Aerodynamic roughness of rippled beds under active saltation at Earth-to-Mars atmospheric pressures

Domain: earth_science
Published: 2025-06-02
Editorial outcome: minor_revision

Abstract
Aswindsblowoversand,grainsaremobilizedandreorganizedintobedforms
suchasripplesanddunes.Inturn,sandtransportandbedformsaffectthe
windsthemselves.Thesecomplexinteractionsbetweenwindsandsediment
rendermodelingofwindsweptlandscapeschallenging.Acriticalparameterin
suchmodelsistheaerodynamicroughnesslength,z ,definedastheheight
0
abovethebedatwhichwindvelocitypredictedfromtheloglawdropstozero.
Inaeolianenvironments,z canvariablybecontrolledbythelaminarviscous
0
sublayer,grainroughness,formdragfrombedforms,orthesaltationlayer.
Estimatesofz areusedonMars,notably,topredictwindspeeds,sandfluxes,
0
andglobalcirculationpatterns;yet,norobustmeasurementsofz havebeen
0
performedoverrippledsandonMarstodate.Here,wemeasurez over
0
equilibratedrippledsandbedswithactivesaltationunderatmosphericpres-
suresintermediatebetweenthoseofEarthandMars.ExtrapolatedtoMars,our
resultssuggestthatz overrippledbedsandunderactivesaltationmaybe
0
dominatedbyformdragacrossaplausiblerangeofwindvelocities,reaching
valuesupto1cm—twoordersofmagnitudelargerthantypicallyassumedfor
flatbedsundersimilarsedimenttransportconditions.

Introduction
Interactionsbetweenwindsandsedimentoccuroverawiderangeof
scales,fromthemobilizationofindividualsandgrainstotheformation
of bedforms and overall landscape evolution. Such interactions are
governed bytheshear stressimparted bywinds onto the sediment
bed; in turn, the bed’s responseto shearing winds affects the wind
profile,andthus,bedstresses1.Determiningbasalwindstressesisthus
criticaltopredictingsandfluxesandlandscapeevolutioninresponse
towindsacrossplanetarybodies.

Theshearstressimpartedbywindsontoasurface,τ ,iscontrolled
b
byalengthscale,knownastheaerodynamicroughnesslength,z .
0
This
lengthscaleistheheightatwhichwindspeedispredictedtobecome
nullunderneutralatmosphericconditions—thatis,whentemperature-
drivenbuoyancyeffectsarenegligible-suchthat

u(z)=
u(cid:2)
ln
z
, (1)
κ z
0

whereu(z)istheverticalwindvelocity,u(cid:2)= pffiffiffiffiffiffiffiffiffiffi
τ
b
=ρistheshearvelocity
(withρtheatmosphericdensity),andκ≈0.41isthevonKármáncon-
stant. The parameter z can also be interpreted as a mixing length
0
governing turbulent fluctuations over a solid surface2. It plays an
essential role in boundary layer dynamics and controls energy
exchanges between planetary surfaces and overlying atmospheres3.
Forexample,characterizationsofz arerequiredtounderstandhow
0
topography,vegetation,andotherobstaclesimpactwindpatternson
Earth4–8.Italsoplaysacrucialroleinregulatingtheverticalexchangeof
heatbetweenthesurfaceandtheatmosphere9,10.

The value ofz 0 varies with the characteristics ofplanetarysur-
faces.Oversandbedswithatypicallengthscale,r,ofbedroughness
elements (such as individual grains or bedforms), one can define a
roughness-basedReynoldsnumber,

Re r = ru ν (cid:2), (2)

whereνisthekinematicviscosityoftheatmosphere11.WhenRe ≲10,
the bed is said to be aerodynamically smooth. In the absence of
saltation, z for aerodynamically smooth beds is controlled by the
0
thicknessofthelaminarsublayer12,suchthat

z
0
=
ν
9u(cid:2)
: (3)

In turn,whenRe ≳100andsandisimmobile,thebedissaid tobe
r
aerodynamicallyrough,andz iscontrolledbyr.Forflatbeds(i.e.,in
0
theabsenceofbedforms),rscaleswithgrainsize.Ref.13determined
experimentallythatz isgivenbyk/30,wherek istheequivalentsand-
0 s s
grainroughnessheight.Formixedgrainpopulations,k ≈nd,wheren
s i
is of the order 2–3, and d is the i th percentile of the grain size
i
distribution(oftend ,d ,ord )14–16.Thus,
50 65 95

z (cid:3) d 50: (4)
0 12

Asgrainsareliftedfromthesurfacebywindsandsaltate(followinga
series of short, ballistic trajectories before impacting the surface
again),asaltationlayerforms,whichreducesthewindspeednearthe
surface, steepening the velocity profile17,18. This feedback between
saltationandthewindprofilepreventsthesaltationlayerfromgrow-
inguncheckedatanexponentialratetoanyheightabovethesurface19.
Inthiscase,z isinfluencedbythethicknessofthesaltationlayer.
0
Underterrestrialconditions,thethicknessofthesaltationlayer
wasshowntorelatetotheso-calledfocalpoint,definedasthevertical
heightabovewhichsaltationdoesnotaffectthewindprofile17.Below
thefocalheight,H,theaverageupwardgrainvelocityisindependent
f
of wind shear velocity, u∗. At the focal point, the wind velocity, U
f
, scaleswiththethresholdshearvelocity,u∗t .Consideringthecontinuity
ofthevelocityprofileatthefocalpoint,theaerodynamicroughness
lengthimpartedbyactivesaltationcanbeexpressedas

z =H exp (cid:4)κ U f : (5)
0 f u(cid:2)

However,thereisnoconsensusonhowparameterssuchasgrainsize
affectH
f
andU fp.Fffiffiffiorexample,itisunclearwhetherH
f
scaleslinearly
withd20,21,with d22,23,ornotatall21.Ifoneofthelattertwomodelsis
correct, then dimensional analysis dictates that another parameter,
likelythekinematicviscosityofair,ν,alsocontrolstheposition(and
possiblythe very existence) of the focal point21–23; Methods). In the
following, we test two different formulations for H21,22, which both
f
account, at least partially, for variations in atmospheric density
throughkinematicviscosity(Methods).

Whereasnoacceptedanalyticalexpressionexiststodateforthe
focal height and velocity, it was shown experimentally that in the
presence of active saltation, the aerodynamic roughness follows an
empiricalrelationshipoftheform

z = Cu2
0 2g (cid:2), (6)

where C is a constant that varies with the type of surface or
environment18,24,25.Inthisstudy,weassumeC=0.0126.

Through saltation, the bed often self-organizes into bedforms,
which in turn affect the flow. The bedforms multiply the
skinfriction from grainroughnessand form dragfromallscalesof
bedformsaffectz .Toestimatez insuchcomplexconditions,ref.2
0 0
developedasemi-analyticalmodel(herereferredtoasJiaetal.,2023;
Methods)formultiscaleroughness,whichincludesskinfrictionand
formdragfromtwoscalesofbedformsthroughloopedcalculations
(Methods).However,thismodeldoesnotcapturetheeffectofactive
saltationoverarippledbed.

