∎

11institutetext:  C. Gadal 22institutetext: Institut de Mécanique des Fluides
de Toulouse, Université de Toulouse Paul Sabatier, CNRS, Toulouse INP-
ENSEEIHT, Toulouse, France. 22email<EMAIL_ADDRESS>33institutetext: P.
Delorme 44institutetext: Energy and Environment Institute, University of Hull,
Hull, UK. 55institutetext: School of Geography and Environmental Science,
University of Southampton, Southampton, UK. 66institutetext: C. Narteau
77institutetext: Université Paris Cité, Institut de physique du globe de
Paris, CNRS, Paris, France 88institutetext: Giles F.S. Wiggs 99institutetext:
School of Geography and the Environment, University of Oxford, Oxford, UK.
1010institutetext: M.C. Baddock 1111institutetext: Geography and Environment,
Loughborough University, Loughborough, UK. 1212institutetext: J.M. Nield
1313institutetext: School of Geography and Environmental Science, University
of Southampton, Southampton, UK. 1414institutetext: P. Claudin
1515institutetext: Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI
Paris, PSL Research University, Université de Paris, Sorbonne Université,
Paris, France.

# Local Wind Regime Induced by Giant Linear Dunes: Comparison of ERA5-Land
Reanalysis with Surface Measurements

Cyril Gadal  Pauline Delorme  Clément Narteau  Giles F.S. Wiggs  Matthew
Baddock  Joanna M. Nield  Philippe Claudin

(Received: DD Month YEAR / Accepted: DD Month YEAR)

###### Abstract

Emergence and growth of sand dunes results from the dynamic interaction
between topography, wind flow and sediment transport. While feedbacks between
these variables are well studied at the scale of a single and relatively small
dune, the average effect of a periodic large-scale dune pattern on atmospheric
flows remains poorly constrained, due to a pressing lack of data in major sand
seas. Here, we compare local measurements of surface winds to the predictions
of the ERA5-Land climate reanalysis at four locations in Namibia, both within
and outside the giant linear dune field of the Namib Sand Sea. In the desert
plains to the north of the sand sea, observations and predictions agree well.
This is also the case in the interdune areas of the sand sea during the day.
During the night, however, an additional wind component aligned with the giant
dune orientation is measured, in contrast to the easterly wind predicted by
the ERA5-Land reanalysis. For the given dune orientation and measured wind
regime, we link the observed wind deviation (over 50°) to the daily cycle of
the turbulent atmospheric boundary layer. During the night, a shallow boundary
layer induces a flow confinement above the giant dunes, resulting in large
flow deviations, especially for the slower easterly winds. During the day, the
feedback of the giant dunes on the atmospheric flow is much weaker due to the
thicker boundary layer and higher wind speeds. Finally, we propose that the
confinement mechanism and the associated wind deflections induced by giant
dunes could explain the development of smaller-scale secondary dunes, which
elongate obliquely in the interdune areas of the primary dune pattern.

###### Keywords:

Atmospheric boundary layer Sand dunes Flow over hills

An edited version of this paper was published by Springer Nature: Gadal, C.,
Delorme, P., Narteau, C. et al. Local Wind Regime Induced by Giant Linear
Dunes: Comparison of ERA5-Land Reanalysis with Surface Measurements. Boundary-
Layer Meteorol (2022). https://doi.org/10.1007/s10546-022-00733-6 .

##  1 Introduction

The description of turbulent flows over complex topography is relevant for a
large variety of different environmental systems (Sherman 1978; Walmsley et
al. 1982; Baines 1995; Wood 2000; Venditti et al. 2013; Finnigan et al. 2020).
For example, the flow over hills is of primary interest for wind power,
meteorological and air pollution phenomena (Taylor et al. 1987). The
properties of these flows are also key to the understanding of geophysical
phenomena, including the formation of wind-driven waves on the ocean surface
(Sullivan and McWilliams 2010), dissolution bedforms (Claudin et al. 2017;
Guérin et al. 2020), or sedimentary ripples and dunes (Bagnold 1941; Charru et
al. 2013; Courrech du Pont 2015). Importantly, the troposphere presents a
vertical structure, with a lower convective boundary layer, of typical
kilometer-scale thickness, capped by a stably stratified region (Stull 1988).
The largest topographic obstacles, such as mountains, can therefore interact
with this upper region and lead to internal wave generation or significant
wind disturbances, such as lee-side downslope winds (Durran 1990).

Compared to hills and mountains, aeolian sand dunes offer idealized elevation
profiles for the study of atmospheric turbulent flow over topographies, due to
their smooth shape, free of canopies. Besides, dunes provide a rather wide
range of scales, from decameters to kilometers, and very often come in a
fairly regular pattern, which further simplifies the flow structure analysis.
Past studies have highlighted two important topographic feedbacks on the wind
flow close to the dune/hill surface. First is the effect on wind speed, with
documented flow acceleration on upwind slopes (Weaver and Wiggs 2011) and
deceleration on downwind slopes (Baddock et al. 2007), where the speed-up
factor is essentially proportional to the obstacle aspect ratio (Jackson and
Hunt 1975). Under multidirectional wind regimes with frequent wind reversals,
this speed-up effect induces large differences in the amplitude and
orientation of the resultant sediment transport between flat sand beds and the
dune crests (Zhang et al. 2014; Rozier et al. 2019; Gao et al. 2021). In
addition, the position of maximum velocity is typically shifted upwind of the
obstacle crest (Jackson and Hunt 1975; Claudin et al. 2013). This behaviour
has been theoretically predicted by means of asymptotic analysis of a
neutrally stratified boundary-layer flow over an obstacle of vanishing aspect
ratio (Jackson and Hunt 1975; Mason and Sykes 1979; Sykes 1980; Hunt et al.
1988; Belcher and Hunt 1998; Kroy et al. 2002). Experiments in flumes (Zilker
et al. 1977; Zilker and Hanratty 1979; Frederick and Hanratty 1988; Poggi et
al. 2007; Bristow et al. 2022), in wind tunnels (Gong and Ibbetson 1989;
Finnigan et al. 1990; Gong et al. 1996) and in field conditions at all scales
(Taylor and Teunissen 1987; Claudin et al. 2013; Fernando et al. 2019; Lü et
al. 2021), have also documented this effect. Interestingly, a similar
behaviour exists for the pressure perturbation, but with a slight downwind
shift for the pressure minimum (Claudin et al. 2021).

The second effect, much less studied, is the flow deflection that occurs when
the incident wind direction is not perpendicular to the ridge crest. While
predicted to be small (less than $10^{\circ}$) in the linear regime valid for
shallow topography (Gadal et al. 2019), significant flow steering has been
reported in the field on the downwind side of steep enough obstacles, such as
well-developed sand dunes (Tsoar and Yaalon 1983; Sweet and Kocurek 1990;
Walker and Nickling 2002; Smith et al. 2017) and in particular coastal
foredunes (e.g. Hunter et al. 1983; Rasmussen 1989; Walker et al. 2006, 2009;
Hesp et al. 2015; Walker et al. 2017; de Winter et al. 2020), mountain ranges
(Kim et al. 2000; Lewis et al. 2008; Fernando et al. 2019), and valley
topographies (Wiggs et al. 2002; Garvey et al. 2005).

Wind measurements over sand dunes have been mainly performed over small
bedforms, typically a few meters high (corresponding to several tens of meters
long) (e.g. Mulligan 1988; Hesp et al. 1989; Lancaster et al. 1996; McKenna
Neuman et al. 1997; Sauermann et al. 2003; Andreotti et al. 2002; Walker and
Nickling 2002; Weaver and Wiggs 2011). For practical reasons, fewer studies
have performed similar measurements on giant dunes (Havholm and Kocurek 1988),
with kilometer-scale wavelengths and heights of tens of meters. However, such
large dunes provide a choice configuration for the study of turbulent flows
over a complex topography. First, one expects larger wind disturbances for
larger obstacles. Secondly, their large size can make them interact with the
vertical structure of the atmosphere (Andreotti et al. 2009). Third, they
usually form large patterns in sand seas and thus behave as rather clean
periodic perturbations, in contrast with isolated dunes. Finally, because the
morphodynamics of aeolian bedforms is strongly dependent on the local wind
regime (Livingstone and Warren 2019), one can expect to see the consequences
of windflow disturbance by large dunes on neighbouring small dunes (Brookfield
1977; Ewing et al. 2006). A similar effect is observed on the properties of
impact ripple patterns due to the presence of dunes (Howard 1977; Hood et al.
2021).

