Boundary-Layer Meteorology

, Volume 147, Issue 1, pp 83–102 | Cite as

Estimating a Lagrangian Length Scale Using Measurements of CO2 in a Plant Canopy

  • Shannon E. Brown
  • Jon S. Warland
  • Eduardo A. Santos
  • Claudia Wagner-Riddle
  • Ralf Staebler
  • Meaghan Wilton


Analytical Lagrangian equations capable of predicting concentration profiles from known source distributions offer the opportunity to calculate source/sink distributions through inverted forms of these equations. Inverse analytical Lagrangian equations provide a practical means of estimating source profiles using concentration and turbulence measurements. Uncertainty concerning estimates of the essentially immeasurable Lagrangian length scale (\({\mathcal{L}}\)), a key input, impedes the operational practicality of this method. The present study evaluates \({\mathcal{L}}\) within a corn canopy by using field measurements to constrain an analytical Lagrangian equation. Measurements of net CO2 flux, soil-to-atmosphere CO2 flux, and in-canopy profiles of CO2 concentration provided the information required to solve for \({\mathcal{L}}\) in a global optimization algorithm for 30-min time intervals. For days when the canopy was a strong CO2 sink, the optimization frequently located \({\mathcal{L}}\) profiles that follow a convex shape. A constrained optimization then fit the profile shape to a smooth sigmoidal equation. Inputting the optimized \({\mathcal{L}}\) profiles in the forward and inverse Lagrangian equations leads to strong correlations between measured and calculated concentrations and fluxes. Coefficients of the sigmoidal equation were specific to each 30-min period and did not scale with any measured variable. Plausible looking \({\mathcal{L}}\) profiles were associated with negative bulk Richardson number values. Once the canopy senesced, a simple eddy diffusivity profile sufficed to relate concentrations and sources in the analytical Lagrangian equations.


Canopy turbulence Lagrangian analysis Lagrangian length scale Micrometeorology 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Shannon E. Brown
    • 1
  • Jon S. Warland
    • 1
  • Eduardo A. Santos
    • 2
  • Claudia Wagner-Riddle
    • 1
  • Ralf Staebler
    • 3
  • Meaghan Wilton
    • 4
  1. 1.School of Environmental Sciences, University of GuelphGuelphCanada
  2. 2.Department of Agronomy, Kansas State UniversityManhattanUSA
  3. 3.Climate Research DivisionEnvironment CanadaTorontoCanada
  4. 4.University of WaterlooWaterlooCanada

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