ROUGH DRAFT authorea.com/41056

# Background

Dust devils are small-scale (few to many tens of meters) low-pressure vortices rendered visible by lofted dust. They usually occur in arid climates on the Earth and ubiquitously on Mars. Martian dust devils have been studied with orbiting and landed spacecraft and were first identified on Mars using images from the Viking Orbiter (Thomas et al., 1985). On Mars, dust devils may dominate the supply of atmospheric dust and influence climate (Basu 2004), pose a hazard for human exploration (Balme et al., 2006), and they may have lengthened the operational lifetime of Martian rovers (Lorenz et al., 2014). On the Earth, dust devils significantly degrade air quality in arid climates (Gillette et al., 1990) and may pose an aviation hazard (Lorenz 2005).

The dust-lifting capacity of dust devils seems to depend sensitively on their structures, in particular on the pressure wells at their centers (Neakrase et al., 2006), so the dust supply from dust devils on both planets may be dominated by the seldom-observed larger devils. Using a martian global climate model, Basu (2004) showed that observed seasonal variations in Mars’ near-surface temperatures could not be reproduced without including the radiative effects of dust and estimated the dust contributes more than 10 K of heating to the heating budget. Thus, elucidating the origin, evolution, and population statistics of dust devils is critical for understanding important terrestrial and Martian atmospheric properties and for in-situ exploration of Mars.

Studies of Martian dust devils have been conducted through direct imaging of the devils and identification of their tracks on Mars’ dusty surface (cf. Balme et al., 2006). Studies with in-situ meteorological instrumentation have also identified dust devils, either via obscuration of the Sun by the dust column (Zorzano et al., 2013) or their pressure signals (Ellehoj et al., 2010). Studies have also been conducted of terrestrial dust devils and frequently involve in-person monitoring of field sites. Terrestrial dust devils are visually surveyed (Pathare et al., 2010), directly sampled (Balme et al., 2003), or recorded using in-situ meteorological equipment (Sinclair, 1973; Lorenz, 2012).

As noted in 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 (Lorenz et al., 2015). Recently, terrestrial surveys similar to Martian dust devil surveys have been conducted using in-situ single barometers (Lorenz, 2012; Lorenz, 2014; Jackson et al., 2015) and photovoltaic sensors (Lorenz et al., 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 (in a dollars per data point sense).

In single-barometer surveys, a sensor is deployed in-situ and records a pressure time series at a sampling period $$\lesssim 1$$ s. Since it is a low-pressure convective vortex, a dust devil passing nearby will register as pressure dip discernible against a background ambient (but not necessarily constant) pressure. Figure \ref{fig:conditioning_detection_b_inset} from Jackson et al. (2015) shows a time-series with a typical dust devil signal.

\label{fig:conditioning_detection_b_inset} Example dust devil profile from Jackson et al. (2015). The black dots show the pressure $$p$$ measurements (in hectoPascal hPa) as a function of local time in hours. The blue line shows the best-fit Lorentz profile model.

Three spacecraft landed on Mars carried meteorological instrumentation that allows investigators to conduct such surveys, providing a wealth of data on Martian dust devils and other meteorological phenomena, but such surveys suffer from important biases when it comes to studying dust devils. Foremost among these biases is the fact that a pressure dip does not necessarily correspond to a dust-lofting vortex. Indeed, recent studies (Steakley et al., 2014) suggest pressure dips are often unaccompanied by lofted dust, likely because the attendant wind velocities are insufficient to lift dust. The problem of identifying dustless vortices can be mitigated if barometers are deployed alongside solar cells, which can register obscuration by dust, and such sensor pairs have recently been deployed in terrestrial studies (Lorenz 2015). However, such an arrangement is not fool-proof since a dusty 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 arises from 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 from the devil’s center, 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 Lorenz (2014), but, 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 insight into the problem. As we discuss, though, our model involves some important assumptions and simplifications.

The plan of this paper is as follow: In Section \ref{sec:formulating_the_signal_distortions_and_recovery_biases}, we discuss the typical encounter geometry for a dust devil detection, how the geometry distorts and biases the recovered parameters, and how to convert from the observed to the underlying distribution of dust devil parameters. In Section \ref{sec:comparison_to_observational_data}, we apply our scheme to recent datasets for martian and terrestrial dust devils. Finally, in Section \ref{sec:discussion_and_conclusions}, we discuss some of the limitations and future improvements for our model.