## Abstract

A simple formula for computation of the effective roughness length *z*_{0Heff} for heat transfer or rather for the parameter *kB*^{−1}_{eff}*z*_{0Meff}/*z*_{0Heff}) with *z*_{0Meff} = roughness length for momentum], which are needed in single-source models for evaluating sensible heat fluxes, is derived. This formula allows the calculation of *z*_{0Heff} 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 *σ*_{f} 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 *D*_{f}. The influence of stand geometry can be taken into consideration by providing the effective roughness length for momentum *z*_{0Meff} (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 *z*_{0Heff}. After definition of effective roughness lengths for momentum *z*_{0Meff} and for heat *z*_{0Heff} by a single-source model (bulk transfer equations), these quantities as well as *kB*^{−1}_{eff}*kB*^{−1}_{eff}

The desired simple estimation formula for *kB*^{−1}_{eff}

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*^{−1}_{eff}

*Corresponding author address:* Klaus Blümel, Institut für Meteorologie der Freien Universität Berlin, Carl-Heinrich-Becker-Weg 6-10, 12165 Berlin, Germany.