# Field evidence for the initiation of isolated aeolian sand patches

# Supporting Information for ”Field evidence for the initiation of isolated
aeolian sand patches”

###### Abstract

Sand patches are one of the precursors to early-stage protodunes and occur
widely in both desert and coastal aeolian environments. Here we show field
evidence of a mechanism to explain the initiation of sand patches on non-
erodible surfaces, such as desert gravels and moist beaches. Changes in sand
transport dynamics, directly associated with the height of the saltation layer
and variable transport law, observed at the boundary between non-erodible and
erodible surfaces lead to sand deposition on the erodible surface. This
explains how sand patches can form on surfaces with limited sand availability
where linear stability of dune theory does not apply. This new mechanism is
supported by field observations that evidence both the change in transport
rate over different surfaces and in-situ patch formation that leads to
modification of transport dynamics at the surface boundary.

Geophysical Research Letters

School of Geography and Environmental Science, University of Southampton,
Southampton, UK now at: Energy and Environment Institute, University of Hull,
Hull, UK School of Geography and the Environment, University of Oxford,
Oxford, UK Geography and Environment, Loughborough University, Loughborough,
UK Mechanical Engineering, St Anthony Falls Laboratory, University of
Minnesota, Minneapolis, USA Departments of Geology, Geography and GIS,
Mechanical Science and Engineering and Ven Te Chow Hydrosystems Laboratory,
University of Illinois at Urbana-Champaign, USA Departments of Mechanical,
Materials and Aerospace Engineering and Civil, Architectural and Environmental
Engineering, Illinois Institute of Technology, USA Physique et Mécanique des
Milieux Hétérogènes, CNRS, ESPCI Paris, PSL Research University, Université
Paris Cité, Sorbonne Université, Paris, France

Pauline<EMAIL_ADDRESS>
Sand patches can emerge on non-erodible surfaces.

Differing surface characteristics control particle behaviour.

Field measurements demonstrate the key role of sand transport in bedform
initiation.

## Plain Language Summary

Sand patches can be observed in various environments such as beaches and
gravel plains in deserts. Expected to be precursors of dunes when sediment
supply is limited, these bedforms are typically a few centimeters high and
present a reverse longitudinal elevation profile, with a sharp upwind edge and
a smooth downwind tail. Based on field measurements, we propose a formation
mechanism for these patches associated with the sensitive nature of wind-blown
sand transport to changing bed conditions: sand saltation is reduced at the
transition from a solid to an erodible surface, hence favouring deposition on
the patches. This allows us to explain their typical meter-scale length as
well as their asymmetric shapes.

##  1 Introduction

Isolated low-angle sand patches are commonly observed in desert and coastal
regions on non-erodible surfaces, such as gravel plains or moist beaches
[<]Figure 1, e.g.¿lancaster1996field, hesp1997crescentic, nield2011surface.
These bedforms are typically several centimeters high, exhibit reverse
longitudinal asymmetry compared to mature dunes, and can develop rapidly over
several hours. Extensive research has explored the physical dynamics and
morphology of mature desert sand dunes [Bagnold (1937), Bagnold (1941),
Lancaster (1982), Werner (1990), Andreotti . (20021), Charru . (2013), du Pont
(2015), Wiggs (2021)]. We also have some evidence of the dynamics by which
emerging dunes might grow into early-stage protodunes and more mature dune
forms [Kocurek . (1992), Nield . (2011), Elbelrhiti (2012), Hage . (2018),
Montreuil . (2020)], where the subtle coupling of topography, wind flow, and
sediment transport acts to reinforce their growth [Baddock . (2018), Delorme .
(2020), Gadal, Narteau, Ewing . (2020), Lü . (2021), Bristow . (2022)].
However, our knowledge of the processes resulting in, and the relevant time
and length scales associated with, the initial deposition of sand on a non-
erodible surface remains incomplete and unquantified, although such processes
possibly represent a fundamental stage in the origin of aeolian dunes.

Figure 1: Sand patches formed on different surfaces. Brancaster beach Norfolk,
UK (a, d and g), Helga’s dunefield, Namib Desert, Namibia (b, e and h), and
Medano Creek, Great Sand Dunes National Park, Colorado, USA (c, f and i).

There are two clear sets of processes by which aeolian dunes are thought to be
established [Courrech du Pont . (2014), du Pont (2015)]. The first is
associated with the hydrodynamic instability of an erodible granular flat bed
with unlimited sand availability [Warren (1979), Andreotti . (20021), Claudin
. (2013), Charru . (2013)]. This instability results from the combination of
the response of wind stress to the modulated topographic profile, and the
response of sand transport to the spatial variation in that wind stress
[Charru . (2013)]. The former drives the instability where the wind stress
maximum is shifted upwind of a dune crest [Claudin . (2013), Lü . (2021)]; the
latter controls the emerging dune size with a relaxation process over a
(saturation) length, $L_{\mathrm{sat}}$ [Sauermann . (2001), Andreotti .
(2010), Pähtz . (2013), Selmani . (2018)]. The resulting dune pattern consists
of straight-crested bedforms growing in amplitude with an orientation
controlled by the wind regime [Gadal . (2019), Delorme . (2020)]. The second
set of processes is associated with the growth of finger-like dunes developing
across a non-erodible surface from isolated sand sources [Courrech du Pont .
(2014), Rozier . (2019), Gadal, Narteau, Du Pont . (2020)]. In this case, the
dunes, well separated by interdunes where sand is scarce, present a finger-
like shape and grow in length in a direction between those of the dominant
winds [Rozier . (2019)]. Experiments in wind tunnels have also highlighted the
critical role of boundary conditions in determining saltation dynamics and
sand transport rates [<]e.g.¿ho2012particle, kamath2022scaling and this offers
a potential further means by which dunes may establish. These experiments have
provided evidence for the existence of distinctly different transport rates on
erodible and non-erodible or moist surfaces [Neuman Scott (1998), Ho .
(2011)]. Larger sediment fluxes on non-erodible beds have been interpreted as
a consequence of a negligible feedback between the mobile grains on the flow.
This is in contrast to the wind velocity ‘focal point’ that exists when
saltation takes place over an erodible granular bed where the saltating grains
comprise a momentum sink on the overlying flow [Bagnold (1937), Ungar Haff
(1987), Creyssels . (2009), Durán . (2011), Ho . (2014), Valance . (2015)].

