deletions | additions       diff --git a/To_derive_the_density_of__.tex b/To_derive_the_density_of__.tex  index c9b100c..ba6ecb3 100644  --- a/To_derive_the_density_of__.tex  +++ b/To_derive_the_density_of__.tex 
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What does this result imply? Primarily, it implies that converting from the observed temporal widths to the spatial widths is challenging since even a moderate variability in ambient windspeed (from 1 to 10 m/s) could easily contribute an order of magnitude variation in observed width for a single devil. It also highlights the important role played by the detection scheme employed to sift devils out of the pressure time series. \cite{Ellehoj_2010} employed windows 20 s wide, which would have necessarily biased their detections toward devils with profiles less wide than that -- a devil with profile 20-s or more wide would have been filtered out. This detection bias probably contributes some to the decline in density toward larger $\Gamma_{\rm act}^\prime$. As discussed in Section \ref{sec:discussion_and_conclusions}, a completeness assessment for the detection scheme could help mitigate this bias.  Turning to the distribution of $P_{\rm act}$, we see a decline moving from moderate to small $P_{\rm act}$-values, which is probably due in part to a similar detection bias: devils with smaller $P_{\rm act}$ are less likely to exceed the threshold for detection.   However, we also do expect a peak in the density of $P_{\rm obs}$ to manifest as a peak at larger $P_{\rm act}$ due to the miss distance effects. In Figure \ref{fig:Ellehoj_data}, a peak in density occurs at $P_{\rm obs} \approx 10^{-0.15} Pa = 0.7 Pa$, while a peak occurs at $P_{\rm act} \approx 10^{-0.15} 10^{-0.15}\  Pa = 0.7 0.7\  Pa$ ased on the estimate $\langle b \rangle = \Gamma_{\rm act}$ from Section \ref{sec:},