Estimating scalar sources, sinks, and fluxes in a forest canopy using Lagrangian, Eulerian, and hybrid inverse models

A new method was developed to estimate canopy sources and sinks from measured mean concentration profiles within the canopy (referred to as the “inverse” problem). The proposed method combined many of the practical advantages of the Lagrangian localized near-field (LNF) theory and higher-order Eulerian (EUL) closure principles. Particularly, this “hybrid” method successfully combined the essential conservation equations of closure modeling and the robustness of the regression source inversion developed for LNF theory. The proposed method along with LNF and EUL were tested using measurements from two field experiments collected in a pine forest and published measurements from a wind tunnel experiment. The field experiments were conducted to investigate the vertical distribution of the scalar fluxes within the canopy and the temporal patterns of the scalar fluxes above the canopy. This comparison constitutes the first “inverse method” comparison performed using the same data sets on all three models. For the wind tunnel data, all three models well reproduced the measured flux distribution. For the field experiments, all three models recovered the measured spatial and temporal flux distribution in an ensemble sense. The agreement between these three models is desirable to the inverse problem because it adds the necessary confidence in the computed flux distributions. However, the agreement among all three models with the field measurements, on a 30-min time step, was less than satisfactory. Additionally, the divergence between models and measurements increased with departure from a nearneutral atmospheric state. Despite fundamental differences in these model approximations, this similarity in model performance suggests that the source information recovered from a measured one-dimensional mean concentration profile will not be further enhanced by a one-dimensional steady state, planar homogeneous model of neutral flows.