Circadian rhythm of dune-field activity

TL;DR

This study uncovers a daily rhythm in dune activity driven by atmospheric boundary layer convection, linking climate dynamics to sand and dust transport in desert environments on Earth and Mars.

Contribution

It provides the first empirical evidence connecting diurnal temperature cycles with dune activity through multi-scale field experiments and global analysis.

Findings

Daily sand and dust transport rhythms are driven by atmospheric convection.

Surface wind speed correlates with diurnal temperature cycles across dune fields.

Climate feedback mechanisms influence desert growth and dune activity on Mars.

Abstract

Wind-blown sand dunes are both a consequence and a driver of climate dynamics; they arise under persistently dry and windy conditions, and are sometimes a source for airborne dust. Dune fields experience extreme daily changes in temperature, yet the role of atmospheric stability in driving sand transport and dust emission has not been established. Here we report on an unprecedented multi-scale field experiment at the White Sands Dune Field (New Mexico, USA), where we demonstrate that a daily rhythm of sand and dust transport arises from non-equilibrium atmospheric boundary layer convection. A global analysis of 45 dune fields confirms the connection between surface wind speed and diurnal temperature cycles, revealing an unrecognized climate feedback that may contribute to the growth of deserts on Earth and dune activity on Mars.

Equations

$$\tau ={\int }_0^T{R}_{PP}(t)dt$$

$$u=\{\begin{array}{ll}\frac{u_{\ast }}{\kappa }\{\ln \left(\frac{z-d}{z_0}\right)-2\ln \left(\frac{1+x}{2}\right)-\ln \left(\frac{1+x^2}{2}\right)+2\arctan (x)-\frac{\pi }{2}\}& ,\zeta <0\\ \frac{u_{\ast }}{\kappa }\left\{\ln \left(\frac{z-d}{z_0}\right)+\beta \frac{z-d}{L}\right\}& ,\zeta >0\text{numberthis}\end{array}$$

$$\sigma =\frac{1}{N}\sum _{i=1}^N|{\left\{\hat{u},{\hat{P}}_s\right\}}_i-\{\hat{u},F\}|$$

$$\frac{d⟨\theta ⟩}{dt}=\frac{1+A}{z_i}{b}_0$$

$$\frac{dT}{dt}=\frac{1+A}{z_i}{b}_0-\frac{1}{2}\frac{d⟨{\Gamma }_d{z}_i⟩}{dt}\text{numberthis}$$

$$\max \frac{dT}{dt}=\frac{\pi \delta T}{{\tau }_D}\text{numberthis}$$

Full text

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This manuscript was compiled on

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Wind-blown sediments define the regional climate and topography of large swaths of Earth and other planets (1, 2, 3, 4). Sand saltates across deserts creating forms like dunes and ripples (5), while dust lofted high into the atmosphere serves as a catalyst for other Earth-system processes (6) like cloud nucleation (7) and phytoplankton growth (8). Appropriate descriptions of sediment dynamics are important for revealing both past climate, through aeolian stratigraphic interpretations (9), and future climate, through dust in Earth-system models (ESMs) (5). The latter is an especially important challenge considering predictions of increased aridity in Earth’s future (10). Current ESMs used to estimate dust and sand fluxes employ sediment transport algorithms to find the critical friction velocity required to initiate particle motion (11). A shortcoming of these algorithms is their neglect of atmospheric stability (5), a property of the atmospheric boundary layer (ABL) important for momentum transfer (12, 13, 14). Some ESMs use ABL schemes that account for stability; however, free-parameters in sediment transport algorithms are calibrated neglecting stability, resulting in biased predictions for global dust. Furthermore, all ABL schemes neglect the role of time-varying stability, instead opting for time-invariant alternatives (14, 15), introducing another bias in predictions. Current methods can therefore be poor predictors of the conditions that lead to sediment transport, suggesting overall that we must better understand the bridge between atmospheric stability and wind-blown sand & dust.