OnEarth,windflowsaretypicallyaerodynamicallyrough,andz is
0
controlled by either the surface roughness (below the transp
ort
threshold,u∗t )orthethicknessofthetransportlayer(aboveit)27.In
turn, surface roughnesscompounds both skinfriction (Eq. (4))and
formdrag(2).Whereasmodelsforz arerelativelywellestablishedfor
0
Earth(Eqs.(3)–(6)),severalfactorscomplicatetheapplicationofEarth-
basedmodelstoMars,severelyimpedingpredictivecapabilitiesfora
broadrangeofphenomena,fromdustlifting28–30tosandfluxes31,32and
aeolianerosionrates33–35.

First, as atmospheric density decreases, atmospheric kinematic
viscosity increases, thickening the viscous sublayer. As a result, the
roughness-basedReynoldsnumberdecreases(foragivenroughness
scale and shear velocity; Eq. (2)), increasing the likelihood of aero-
dynamicallysmoothwindevents,andthus,ofz beinginfluencedby
0
thelaminarsublayer(Eq.(3)).However,itisunclearwhetherthiseffect
isannulledbyactivesaltationunderMars-likeconditions(Eqs.(5)–(6)).
Second,underlow-pressureconditions,twotypesofwindblown
ripplesmayemerge—impactripplesanddragripples11,20,36–40.Aeolian
drag ripples are analogous to subaqueous ripples41,42 and aeolian
dunes11,20,38,andresultfromahydrodynamicinstabilitythatonlyarises
under aerodynamically smooth conditions11,20,39,40. On Mars, aeolian
drag ripples are characterized by meter-scale wavelengths and
decimeter-scale heights, possibly enhancing the role of form drag
relativetothecaseofEarth’smuchmoresubduedimpactripples43.
Measurements ofz havebeen performed overcoarseregolith
0
androckysurfacesonMarsbefore44,butneveroveractivesandyrip-
pledbeds,suchthatitremainsunknownwhetherthethickerboundary
layerandmultipleripplescalesimpactz
0
underactivetransportcon-
ditions.Here,wemeasuretheaerodynamicroughnessofrippledsand
beds under varying atmospheric pressures. For the first time, we
characterize the behavior of z in low-pressure wind tunnel experi-
0
mentsinwhichtwoscalesofripples(impactanddragripples)form
andactivesaltationispresent.

Results
Experiments were conducted over beds of loose sand-sized proxy
material (~195μm crushed nutshells) at freestream wind velocities
exceeding the corresponding freestream threshold for the onset of
saltationbyabout 20%.Bedswereallowedtodevelopbedformsand
equilibrate(Figs.1cand2)40beforeverticalwindprofilesweremea-
suredusinga variable-height pitot tube at a frequency of 0.3 Hz
(Fig.1d).Measurementswereperformedat4–5differentheightsabove
thebed,andaveragedover45–60sateachheight40(Methods).Wind
profilesweremeasuredat1020,500,100,and50mbar,andz
0
wa(cid:6)s
derived from those measurements by finding the best fit u(cid:2),z
0
valuesusingthelogarithmiclaw(Eq.(1);Figs.3and4;Methods).These
experiments,whichcapturethecorrectphysicalregimesdespite
higher absolute pressures than on Mars, allow us to extrapolate
observationstoMars-likesurfaceconditions(SupplementaryTextS1
andSupplementaryTableS1).

Decimeter-scaleimpactripplesformedatallpressures45,whereas
larger, drag ripples only formed at pressures less than terrestrial
(Fig.2),aspredictedbydrag-rippletheory11,20,40.Thesizeofdragrip-
plesincreasedwithdecreasingatmosphericpressure,consistentwith
observations on Mars36,38,46 (Fig. 1a). Similarly, the thickness of the
viscous sublayer in the absence of saltation(calculated as11:6ν) is
expectedtoincreasebyaboutoneorderofmagnitudefromamb
ient
terrestrialpressureto50mbar(Fig.2).

Like several of the relevant length scales (Fig. 2), measured z
0
values increase with decreasing atmospheric pressure, from
≈2×10−4m at 1020mbar to over 5×10−4m at 50mbar under our
experimental conditions (Fig. 4a). Similarly, predicted values of z 0
fromviscoussublayerthicknessandsaltationincreasewithdecreasing
pressure (Fig. 4b) due to decreasing atmospheric density and
increasingthresholdofmotion,respectively(SupplementaryFig.S3).

Derived values of z are compared against model predictions
0
(Fig. 4b; Eqs. (3)–(6); and model of ref. 2; Methods). The large dis-
crepancybetweenmeasuredz andthatexpectedfromtheviscous
0
sublayermodelisconsistentwitheitheraerodynamicallyroughcon-
ditions(at1020mbar)ordisruptionoftheviscoussublayerbysalta-
tionatallpressures.At1020mbar,themodelofref.2,whichpredicts
the compounded effect ofskin friction and form drag from impact
ripples,isdominatedbyskinfrictionandunderpredictsthemeasured
z value,confirmingthatsaltation(Eq.(6))isthedominantcontrolon 0
z underEarth-likeconditions.Atallpressures,observedz aremost 0 0
closely matched by the empirical saltation model (Eq. (6)) and the
compound form drag model of ref. 2. However, both models con-
sistentlyunderpredictz ,suggestingthatbothsaltationandformdrag
0
contributetooverallaerodynamicroughness.

Next,weinvestigatetherelativeinfluenceofsaltationandform
dragonz .Toestimatethecontributionofsaltationtoz basedonour
0 0
experimentalmeasurements,weusethemodelofref.2inaninverse
fashion (Methods). Specifically, we adjust the value of an effective
grain size in this model such that, given the observed bedform
dimensionsateachpressure,itproducesthecorrect,observedvalue
of z . Assuming that skin friction is negligible relative to other
0
roughnesscontributorsunderactivesaltation(Fig.4b),theeffective
grainsizeparameter,insteadofgrainsize,representsacharacteristic
lengthscaleassociatedwiththesaltationlayer,fromwhichz
0,saltation
canbecalculated(Fig.5;Methods;2).

The relative influenceof saltation on totalaerodynamic rough-
ness, z /z , varies in a nonlinear fashion with atmospheric
0,saltation 0
pressure(Fig.5a).Specifically,wefindthatz isabout80%ofz
0,saltation 0
at 1020mbar, when only subdued impact ripples are present. As
pressuredecreasesanddragripplesform,thecontributionofsaltation
to z drops to 45% at 500mbar, and increases again progressively
0
under our experimental conditions as pressure decreases, to reach
about ≈90%at50mbar(Fig.5b).

Focalpointatlowpressure

Althoughtheexistenceofafocalpointiswellestablishedunderter-
restrialconditions(e.g.,47–51),howviscositymayinfluenceitsexistence,
and if it exists, its behavior at low atmospheric pressures remain
unknown.Here,wetestitsexistenceandbehaviorby(i)invertingforH
f
andU fromz usingEq.(5)and(ii)comparingH andU values
f 0,saltation f f
withthemodelsofrefs.22,21.

Based on dimensional analysis, theory, and empirical observa-
tions,refs.22,21proposedformulationsforfocalheightandvelocity
that incorporate the influence of atmospheric density and viscosity
(Methods). Each model contains two constant coefficients, α and β
(Methods).Forbothmodels,best-fitvaluesofαandβwereinvertedat
all pressure conditions by minimizing the difference between the
estimated z and those modeled using the formulations of
0,saltation
refs.22,21(Methods).

