deletions | additions       diff --git a/section_Formulating_the_Recovery_Biases__.tex b/section_Formulating_the_Recovery_Biases__.tex  index 51e5944..d2e25f9 100644  --- a/section_Formulating_the_Recovery_Biases__.tex  +++ b/section_Formulating_the_Recovery_Biases__.tex 
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\begin{enumerate}  \item The Lorentz profile is a good fit to the radial pressure profile of dust devils. That is, each dust devil pressure profile has one well-defined center, and the pressure dip (relative to the ambient pressure) observed at a radial distance $r$ from the center of the dust devil is $P(r) = -\dfrac{P_{\rm \dfrac{P_{\rm  act}}{1 - +  \left( 2r/\Gamma_{\rm act} \right)^2 }$. Here $P_{\rm act}$ represents the actual pressure depth at the devil's center, and $\Gamma_{\rm act}$ the profile full-width at half-max. This profile is also assumed not to change with time. \item A dust devil is carried past the sensor with the ambient wind field at a velocity $\upsilon$. For simplicity, we will assume the wind velocity vector is constant in magnitude and direction, while in reality, the ambient wind field carrying a devil can be complex, even causing multiple encounters between devil and sensor and consequently more complex pressure signals \citep{Lorenz_2013}. The upshot of this assumption is that a devil whose center passes directly over the sensor will register a pressure dip with a full-width at half-max in time $\Gamma^\prime_{\rm act} = \Gamma_{\rm act}/\upsilon$. For a more distant encounter, the profile width in time observed is $\Gamma^\prime_{\rm obs}$. 
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