35.2.1.2 The effective $\beta$ parameter

The parameter $\beta_{eff}$ incorporates both planetary vorticity gradients and gradients in the large-scale topography

$$\beta_{eff} H \vert \nabla_{h} (f/H) \vert$$ =

$$\biggl( (\beta - f \, H_{y}/H)^{2} + (f \, H_{x} /H)^{2} \biggr)^{1/2}$$ = (35.89)

where $\beta = \partial_{y}f$ is the planetary vorticity gradient, $H = H(\lambda,\phi) \ge 0$ is the total depth of the ocean, and

$$\frac{H_{\lambda}}{a \, \cos\phi}$$ H_x = (35.90)

$$\frac{H_{\phi}}{a}.$$ H_y = (35.91)