Usingthemodelofref.22,wefindthat(i)invertedvaluesofαand
βareroughlyconstantacrosstheinvestigatedpressurerange,and(ii)
inverted β values closely match that estimated by ref. 22 at Earth
pressure(SupplementaryFig.S7).Invertedvaluesofαareofthesame
orderofmagnitudeas,butdiffersubtlyfrom,thoseofref.22atEarth
pressure(SupplementaryFig.S7).Thissmalldifferenceisattributedto
thepresenceofimpactripplesintheexperimentsofref.52(andthe
formdragtheyimpartedonwinds),whereasanycontributionsfrom
formdragisremovedfrommeasuredz valueshere(i.e.,αandβare
0
estimatedfromz ).These findingssuggestthatafocal point
0,saltation
doesexistunderallinvestigatedpressures,andthattheformulationof
ref. 22 appropriately describes the dependency of H and U on
f f
atmosphericdensityandviscosity.

Whereassetsofαandβvaluesthatyieldequallygoodfitstothe
datacouldberetrievedfrombothmodels,wefindthatβcannotbe
reasonably assumed to be constant over the range of investigated
pressuresunderthemodelofref.21,andthatβ/ρ(cid:4) 3 1 instead(Sup-
plementaryTextS2).Thus,themodelofref.22appearstocapturethe
dependencyofH onρmoreadequately,andweadoptthatformula-
f
tionforextrapolationstoMarspressure.

Relativeinfluenceofsaltationandformdragonaerodynamic
roughness

Followingthemodelofref.22,H f /ρ(cid:4) 6 5 (Eqs.(8)–(9);Methods).Fur-
thermore, the wavelength of drag ripples is proportional to
ρ(cid:4)2 3 36–38,40–42. Thus, under low atmospheric pressures (such that
Re
r
≲10),h
max
/ρ(cid:4)2 3(foragivenbedformaspectratio).Asaresult,

H f /ρ(cid:4)
6
1 /p(cid:4)
6
1 (7)
h
max

at a constant temperature. This prediction, which relies on β being
independent of atmospheric density, is well matched by the data
(R2=0.98;Fig.5b).

At Earth pressure, drag ripples cannot formand Hf (cid:3)90%. As
pressuredecreases,dragripplesform,protrudinghighe h r m i a n x totheflow
(Hf (cid:3)25%at500mbar;Fig.5b)enhancingthecontributionofform
drag to total aerodynamic roughness (Fig. 5a). As pressure further
decreasedinourexperiments,thesaltationlayerthickenedfasterthan
dragripplesgrew,suchthat h H m f ax increasedwithdecreasingpressure.
WhereasH increaseswithdecreasingpressure,sodoesU,such
f f
that the behavior of z may vary depending on specific
0,saltation
conditions is implicit to Eq. 1. Theoretical53, experimental54, and
7 insitu44evidenceindicatethatthermallyinducedvariationsinatmo-
sphericconditions(e.g.,fromdiurnaltemperatureswings)resultsin
minor deviations in z 0 that are well within the uncertainty of our
measurements(SupplementaryTextS1andSupplementaryTableS1).

Based on our validation and calibration of Eqs. (8)–(9),we can
estimate z on Mars. In parallel, we estimate the combined
0,saltation
contributionsofskinfrictionandformdragfromallbedformscales
(z ) using the Jia et al. (2023) model2 assuming grain and
0,bedforms
bedform sizes as measured at Gale crater (grain size, d=125μm55;
impact-ripplewavelength,λ =8cm;drag-ripplewavelength,λ =2m;
i l
bedform height-to-wavelength ratios of 0.0536,42). Typical values for
Mars were used for all other parameters (e.g., ρ=0.020kg/m3,
ρ =2900kg/m3,g=3.71m/s2).Bothaerodynamiclengthscalesarealso
s
comparedwithz (Eq.(3)).
0,sublayer

Wefindthatz
0,bedforms
≈1cm,whichisconsistently1–2ordersof
magnitudelargerthanz andz acrossarangeofplau-
0,sublayer 0,saltation
siblewindshearvelocities(Fig.6),i.e.,itis1–2ordersofmagnitude
largerthanoveraflatbed.Thus,z isexpectedtobedominatedby
0
formdragoverrippledbedsonMarsregardlessofwhethertransportis
ongoing. This extrapolation implicitlyrelies on the assumption that
fluxsaturationwasreachedwithinourwind-tunnelexperiments.Esti-
matesofthesedimenttransportsaturationlengthunderourexperi-
mentalconditionsarelowerthanthelengthofthewind-tunnel’stest
section (Methods), though the true distance required to reach
saturation from a zero flux can be several times larger than the
saturationlength56.Measurementsofimpact-ripplemigrationspeeds
intheexperiments(40;SupplementaryFig.S8)andourestimatesof
focal-height parameters (Supplementary Fig. S7) compare favorably
with models that were developed to describe fully saturated
conditions22,49,suggestingthatnear-saturationconditionswerelikely
reached. However, these models were themselves calibrated using
empiricalconstantsthatcouldpossiblyobscurethesignatureofnon-
saturatedtransportconditions.Iftransportwassubstantiallyunder-
saturatedinourexperiments,theaboveextrapolationstoMarswould
underpredictz ,renderingthecontributionofsaltationtoz
0,saltation 0
comparabletothatofformdragfrombedform(cid:7)s. (cid:8)

Finally,wenotethatcalculatingrfrommax z ,z 2,
0,sublayer 0,saltation
wefindthatRe <10—evenduringactivetransport—overflatbedson
r
Mars. Specifically, we find that wind shear velocities, u∗>1m/s are
requiredforRe toexceed10.
r
Extrapolatedtotheheightofthewind
sensor onboard NASA’s Curiosity rover (1.5m above ground), such
windshearvelocitiescorrespondtowindspeedsof >22.5m/s(Eq.(1)),
orstrongerthanover99.9%ofwindsmeasuredbyCuriosityatGale
Crater57.Thisresultissignificantbecauseitdisprovesthenotionthat
saltationonMarswouldinhibittheformationofdragripplesbypro-
motingaerodynamicallyroughflat-bedconditions.

Methods
Experimentalconditions
ExperimentswereconductedintheMarsSurfaceWindTunnel(MARS-
WIT)atthePlanetaryAeolianLaboratory,NASAAmesResearchCenter,
California.TheMARSWIToperateswithinapressurechambercapableof
simulatingEarth-to-Marspressureconditions(~1bar–5mbar).This13-m
long,open-circuit,atmosphericboundarylayerwindtunnelcanachieve
maximumwindspeedsof100m/sat5mbarusingairinjectors.LabView
data acquisition software is utilized for operations, measuring, and
providing data on chamber temperature, air density, pressure, free-
stream,andverticaldifferentialpressures,pitottubeverticalposition,
relativehumidity,andcorrespondingwindspeeds.Thepitottubewas
placedatthedownwindendofthetestsection.Thetestsectionwas
~6.5mlongand1.3mwide(Fig.1).

Foreachexperiment,pressure,airdensity,andtemperaturewere
recorded, and the dynamic viscosity of air was assumed to be
1.81×10−5Pas.Crushednutshells(ρ =1300kg/m3)servedassediment
s
with a median particle size (d ) of 195μm. Grain-size distributions
50
were determined using a Retsch Camsizer grain-size analyzer. Nut-
shellswereusednottosimulateMars’lowergravitationalacceleration
(g=3.71m/s2)onsaltationtrajectoriesbuttoreducethetimerequired
togenerate bedforms underour lowestexperimental pressurecon-
ditions(50and100mbar)40.Amanuallysmoothed,flatsedimentbed
wasinitiallypreparedinsidethewindtunnelbeforeeachexperiment,
ensuringuniformsedimentdistributionacrossthetestsection(Sup-
plementaryFig.S2).Thebedhadathicknessof3cmacrossthewind
tunnel,andasedimentbermwasplacedattheupwindendofthebed
toactasacontinuoussedimentsource.

