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Brian Jackson edited The_fact_that_larger_faster__.tex
over 8 years ago
Commit id: 9e483ff4b6a5cf302961e2f7d9e21beaa2b04c92
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\label{eqn:recovery_bias}
f = \dfrac{A(P_{\rm act}, \Gamma_{\rm act})}{A_{\rm max}} = \left( \dfrac{\Gamma_{\rm act}}{\Gamma_{\rm max}} \right) \sqrt{\dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm max} - P_{\rm min}}} \left( \dfrac{\upsilon}{\upsilon_{\rm max}} \right) \left( \dfrac{\tau}{\tau_{\rm max}} \right).
\end{equation}
{\it A priori}, the The devil with the deepest profile need not also have the widest profile or the largest velocity. \cite{Renn__2001} argue that the diameter of a vortex is set, in part, by the local vorticity field, while \cite{Balme_2012}, from their field
study of dust devils, studies, find no correlation between diameter and velocity from their field work.
However, in quantifying the recovery bias $f$, it's only important that we apply a uniform normalizing factor to the whole population, and the denominator in Equation \ref{eqn:recovery_bias} just provides a convenient expression for that. Any other uniform normalizing (e.g., using average parameters) would suffice.