Estimating a Lagrangian Length Scale using Measurements of Carbon Dioxide in a Corn and a Forest Canopy

Studies of trace gas fluxes have advanced the understanding of bulk interactions between the atmosphere and ecosystems. Micrometeorological instrumentation is currently unable to resolve vertical scalar sources and sinks within plant canopies. Inverted analytical Lagrangian equations provide a non-intrusive method to calculate source distributions. These equations are based on Taylor's (1921) equation for scalar dispersion, which requires a measure of the degree of correlation between turbulent motions, defined by the Lagrangian length scale (L_L). Inverse Lagrangian analyses can be unstable, and the uncertainty in L_L leads to uncertainty in source predictions.

The present study investigated L_L in plant canopies by using field measurements to constrain the Warland and Thurtell (2000) (WT2000) analytical Lagrangian equation. Measurements of two sources, the net and soil CO₂ fluxes, along with in-canopy profiles of CO₂ concentrations taken in a cornfield and a mixed forest near Toronto, Canada, provided the information required to solve for L_L in each location. This nonlinear system of equations is unstable and capable of producing an infinite number of solutions. A test of the optimization with wind tunnel data of turbulence statistics, a known heat source, and temperature profiles from Coppin et al. (1986) shows that the parameter estimation routine is capable of closely estimating the measured Eulerian length scale. The optimization with the cornfield data found a general Gaussian-shaped L_L profile for the majority of the summertime measurement intervals. Magnitudes of the optimized L_L varied across each half hour interval and did not scale with any measured statistic. This suggests that either (a), there are factors influencing the value of L_L that are unrelated to Eulerian measurements; or (b), other processes may be working to relate the sources and concentrations that are not captured by the WT2000 equations. Results from the optimization for the forest canopy were less clear than the corn canopy.