Dust Emissions on Mars From Phoenix Lidar Measurements in Relation to Local Meteorological Conditions

The diurnal cycle of dust aerosols on Mars is studied by analyzing lidar observations at the Phoenix landing site under cloud‐ and fog‐free conditions and in the absence of elevated, long‐range transported dust layers. There is a pronounced diurnal cycle in the dust‐layer height with minimum heights of 4–6 km occurring between 11:00 and 17:00 local time. The ratio of the aerosol optical depth (AOD) within the lowermost 2 km to the total AOD reaches peak values at the same time. This can be explained by local dust emissions driven by the diurnal cycle of heating and cooling in the boundary layer. Analysis of wind and pressure measurements show that the gustiness of surface winds and the frequency of convective vortices undergo diurnal variations resembling those of AOD, indicating that these processes are the main drivers for local dust emissions.


Introduction
Dust emissions on Mars are driven by processes ranging from local dust eddies to global dust storms.General circulation models account for lifting of dust by wind stress and by convective vortices (dust devils) (Kahre et al., 2006).The primary process in wind-stress generated dust is saltation, a predominantly horizontal flow of coarse particles in close proximity to the ground.These particles can, upon impact with the surface, transfer part of their momentum and kinetic energy to smaller particles, which can be kicked off the surface and remain airborne for extended periods of time (Kok et al., 2012).Saltation is initiated if the wind speed exceeds a threshold drag velocity known as the fluid threshold; it can be maintained if the wind speeds exceeds the so-called dynamic or impact threshold, which on Mars is an order of magnitude less than the fluid threshold (Kok, 2010a(Kok, , 2010b)).This hysteresis effect suggests that dust emission related to saltation can take place at wind speeds much lower than the fluid threshold if strong wind gusts assist in initiating the process (Kahre et al., 2006).Dust-devil lifting mainly depends on the vertical sensible heat flux, on the surface pressure, and the pressure at the top of the planetary boundary layer (PBL) (Kahre et al., 2006).Other mechanisms have been proposed to contribute to dust emissions, such as solid state greenhouse and photophoretic effects (Wurm et al., 2008) as well as forced convection within porous soils (de Beule et al., 2014).
Here, data from the Phoenix lander are analyzed with a focus on local dust emissions.Phoenix observations have previously been used to investigate clouds (Dickinson et al., 2010(Dickinson et al., , 2011;;J. A. Whiteway et al., 2009), dust aerosols (Daerden et al., 2015;Davy et al., 2009;Dickinson et al., 2011;Komguem et al., 2013), soil properties (Shaw et al., 2009), turbulent heat fluxes (Davy et al., 2010), and dust devils (Ellehoj et al., 2010).The main novelty of the present study is that the diurnal cycle of local dust emissions as observed by the Phoenix lidar is analyzed in relation to the diurnal cycle of local meteorological conditions, particularly wind speed, gustiness, and the frequency of convective vortices.The analysis software and output data are made freely available (Kahnert & Ceolato, 2024).