Friction velocity, $u_{*}$, is a parameter that represents the shear of wind impinging on a rough boundary (12). In sediment transport studies, $u_{*}$ is usually derived by fitting time-averaged vertical profiles of horizontal wind velocity with the so-called Law of the Wall (or log law) theory (16, 17), which is derived under the assumptions of a steady and uniform, turbulent boundary-layer flow of an unstratified fluid. Although this theory may approximate flow in some portions of the Atmospheric Boundary Layer (ABL) sometimes, vertical density gradients create buoyancy forces that lead to large deviations (12, 13, 14, 18). Empirical functions have been developed in studies of the ABL to characterize this deviation via the Monin-Obukhov similarity theory (MOST) (12, 13, 14), which predicts enhanced $u_{*}$ aiding sand transport in unstably stratified conditions, and suppressed $u_{*}$ in stable conditions (19). MOST, however, assumes steady-state stratification and is therefore unable to capture the daily evolution of the boundary stress imparted by the ABL if there is sufficiently strong periodic solar heating (20). Moreover, knowledge of $u_{*}$ is necessary but not sufficient to forecast sand and dust transport. Winds must exceed a critical shear velocity, $u_{*,cr}$, for transport and erosion to occur, and this threshold increases rapidly with soil moisture due to formation of liquid bridges (21, 22, 23). Fast and warm surface winds drive evaporation and a lower $u_{*,cr}$, while calm and cool conditions facilitate condensation and a rise in $u_{*,cr}$.

Considering the above dynamics, we present a unprecedented multi-scale dataset suggesting that a solar-driven daily cycle of wind, heat and humidity variation in the ABL can lead to a circadian rhythm of dune-field activity as follows (Fig. 1). As the Sun warms the ground from sunrise into the day, that strong radiative flux evaporates water and heats air at the surface. This leads to thermal instability where near-surface vertical temperature gradients become out of equilibrium with the rest of the ABL. This departure from classical MOST, since the connection between momentum and heat throughout the column is lost, is due to the low thermal-inertia of the dune field. Convective forcing enhances turbulent mixing, eventually bringing momentum sourced from aloft down to the surface. As a result, surface winds speed up in the afternoon once the ABL has been fully mixed, by which point any surface moisture has been wicked away. Sand and dust transport are most likely to occur at this point, when surface winds are fast and the ground is dry. From sunset onward, surface air cools with the land faster than air aloft, slowly setting up stable thermal stratification (12, 13, 14) that blocks vertical mixing of momentum—and hence sediment transport from this mechanism—at night. Finally, night-time cooling eventually increases humidity and leads to condensation of water within surface sediments.

In situ results

We report concurrent observations of the ABL, sand saltation and dust emission at the White Sands Dune Field (New Mexico, U.S.A.) that strongly support our hypothesis. For 24 days during the known March-April windy season associated with dune activity (24), we conducted a field campaign we call Field Aeolian Transport Events (FATE) (Fig. 2 and SI Appendix, Fig. S1) that measured: sand saltation impacts; humidity; atmospheric stability; and horizontal wind speeds at 16 elevations in situ. We developed a novel machine-learning dust-detection algorithm operating on images from the GOES-16 satellite (see Materials and Methods, SI Appendix Fig. S2 and Movie S1) to obtain synchronous synoptic-scale data on atmospheric dust. Together, these data provide an comprehensive view of the genesis of transport events that sculpt dunes and pump dust into the atmosphere at White Sands.