Twoseriesofexperimentswereperformed.Inthefirstseries,we
determined the onset of saltation over flat beds by progressively
increasingthewindspeeduntilthebedbecamefullymobile58.This
setupallowedforthedeterminationofthethresholdfreestream(U∞)
andshear(u∗t )velocitiesoveraflatbedatpressuresof50,100,500,
and1020mbar(SupplementaryFig.S3).Inthesecondseries,thewind
velocitywasset ≈20%abovethethresholdfreestreamvelocity,and
maintainedforseveralminutestoallowthesedimentbedtoevolve
naturally from a flat to a rippled configuration. Once the ripples
reachedequilibrium,windvelocitymeasurementswereperformedat
pressures of 50, 100, 500, and 1020mbar. In the latter series of
experiments,multipleruns(pumpdowns)weresometimesnecessary
atagivenatmosphericpressuretoreplenishthebermandmaintain
depositionalconditionswhilethebedformsreachedequilibrium.For
the 1020mbar and 500mbar experiments, a singlepumpdownsuf-
ficed,whilethe100mbarexperimentsrequiredtwopumpdowns,and
the50mbarexperimentsrequiredthree.Transportsaturationlengths
underourexperimentalconditionswereestimatedtwodifferentways
using the formulations in refs. 20,39, and were found to always be
shortertocomparabletothelengthofthetestsection(~6.5m),even
underourlowestpressurecondition(~5.5–6mat50mbar).

Rippledimensions
At each specific pressure, the evolution of the bedforms was con-
tinuously recorded with high-resolution infrared cameras at 30fps,
whichprovidedtop-down,side,andwindwardviewsofthetestsection
(Fig.1).Thissetup enabled precisemeasurementofthewavelength
andmigrationrate(celerity)ofincipientripplesandtheirfinalstabi-
lizedstates.Eachtestconcludedoncethebedformsceasedgrowing,
indicatingequilibrium(Fig.1c).Attheendofeachexperiment,after
thewindsstopped,thepressurechamberwasresettoambientpres-
sure.Thisallowedforadditionaldocumentationofthefinalbedstate
throughthree-dimensional(3D)scansandhigh-resolutioncolorima-
ging.3DscanswereacquiredusingLiDARsensorsbuiltintoaniPadPro
4th generation59 with Pix4Dcatch software, and the data were pro-
cessed with MeshLab 2023.12 (Supplementary Fig. S4). These scans
allowed us to document the dimensions of equilibrium bedforms
along downwind-oriented topographic profiles, including crest-to-
crestwavelengthandtrough-to-peakheight,underconsistentlighting
conditions. The 3D scans enabled the accurate calculation of the
heightandwavelengthofdrag(large)ripples,aswellasthewavelength
oftheimpact(small)ripples.Theheightofimpactrippleswascalcu-
latedas5%ofmeasuredripplewavelengths60.Calculatedimpactripple
heightsrangefrom~1to3mmatallpressures,ingoodagreementwith
ripple heights as determined from the length of ripple shadows at
50mbar40(SupplementaryFig.S5).Bedformdimensionsarereported
inSupplementaryTableS2foreachpressurecondition.

Measurementsofaerodynamicroughnesslength,z
0
Windspeedmeasurementswereconductedusingapitottubeposi-
tionedatvaryingheightsabovethesedimentbed.Windvelocitydata
werecollectedatfourtofivedifferentverticalpositions—atelevations
of4,33,103,160,and320mmabovetheinitialsurfaceelevation—for
45–60s at each position, with a sampling frequency of 0.3Hz. The
elevations were automatically set using a dedicated routine in Lab-
View, with a precision of ±0.05mm (Supplementary Fig. S1). The
controlsystemcanmaintainaconstantwindspeedwithvariationsof
lessthan1%ofthesetvalue.Inthesamewindtunnelfacility,ref.58
performedwindmeasurementsatnearlythesameelevationsabove
thebedtodeterminethethresholdshearvelocityofgrainssimilarto
those in this study. Changes in bed elevation were continuously
monitored using a high-resolution infrared camera positioned for a
side-viewperspective.Theinitialheightofthebedwascheckedrela-
tive to the position of the pitot tube and confirmed using a digital
caliper.Forexperimentsthatrequiredmorethanonepumpdown,i.e.,
at100and50mbar,theheightofthebedwasalsomonitoredwitha
digitalcaliperbetweenpumpdownsastheripplesstartedtoform,and
anewreferencelevelwasrecorded.

The wind speed measurements were used to calculate the
threshold shear velocity u∗t (flat-bed series) or shear velocity u∗
(equilibrium-rippledbed)usingthelawofthewall(Eq.(1)).Tothat
end,weusedMATLAB’sbuilt-inNonlinearLeastSquaresfunction.The
method worksby finding theparametersofanonlinear modelthat
minimizethesumofthesquareddifferences(residuals)betweenthe
observed data and the model predictions (Eq. (1)). Instantaneous
measurementsprovidedsetsof135–180datapointsforeachelevation.
The time between measurements at each elevation was 45–60s,
allowingtoaveragewindmeasurementsoverturbulentfluctuations3.
Only fits with R2 values larger than 0.98 were considered, which
resultedintheexclusionof8–13%ofthedataset.Remainingdatawere
averagedtodetermineu∗andz
0
ateachspecificpressure(Fig.3).As
measurements for each elevation were repeated 2 or 3 times, an
additionalaveragingprocesswasperformedtoobtainthefinalvalues
ofu∗andz
0
.Uncertaintyinu∗,andu∗t wascalculatedas±onestandard
deviation,andinz
0
as ± d/2.Valuesanduncertaintiesofu∗t ,u∗,andz
0
foreachpressureconditionarereportedinSupplementaryTableS2.

Scalingrelationshipforthefocalpoint
Ref. 22, using experimental surface roughness data from ref. 52,
showedthatunderterrestrialconditionsthefocalvelocityandfocal
height canbereasonablywellpredictedby

U (cid:3)α rffiffiffiffiffiffiffiffiffiffiffiffi
ρ
ρ
sgd, (8)
f

and

H f (cid:3)β A U f g2 (cid:1) (cid:3)
ν 1=3
, (9)

whereαandβ areconstants,ρ andρarethesedimentandatmo-
A s
sphericdensities,respectively,gistheaccelerationofgravity,anddis
graindiameter.

In turn, ref. 21 proposed a different formulation for the focal
height,

H f (cid:3)β P+T g (cid:1) (cid:3)
ν2 1=3
, (10)

whereβ isaconstant.
P+T

Usinganoptimizationsubroutine,weminimizedthedifference
betweeneachofthetwomodelsandz .Thisapproachallowed
0,saltation
ustoiterativelysolveforsetsofαandβparametersacrossallpressure
conditions.

Asreportedinthemaintext,bothmodelsyieldsatisfyingfitsto
the data, but β is not well approximated by a constant over the
P+T
rangeofinvestigatedpressures.Eqs.(8)and(9)werethusadopted,
andtheaverageofinvertedαandβ valueswereusedinouranalysis
A
(1.707and0.163,respectively;Fig.2).Uncertaintyinαandβwascal-
culatedas ±onestandarddeviation.