Here, we propose a new mode for sand patch and protodune initiation associated
with the sensitive nature of the transport law in response to changing bed
conditions. We find that sand transport rates responding to non-erodible to
erodible bed conditions can explain the emergence of isolated, meter-scale
sand patches on gravelly interdune areas or moist beaches (Figure 1). Our
field data in support of this process, quantitatively capturing the emergence
of a sand patch and the change in saltation this produces, allows us to
propose a conceptual model for early-stage protodune growth from a flat bed.

##  2 Methods

Sediment transport measurements were undertaken in the Skeleton Coast National
Park, Namibia on sand and gravel surfaces between the 13th and 15th September
2019. Here, wind speed was measured simultaneously on both surfaces using
hotwire anemometers (DANTEC 54T35 probes) at a height of 0.085 m and a
frequency of 0.1 Hz. Co-located sediment transport was measured via laser
particle counters (Wenglor YH03PCT8, following the methods of
barchyn2014particle), Sensit contact particle counters and modified Bagnold
sand traps. Saltation height was measured, using a Leica P20 terrestrial laser
scanner (TLS) following the methods of nield2011application, in a 1 m2 area
immediately upwind of the wind and sand transport instrument arrays,
alternating between each of the gravel and sand sites. Additional measurements
were undertaken to quantify both saltation height and surface topographic
change during the initial formation of a sand patch using Leica P20 and P50
TLS instruments placed downwind of an emerging patch at Great Sand Dunes
National Park, Colorado, USA on the 15th April 2019. Details on the data
processing methods can be found in the Supplementary Information.

##  3 Evidence for Differing Sand Transport Processes on Surfaces with
Different Erodibility

Our measurements show evidence of different particle behavior over the
erodible and non-erodible beds. We find that the saltation height on the
erodible surface is invariant with wind velocity whereas it increases with
wind velocity on the non-erodible surface, as has been noted by other
researchers [Bagnold (1937), Bagnold (1941), Creyssels . (2009), Ho . (2012),
Martin Kok (2017), Figure 2a]. This field measured saltation height behavior
then drives a change in sediment transport law on the erodible and non-
erodible surface, as confirmed by our three independent measures of sand
transport: a vertical array of Wenglor laser counters (Figure 2b), Bagnold
type sand traps (Figure 2c), and Sensit piezoelectric counters (Figure 2d).

Figure 2: Saltation height (a) and sediment flux (Q) as a function of wind
velocity on both surfaces, as measured from Wenglor vertical array (b),
Bagnold trap (c), and Sensit counters (d).

Figures 2 b, c, and d show that for a given wind velocity, the amount of sand
transported over the non-erodible surface is greater than that transported
over the erodible surface. According to bagnold1937transport, the velocity of
saltating grains over the erodible bed is independent of the wind velocity,
and consequently the sand flux over an erodible surface scales quadratically
with the wind speed [Ungar Haff (1987), Werner (1990), orange dashed lines
Figure 2b and d]. However, over the non-erodible bed, the particle velocity
increases with wind velocity, thereby establishing a cubic dependence of sand
transport on wind velocity [Ho . (2011), black dashed lines Figure 2b and d].
Two equations can thus be proposed to fit our datasets:

$Q_{\mathrm{sat}}=p\,Q_{\mathrm{ref}}\frac{u^{2}-u_{t}^{2}}{u_{t}^{2}},$ (1)

for the erodible surface datasets, and,

$Q_{\mathrm{sat}}=p\,Q_{\mathrm{ref}}\frac{u^{2}-u_{t}^{2}}{u_{t}^{2}}\frac{u}{u_{t}},$
(2)

for the non-erodible surface datasets, with $Q_{\mathrm{ref}}$ as the
reference flux that is dependent on the sand characteristics, $u_{t}$, the
threshold velocity, and $p$, a fitting parameter (see Supplementary
Information for details on values for each measurement method). Because of
this change in transport law, to respect mass balance, the transition from
non-erodible to erodible bed should thus generate sand deposition.

##  4 Bedform Development

###  4.1 Conceptual Model

Based on our field measurements, we propose a conceptual model to explain the
emergence of an isolated sand patch on a flat, non-erodible bed with limited
sand availability. We consider a flat, non-erodible surface (represented in
black on Figure 3a) adjacent to an erodible zone (in orange). Due to this
change in surface characteristics, and according to equations 1 and 2, a drop
in the saturated sand flux at the transition from the non-erodible to erodible
surface should occur (blue line on Figure 3a). However, the flux does not
adjust instantaneously to its new saturated value, but responds with a
characteristic relaxation length, called the saturation length
$L_{\mathrm{sat}}$, to reach $Q_{\mathrm{sat}}$ [Sauermann . (2001), Andreotti
. (2010), Pähtz . (2013), Selmani . (2018)]. The red line represents this
decrease in sand flux downwind of the non-erodible/erodible bed boundary
(Figure 3b). To respect mass balance, the excess sand transported on the non-
erodible surface must deposit at the non-erodible/erodible transition
following the decrease in sand flux over $L_{\mathrm{sat}}$, which thereby
leads to the formation of a sand deposit (Figure 3b). The rapid decrease in
sand flux at the transition from a non-erodible to erodible surface (red line)
thus generates a sand patch with an asymmetric shape, possessing a sharp
upwind edge with a smooth downwind tail (Figure 3b).