Phoenix Data and Processing
Phoenix landed in Green Valley within the lowland region Vastita Borealis at 68.22°N, 125.75°W on 25 May 2008 (solar longitude L s = 77°), 30 sols before summer solstice.Lidar observations are available until 24 October 2008 (148 sols after landing, solar longitude L s = 147°).
The Phoenix lidar is a diode pumped, passively Q-switched Nd:YAG elastic backscatter lidar emitting 532 and 1,064 nm light into the zenith direction.The backscattered light was collected by a 10 cm telescope and detected as an analog signal by an avalanche photodiode (APD) at 1,064 nm, as well as by a photon multiplier tube at 532 nm as both an analog and a photon-counting signal.The analog signal was averaged, and the photon count accumulated over 2,048 pulses, resulting in a temporal resolution of 20.48 s.After averaging over height bins, the vertical resolution was 20 and 50 m for the analog and photon signals, respectively.Here, only data at 532 nm are analyzed, since the signal at 1,064 nm had a fairly low signal-to-noise ratio above 2 km altitude (Komguem et al., 2013).It was not possible to perform a relative calibration of the 532 and 1,064 nm channels, since the pulse energy at these two wavelengths depends on the instrument internal temperature, but the output energies of the laser pulses at the two wavelengths were not recorded with sufficient accuracy during the operation on Mars (Komguem et al., 2013).A more detailed description of the lidar instrument and calibration can be found in J. Whiteway et al. (2008).
1. Photon counting is used for detecting the weak signal at high altitudes.At low altitudes the analog signal is used, because the photon signal can be outside the detector's linear dynamic range.Thus the analog and photon signals need to be merged (with a smooth overlap region) around a critical altitude at which the nonlinearity becomes significant.We found that a smooth mearger can generally be obtained by considering the photon/ analog ratio (normalized to unity at high altitudes) and its standard deviation σ r , and by defining a nonlinearity threshold of max{1.01, 1 + 3σ r }.When exceeding this threshold, the photon signal is considered to be nonlinear.2. The backscattered signal near the ground lies outside the telescope's field of view (FOV), followed by an altitude range of incomplete overlap between the returning laser pulse and the telescope FOV, while above that range the return signal lies fully within the FOV.The alignment of transmitter and receiver, hence the degree of incomplete overlap and its altitude range vary with temperature.A temperature-dependent correction has been applied to account for the incomplete capture of the return signal at low altitudes.3. The data were averaged over time (up to a maximum of 1 hr).4. The background signal was modeled by vertically averaging the photon counts at high altitudes (≥19 km), and the background was subtracted. 5.The observed lidar return signal is given by where β(z) and α(z) are the backscattering and extinction coefficients, respectively, at altitude z, and C is a calibration constant.The extinction coefficient was retrieved by the method of Fernald (1984) for a turbid atmosphere (Equation 10 in that paper), that is, scattering by aerosols dominates over scattering by air.The lidar equation was integrated from the top downwards with the constraint that the total aerosol optical depth (AOD) be equal to that observed by the Phoenix Surface Stereo Imager (SSI) (Lemmon et al., 2008).The SSI observations have been linearly interpolated in both time (based on 360 observations in total, typically 1-3 per sol), and in wavelength (between 451 and 671 nm) to match those of the Phoenix lidar.
6.During midday the background skylight often limited the detection of the backscattered laser light to low altitudes, typically z ≤ 7 km, making it difficult to use the AOD measurement as a constraint in the extinction retrieval.This problem has been addressed by merging the low-altitude extinction profile with a high-altitudes background profile, either taken from the nearest nighttime observation, if available, or else taken to be an average over all nighttime profiles.
The Phoenix lander contained pressure, temperature, and wind instrumentation (Taylor et al., 2008).Here the wind and pressure measurements are analyzed.The horizontal wind speed u is a derived product from the telltale (TT) instrument (Holstein-Rathlou et al., 2010), which was mounted 1 m above the lander deck, hence 2 m above the surface.There are over 7,400 wind-speed data points available at irregular time intervals, usually clustered in time with an average rate of one observation every 2.3 ± 0.3 s.To investigate the diurnal cycle of gustiness, the wind-speed data are first divided into 12 two-hour time slots, that is, the slots comprise observation times at local midnight ±1 hr, 2:00 a.m. ± 1 hr, etc.Within each subset, the data are further grouped into observations that are no more than 5 min apart.For each group that contains, at least, five observations u(t), the maximum, mean, and standard deviation, max(u), ū, and σ(u), are computed.Two dimensionless measures of gustiness are considered, namely, σ(u)/ ū and |max(u) ū|/ ū.This approach gives the gustiness over a timescale of 5 min.To obtain the diurnal variation of the mean gustiness one computes 〈σ(u)/ ū〉 and 〈|max(u) ū|/ ū〉 , where 〈 ・・・〉 denotes the ensemble mean over each of the 2-hr time slots, and the ensemble comprises data from the entire 148-sol operation period.
The pressure sensor was near the lander deck (1 m above the ground) and had a temporal resolution of 2 s.Convective vortices passing the landing site can be detected by drops in surface pressure, as analyzed in detail in Ellehoj et al. (2010), who attributed convective vortices to pressure drops Δp with a magnitude of, at least, 0.3 Pa and a duration of 10-20 s.A stricter criterion with amplitudes >0.5 Pa had also been considered.Since the data of that study are not freely available, parts of the pressure-drop analysis are reproduced here.This reanalysis is based on Release 3 corrected pressure data of the Phoenix meteorological data product.The earlier Releases 1 and 2 contained incorrect values (Dickinson, 2008).An even more recent corrected data set by Kahanpää et al. (2020) only contains sample intervals of 512 s, which is too coarse for detecting convective vortices.

