A Cramer-Rao bound on acoustic measurement of ocean climate change in the presence of mesoscale sound-speed variability

The ability to measure climate-related mean changes in ocean temperature is fundamentally limited by the presence of mesoscale variability. In the paper, the Cramer-Rao lower bound on the estimation of the mean depth-dependent temperature profile is evaluated to determine the highest accuracy which could be achieved by acoustic thermometry of ocean climate (ATOC). Evaluation of the bound is performed using a model of sound-speed variability derived from real Pacific ocean environmental data. Results indicate that a low-order Chebyshev polynomial may be a good choice for climate signal representation. The general behavior the bound is determined by a subtle interaction between the climate signal basis, a priori mesoscale noise statistics, and observation-time-bandwidth-signal-to-noise ratio product