A PHYSICAL-NUMERICAL MODEL FOR THE PREDICTION OF SYNOPTIC-SCALE LOW CLOUDINESS

Abstract

A system of equations governing the behavior of a physical model of the atmospheric, planetary boundary layer was formulated for solution on a digital computer. The physical-numerical model was designed to permit the investigation of the significance of certain boundary-layer processes for the development of horizontally extensive areas of low cloudiness. Numerical solutions of the equations were computed for three synoptic cases. In each case, the forecast period was 12 hr. The initial state of the atmosphere was analyzed from synoptic surface and upper-air observations in the eastern United States. The computations were made for a finite difference grid with 1200 grid points, using a 15-min. time step. The vertical coordinate was defined by 12 grid points over each of 100 grid points in the horizontal plane. The average spacing of the horizontal grid points was 160 km. The separation of the vertical grid points expanded from 50 m. near the ground to 450 m. at the uppermost level. The model boundary layer was subdivided into a 50-m. deep, surface contact layer and a 1950-m. deep, transition layer. Stability-dependent, constant-flux profile formulas were applied within the surface contact layer. These were used in conjunction with semi-empirical formulas to derive boundary conditions applicable at the base of the transition layer. Observed data were used to prescribe the horizontal pressure gradient force at the upper boundary of the transition layer. Within the transition layer the horizontal wind was computed by means of a diagnostic equation implying a balance of the Coriolis, pressure gradient, and eddy viscous forces. The eddy viscosity coefficient was held equal to its value at the top of the surface contact layer. The pressure gradient force was assumed to be a linear function of height; its variation was computed from the predicted temperature field. The eddy conductivity and diffusivity coefficients were assumed to be equal. They were computed as functions of the stability. The results obtained in one of the synoptic case studies is presented in some detail. Certain statistics are presented for all three cases studied. It is concluded that, despite certain deficiencies, the model seems capable of improving the accuracy of low-cloud predictions for data-dense regions. It is also suggested that the model may have diagnostic and predictive utility for other applications which require a knowledge of the structure of the atmosphere within the planetary boundary layer.