A Retrieval Algorithm of Vegetation Water Content and Soil Surface Emissivity - Theory and Application of Maximum Entropy Production (MEP) Method

A new method based on the theory of maximum entropy production (MEP) is developed for simultaneous retrieval of vegetation water content (VWC) and soil surface emissivity using L-band microwave brightness temperature data. The MEP principle asserts that a non-equilibrium thermodynamic system corresponds to the state of fluxes determined by the minimization of a dissipation function under the constraint of energy conservation. The dissipation function for radiative transfer through canopy is formulated in terms of radiation fluxes as an analogy of thermal dissipation function. Two new physical parameters, "radiation inertia" and "radiative diffusivity", are introduced to characterize the conversion of radiation energy into thermal energy. The penetration depth is inversely proportional to refractive index of the medium as a function of both real and imaginary part of complex dielectric constant. The L-band radiation received by microwave radiometer represented by brightness temperature comes from canopy and soil dominated by vegetation water content and surface soil moisture under the canopy. The total radiation energy proportional brightness temperature is related to canopy transmissivity and surface soil emissivity according to the tau-omega model of radiative transfer through canopy as a representation of energy conservation. Minimizing the dissipation function under the constraint of the tau-omega model leads to an analytical solution of canopy transmissivity and soil surface emissivity. The MEP algorithm is tested using the data SMAP L-band brightness temperature observations complemented by in situ data of canopy and soil surface temperature. The MEP based estimates of VWC, derived from the canopy transmissivity, is consistent with previously reported studies on biomass for the Amazon basin. Surface soil moisture derived from the SMAP algorithm using the MEP retrieved soil surface emissivity has much reduced (~90%) bias compared with the field measurements in the Amazon. The algorithm allows microwave radiometer to "see through" thick canopy of VWC up to 100 kg m-2. The MEP algorithm does not need ancillary data of vegetation transmissivity, surface roughness, etc. currently used in the SMAP soil moisture retrieval algorithms.