deletions | additions       diff --git a/section_Discussion_and_Conclusions_label__.tex b/section_Discussion_and_Conclusions_label__.tex  index 5fe71c0..7ee3f3e 100644  --- a/section_Discussion_and_Conclusions_label__.tex  +++ b/section_Discussion_and_Conclusions_label__.tex 
...
As discussed in Section \ref{sec:the_recovery_bias}, the miss distance effect biases the recovered population toward the physically widest devils. Because the dynamical processes that form and maintain devils are not well-understood, the relationship between the width of a devil and its other physical properties are not clear, so it's not clear how the recovered properties are skewed by this bias. However, the bias definitely plays a role in estimates of the areal density for dust devil occurrence. For example, by assuming a devil profile width of 100 m, \citet{Ellehoj_2010} combine the number of devils recovered from pressure time-series and wind speed data to estimate a local occurrence rate of 1 event per sol per 10 km$^2$. Although useful, that occurrence rate estimate involves an implicit marginalization over the dust devil population and the efficiency function for their detection scheme. The occurrence rate for small dust devils (those with narrow profiles) could be considerably larger since they are less likely to be detected. Likewise, the rate for large devils (wider profiles) could also be larger since the detection scheme probably filters out devils with profiles much wider than 20-s.  An improved understanding of the scheme used to detect dust devils is critical for relating the observed to the underlying population, and a simple way to assess a scheme's detection efficiency is to inject synthetic devil signals (with known parameters) into the real data streams. Then the detection scheme can be applied to recover the synthetic devils and the efficiency of detection assessed across a swath of devil parameters. Such an approach is common in exoplanet transit searches \citep[e.g.][]{Sanchis_Ojeda_2014}, for instance. where dips in photometric time series from planetary shadows closely resemble dust devil pressure signals.  By injecting synthetic devils into real data, the often complex noise structure in the data is retained and simplifying assumptions (such as stationary white noise) are not required. Among important limitations of our model, the advection velocity $\upsilon$ for devils remains an critical uncertainty for relating physical and statistical properties. This limitation points to the need for wind velocity measurements made simultaneously with pressure measurements in order to accurately estimate dust devil widths. In particular, correlations between $\upsilon$ and dust devil properties will skew the recovered parameters in ways not captured here. For example, the devils with the deepest pressure profiles seem to occur preferentially around mid-day local time both on Mars \cite{Ellehoj_2010} and the Earth \cite{Jackson_2015}. If winds at that time of day are preferentially fast or slow, then the profile widths recovered for the deepest devils will be skewed toward smaller or larger values. In addition, some field observations suggest devils with larger diameters may be advected more slowly than their smaller counterparts \cite{Greeley_2010}, which would tend to make their profiles look wider. The formulation described here could, in principle, account for this uncertainty by incorporating a distribution of $\upsilon$ determined observationally, $n(\upsilon)$. Then the physical width of a devil profile could be represented using a probability density $\dfrac{dp}{d\Gamma_{\rm act}} \propto n(\upsilon)\ d\upsilon$.