Articles | Volume 9, issue 6
The Cryosphere, 9, 2101–2117, 2015
The Cryosphere, 9, 2101–2117, 2015

Research article 16 Nov 2015

Research article | 16 Nov 2015

Microwave scattering coefficient of snow in MEMLS and DMRT-ML revisited: the relevance of sticky hard spheres and tomography-based estimates of stickiness

H. Löwe1 and G. Picard2,3 H. Löwe and G. Picard
  • 1WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland
  • 2University Grenoble Alpes, LGGE UMR5183, 38041 Grenoble, France
  • 3CNRS, LGGE UMR5183, 38041 Grenoble, France

Abstract. The description of snow microstructure in microwave models is often simplified to facilitate electromagnetic calculations. Within dense media radiative transfer (DMRT), the microstructure is commonly described by sticky hard spheres (SHS). An objective mapping of real snow onto SHS is however missing which prevents measured input parameters from being used for DMRT. In contrast, the microwave emission model of layered snowpacks (MEMLS) employs a conceptually different approach, based on the two-point correlation function which is accessible by tomography. Here we show the equivalence of both electromagnetic approaches by reformulating their microstructural models in a common framework. Using analytical results for the two-point correlation function of hard spheres, we show that the scattering coefficient in both models only differs by a factor which is close to unity, weakly dependent on ice volume fraction and independent of other microstructural details. Additionally, our analysis provides an objective retrieval method for the SHS parameters (diameter and stickiness) from tomography images. For a comprehensive data set we demonstrate the variability of stickiness and compare the SHS diameter to the optical equivalent diameter. Our results confirm the necessity of a large grain-size scaling when relating both diameters in the non-sticky case, as previously suggested by several authors.

Short summary
The paper establishes a theoretical link between two widely used microwave models for snow. The scattering formulations from both models are unified by reformulating their microstructure models in a common framework. The results show that the scattering formulations can be considered equivalent, if exactly the same microstructure model is used. The paper also provides a method to measure a hitherto unknown input parameter for the microwave models from tomography images of snow.