Figure 3: Conceptual model for emergence of a sand patch driven by change in
sand transport in the case of limited sand availability surface. (a) Pre-
deposition state with the associated potential saturated sand flux (blue
line). (b) Post-deposition state, with red line representing the actual sand
flux.

This simple conceptual model assumes a constant wind velocity above threshold,
and a sharp transition from a non-erodible to erodible surface. In the next
section, we compare qualitatively the topography of an incipient bedform in
the field to the idealized patch presented in Figure 3b.

###  4.2 Field Evidence

Sand transport measurements over a centimeter-high initial sand patch are
challenging in the field as the placement of instruments can modify or destroy
the emerging bedform by disrupting the windflow. Consequently, we measure
concurrently the topography of an emerging sand patch and the saltation layer
height with a non-invasive TLS. According to the measurements presented in
Figure 2a, we can use the dependence of the saltation layer height upon the
wind velocity as a proxy for the appropriate transport law. To confirm that
the change in sand flux acts as a driver for sand patch initiation, we
measured the topography and saltation layer height pre-(black) and
post-(orange) emergence of a sand patch on a sediment availability-limited,
non-erodible surface (Figure 4; field site and method are described in
Supplementary Information). Figure 4 shows the height of the saltation layer
is constant above the non-erodible surface, whereas it decreases over the
developing patch due to its erodible sand surface. When sand particles start
to travel over the erodible surface, each grain impact with the bed generates
a particle ejection (splash effect), so that this process is consumes energy.
Consequently, saltating particles lose energy and experience a lower jump
height, causing a decrease in the height of the saltation layer [Bagnold
(1937), Ho . (2012), Ho . (2014), Valance . (2015)].

Figure 4: TLS measured surface over an hour during the initial development of
a sand patch and the corresponding relative saltation height over the same
surface. Measurements were undertaken in the Great Sand Dunes National Park.
The average wind speed measured at 0.1m above the surface during the
experiment was 6.35 m$\,s^{-1}$. Relative saltation height is normalized by
the maximum saltation height within each x-minute measurement period (the
methods are detailed in the Supplementary Information).

As predicted by our conceptual model (Figure 3), the observed initial sand
patch exhibits a reverse asymmetry, with the steepest slope at the upwind
edge. Our field measurements (Figure 4) show a rapid decrease in saltation
height from the upwind edge of the patch to a distance 1.4$\pm$0.3 m downwind
of the patch toe. According to our conceptual model, sand deposition occurs
over the saturation length. Although the relationship between
$L_{\mathrm{sat}}$ and the grain diameter is still a matter of debate [Pähtz .
(2013), Pähtz Durán (2017), Selmani . (2018)], here we follow
andreotti2010measurements to estimate $L_{\mathrm{sat}}$ as

$L_{\mathrm{sat}}\approx 2.2\,\frac{\rho_{s}}{\rho}\,d$ (3)

At the Great Sand Dunes field site, the grain size is d=350 $\pm$ 50 $\mu$m,
mass density is $\rho_{s}$ =2650 kg m-3, and the air density $\rho$ = 1.2 kg
m-3 that yields a saturation length of 1.7 $\pm$ 0.25 m, in good agreement
with our field measurements. This therefore suggests that the saturation
length sets the length of the incipient sand patch.

##  5 Discussion and Conclusions

Combining field measurements and a simple physically-based model, we propose a
mechanism to explain the initiation of aeolian sand patches where there is
limited sand availability. A change in surface characteristics (erodible/non-
erodible or dry/moist) is critical, and leads to a modification of the sand
transport dynamics. In agreement with previous studies, we show that the
quantity of transported sand, and height of particle saltation, drops when
encountering an erodible surface. The corresponding decrease in sand flux
generates deposition in order to satisfy mass balance, thus adding sediment to
the patch. Moreover, our field measurements demonstrate that the saturation
length controls the size of the emerging deposit associated with the spatial
relaxation of flux. Besides a change in surface mobility, the second critical
parameter controlling sand patch emergence is the incoming sand flux. In our
conceptual model, we assume the incoming sand flux equals the saturated sand
flux associated with the non-erodible surface. However, the value of incoming
flux depends largely on the sand source availability upwind of the initial
patch. Without appropriate sand supply, such incipient bedforms are likely to
degrade rapidly [Lancaster (1996), Nield (2011)]. The majority of sand patches
develop in interdune areas [Lancaster (1996)] and beaches [Hesp Arens (1997),
Nield . (2011), Baddock . (2018), Hage . (2018), Montreuil . (2020)], and in
these cases sand sources are provided by the surrounding dry sandy surfaces.
However, in the case of a succession or field of patches, if all the excess
sand is deposited on the upwind erodible surfaces (as in the case of our
conceptual schematics), then sediment supply would be further reduced to
downwind patches. This condition likely creates a control on sand feeding of
downwind patches and suggests there is a role for temporal wind fluctuations,
both in strength and direction, in maintaining a broad field of multiple sand
patches. As sand starts to be deposited, the initial bedform will interact
with the wind flow and consequently the downwind variation of the sand flux
will depend not only on the nature of the substrate (erodible/ non-erodible)
but also on the underlying and developing topography [Claudin . (2013), du
Pont (2015), Bristow . (2022)]. Consequently, to develop the conceptual
arguments presented herein and investigate the conditions under which the
aeolian sand patch is most likely to evolve, the present model needs further
development to include full coupling between wind, transport and topography.
In order to examine propagative solutions in a simplified dune model that
accounted for these couplings, andreotti2002bselection identified flat bedform
profiles without slipfaces (patches), but these solutions did not account for
the change of transport law when bed conditions varied. However, these results
did show the necessity of an incoming flux for these solutions to exist. The
present study shows, for the first time, that it is possible to develop a sand
patch on a non-erodible surface without any additional perturbation from the
topography of the bed, and opens the way for study of the evolution of
isolated sand patches towards larger bedforms and fully developed dunes
[Kocurek . (1992), Bristow . (2022)].

