\label{sec:comparison_to_observational_data} In this section, we apply our statistical formulation to results from previous single-barometer surveys. A very important assumption we make here is that dust devils are advected past the barometer with some characteristic velocity \(\upsilon\), which allows us to treat the width of a profile in time \(\tau_{\rm act}\) as a proxy for the width in space \(\Gamma_{\rm act}\). As we discuss below, this assumption complicates our analysis of the distribution of observed profile widths but is unavoidable without wind speed data for each observed devil, usually lacking for martian studies.
\citet{Ellehoj_2010} analyzed 151 sols worth of time-series data, including pressures, temperatures, wind speeds, and images, from instruments on-board the Phoenix Lander \citep{Smith_2008}. To identify dust devil passages in the barometric data, they compared the average pressure in a 20-s window to the average pressure in 20-s windows to either side of the former window. Average pressures in the middle window different by more than 0.1 Pa from the average on either side were identified as possible dust devil passages. Then for every pressure event found, they analyzed the surrounding pressure and temperature values, and non-significant and false events, e.g., from data transfer gaps, were removed by hand (the precise criteria used to exclude an event are not given). In this way, \citet{Ellehoj_2010} identified 197 vortices with a pressure drops larger than 0.5 Pa = \(10^{-0.3}\) Pa, which we will take as \(P_{\rm th}\) for this dataset.
Figure \ref{fig:Ellehoj_data_obs_to_act_dist} shows a scatter plot of their reported detections. The colored contours are calculated using a Gaussian kernel density estimator and a bandwidth of 0.75, analogous to histogram bin widths. The narrower bandwidth, 0.5, provided by Scott’s rule \citep{SCOTT_1979} results in apparently spurious structure in the density contours. The marginalized and normalized densities are shown along each axis.