Our data confirm previous findings (5, 16, 17) that sand saltation is initiated around a threshold wind speed, and on average becomes more intense as winds pick up (Fig. 3a). This behavior is variable, however, in part due to additional role of humidity. We find that the probability of occurrence of saltation diminishes with humidity; little to no transport occurs when relative humidity exceeds 40% (Fig. 3b). Similar trends are also observed for atmospheric dust (Fig 3c-d), confirming the expected link between sand saltation and dust emission (5). Having demonstrated high wind speed and low humidity at the surface indeed necessitate transport at White Sands, we now consider daily cycles in ABL dynamics that drive those surface conditions. In particular, we average data from all 24 days to produce a daily ‘climatology’ of the windy season. Our highest wind measurement is from 300 m elevation ($u_{300}$). The ABL thickness varies from $\sim 10^{2}$ m to $\sim 10^{3}$ m over a 24-hr period (25); although this implies that $u_{300}$ is sometimes within the ABL, it is our closest approximation to the free-stream synoptic-controlled winds. The closest measurement to the surface occurs at 0.32 m ($u_{0.32}$). We see that on the average day, $u_{300}$ and $u_{0.32}$ do not co-vary (Fig. 3e). Instead, high-elevation winds are fastest at night while low-elevation winds peak in the afternoon, a dynamic also observed in other arid landscapes (15). We believe this is due to thermal instability. We quantify stability using the potential virtual temperature lapse rate at 5.5 m (see Materials and Methods), $\gamma_{5.5}$, and find that peak negative stability occurs around the solar insolation maximum at noon, triggering enhanced surface winds that strengthen as the ABL is progressively mixed. Also in the afternoon, near-surface humidity reaches its daily minimum, indicating the desert surface is at its driest. As hypothesized, these dynamics culminate in sand saltation and dust emission that is focused in the afternoon (Fig. 3e). At sunset (roughly 18:00) the atmosphere becomes positively stable, the surface winds and transport activity die off, and the upper atmospheric winds speed up.

These observations are hard to reconcile with the Law of the Wall theory, which is often used in sand and dust transport studies (5, 16, 17). Indeed, friction velocities derived from this method are poor predictors of saltation, although prediction is enhanced when MOST equations are used to compute $u_{*}$ (see Materials and Methods and SI Appendix, Fig. S3). Nonetheless, the best predictor of saltation is the surface wind velocity, as observed in other studies (17). Although MOST explicitly incorporates atmospheric stability conditions, the steady-state assumption is broken in the strongly transient daily dynamics of the desert ABL (SI Appendix, section 1, Figs. S4 & S5).

One way to demonstrate violation of equilibrium is to examine the daily evolution of wind speed vs. stability as a trajectory in state-space (Fig. 4 and a longer Doppler lidar wind-velocity profiler deployment in 2017 shown in SI Appendix, Fig. S6). An ABL with constant free-stream winds would have no path dependence, and hence a unique relation between the variables. We compare wind speed measured at three elevations—the lowest ($u_{0.32}$) and highest ($u_{300}$), and a popular reference ($u_{10}$)—to low-level ABL stability $\gamma_{5.5}$ (Fig. 4a). It is clear that the ABL exhibits path dependence and hence a memory of state; winds at all elevations are slower at dawn than dusk for equal stability. We observe similar dynamics at White Sands on a nearby, low-roughness playa during an earlier field deployment in 2017 (SI Appendix, Fig. S6). We find that such hysteresis does not arise for weakly-forced conditions, such as the authoritative CASES99 experiment (26) (SI Appendix, Fig. S7). The loops (Fig. 4a) have an internal area because of this hysteresis; however, the loop skews toward a positive relation between stability and speed aloft, and is opposite for near-surface winds. This is because daytime instability ‘props open the door’ for momentum to be mixed down toward the ground, and nighttime stability closes it allowing a nocturnal jet to skim over the underlying cold air (12, 15, 20, 26). On average the fastest near-surface winds are not seen during the strongest instability, but actually at neutral stability. This is a consequence of the hysteresis: it takes time for thermal plumes to entrain free-stream momentum. Scaling $u_{300}$ and $u_{0.32}$ by their expected values derived from the Law of the Wall (see Materials and Methods) highlights their distinctly opposing state-space trajectories (Fig. 4b). This provides insight that the neutral-stability assumption breaks down at the most crucial time for sediment transport (when the surface ABL momentum is greatest) and, paradoxically, is most correct at times when buoyancy influence is extreme.

Global results

We now generalize the insight from our field site by scrutinizing the diurnal ABL cycle over 45 dune fields during the past decade. We pair a newly constructed comprehensive atlas of active dune fields with a global hourly 32-km gridded reanalysis of meteorological observations from 2008-2017 derived from the ERA5 dataset (27) (see Materials and Methods and SI Appendix, Fig. S8). The magnitude of the diurnal near-surface temperature cycle is represented by the daily 2-m temperature range ($\delta T_{2}$), while the daily maximal 10-m wind speed ($u_{10,max}$) is our proxy for formative near-surface winds for sand transport that day. Dune-field size is represented by area ($A$), mapped from satellite data (see Materials and Methods). As expected, we see that dune fields correspond to regions of the planet having the largest diurnal temperature ranges (Fig. 5c).