## Data Availability

The data used in this manuscript can be found in the NERC National Geological
Data Center: Huab river valley dataset
[<]https://doi.org/10.5285/99e4446f-c43a-492d-83c9-e896206649c0,¿huabdata and
Great Sand Dunes National Park dataset
[<]https://doi.org/10.5285/46e9ff95-27ca-4d3b-b587-fc9ce22c5781,¿medanodata.
Supplementary figures and text can be found in the supporting information.

###### Acknowledgements.

This work was funded by the TOAD (The Origin of Aeolian Dunes) project (funded
by the Natural Environment Research Council, UK and National Science
Foundation, USA; NE/R010196NSFGEO‐NERC, NSF-GEO‐1829541 and NSF‐GEO‐1829513).
Research was undertaken at GSD under a Scientific Research and Collection
permit GRSA‐2018‐SCI‐004, and we are very grateful for support from A. Valdez
and F. Bunch. For the Huab fieldwork, we acknowledge Gobabeb Namib Research
Institute, J. Kazeurua, I. Matheus, L. Uahengo, MET and NCRST (permits
1913/2014; 2051/2015; 2168/2016, RPIV00022018). Data processing used the
IRIDIS Southampton Computing Facility. J. M. Nield was supported by a
Department of Geology and Geophysics, Texas A$\&$M University, Michel T
Halbouty Visiting Chair during the GSD field campaign. We thank B. Andreotti,
C. Gadal, C. Narteau and TOAD project partners for useful discussions. We also
thank Patrick Hesp and an anonymous reviewer for their careful reading of our
manuscript and their insightful comments and suggestions.
School of Geography and Environmental Science, University of Southampton,
Southampton, UK now at: Energy and Environment Institute, University of Hull,
Hull, UK School of Geography and the Environment, University of Oxford,
Oxford, UK Geography and Environment, Loughborough University, Loughborough,
UK Mechanical Engineering, St Anthony Falls Laboratory, University of
Minnesota, Minneapolis, USA Departments of Geology, Geography and GIS,
Mechanical Science and Engineering and Ven Te Chow Hydrosystems Laboratory,
University of Illinois at Urbana-Champaign, USA Departments of Mechanical,
Materials and Aerospace Engineering and Civil, Architectural and Environmental
Engineering, Illinois Institute of Technology, USA Physique et Mécanique des
Milieux Hétérogènes, CNRS, ESPCI Paris, PSL Research University, Université
Paris Cité, Sorbonne Université, Paris, France Contents of this file

  1. 1.

Text S1 to S4

  2. 2.

Figures S1 to S3

##  6 Introduction

Our study involved two field campaigns. Data collected in the Skeleton Coast
National Park, Namibia, was used to confirm the differences in sand transport
dynamics on erodible and non- erodible surfaces. The saltation dynamics that
occurred during the emergence of a sand patch on a non-erodible surface were
measured at Great Sand Dunes National Park, Colorado, USA. The following
section contain the description of the field sites and the methods used to
collect and analyze the data.

##  7 Text S1-Field sites

The study area in the Huab Valley dune field of the Skeleton Coast National
Park, northwest Namibia, consisted of a flat surface covered with gravel and
an ephemeral sand patch aligned with the predominant south-southwest winds
[Lancaster (1982)]. The gravel acts as an armor layer, which makes the surface
non-erodible, in contrast to sand patches that are erodible. We measured sand
transport, saltation height and wind velocity over both surfaces during
periods of high sand transport. The measurements were performed simultaneously
over both surfaces, a co-located sand patch and gravel surface from the 13th
to the 15th September 2019. The Medano Creek site, close to the Visitor Center
at Great Sand Dunes National Park, Colorado, USA, consisted of a moist sand
surface, adjacent to an ephemeral creek bed, with sand being supplied upwind
from a field of protodunes. The moisture was large enough to prevent sand
being eroded from the surface (i.e. it was a non-erodible surface), but not
moist enough for adhesion to occur. We measured saltation height and surface
change over this surface during an hour-long period on the 15th April 2019.

##  8 Text S2-Wind Velocity and Sand Transport (Skeleton Coast National Pak,
Namibia)

We measured the wind velocity at a height of 0.085 m with a hotwire anemometer
(DANTEC 54T35 probes), at a frequency of 0.1 Hz. We used three different
methods to quantify sand transport on both erodible and non-erodible surfaces.
i) Five laser particle counters (Wenglor YH03PCT8) were positioned in a
vertical array at height of 0.025, 0.05, 0.115, 0.18 and, 0.5 m measuring at a
frequency of 0.1 Hz (Figure 5a).