Atmospheric flows have been much studied at the desert-scale with climate
reanalyses based on global atmospheric models (Blumberg and Greeley 1996;
Livingstone et al. 2010; Ashkenazy et al. 2012; Jolivet et al. 2021; Hu et al.
2021; Gunn et al. 2021), such as ERA-40, ERA-Interim or ERA5 (Uppala et al.
2005; Dee et al. 2011; Hersbach et al. 2020). However, the spatial resolution
of these reanalyses (tens of kilometers) implies average quantities that do
not resolve the smaller scales of interest, which range from individual dunes
to small mountains (Livingstone et al. 2010). Recently, the release of
ERA5-Land has partly resolved this limitation by providing up to 70 years of
hourly wind predictions at a $9$ km spatial resolution (Muñoz-Sabater et al.
2021). However, its validity remains to be studied, especially in remote
desert areas where assimilation of measured data is very low.

In this work, we compare local wind speeds and directions measured by
meteorological stations at four different locations inside and north of the
giant linear dune field of the Namib sand sea to the regional predictions of
the ERA5-Land climate reanalysis. Where the meteorological stations are
surrounded by a relatively flat environment, we show that local measurements
and regional predictions agree well. The agreement is also good in the
interdune areas of the sand sea, except for some weak winds blowing at night,
which exhibit an additional component aligned with the giant dune orientation.
These winds are not predicted by the ERA5-Land reanalysis (Sect. 2). Further,
we are able to link the magnitude of these differences to the circadian cycle
of the atmospheric boundary layer (Sect. 3). Finally, we draw implications for
the wind disturbances on smaller-scale dunes (Sect. 4), suggesting a possible
origin for crossing dunes, a distinctive secondary dune form observed in the
Namib and other sand seas.

Figure 1: Studied field sites. a Location of the different sites in Namibia.
b-e: Photographs of the meteorological stations. Figure 2: Wind data used in
this study. Satellite images of the different environments (Google-Earth,
Maxar Technologies, CNES/Airbus) are shown on the left. The black dots show
the location of the wind measurements stations. On the right of the photos,
the corresponding wind roses representing the data from the ERA5-Land climate
reanalysis and the local wind stations are displayed. Note: the graphical
convention for the wind roses is that the bars show the direction towards
which the wind blows (see color bar for velocity scale).

##  2 Wind Regimes Across The Namib Sand Sea

We measured the wind regime at four different locations in Namibia,
representative of various arid environments across the Namib desert (Figs. 1
and 2). The Etosha West station was located at the Adamax waterhole to the
west of Etosha Pan in northern Namibia, in a sparsely vegetated area. The Huab
station was near the coast on a hyper-arid flat gravel plain lying north of
the ephemeral Huab river. Here, barchan dunes up to a few meters in height
develop from the sediment blowing out of the river valley (Nield et al. 2017;
Hesp and Hastings 1998). These two stations were both located in relatively
flat environments. In contrast, the North Sand Sea and South Sand Sea stations
were located in the interdunes between linear dunes with kilometer-scale
wavelengths, hectometer-scale heights and superimposed patterns. In this
section, we describe and compare winds from local measurements and climate
reanalysis predictions.

###  2.1 Wind and Elevation Data

At each meteorological station (Fig. 1), wind speed and direction were sampled
every 10 minutes using cup anemometers (Vector Instruments A100-LK) and wind
vanes (Vector Instruments W200-P) at a single height, which was between 2 m
and 3 m depending on the station. The available period of measurements at each
station ranged from 1 to 5 discontinuous years distributed between 2012 and
2020 (Online Resource Fig. S1). We checked that at least one complete seasonal
cycle was available for each station. Regional winds were extracted at the
same locations and periods from the ERA5-Land dataset, which is a replay at a
smaller spatial resolution of ERA5, the latest climate reanalysis from the
ECMWF (Hersbach et al. 2020; Muñoz-Sabater et al. 2021). This dataset provided
hourly predictions of the 10-m wind velocity and direction at a spatial
resolution of $0.1^{\circ}\times 0.1^{\circ}$ ($\simeq 9~{}\textup{km}$ in
Namibia).

To enable direct comparison, the local wind measurements were averaged into
1-hr bins centered on the temporal scale of the ERA5-Land estimates (Online
Resource Fig. S2). As the wind velocities of both datasets were provided at
different heights, we converted them into shear velocities $u_{*}$ (Online
Resource section 1), characteristic of the turbulent wind profile. Wind roses
in Fig. 2 show the resulting wind data.

Dune properties were computed using autocorrelation on the 30-m Digital
Elevation Models (DEMs) of the shuttle radar topography mission (Farr et al.
2007). For the North and South Sand Sea stations, we obtain, respectively,
orientations of $85^{\circ}$ and $125^{\circ}$ with respect to the North,
wavelengths of $2.6~{}\textup{km}$ and $2.3~{}\textup{km}$ and amplitudes (or
half-heights) of $45~{}\textup{m}$ and $20~{}\textup{m}$ (Online Resource Fig.
S4 for more details). This agrees with direct measurements made on site.

Figure 3: Temporal comparison between the wind data coming from the ERA5-Land
climate reanalysis (orange lines) and from the local measurements (blue
lines). Coloured swathes indicate day (between 10.00 UTC and 22.00 UTC) and
night (before 10.00 UTC or after 22.00 UTC). Numbers in legends indicate the
average flow deflection $\delta_{\theta}$ and relative wind modulation
$\delta_{u}$ over the displayed period (see Sect. 3.2 for their definitions),
as well as the percentage $f_{\theta}$ and $f_{u}$ of occurrence of extreme
events ($\delta_{\theta}>50^{\circ}$, $|\delta_{u}|>0.6$). a,b: Huab station
in summer. b,c: Huab station in winter. d,e: Etosha West station in summer.
f,g: Etosha West station in winter. Time series of the two other stations are
shown in Fig. 5. Figure 4: Distributions of wind direction at Huab and Etosha
West stations for the ERA5-Land climate reanalysis (orange) and the local
measurements (blue). In each subplot, both distributions are plotted from the
same time steps, selected for different ranges of the wind wind velocity
(rows) in the ERA5-Land dataset. The numbers at the upper right corners give
the percentage of time steps selected in each sub-range (top), as well as the
percentage of them corresponding to the day – defined between 10.00 UTC and
22.00 UTC (bottom).

###  2.2 Comparison of Local and Regional Winds

The measured and predicted wind regimes are shown in Fig. 2. In the Namib, the
regional wind patterns are essentially controlled by the sea breeze, resulting
in strong northward components (sometimes slightly deviated by the large scale
topography) present in all regional wind roses (Lancaster 1985). These daytime
winds are dominant during the period October–March (Fig. 3f and Online
Resource Fig. 4f). During April–September, an additional (and often nocturnal)
easterly component can also be recorded, induced by the combination of
katabatic winds forming in the mountains, and infrequent ‘berg’ winds, which
are responsible for the high wind velocities observed (Lancaster et al. 1984).
The frequency of these easterly components decreases from inland to the coast.
As a result, bidirectional wind regimes within the Namib Sand Sea and at the
west Etosha site (Fig. 2a,c and d) and a unidirectional wind regime on the
coast at the outlet of the Huab River (Fig. 2b) are observed.

