Parameterization of Joint Frequency Distributions of Potential Temperature and Water Vapor Mixing Ratio in the Daytime Convective Boundary Layer

Abstract

Joint frequency distributions (JFDs) of potential temperature (?) versus water vapor mixing ratio (r) within the convective boundary layer were measured during a new field experiment named Boundary Layer Experiment 1996 (BLX96). These JFDs were found to be tilted, with the tilt a function of both height and boundary layer dynamics. These distributions are also skewed and more peaked than a joint Gaussian distribution. Three different methods are used to generate joint probability density functions (JPDFs) that approximate observed JFDs. Two classical methods, one based on a Gaussian fit and another based on surface-layer processes, are reviewed. A new method is devised, which treats the observed JFD as a mixing diagram. In the absence of advection, the only source regions for air in the mixing diagram are the surface and the entrainment zone. Thus, the tilt of the JFD can be explained by various mixtures from these two source regions. Methods that can be used to parameterize the mixing JPDF are presented. The primary advantage of this method is that the tilt is determined explicitly from properties of the surface, mixed layer, and entrainment zone. Similarity methods are used to parameterize all variables needed by the Gaussian model. The Bowen ratio and the total energy input are used to parameterize the tilt of the surface energy budget JPDF, while similarity methods are used to define the spread of the JPDF along the two axes. Relationships between the surface and mixed layer, and the mixed layer and free atmosphere are used to tilt the mixing diagram JPDF, while similarity methods are used to estimate the spread of the JPDF. The parameterizations are developed using a ?calibration? subset of data acquired during BLX96. A ?verification? subset of data, also acquired during BLX96, is used to show that the parameterized mixing diagram method is superior to the other two methods, because it has either a smaller error or is less sensitive to the value of the correlation between ? and r.