In this paper, we derived Analytical Kirchhoff Solutions (AKS) for bistatic scattering near the specular directions at P band and L band for applications in Signals of Opportunity (SoOp). The land surface profiles are divided into three scales: microwave roughness f 1 , fine scale topography f 2 , and coarse scale 30-meter DEM f 3 . The microwave roughness and the fine scale topography are treated as random rough surfaces, while the coarse scale topography from DEM data are treated as deterministic planar patches. The salient features of the AKS model are (i) analytical expressions are obtained for both coherent waves and incoherent waves, (ii) Monte Carlo simulations are not required making the AKS computationally efficient, (iii) the analytical solutions are expressed in terms of the spectrum, so that the dividing line between microwave roughness and fine scale topography is not required, and the rough surface spectrum derived from lidar elevation measurements can be incorporated directly. The results of the three approaches, AKS, the Numerical Kirchhoff Approach (NKA) and the Fine Scale Partial Coherent Patch (FPCP) model, are indistinguishable for both the coherent waves and the incoherent waves. The agreements validate the AKS and FPCP approaches as NKA is a brute force accurate method based on Kirchhoff integral using 2 cm discretization and high-performance computers. Results show that the f 2 profiles of fine scale topography have significant effects. The results of three Kirchhoff approaches fall in-between the results of the two versions of Geometric Optics (GO) approximations to the Kirchhoff integral [1,2]. The two GO versions are with and without attenuation due to microwave roughness. The GO with microwave attenuation is also known as the "Improved Geometric Optics Model (IGOM)". Numerical results of coherent waves and incoherent waves are illustrated for remote sensing of snow and soil moisture at P band and L band. For P band, the histograms of the phase are shown. Results of the coherent waves are dependent on the sizes of the area as well as topographical elevations and slopes. AKS results are used to illustrate the coherent waves at P band on area sizes up to 1.5 km using 30-meter DEM topography elevations and derived slopes at Sanford, Brazos Peak, and Lobato Tank, Colorado, USA. For L band, the AKS results of Cross-Track are in good agreement with CYGNSS data over San Luis Valley, USA. In comparing CPU, it takes merely 25 seconds on a single CPU core for AKS to compute for a 15 km by 15 km DDM pixel which has 250000 DEM 30-meter patches. The CPU for AKS is slightly more than the 20 seconds required for GO.
Abstract. Seasonal snow cover is the largest single component of
the cryosphere in areal extent, covering an average of 46 × 106 km2
of Earth's surface (31 % of the land area) each year, and is thus an
important expression and driver of the Earth's climate. In recent
years, Northern Hemisphere spring snow cover has been declining at about the
same rate (∼ −13 % per decade) as Arctic summer sea ice. More
than one-sixth of the world's population relies on seasonal snowpack and
glaciers for a water supply that is likely to decrease this century. Snow is
also a critical component of Earth's cold regions' ecosystems, in which
wildlife, vegetation, and snow are strongly interconnected. Snow water
equivalent (SWE) describes the quantity of water stored as snow on the land
surface and is of fundamental importance to water, energy, and geochemical
cycles. Quality global SWE estimates are lacking. Given the vast seasonal
extent combined with the spatially variable nature of snow distribution at
regional and local scales, surface observations are not able to provide
sufficient SWE information. Satellite observations presently cannot provide
SWE information at the spatial and temporal resolutions required to address
science and high-socio-economic-value applications such as water resource
management and streamflow forecasting. In this paper, we review the
potential contribution of X- and Ku-band synthetic aperture radar (SAR) for
global monitoring of SWE. SAR can image the surface during both day and
night regardless of cloud cover, allowing high-frequency revisit at high
spatial resolution as demonstrated by missions such as Sentinel-1. The
physical basis for estimating SWE from X- and Ku-band radar measurements at
local scales is volume scattering by millimeter-scale snow grains. Inference
of global snow properties from SAR requires an interdisciplinary approach
based on field observations of snow microstructure, physical snow modeling,
electromagnetic theory, and retrieval strategies over a range of scales. New
field measurement capabilities have enabled significant advances in
understanding snow microstructure such as grain size, density, and layering.
We describe radar interactions with snow-covered landscapes, the small but
rapidly growing number of field datasets used to evaluate retrieval
algorithms, the characterization of snowpack properties using radar
measurements, and the refinement of retrieval algorithms via synergy with
other microwave remote sensing approaches. This review serves to inform the
broader snow research, monitoring, and application communities on progress
made in recent decades and sets the stage for a new era in SWE
remote sensing from SAR measurements.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.