deletions | additions       diff --git a/section_Formulating_the_Recovery_Biases__.tex b/section_Formulating_the_Recovery_Biases__.tex  index c9d6035..2a73900 100644  --- a/section_Formulating_the_Recovery_Biases__.tex  +++ b/section_Formulating_the_Recovery_Biases__.tex 
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\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 2-dimensional two-dimensional  distribution of $P_{\rm act}$ and $\Gamma_{\rm act}$, $n(P_{\rm $\rho(P_{\rm  act}, \Gamma_{\rm act})$ respectively, is integrable and differentiable. The same is true for the distributions of observed dust devil parameters. \item The uncertainties on the profile depth and width estimated for a dust devil are negligible.