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A formalism exists for estimating the intensity recorded by a sonar system due to scattering from a ocean plume of suspended, nonspherical scatterers in the Rayleigh region. In this paper, we extend this framework to include the possibility that the plume is located near a planar ocean boundary. Using the theory of isoperimetric inequalities, bounds are obtained for the magnitude of the scattering amplitude that are independent of shape and the aspect of the individual plume constituents. Two examples are considered to illustrate the application of the analysis: scattering from the particulates that comprise black smoker hydrothermal plumes and scattering from bubbles.