In the case of the Etosha West and Huab stations, the time series of wind
speed and direction from the regional predictions quantitatively match those
corresponding to the local measurements (Figs. 3, 4 and Online Resource Fig.
S5). For the North Sand Sea and South Sand Sea stations within the giant
linear dune field, we observe that this agreement is also good, but limited to
the October-March time period (Fig. 4a, b and e, f). However, the field-
measured wind roses exhibit additional wind components aligned with the dune
orientation, as evidenced on the satellite images (Fig. 2c and d).

More precisely, during the April–September period, the local and regional
winds in the interdune match during daytime only, i.e when the
southerly/southwesterly sea breeze dominates (Figs. 5c,d,g,h and 6). In the
late afternoon and during the night, when the easterly ‘berg’ and katabatic
winds blow, measurements and predictions differ. In this case, the angular
wind distribution of the local measurements exhibits two additional modes
corresponding to reversing winds aligned with the dune orientation (purple
frame in Fig. 6, Online Resource Fig. S6). This deviation is also associated
with a general attenuation of the wind strength (Online Resource Fig. S7).
Remarkably, all these figures show that these wind reorientation and
attenuation processes occur only at low velocities of the regional wind,
typically for $u_{*}^{\textup{ERA5-Land}}\lesssim
0.2~{}\textrm{m}~{}\textrm{s}^{-1}$. For shear velocities larger than
$u_{*}^{\textup{ERA5-Land}}\simeq 0.3~{}\textrm{m}~{}\textrm{s}^{-1}$, the
wind reorientation is not apparent. Finally, for intermediate shear
velocities, both situations of wind flow reoriented along the dune crest and
not reoriented can be successively observed (Online Resource Fig. S6).
Importantly, these values are not precise thresholds (and certainly not
related to the threshold for sediment transport), but indicative of a
crossover between regimes, whose physical interpretation is discussed in the
next section.

Figure 5: Same as Fig. 3 for North Sand Sea station in summer (a,b), North
Sand Sea station in winter (b,c), South Sand Sea station in summer (d,e) and
South Sand Sea station in winter (f,g). Figure 6: Same as Fig. 4 but for North
Sand Sea (a) and South Sand Sea (b) stations. Here, subplots correspond to
different ranges for the wind direction (columns) and wind velocity (rows) of
the ERA5-Land dataset. The grey vertical dashed lines indicate the main dune
orientation. In contrast with observations at the Huab and Etosha West
stations (Fig. 4), histograms do not match well at low wind velocities, and
the purple frame highlights the regime (low wind velocities, nocturnal
easterly wind) in which the data from both datasets differ most.

##  3 Influence of Wind Speed and Circadian Cycle on the Atmospheric Boundary
Layer

The wind deflection induced by dunes has previously been related to the
incident angle between wind direction and crest orientation, with a maximum
deflection evident for incident angles between $30^{\circ}$ and $70^{\circ}$
(Walker et al. 2009; Hesp et al. 2015). In the data analysed here, the most
deflected wind at both the North and South Sand Sea stations is seen to be
where the incident angle is perpendicular to the giant dunes (Figs. 2 and 6).
It therefore appears that in our case, the incident wind angle is not the
dominant control on maximum wind deflection. Further, and as shown in Fig. 6,
winds of high and low velocities show contrasting behaviour in characteristics
of deflection. This suggests a change in hydrodynamical regime between the
winds. In this section, we discuss the relevant parameters associated with the
dynamical mechanisms that govern the interactions between the atmospheric
boundary layer flow and giant dune topographies. This analysis allows us to
provide a physics-based interpretation of our measured wind data.

Figure 7: a,b: Vertical profiles of the virtual potential temperature $T_{\rm
vp}$ at two different time steps (day - 03/11/2015 - 12.00 UTC, night -
01/13/2013 - 09.00 UTC) at the North Sand Sea station. Dots: data from the
ERA5 reanalysis. Dashed lines: boundary layer height given by the ERA5
reanalysis (Online Resource section 2). Plain lines: vertical (boundary layer)
and linear (free atmosphere) fits to estimate the stratification properties.
c–f: Sketches representing the interaction between the giant dunes and the
atmospheric flow for different meteorological conditions. g: Streamlines over
a sinusoidal topography $\xi(x,y)$ qualitatively representing the effect of
low, medium and strong flow confinement, in relation to the above panels (see
Appendix Appendix 1: Linear Theory of Wind Response to Topographic
Perturbation for more details). The blue arrow indicates the undisturbed wind
direction.

###  3.1 Flow Over a Modulated Bed

Taking as a reference the turbulent flow over a flat bed, the general
framework of our study is understanding and describing the flow response to a
bed modulation (e.g. a giant dune). Without loss of generality, we can
consider in this context an idealised bed elevation in the form of parallel
sinusoidal ridges, with wavelength $\lambda$ (or wavenumber $k=2\pi/\lambda$)
and amplitude $\xi_{0}$, and where the reference flow direction makes a given
incident angle with respect to the ridge crest (Andreotti et al. 2012). Part
of this response, on which we focus here, is the flow deflection by the
ridges. In a simplified way, it can be understood from the Bernoulli principle
(Hesp et al. 2015): as the flow approaches the ridge crest, the compression of
the streamlines results in larger flow velocities, and thus lower pressures
(Jackson and Hunt 1975). An incident flow oblique to the ridge is then
deflected towards lower pressure zones, i.e towards the crest. Turbulent
dissipation tends to increase this effect downstream, resulting in wind
deflection along the crest in the lee side (Gadal et al. 2019).

Flow confinement below a capping surface, which enhances streamline
compression, has a strong effect on the hydrodynamic response and typically
increases flow deflection. This is the case for bedforms forming in open
channel flows such as rivers (Kennedy 1963; Chang and Simons 1970; Mizumura
1995; Colombini 2004; Fourrière et al. 2010; Andreotti et al. 2012; Unsworth
et al. 2018). This is also relevant for aeolian dunes as they evolve in the
turbulent atmospheric boundary layer (ABL) capped by the stratified free
atmosphere (FA) (Andreotti et al. 2009). Two main mechanisms, associated with
dimensionless numbers must then be considered (Fig. 7). First, topographic
obstacles typically disturb the flow over a characteristic height similar to
their length. As flow confinement is characterised by a thickness $H$, the
interaction between the dunes and the wind in the ABL is well captured by the
parameter $kH$. The height $H$ is directly related to the sensitive heat flux
from the Earth surface. It is typically on the order of a kilometre, but
significantly varies with the circadian and seasonal cycles. Emerging and
small dunes, with wavelengths in the range $20$ to $100$ m, are not affected
by the flow confinement, corresponding to $kH\gg 1$. For giant dunes with
kilometer-scale wavelengths, however, their interaction with the FA can be
significant (Andreotti et al. 2009). This translates into a parameter $kH$ in
the range $0.02$–$5$, depending on the moment of the day and the season. A
second important mechanism is associated with the existence of a thin
intermediate so-called capping layer between the ABL and the FA. It is
characterised by a density jump $\Delta\rho$, which controls the ‘rigidity’ of
this interface, i.e. how much its deformation affects streamline compression.
This is usually quantified using the Froude number (Vosper 2004; Stull 2006;
Sheridan and Vosper 2006; Hunt et al. 2006; Jiang 2014):

$\mathcal{F}=\displaystyle\frac{U}{\sqrt{\displaystyle\frac{\Delta\rho}{\rho_{0}}gH}},$
(1)

where $U$ is the wind velocity at the top of the ABL and $\rho_{0}$ its
average density. The intensity of the stratification, i.e. the amplitude of
the gradient $\left|\partial_{z}\rho\right|$ in the FA, also impacts the
ability to deform the capping layer under the presence of an underlying
obstacle, and thus affects the influence of flow confinement. This can be
quantified using the internal Froude number (Vosper 2004; Stull 2006; Sheridan
and Vosper 2006; Hunt et al. 2006; Jiang 2014)
$\mathcal{F}_{\textup{I}}=kU/N$, where $N=\sqrt{-g\partial_{z}\rho/\rho_{0}}$
is the the Brunt-Väisälä frequency (Stull 1988). Both Froude numbers have in
practice the same qualitative effect on flow confinement (a smaller Froude
corresponding to a stiffer interface), and we shall restrict the main
discussion to $\mathcal{F}$ only.

