Estimating statistical errors in retrievals of ice velocity and deformation parameters from satellite images and buoy arrays

The objective of this note is to provide the background and basic tools to estimate the statistical error of deformation parameters that are calculated from displacement fields retrieved from synthetic aperture radar (SAR) imagery or from location changes of position sensors in an array. We focus here specifically on sea ice drift and deformation. In the most general case, the uncertainties of divergence/convergence, shear, vorticity, and total deformation are dependent on errors in coordinate measurements, the size of the area and the time interval over which these parameters are determined, as well as the velocity gradients within the boundary of the area. If displacements are calculated from sequences of SAR images, a tracking error also has to be considered. Timing errors in position readings are usually very small and can be neglected. We give examples for magnitudes of position and timing errors typical for buoys and SAR sensors, in the latter case supplemented by magnitudes of the tracking error, and apply the derived equations on geometric shapes frequently used for deriving deformation from SAR images and buoy arrays. Our case studies show that the size of the area and the time interval for calculating deformation parameters have to be chosen within certain limits to make sure that the uncertainties are smaller than the magnitude of deformation parameters.