphere. The model treats the photochemistry of the carbon-hydrogen-oxygen-nitrogen system and is (with the exception of H2o) self-consistent in the sense of requiring no assumptions regarding minor constituent distributions.
Abstract
The effects of parameterizations of subgrid-scale mixing on simulated distributions of natural 14C, temperature, and salinity in a three-dimensional ocean general circulation model are examined. The parameterizations studied are 1) the Gent–McWilliams parameterization of lateral transport of tracers by isopycnal eddies; 2) horizontal mixing; 3) a parameterization of vertical mixing in which the amount of mixing depends on the local vertical density gradient; and 4) prescribed vertical mixing. The authors perform and analyze four ocean GCM simulations that use different combinations of these parameterizations. It is confirmed that the Gent–McWilliams parameterization largely eliminates the tendency of GFDL-based models to overestimate temperatures in the thermocline. However, in the authors’ simulations with the Gent–McWilliams parameterization the deep ocean is too cold, in places by more than 3 degrees. Our results are the first known to assess the effects of the Gent–McWilliams parameterization on the simulated distribution of natural 14C. The most important change (compared to results obtained with horizontal mixing) is that interior ocean 14C values are lower; that is, the water is “older” with Gent–McWilliams. In most locations in the deep North Atlantic, simulated Δ14C values are much too low with horizontal mixing and are even lower with Gent–McWilliams. Both this problem and the problem of the simulated deep ocean being too cold are probably due, at least in part, to insufficient downward penetration of NADW, resulting in the deep North Atlantic in the model being ventilated primarily via AABW. This problem exists when Gent–McWilliams is not used, but Gent–McWilliams makes the symptoms it presents (an overly cold and old deep North Atlantic) worse. Gent–McWilliams also results in a dramatic reduction in convective adjustment in the model, compared to results obtained with horizontal mixing; as a result, simulated tracer distributions are improved at high latitudes. Finally, Gent–McWilliams increases the susceptibility of the authors’ model to some types of numerical problems. The stability-dependent vertical mixing parameterization causes relatively small changes in simulated distributions of temperature and natural 14C (compared to results with a prescribed uniform vertical diffusivity), but these changes tend to improve agreement with observations. Assuming they are based on correct physical premises and are properly calibrated, both the stability-dependent vertical mixing parameterization and the Gent–McWilliams parameterization should give the model more predictive capability than simpler parameterizations do in that they allow the amount or direction of mixing to change in response to changes in ocean density.
Abstract
The effects of parameterizations of subgrid-scale mixing on simulated distributions of natural 14C, temperature, and salinity in a three-dimensional ocean general circulation model are examined. The parameterizations studied are 1) the Gent–McWilliams parameterization of lateral transport of tracers by isopycnal eddies; 2) horizontal mixing; 3) a parameterization of vertical mixing in which the amount of mixing depends on the local vertical density gradient; and 4) prescribed vertical mixing. The authors perform and analyze four ocean GCM simulations that use different combinations of these parameterizations. It is confirmed that the Gent–McWilliams parameterization largely eliminates the tendency of GFDL-based models to overestimate temperatures in the thermocline. However, in the authors’ simulations with the Gent–McWilliams parameterization the deep ocean is too cold, in places by more than 3 degrees. Our results are the first known to assess the effects of the Gent–McWilliams parameterization on the simulated distribution of natural 14C. The most important change (compared to results obtained with horizontal mixing) is that interior ocean 14C values are lower; that is, the water is “older” with Gent–McWilliams. In most locations in the deep North Atlantic, simulated Δ14C values are much too low with horizontal mixing and are even lower with Gent–McWilliams. Both this problem and the problem of the simulated deep ocean being too cold are probably due, at least in part, to insufficient downward penetration of NADW, resulting in the deep North Atlantic in the model being ventilated primarily via AABW. This problem exists when Gent–McWilliams is not used, but Gent–McWilliams makes the symptoms it presents (an overly cold and old deep North Atlantic) worse. Gent–McWilliams also results in a dramatic reduction in convective adjustment in the model, compared to results obtained with horizontal mixing; as a result, simulated tracer distributions are improved at high latitudes. Finally, Gent–McWilliams increases the susceptibility of the authors’ model to some types of numerical problems. The stability-dependent vertical mixing parameterization causes relatively small changes in simulated distributions of temperature and natural 14C (compared to results with a prescribed uniform vertical diffusivity), but these changes tend to improve agreement with observations. Assuming they are based on correct physical premises and are properly calibrated, both the stability-dependent vertical mixing parameterization and the Gent–McWilliams parameterization should give the model more predictive capability than simpler parameterizations do in that they allow the amount or direction of mixing to change in response to changes in ocean density.
Abstract
Studies of paleoclimate and modern observations indicate that evaporative effects limit thermal response in equatorial regions. We develop a latitude-resolved, steady-state energy balance model which incorporates the effect of an evaporative constraint on the variation of equatorial temperature with solar luminosity. For a diffusive model of surface heat transport the constraint requires the diffusion coefficient to vary with insolation. We find that the movement of the iceline with insolation is four times larger than in standard energy balance models with a constant thermal diffusion coefficient. This is a consequence of the global energy balance which forces temperature changes to occur at high latitudes when they are evaporatively buffered at the equator. Nonlinear temperature-ice albedo feedback at high latitudes then amplifies the response leading to greater sensitivity in the vicinity of current climate.
Abstract
Studies of paleoclimate and modern observations indicate that evaporative effects limit thermal response in equatorial regions. We develop a latitude-resolved, steady-state energy balance model which incorporates the effect of an evaporative constraint on the variation of equatorial temperature with solar luminosity. For a diffusive model of surface heat transport the constraint requires the diffusion coefficient to vary with insolation. We find that the movement of the iceline with insolation is four times larger than in standard energy balance models with a constant thermal diffusion coefficient. This is a consequence of the global energy balance which forces temperature changes to occur at high latitudes when they are evaporatively buffered at the equator. Nonlinear temperature-ice albedo feedback at high latitudes then amplifies the response leading to greater sensitivity in the vicinity of current climate.
