Stochastic Models for Precipitable Water in Convection

Atmospheric precipitable water vapor (PWV) is the amount of water vapor in the atmosphere within a vertical column of unit cross-sectional area and is a critically important parameter of precipitation processes. However, accurate high-frequency and long-term observations of PWV in the sky were impossible until the availability of modern instruments such as radar. The United States Department of Energy (DOE)'s Atmospheric Radiation Measurement (ARM) Program facility made the first systematic and high-resolution observations of PWV at Darwin, Australia since 2002. At a resolution of 20 seconds, this time series allowed us to examine the volatility of PWV, including fractal behavior with dimension equal to 1.9, higher than the Brownian motion dimension of 1.5. Such strong fractal behavior calls for stochastic differential equation modeling in an attempt to address some of the difficulties of convective parameterization in various kinds of climate models, ranging from general circulation models (GCM) to weather research forecasting (WRF) models. This important observed data at high resolution can capture the fractal behavior of PWV and enables stochastic exploration into the next generation of climate models which considers scales from micrometers to thousands of kilometers. As a first step, this thesis explores a simple stochastic differential equation model of water mass balance for PWV and assesses accuracy, robustness, and sensitivity of the stochastic model. A 1000-day simulation allows for the determination of the best-fitting 25-day period as compared to data from the TWP-ICE field campaign conducted out of Darwin, Australia in early 2006. The observed data and this portion of the simulation had a correlation coefficient of 0.6513 and followed similar statistics and low-resolution temporal trends. Building on the point model foundation, a similar algorithm was applied to the National Center for Atmospheric Research (NCAR)'s existing single-column model as a test-of-concept for eventual inclusion in a general circulation model. The stochastic scheme was designed to be coupled with the deterministic single-column simulation by modifying results of the existing convective scheme (Zhang-McFarlane) and was able to produce a 20-second resolution time series that effectively simulated observed PWV, as measured by correlation coefficient (0.5510), fractal dimension (1.9), statistics, and visual examination of temporal trends.