The relation between $u_{10,max}$ and $\delta T_{2}$ for each dune field exhibits a striking threshold behavior (Fig. 5a). Below a critical temperature range $\delta T_{2,cr}\approx 18$ K, the day’s fastest winds do not vary with changes in the daily heat cycle for any dune field. For strongly forced days where $\delta T_{2}>\delta T_{2,cr}$, however, fast winds are overwhelmingly positively correlated with the daily temperature range. We posit that this is a macroscopic signature of the onset of convective instability, a non-equilibrium phenomenon that arises only under sufficiently large thermal forcing. At White Sands, these dynamics correspond to observed wind profiles (Fig. 4) that deviate from a steady-state description such as MOST (20); we expect similar behavior at other dune fields, but in situ measurements are lacking. We use a classical ABL model (12) to determine the maximum value for near-surface $\delta T$ at which a well-mixed characteristic ABL can maintain equilibrium. We find a critical value of $\delta T_{2,cr}=18.1$ K, consistent with the proposed onset of non-equilibrium dynamics in the global data (see Materials and Methods and SI Appendix, Fig. S9).

A secondary trend in the global data is that the relation between $u_{10,max}$ and $\delta T_{2}$ appears to be stronger for larger dune fields beyond $\delta T_{2,cr}$ (Fig. 5a). We hypothesize this is due to the ABL residence time over the dune field; the larger the dune field, the longer a column of air will experience its daily heat cycle. We compare the slope $K$ of the relation $u_{10,max}=K\delta T_{2}+c$, for $\delta T_{2}>\delta T_{2,cr}$, to a characteristic residence time of the ABL (Fig. 5b). The overall positive trend indicates that longer residence times lead to maximal daily wind speeds that are more sensitive to diurnal temperature range. Therein lies a potential—and previously unidentified—positive climate-land feedback: larger sand seas create stronger winds by fostering non-equilibrium ABL dynamics through their high-amplitude daily temperature cycles (Fig. 5c), in turn promoting dune activity and the outward migration of the sand-sea boundary. We attribute the scatter in this relationship, which grows with area, to coincident controls on dune field growth unique to each region (28, 29); be they orographic, coastal, lithologic, biologic, tectonic or climatic ($\sim 10^{4}$ yr and greater). In short, we suggest that very large sand seas are more likely to be affected in their extent by sediment supply, basin boundaries, and long-term climate change.

Implications

White Sands’ season of geomorphic work, when the most dust is emitted (30) and dunes migrate most (24), is also the driest and has the largest diurnal temperature range (25). FATE provides a mechanistic explanation for this observation: both atmospheric instability and low humidity are necessary to initiate sediment transport. Our in situ study is the first explicit demonstration of these dynamics, and the accompanying global study of many active dune fields on Earth serves to generalize them. Desert environments have the highest aridity and diurnal temperature ranges on Earth (31). We posit that the dynamics reported here are not unique to the modern dune fields and time periods we studied, and point out that previous research has hinted at similar behavior in other dune fields (18, 19, 32). Further, we suggest that dune fields nurture the ABL properties that lead to wind-blown sand, and that this coupling may strengthen as they grow, in-turn creating a positive feedback. In some cases this feedback may outpace stabilizing mechanisms for dune field boundaries, such as vegetation growth (33, 34).

The understanding gained through this work may help to explain other phenomena. The positive feedback likely acts over geologic timescales in the expansion of sand seas, extending to the large dune systems during the Last Glacial Maximum and across subtropical supercontinents (9). We also expect the Martian ABL to adhere to these dynamics. Based on recent data (35, 36) we believe that Nili Patera, a well-studied and representative active dune field on Mars (37), has a daily near-surface temperature range approximately 25% greater than $\delta T_{2,cr}$ during the dusty season (38) (see Materials and Methods). We hypothesize that enhancement of surface winds by non-equilibrium ABL dynamics may help to resolve a current riddle on Mars, where surface winds simulated with MOST are too weak to explain actively migrating dunes (39, 40).

