Diurnal Variation in Martian Dust Devil Activity

We show that the dust devil parameterisation in use in most Mars Global Circulation Models (MGCMs) results in an unexpectedly high level of dust devil activity during morning hours. Prior expectations of the diurnal variation of Martian dust devils are based mainly upon the observed behaviour of terrestrial dust devils: i.e. that the majority occur during the afternoon. We instead find that large areas of the Martian surface experience dust devil activity during the morning in our MGCM, and that many locations experience a peak in dust devil activity before mid-sol. We find that the diurnal variation in dust devil activity is governed by near-surface wind speeds. Within the range of daylight hours, higher wind speeds tend to produce higher levels of dust devil activity, rather than the activity simply being governed by the availability of heat at the planet’s surface, which peaks in early afternoon. Evidence for whether the phenomenon we observe is real or an artefact of the parameterisation is inconclusive. We compare our results with surface-based observations of Martian dust devil timings and obtain a good match with the majority of surveys. We do not find a good match with orbital observations, which identify a diurnal distribution more closely matching that of terrestrial dust devils, but orbital observations have limited temporal coverage, biased towards the early afternoon. We propose that the generally accepted description of dust devil behaviour on Mars is incomplete, and that theories of dust devil formation may need to be modified specifically for the Martian environment. Further surveys of dust devil observations are required to support any such modifications. These surveys should include both surface and orbital observations, and the range of observations must encompass the full diurnal period and consider the wider meteorological context surrounding the observations.

devils -usually visible as dark streaks against the higher albedo surface -have also been 8 observed in many orbiter images (Cantor et al., 2006). 9 Martian dust devils are named after the apparently similar features observed on Earth. 10 These are near-surface atmospheric vortices that are visible due to the particles they lift 11 from the ground and entrain in a vertical, upwardly-spiraling column of air. The core 12 of a dust devil is commonly at a lower pressure than the surrounding vortex (Sinclair,13 1964). Dust devils are able to lift surface dust particles due to the wind shear stress 14 present within the walls of the vortex (Balme et al., 2003a). The lower central pressure 15 within the column may also contribute to dust lifting by providing an upwards force that 16 assists the shear stress in overcoming interparticle cohesion forces (Greeley et al., 2003; 17 Balme and Hagermann, 2006). Dust devil activity on Mars is highly variable between 18 regions and seasons (Fisher et al., 2005), and Martian dust devils are more frequently 19 observed in local spring and summer months (Thomas and Gierasch, 1985;Balme et al., 20 2003b; Cantor et al., 2006).  In Section 2 we discuss the model parameterisation that simulates dust devils in the 27 Martian atmosphere; in Section 3 we present the results from the model; in Section 4 28 we explore in detail the components of the dust devil parameterisation and consider how 29 our results compare against orbital and surface observations. Section 5 summarises this 30 work and in Section 6 we detail our conclusions. The MGCM used in this work (henceforth referred to as "the MGCM") is a global, 33 multi-level spectral model of the Martian atmosphere up to an altitude of ∼100 km, 34 as described by Forget et al. (1999). Simulations were completed at a resolution of 5°35 latitude × 5°longitude, resulting in a gridbox at the equator measuring ∼300 × 300 km. 36 Each simulation begins with a two-year 'spin-up' period from a dynamically static  The dust devil parameterisation was implemented by Newman et al. (2002). The subroutine was modified by Mulholland (2012) to add a two-moment tracer scheme, but 48 A C C E P T E D M A N U S C R I P T the core of the parameterisation remained the same. Here, we outline the components 49 of this dust devil parameterisation; in Section 4, we assess in detail the impact of each 50 component on the diurnal timing of dust devil lifting. 51 The flux of surface dust lifted by dust devils within an MGCM gridbox, F devil , is 52 calculated from the sensible heat flux, F s , and the dust devil thermodynamic efficiency, 53 η: where α D is a tuneable parameter representing the 'dust devil lifting efficiency', required  The quantity η arises from the modelling of a dust devil as a 'heat engine', following 61 Rennó et al. (1998). η is the thermodynamic efficiency of a dust devil: the fraction of 62 the input heat that is converted into mechanical work. This thermodynamic efficiency is in which p surf is the local surface pressure, p top is the pressure at the top of the convective 65 boundary layer (CBL) within the Martian atmosphere, and χ is equal to the specific gas 66 constant (R) divided by the specific heat capacity at constant pressure (c p ).

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The sensible heat flux, F s , represents the input heat available to drive the dust devil 68 'heat engine', and can be written as: where ρ is the near-surface atmospheric density, C D is the surface drag coefficient, U is 70 the horizontal wind speed, t surf is the surface temperature, and t atm is the temperature 71 in the lowest layer of the atmosphere.

