Some Practical Notes on the Parameter kB−1 for Sparse Vegetation

Abstract

This paper deals with the parameter kB?1, the logarithm of the ratio between momentum and heat roughness length, of sparsely vegetated surfaces and bare soil. The bare soil surface is included as a reference, since it is fairly homogenous and smooth, having no distinguishable roughness elements. The mean value of kB?1 is about 8 for the vineyard and 12 for the savannah. These values are significantly greater than kB?1 = 2, which is usually assumed to hold for vegetation. The mean value of kB?1 for bare soil is small and negative, which agrees with the literature. A large variation of kB?1 during the day is measured for all three surfaces. This behavior has been observed for sparse vegetation in previous studies. Some authors explained the phenomenon with a vertical movement of the source of heat through the day as solar angle varies, or with the use of an inappropriate value of effective surface temperature to calculate kB?1. For the first time, this diurnal variation is measured for a smooth surface, the bare soil, for which neither explanation is valid. A sensitivity study reveals that the calculated kB?1 is very sensitive to measuring errors in the micrometeorological variables and errors in the roughness length for momentum. This explains the large range in observed kB?1 values for one particular surface type. In addition, several semiempirical expressions for kB?1 from the literature are tested. Two well-established formulas, both based on a simple combination of Reynolds and Prandtl numbers, appear to produce the best estimates of daily averaged kB?1 values. None of the formulas are able to describe the diurnal variation. The authors conclude that the concept of kB?1 is questionable as it is based upon extrapolating a theoretical profile through a region where this profile does not hold, toward a ?surface temperature? that is difficult to define and to measure. It should therefore be avoided in meteorological models, for example, by applying canopy boundary layer resistances. Unfortunately, in remote sensing, the bulk transfer equations are up to now the only option, which therefore requires the use of kB?1.