\matmethods

Doppler lidar wind-velocity profiler

The Zephir 300 machine measures the Doppler shift of a 1560 nm continuous-wave laser beam off passive tracers in the atmosphere. The beam is iteratively focused around distances with a lens as it traces a cone above using a revolving mirror, measuring averages of wind vectors centered within an Eulerian area at heights $z$ during revolution time (41). After omitting revolutions with insufficient backscatter and power, the raw averages are linearly interpolated onto a grid at the most frequent raw timestep (17 s). The heights $z$ are chosen to distribute evenly in $\ln(z)$ between the machine’s maximum (300 m, set by a maximum lens probe volume at $d$), minimum (10 m, safety), including a mandatory (38 m) height. Temperature is measured on the machine at 1 m. The machine stores data locally and is powered by solar panels. Note that the lidar was also deployed for 70 days (March-May 2017) at White Sands in a different location at the playa-dune boundary, where surface roughness was much lower and concurrent measurements of other quantities were not made (SI Appendix, Fig. S6). The locations (during FATE and in 2017), outside the influence of dune-steered flow in the formative direction, are shown in SI Appendix Fig. S1.

Met tower

This study uses measurements of humidity, pressure, temperature (all at 10 m) and wind speed (at 5 and 2 m) from a meteorological tower erected by the National Parks Service and Texas A&M University marked in SI Appendix Fig. S1. Data are output at 10-min timesteps as averages (set by local memory) using a Campbell Scientific CS1000 logger and linearly interpolated onto the same grid as the lidar for lapse rate calculations. The tower sends data by cellular modem (available as WHS02 at https://mesowest.utah.edu) and is powered by solar panels.

Cup anemometers

We present data from 3 cups of a 4 cup anemometer mast (one cup had an electrical failure during the campaign) taking wind speed measurements at approximately log-spaced (0.32 m, 0.76 m and 1.68 m) heights. The cups are each calibrated with an optical gate to match the cup anemometers on the Met tower. Data are stored at 1 s timesteps (set by cup inertia). An Arduino stores data locally and is powered by solar panels. This small mast was erected adjacent to the lidar (location in SI Appendix Fig. S1) to understand near-surface flow better.

Saltation sensor

The Sensit H14-LIN saltation sensor uses changes in resistivity of a crystal, housed in an aluminum cylinder, due to its deformation to infer the energy of sand grain impacts. The kinetic energy of all impacts within 10 s timesteps (set by local memory) are summed using a pulse height analyzer method, effectively ensuring no impact is uncounted. Mounted vertically with the instrument body above ground (Fig. 1), the crystal had an average height of 0.2 m above the surface of a barchan stoss during the deployment (SI Appendix, Fig. S1). The sensor data are stored on a Campbell Scientific CS1000 logger and the system is powered by solar panels. Saltation events are defined as periods of time for which a smoothed power timeseries continuously exceeds the lower quartile of observed non-zero powers, with the smoothing timescale chosen as the integral timescale,

[TABLE]

Where $R_{PP}$ is the two-point correlation function of the unsmoothed power timeseries and $T$ is the campaign duration.

