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Gregory J. Hakim

, which is simply the inversion operator, 𝗟 = 𝗛 −1 . This means that state variables are constrained by linear regression onto the control variables. 3. Experiments for rotating shallow water The Gaussian theory is illustrated here for the rotating shallow water equations. An elliptical-vortex example is chosen for simplicity and because it is not sensitive to the initial conditions, allowing a small ensemble to be used for the calculations. Balance inversion is illustrated first for solutions to a

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Shuguang Wang, Fuqing Zhang, and Chris Snyder

design. Wave generation from different types of dipoles is discussed in section 3 . Ray tracing analysis is performed in section 4 . Dependence of wave amplitude on the Rossby number is explored in section 5 through the distant dipole experiments. A summary and discussion will be presented in section 6 . 2. Experimental design This study employs a nonhydrostatic, compressive, mesoscale model [the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale

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