deletions | additions       diff --git a/section_Formulating_the_Recovery_Biases__.tex b/section_Formulating_the_Recovery_Biases__.tex  index 245343f..a8a1bc5 100644  --- a/section_Formulating_the_Recovery_Biases__.tex  +++ b/section_Formulating_the_Recovery_Biases__.tex 
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\begin{enumerate}  \item Each dust devil pressure profile has one well-defined center, and the pressure dip (relative to the ambient pressure) observed profile  at a radial distance $r$ from the centerof the dust devil  follows a Lorentz profile: Lorentzian:  $P(r) = \dfrac{P_{\rm act}}{1 + \left( 2r/\Gamma_{\rm act} \right)^2 }$. 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. However, alternative Alternative  profiles have been suggested. \cite{Lorenz_2014} suggested either a suggested, including  Burgers-Rott or Vastitas profile profiles that  might provide more accurate physical description of a dust devil profile. Using a profile \citep{Lorenz2014}. A  different profile would likely change the modify our  results here but not substantially.Given that the Lorentz profile is more commonly used in the field, we opt to use it here. The 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 $\Gamma^\prime_{\rm act} = \Gamma_{\rm act}/\upsilon$. The profile width in time that is actually observed is $\Gamma^\prime_{\rm obs}$.