With this theoretical framework in mind, and in the context of the measured
wind data in the North and South Sand Sea stations, the smallest wind
disturbances are expected to occur during the day, when the ABL depth is the
largest and comparable to the dune wavelength ($kH\gtrsim 1$), which
corresponds to a weak confinement situation (Fig. 7c and d). In contrast,
large wind disturbances are expected to occur during the night, when the
confinement is mainly induced by a shallow ABL (Fig. 7e). However, this strong
confinement can be somewhat reduced in the case of strong winds, corresponding
to large values of the Froude number and a less ‘rigid’ interface (Fig. 7f).
This is in qualitative agreement with the transition from deflected to non-
deflected winds related to low and high velocities observed in our data (Sec.
2.2).

Figure 8: Regime diagrams of the wind deviation $\delta_{\theta}$ (a) and
relative attenuation/amplification $\delta_{u}$ (b) in the space
$(\mathcal{F},\,kH)$, containing the data from both the North Sand Sea and
South Sand Sea stations. The green dashed lines empirically delimit the
different regimes. The point density in each bin of the diagrams is shown in
Online Resource Fig. S10 – 95% of the data occur in the range $-1<\delta u<1$.
Similar regime diagrams in the spaces $(\mathcal{F}_{\textup{I}},\,kH)$ and
$(\mathcal{F}_{\textup{I}},\,\mathcal{F})$ are shown in Online Resource Fig.
S11.

###  3.2 Data Distribution in the Flow Regimes

We can go one step further and analyse how our data quantitatively spread over
the different regimes discussed above. For that purpose, one needs to compute
$kH$ and $\mathcal{F}$ from the time series. $H$, $U$ and the other
atmospheric parameters can be deduced from the various vertical profiles
(temperature, humidity) available in the ERA5 climate reanalysis (Online
Resource section 2). We quantify the flow deflection $\delta_{\theta}$ as the
minimal angle between the wind orientations comparing the local measurements
and the regional predictions. We also compute the relative velocity modulation
as

$\delta_{\textup{u}}=\frac{u_{*}^{\textup{ERA5-Land}}-u_{*}^{\textup{Local
mes.}}}{u_{*}^{\textup{ERA5-Land}}}.$ (2)

These two quantities are represented as maps in the plane $(\mathcal{F},\,kH)$
(Fig. 8a and b), and one can clearly identify different regions in these
plots. Small wind disturbances (small $\delta_{\theta}$ and
$\delta_{\textup{u}}$) are located in the top-right part of the diagrams,
corresponding to a regime with low-interaction as well as low-confinement
($kH$ and $\mathcal{F}$ large enough, Fig. 7d). Lower values of $kH$ (stronger
interaction) or of Froude number (stronger confinement) both lead to an
increase in wind disturbances, both in terms of orientation and velocity.
Below a crossover value $kH\simeq 0.3$, wind disturbance is less sensitive to
the $\mathcal{F}$-value. This is probably due to enhanced non-linear effects
linked to flow modulation by the obstacle when confinement is strong (e.g.
wakes and flow recirculations). The Froude number also controls a transition
from damped to amplified wind velocities in the interdune, with a crossover
around $\mathcal{F}\simeq 0.4$ (Fig. 8b). Such an amplification is rather
unexpected. Checking the occurrence of the corresponding data, it appears that
these amplifications are associated with the southerly sea breeze, and occur
dominantly during the October-March period, when the other easterly wind is
not present (Online Resource Fig. S12a–b). Furthermore, they occur less
frequently during the afternoon, and more frequently at the end of the day
(Online Resource Fig. S12c). This effect may be linked to a change in the flow
behaviour in the lee side of the obstacles but further measurements are needed
in order to assess the different possibilities (Baines 1995; Vosper 2004).

As the hydrodynamic roughness $z_{0}$ determine the magnitude of wind shear
velocities, Froude number $\mathcal{F}$ and relative velocity modulation
$\delta_{u}$, it is important to discuss the sensitivity of the results to the
$z_{0}$-values chosen for both the ERA5-Land and the field data (see Online
Resource Sect. 1\. Shear velocity and calibration of the hydrodynamical
roughness). Other quantities associated with wind direction are independent of
this choice. Considering the possible range of realistic roughness values, the
uncertainty on velocities estimated using the law of the wall is at most 30 %.
A similar maximum uncertainty applies to the Froude number. This uncertainty
also propagates to $\delta_{u}$, for which Figure S14 shows that the choice of
roughness has little influence on its temporal variations,even if it can
induce a global increase or decrease of its values. Hence, the choice of the
$z_{0}$-values will not qualitatively affect the overall aspect of the regime
diagram presented in Figure 8b. It may only change the value of $\delta_{u}$
for which the transition between regimes is observed (dashed green lines in
Figure 8b). Our conclusions are thus robust with respect to the somewhat
arbitrary choice of the hydrodynamic roughness values.

Figure 9: Implications for smaller scale patterns in (a) the South Sand Sea
and (b) North Sand Sea. The ellipses indicate the different types of
elongating dunes, at large (plain line) and small (dashed line) scales. Dune
orientation are predicted using the model of Courrech du Pont et al. (2014)
from the sand flux angular distributions, shown here (roses) along with the
resultant transport direction (brown arrow) for typical values (grain size
$180~{}\mu$m, flux-up ratio of $1.6$). Code for corresponding arrows: use of
ERA5-Land data (plain line), use of local measurements (dashed line),
prediction for the bed instability growth mechanism (blue), prediction for the
elongation growth mechanism (red). Wedges show the uncertainty on the
orientation calculation when parameters are varied. The black dots indicate
the location of the meteorological stations in the interdune. See Appendix
Appendix 2: Sediment Transport and Dune Morphodynamics for additional details.

##  4 Discussion and Conclusion

The feedback of the giant dunes on the wind flow has important implications
for smaller scale bedforms. As illustrated in Fig. 9, small linear dunes
($\sim 50$ m wide) are often present within the 1–2 km interdune spaces
between giant linear dunes in the Namib Sand Sea (Livingstone et al. 2010).
These smaller dunes do not exhibit the same orientation as the large ones, and
are sometimes named ‘crossing dunes’ (Chandler et al. 2022). Whilst
differences between large and small scale dune patterns are observed
ubiquitously, they are usually attributed to the presence of two different
dune growth mechanisms, leading to two different dune patterns (orientations
and/or morphologies) for the same wind regime (Courrech du Pont et al. 2014;
Runyon et al. 2017; Lü et al. 2017; Song et al. 2019; Gadal et al. 2020; Hu et
al. 2021). Here, however, our arguments enable the development of differing
orientations for the small and giant linear dunes governed by the same dune
growth mechanism (elongating mode). Figure 9 shows how the orientations for
the small and giant dunes can be derived from the locally measured and
regionally predicted winds respectively (red arrows in Fig. 9). These
predictions require the threshold of aeolian sand transport to be specified.
Importantly, its value (a shear velocity estimated at $u_{\textup{th}}\simeq
0.15~{}\textup{m}~{}\textup{s}^{-1}$ – see Appendix Appendix 2: Sediment
Transport and Dune Morphodynamics) can be reached in periods during which
deflected winds are observed (recall that the stronger winds, responsible for
most of the sediment transport and associated dune morphodynamics, are not
deflected – see Fig. 6). The feedback of the giant dunes on the wind described
in this study, through wind deflection and attenuation, thus provides a
potential explanation for the existence of these small linear dunes elongating
across the interdune, a dynamic which has remained unresolved to date. These
crossing dunes could provide additional constraints for the inference of local
winds from bedforms, similarly to that currently performed on Mars using
ripple orientations (Liu and Zimbelman 2015; Hood et al. 2021). Further work
is needed to investigate these processes in more detail, including
measurements of sediment transport and flow on the top of dunes.

