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A Perspective on Thirty Years of the Webb, Pearman and Leuning Density Corrections

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Abstract

The density correction theory of Webb et al. (1980, Q J Roy Meteorol Soc 106: 85–100, hereafter WPL) is a principle underpinning the experimental investigation of surface fluxes of energy and masses in the atmospheric boundary layer. It has a long-lasting influence in boundary-layer meteorology and micrometeorology, and the year 2010 marks the 30th anniversary of the publication of the WPL theory. We provide here a critique of the theory and review the research it has spurred over the last 30 years. In the authors’ opinion, the assumption of zero air source at the surface is a fundamental novelty that gives the WPL theory its enduring vitality. Considerations of mass conservation show that, in a non-steady state, the WPL mean vertical velocity and the thermal expansion velocity are two distinctly different quantities of the flow. Furthermore, the integrated flux will suffer a systematic bias if the expansion velocity is omitted or if the storage term is computed from time changes in the CO2 density. A discussion is provided on recent efforts to address several important practical issues omitted by the original theory, including pressure correction, unintentional alternation of the sampled air, and error propagation. These refinement efforts are motivated by the need for an unbiased assessment of the annual carbon budget in terrestrial ecosystems in the global eddy flux network (FluxNet).

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Abbreviations

T :

Temperature

p :

Atmospheric pressure

S :

Source term

W :

Total mean vertical velocity

z :

Measurement height

χ :

Molar mixing ratio

μ :

Ratio of molecular mass relative to dry air

ω :

Mass mixing ratio

ρ :

Mass density

ϱ :

Molar density

a :

Moist air

c :

CO2

d :

Dry air or density term

o :

Oxygen

v :

Water vapour

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  1. School of Forestry and Environmental Studies, Yale University, 21 Sachem Street, New Haven, CT, 06511, USA

    Xuhui Lee

  2. USDA Forest Service, Rocky Mountain Research Station, Fort Collins, CO, USA

    William J. Massman

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  1. Xuhui Lee
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Lee, X., Massman, W.J. A Perspective on Thirty Years of the Webb, Pearman and Leuning Density Corrections. Boundary-Layer Meteorol 139, 37–59 (2011). https://doi.org/10.1007/s10546-010-9575-z

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