The Impact of System Distortions and Noise on HV Backscatter and Its Relevance to Above-Ground Biomass Estimation from Spaceborne P-Band SAR Data

This article analyses the effects of system distortions (crosstalk and channel imbalance), Faraday rotation and system noise on estimates of the cross-polarized backscattering coefficient, ${\boldsymbol{\sigma }}_{{{\bf hv}}}^0$ , by a spaceborne synthetic aperture radar. Modeling the unknown system errors and noise by a joint complex Gaussian distribution allows analytic first-order approximations to the mean and variance of the error in ${\boldsymbol{\sigma }}_{{{\bf hv}}}^0$ to be derived that do not depend on the SAR operating frequency. Simulation shows these approximations to be very accurate, given the statistical model and the expected magnitudes of system errors and noise for the P-band instrument to be carried by the European Space Agency BIOMASS mission. Simulation further shows that the ${\boldsymbol{\sigma }}_{{{\bf hv}}}^0$ errors are Gaussian distributed, so their exceedance probabilities can be calculated from just the analytic expressions for the mean and variance of the errors. Exceedance probabilities for above-ground biomass (AGB) can then be calculated under a power law relation between ${\boldsymbol{\sigma }}_{{{\bf hv}}}^0{{\rm{\sigma }}_{{\rm{hv}}}}$ and AGB that is consistent with P-band observations. This allows tradeoff curves between crosstalk and channel imbalance (shown to be segments of hyperbolas) to be calculated, along which the relative error in AGB is within a given percentage of its true value, from which limits on the permissible size of the errors can be determined if BIOMASS mission requirements are to be met.