Results and Discussion
Figure 1 shows the retrieved extinction coefficient versus time and altitude.During the first half of the mission (sol ≤ 75) one typically sees a distinct dust layer extending to an altitude of 4-6 km, consistent with J. A. Whiteway et al. (2009); Komguem et al. (2013).A boundary-layer height extending up to 6 km is common on Mars (Petrosyan et al., 2011).Later in the summer (sol ≥ 80), there are numerous ice-cloud layers around 3-6 km and near-surface ice-fog.One reason is that the temperature started to decrease after sol 80 (Dickinson et al., 2011).Another reason is that clouds and fog were typically observed at night, and they dissipate in the morning (Dickinson et al., 2010).Before sol 75%, 66% of all measurements are daytime observations (between 8:00 and 18:00 local true solar time (LTST)), while after sol 75%, 70% of all measurements are nighttime observations.
Figure 2 presents selected profiles of the extinction coefficient.The left and center panels illustrate a typical diurnal cycle of dust in the PBL.On sol 50 (left) during the day (red) there is a distinct dust layer extending up to 4-5 km, above which the extinction decreases sharply.During the evening (blue) and early night (black), this dust layer becomes less and less distinct.On sol 56 (center) late at night (black), the extinction coefficient is a smooth, decreasing function of altitude, while from the early morning (blue) until noon (red) it increases in the PBL.
The right panel in Figure 2 shows a typical example for a fog layer near the ground and a cloud layer between 3 and 4 km (red), and an elevated dust layer around 5 km (black).In Daerden et al. (2015) such elevated, long-range transported dust layers were investigated in detail.Measurements in which fog, clouds or elevated dust layers were present have been excluded in the analysis of the dust-layer height.
The sensitivity of the retrieved extinction coefficient to the AOD constraint has been tested by varying the AOD within a range ±σ, where σ indicates the standard deviation of the AOD data record from the entire mission.The range of variation is shown for two cases in Figure 2 as a red shading.The retrieved extinction coefficient is quite sensitive to the AOD constraint, but the dust-and cloud-layer heights are highly robust.
The dust-layer height is quantified by defining α ground max as the maximum extinction in the lowermost 1 km, and by defining the dust-layer height z dust as that altitude at which the extinction has dropped below 15% of α ground max .For most daytime measurements, this is close to the altitude at which the extinction coefficient has just dropped to the background values in the free atmosphere.In the examples profiles in Figure 2 (left and center), z dust is indicated by horizontal lines in the corresponding colors.
Figure 3 (top) shows the diurnal variation of z dust .The symbols represent data from the entire 148-sol period that pass the selection criteria (no clouds, fog, or elevated dust).The red line shows arithmetic mean values for each 2hr bin.Minimum values around 4-6 km are found between 11:00 and 17:00.During nighttime the vertical distribution of dust is more featureless, resulting in maximum layer heights up to 10-12 km between 22:00 and 2:00.This confirms that the diurnal variation of z dust , which the examples in Figure 2 (left and center) suggested, is a phenomenon that can be found in the majority of lidar observations in the absence of clouds, fog, and elevated dust.The scattering of the data points about the mean is on the order of only ±1 km, indicating that these results are quite robust.
The retrieved extinction coefficient at 532 nm can be used to compute the AOD in the altitude range 0.1-2.0km.To minimize the impact of possible long-term trends in AOD, we normalized this near-ground AOD by the total column AOD from the SSI instrument (interpolated in time and wavelength to match the lidar observations, as explained earlier).This displays a distinct diurnal variation (Figure 3, bottom).
Between 12:00 and 14:00 LTST, dust between 0.1 and 2.0 km contributes, on average, 40% to the total AOD, while around midnight this contribution drops to a minimum around 20%, most likely caused by dust deposition and/or vertical mixing to higher altitudes.The daytime maximum suggests that there is an analogous peak in local dust emissions near the surface driven by a corresponding diurnal cycle in boundary-layer processes.
Lifting by near-surface wind stress is one important cause for injection of dust into the atmosphere (Kahre et al., 2006(Kahre et al., , 2017;;Newman et al., 2002).If the drag velocity u drag near the surface exceeds the fluid threshold u t drag , then a horizontal saltation flux is established.Very large particles are too heavy, while lifting of small particles is inhibited by cohesive forces binding the particles to the soil.The optimum particle size depends on the inter-particle cohesion I p .A typical value on Mars (as well as on Earth) is I p = 6 × 10 7 Nm 1/2 (Newman et al., 2002).Inspection of, for example, Figure 1 in Newman et al. (2002) shows that for this value the minimum drag velocity is roughly u t drag = 1.6 m/s.Within the surface layer of the PBL, the wind at a height z can be modeled as (Garratt, 1992) where k = 0.4 is von Kármán's constant, and the surface-roughness scale z 0 is the height at which the wind velocity goes to zero.Assuming z 0 = 0.01 m (Newman et al., 2002) and u t drag = 1.6 m/s, this yields u(z) = 21 m/s at z = 2 m, where the TT instrument was mounted.
Figure 4 (top left) shows the lidar extinction coefficient at 150 m altitude versus TT wind speed for the whole 148sol period (if the data pass the selection criteria).The TT measurements have been linearly interpolated in time to the instances of the lidar measurements.There is no clear trend of growing aerosol extinction with increasing wind speed, nor is there a diurnal trend in wind speed (top right).The TT wind velocities only vary within a narrow range between 2 and 7 m/s, which is well below the fluid threshold of 21 m/s.
Since the impact threshold can be 1 order of magnitude lower than the fluid threshold (Kahre et al., 2017;Kok, 2010aKok, , 2010b)), saltation can be initiated by strong wind gusts (Newman et al., 2002), and subsequently maintained by relatively low wind velocities.Figure 4 (center left) shows the diurnal cycle of the gustiness of the TT winds.The two measures of gustiness shown in the Figure were explained in Section 2. There is a pronounced gustiness maximum in the early afternoon, and a minimum at night.This mirrors the diurnal cycle of AOD, especially within the altitude range 0.1-2 km (Figure 3

