Inversion Method for Evapotranspiration from 2D Measurements of Water Vapor Concentration

A method has been developed to use 2D measurements of water vapor concentration to make spatial estimates of evapotranspiration. The method is based on theoretical solutions to the conservation of water vapor equation (similar to Sutton, Sienfeld) and is related to methods used to generate footprints. The method uses a diffusion coefficient to close the conservation equation and assumes uniformity of the surface with respect to turbulent processes. This solution allows the development of a transfer coefficient between each location at the surface and each of the water vapor measurements. The problem has been constrained to two dimensions for development, but is easily expanded to three. The method assumes water vapor concentration measurements in a plane at arbitrary positions above the field. Evapotranspiration is allowed to vary in increments across the field. This geometry and the transfer coefficients allow the water vapor concentration at each of the measured locations to be expressed as the sum of the contributions from the entire surface. A least squares solution is found that estimates the evapotranspiration across the field as a function of position. To evaluate the accuracy of the approach in solving for evaporation rates two artificial data sets of water vapor concentration (with varying amounts of artificial noise added) for known evaporation rates were generated and used to estimate the surface evaporation. The method is sensitive to the assumptions made near the edges of field. Results and details of the methods used to resolve edge effects will be shown.