Figure 5: a) Vertical array of Wenglor counters used in the field. b) Sand
flux measured at each elevation (red dots), the hatched area is the total flux
Q, and the blue area is the error calculated from the exponential fit.

ii) A Sensit contact particle counter, which counts sand particles within 0.03
m from the surface recorded total counts every 10 seconds. iii) A modified
Bagnold sand trap sampled moving sand between 0 to 0.5 m above the surface
over a time period varying between 10 and 30 minutes (Figure 6a). The sand
traps allowed us to quantify the physical characteristics of the transported
sand. We measured the grain size using a laser granulometer (Malvern
Mastersizer 3000), and the density of the sand using a pycnometer. We then
used this particle size distribution to convert particle counts from the
Wenglors into sand flux following the method of barchyn2014particle. All the
datasets are subdivided into 30-sec intervals. The methods used to estimate
the sand flux are described below:

  * •

Wenglor array: The particle count recorded by each Wenglor instrument is
converted into sand flux using the method proposed by barchyn2014particle. For
each time period, we integrated the sand flux density at each elevation, $q$,
using the corresponding exponential law to obtain the sand flux, $Q$ (equation
4 and Figure 5b).

$Q=\int_{\mathrm{z=0}}^{\mathrm{z=\infty}}q_{0}exp\left(\frac{-z}{z_{0}}\right)dz,$
(4)

where $q_{0}$ and $z_{0}$ are the parameters of the exponential fit.

  * •

Bagnold sand traps: We positioned four Bagnold traps approximately 50 cm from
each other and spanwise to incoming sand transport. Each trap comprised 25
slots of 2 cm-height. By measuring the amount of sand trapped in each slot, we
could estimate the sand flux density at each elevation, $q$. We finally fit
the exponential law (equation 4) to the averaged sand flux (averaged over the
four Bagnold traps), to calculate the sand flux, $Q$ (Figure 6).

Figure 6: a) Frontal view of Bagnold traps in the field. b) Sand flux measured
at each elevation (red dots), the hatched area is the total flux $Q$, and the
blue area is the error calculated from the exponential fit.

  * •

Sensit-piezoelectric counter: The Sensit piezoelectric counter detects
particle impacts from all directions between 0 and 3 cm above the surface. We
converted the particle counts into a flux using:

$Q=\frac{nV\rho}{A}h,$ (5)

where $n$ is the counts per second, $V$ the volume of each sand particle, $A$
the area of the Sensit and $h$ the measurement height.

To compare transport at similar wind speeds on different surfaces, we
concatenated all the data to generate datasets for erodible and non-erodible
surfaces that we then binned according to the wind velocity, with an increment
of 0.1 m s-1. Finally, we fitted the transport law, Equation (1) and (2), to
the two datasets, erodible and non-erodible, respectively. The reference flux
$Q_{\mathrm{ref}}$ is defined as,

$Q_{\mathrm{ref}}=\rho_{s}d\sqrt{\frac{\rho_{s}}{\rho}gd},$ (6)

equals 1.8 kg m-1s-1. Using the Wenglor counter dataset, we find a threshold
velocity $u_{t}$ = 6.2 m s-1 (at 0.085 m), and the fitting parameter $p$
equals 0.004 and 0.009 respectively for the erodible and non-erodible
surfaces. For the Sensit datasets, we obtain $u_{t}$ = 5.5 m s-1 and $p$
equals 0.0007, and 0.0014 respectively for the erodible and non-erodible
surfaces. Due to the intermittency of the measurement with the Bagnold traps,
there was insufficient data to fit a transport law. However, the Bagnold trap
data show qualitatively the difference in transport capacity over each
surface.

##  9 Text S3-Maximum Saltation Height and Surface Change (Skeleton Coast
National Park and Great Sand Dunes National Park)

We measured the maximum saltation height over each surface using terrestrial
laser scanning (TLS), following the methods of nield2011application. An area
of approximately 1 m2 was scanned using a Leica P20 TLS over a 3-minute
period, and a filter of 35° was applied to separate laser returns from above,
and on, the surface. Data was gridded in 0.01 m2 to minimize the impact of
mixed pixels or large-scale topography. Within each scan, saltation heights
were obtained for each grid square based on the maximum height of the laser
returns above the surface and the minimum height of the surface. The maximum
value for each scan was assigned a mean velocity from the hotwire anemometer.
Data were then binned for each surface using 0.3 m s-1 velocity brackets, with
a minimum of four points in each bracket and points where the standard
deviation was greater than the mean value within the bracket were excluded.

Additionally, at Great Sand Dunes National Park we used two TLS instruments, a
Leica P20 and a Leica P50. As the sand patch that developed was the same order
of magnitude in height as the saltating grains, we first concatenated four
consecutive scans of the surface and applied the saltation filter to maximize
the chance that scanning of the surface was not occluded by saltation. We then
use each individual scan to plot the surface (gridded at 0.0001 m2) and
saltation (gridded at 0.01 m2) at the start and end of the measurement period
(1 hour).

##  10 Text S4-Estimation of the Saturation Length from the Evolution of the
Saltation Layer Height

The transition appears as a decreasing sigmoidal curve (Figures 4 and 7). To
quantify this observation, we fit a hyperbolic tangent to the height profile,
defined as,

$H=\left(H_{ne}-H_{e}\right)\frac{tanh(-(x-x_{0})/l+1}{2}+H_{e},$ (7)

where $H_{e}$ and $H_{ne}$ are the normalized saltation height over the
erodible and non-erodible surface, $x_{0}$ is the location of the transition
and $l$ is the exponential length.

We find that the normalized saltation height plateaus at about 0.67 on the
non-erodible surface ($H_{ne}$), and at about 0.08 on the erodible surface
($H_{e}$). The transition between these two areas is a smooth transition with
a characteristic length 2$l$ = 1.4$\pm$ 0.3 m.

