A numerical model of the cloud-topped planetary boundary-layer: Radiation, turbulence and spectral microphysics in marine stratus

A numerical model of the cloud-topped planetary boundary-layer is presented. The model is one-dimensional with special emphasis on a detailed description of cloud microphysical processes. Aerosols and cloud droplets are treated in a two-dimensional particle-distribution whereby the activation of aerosols is calculated explicitly by solving the droplet-growth equation at all relative humidities. Atmospheric radiation is determined with a δ-two-stream radiation scheme. Turbulent fluxes are parametrized as a function of the turbulent kinetic energy. Numerical results are presented which are obtained by utilizing measurements made over the North Sea. The interaction between radiation, turbulenc…

Reply to a comment by R. Brown on ‘a numerical model of the cloud‐topped planetary boundary‐layer: Radiation, turbulence and spectral microphysics in marine stratus’ (april A, 1996, 122, 635‐667)

A Fast Solar Radiation Transfer Code for Application in Climate Models

A method is presented for the calculation of solar heating rates in turbid and cloudy atmospheres. In contrast to other typical two-stream procedures, the system of differential equations describing the radiative transfer is decoupled through the application of a series expansion of the flux densities resulting in a single analytical expression for each flux. The present method (PM) yields a solution for the entire atmosphere instead of individual atmospheric layers. This procedure avoids as part of the solution scheme the inversion of a rather complex matrix thus resulting in high numerical efficiency. The model includes the absorption by atmospheric gases such as water vapor, CO2, O3 and …

Explicit Microphysical Simulations of Boundary Layer Clouds over the Sea and over Vegetated Land Surfaces

State functions of ideal gases

A one-dimensional simulation of the interaction between land surface processes and the atmosphere

A one-dimensional soil-vegetation model is developed for future incorporation into a mesoscale model. The interaction of land surface processes with the overlying atmosphere is treated in terms of three coupled balance equations describing the energy and moisture transfer at the ground and the energy state of the vegetation layer. For a complete description of the interaction, the coupled processes of heat and moisture transport within the soil are included as a multilayer soil model. As model verification, successful reproductions of the observed energy fluxes over vegetated surfaces from the HAPEX-MOBILHY experiment in southwestern France and from the LOTREX-10E/HIBE88 field experiment in…

Thermodynamic potentials, identities and stability

A Radiation Fog Model with a Detailed Treatment of the Interaction between Radiative Transfer and Fog Microphysics

Abstract A one-dimensional radiation fog model is presented which includes a detailed description of the interaction between atmospheric radiative transfer and the microphysical structure of the fog. Aerosol particles and activated cloud droplets are treated using a two-dimensional joint size distribution whereby the activation process of aerosols is explicitly modeled. For this purpose a new positive definite semi-Lagrangian advection scheme is developed that produces only small numerical diffusion and is numerically very efficient. For the radiative calculations, time dependent attenuation parameters are determined from the actual particle size distributions. The diffusional growth of the…

Radiation in the Atmosphere - A Course in Theoretical Meteorology

This book presents the theory and applications of radiative transfer in the atmosphere. It is written for graduate students and researchers in the fields of meteorology and related sciences. The book begins with important basic definitions of the radiative transfer theory. It presents the hydrodynamic derivation of the radiative transfer equation and the principles of variance. The authors examine in detail various quasi-exact solutions of the radiative transfer equation and give a thorough treatment of the radiative perturbation theory. A rigorous treatment of Mie scattering is given, including Rayleigh scattering as a special case, and the important efficiency factors for extinction, scat…

The stereographic coordinate system

The barotropic model

The effects of different radiation parametrizations on cloud evolution

With the use of the microphysical stratus model (MISTRA), investigations into the effects of variations in the radiative-transfer parametrizations on cloud development have been undertaken. Two radiative-transfer schemes were coupled with the microphysical-thermodynamical section of MISTRA, one based on the exponential sumfitting method and the other based on the correlated k-distribution method of determining gaseous absorption properties. Model runs were initiated with parameter values in accordance with measurements made over the North Sea and comparisons made between model runs where only the radiation schemes were altered. Results indicated that differences between the two schemes had …

Comments on “Four-Stream Spherical Harmonic Expansion Approximation for Solar Radiative Transfer”

Comments on : four-stream spherical harmonic expansion approximation for solar radiative transfer.

Electromagnetic energy within dielectric spheres

We present exact and approximate analytic expressions for the time-averaged electromagnetic energy within dielectric spheres on the basis of rigorous Mie theory. Such information is of importance for the study of photochemical reactions within atmospheric water spheres. Numerical results show that on the average the energy inside a cloud droplet is enlarged by a factor exceeding 2 compared with that of a sphere of the same radius of the surrounding medium. In regions of resonance peaks the electromagnetic energy may be increased by more than 2 orders of magnitude.

A numerical simulation scheme for the albedo of city street canyons

A numerical scheme is described for the calculation of effective albedo values of long city street canyons. The method is based on a generalization of the radiation model for inclined surfaces recently presented by Bruhl and Zdunkowski (1983). Calculated albedo values are compared with Aida's (1982) experimentally determined results. It is found that experiment and theory are in reasonable and in some cases in excellent agreement. Additional results obtained by varying the geometry of the street canyon as well as the surface reflectivities are shown to demonstrate the versatility of the calculation scheme.

References and bibliography