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Noah D. Brenowitz, Tom Beucler, Michael Pritchard, and Christopher S. Bretherton

continuous elliptical vertical differential operator defined by Aw = (∂/∂ z )[(1/ ρ 0 )(∂/∂ z )( ρ 0 w )]. When endowed with rigid-lid boundary conditions, w (0) = w ( H ) = 0, this linear operator can be inverted to give A −1 . In practice, we discretize these continuous operators using finite differences so that these operations can be performed with matrix algebra. Since we are focused on free-tropospheric dynamics, we have neglected the virtual effect of water vapor and approximated the buoyancy

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