Figure 7: Evolution of the saltation layer height (red line) with distance
from the sand patch upwind toe (see orange line on Figure 4). The black
vertical dashed marks the transition from non-erodible to erodible substrate.
The dashed blue line is the sigmoidal fit, with the uncertainty represented by
the blue shading.

## References

  * Andreotti . (20021) andreotti2002selectionAndreotti, B., Claudin, P. Douady, S.  20021\.  Selection of dune shapes and velocities Part 1: Dynamics of sand, wind and barchans Selection of dune shapes and velocities part 1: Dynamics of sand, wind and barchans.  The European Physical Journal B-Condensed Matter and Complex Systems283321–339.
  * Andreotti . (20022) andreotti2002bselectionAndreotti, B., Claudin, P. Douady, S.  20022\.  Selection of dune shapes and velocities part 2: A two-dimensional modelling Selection of dune shapes and velocities part 2: A two-dimensional modelling.  The European Physical Journal B-Condensed Matter and Complex Systems283341–352.  https://doi.org/10.1140/epjb/e2002-00237-3
  * Andreotti . (2010) andreotti2010measurementsAndreotti, B., Claudin, P. Pouliquen, O.  2010\.  Measurements of the aeolian sand transport saturation length Measurements of the aeolian sand transport saturation length.  Geomorphology1233-4343–348.  https://doi.org/10.1016/j.geomorph.2010.08.002
  * Baddock . (2018) baddock2018earlyBaddock, MC., Nield, JM. Wiggs, GFS.  2018\.  Early-stage aeolian protodunes: Bedform development and sand transport dynamics Early-stage aeolian protodunes: Bedform development and sand transport dynamics.  Earth Surface Processes and Landforms431339–346.  https://doi.org/10.1002/esp.4242
  * Bagnold (1937) bagnold1937transportBagnold, RA.  1937\.  The transport of sand by wind The transport of sand by wind.  The Geographical Journal895409–438.  https://doi.org/10.2307/1786411
  * Bagnold (1941) bagnold1941physicsBagnold, RA.  1941\.  The Physics of Blown Sand and Desert Dunes The physics of blown sand and desert dunes.  Methuen London.
  * Barchyn . (2014) barchyn2014particleBarchyn, TE., Hugenholtz, CH., Li, B., Neuman, CM. Sanderson, RS.  2014\.  From particle counts to flux: Wind tunnel testing and calibration of the ‘Wenglor’aeolian sediment transport sensor From particle counts to flux: Wind tunnel testing and calibration of the ‘wenglor’aeolian sediment transport sensor.  Aeolian Research15311–318.  https://doi.org/10.1016/j.aeolia.2014.06.009
  * Bristow . (2022) bristow2022topographicBristow, NR., Best, J., Wiggs, GFS., Nield, JM., Baddock, MC., Delorme, P. Christensen, KT.  2022\.  Topographic perturbation of turbulent boundary layers by low-angle, early-stage aeolian dunes Topographic perturbation of turbulent boundary layers by low-angle, early-stage aeolian dunes.  Earth Surface Processes and Landforms.  https://doi.org/10.1002/esp.5326
  * Charru . (2013) charru2013sandCharru, F., Andreotti, B. Claudin, P.  2013\.  Sand ripples and dunes Sand ripples and dunes.  Annual Review of Fluid Mechanics45469–493.  https://doi.org/10.1146/annurev-fluid-011212-140806
  * Claudin . (2013) claudin2013fieldClaudin, P., Wiggs, GFS. Andreotti, B.  2013\.  Field evidence for the upwind velocity shift at the crest of low dunes Field evidence for the upwind velocity shift at the crest of low dunes.  Boundary-layer meteorology1481195–206.  https://doi.org/10.1007/s10546-013-9804-3
  * Courrech du Pont . (2014) courrech2014twoCourrech du Pont, S., Narteau, C. Gao, X.  2014\.  Two modes for dune orientation Two modes for dune orientation.  Geology429743–746.  https://doi.org/10.1130/G35657.1
  * Creyssels . (2009) creyssels2009saltatingCreyssels, M., Dupont, P., El Moctar, AO., Valance, A., Cantat, I., Jenkins, JT.Rasmussen, KR.  2009\.  Saltating particles in a turbulent boundary layer: experiment and theory Saltating particles in a turbulent boundary layer: experiment and theory.  Journal of Fluid Mechanics62547–74.  https://doi.org/10.1017/S0022112008005491
  * Delorme . (2020) delorme2020duneDelorme, P., Wiggs, GFS., Baddock, MC., Claudin, P., Nield, JM. Valdez, A.  2020\.  Dune initiation in a bimodal wind regime Dune initiation in a bimodal wind regime.  Journal of Geophysical Research: Earth Surface12511e2020JF005757.  https://doi.org/10.1029/2020JF005757
  * du Pont (2015) courrech2015dunedu Pont, SC.  2015\.  Dune morphodynamics Dune morphodynamics.  Comptes Rendus Physique161118–138.  https://doi.org/10.1016/j.crhy.2015.02.002.
  * Durán . (2011) duran2011aeolianDurán, O., Claudin, P. Andreotti, B.  2011\.  On aeolian transport: Grain-scale interactions, dynamical mechanisms and scaling laws On aeolian transport: Grain-scale interactions, dynamical mechanisms and scaling laws.  Aeolian Research33243–270.  https://doi.org/10.1016/j.aeolia.2011.07.006
