Wilford Zdunkowski

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 particles is calculated by considering radiative effects in the droplet growth equation. Numerical results elucidate that the strong interaction between the radiatively induced droplet growth and their gravitational settling is responsible for a distinct reduction of the liquid water content which also shows quasi-peri...

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 Germany are presented. Finally, some sensitivity studies are performed and discussed in order to investigate the influence of different soil and vegetation types on the energy state of the atmosphere.

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 Brühl and Zdunkowski (1983). Calculated albedo values are compared with Aidas (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.

A Fast Approximate Method for the Calculation of the Infrared Radiation Balance Within City Street Cavities

SummaryThe approximate calculation method for diffuse solar irradiances in street cavities presented in an earlier paper is extended to include infrared flux densities. By expanding the infrared sky radiance as a truncated trigonometric series, it becomes possible to solve the integrals representing the obstruction of the sky analytically. An example is worked out to demonstrate the numerically very efficient calculation procedure.ZusammenfassungDie in einer früheren Arbeit angegebene approximative Methode zur Berechnung solarer diffuser Bestrahlungsstärken in Straßenschluchten- ist erweitert worden, um ebenfalls infrarote Strahlungsstromdichten zu erfassen. Die infrarote Himmelsstrahlung wird als eine trigonometrische Reihe weniger Terme angesetzt. Dadurch wird es möglich, die Abschattung der Himmelsstrahlung durch Gebäude analytisch zu erfassen. Ein Beispiel wird diskutiert.

A Fast Solar Radiation Transfer Code for Application in Climate Models

SummaryA 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 NO2. This list can be extended if desired. Moreover absorption by aerosols and cloud particles is accounted for in addition to multiple scattering. A comparison with the rather accurate and already efficient transfer code of Zdunkowski et al. [6] shows that the present method is similarly accurate but numerically even more efficient. Therefore, this radiation scheme becomes very suitable for use in some circulation models of the atmosphere, such as prediction models of radiation fog.[/p]ZusammenfassungDas hier vorgestellte Verfahren dient zur Berechnung solarer Erwärmungsraten in trüben und bewölkten Atmosphären. Im Gegensatz zu sonst üblichen Zweistrommethoden wird das hier auftretende gekoppelte Differentialgleichungssystem für die nach oben und unten gerichteten Strahlungsflußdichten mit Hilfe eines Reihenansatzes entkoppelt. Dadurch wird die numerisch aufwendige Invertierung einer Matrix umgangen und somit die Rechenzeit erheblich reduziert. Das Modell erfaßt die Absorption atmosphärischer Gase wie Wasserdampf, CO2, O3 und NO2. Diese Liste kann - wenn gewünscht - erweitert werden. Weiterhin wird die Absorption von Aerosolen und Wolkenteilchen zusätzlich zur Vielfachstreuung erfaßt. Ein Vergleich mit dem von Zdunkowski et al. [6] angegebenen Zweistromverfahren zeigt, daß dessen Genauigkeit fast erreicht, aber die numerische Effektivität noch erheblich übertroffen wird. Deshalb eignet sich das gegenwärtige Berechnungsverfahren solarer Erwärmungsraten z.B. zum Einbau in Vorhersagemodelle von Strahlungsnebeln.[/p]