Determination of Sea Ice Thickness from Angular and Frequency Correlation Functions and by Genetic Algorithm: A Theoretical Study of New Instrument Technology

Thickness and extent of Arctic sea ice play a critical role in Earth's climate and ocean circulation. An accurate measurement of these parameters on synoptic scales at regular intervals would enable characterization of this important component for the understanding of ocean circulation and global heat balance. Currently, IceSAT (laser altimeter) and EnviSAT (radar altimeter) and the upcoming CryoSAT (radar altimeter) measurement systems provide estimates of the sea ice freeboard, i.e. that portion of the ice that is above the sea level. The sea ice thickness and changes in thickness are inferred from these measurements. In this paper, we develop the theoretical basis for application of radar interferometry in the VHF band to the direct estimation of sea ice thickness. We employ angular and frequency correlation functions (ACF/FCF) of the electromagnetic wave scattered from sea-ice, using small perturbation and Kirchhoff rough surface scattering and Rayleigh volume scattering models. The medium is modeled as multi-layered stratification consisting of snow, sea ice (including spherical particles of air bubbles and brine inclusions), and sea water. Each surface interface is modeled as a rough surface with a Gaussian roughness spectrum. To characterize the ACF/FCF, the correlation between two waves with different frequencies, incidence and observation angles, is employed, forming a combined spatial- and frequency-domain interferometer. This technique exploits the difference in the correlation properties (phase matching conditions) of surface and volume scattering. The surface correlation function exhibits a strong correlation along a "memory line." The volume scattering shows a strong correlation at specific points - "memory dots." The effect of volume scattering can be suppressed by choosing appropriate combinations of frequencies and angles. The phase of the surface correlation function depends on the scattering geometry (location of the antennas), and provides information about the thickness of the layers. However, the amplitude of the surface ACF/FCF is impacted by the surface roughness characteristics, and reliable ACF/FCF phase information is obtained when its amplitude is sufficiently above the instrument system noise level. Using this aforementioned model, we were able to estimate the sea ice thickness, h, from ACF/FCF. We apply a Genetic Algorithm (GA) to the estimation. The GA method is developed to maximize a fitness function exp(Pm(h)-P(h))2 where P(h) is the phase of ACF/FCF calculated from forward model, and Pm(h) is the measured phase of ACF/FCF- in this case the phase is obtained from simulated forward data using this model. These results show that the sea ice thickness retrieval can be done by the ACF/FCF method. We are currently developing this new instrument technology under the NASA/ESTO instrument incubator program (IIP). We are planning on an Arctic sea ice field experiment from an aircraft in March-April 2005 to validate and improve the inversion model.