  * Elbelrhiti (2012) elbelrhiti2012initiationElbelrhiti, H.  2012\.  Initiation and early development of barchan dunes: A case study of the Moroccan Atlantic Sahara desert Initiation and early development of barchan dunes: A case study of the moroccan atlantic sahara desert.  Geomorphology1381181–188.  https://doi.org/10.1016/j.geomorph.2011.08.033
  * Gadal . (2019) gadal2019incipientGadal, C., Narteau, C., Du Pont, SC., Rozier, O. Claudin, P.  2019\.  Incipient bedforms in a bidirectional wind regime Incipient bedforms in a bidirectional wind regime.  Journal of Fluid Mechanics862490–516.  doi:10.1017/jfm.2018.978.
  * Gadal, Narteau, Du Pont . (2020) gadal2020periodicityGadal, C., Narteau, C., Du Pont, SC., Rozier, O. Claudin, P.  2020\.  Periodicity in fields of elongating dunes Periodicity in fields of elongating dunes.  Geology484343–347.  https://doi.org/10.1130/G46987.1
  * Gadal, Narteau, Ewing . (2020) gadal2020spatialGadal, C., Narteau, C., Ewing, R., Gunn, A., Jerolmack, D., Andreotti, B. Claudin, P.  2020\.  Spatial and temporal development of incipient dunes Spatial and temporal development of incipient dunes.  Geophysical Research Letters4716e2020GL088919.  https://doi.org/10.1029/2020GL088919
  * Hage . (2018) hage2018determiningHage, P., Ruessink, B. Donker, J.  2018\.  Determining sand strip characteristics using Argus video monitoring Determining sand strip characteristics using argus video monitoring.  Aeolian Research331–11.  https://doi.org/10.1016/j.aeolia.2018.03.007
  * Hesp Arens (1997) hesp1997crescenticHesp, PA. Arens, SM.  1997\.  Crescentic dunes at Schiermonnikoog, the Netherlands Crescentic dunes at schiermonnikoog, the netherlands.  Earth Surface Processes and Landforms: The Journal of the British Geomorphological Group228785–788.  https://doi.org/10.1002/(SICI)1096-9837(199708)22:8¡785::AID-ESP813¿3.0.CO;2-F
  * Ho . (2012) ho2012particleHo, TD., Dupont, P., El Moctar, AO. Valance, A.  2012\.  Particle velocity distribution in saltation transport Particle velocity distribution in saltation transport.  Physical Review E855052301.  https://doi.org/10.1103/PhysRevE.85.052301
  * Ho . (2011) ho2011scalingHo, TD., Valance, A., Dupont, P. El Moctar, AO.  2011\.  Scaling laws in aeolian sand transport Scaling laws in aeolian sand transport.  Physical Review Letters1069094501.  https://doi.org/10.1103/PhysRevLett.106.094501
  * Ho . (2014) ho2014aeolianHo, TD., Valance, A., Dupont, P. El Moctar, AO.  2014\.  Aeolian sand transport: Length and height distributions of saltation trajectories Aeolian sand transport: Length and height distributions of saltation trajectories.  Aeolian Research1265–74.  https://doi.org/10.1016/j.aeolia.2013.11.004
  * Kamath . (2022) kamath2022scalingKamath, S., Shao, Y. Parteli, EJR.  2022\.  Scaling laws in Aeolian sand transport under low sand availability Scaling laws in aeolian sand transport under low sand availability.  Geophysical Research Letters4911e2022GL097767.  https://doi.org/10.1029/2022GL097767
  * Kocurek . (1992) kocurek1992duneKocurek, G., Townsley, M., Yeh, E., Havholm, KG. Sweet, ML.  1992\.  Dune and dune-field development on Padre Island, Texas, with implications for interdune deposition and water-table-controlled accumulation Dune and dune-field development on padre island, texas, with implications for interdune deposition and water-table-controlled accumulation.  Journal of Sedimentary Research624622–635.  https://doi.org/10.1306/D4267974-2B26-11D7-8648000102C1865D
  * Lancaster (1982) lancaster1982dunesLancaster, N.  1982\.  Dunes on the Skeleton Coast, Namibia (South West Africa): geomorphology and grain size relationships Dunes on the skeleton coast, namibia (south west africa): geomorphology and grain size relationships.  Earth surface processes and landforms76575–587.  https://doi.org/10.1002/esp.3290070606
  * Lancaster (1996) lancaster1996fieldLancaster, N.  1996\.  Field studies of sand patch initiation processes on the northern margin of the Namib sand sea Field studies of sand patch initiation processes on the northern margin of the namib sand sea.  Earth Surface Processes and Landforms2110947–954.  https://doi.org/10.1002/(SICI)1096-9837(199610)21:10¡947::AID-ESP634¿3.0.CO;2-7.
  * Lü . (2021) lu2021directLü, P., Narteau, C., Dong, Z., Claudin, P., Rodriguez, S., An, Z.Courrech du Pont, S.  2021\.  Direct validation of dune instability theory Direct validation of dune instability theory.  Proceedings of the National Academy of Sciences11817e2024105118.  https://doi.org/10.1073/pnas.2024105118.
  * Martin Kok (2017) martin2017windMartin, RL. Kok, JF.  2017\.  Wind-invariant saltation heights imply linear scaling of aeolian saltation flux with shear stress Wind-invariant saltation heights imply linear scaling of aeolian saltation flux with shear stress.  Science advances36e1602569.  https://doi.org/10.1126/sciadv.1602569
  * Montreuil . (2020) montreuil2020earlyMontreuil, AL., Chen, M., Brand, E., De Wulf, A., De Sloover, L., Dan, S. Verwaest, T.  2020\.  Early-stage aeolian dune development and dynamics on the upper-beach Early-stage aeolian dune development and dynamics on the upper-beach.  Journal of Coastal Research95SI336–340.  Doi: 10.2112/SI95-065.1
