deletions | additions       diff --git a/section_Background_Dust_devils_are__.tex b/section_Background_Dust_devils_are__.tex  index 2401158..04f4604 100644  --- a/section_Background_Dust_devils_are__.tex  +++ b/section_Background_Dust_devils_are__.tex 
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As noted in \citet{Lorenz_2009}, in-person visual surveys are likely to be biased toward detection of larger, more easily seen devils. Such surveys would also fail to recover dustless vortices \citep{Lorenz_2015}. Recently, terrestrial surveys similar to Martian dust devil surveys have been conducted using in-situ single barometers \citep{Lorenz_2012, Lorenz_2014, Jackson_2015} and photovoltaic sensors \citep{Lorenz_2015}. These sensor-based terrestrial surveys have the advantage of being directly analogous to Martian surveys and are highly cost-effective compared to the in-person surveys.  Single-barometer surveys have been highly successful on both planets in identifying and elucidating the properties of dust devils. In this kind of survey, a sensor is deployed in-situ and records a pressure time series at a sampling rate $\lesssim 1$ s. Since it is a low-pressure convective vortex, the nearby passage of a dust devil will register as pressure dip discernible against a background ambient (but not necessarily constant) pressure. Figure \ref{fig:conditioning_detection_b_inset} from \citet{Jackson_2015} shows a time-series with a typical dust devil signal.However, single-sensor barometer surveys also suffer from important biases. Foremost among these biases is the fact that a pressure dip does not necessarily correspond to a dust-lofting vortex. Indeed, recent studies \citep{2014DPS....4630006S} suggest pressure dips are often unaccompanied by lofted dust, likely because the attendant wind velocities are not sufficient to lift dust. The problem of identifying dustless vortices can be mitigated is barometers are deployed alongside solar cells, which can register obscuration by dust, and such sensor pairs have recently been deployed in terrestrial studies \cite{Lorenz_2015}. However, such an arrangement is not fool-proof since a devil can easily pass by the sensors on the anti-sunward side and not register an obscuration signature.  Another key bias confronted by single-barometer surveys is the ``miss distance'' effect: a fixed barometric sensor is more likely to have a more distant than closer encounter with a dust devil. Since the pressure perturbation associated with a devil falls off with distance, the deepest point in the observed pressure profile will almost always be less than the actual pressure well at the devil's center. The observed shape of the profile will be distorted as well. These miss distance biases are intrinsic to the detection methods, and additional biases can influence the inferred statistical properties. For instance, noise in the pressure time series from a barometer may make more difficult detection of a dust devils with smaller pressure perturbations, depending on the exact detection scheme. Although it is inherent in single-barometer surveys for dust devils, simple geometric considerations can mitigate the influence of the miss distance effect, allowing single-barometer surveys to be corrected. In particular, the physical parameters for dust devils estimated from the pressure time-series can be corrected for the miss distance effect, at least in a statistical sense.  In this study, we consider the geometry of encounters between dust devils and barometers and present a statistical model for correcting the miss distance effect. This study is similar to and motivated by \cite{Lorenz_2014}. However, where that study used a numerical simulation to investigate biases in the recovered population of dust devil properties, we employ an analytic framework that allows wider applicability and provides more intuitive insight into the problem.  The plan of this paper is as follow: In Section \ref{sec:formulating_the_recovery_biases_and_signal_distortions}, we discuss the typical encounter geometry for a dust devil detection and how the geometry both biases and distorts the recovered parameters. In Sections \ref{sec:the_Pact_recovery_bias_and_distortion} and \ref{sec:the_Gammaact_recovery_bias_and_distortion}, we discuss these effects on the profile depth and width recovered for a dust devil, and in Section \ref{sec:combining_the_Pact-Gammaact_biases_and_distortions}, we show how to combine the effects on profile depth and width together. In Section \ref{sec:comparison_to_observational_data}, we provide a preliminary application of our model to data from two recent dust devil surveys, and in Section \ref{sec:discussion_and_conclusions}, we discuss some of the limitations of our model, ways to improve it, and future work.