Angular and frequency correlation for sea-ice thickness retrieval

A combined spatial and frequency domain interferometer or angular and frequency correlation (ACF/FCF) between two radar beams in the VHF-band is applied for the direct measurement of sea-ice thickness. This measurement is critical because the thickness of sea ice within the polar region indicates the state of ocean circulation and the associated air-sea heat exchange, which profoundly affects the global heat balance and ocean thermohaline circulation. This new instrument technology - cryospheric advanced sensor (CAS) - can measure sea-ice thickness, tilling a critical gap in measuring the polar region. In this paper, we present the algorithm development and demonstration by simulations of estimating the height of the sea-ice that led to the robust design of CAS interferometric system. Sea-ice thickness is derived from the interferometric phase of the ACF/FCF function of two VHF-band-scattered returns of two radar waves that have different frequencies, incident angles, and observation angles. The inversion calculation to estimate the ice thickness is based on several methods, gradient-descent (GD). least-square (LSQ) method, and genetic algorithm (GA). Compared with a GD method, and LSQ method, GA does not require the knowledge of the derivative of the ACF/FCF function. Good agreement is shown with GD and LSQ results, when a single unknown variable - sea-ice thickness - is to be determined. To support the inversion calculations and analysis, we developed an analytical model. The analytical model used to formulate the ACF/FCF function depends on the age of the ice being measured. The analytical model for first-year ice is based on the small perturbation method (presented here) and, for multiyear ice, the Kirchhoff approximation (presented in accompanying paper by the authors).