This study presents field and reanalysis-based evidence that wind flow
patterns around giant dunes are influenced by the atmospheric boundary layer,
particularly during nocturnal conditions. However, we do not address here the
question of the limitation of the giant dune pattern coarsening, and leave
open the debate as to whether their size is controlled by the depth of this
layer (Andreotti et al. 2009), in contrast to sediment supply limited and
ever-slower growth with size (Werner and Kocurek 1999; Gunn et al. 2022). More
field evidence is definitively needed from additional dune fields, but this
mechanism would allow for the inference of the ABL depth from giant bedform
wavelengths where measurements are not feasible or available, such as Titan
(Lorenz et al. 2010).

To conclude on conditions under which the ERA5-Land reanalysis data can
reliably be used to study dune morphodynamics, we summarise the comparison of
local (direct measurements) and regional (climate reanalysis) wind data as
follows. In flat areas, the agreement between the two confirms the ability of
the ERA5-Land climate reanalysis to predict the wind regime down to scales
$\sim 10$ km, i.e the model grid. When smaller scale topographies are present
(giant dunes in our case), locally measured winds can significantly differ
from the regionally predicted ones. This is the case when the disturbances
induced by the dunes interact with the lower part of the ABL vertical
structure, which presents circadian variations. During the day, when the
capping layer is typically high, this interaction is small, and the ERA5-Land
predictions are also quantitatively consistent with the local data. During the
night, however, the presence of a shallow atmospheric boundary layer induces a
strong confinement of the flow, and is associated with large wind deflection
by the dunes. Importantly, we find that this effect can be counterbalanced for
large wind velocities, which are capable of deforming the capping layer, thus
decreasing the influence of the confinement.

The theoretical computation of the wind disturbances induced by sinusoidal
ridges under flow confinement has been performed in the linear limit
(Andreotti et al. 2009, 2012), i.e. when the aspect ratio of these ridges is
small ($k\xi_{0}\ll 1$). These models are able to qualitatively reproduce the
observed wind deflection (Appendix Appendix 1: Linear Theory of Wind Response
to Topographic Perturbation, Online Resource Figs. S11 and S13), and thus
provide the physical support for the interpretation we propose here based on
hydrodynamic regimes. However, these models cannot quantitatively predict the
magnitude of our observations, probably due to the presence of expected non-
linearities in high confinement situations linked to strong flow modulations.
Besides, these linear calculations only predict wind attenuation in the
interdune, in contrast with the observed enhanced velocities associated with
particular evening winds from the south during the period October-March
(Online Resource Fig. S12). Some other models predict different spatial flow
structures in response to a modulated topography, such as lee waves and rotors
(Baines 1995; Vosper 2004). However, our measurements are located at a single
point in the interdune, and we are thus unable to explore these types of
responses. Data at different places along and across the ridges are needed to
investigate and possibly map such flow structures, and for further comparisons
with the models.

###### Acknowledgements.

We would like to acknowledge the contributors of the following open-source
python librairies, Matplotlib (Hunter 2007), Numpy (Harris et al. 2020) and
Scipy (Virtanen et al. 2020), which provide an incredibly efficient ecosystem
allowing scientific research in Python. We also thank B. Andreotti and A. Gunn
for useful discussions.

Data Availability All data used in this study can be found in Gadal et al.
(2022). Note that it contains modified Copernicus Climate Change Service
Information (2021). Neither the European Commission nor ECMWF is responsible
for any use that may be made of the Copernicus Information or Data it
contains. Documented codes used in this study to analyse this data are
available at https://github.com/Cgadal/GiantDunes (will be made public upon
acceptance of this manuscript for publication).

Fundings Multiple grants have supported the collection of wind data through
visits to the four sites between 2013 and 2020 (John Fell Oxford University
Press (OUP) Research Fund (121/474); National Geographic (CP-029R-17); Natural
Environment Research Council UK (NE/R010196/1 and NE/H021841/1 NSFGEO-NERC);
Southampton Marine and Maritime Institute SMMI EPSRC-GCRF UK), along with
research permits (1978/2014, 2140/2016, 2304/2017, 2308/2017, RPIV00022018,
RPIV0052018, RPIV00230218). The authors are very grateful for support from
Etosha National Park (especially Shyane Kötting, Boas Erckie, Pierre du Preez,
Claudine Cloete, Immanuel Kapofi, Wilferd Versfeld, and Werner Kilian),
Gobabeb Namib Research Institute (Gillian Maggs-Kölling and Eugene Marais),
The Skeleton Coast National Park (Joshua Kazeurua). Various researchers and
desert enthusiasts have assisted with instruments and the logistics of
expeditions, especially Mary Seely for expert guidance at the North Sand Sea
site. Finally, we acknowledge financial support from the Laboratoire
d’Excellence UnivEarthS Grant ANR-10-LABX-0023, the Initiative d’Excellence
Université de Paris Grant ANR-18-IDEX-0001, the French National Research
Agency Grants ANR-17-CE01-0014/SONO and the National Science Center of Poland
Grant 2016/23/B/ST10/01700.

Conflict of interest The authors declare that they have no conflict of
interest.

## Appendix 1: Linear Theory of Wind Response to Topographic Perturbation

Following the work of Fourrière et al. (2010), Andreotti et al. (2012) and
Andreotti et al. (2009), we briefly describe in this appendix the framework
for the linear response of a turbulent flow to a topographic perturbation of
small aspect ratio. As a general bed elevation can be decomposed into Fourier
modes, we focus here on a sinusoidal topography:

$\xi=\xi_{0}\cos\left[k\left(\cos(\alpha)y-\sin(\alpha)x\right)\right],$ (3)

which is also a good approximation for the giant dunes observed in the North
Sand Sea and South Sand Sea Station (Fig. 2 and Online Resource Fig. S4).
Here, $x$ and $y$ are the streamwise and spanwise coordinates,
$k=2\pi/\lambda$ the wavenumber of the sinusoidal perturbation, $\alpha$ its
crest orientation with respect to the $x$-direction (anticlockwise) and
$\xi_{0}$ its amplitude. The two components of the basal shear stress
$\boldsymbol{\tau}=\rho_{0}u_{*}\boldsymbol{u}_{*}$, constant in the flat
bottom reference case, can then be generically written as:

$\displaystyle\tau_{x}$
$\displaystyle=\tau_{0}\left(1+k\xi_{0}\sqrt{\mathcal{A}_{x}^{2}+\mathcal{B}_{x}^{2}}\cos\left[k\left(\cos(\alpha)y-\sin(\alpha)x\right)+\phi_{x}\right]\right),$
(4) $\displaystyle\tau_{y}$
$\displaystyle=\tau_{0}\,k\xi_{0}\sqrt{\mathcal{A}_{y}^{2}+\mathcal{B}_{y}^{2}}\cos\left[k\left(\cos(\alpha)y-\sin(\alpha)x\right)+\phi_{y}\right],$
(5)

where $\tau_{0}$ is the reference basal shear stress on a flat bed. We have
defined the phase
$\phi_{x,y}=\tan^{-1}\left(\mathcal{B}_{x,y}/\mathcal{A}_{x,y}\right)$ from
the in-phase and in-quadrature hydrodynamical coefficients $\mathcal{A}_{x,y}$
and $\mathcal{B}_{x,y}$. They are functions of $k$ and of the flow conditions,
i.e the bottom roughness, the vertical flow structure and the incident flow
direction, and the theoretical framework developed in the above cited papers
proposes methods to compute them in the linear regime.

