Impact and Correction of Sea Ice, Snow, and Seawater Density on Arctic Sea-Ice Thickness Retrieval From Ku-Band SAR Altimeters

Abstract

Satellite radar altimeters (RAs) can measure sea-ice thickness on a large scale. According to the assumption of isostatic equilibrium, knowing the density of water, snow, and ice is crucial to estimating the thickness of sea ice from altimeters. Therefore, using inaccurate density values to estimate sea-ice thickness from RAs will lead to unreliable results. This article proposes a method to evaluate and correct density ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho $ </tex-math></inline-formula> ) ratios, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{w}/{(}\rho _{w}-\rho _{i}{)}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{s}/{(}\rho _{w}-\rho _{i}{)}$ </tex-math></inline-formula> , where subscripts <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${i}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${w}$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${s}$ </tex-math></inline-formula> represent sea ice, water, and snow, respectively, by using sea ice freeboard of CryoSat-2 (CS-2) and Sentinel-3A (S3), Operational IceBridge ice thickness, and modified climatological snow depth data. In addition to comparing the calculated density ratio (DR) with the DR commonly used in the previous studies, we also investigate how input density parameters affect the accuracy of freeboard-to-thickness conversion of the satellite RA. Our results indicate that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{i}$ </tex-math></inline-formula> of first-year ice (FYI) region used by the ESA sea ice climate change initiative product (ESA SICCI) is generally large, whereas <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{s}$ </tex-math></inline-formula> is significantly small. For a more accurate inversion of Arctic sea-ice thickness, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{w}/{(}\rho _{w}-\rho _{i}{)} = 9.01$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{s}/{(}\rho _{w}-\rho _{i}{)} = 3.52$ </tex-math></inline-formula> can be used for FYI, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{w}/{(}\rho _{w}-\rho _{i}{)} = 7.20$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{s}/(\rho _{w}-\rho _{i}) =2.30$ </tex-math></inline-formula> can be used for multiyear ice (MYI) region. Because <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{w}$ </tex-math></inline-formula> is relatively stable and easy to observe, the proposed method also can be used to invert sea ice density <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{i}$ </tex-math></inline-formula> and snow layer density <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho _{s}$ </tex-math></inline-formula> from estimated DRs.