An analysis and implications of alternative methods of deriving the density (WPL) terms for eddy covariance flux measurements

We explore some of the underlying assumptions used to derive the density or WPL terms (Webb et al. (1980) Quart J Roy Meteorol Soc 106:85-100) required for estimating the surface exchange fluxes by eddy covariance. As part of this effort we recast the origin of the density terms as an assumption regarding the density fluctuations rather than as a (dry air) flux assumption. This new approach, which is similar to the expansion/compression approach of Liu (Boundary-Layer Meteorol 115:151-168, 2005), eliminates the dry-air mean advective vertical velocity from the development of the WPL terms and allows us to directly compare Liu's assumptions for deriving the WPL terms with the analogous assumptions appropriate to the original expression of the WPL terms. We suggest, (i) that the main difference between these two approaches lies in the interpretation of the turbulent exchange flux, and (ii) that the original WPL formulation is the more appropriate approach. Given the importance of the WPL terms to accurate and reliable measurements of surface exchange fluxes, a careful analysis of their origins and their proper mathematical expression and interpretation is warranted.