A re-evaluation of long-term flux measurement techniques - Part I: Averaging and coordinate rotation

Experience of long term flux measurements over tall canopies during the last two decades has revealed that the eddy flux of sensible plus latent heat is typically 30% smaller than the available radiant energy flux. This failure to close the energy balance is less common close to the surface over short roughness but is still sometimes seen, especially in complex topography. These observations cast doubt on the results obtained from long term flux studies where daily and annual net ecosystem exchange is usually the small difference between large positive and negative fluxes over 24 h. In this paper we investigate this problem by examining some fundamental assumptions entailed in analysis of surface exchange by the eddy flux method. In particular, we clarify the form and use of the scalar conservation equation that underlies this analysis and we examine the links between averaging period and rotation of coordinates in the situation where coordinates are aligned with the wind vector. We show that rotating coordinates so that the x axis is aligned with the mean wind vector has the effect of high pass filtering the scalar covariance, (wc) over bar, such that contributions to the aerodynamic flux from atmospheric motions with periods longer than the averaging period are lost while those of shorter period are distorted. We compare the effect of computing surface exchange by averaging many short periods, in each of which the coordinates are rotated so that the mean vertical velocity is zero ( the method currently adopted in most long-term flux studies), with analysis in long-term coordinates and show a systematic underestimation of surface exchange in the former case. This is illustrated with data from three long-term forest field sites where underestimations of sensible and latent heat fluxes of 10-15% averaged over many days are seen. Crucial factors determining the loss of flux are the averaging period T, the measurement height and the content of the scalar cospectrum at periods longer than T. The properties of this cospectrum over tall canopies in both homogeneous and complex terrain are illustrated by measurements at our three sites and we see that over tall canopies on flat ground in convective conditions, or on hilly sites in near neutral flow, the scalar cospectra have much more low frequency content than classical surface-layer spectral forms would predict. We believe that the filtering of this low frequency covariance by the averaging-rotation operations in common use is a large contributory factor to the failure to close the energy balance over tall canopies.