Displacement Heights Research Articles

An Error Analysis of the Thornthwaite-Holzman Equations for Estimating Sensible and Latent Heat Fluxes over Crop and Forest Canopies

Abstract Computations of sensible and latent heat fluxes over forest and crop canopies using the Thornthwaite-Holzman equations require an a priori knowledge of roughness and data displacement heights. If the values of these parameters are not representative of the wind structure above the canopy, then errors will be induced in the heat flux calculations. A detailed error transfer analysis is derived and tested against tower data taken in a tropical dry ever-green forest in Thailand. It is shown that significant errors may occur in heat flux computations if mean values of roughness parameter and datum displacement height are used during periods of significant variation of those parameters. Further, the sensitivity of a heat flux calculation to the discrepancy in the profile parameters used may be either suppressed or amplified. A simple model is derived to estimate this error transfer from estimates of the mean values and variances of the roughness parameter and data displacement height.

Comments on “Turbulent Exchange Coefficients for Sensible Heat and Water Vapor under Advective Conditions”

The convincing evidence of Verma et al. that K/sub H/ does not equal K/sub W/ in conditions when H and LE are of opposite sign is not necessarily in conflict with the predictions of conventional flux-gradient relations, particularly when the gradient measurements are made very close to the canopy. Almost all the extensive flux-gradient investigations of the past 20 years have been conducted over relatively short, often sparse, vegetation. Before formulations derived from such circumstances can be extended to the case of deeper canopies, it must be assured that the zero-plane displacement heights are known to sufficient accuracy. Citing other studies the authors state that the suggestion that different zero planes might be appropriate to the cases of temperature and humidity profiles is fairly clear. The heights of observations listed in the data of Verma indicate that in their particular experiment zero-plane displacement inequalities might explain part of the observed differences between K/sub H/ and K/sub W/. On analysis of Verma's data for k/sub H//K/sub W/, the authors conclude that part of the observed difference between K/sub H/ and K/sub W/ might have been done to this effect. The authors also point out that attempts to relate K/sub H//K/sub W/more » to ..delta..T/..delta..e and LE/(R/sub n/ + S) are likely to be quite misleading. To illustrate this point, a surrogate data set was constructed from random numbers to provide values simulating ..delta..T/..delta..e ranging from -0.15 to -0.85 and uncorrelated values of LE/(R/sub n/ + S) ranging from -1.2 to -2.4. The data were treated in the same manner used by Verma. These values are then compared to those reported by Verman et al.« less