deletions | additions       diff --git a/section_Formulating_the_Recovery_Biases__.tex b/section_Formulating_the_Recovery_Biases__.tex  index d702ccc..76756ab 100644  --- a/section_Formulating_the_Recovery_Biases__.tex  +++ b/section_Formulating_the_Recovery_Biases__.tex 
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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 will sense dust devils over a certain area, spanning a maximum radial distance $b_{\rm max}$, beyond which devils will produce pressure signals smaller than the detection threshold, $P_{\rm obs} < P_{\rm min}$. $b_{\rm max}$ is set by the area of the devil with the broadest detectable $P_{\rm min}$ contour, which may not correspond to the devil with $P_{\rm act} = P_{\rm max}$ and $\Gamma_{\rm act} = \Gamma_{\rm max}$. If, for instance, a temporal variation in the local vorticity field may give a devil with $P_{\rm min}$ a very large $\Gamma_{\rm act}$, thereby producing a devil that is detectable over a very wide area (i.e., with large $b_{\rm max}$). However, without a detailed knowledge of the relationship between dust devil area, $P_{\rm act}$, and $\Gamma_{\rm act}$, we will take $b_{\rm max} = \left(  \dfrac{\Gamma_{\rm max}}{2} \right)  \sqrt{\dfrac{P_{\rm max} - P_{\rm min}}{P_{\rm min}}}$. 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. 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.