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S. A. Lebedeff
and
S. Hameed

Abstract

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S. A. Lebedeff
and
S. Hameed

Abstract

The two-dimensional diffusion equation has been solved by an integral method to obtain the distribution of ground-level concentration of an inert effluent emitted from a semi-infinite area source in a steady-state and horizontally homogeneous atmospheric surface layer. Mean wind velocity and eddy diffusivity profiles derived from empirically determined flux-profile relations of Businger et al. (1971) for stable and unstable surface layers were used. It is found that concentration as a function of downwind distance can be described by a simple formula over distances of practical interest in surface layer dispersion. Corresponding results for a cross-wind infinite line source are obtained by simple differentiation. The concentration distribution is completely determined by the friction velocity u *, the Monin-Obukhov length L, the roughness length z0, and the effluent source strength Q. The generalization of the integral method needed to obtain accurate solutions of the diffusion equation with the given wind velocity and diffusivity profiles is discussed in an appendix.

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S. A. Lebedeff
and
S. Hameed

Abstract

Turbulent transport of material emitted from a surface may be described by the steady-state, two-dimensional, semi-empirical diffusion equation. It is shown that, with wind velocity and eddy diffusivity expressed as power functions of the vertical coordinate, this equation can be solved exactly by introducing a similarity variable. The solution gives the vertical distribution of concentration for area sources in terms of the incomplete gamma function. Implications of the solution are discussed.

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J. Hansen
,
G. Russell
,
D. Rind
,
P. Stone
,
A. Lacis
,
S. Lebedeff
,
R. Ruedy
, and
L. Travis

Abstract

A global atmospheric model is developed with a computational efficiency which allows long-range climate experiments. The model solves the simultaneous equations for conservation of mass, energy and momentum, and the equation of state on a grid. Differencing schemes for the dynamics are based on work of Arakawa; the schemes do not need any viscosity for numerical stability, and can thus yield good results with coarse resolution. Radiation is computed with a semi-implicit spectral integration, including all significant atmospheric gases, aerosols and cloud particles. Cloud cover and vertical distribution are computed. Convection mixes moisture, heat and momentum, with buoyant air allowed to penetrate to a height determined by its buoyancy. Ground temperature calculations include diurnal variation and seasonal heat storage. Ground hydrology incorporates a water-holding capacity appropriate for the root zone of local vegetation. Snow depth is computed. Snow albedo includes effects of snow age and masking by vegetation. Surface fluxes are obtained from a drag-law formulation and parameterization of the Monin-Obukhov similarity relations.

The initial Model I is used for 60 climate sensitivity experiments with integration times from 3 months to 5 years. These experiments determine the dependence of model simulation on various physical assumptions and model parameters. Several modifications are incorporated to produce Model II, the greatest changes arising from more realistic parameterization of the effect of boundary layer stratification on surface fluxes and the addition of friction in the top stratospheric layer to minimize effects of wave reflection from the rigid model top. The model's climate simulations are compared to observations and a brief study is made of effects of horizontal resolution. It is verified that the major features of global climate can be realistically simulated with a resolution as coarse as 1000 km, which requires an order of magnitude less computation time than used by most general circulation models.

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