deletions | additions       diff --git a/To_derive_the_density_of__.tex b/To_derive_the_density_of__.tex  index d55a6b2..9379e91 100644  --- a/To_derive_the_density_of__.tex  +++ b/To_derive_the_density_of__.tex 
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To derive the density of actual parameters, we can apply Equation \ref{eqn:obs_to_act_dist} to the density of observed parameters in Figure \ref{fig:Ellehoj_data_obs_to_act_dist}. The white contours within the bottom-left panel illustrates the density estimate, while the top- and rightmost curves show the marginalized and normalized densities for $\Gamma_{\rm act}$ and $P_{\rm act}$. Several features stand out.  Foremost is the fact that the contour lines terminate near a value $\Gamma_{\rm act}^\prime =$ 6 s, indicating that the observed distribution implies very few dust devils with actual profile widths longer than that and the dust devils with apparently wider profiles were actually observed with relatively large miss distances. Assuming all the devils traveled past the sensor with $\upsilon \approx$ 3 m/s, the cutoff in temporal width at 6 s translates to a cutoff in dust devil diameter of about 18 m, consistent with the typical devil width of 10-20 m reported by \citet{Greeley_2006}. The sharp drop-off feature also arises, in part, because our model for the miss distance effects indicates the observed distribution should be skewed toward wider profiles, but the distribution observed by \cite{Ellehoj_2010} \citet{Ellehoj_2010}  actually drops off longward of about 6 s. This decline in density manifests as a very steep drop in the inferred density for $\Gamma_{\rm act}^\prime$. 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.