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Strictly speaking, $\lim_{\Delta z \to 0} Ri=Ri_b$. This is because the gradient Richardson number: $$Ri=\frac{\frac{g}{T_v}\frac{\partial \theta_v}{\partial z}}{\left(\frac{\partial U}{\partial z}\right)^2++\left(\frac{\partial V}{\partial z}\right)^2}$$ can be approximated as $$Ri \approx\frac{\frac{g}{T_v}\frac{\Delta \theta_e}{\Delta z}}{\left(\frac{\...


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