Parameter estimation in surface exchange models using nonlinear inversion: how many parameters can we estimate and which measurements are most useful?

Models of mass and energy exchanges between the biosphere and the atmosphere generally contain a nonlinear dependence between fluxes and model parameters, and thus estimation of these parameters from measurements in a heterogeneous landscape depends on the scale of the observations. The scale‐dependence of a typical surface‐exchange model (the CSIRO Biospheric Model, CBM) is examined using the diurnal variation of hourly fluxes of CO₂, latent heat, sensible heat and soil heat. The fluxes were measured using micrometeorological techniques over six sites in a grazing/pasture system in SE Australia during a period of three weeks in 1995. Nonlinear parameter inversion was used to determine model parameters. Analysis of the covariance of the estimates of the parameters and the unexplained residuals of the model showed that a maximum of three or four parameters could be determined independently from the observations for all six sites. Estimates of a key model parameter, j_max, the mean of maximum potential electron transport rate of all leaves within the canopy, was best determined by the measurements of net CO₂ flux at all sites examined. Measurements of ground heat flux provide little information about any of the model parameters in CBM. Because of nonlinearities in the surface exchange model, calculated fluxes will be in error if parameters for the component vegetation types are simply averaged in proportion to their areal fraction. The magnitude of these errors was examined for CBM using a hypothetical land surface consisting of two surface types, each with different parameter values. Predictions of net CO₂, latent heat and ground heat fluxes using a linear combination of model parameters for the two surface types were quite similar with those found using optimal estimates of the parameters for the landscape, but were significantly poorer for sensible heat fluxes.