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The surface drag coefficient C D is parameterised using the classical expression for a 73 boundary layer drag coefficient (Esau, 2004): where the von Kármán constant κ ≈ 0.4, z is the height of the lowest layer of the 75 atmosphere, and z 0 is the surface roughness length. In these simulations z ∼ 5 m. The 76 surface roughness length was kept constant at z 0 = 0.01 m, resulting in a constant value 77 of C D across the planet's surface.

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The wind speed U is the magnitude of the near-surface wind speed, calculated from 79 the large-scale zonal and meridional wind components (u and v) within the lowest layer 80 of the atmosphere.

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The dust devil parameterisation in operation within the MGCM has been used as the  The simulations were completed using prescribed dust fields. In the current approach, 100 dust lifted by both dust devils and near-surface wind stress is combined into a total 101 atmospheric dust field, which is then scaled (at gridbox resolution) to match daily global 102 maps of the optical depth of the Martian atmosphere (Montabone et al., 2015). Dust from 103 both surface-level processes is treated as equivalent once it is within the atmosphere. The 104 local atmospheric dust environment during a lander's observations can be approximated 105 using these fields: the modelled optical depth that would be reported at a surface location 106 in the vicinity of a lander's position can be compared to the optical depth recorded by 107 that lander during its observations.

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If a dust map has been constructed for the year in which a mission took place (for 109 example, the Phoenix mission landed in MY29), a simulation using the relevant atmo-   The amount of dust present in the atmosphere has an effect on dust devil lifting 117 primarily through its impact on surface and near-surface temperatures. Atmospheric 118 dust absorbs incident solar radiation, resulting in a heating of the atmosphere and a 119 reduction of surface insolation (Zurek, 1978). A high level of atmospheric dust, such 120 as that observed during dust storms, will therefore cause an increase in near-surface    Hemisphere spring. Figure 2a shows the same data plotted as a histogram. These figures year, illustrating the seasonal shift in the distribution.

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Surface observations provide more dust devil lifting diurnal variation information 150 than orbital observations. We completed simulations for direct comparison with pre-151 vious studies that use data from the four surface missions identified in  The following figures display the diurnal variation in dust devil lifting for each site.

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The envelope encompassing all of the results obtained through the analysed time period is shown, as well as the average across that period. Note that the amounts of dust lifted 163 vary by two orders of magnitude between the different lander sites.     locally-forced wind flows and large-scale, regional circulations (e.g. lower-level Hadley 284 circulation) must also be considered .

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Observations of terrestrial dust devil activity suggest that near-surface winds must be 286 present for the initiation of dust devils, but that high wind speeds may inhibit their for-     We compare our results directly with results from the comparison studies mentioned 327 in Section 3 (and displayed in Figures 4 and 5). The comparisons are detailed below and 328 summarised in Table 2.  Table 2.

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Parameterised dust devil activity depends on the sensible heat available to the dust 456 devil and its thermodynamic efficiency (how readily it converts available heat into work).

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The thermodynamic efficiency of a dust devil is driven by the depth of the local CBL, 458 which follows a predictable diurnal pattern driven by atmospheric heating due to in-  Our results agree with a majority of published surveys, and disagree with the as-491 sumption that Martian dust devil timing distributions can be simply extrapolated from 492 terrestrial observations. Dust devil activity will not necessarily peak in the early after-493 noon, and local wind speeds may act as a strong governor of the timings of dust devils. 494 We suggest that the generally accepted description of dust devil behaviour on Mars is 495 incomplete.

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Theories of dust devil formation may need to be further developed (or specifically 497 tailored) in order to be truly applicable to vortices forming in a thin atmosphere over a 498 desert that covers the entire surface of a planet. Lorenz and Radebaugh (2016) suggest 499 that dust devils are "systematically more common" within low pressure environments.  While dust devil theories may not transfer directly between terrestrial and Martian 506 dust devils, the parameterisation may also need improvement. One factor that must be 507 considered is that of the input heat source driving the model dust devil 'heat engine'.

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A near-future surface mission that may facilitate such observations is NASA's InSight 526 (planned to carry temperature, pressure and wind sensors, and cameras (Smrekar, 2015)).

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Orbital images that span the diurnal period may be obtained from the Colour and Stereo  In this paper we have presented the results of our investigation into the diurnal varia-532 tion of dust devil activity, discussed the details of the MGCM dust devil parameterisation, 533 and compared our results with lander and spacecraft observations. In conclusion:

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• The modelled dust devil activity displays a wider than anticipated diurnal range, 535 with more activity occurring during the morning than was expected. Heating due 536 to insolation produces conditions suitable for dust devil formation, but we identify 537 that the diurnal variability of dust devil activity is governed by local wind speeds: 538 higher wind speeds generate higher levels of dust devil activity.