Modelforaerodynamicroughnessinducedbymultiscale
topography
Experimentally derived z values are compared to the theoretical
0
modelofref.2,whichpredictstheinfluenceofmultiscaletopography
(grainsofsized,andsmallandlargeripplescharacterizedbywave-
lengths,λ,andamplitudes,ζ).Inthismodel,z iscalculatedforthree
0
scalesbyconsideringtheroughnessinducedbygrainsonsmallrip-
ples,theroughnessinducedbysmallripplesonlargeripples,andthe
roughnessinducedbylargeripplesthemselves.Acompletedescrip-
tionofthemodelcanbefoundinref.2.

Ourcalculationsofu∗,theheightandwavelengthofbothsmall
and large ripples (h and λ ), as well as the experimental data on
i,l i,l
kinematicviscosityofair,ν,andthemediangrainsize(d=195μm),
wereusedasinputtothemodel.Theeffectiveroughnessiscalculated
foraspecificbedformaspectratio,

kζ= 2π h
λ i,l, (11)
i,l 2

wherekisthebedform’swavenumber.Compoundroughnessvalues
fromskinfrictionandallbedformscalesarereportedforeachpres-
sureconditioninSupplementaryTableS2.

Themodelofref.2underestimatesmeasuredz values(Fig.4)
0
because,whileitaccountsforformdragfromtwoscalesofbedforms,
it does not incorporate the influence of saltation. Thus, comparing
measured and modeled values of z allows to quantify the relative
0
influenceofsaltation(z ).Themodelofref.2wasusedtothat
0,saltation
end as described in the Results and discussion section. To further
validate this approach,the inverted value ofz
0,saltation
at 1020mbar
wascomparedtopredictionsfromnumericalsimulations49(Supple-
mentaryFig.S6).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study investigates aeolian sand transport (windblown sand) under Earth’s atmospheric surface pressure (around 1000 mbar) and lower-pressure conditions (down to 50 mbar) in a pressure-controllable wind tunnel. The purpose is to come somewhat close to atmospheric-pressure conditions on the surface of Mars (typically 6-7 mbar), where aeolian sand transport is known to be ubiquitous. Unlike for high-pressure conditions, for lower-pressure conditions, another kind of bedform emerges (drag ripples). The authors are particularly interested in the aerodynamic roughness z0, a parameter that plays a crucial role in many aeolian transport and landscape evolution models. They aim to better understand the relative roles of different processes on the values of z0 (bedforms, sand transport, viscous-sublayer thickness, grain size). Based on their measurements, interpreted via models from the literature, they conclude that the effects of sand transport dominate in high-pressure conditions (Earth), whereas both sand transport and bedforms are important for lower pressures.\n\nThe novelty of this work lies in the report of measurements of z0 with systematically varied atmospheric conditions in a single experimental setup. Though they may be other measurements of z0 for low-pressure conditions from different studies, they are difficult to interpret if not carried out in the same experimental facility and protocol. This could turn out very helpful for a large range of future studies related to planetary geomorphology. Another novelty lies in their conclusion, which if true, furthers our physical understanding of aeolian sand transport.\n\nI am, in principle, sympathetic to this study, though I have a potentially serious concern, which I would like the authors to address. I am not convinced that the authors are able to establish saturated aeolian sand transport in their wind tunnel for the lower-pressure conditions. The wind tunnel is 13 m long (they do not report the length of the actual test section). Assuming the test section is the full 13 m, this is just approximately twice the fetch length needed for establishing saturated sand transport for Earth pressure conditions. We have no good understanding of how much fetch one would need in lower-pressure atmospheric conditions, we only know it would be longer than on Earth, but by how much, we do not know. It is my personal opinion (I do not have convincing proof for that, since there is no good data) that the fetch needed to establish saturated conditions may be vastly longer than on Earth. If that was true, the effect of sand transport on z0 could be grossly underestimated in the present experiments (when compared with conditions on low-pressure planetary surfaces), thus challenging the authors’ conclusions. To be fair, similar concerns apply to literally all studies on aeolian sand transport that have ever been done using low-pressure wind tunnels, which is why I have strong doubts regarding all results that have ever been reported on the basis of low-pressure wind tunnels. I would like the authors to either present a clear refutation of my concern or PROMINENTLY highlight it as a major potential caveat of their results in their text.\n\nIn addition, I am curious if the authors could test the model by Pähtz & Tholen (Aeolian Research, 2021) and its implications on their results as an alternative to Eq. (9). This study found that many aeolian transport conditions may be dominated by the buffer layer between the viscous sublayer and the log-layer, leading to the prediction H_f \\approx 30 (nu*g)^(2/3)/g (the authors may also vary the prefactor 30). Unlike the two equations discussed in the present study, this expression exhibits no grain size dependence whatsoever and a stronger dependence on the atmospheric pressure (via the kinematic viscosity), which could potentially alter the conclusions.", "reviewer_2": "The manuscript presents interesting results for aeolian predictions based on wind tunnel estimations of aerodynamic roughness length at lower pressures than on Earth, and intended to be applied to Mars conditions.\n\nAlthough the results are promising, their application to Mars conditions is questionable given the significant difference between the experimental setup performed in the study and the Mars atmosphere. Therefore, I suggest that this paper would deserve publication, but in a journal other than Nat. Communications. Some comments are detailed below that hopefully will be useful to the authors:\n\n1) Lines 54 – 102, including equations 1-6 -> this should be included in the methods section and/or in the supplementary information, more than in the introduction.\n\n2) Lines 70 – 71 -> please add references\n\n3) Lines 93-97 -> these assumptions are questionable as they are presented.\n\n4) Lines 131 – 136 -> this is not correct. The direct measurement of near-surface wind profiles on Mars, including determination of aerodynamic roughness length and wind friction speeds, was published in Sullivan et al. (2000)\nSullivan, R., R. Greeley, M. Kraft, G. Wilson, M. Golombek, K. Herkenhoff, J. Murphy, and P. Smith (2000), Results of the Imager for Mars Pathfinder windsock experiment, J. Geophys. Res., 105(E10), 24547–24562, doi:10.1029/1999JE001234.\n\n5) Fig. 3 -> the x-axis should be “wind velocity, u (m/s)” instead of “vertical wind velocity, u (m/s)”\n\n6) Line 250: this is assuming a neutral wind profile. However, the Martian atmosphere is almost never statically neutral, as assumed by Eq. 1. The authors should discuss how unstable conditions, typically present during the Martian daytime, or stable conditions during the night, influence the results presented in this paper.\n\n7) Line 280 -> the experimental setup considers a minimum pressure of 50 mbar, which is several times greater than the atmospheric pressure on the Martian surface (~6 mbar), hence is questionable that the results presented in this study could be applicable to the Mars atmosphere.\n\n8) Line 330: The nonlinear routine employed to fit the data to Eq. 1 should be described, including figures/tables showing the resulting fits, particularly if some of them (with low R^2) are omitted, as is stated in lines 333-334. Perhaps, the criteria should be better described.