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 …

State functions of ideal gases

A numerical model of the cloud-topped planetary boundary-layer: radiative forcing of aerosols in stratiform clouds

In a numerical sensitivity study with the microphysical stratus model MISTRA the impact of aerosol particles on the time evolution of stratiform clouds is investigated. Four model runs with different aerosol size distributions are presented. Two size distributions are typical for maritime and continental air masses. The third model run consists of a mixture of maritime and rural aerosol particles, while in the fourth case study rural aerosol particles with a reduced water solubility are utilized. The numerical results show that the microphysical structure of the clouds is strongly affected by the physico-chemical properties of the aerosol particles. In the maritime case, with a relatively l…

Thermodynamic potentials, identities and stability

A numerical model of the cloud-topped planetary boundary-layer: chemistry in marine stratus and the effects on aerosol particles

Abstract In a numerical study the effect of stratiform clouds on aerosol particles is investigated. This is done with the one-dimensional chemical microphysical stratus model CHEMISTRA. In the microphysical part of the model special emphasis is layed on a detailed description of cloud microphysical processes by means of a joint two-dimensional particle distribution for aerosols and cloud droplets. In the chemical part of the model the particle spectrum is subdivided into three categories referring to unactivated aerosols, small and large cloud droplets. Aqueous-phase chemical reactions are separately treated in the two droplet size classes. Numerical results show that within the boundary-la…

On the influence of the physico-chemical properties of aerosols on the life cycle of radiation fogs

A one-dimensional model of radiation fog with detailed microphysics is presented. Aerosols and cloud droplets are treated in a joint two-dimensional size distribution. Radiative fluxes are calculated as functions of the radiative properties of the time-dependent particle spectra. The droplet growth equation is solved by considering radiative effects. Turbulence is treated by means of a higher order closure model. The interaction between the atmosphere and the earth's surface is explicitly simulated. Three numerical sensitivity studies are performed to investigate the impact of the different physico-chemical properties of urban, rural and maritime aerosols on fog formation. Numerical results…

A Positive Definite Advection Scheme Obtained by Nonlinear Renormalization of the Advective Fluxes

Abstract A new method is developed to obtain a conservative and positive definite advection scheme that produces only small numerical diffusion. Advective fluxes are computed utilizing the integrated flux form of Tremback et al. These fluxes are normalized and then limited by upper and lower values. The resulting advection equation is numerically solved by means of the usual upstream procedure. The proposed treatment is not restricted to the integrated flux form but may also be applied to other known advection algorithms which are formulated in terms of advective fluxes. Different numerical tests are presented illustrating that the proposed scheme strongly reduces numerical and diffusion an…

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

A numerical model of the cloud-topped planetary boundary-layer: Impact of aerosol particles on the radiative forcing of stratiform clouds

In a numerical sensitivity study, the microphysical model of stratus MISTRA, is used to investigate the impact of aerosol particles on the evolution of stratiform clouds. Four model runs are presented, each for a different type of background aerosol. Two include aerosol particle size-distributions which are typical of marine and rural continental air masses; a third represents a mixture of marine and rural continental aerosol particles, and the fourth rural continental aerosol particles with a reduced solubility in water. The results show that the microphysical structure of layer clouds was strongly affected by the physico-chemical properties of the aerosol particles from which the cloud dr…

The barotropic model

A Positive Definite Advection Scheme for Use in Long Range Transport Models: Extension to Monotonicity

Numerical modeling of atmospheric transport processes requires the solution of the continuity equation for prognostic variables such as momentum, heat, water vapor, liquid water or chemical species of the atmosphere. Although in the literature many advection schemes are known to solve this problem (Lax and Wendroff 1964, Crowley 1968, Tremback et al. 1987, Bott 1989a,b), these algorithms show different disadvantages, which sometimes yield undesirably poor numerical results. For instance, the upstream method is known to produce large numerical diffusion. The higher order versions of the advection schemes of Tremback et al. (1987) are much less diffusive. Unfortunately, the schemes are not po…

