A Simple Formula for Estimation of the Roughness Length for Heat Transfer over Partly Vegetated Surfaces

A simple formula for computation of the effective roughness length z0Heff for heat transfer or rather for the parameter kB−1eff [=ln(z0Meff/z0Heff) with z0Meff = roughness length for momentum], which are needed in single-source models for evaluating sensible heat fluxes, is derived. This formula allows the calculation of z0Heff over (bluff–rough) bare soil, dense vegetation, and for surfaces that are only partly covered by vegetation. In addition to the wind speed only a minimum of information about the considered surface must be known as input information: the horizontal fraction (covering) of vegetation σf and the mean vegetation height. The reliability of the formula can be improved further if there are proper estimates for the leaf stem area index and for the characteristic leaf size Df. The influence of stand geometry can be taken into consideration by providing the effective roughness length for momentum z0Meff (e.g., from measurements). First, a quite simple triple-source transfer model is developed that allows the computation of the total sensible heat flux and of the total momentum flux without knowledge of z0Heff. After definition of effective roughness lengths for momentum z0Meff and for heat z0Heff by a single-source model (bulk transfer equations), these quantities as well as kB−1eff can be derived using these simulated fluxes. Selected simulations for different scenarios show the dependence of kB−1eff on the fraction of vegetation and other parameters. The desired simple estimation formula for kB−1eff is found by adjustment to the above-mentioned simulations and by theoretical determination of the boundary values (bare soil and complete vegetation covering). This formula is verified successfully by means of data sampled at different field campaigns over various surface types and is compared to various semiempirical parameterizations of kB−1eff, which have been presented in the literature.