bottom).
Figure 4 (center right, black line) shows the normalized frequency distribution, f(u), of TT wind velocities, considering the entire TT data set (i.e., no time-interpolation to the instances of lidar measurements has been performed).f(u) resembles a Weibull distribution (Seguro & Lambert, 2000) where κ is a gustiness scale parameter (the lower κ, the higher the gustiness), and c is a velocity scale parameter.The red dashed line shows the best fit obtained with κ = 2.6 m/s and c = 4.7 m/s.Even the strongest wind gusts observed during the operation of Phoenix rarely exceeded 15 m/s.This is confirmed in Figure 4 (bottom left), which shows the normalized frequency of wind gusts exceeding 10 m/ s (black solid line) and 15 m/s (red dashed line).There is a diurnal cycle similar to that of the gustiness (center left), albeit confined to a narrower temporal range between 9:00 to 20:00 LTST.Wind gusts exceeding 10 m/s occur with a maximum frequency of 1%, while wind gusts stronger than 15 m/s are extremely rare.There was not a single occurrence of wind velocities exceeding the fluid threshold, 21 m/s, at 2 m above ground level.However, it was explained in Section 2 that the measurements and methodology used here for analyzing gustiness can only account for variations on a 5-min timescale.
For shorter timescales a higher gustiness is expected.For instance, the value of κ = 2.6 m/s obtained from the Weibull fit of the TT frequency distribution indicates a relatively low degree of gustiness.In Newman et al. (2002) it was proposed that κ in the range of 1-2 m/s (Lorenz et al., 1996) can be considered an upper limit for gustiness on minute timescales.Thus it is possible that strong gusts on shorter timescales could be responsible for initiating saltation, hence be a primary cause for the dust aerosols and its diurnal variation that are observed by the Phoenix lidar.
Another important emission process is dust lifting by convective vortices (Kahre et al., 2006(Kahre et al., , 2017;;Newman et al., 2002), which can be detected as pressure-drop events.Figure 4 (bottom right) shows the diurnal variation of the frequency of pressure-drop events at the Phoenix lander (averaged over the 148-sol period).Two pressuredrop thresholds have been considered, as explained in Section 2. The results are consistent with those in Ellehoj et al. (2010).The diurnal cycle of convective vortices largely agrees with that of the near-surface AOD (Figure 3 bottom), although the latter is temporally broader.

