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Brian Jackson edited section_Formulating_the_Recovery_Biases__.tex
over 8 years ago
Commit id: ada46854620491d131d05cf47db2ad8e73cee49d
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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
distributions two dimensional distribution of $P_{\rm act}$ and $\Gamma_{\rm act}$, $n(P_{\rm
act})$ and $n(\Gamma_{\rm act}, \Gamma_{\rm act})$ respectively,
are 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.
\end{enumerate}