\n\n9) Line 337: It is unclear if the uncertainty is calculated using the 2-3 groups of measurements as stated in line 335. Also, how much is the uncertainty of the parameters related to the nonlinear model?"}, "author_response": "Response to Reviewers for\n“Aerodynamic Roughness of Rippled Beds Under Active Saltation\nat Earth-to-Mars Atmospheric Pressures”\nby Alvarez et al.\nUnless otherwise noted, all cited line numbers refer to the revised manuscript (without changes\ntracked). All reviewer comments were addressed point by point and in full, as detailed in our\nresponses below.\n---------------------------------------------------------------------------------------------------------------------\nReviewer #1: Anonymous\n---------------------------------------------------------------------------------------------------------------------\nThis study investigates aeolian sand transport (windblown sand) under Earth’s atmospheric surface\npressure (around 1000 mbar) and lower-pressure conditions (down to 50 mbar) in a pressure-\ncontrollable wind tunnel. The purpose is to come somewhat close to atmospheric-pressure\nconditions on the surface of Mars (typically 6-7 mbar), where aeolian sand transport is known to\nbe ubiquitous. Unlike for high-pressure conditions, for lower-pressure conditions, another kind of\nbedform emerges (drag ripples). The authors are particularly interested in the aerodynamic\nroughness z0, a parameter that plays a crucial role in many aeolian transport and landscape\nevolution models. They aim to better understand the relative roles of different processes on the\nvalues of z0 (bedforms, sand transport, viscous-sublayer thickness, grain size). Based on their\nmeasurements, interpreted via models from the literature, they conclude that the effects of sand\ntransport dominate in high-pressure conditions (Earth), whereas both sand transport and bedforms\nare important for lower pressures.\nThe novelty of this work lies in the report of measurements of z0 with systematically varied\natmospheric conditions in a single experimental setup. Though they may be other measurements\nof z0 for low-pressure conditions from different studies, they are difficult to interpret if not carried\nout in the same experimental facility and protocol. This could turn out very helpful for a large\nrange of future studies related to planetary geomorphology. Another novelty lies in their\nconclusion, which if true, furthers our physical understanding of aeolian sand transport.\n>> We thank the reviewer for recognizing the novelty and importance of our work, as well as for\ntheir detailed review of our manuscript. The reviewer's comments helped us to clarify important\npoints and enhance the impact of our experimental results. Our responses to each comment and\nsuggestion are detailed below.\nI am, in principle, sympathetic to this study, though I have a potentially serious concern, which I\nwould like the authors to address. I am not convinced that the authors are able to establish saturated\naeolian sand transport in their wind tunnel for the lower-pressure conditions. The wind tunnel is\n13 m long (they do not report the length of the actual test section). Assuming the test section is the\nfull 13 m, this is just approximately twice the fetch length needed for establishing saturated sand\ntransport for Earth pressure conditions. We have no good understanding of how much fetch one\nwould need in lower-pressure atmospheric conditions, we only know it would be longer than on\nEarth, but by how much, we do not know. It is my personal opinion (I do not have convincing\n1\nproof for that, since there is no good data) that the fetch needed to establish saturated conditions\nmay be vastly longer than on Earth. If that was true, the effect of sand transport on z0 could be\ngrossly underestimated in the present experiments (when compared with conditions on low-\npressure planetary surfaces), thus challenging the authors’ conclusions. To be fair, similar concerns\napply to literally all studies on aeolian sand transport that have ever been done using low-pressure\nwind tunnels, which is why I have strong doubts regarding all results that have ever been reported\non the basis of low-pressure wind tunnels. I would like the authors to either present a clear\nrefutation of my concern or PROMINENTLY highlight it as a major potential caveat of their\nresults in their text.\n>> We thank the reviewer for raising this important point, which future readers may also find to\nbe of possible concern. In addition to now reporting the dimensions of the test section (~6.5 m x\n1.3 m, with wind measurements conducted at the downwind end (lines 298–299). We address this\ncomment in two independent and complementary ways.\nFirst, we calculated and report the predicted sediment saturation length, 𝑙 , using the\nformulations of Durán et al. (2019) and Yizhaq et al. (2024) for transport in eolian saltation. For\nDurán et al. (2019), the saturation length is defined as\n𝑙 = 𝑎\nwhere 𝑎 is a constant, 𝜌 is sediment density, 𝑢 is the threshold shear velocity, and 𝑔 is the\ngravitational acceleration. The saturation length is the fetch required for flux to saturate; thus,\nsediment flux in our experiments can be expected to be at capacity as long as 𝑙 is less than the\nlength of the test section. Duran et al. (2019) estimated 𝑎 to be ~100. Table 1 below summarizes\nestimated values of 𝑙 under our experimental conditions. We find that 𝑙 increases with\ndecreasing pressure, but does not exceed the length of our test section even at 50 mbar.\npressure 𝑙 (m)\n(mbar)\n1020 0.8\n500 1.2\n100 4.5\n50 6.0\nTable 1. Estimated saturation length, 𝑙 , under our experimental conditions, using the\nformulation of Durán et al. (2019).\nAs an additional verification, we calculated 𝑙 as 50 times the subscale saturation length of\nYizhaq et al. (2024), i.e.,\n𝑙 ≈ 50\nwhere the subscale saturation length is calculated from the initial wavelength of drag ripples, 𝜆, as\nwell as 𝑢 and 𝜈, the wind shear velocity and kinematic viscosity, respectively. The factor of 50 is\nproposed by Yizhaq et al. (2024) based on the relative scaling of the two saturation lengths with\n2\nthe characteristic hop length. For our lowest pressure –and thus the largest possible value of 𝑙 –\nwe get 𝑙 = 5.5 m. This length is similar to that calculated using the formulation of Durán et al.\n(2019), and importantly, it is smaller than the text section. Thus, the wind tunnel is long enough to\nreach saturated sand flux conditions.\nSecond, we calculate the predicted migration speed of impact ripples using a mechanistic model\nthat assumes transport capacity, and compare these estimates with in-situ measurements during\nour experiments. These measurements are reported in Alvarez et al. (accepted), Nature\nCommunications. Andreotti et al. (2021) proposed that the celerity of impact ripples can be\ncalculated as\n𝑐 = 𝑎 𝑢\nwhere 𝑎 is a constant, 𝜌 is the fluid density, and 𝑢 and 𝑢 are the shear and threshold shear\nvelocities. Figure 1 below (now also included as Supplementary Figure S8) shows that the\nmeasured impact ripple speeds are within < 20% of those predicted by Eq. (3), further supporting\nthat flux saturation was achieved within the test section. (We note that the quality of our IR\nrecording of the experiment did not permit tracking of impact ripple migration at 500 mbar.)\nTogether, these two tests confirm that sediment flux reached saturation within the wind tunnel and\nthat measurements were performed under saturated conditions. This is now discussed at l. 300-\n305.\nFigure 1. Predicted vs. measured migration rates, 𝑐 of small, impact ripples. Measured values were\n6\nderived from postprocessing of top-down movies recorded during experiments. Shaded area\n5\nindicates an error of ±17%. Predicted values were calculated as 𝑐 = 0.1\nImpact ripples forming at 500 mbar were not clearly visible in the IR footage, such that their\nmigration rate could not be measured.