Multiphase chemistry in a microphysical radiation fog model—A numerical study

A microphysical radiation fog model is coupled with a detailed chemistry module to simulate chemical reactions in the gas phase and in fog water during a radiation fog event. In the chemical part of the model the microphysical particle spectrum is subdivided into three size classes corresponding to non-activated aerosol particles, small and large fog droplets. Chemical reactions in the liquid phase are separately calculated in the small and in the large droplet size class. The impact of the chemical constitution of activated aerosols on fogwater chemistry is considered in the model simulations. The mass transfer of chemical species between the gas phase and the two liquid phases is treated …

A Flux Method for the Numerical Solution of the Stochastic Collection Equation: Extension to Two-Dimensional Particle Distributions

Abstract In the present paper a new method is introduced for the numerical solution of the stochastic collection equation in cloud models dealing with two-dimensional cloud microphysics. The method is based on the assumption that the probability for the collision of two cloud drops only depends on the water mass of each and not on the mass of the aerosol nuclei. With this assumption it is possible to reduce the two-dimensional solution of the stochastic collection equation to a one-dimensional approach. First, the two-dimensional particle spectrum is integrated over the aerosol mass yielding a one-dimensional drop spectrum in the water mass grid. For this intermediate drop distribution the …

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 …

Interaction of radiation fog with tall vegetation

Abstract A one-dimensional radiation fog model is presented. It is coupled with a second model to include the effects of tall vegetation. The fog model describes in detail the dynamics, thermodynamics, and microphysical structure of a fog, as well as the interactions with the atmospheric radiative transfer. A two-dimensional joint size distribution for the aerosol particles and activated fog droplets is used, the activation of aerosol particles is explicitly modeled. The implications of the presence of tall vegetation on the state of the atmosphere and on the evolution of radiation fog are stated. It is shown that the existence of tall vegetation impedes the evolution of radiation fog. The …

A Flux Method for the Numerical Solution of the Stochastic Collection Equation

Abstract A new mass conservative flux method is presented for the numerical solution of the stochastic collection equation. The method consists of a two-step procedure. In the first step the mass distribution of drops with mass x′ that have been newly formed in a collision process is entirely added to grid box k of the numerical grid mesh with xk ⩽ x′ ⩽ xk+1. In the second step a certain fraction of the water mass in grid box k is transported to k + 1. This transport is done by means of an advection procedure. Different numerical test runs are presented in which the proposed method is compared with the Berry–Reinhardt scheme. These tests show a very good agreement between the two approaches…

A numerical model of the cloud-topped planetary boundary-layer: cloud processing of aerosol particles in marine stratus

Abstract In a numerical study with the one-dimensional chemical microphysical stratus model CHEMISTRA the effect of stratiform clouds on aerosol particles is investigated. The microphysical part of CHEMISTRA consists of a detailed description of cloud microphysical processes by means of a joint two-dimensional particle distribution for aerosols and cloud droplets. In the chemical part of the model the particle spectrum is subdivided into three categories referring to inactivated aerosols, small and large cloud droplets. Aqueous phase chemical reactions are separately treated in the two droplet size classes. Numerical results are presented demonstrating that the uptake of trace gases by clou…

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.

The Monotone Area-preserving Flux-Form Advection Algorithm: Reducing the Time-splitting Error in Two-Dimensional Flow Fields

A numerical model of the cloud-topped planetary boundary-layer: influence of the physico-chemical properties of aerosol particles on the effective radius of stratiform clouds

The present investigation deals with the impact of different aeorosol types on the value of the effective radius of stratiform clouds. In several numerical sensitivity studies with the microphysical stratus model MISTRA, the aerosol composition was linearly changed from pure maritime to pure rural aerosol particles. Numerical results show that in environments with pure maritime aerosols, the effective radius is usually much larger than in continental regions. Values of the effective radius are also time-dependent with minima and maxima during day and night, respectively. In precipitating clouds, the effective radius might achieve values larger than 30 μm. In continental regions, the effecti…

References and bibliography