How universal is the C function in the bulk atmospheric boundary layer similarity approach for estimating surface sensible heat flux?

The C function which appears in the formulation for the bulk atmospheric boundary layer similarity (BAS) approach estimating sensible heat flux (H) at the surface under unstable stability conditions was examined to investigate its universality and whether or not it is a function of atmospheric stability alone, using data sets obtained from five large-scale experiments that took place in diverse geographical locations with different surface covers and climate conditions (ranging from the tropics to the boreal zone). Coefficients in several forms of the C function, first assumed as a function of the stability alone, were calibrated against these data sets to maximize the agreement between H values derived from the BAS and those reference values independently determined. The agreement of H values for this calibration, for all data sets except one, was excellent, with a root-mean-square error on the order of 20 W m(-2) under the condition that the exact values of surface scalar roughness and atmospheric stability were known. The findings indicate that the C function is a function of stability only and is universal within this accuracy level. Inclusion of another possible parameter, the ratio of the rotational height scale and the actual depth of the mixed layer, did not improve the results. A selection of different scaling for surface layer height did not produce better results, either. Practical limitations of the BAS approach were also investigated by considering one site that did not yield satisfactory results. Using an error propagation analysis, it was determined that this finding was mainly caused by weak surface heating in this area under near neutral conditions and that the difference between the potential temperature at the surface and that in the mixed layer was too small to be used beyond the measurement error limit in the BAS approach. The need for a method to estimate surface scalar roughness was also identified as the largest remaining problem in the BAS approach used for actual flux estimations.