deletions | additions       diff --git a/section_Discussion_and_Conclusions_label__.tex b/section_Discussion_and_Conclusions_label__.tex  index 7213727..4135e43 100644  --- a/section_Discussion_and_Conclusions_label__.tex  +++ b/section_Discussion_and_Conclusions_label__.tex 
...
\section*{Discussion and Conclusions}  \label{sec:discussion_and_conclusions}  Our formulation here provides a starting place for relating the population statistics of dust devils as recovered by single-barometer surveys to their physical structures. Understanding these relationships is critical for understanding the atmospheric influence of devils on both planets since it depends so sensitively on both the devils' statistical and physical properties. As noted in \cite{Jackson_2015} and \cite{Lorenz_2014}, in estimating the total flux of dust injected into the martian atmosphere, it is important to consider the population-weighted flux and not the flux from the average dust devil. Of course, knowing the population is critical to calculating that population-weighted flux. Moreover, lab work reported in \citet{Neakrase_2006} suggested an exponential dependence of dust flux on a dust devil's pressure depth, and so even small shifts in the distribution of dust devil pressure depths can result in large shifts in the dust flux. For instance, using the exponential dependence indicated in Figure X 4  of \citet{Neakrase_2006}, we find that the dust flux given by the distribution of $P_{\rm act}$ in Figure \ref{fig:} \ref{fig:Ellehoj_data_obs_to_act_dist}  isXX times  more than 30\% larger than  that given by the $P_{\rm obs}$ distribution. The model for the miss distance effect developed here serves to highlight the many important uncertainties and degeneracies involved in single-barometer dust devil surveys. In particular, these results show that it is difficult to disentangle the geometry of an encounter between a devil and a detector from the devil's structure. The pressure profile observed for a devil will almost always be wider and less deep than the devil's actual profile.  
...
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 $\dfrac{dp}{d\Gamma_{\rm act}} \propto n(\upsilon)\ d\upsilon$.  As highlighted in Section \ref{sec:comparison_to_observational_data} and discussed in \citet{Lorenz_2011}, the choice of the binning procedure (bin size, etc.) in constructing the distributions of physical properties shapes the result in non-trivial ways, and the approach used to describe the distributions will also depend on the procedure. Fortunately, the field of data science has provided several statistically robust and objective procedures for binning data that frequently use the data themselves to determine to they are binned \citep[e.g.][]{Feigelson_2009}\citep[e.g.][]. \citep[e.g.][]{Feigelson_2009}.  One simple way to ascertain the optimal binning procedure would be to generate synthetic populations according to prescribed distribution functions (power-laws, exponential, etc.) and then investigate which binning procedure allowed the most accurate recovery of the assumed distribution. This approach will be the subject of future work. Clear predictions of the distributions of physical parameters for dust devils from high resolution meteorological models would be especially helpful for constraining and directing this work, and some progress in this area has been made. For example, \citet{2005QJRMS.131.1271K} applied a large-eddy simulation of a planetary convective boundary layer to study vortical structures and the influence of ambient conditions on their formation. For the handful of vortices formed in the simulations, there was good qualitative agreement with observation. \citet{2010BoLMe.137..223G} also studied vortex formation on Earth and Mars and noted the role of the boundary layer's depth on vortex scale. Given the stochastic nature of boundary layer dynamics, detailed statistical predictions from such models are needed for comparison to observation. However, the computational expense of such high-resolution models makes that prohibitive.  
...
In the decade since, technological developments in miniaturization and data storage now provide a wealth of robust and inexpensive instrumentation, ideally suited for the long-term field deployment required to study dust devils, without the need for direct human involvement. Recently, \citet{Lorenz_2015} deployed an array of ten miniature pressure- and sunlight-logging stations at La Jornada Experimental Range in New Mexico, providing a census of vortex and dust-devil activity at this site. The simultaneous measurements resolved horizontal pressure structures for several dust devils, giving a sense for vortex size and intensity.   The rich and growing databases of high-time-resolution meteorological data, both for the Earth and Mars, combined with the wide availability and affordability of robust instrumentation, point to bright future for dust devil studies. In particular, the The  data streaming in from the Mars Science Laboratory Rover Environmental Monitoring Station (REMS) \citep{G_mez_Elvira_2012} may provide new insight into Martian dust devils. devils, although preliminary studies \citep[e.g.][]{2015DPS....4741907M} have found very few dust devils in Gale Crater.  The formulation presented here provides a simple but robust scheme for relating the dust devils' statistical and physical properties, and though it has some limitations, it represents an important next step in improving our knowledge of these dynamic and ethereal phenomena.