Moisture Advection Using Relative Humidity

Abstract

This study introduces a moisture advection formulation that contains relative humidity. In the sigma coordinate system, rewriting the mixing ratio conservation equation in terms of relative humidity leads to an equation that explicitly contains temperature and pressure. Consequently, the governing equation, containing relative humidity, is significantly different from that used for a fluid tracer. It is shown analytically that the homogeneous part of the governing equation for relative humidity is contained in the class of differential equations that yield solutions with lognormal distributions. These findings are relevant to the large number of observations of cloud and rainfall distributions that statistically have a lognormal component. (The relationship between clouds and the probability distribution function for relative humidity is examined in the appendix.) The equation describing the temporal and spatial distribution of relative humidity can be solved using any reliable numerical approximation. All solutions are positive definite. The formulation containing relative humidity provides an alternative method to test the sensitivity of the forecast to the moisture equation. In this study only the gridscale advection process is calculated using the relative humidity equation. Otherwise, all turbulence, physics, and numerical filtering involving moisture are performed using the conservative mixing ratio quantity. Forecast comparisons between mixing ratio and relative humidity methods show that the major differences occur in regions with large gradients. In some instances the numerical approximation of the mixing ratio conservation equation tends to produce slightly tighter gradients in regions with sharp changes. The tightness of the water vapor gradients directly influences the rainfall amounts. Consequently, rainfall maxima are slightly reduced with the relative humidity approach. Because these changes are very localized in the limited area forecasts used here, the differences in global verification statistics are small but favor the relative humidity approach. Verification statistics include dewpoint temperature, total precipitable water, and precipitation. For precipitation, forecast results are presented using 40-km and 80-km horizontal grid configurations. All other statistics use only the 80-km horizontal grid spacing.