deletions | additions       diff --git a/subsection_The_Signal_Distortion_The__.tex b/subsection_The_Signal_Distortion_The__.tex  index 43b08a9..3daae24 100644  --- a/subsection_The_Signal_Distortion_The__.tex  +++ b/subsection_The_Signal_Distortion_The__.tex 
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\end{equation}  Clearly, unless $b = 0$, $P_{\rm obs} < P_{\rm act}$. Likewise, non-central encounters will distort the profile full-width/half-max, giving a full-width/half-max $\Gamma_{\rm obs}$.   Having passed through its minimum at the devil's closest approach distance, the observed pressure signal reaches half its value at a time $t = \frac{1}{2} \Gamma_{\rm obs}^\prime = \frac{1}{2} \Gamma_{\rm obs}/\upsilon$ by definition. At this time, the center of the devil is a radial distance from the barometer $r(t = \Gamma_{\rm obs}^\prime/2) = \sqrt{b^2 + \left( \frac{1}{2} \Gamma_{\rm obs} \right)^2}$ and $P(r) = \frac{1}{2} P_{\rm obs} = \frac{1}{2} \dfrac{P_{\rm act}}{1 + \left( 2 b /\Gamma_{\rm act} \right)^2} = \dfrac{P_{\rm act}}{1 + \left( 2r(\Gamma_{\rm obs}^\prime/2)/\Gamma_{\rm act} \right)^2 }$. Solving for $\Gamma_{\rm obs}$ gives $\Gamma_{\rm obs}^2 = \Gamma_{\rm act}^2 + \left( 2b \right)^2$. and Figure \ref{fig:compare_profiles} shows how a non-central encounter modifies  theprofile width  observed in the time series $\Gamma_{\rm obs}^\prime > \Gamma_{\rm act}^\prime$, as pointed out by \citet{Ellehoj_2010} and \citet{Lorenz_2014}. These effects represent the signal distortion induced by the miss distance effect. pressure profile.  Given $P_{\rm obs}$- and $P_{\rm act}$-values, we can solve Equation \ref{eqn:Pobs_from_Lorentz_profile} for $b$:  \begin{equation}\label{eqn:b_from_Lorentz_profile}  b = \left( \dfrac{\Gamma_{\rm act}}{2} \right) \sqrt{ \dfrac{P_{\rm act} - P_{\rm obs}}{P_{\rm obs}}}.  \end{equation}  A single barometer at a fixed location can sense a dust devil only over a certain area, spanning a maximum radial distance $b_{\rm max}$, beyond which devils will produce pressure signals smaller than the detection threshold, $P_{\rm obs} < P_{\rm min}$: $b_{\rm max} = \left( \dfrac{\Gamma_{\rm act}}{2} \right) \sqrt{\dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm min}}}$. 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. Again, this recovery bias results from the miss distance effect.   The pressure profile time series is $P(r) = \dfrac{P_{\rm act}}{1 + \left( 2r/\Gamma_{\rm act} \right)^2 }$. For a closest encounter distance $b$, $P(b) = P_{\rm obs} = \dfrac{P_{\rm act}}{1 + \left( \dfrac{2 b}{\Gamma_{\rm act}} \right)^2}$. Even if a dust devil is detected, the miss distance effect will usually cause the deepest point in the pressure profile observed $P_{\rm obs}$ to be less than $P_{\rm act}$.   The following figure shows how a non-central encounter modifies the observed pressure profile. detected.