deletions | additions       diff --git a/The_fact_that_larger_faster__.tex b/The_fact_that_larger_faster__.tex  index d3be9e3..f9024e1 100644  --- a/The_fact_that_larger_faster__.tex  +++ b/The_fact_that_larger_faster__.tex 
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\end{equation}  The devil with the deepest profile need not also have the widest profile or the largest velocity. \citet{Renn__2001} argue that the diameter of a vortex is set, in part, by the local vorticity field, while \citet{Balme_2012}, from their field studies, find no correlation between diameter and velocity from their field work. However, in quantifying the recovery probability $f(\Gamma_{\rm act}, P_{\rm act})$, 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 normalization (e.g., using average parameters) would suffice.   Figure \ref{fig:recovery_bias} shows contours of $f(\Gamma_{\rm act}, P_{\rm act})$, assuming $\upsilon = \upsilon_{\rm max}$. Not surprisingly, the recovery probability increases toward the upper-right corner, indicating that the deepest, widest dust devils are the most likely to be recovered. Taking the distribution of observed devils as $\rho(\Gamma_{\rm act}, P_{\rm act})$, the product $f(\Gamma_{\rm act}, P_{\rm act}) \times \rho(\Gamma_{\rm act}, P_{\rm act})$ would represent the population of devils that are detected but not what how  the recovered population would  actually looks like. look.