Following Andreotti et al. (2012), the effect of the incident wind direction
can be approximated by the following expressions:

$\displaystyle\mathcal{A}_{x}$ $\displaystyle=\mathcal{A}_{0}\sin^{2}\alpha,$
(6) $\displaystyle\mathcal{B}_{x}$
$\displaystyle=\mathcal{B}_{0}\sin^{2}\alpha,$ (7)
$\displaystyle\mathcal{A}_{y}$
$\displaystyle=-\displaystyle\frac{1}{2}\mathcal{A}_{0}\cos\alpha\sin\alpha,$
(8) $\displaystyle\mathcal{B}_{y}$
$\displaystyle=-\displaystyle\frac{1}{2}\mathcal{B}_{0}\cos\alpha\sin\alpha,$
(9)

where $\mathcal{A}_{0}$ and $\mathcal{B}_{0}$ are now two coefficients
independent of the dune orientation $\alpha$, corresponding to the transverse
case ($\alpha=90$). In the case of a fully turbulent boundary layer capped by
a stratified atmosphere, these coefficients depend on $kH$, $kz_{0}$,
$\mathcal{F}$ and $\mathcal{F}_{\textup{I}}$ (Andreotti et al. 2009). For
their computation, we assume here a constant hydrodynamic roughness
$z_{0}\simeq 1$ mm (Online Resource section 1). For the considered giant
dunes, this leads to $kz_{0}\simeq 2\cdot 10^{-6}$, as their wavelength is
$\lambda\simeq 2.4$ km (or $k\simeq 2\cdot 10^{-3}$ m-1). Values of $z_{0}$
extracted from field data indeed typically fall between 0.1 mm and 10 mm
(Sherman and Farrell 2008; Field and Pelletier 2018). Importantly,
$\mathcal{A}_{0}$ and $\mathcal{B}_{0}$ do not vary much in the corresponding
range of $kz_{0}$ (Fourrière et al. 2010), and the results presented here are
robust with respect to this choice.

With capping layer height and Froude numbers computed from the ERA5-Land time
series, the corresponding $\mathcal{A}_{0}$ and $\mathcal{B}_{0}$ can be
deduced, as displayed in Online Resource Fig. S13. Interestingly, it shows
similar regimes as in the diagrams of Fig. 8 and Online Resource Fig. S11a,b,
supporting the underlying physics. However, the agreement is qualitative only.
Further, the linearity assumption of the theoretical framework requires
$\left(|\tau|-\tau_{0}\right)/\tau_{0}\ll 1$, which translates into
$k\xi\sqrt{\mathcal{A}_{0}^{2}+\mathcal{B}_{0}^{2}}\ll 1$. In our case, the
giant dune morphology gives $k\xi_{0}\simeq 0.1$, which means that one quits
the regime of validity of the linear theory when the coefficient modulus
$\sqrt{\mathcal{A}_{0}^{2}+\mathcal{B}_{0}^{2}}$ becomes larger than a few
units. In accordance with the theoretical expectations, these coefficients
present values on the order of unity ($\mathcal{A}_{0}\simeq 3$ and
$\mathcal{B}_{0}\simeq 1$) in unconfined situations (Claudin et al. 2013; Lü
et al. 2021). In contrast and as illustrated in Online Resource Fig. S13a,b,
larger values are predicted in case of strong confinement, which does not
allow us to proceed to further quantitative comparison with the data.

Finally, the linear model is also able to reproduce the enhancement of the
flow deflection over the sinusoidal ridges when
$\sqrt{\mathcal{A}_{0}^{2}+\mathcal{B}_{0}^{2}}$ is increased (Online Resource
Fig. S13). Here, using $k\xi_{0}\simeq 0.1$ to be representative of the
amplitude of the giant dunes at the North Sand Sea station, the coefficient
modulus is bounded to $10$.

## Appendix 2: Sediment Transport and Dune Morphodynamics

We summarise in this appendix the sediment transport and dune morphodynamics
theoretical framework leading to the prediction of sand fluxes and dune
orientations from wind data.

#### Sediment Transport

— The prediction of sand fluxes from wind data has been a long standing issue
in aeolian geomorphological studies (Fryberger and Dean 1979; Pearce and
Walker 2005; Sherman and Li 2012; Shen et al. 2019). Based on laboratory
studies in wind tunnels (Rasmussen et al. 1996; Iversen and Rasmussen 1999;
Creyssels et al. 2009; Ho et al. 2011), as well as physical considerations
(Ungar and Haff 1987; Andreotti 2004; Durán et al. 2011; Pähtz and Durán
2020), it has been shown that the steady saturated saltation flux over a flat
sand bed depends linearly on the shear stress:

$\frac{q_{\textup{sat}}}{Q}=\Omega\sqrt{\Theta_{\textup{th}}}\left(\Theta-\Theta_{\textup{th}}\right),$
(10)

where $\Omega$ is a proportionality constant,
$Q=d\sqrt{(\rho_{\textup{s}}-\rho_{0})gd/\rho_{0}}$ is a characteristic flux,
$\Theta=\rho_{0}u_{*}^{2}/(\rho_{\textup{s}}-\rho_{0})gd$ the Shields number,
and $\Theta_{\textup{th}}$ its threshold value below which saltation vanishes.
$\rho_{\textup{s}}=2.6~{}\textup{g}~{}\textup{cm}^{-3}$ and
$d=180~{}\mu\textup{m}$ are the grain density and diameter, and $g$ is the
gravitational acceleration. The shear velocity, and consequently the Shields
number as well as the sediment flux, are time dependent.

Recently, Pähtz and Durán (2020) suggested an additional quadratic term in
Shields to account for grain-grain interactions within the transport layer at
strong wind velocities:

$\frac{q_{\textup{sat,
t}}}{Q}=\frac{2\sqrt{\Theta_{\textup{th}}}}{\kappa\mu}\left(\Theta-\Theta_{\textup{th}}\right)\left(1+\frac{C_{\textup{M}}}{\mu}\left[\Theta-\Theta_{\textup{th}}\right]\right),$
(11)

where $\kappa=0.4$ is the von Kármán constant, $C_{\rm M}\simeq 1.7$ a
constant and $\mu\simeq 0.6$ is a friction coefficient, taken to be the
avalanche slope of the granular material. The fit of this law to the
experimental data of Creyssels et al. (2009) and Ho et al. (2011) gives
$\Theta_{\textup{th}}=0.0035$. The fit of Eq. 10 on these same data similarly
gives $\Omega\simeq 8$ and $\Theta_{\textup{th}}=0.005$. The sand flux angular
distributions and the dune orientations in Fig. 9 are calculated using this
law (11). We have checked that using the ordinary linear relationship (10)
instead does not change the predicted dune orientations by more than a few
degrees.

#### Dune Orientations

— Dune orientations are predicted with the dimensional model of Courrech du
Pont et al. (2014), from the sand flux time series computed with the above
transport law. Two orientations are possible depending on the mechanism
dominating the dune growth: elongation or bed instability. The orientation
$\alpha$ corresponding to the bed instability is then the one that maximises
the following growth rate (Rubin and Hunter 1987):

$\sigma\propto\frac{1}{H_{d}W_{d}T}\int_{0}^{T}q_{\textup{crest}}|\sin\left(\theta-\alpha\right)|\,\textup{d}t,$
(12)

where $\theta$ is the wind orientation measured with respect to the same
reference as $\alpha$, and $H_{d}$ and $W_{d}$ are dimensional constants
respectively representing the dune height and width. The integral runs over a
time $T$, which must be representative of the characteristic period of the
wind regime. The flux at the crest is expressed as:

$q_{\textup{crest}}=q_{\textup{sat}}\left[1+\gamma|\sin\left(\theta-\alpha\right)|\right],$
(13)

where the flux-up ratio $\gamma$ has been calibrated to $1.6$ using field
studies, underwater laboratory experiments and numerical simulations.
Predictions of the linear analysis of Gadal et al. (2019) and Delorme et al.
(2020) give similar results.

Similarly, the dune orientation corresponding to the elongation mechanism is
the one that verifies:

$\tan(\alpha)=\frac{\langle
q_{\textup{crest}}(\alpha)\boldsymbol{e}_{\theta}\rangle\cdot\boldsymbol{e}_{WE}}{\langle
q_{\textup{crest}}(\alpha)\boldsymbol{e}_{\theta}\rangle\cdot\boldsymbol{e}_{SN}},$
(14)

where $\langle.\rangle$ denotes a vectorial time average. The unitary vectors
$\boldsymbol{e}_{WE}$, $\boldsymbol{e}_{SN}$ and $\boldsymbol{e}_{\theta}$ are
in the West-East, South-North and wind directions, respectively.