\n2021) and its implications on their results as an alternative to Eq. (9). This study found that many\naeolian transport conditions may be dominated by the buffer layer between the viscous sublayer\nand the log-layer, leading to the prediction H_f \\approx 30 (nu*g)^(2/3)/g (the authors may also\nvary the prefactor 30). Unlike the two equations discussed in the present study, this expression\nexhibits no grain size dependence whatsoever and a stronger dependence on the atmospheric\npressure (via the kinematic viscosity), which could potentially alter the conclusions.\n>> We are grateful for this great suggestion. Following the reviewer’s suggestion, we calculated\nthe focal height, using the formulation of Pähtz and Tholen (2021), as\n𝐻 ≈ 𝑏\nand assumed that, as per Andreotti’s model,\n𝑈 = 𝑎\nwhere 𝑎 and b are constants (with a ≈ 𝛼 from the Andreotti model). The values of 𝑎 and b were\ntuned to maximize the goodness of fit between Eqs. 4-5 and our experimental data following the\nsame approach as for the constants in Andreotti’s formulation (𝛼 and 𝛽).\nBoth the Andreotti (2004) and Pähtz and Tholen (2021) models could be fitted equally well to the\ndata. Using average values of a and b (Pähtz and Tholen), and 𝛼 and 𝛽 (Andreotti) over the four\npressure conditions, we calculated 𝐻/ℎ (with ℎ the height of the largest ripples present at\na given pressure) for both models.\nUsing the Andreotti (2004) model, scaling relationships predict that , for p < 1 bar should be\nproportional to 𝜌 as long as 𝛽 is constant – a trend that is indeed well reflected in calculated\n𝐻/ℎ using the Andreotti model. Thus, the assumption of a constant 𝛽 over the range of\ninvestigated pressures is deemed reasonable (R2 = 0.98). In contrast, using the model of Pähtz and\nTholen (2021), scaling relationships predict that , should not vary with 𝜌 if b is constant (as\nboth 𝐻 and ℎ vary as 𝜌). Yet, the fit to a constant is poor (R2 = 0.82), and we find that\n, ∝ 𝜌 (R2 = 0.99), suggesting that b cannot be approximated as a constant within the\nconsidered pressure range under the Pähtz and Tholen model and that 𝑏 ∝ 𝜌 instead. Thus, it\nappears that the model of Andreotti (2004) does a better job at capturing the dependency of H on\nf\n𝜌 over the full range of investigated pressures.\nWhereas neither model may capture all aspects of the underlying physics—and some residual\ndependence on 𝜌 might persist even in the Andreotti (2004) model—the latter shows no significant\ndiscrepancies between predictions and observations over a pressure range from 1 bar to 50 mbar.\nWe thus feel more confident extrapolating H down to 5 mbar (Mars pressure) using the Andreotti\nf\n(2004) model.\nTholen (2021) is now discussed at l. 92-93, 96-97, 197-203, 215-220, 227-228, and 380-389.\n5\n---------------------------------------------------------------------------------------------------------------------\nReviewer #2: Anonymous\n---------------------------------------------------------------------------------------------------------------------\nThe manuscript presents interesting results for aeolian predictions based on wind tunnel\nestimations of aerodynamic roughness length at lower pressures than on Earth, and intended to\nbe applied to Mars conditions.\nAlthough the results are promising, their application to Mars conditions is questionable given\nthe significant difference between the experimental setup performed in the study and the Mars\natmosphere. Therefore, I suggest that this paper would deserve publication, but in a journal\nother than Nat. Communications. Some comments are detailed below that hopefully will be\nuseful to the authors:\n>> We appreciate the reviewer’s recognition of the value and potential of our results and are\nthankful for their insightful comments. We responded to all comments below, and detailed why\nour experimental conditions, though they differ from those on Mars, allow us to make predictions\nfor Mars-like conditions.\n1. Lines 54 – 102, including equations 1-6 -> this should be included in the methods section\nand/or in the supplementary information, more than in the introduction.\n>> While we agree that an expert reader might not need this refresher, we do not expect the broad\nreadership of the journal to be already familiar with technicalities of bed roughness and when each\nmodel is applicable. This background is necessary to understand the analysis and appreciate the\nimportance of our results. We thus respectfully decline the suggestion and kept this description in\nthe Introduction section.\n2. Lines 70 – 71 -> please add references\n>> Done.\n3. Lines 93-97 -> these assumptions are questionable as they are presented.\n>> We recognize that the original wording might have been confusing. No assumptions were made\nhere - the sentence was clarified (l. 93 and 96-97).\n4. Lines 131 – 136 -> this is not correct. The direct measurement of near-surface wind\nprofiles on Mars, including determination of aerodynamic roughness length and wind\nfriction speeds, was published in Sullivan et al. (2000)\nSullivan, R., R. Greeley, M. Kraft, G. Wilson, M. Golombek, K. Herkenhoff, J. Murphy,\nand P. Smith (2000), Results of the Imager for Mars Pathfinder windsock experiment, J.\nGeophys. Res., 105(E10), 24547–24562, doi:10.1029/1999JE001234.\n>> The original manuscript stated that no such measurements have been performed over active\nsandy rippled beds. Indeed, the in-situ measurements of Sullivan et al. (2000) were conducted at\n6\nthe Pathfinder landing site, which was largely composed of coarse regolith and rocks. We agree\nwith the reviewer, however, that this work should be recognized, and opted to cite it at l. 132–133.\n5. Fig. 3 -> the x-axis should be “wind velocity, u (m/s)” instead of “vertical wind velocity,\nu (m/s)”.\n>> Done.\n6. Line 250: this is assuming a neutral wind profile. However, the Martian atmosphere is\nalmost never statically neutral, as assumed by Eq. 1. The authors should discuss how\nunstable conditions, typically present during the Martian daytime, or stable conditions\nduring the night, influence the results presented in this paper.\n>> We thank the reviewer for raising this important point. In our study, we indeed assume neutral\nconditions when calculating the wind velocity 𝑢(𝑧) using the traditional law of the wall (Eq. 1 in\nthe manuscript). This approach disregards the stability-dependent correction function, 𝜓 (𝑧/𝐿),\nfrom the Monin-Obukhov similarity theory. Under non-neutral conditions, 𝑢(𝑧) can be calculated\nas\n𝑢(𝑧) =\nwhere 𝑧 is the height above the bed and 𝜅 is the von Kármán constant. Our assumption of a neutral\natmosphere is based on several considerations, both practical and theoretical.\nFirst, although Eq. 6 accounts for thermally induced variations in atmospheric conditions—\ncapturing day-to-night temperature changes—the correction provided by 𝜓 (𝑧/𝐿) can be\nreasonably neglected. Using the same wind tunnel as the one used for our experiments, White\n(1991) measured z at 13 mbar with 100‑micron grains, under a temperature gradient produced by\n0\nheating the wind tunnel’s bottom wall (resulting in surface–air temperature differences of\napproximately 125–150 °C). The authors observed an 8.8% decrease in the threshold wind velocity\ncompared to the unheated (neutral) condition, which in turn resulted in an approximately 4%\nreduction in z . This small variation is well within the dispersion of our z measurements at neutral\n0 0\nconditions and a pressure of 50 mbar.\nSecond, despite large near-ground temperature gradients on Mars, applying stability functions to\ncorrect for unstable conditions results in z values that only slightly differ from those calculated\n0\nunder neutral conditions (see Table 5 in Sullivan et al., 2000).