Satellite dust detection

GOES-16 is a geostationary satellite with a radiometer imaging at 16 wavelengths at 5-min intervals. We downloaded L2 reflectance and brightness temperature data for the continental USA (available at https://registry.opendata.aws/noaa-goes/) during the deployment. Using true color reconstructions from the 3 shortest wavelengths, and a residual of the 8.5 $\mu$m and 11.2 $\mu$m wavelengths (revealing nocturnal clouds (42), we manually identify two time periods each of dust emission, clear sky and cloud cover over a region of White Sands (Movie S1), totaling 1.3%, 3.2% and 4.5% (to 1 decimal place) of the deployment period, respectively. This constitutes a training set for a perceptron machine with 1 hidden layer of 100 rectified linear unit function nodes (43), where wavelengths 3.9 $\mu$m, 8.5 $\mu$m, 10.35 $\mu$m and 11.2 $\mu$m are features, that classifies image pixels into dust (red), clear sky (blue) or cloud cover (green) with probability $\chi$. These features were used as they are non-zero throughout an entire 24-hr period, provide unique information and pertain to the low-atmosphere alone (42). Samples are passed to the machine scaled by a function that transforms each feature of the training set to have zero mean and unit variance. Each pixel at each timestep is then classified, where $\chi_{d}$ is the average probability of dust suspension for the region, and an event is defined as $\chi_{d}>0.5$. Without common methods of validation, we look to our concurrent saltation measurements to verify the algorithm, finding that during ‘certain’ dust suspension ($\chi_{d}>0.95$) saltation occurs 77% of the time, and during ‘certain’ inactivity ($\chi_{d}<0.05$) saltation occurs 13% of the time (SI Appendix, Fig. S2). We believe mismatches are primarily due to (i) cloud coverage masking dust emissions, and (ii) that most dust from White Sands is from the playa upwind of the dunes (44) and therefore not local to, or subject to the same sediment availability constraints as, the dunes where the saltation sensor is.

Potential virtual temperature lapse rate

This quantity, $\gamma_{5.5}$, is the vertical gradient in virtual potential temperature between 1 m (at the Zephir 300) and 10 m (at the Met One tower). Virtual potential temperature is the temperature a parcel of air has when adiabatically transported to a reference pressure, defined as $\theta_{v}\equiv(1+a_{1}r_{v})(T(p_{ref}/p)^{a_{2}(1+a_{3}r_{v})})$ (where $r_{v}=a_{4}e/(p-e)$ is the mixing ratio, $e=a_{5}h10^{a_{6}(T+a_{7})/T}$ is the vapor pressure, and $a_{n}$ are empirical constants defined at http://glossary.ametsoc.org/wiki/). Only the Met One tower measured pressure and humidity, so we assume they are identical at 1 m and 10 m in this calculation.

Friction velocity derivations

The ABL flow parameters friction velocity $u_{*}$, roughness length $z_{0}$, Obukhov length $L$, and displacement height $d$ are derived separately for 10-min smoothed data for each measurement system. We smooth at this timescale because it is the shortest timescale of the longest timestep system, the met tower. For the cup anemometers, only neutral Law of the Wall fits without displacement height are performed because the measurements are not fully within the flow region where stability effects are noticeable, and we do not want to over-constrain the fit. We fit an $O(1)$ polynomial to the measurements in $\ln(z)$ to find $u_{*}$ and $z_{0}$ in $u=u_{*}\ln(z/z_{0})/\kappa$. The same calculation is performed on the met tower measurements. For the Doppler lidar, a subregion of wind profiles are fitted to integral forms of the Monin-Obukhov similarity theory and a neutral Law of the Wall theory. The subregions are where speed monotonically increases with height (with a maximum height of 109 m) from the lowest (10 m) measurement, and there are 4 or more data points available. This definition ensures no over-constraint and application of the theory to the appropriate region of the ABL (12). The integral form of MOST is given in Eqn. Friction velocity derivations,

where $x=(1-\gamma(z-d)/L)^{1/4}$, the stability parameter $\zeta=z/L$, $\beta=5$ and $\gamma=16$ (14). Both definitions are fit to each profile and the one with lowest variance is chosen. The form of the neutral Law of the Wall theory (with displacement height) is $u=u_{*}\ln((z-d)/z_{0})/\kappa$. All Doppler lidar fits are performed using a least-squares regression with a Cauchy loss function (45), starting on a landscape at typical values of flow parameters scaled by characteristic scale $\{u_{*}:4\cdot 10^{-1},10^{-2};z_{0}:10^{-1},10^{-2};L:\pm 10^{3},10^{1};d:10^{0},10^{-1}\}$, respectively. Von Karman’s constant is $\kappa=0.38$ in all calculations. From this, we see that the nearest-surface horizontal wind speed is the best predictor of saltation flux.