  * Neuman Scott (1998) neuman1998windNeuman, CM. Scott, MM.  1998\.  A wind tunnel study of the influence of pore water on aeolian sediment transport A wind tunnel study of the influence of pore water on aeolian sediment transport.  Journal of Arid Environments393403–419.  https://doi.org/10.1006/jare.1997.0371
  * Nield (2011) nield2011surfaceNield, JM.  2011\.  Surface moisture- induced feedback in aeolian environments Surface moisture- induced feedback in aeolian environments.  Geology3910915–918.  https://doi.org/10.1130/G32151.1
  * Nield Wiggs (2011) nield2011applicationNield, JM. Wiggs, GFS.  2011\.  The application of terrestrial laser scanning to aeolian saltation cloud measurement and its response to changing surface moisture The application of terrestrial laser scanning to aeolian saltation cloud measurement and its response to changing surface moisture.  Earth Surface Processes and Landforms362273–278.  https://doi.org/10.1002/esp.2102
  * Nield . (20221) huabdataNield, JM., Wiggs, GFS., Baddock, MC. Delorme, P.  20221\.  Surface and Meteorological Data at Huab River Valley, Skeleton Coast National Park, Namibia in September 2019. Surface and meteorological data at huab river valley, skeleton coast national park, namibia in september 2019\.  NERC EDS National Geoscience Data Centre. (Dataset).  https://doi.org/10.5285/99e4446f-c43a-492d-83c9-e896206649c0
  * Nield . (20222) medanodataNield, JM., Wiggs, GFS., Baddock, MC. Delorme, P.  20222\.  Surface and Meteorological Data at Medano Creek, Great Sand Dunes National Park, Colorado, USA on 15th April 2019. Surface and meteorological data at medano creek, great sand dunes national park, colorado, usa on 15th april 2019.  NERC EDS National Geoscience Data Centre. (Dataset).  https://doi.org/10.5285/46e9ff95-27ca-4d3b-b587-fc9ce22c5781
  * Nield . (2011) nield2011aeolianNield, JM., Wiggs, GFS. Squirrell, RS.  2011\.  Aeolian sand strip mobility and protodune development on a drying beach: examining surface moisture and surface roughness patterns measured by terrestrial laser scanning Aeolian sand strip mobility and protodune development on a drying beach: examining surface moisture and surface roughness patterns measured by terrestrial laser scanning.  Earth Surface Processes and Landforms364513–522.  Doi: 10.1002/esp.2071
  * Pähtz Durán (2017) pahtz2017fluidPähtz, T. Durán, O.  2017\.  Fluid forces or impacts: What governs the entrainment of soil particles in sediment transport mediated by a Newtonian fluid? Fluid forces or impacts: What governs the entrainment of soil particles in sediment transport mediated by a newtonian fluid?  Physical Review Fluids27074303.  https://doi.org/10.1103/PhysRevFluids.2.074303
  * Pähtz . (2013) pahtz2013fluxPähtz, T., Kok, JF., Parteli, EJR. Herrmann, HJ.  2013\.  Flux saturation length of sediment transport Flux saturation length of sediment transport.  Physical review letters11121218002.  https://doi.org/10.1103/PhysRevLett.111.218002
  * Rozier . (2019) rozier2019elongationRozier, O., Narteau, C., Gadal, C., Claudin, P. Courrech du Pont, S.  2019\.  Elongation and stability of a linear dune Elongation and stability of a linear dune.  Geophysical Research Letters462414521–14530.  https://doi.org/10.1029/2019GL085147
  * Sauermann . (2001) sauermann2001continuumSauermann, G., Kroy, K. Herrmann, HJ.  2001\.  Continuum saltation model for sand dunes Continuum saltation model for sand dunes.  Physical Review E643031305.  https://doi.org/10.1103/PhysRevE.64.031305
  * Selmani . (2018) selmani2018aeolianSelmani, H., Valance, A., Ould El Moctar, A., Dupont, P. Zegadi, R.  2018\.  Aeolian sand transport in out-of-equilibrium regimes Aeolian sand transport in out-of-equilibrium regimes.  Geophysical Research Letters4541838–1844.  https://doi.org/10.1002/2017GL076937
  * Ungar Haff (1987) ungar1987steadyUngar, JE. Haff, PK.  1987\.  Steady state saltation in air Steady state saltation in air.  Sedimentology342289–299.  https://doi.org/10.1111/j.1365-3091.1987.tb00778.x
  * Valance . (2015) valance2015physicsValance, A., Rasmussen, KR., El Moctar, AO. Dupont, P.  2015\.  The physics of Aeolian sand transport The physics of aeolian sand transport.  Comptes Rendus Physique161105–117.  https://doi.org/10.1016/j.crhy.2015.01.006
  * Warren (1979) warren1979aeolianWarren, A.  1979\.  Aeolian processes Aeolian processes.  Process in geomorphology325S1.
  * Werner (1990) werner1990steadyWerner, BT.  1990\.  A steady-state model of wind-blown sand transport A steady-state model of wind-blown sand transport.  The Journal of Geology9811–17.  https://doi.org/10.1086/629371
  * Wiggs (2021) wiggs2021Wiggs, G.  2021\.  7.17 Dune Morphology and Dynamics 7.17 dune morphology and dynamics.  Treatise on Geomorphology (Second Edition), Academic Press.  https://doi.org/10.1016/B978-0-12-818234-5.00073-