deletions | additions       diff --git a/To_derive_the_density_of__.tex b/To_derive_the_density_of__.tex  index dcf3758..8db9d34 100644  --- a/To_derive_the_density_of__.tex  +++ b/To_derive_the_density_of__.tex 
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What does this result mean? 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 20 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. \citet{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 as wide as or wider than 20-s 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 $P_{\rm act}$, there is 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 might expect the peak in the density for $P_{\rm obs}$-values to originate from a peak at a larger $P_{\rm act}$-value due to the miss distance effects. In Figure \ref{fig:Ellehoj_data_obs_to_act_dist}, the observed density peaks at $P_{\rm obs} \approx 10^{-0.15}\ {\rm Pa} = 0.7\ {\rm Pa}$, while the inferred actual density peaks at $P_{\rm act} \approx 10^{0.2}\ {\rm Pa} = 1.6\ {\rm Pa}$. We can compare these peaks to our expected average miss distance from Section \ref{sec:the_signal_distortion}: $\langle b/\Gamma_{\rm act} \rangle \approx \frac{1}{3} \sqrt{P_{\rm act}/P_{\rm min}} = \frac{1}{3} \sqrt{1.6/0.5} \approx 0.6$. With that average miss distance, we'd expect a dust devil with $P_{\rm act}$, on average, to observed with $P_{\rm obs} = P_{\rm act}/\left( 1 + \left( 2\times 0.6 \right)^2 \right) \approx 0.4\ P_{\rm act}$, in line with not too different from  where the peaks do  occur for two distributions. Deciding whether the observed peak is due primarily to difficulties detecting small $P_{\rm obs}$ signals or the miss distance effect also requires a completeness assessment, however.