Variance of flow parameters and saltation

The coupling between ABL flow parameters, be it friction velocity or horizontal wind speed, and saltation power is calculated through the following routine that standardizes their different thresholds, magnitudes and sample sizes. Firstly, average saltation power values in bins of flow values (chosen such that there are 25 between the mean non-zero flow values and 0) are found. The bin where the average saltation power first exceeds 0.5 W is chosen as the threshold flow value for saltation (SI Appendix, Fig. S3). Because threshold wind speeds and friction velocities from different measurements are all different, we then collapse the data by scaling to the threshold flow values and saltation power. Then, average scaled saltation powers $\hat{P_{s}}$ are found for all scaled flow values $\hat{u}$ when binned similarly (100 bins between 0 and 1). Finally, the average distance between the scaled data and its mean relationship with saltation power $F=\langle\hat{P_{s}}(\hat{u})\rangle$ is defined as the variance,

[TABLE]

Where $N$ is the total number of samples for the flow parameter. The lower the variance, the less scatter in the fit. The values are 0.0305 for $u_{0.32}$, 0.0309 for $u_{2}$, 0.0316 for $u_{10}$, 0.0454 for cup anemometer $u_{*}$, 0.0568 for met tower $u_{*}$, 0.0792 for netural Law of the Wall lidar $u_{*}$, and 0.0646 for Monin-Obukhov similarity theory derived lidar $u_{*}$.

CASES99 comparison

The Cooperative Atmosphere-Surface Exchange Study (referred to in this paper as CASES99) was carried out to understand phenomena in the weakly-forced and primarily nocturnal atmospheric boundary layer. The location and timing of the experiment was chosen for clear and calm conditions over land (26). This leads us to expect conditions close to steady-state, acting as a useful counter-example to the strongly-forced, non-equilibrium dynamics observed at White Sands. Extensive measurements were taken to comprehensively document the boundary layer; in this study we only make use of a small subset of the data. Main tower high temporal resolution data from CSAT3 sonic anemometers was downloaded (https://data.eol.ucar.edu/) for October 1999 near Leon, Kansas (26). Prevailing wind speed and virtual temperature measurements were down-sampled from 20 Hz to 18 s temporal resolution using a box-car average to approximately match the doppler lidar at White Sands. 1.5 m and 10 m elevation virtual temperature measurements were converted to potential temperature $\theta_{v}\equiv T_{v}(p_{ref}/p)^{a_{2}(1+a_{3}r_{v})}$ with $r_{v}$ fixed to the mean FATE value 2.33 g/kg, giving a gradient of potential virtual temperature lapse rate (SI Appendix, Fig. S7c).

Global sand sea ERA5 reanalysis

Polygons of 45 active sand seas with a distribution in area and latitude similar to all sand seas were created (SI Appendix, Fig. S8). Each sand sea boundary was mapped as a shapefile using Google Earth to identify contiguous areas of dunes, recognizing that dune field boundaries are often not sharp. All polygons were drawn in the exact same manner on the same projection. Mapping was carried out at a coarse scale depending on the size of the sand sea, but always at a much finer resolution than the ERA5 grid spacing (see SI Appendix, Fig. S8). Dune field naming is based on a combination of common-place convention in the scientific literature and the local naming, and these are chosen neutral to jurisdiction claims. A shoelace algorithm was used to find the area of each sand sea.

The ERA5 reanalysis dataset (27) was downloaded (https://registry.opendata.aws/ecmwf-era5/), giving hourly 2-m temperature and 10-m prevailing wind speed over the decade 2008-2017. These data are gridded at 32-km resolution from a GCM strongly constrained by many forms of observation (27). Data for each sand sea is derived from land grid cells from the ERA5 that overlap with their respective polygons. Mean relationships between daily maximum 10-m winds and 2-m temperature change are found using averages of the former in 35 bins between 0 K and 40 K of the latter (Fig. 5a). Bins including less than 0.01% of the total data for a given sand sea are excluded from the relationship. In total the sand seas analyzed in this study account for 1.63% of the global land data used, and each day of the decade for each land grid cell totals $9.9\cdot 10^{7}$ points.

