Differences Between the HUT Snow Emission Model and MEMLS and Their Effects on Brightness Temperature Simulation

Abstract

Microwave emission models are a critical component of snow water equivalent retrieval algorithms applied to passive microwave measurements. Several such emission models exist, but their differences need to be systematically compared. This paper compares the basic theories of two models: the multiple-layer Helsinki University of Technology (HUT) model and the microwave emission model of layered snowpacks (MEMLS). By comparing the mathematical formulation side by side, three major differences were identified: 1) by assuming that the scattered intensity is mostly (96%) in the forward direction, the HUT model simplifies the radiative transfer equation in $4\pi$ space into two one-flux equations, whereas MEMLS uses a two-flux theory; 2) the HUT scattering coefficient is much larger than the one of MEMLS; and 3) MEMLS considers the trapped radiation inside snow due to internal reflection by a six-flux model, which is not included in HUT. Simulation experiments indicate that the large scattering coefficient of the HUT model compensates for its large forward scattering ratio to some extent, but the effects of one-flux simplification and the trapped radiation still result in different $T_{B}$ simulations between the HUT model and MEMLS. The models were compared with observations of natural snow cover at Sodankyla, Finland; Churchill, Canada; and Colorado, USA. No optimization of the snow grain size was performed. It shows that the HUT model tends to underestimate $T_{B}$ for deep snow. MEMLS with the physically based improved Born approximation performed best among the models, with a bias of −1.4 K and a root-mean-square error of 11.0 K.