### Quantifying ocean acoustic environmental sensitivity

#### Abstract

Linear, linearized, and nonlinear measures of environmental sensitivity for ocean acoustic propagation that accounts for realistic uncertainties in various environmental parameters are examined. The implicit assumption of a linear relationship between parameter sensitivity and parameter uncertainty is examined by comparing the three sensitivity measures over a range of parameter uncertainties about the actual assumed environmental uncertainty. The interpretation of sensitivity is well defined for linear problems such as ocean acoustic propagation. Mathematical equations represent how the uncertainties transfer from parameter to data for a linear problem and the ratio of the standard deviation of the specified datum to its expected value. The ocean sound speed profile (SSP) uncertainty is taken to represent oceanographic variability due to surface heating/cooling and wind mixing, with the effects decaying exponentially with depth over the top 30 meter.

#### Keywords

Acoustic waves; Environmental impact; Nonlinear systems; Oceanography; Parameter estimation; Sensitivity analysis; Environmental uncertainty; Mathematical equations; Nonlinear measures

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