Critical diurnal temperature range

We employ characteristic scales for parameters in the so-called ‘slab model’ of well-mixed ABL growth (12) to estimate a critical diurnal temperature range for which the ABL evolution transfers from being in equilibrium to out-of-equilibrium with surface heating (Fig. 5a). The change in the average potential temperature in the mixed layer is modeled as,

[TABLE]

where $A$ is the so-called Ball parameter (46), $z_{i}$ is the layer height, and $b_{0}$ is the heat flux at the surface. Assuming a dry mixed layer, often the case in sand seas (25, 31), so $\theta=T+\Gamma_{d}z$, the near-surface air temperature ($T$) evolution is,

[TABLE]

If we assume a sinusoidal near-surface air temperature evolution during the day, $T=\delta T\sin(2\pi t/\tau_{D})/2+\bar{T}$, then the maximum daily change in $T$ is,

[TABLE]

Substituting Eqn. Critical diurnal temperature range into Critical diurnal temperature range, and employing characteristic scales (including $dz_{i}/dt\sim z_{i}/(\tau_{D}/2)$) for this equation, we find $\delta T=((1+A)\tau_{D}b/H_{ABL}-\Gamma_{d}H_{ABL})/\pi$ when $T$ is changing most. Assuming $\delta T$ is approximately $\delta T_{2}$ a critical range of $\delta T_{2,cr}=18.1$ K occurs for typical values of $A=0.2$, $\tau_{D}=1$ day, $F_{Hs}=550$ W/m2 (where $F_{Hs}=b_{0}\rho c_{p}$, $\rho=1.2$ kg/m3 and $c_{p}=1004$ J/kg/K), $H_{ABL}=1$ km, and $\Gamma_{d}=-9.8$ K/km. See SI Appendix Fig. S9 for a sensitivity diagram of $\delta T_{cr}$ to $F_{Hs}$ and $H_{ABL}$.

Nili Patera, Mars, ABL calculation

The dune field Nili Patera is located at 8*∘N, 67∘W and has active dune migration, especially in the ‘dusty season’ (Solar Longitude $L_{s}$ of 270±15∘*) on Mars (37). Using the Mars Climate Database (35, 36), the most common GCM dataset used in studies of Mars’ atmosphere that is validated using observations, we found values for 4 of the free parameters in our characteristic equation for the critical daily near-surface temperature range, $\delta T=((1+A)\tau_{D}F_{Hs}/H_{ABL}-\Gamma_{d}H_{ABL})/\pi$ (see the Materials and Methods section above for a derivation). The values at Nili Patera ($L_{s}=270$) are also quite representative of the Martian ABL in general: $F_{Hs}=85$ W/m2, $\rho=0.015$ kg/m3, $c_{p}=770$ J/kg/K, $H_{ABL}=6$ km. With $A=0.2$ and $\tau_{D}=88775$ s fixed, this leaves the dry adiabatic lapse rate, which is estimated as $\Gamma_{d}=-4.3$ K/km elsewhere (47, 38). The resultant critical range is $\delta T_{2,cr}=49.8$ K. With the Mars Climate Database (35, 36) predicting a diurnal temperature range of $\delta T_{2}=62$ K at Nili Patera ($L_{s}=270$), similar to measurements at Bagnold Dune Field (40), we find $\delta T_{2}=1.25\cdot\delta T_{2,cr}$, a value that sits comfortably in the observed range of above-critical $\delta T_{2}$ on Earth.

Data Availability

In situ data and all code from this study are publicly available at https://github.com/algunn/FATE. GOES-16 satellite data are available at https://registry.opendata.aws/noaa-goes/. ERA-5 reanalysis data are available at https://registry.opendata.aws/ecmwf-era5/.

\showmatmethods

\acknow

We thank David Bustos and White Sands National Monument for field support, Scott R. David for field assistance, and Keaton Cheffer for constructing equipment. Funding provided by; National Science Foundation NRI INT award #1734355 to D.J.J.; White Sands National Monument through NPS-GC-CESU Cooperative Agreement #P12AC51051 to R.C.E; and International Society of Aeolian Research through the Elsevier Aeolian Research Scholarship to A.G..

\showacknow