Brian Jackson edited section_Formulating_the_Recovery_Biases__.tex  almost 9 years ago

Commit id: 6136446a93f1edcaf63a794b436c77e672586900

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\item We assume 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 $P(r) = -\dfrac{P_{\rm act}}{1 - \left( 2r/\Gamma_{\rm act} \right)^2 }$. 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 $\upsilon$. The wind vector does not change direction or magnitude during the course of the encounter with the sensor. The upshot of this assumption is that a devil whose center passes directly over the sensor will register a pressure dip with a width in time $\Gamma^\prime_{\rm act} = \Gamma{\rm \Gamma_{\rm  act}/\upsilon$. \end{enumerate}