deletions | additions       diff --git a/section_Formulating_the_Recovery_Biases__.tex b/section_Formulating_the_Recovery_Biases__.tex  index 940d260..23896f8 100644  --- a/section_Formulating_the_Recovery_Biases__.tex  +++ b/section_Formulating_the_Recovery_Biases__.tex 
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\item The uncertainties on the profile depth and width estimated for a dust devil are negligible.  \item Dust devils all have the same lifetimes. \cite{Lorenz_2013} suggested a dependence of dust devil lifetime on diameter, $D$ as $D^0.66$. In principle, this effect probably skews the distribution of observed dust devils toward larger ones. However, for single-barometer surveys, the encounter geometry plays the dominant role in setting the observed distribution, and as a first cut, we neglect the difference in dust devil lifetimes in this study.  \end{enumerate}  It is important to note that we have assumed dust devil pressure profiles follow a Lorentz function. However, alternative assumptions have been suggested. \cite{Lorenz_2014} suggested either a Burgers-Rott or Vastitas profile might provide more accurate physical description of a dust devil profile. Using a different profile would likely change the results here but not substantially. Given that the Lorentz profile is more commonly used in the field, we opt to use it here. 
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There is a maximum closest approach distance $b_{\rm max}$ beyond which a devil will produce an undetectably small pressure signal, $P_{\rm obs} < P_{\rm min}$, and $b_{\rm max} = \left( \dfrac{\Gamma_{\rm act}}{2} \right) \sqrt{ \dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm min}}}$. Devils with $b > b_{\rm max}$ will not be detected, which will bias our recovered population of devil parameters in ways that depend on the parameters themselves. It's worth noting that $\Gamma_{\rm act}$ may depend on $P_{\rm act}$, a point we will return to in Section. Again, this recovery bias results from the miss distance effect. Next, we use these equations to formulate the recovery biases and signal distortions resulting from the miss distance effect.