deletions | additions       diff --git a/To_derive_the_density_of__.tex b/To_derive_the_density_of__.tex  index e9c7513..8f2b547 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 from Figure \ref{fig:Ellehoj_data}, resulting of observed parameters  in Figure \ref{fig:Ellehoj_data_to_actual_dist}. \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 \cite{Greeley_2006}. The sharp drop-off feature also arises, in part, because our model for the miss distance effects implies the observed distribution should be skewed toward wider profiles, but the distribution observed by \cite{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 $\Gamma_{\rm act}^\prime$.