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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. Since a devil's dust-lift capacity seems to depend very sensitively on its depth \cite{Neakrase_2006}, it's very likely the dust flux from devils on Mars and Earth are significantly underestimated since the deepest pressure wells are probably not observed directly.   As discussed in Section \ref{sec:the_gammaact_recovery_bias_and_distortion}, \ref{sec:the_Gammaact_recovery_bias_and_distortion},  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. The An improved understanding of the scheme used to detect dust devils is critical for relating the observed to the underlying population, and 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 astronomical exoplanet transit searches \citep[e.g.][]{Sanchis_Ojeda_2014}. 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, and our assumption of a constant velocity is an important limitation of the model. 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 functional form 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.][]. 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 meteorlogical 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 qualitatively 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. Likely the best way to study dust devil formation and dynamics in the field is not statistically, but directly via deployment of sensor networks that produce a variety of data streams with high spatial and time resolution. Field work with small sensor networks has a long history \citep[e.g.][]{Sinclair_1973}. \citet{2004JGRE..109.7001R} conducted a concerted field study, deploying an vast arsenal of sensors to measure surface heat fluxes of heat, water vapor, short and long wave radiation, soil heat flux, pressure, wind, temperature, water vapor and dust concentration, and electric field on Santa Cruz Flats in Arizona. The results showed that terrestrial dust devils produce heat and dust fluxes orders of magnitude larger than their background values and often involve strong electric fields that might play a significant role in dust sourcing.  
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Even though such a sensor network can provide spatially resolved information, the resulting estimates of devil structural parameters are still somewhat degenerate as a result of the uncertain encounter geometry. In fact, the distortion biases discussed here can be incorporated via a Bayesian inference scheme to work out the likely devil structure: Equations \ref{eqn:dpdP_obs} and \ref{eqn:dpdGamma_obs} actually represent likelihood functions, providing the probability to recover $P_{\rm obs}$ and $\Gamma_{\rm obs}$, given a devil with $P_{\rm act}$ and $\Gamma_{\rm act}$.