Boundary Layer Evolution in the Region Between Shore and Cloud Edge during Cold-Air Outbreaks

Abstract

Equations for the evolution of the atmospheric boundary layer during cold air outbreaks are examined and analytic solutions are obtained which apply to the region prior to cloud formation whenever the soundings of potential temperature and water vapor mixing ratio at the shore may be treated as linear. The solutions have non-dimensionalized boundary layer depth as the independent parameter. Layer depth, potential temperature, mixing ratio, dewpoint, lifting condensation level, distance from shore (fetch), net sensible heat input, and not latent heat input are found as explicit functions of a nondimensional mixed-layer height. A perturbation method is used to derive solutions when divergence is significant and is shown to be a good approximation for realistically strong divergences. The solution is implicit for the problem of finding the fetch at which clouds will form for given sea surface temperature and soundings at the shore but can readily be solved using numerical techniques. For cases in which divergence is negligible, cloud formation can be found using simple nomograms. A test example based on a cold air outbreak off New York is studied and it is shown that the prediction for cloud edge agrees well with satellite observations. Analysis of the solution indicates that the sensible and latent heat fluxes per unit travel can be modeled by transfer coefficients times the difference in virtual temperature of the air at the shore and the sea surface and by the mixing ratio difference between the air at the shore and the sea surface. Methods of using the solution in analysis of satellite observations are discussed.