Airborne dust is an important constituent in the Martian atmosphere because of its radiative interaction with the atmospheric circulation. Dust size is one crucial factor in determining this effect. In reality dust sizes are varied; however, in numerical modeling of dust processes, dust size has usually been described by choice of a particular size distribution function, or by use of fixed values of effective radius (ER) and effective variance (EV). In this work, we present analytical expressions that have been derived to specify ER and EV for N-bin dust schemes, based on a model-calculated dust mixing ratio. Numerical simulations based on this approach thus would consider the effects of variable ER on the atmospheric radiation and their interaction. Results have revealed some interesting features of the dust distribution parameters, such as seasonal and spatial variation of ER and EV, which are generally consistent with some previous observational and modeling studies. Compared with the usual approach of using a fixed ER, simulation results from the present approach suggest that the variability of ER can have significant effects on the simulated thermal field of the Martian atmosphere.
A two-dimensional energy balance climate model has been built to investigate the climate on Mars. The model takes into account the balance among solar radiation, longwave radiation, and energy transmission and can be solved analytically by Legendre polynomials. With the parameters for thermal diffusion and radiation processes being properly specified, the model can simulate a reasonable surface atmospheric temperature distribution but not a very perfect vertical atmospheric temperature distribution compared with numerical results, such as those from the Mars Climate Database. With varying solar radiation in a Martian year, the model can simulate the seasonal variation of the air temperature on Mars. With increasing dust content, the Martian atmosphere gradually warms. However, the warming is insignificant in the cold and warm scenarios, in which the dust mixing ratio varies moderately, whereas the warming is significant in the storm scenario, in which the dust mixing ratio increases dramatically. With an increasing albedo value of either the polar cap or the non-ice region, Mars gradually cools. The mean surface atmospheric temperature decreases moderately with an increasing polar ice albedo, whereas it increases dramatically with an increasing non-ice albedo. This increase occurs because the planetary albedo of the ice regions is smaller than that of the non-ice region.