The resulting computed dune orientations, blue and red arrows in Fig. 9, then
depend on a certain number of parameters (grain properties, flux-up ratio,
etc.), for which we take typical values for aeolian sandy deserts. Due to the
lack of measurements in the studied places, some uncertainties can be
expected. We therefore run a sensitivity test by calculating the dune
orientations for grain diameters ranging from $100~{}\mu\textup{m}$ to
$400~{}\mu\textup{m}$ and for a speed-up ratio between $0.1$ and $10$ (wedges
in Fig. 9).

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Local wind regime induced by giant linear dunes
— Supplementary Material —

C. Gadal∗ $\cdot$ P. Delorme $\cdot$ C. Narteau $\cdot$ G.F.S. Wiggs $\cdot$
M. Baddock $\cdot$ J.M. Nield $\cdot$ P. Claudin

∗ Institut de Mécanique des Fluides de Toulouse, Université de Toulouse Paul
Sabatier, CNRS, Toulouse INP-ENSEEIHT, Toulouse, France.
<EMAIL_ADDRESS>
## 1\. Shear velocity and calibration of the hydrodynamical roughness

As the regionally predicted and locally measured velocities are available at
different heights, we can not compare them directly. We therefore convert all
velocities into shear velocities $u_{*}$, characteristic the turbulent
logarithmic velocity profile (Spalding 1961; Stull 1988):

$\frac{u(z)}{u_{*}}=\frac{1}{\kappa}\ln\left(\frac{z}{z_{0}}\right),$ (15)

where $z$ is the vertical coordinate, $\kappa=0.4$ the von Kármán constant and
$z_{0}$ the hydrodynamic roughness. Note that, strickly speaking, this
logarithmic profile is valid for a neutrally stratified ABL only. Vertical
density gradients occuring in other conditions may thus induce large
discrepancies (Monin and Obukhov 1954; Garratt 1994; Dyer 1974). However, as
our wind measurements are in the flow region close enough to the surface,
where these effects are negligible, this logarithmic wind profile remains a
farily good approximation in all conditions (Gunn et al. 2021). Several
measurements of hydrodynamic roughnesses are available (Raupach 1992; Bauer et
al. 1992; Brown et al. 2008; Nield et al. 2014). In the absence of sediment
transport, it is governed by the geometric features of the bed (Flack and
Schultz 2010; Pelletier and Field 2016). When aeolian saltation occurs, it is
rather controlled by the altitude of Bagnold’s focal point (Durán et al. 2011;
Valance et al. 2015), which depends on the wind velocity and grain properties
(Sherman and Farrell 2008; Zhang et al. 2016; Field and Pelletier 2018).
Whether associated with geometric features or with sediment transport, its
typical order of magnitude is the millimetre scale on sandy surfaces.

We do not have precise velocity vertical profiles to be able to deduce an
accurate value of $z_{0}$ in the various environments of the meteorological
stations (vegetated, arid, sandy). Our approach is to rather select the
hydrodynamic roughness which allows for the best possible matching between the
regionally predicted and locally measured winds, i.e. minimising the relative
difference $\delta$ between the wind vectors of both datasets:

$\delta=\frac{\sqrt{\langle\|\boldsymbol{u}_{*,\textrm{era}}-\boldsymbol{u}_{*,\textrm{station}}\|^{2}\rangle}}{\sqrt{\langle\|\boldsymbol{u}_{*,\textrm{era}}\|\rangle\langle\|\boldsymbol{u}_{*,\textrm{station}}\|\rangle}},$
(16)

where $\langle.\rangle$ denotes time average. This parameter is computed for
values of $z_{0}$ in ERA5-Land analysis ranging from $10^{-5}$ m to $10^{-2}$
m for the four different stations. Note that for the North Sand Sea and South
Sand Sea stations, where the giant dunes feedback presumably affect the wind,
we take into account the non-deflected winds only in the calculation of
$\delta$ (with a $15^{\circ}$ tolerance).

As shown in Online Resource Fig. S3, the minimum values of $\delta$ in the
space ($z_{0}^{\textup{ERA5Land}}$, $z_{0}^{\textup{local}}$) form a line. We
thus set the roughness in the ERA5-Land analysis to the typical value
$z_{0}=10^{-3}$ m, and deduce the corresponding ones for the local stations.
It leads to $2.7$, $0.8$, $0.1$ and $0.5$ mm for the Etosha West, North Sand
Sea, Huab and South Sand Sea stations, respectively. Importantly, this
approach somewhat impacts the calculation of the shear velocities, but not
that of the wind directions. As such, most of our conclusions are independent
of such a choice. However, it may affect the magnitude of the wind velocity
attenuation/amplification in flow confinement situations.

## 2\. Computation of the ABL characteristics

The estimation of the non-dimensional numbers associated with the ABL requires
the computation of representative meteorological quantities. In arid areas,
the vertical structure of the atmosphere can be approximated by a well mixed
convective boundary layer of height $H$, topped by the stratified free
atmosphere (Stull 1988; Shao 2008). In this context, one usually introduces
the virtual potential temperature $T_{\textup{vp}}$, which is a constant
$T_{0}$ inside the boundary layer, and increases linearly in the FA (Online
Resource Fig. S8a):

$T_{\textup{vp}}(z)=\begin{cases}T_{0}&\text{for $z\leq H$},\\\
T_{0}\left(1+\displaystyle\frac{\Delta
T_{\textup{vp}}}{T_{0}}+\frac{N^{2}}{g}(z-H)\right)&\text{for $z\geq
H$},\end{cases}$ (17)

where $\Delta T_{\textup{vp}}$ is the temperature discontinuity at the capping
layer and $N=\sqrt{g\partial_{z}T_{\textup{vp}}/T_{0}}$ is the Brunt-Väisälä
frequency, characteristic of the stratification. Note that, under the usual
Boussinesq approximation, temperature and air density variations are simply
related by $\delta T_{\textup{vp}}/T_{0}\simeq-\delta\rho/\rho_{0}$ (see
Online Resource of Andreotti et al. (2009)), so that $N$ can equivalently be
defined from the density gradient as next to (1).

The ERA5 dataset provides vertical profiles of the geopotential $\phi$, the
actual temperature $T$ and the specific humidity $\eta$ at given pressure
levels $P$. The vertical coordinate is then calculated as:

$z=\frac{\phi R_{\textup{t}}}{gR_{\textup{t}}-\phi},$ (18)

where $R_{\textup{t}}=6371229$ m is the reference Earth radius and $g=9.81$ m
s-2 is the gravitational acceleration. One also computes the virtual potential
temperature as:

$T_{\textup{vp}}=T\left[1+\left(\frac{M_{d}}{M_{w}}-1\right)\eta\right]\left(\frac{P_{0}}{P}\right)^{R/C_{p}},$
(19)

where $P_{0}=10^{5}$ Pa is the standard pressure, $R=8.31$ J/K is the ideal
gas constant, $C_{p}\simeq 29.1$ J/K is the air molar heat capacity, and
$M_{w}=0.018$ kg/Mol and $M_{d}=0.029$ kg/Mol are the molecular masses of
water and dry air respectively. The specific humidity is related to the vapour
pressure $p_{w}$ as

$\eta=\frac{\frac{M_{w}}{M_{d}}p_{w}}{p-\left(1-\frac{M_{w}}{M_{d}}\right)p_{w}}\,.$
(20)

The ERA5 dataset also provides an estimate of the ABL depth $H$, based on the
behaviour of the Richardson vertical profile. This dimensionless number is
defined as the ratio of buoyancy and flow shear terms, and can be expressed as
$\textup{Ri}=N^{2}/(\partial_{z}u)^{2}$. It vanishes in the lower well-mixed
layer where $T_{\textup{vp}}$ is constant, and increases in the stratified FA.
Following the method and calibration of Vogelezang and Holtslag (1996); Seidel
et al. (2012), the value $\textup{Ri}(z)\simeq 0.25$ has been shown to be a
good empirical criterion to give $z\simeq H$ within a precision varying from
$50$% for the shallower ABL (e.g. at night) to $20$% for situations of
stronger convection.

