deletions | additions       diff --git a/section_Formulating_the_Recovery_Biases__.tex b/section_Formulating_the_Recovery_Biases__.tex  index 214f272..b93ece9 100644  --- a/section_Formulating_the_Recovery_Biases__.tex  +++ b/section_Formulating_the_Recovery_Biases__.tex 
...
\item The uncertainties on the profile depth and width estimated for a dust devil are negligible.  \item The distributions of $P_{\rm act}$ and $\Gamma_{\rm act}$, $nP_{\rm act})$ and ($n(\Gamma_{\rm act})$ respectively, are integrable and differentiable. The same is true for the distributions of observed dust devil parameters.  \end{enumerate}  With these assumptions, we can relate the geometry of an encounter directly to the observed profile parameters, and Figure \ref{fig:encounter_geometry} illustrates a typical encounter. As a devil passes the barometer, it will have a closest approach distance $b$, where the deepest point in the pressure profile will be observed $P_{\rm obs}$, given by  
...
\end{equation}  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.