Conclusions
Earlier landing missions, such as Curiosity (Vicente-Retortillo et al., 2018) or Perseverance (Smith et al., 2023), contained instrumentation for observations of the total atmospheric opacity.A diurnal variation of the total opacity has been observed (Smith et al., 2023) peaking around mid-sol, when also convective vortices peak (Newman et al., 2022).Unlike those previous missions, the Phoenix lidar provided a unique opportunity to observe the vertical distribution of dust, hence to make a distinction between local emissions and long-range transport.Here, vertical profiles of the extinction coefficient have been retrieved and analyzed for the 148-sol period of operation (from L s = 77°to L s = 147°).Only data obtained in the absence of clouds, fogs, and elevated, long-range transported dust layers were considered, which made it possible to determine a dust-layer height z dust .The main findings are: 1. z dust undergoes a pronounced diurnal cycle, with minimum heights of 4-6 km during LTST between 11:00 and 17:00.2. The relative contribution of the AOD in the lower part of the boundary layer (0.1-2.0 km, retrieved from the Phoenix lidar) to the total AOD (based on SSI observations) has a night-time minimum around 0.2 and a daytime maximum of 0.4 around noon. 3. The gustiness derived from the TT wind speed measurements as well as the frequency of pressure drop events display a diurnal variation that mirrors that of AOD(0.1-2.0 km)/AOD(column).
A plausible explanation is that local dust emissions are driven by saltation and/or convective vortices, which undergo diurnal variations driven by the diurnal cycle of heating and cooling.Saltation on Mars can be initiated by strong wind gusts on short time scales, yet it can be maintained by much calmer balanced winds (Kahre et al., 2017;Kok, 2010aKok, , 2010b)).This could explain the presence of near-surface dust and its daytime maximum even though the recorded wind speeds were below the fluid threshold.
GCM simulations that only account for wind-stress lifting fail to reproduce observed background dust during northern spring and summer (Basu et al., 2004;Newman et al., 2002).Convective vortices have been identified as an important emission process that contributes to background dust loading (Balme et al., 2003;Fisher et al., 2005).This process is accounted for in the NASA Ames Mars general circulation model (Kahre et al., 2006).Dust lifting by convective vortices is a local, small scale event, but it occurs ubiquitously over the entire planet (Kahre et al., 2017).The dust-devil activity at Phoenix, indicated by the frequency of pressure-drop events, displays a diurnal variation that approximately mirrors that of local dust emissions as reflected by the lowaltitude AOD.In addition to a diurnal cycle, dust-devil emissions can also undergo an inter-annual variation (Vicente-Retortillo et al., 2018).

Figure 1 .
Figure 1.Time series of vertical profiles of the extinction coefficient.

Figure 3 .
Figure 3.Diurnal variation of the dust-layer height (top), and optical depth at 532 nm between 0.1 and 2.0 km normalized by the total column aerosol optical depth (AOD) (bottom).The AOD between 0.1 and 2.0 km has been obtained from the lidar extinction, and the total AOD is based on Surface Stereo Imager observations.Symbols show data from all sols of the mission, red lines show 2-hr arithmetic mean values.

Figure 4 .
Figure 4. Top left: Extinction coefficient versus the telltale (TT) wind speed.The circles show the observations, the red line presents a linear fit to the data.Top right: diurnal variation of TT wind speed measurements (circles) and 2-hr arithmetic mean values (red line).Center left: diurnal variation of gustiness, as indicated in the legend.Center right: normalized frequency distribution of TT wind velocities (black solid line) and best-fit Weibull distribution (red dashed line).Bottom left: normalized frequency distribution of TT wind speeds exceeding a threshold u t as indicated in the legend.Bottom right: Diurnal variation of the number of pressure drops per hour exceeding a prescribed threshold, as indicated in the legend.