deletions | additions       diff --git a/section_Formulating_the_Recovery_Biases__.tex b/section_Formulating_the_Recovery_Biases__.tex  index a73380b..5d48d03 100644  --- a/section_Formulating_the_Recovery_Biases__.tex  +++ b/section_Formulating_the_Recovery_Biases__.tex 
...
\item The dust devil center is carried by the ambient wind field at a velocity $\upsilon$, which is constant in magnitude and direction. 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}. A devil whose center passes directly over the sensor will register a pressure dip with a full-width at half-max in time $\Gamma^\prime_{\rm act} = \Gamma_{\rm act}/\upsilon$, so that the observed profile width in time observed is $\Gamma^\prime_{\rm obs}$.  \item A dust devil appears and disappears instantaneously, traveling a distance $\upsilon \tau$ over its lifetime $\tau$ in between. As pointed out by \citet{Lorenz_2013}, $\tau$ seems to depend on dust devil diameter $D$ as $\tau = (40 {\rm s}\ \left( D/{\rm 1\ m} \right)^{0.66}$.  \item The deepest point observed for a devil that is recovered is $P_{\rm obs}$, which must exceed some fixed minimum $P_{\rm min}$, below which a putative pressure fluctuation is deemed statistically insignificant. At the other end of the scale, basic thermodynamic limitations restrict the maximum pressure depth a devil can have to some finite value, $P_{\rm max}$. Likewise, the $\Gamma_{\rm act}$-values fall between $\Gamma_{\rm min}$ and $\Gamma_{\rm max}$. $\Gamma_{\rm min}$ might be set by the sampling rate of the barometric logger, while $\Gamma_{\rm max}$ might be set by the requirement that detected devils are narrow enough to be discernible against long-term (e.g., hourly) pressure variations. The two sets of limits may not be related, i.e. devils with $P_{\rm act} = P_{\rm max}$ don't necessarily have $\Gamma_{\rm act} = \Gamma_{\rm max}$.  \item The distributions of $P_{\rm act}$ and $\Gamma_{\rm act}$, $n(P_{\rm act})$ and $n(\Gamma_{\rm act})$ respectively, are integrable and differentiable. The same is true for the distributions of observed dust devil parameters.