deletions | additions       diff --git a/section_Formulating_the_Signal_Distortions__.tex b/section_Formulating_the_Signal_Distortions__.tex  index 778261c..2a15968 100644  --- a/section_Formulating_the_Signal_Distortions__.tex  +++ b/section_Formulating_the_Signal_Distortions__.tex 
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\item A dust devil appears and disappears instantaneously, traveling a distance $\upsilon L$ over its lifetime $L$. As pointed out by \citet{Lorenz_2013}, $L$ seems to depend on dust devil diameter $D$ as $L = 40\ {\rm s}\ \left( D/{\rm m} \right)^{2/3}$, with diameter in meters. We assume $D = \Gamma_{\rm act}$ \cite{Vatistas_1991}.   \item There are minimum and maximum pressure profile depths that can be recovered by a survey, $P_{\rm th}$ and $P_{\rm max}$, respectively. $P_{\rm th}$ may be set by the requirement that a pressure signal exceeds some minimum threshold set by the noise in the datastream, while basic thermodynamic limitations likely restrict the maximum pressure depth for a devil. devil \citep{Renn__1998}.  Likewise, the profile widths must fall between $\Gamma_{\rm th}$ and $\Gamma_{\rm max}$, possibly set by the ambient vorticity field in which a devil is embedded \cite{Renn__2001}. \cite{Renn__2001} and/or the depth of the planetary boundary layer \citep{Fenton_2015}.  The two sets of limits may not be related, i.e. devils with $P_{\rm max}$ do not necessarily have widths $\Gamma_{\rm max}$. As it turns out, our results are not sensitive to the precise values for each of these limits. \item The two-dimensional distribution of $P_{\rm act}$ and $\Gamma_{\rm act}$, $\rho(P_{\rm act}, \Gamma_{\rm act})$, is integrable and differentiable. The same is true for the distributions of observed dust devil parameters, $\rho(P_{\rm obs}, \Gamma_{\rm obs})$.