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

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.