Examples of vertical virtual potential temperature profiles deduced from ERA5
are shown in Online Resource Fig. S8a. For each of them, an average
temperature is computed below the ABL depth ($z<H$), and a linear function is
fitted above, allowing us to extract the temperature jump $\Delta
T_{\textup{vp}}$. Importantly, some profiles display a vertical structure that
cannot be approximated by the simple form (17) used here (Online Resource Fig.
S8b). In practice, we removed from the analysis all of those leading to the
unphysical case $\Delta T_{\textup{vp}}<0$. We have noticed that these ‘ill-
processed’ profiles dominantly occur in winter and are evenly spread across
the hours of the day. Importantly, they represent $\simeq 12$% of the data
only (Online Resource Fig. S8c,d), and we are thus confident that this data
treatment does not affect our conclusions.

Figure S1: Gantt chart representing the valid time steps for the two data
sets, for all stations. Figure S2: Local wind measurements: comparison between
raw (blue) and hourly-averaged (light blue) data from South Sand Sea station.
a: wind direction. b: wind velocity at height $2.6$ m. Figure S3: Calibration
of hydrodynamic roughness. The parameter $\delta$ (16) quantifying the
difference between local and predicted winds is shown in color scale as a
function of the hydrodynamic roughnesses chosen for the ERA5-Land and for
local winds, for the (a) Etosha West, (b) North Sand Sea, (c) Huab and (d)
South Sand Sea stations. The red dashed and plain lines shows the minima of
$\delta$ and the identity line, respectively. The orange lines and dots
highlight the chosen hydrodynamic roughnesses for the local winds deduced from
setting $z_{0}^{\textup{ERA5-Land}}=1$ mm. Figure S4: Analysis of the DEMs of
the North Sand Sea (left column – panels a, b, c) and South Sand Sea (right
column – panels d, e, f) stations. a–d: Bed elevation detrended by a fitted
second order polynomial base-line. b–e: Autocorrelation matrix shown in color
scale. The black line shows the detected dune orientation, and the red line
represents the autocorrelation profile along which the dune wavelength is
calculated, displayed in c–f. The blue lines and dots show the first peak of
the autocorrelation profile, whose abscissa gives the characteristic
wavelength of the dune pattern. Figure S5: Statistical comparison of the wind
orientation (a) and velocity (b) between the ERA5-Land dataset and the local
measurements for the Huab and Etosha West stations. Data point clustering
around identity lines (dashed and black) provide evidence for agreement of the
two sets. Figure S6: Statistical comparison of the wind orientation between
the ERA5-Land dataset and the local measurements for the South Sand Sea and
North Sand Sea stations, for different velocity ranges. a:
$u_{*}^{\textup{ERA5-Land}}<0.1~{}\textup{m}~{}\textup{s}^{-1}$. b:
$0.1<u_{*}^{\textup{ERA5-Land}}\leq 0.25~{}\textup{m}~{}\textup{s}^{-1}$. c:
$u_{*}^{\textup{ERA5-Land}}\geq 0.25~{}\textup{m}~{}\textup{s}^{-1}$. The
measured dune orientations are subtracted to the wind orientation, which
allows us to plot both stations on the same graph. Black dashed lines indicate
locally measured orientations aligned with the dune crests (here $0^{\circ}$,
$180^{\circ}$ and $360^{\circ}$ – panels a, b), as well as the identity lines
(panels b, c). Figure S7: Statistical comparison of the wind velocity between
the ERA5-Land dataset and the local measurements for the South Sand Sea and
North Sand Sea stations. a: Nocturnal summer easterly wind. b: Diurnal
southerly wind. Black dashed lines are identity lines. The angle ranges used
to select diurnal and nocturnal summer winds are the same as those in Figs. 4
and Figs. 6 of the main article. Figure S8: a: Vertical profiles of the
virtual potential temperature at three different times (blue: 29/11/2012 -
11.00 UTC, orange: 21/03/2017 - 12.00 UTC, green: 21/03/2017 - 20.00 UTC) at
the South Sand Sea station. Dots: data from the ERA5 reanalysis. Dashed lines:
boundary layer height given by the ERA5 reanalysis. Plain lines: vertical
(ABL) and linear (FA) fits to estimate the quantities displayed in Online
Resource Fig. S9. b: Examples of ill-processed vertical profiles at three
different times (blue: 2/12/2013 - 23.00 UTC, orange: 20/03/2017 - 00.00 UTC,
green: 14/07/2017 - 14.00 UTC) at the South Sand Sea station. Distribution of
ill-processed vertical profiles at South (orange) and North (light orange)
Sand Sea station: hourly (c) and monthly (d) counts. Figure S9: Distributions
of the meteorological parameters resulting from the processing of the
ERA5-Land data for the South Sand Sea (orange) and the North Sand Sea (light
orange) stations. Figure S10: Non-dimensional parameters distributions. For
the marginal distributions, the light orange corresponds to the South Sand Sea
station, and the orange to the North Sand Sea station. Figure S11: Regime
diagrams of the wind deviation $\delta_{\theta}$ and relative
attenuation/amplification $\delta_{u}$ in the spaces
$(\mathcal{F}_{\textup{I}},\,kH)$ and
$(\mathcal{F}_{\textup{I}},\,\mathcal{F})$, containing the data from both the
North Sand Sea and South Sand Sea stations. Green dashed lines empirically
delimit the different regimes. The point density in each bin of the diagrams
is shown in Online Resource Fig. S10 – 95% of the data occur in the range
$-1<\delta u<1$. The similar regime diagrams in the space $(\mathcal{F},\,kH)$
are shown in Fig. 8. Figure S12: Normalized distributions of amplified
velocities for the North sand Sea (light orange: $\delta_{u}<0$, orange:
$\delta_{u}<-0.5$). a: Angular distributions. b: Monthly distributions. c:
Hourly distributions. Figure S13: Computation of the flow disturbance with the
linear model of Andreotti et al. (2009). a–b: Magnitude of the hydrodynamic
coefficients $\mathcal{A}_{0}$ and $\mathcal{B}_{0}$, calculated from the time
series of the non-dimensional numbers corresponding to the ERA5-Land wind data
and ERA5 data on vertical pressure levels. c Shear velocity streamlines over
sinusoidal ridges of amplitude $k\xi_{0}=0.1$ and for increasing values of
$\sqrt{\mathcal{A}_{0}^{2}+\mathcal{B}_{0}^{2}}$. From the upper to the lower
streamline, values of $\left(kH,\,\mathcal{F},\,\mathcal{F}_{\rm
I},\,\mathcal{A}_{0},\,\mathcal{B}_{0},\,\sqrt{\mathcal{A}_{0}^{2}+\mathcal{B}_{0}^{2}}\right)$
are (1.9, 0.6, 1.5, 3.4, 1.0, 3.5), (1.5, 0.3, 0.4, 4.8, 1.4, 5.0), (0.1, 3.5,
1.0, 8.6, 0.1, 8.6), (0.5, 0.05, 0.04, 9.6, 2.5, 9.9). Figure S14: Time series
of the relative velocity disturbance $\delta_{u}$ corresponding to Fig. 5, for
different values of the hydrodynamic roughnesses. a: North Sand Sea – summer,
b: North Sand Sea – winter, d: South Sand Sea – summer, e: South Sand Sea –
winter. Note that $\delta_{\theta}$ is independent of the choice of
$z_{0}^{\textup{ERA5-Land}}$ and $z_{0}^{\textup{Local mes.}}$.