Bill Kuperman and the coupled mode parabolic equation

I worked with Bill Kuperman as his first postdoc in the fall of 1993, after he joined the Scripps Institution of Oceanography as director of the Marine Physical Laboratory earlier that summer. I had just completed my Ph.D. at the physics department at UCSD. Bill’s first task for me was to develop a 3D propagation model using normal modes. The resulting model was a modification of the adiabatic parabolic equation, which Bill aptly named the Coupled Mode Parabolic Equation (CMPE). The solution consists of normal modes and modal coefficients that satisfy the coupled horizontal wave equation. The CMPE is an energy conserving model and can be solved efficiently using the operator splitting method. This work led to the publication of [Abawi, Kuperman and Collins, “The coupled mode parabolic equation,” JASA, 102 (1), July 1997]. In this presentation, the CMPE solution is outlined and compared to solutions obtained using more modern techniques. While this work has inspired numerous other studies, it represents only a small fraction of Bill Kuperman’s vast contributions to underwater acoustics and his enduring legacy. Bill was a mentor and a close friend, who is largely responsible for my chosen career path.