\nFinally, we note that, the stability-dependent function 𝜓 (𝑧/𝐿) of Monin & Obukhov (1954) was\ndeveloped for flat terrain at a fixed height under Earth atmospheric pressure. It is not applicable\nover heterogenous terrain (such as martian dune fields due to the development of internal boundary\nlayers; e.g., Figueroa-Espinoza and Salles, 2014) and remains untested at low pressure.\nThis rationale is now briefly discussed at lines 57 and 252–256 as we agree that future readers\nmight have the same concern.\n7\n7. Line 280 -> the experimental setup considers a minimum pressure of 50 mbar, which is\nseveral times greater than the atmospheric pressure on the Martian surface (~6 mbar),\nhence is questionable that the results presented in this study could be applicable to the\nMars atmosphere.\n>> To a first order, z over active rippled beds is determined by n = 6 parameters: grains diameter,\n0\nd (which controls the roughness height, r ~ 2.5d), bedform size, 𝜆, shear velocities, 𝑢 ,\n∗\nkinematic\nviscosity, 𝜈, and sediment and fluid densities, 𝜌 and 𝜌. Together, these 6 parameters encompass\n!\nk = 3 dimensions (mass, length, and time). Thus, according to the Buckingham Pi-theorem, any\nset of n-k = 3 independent dimensionless numbers suffice to describe the physical system. These\ndimensionless numbers can in turn be used to ensure that our experiments are scaled properly so\nas to reproduce comparable conditions to those experienced on Mars. We opt to use a set of two\nReynolds numbers (associated with roughness and ripple length scales) and a Shields number.\nThe roughness-based Reynolds number, 𝑅𝑒 , controls the aerodynamic roughness of the bed, with\n4\na transition from aerodynamically smooth to aerodynamically rough conditions at 𝑅𝑒 ~10.\nThe\n4\nbedform-based Reynolds number, 𝑅𝑒 , arises in drag-ripple theory (Abrams & Hanratty, 1985;\n0\n(𝑅𝑒 > 10G). Finally, the Shields number, Θ, characterizes flow strength relative to sediment-\n0\nstabilizing forces, and dictates the mode of sediment transport. Values of Θ > Θ (threshold) is\n#\nrequired for transport in saltation to occur, whereas values of Θ > ~0.1 (>> Θ ) indicate transport\n#\nin suspension.\nTable 2 below summarizes the values of all three dimensionless quantities under each of our\nexperimental conditions and as estimated on Mars. At 50 mbar, all three dimensionless numbers\nfall within the same regimes as on Mars – aerodynamically smooth beds conducive to drag-ripple\nformation and sand transport in saltation. Therefore, the physics at play on Mars are well captured\nunder our lowest experimental pressure.\nTable 2. Comparison of dimensionless numbers under experimental and Martian conditions.\nPressure 𝑅𝑒 = 𝑟𝑢 /𝜈 𝑅𝑒 = 𝜆𝑢 /𝜈 Θ= 𝑢$/[(𝜌 /𝜌−1)𝑔𝑑]\n! ∗ # ∗ ∗ %\n(mbar)\nthis 1020 13.15 (transitional) 1.40 ×10& 0.081\nstudy 500 9.36 (smooth) 5.50 ×10& 0.079\n100 2.36 (smooth) 1.75 ×10& 0.025\n50 1.64 (smooth) 2.80 ×10& 0.025\nMars 6 0.58 (smooth) 3.70 ×10& 0.015\nValues from our experiments are provided in the manuscript and the Supplemental Information\ndocument. For Mars, typical values were assumed: 𝜌 = 0.02 kg/m3, 𝜇 = 1.08 ×10*1 Pa s, 𝑑 = 125\n𝜇m, 𝑢 = 1 m/s, 𝜌 = 2900 kg/m3, 𝑔 = 3.71 m/s2, and 𝜆 = 2 m. The wavelengths of impact ripples\n∗ !\nand drag ripples were used to calculate 𝑅𝑒 at Earth and low pressures, respectively.\nmanuscript. It is not briefly discussed at l. 148-150 and 245-251, and Table 2 is included as a new\nsupplementary table (Supplementary Information file).\n8\n8. Line 330: The nonlinear routine employed to fit the data to Eq. 1 should be described,\nincluding figures/tables showing the resulting fits, particularly if some of them (with low\nR^2) are omitted, as is stated in lines 333-334. Perhaps, the criteria should be better\ndescribed.\n9. Line 337: It is unclear if the uncertainty is calculated using the 2-3 groups of\nmeasurements as stated in line 335. Also, how much is the uncertainty of the parameters related to\nthe nonlinear model?\n>> We address both comments 8 and 9 together here.\nWe used MATLAB's built-in Nonlinear Least Squares function. The method works by finding the\nparameters of a nonlinear model that minimize the sum of the squared differences (residuals)\nbetween the observed data and the model predictions (Eq. 1). For each single test, a wind velocity\nprofile was generated from measurements taken at four to five different vertical elevations, with\n135 to 180 data points recorded at each position. Next, we selected one data point per vertical\nposition and performed a fit using Eq. 1. This process produced sets of 135 to 180 values for 𝑢\n∗\n(𝑢 for flat-bed conditions), 𝑧 , and R2. We then omitted any sets with R2 < 0.98, which resulted\n∗# 2\nin the exclusion of 8–13% of the sets at each pressure. We did not calculate the uncertainty\nassociated with the chosen fit model.\nThis procedure results in a good fit to our experimental observations, as shown in Fig. 3 of the\nmanuscript. Using the remaining data, we calculated a temporal average to determine the mean\nvalues of 𝑢 (𝑢 for flat-bed conditions) and z . We repeated this process for 2–3 tests and then\n∗ ∗# 0\naveraged the mean values across tests. Finally, we estimated the uncertainty in 𝑢 and 𝑢 as one\n∗ ∗#\nstandard deviation and assigned an uncertainty of ± d/2 for z . Our description of the procedure is\n0\nnow clarified at l. 360-363 and 366-367.\n9"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I reiterate what I already stated in my initial report. This is a nice study that deserves publication in a prominent journal such as Nature Communication. However, I am not satisfied with the authors’ response to my serious concern. The authors responded to my comment on the potentially too short fetch with a small essay on the saturation length and the subscale saturation length. First, let me say that the subscale saturation length is not relevant for my comment, since my concern was about a potential strong underestimation of z0 associated with transport. The largest z0 one expects when transport is fully saturated. So, I will only discuss the authors arguments regarding the “actual” saturation length (see below).\n\n1. I disagree with the notion that, if the test section length exceeds the saturation length, transport can be considered as saturated. The reason is twofold: First, the saturation length refers, roughly speaking, to the length sand transport needs to go back to the saturated state after a small disturbance of the saturated state. The processes governing this response may be substantially different from those that govern the transition from zero towards the saturated state. For example, in my opinion, the main limiting factor when going from zero to saturation in low-pressure conditions is to accelerate grains mobilized by wind or splash towards quasi-steady attractor trajectories. Especially the beginning of this transient process, when grains hops are small, can potentially be very slow. However, the higher a grain hops, the longer will it be exposed to the flow and the more energy it will gain during its hop, creating a positive feedback loop, making the transient process quicker and quicker the higher the grain hops. So, clearly, from this simple picture alone, there is a possibility that the saturation length (grains are already close to the final hop height) is much smaller than the fetch length. Second, even on Earth, where a saturation length of 0.5m-1m is quite well established, it can take up to 6m to reach saturation. This is because the saturation length is just a characteristic length in a differential equation, not the actual length to reach saturation. For example, see Selmani et al. (GRL, 2018, doi: 10.1002/2017GL076937).\n\n2. Using the study by Andreotti et al. (2021), or a scaling reported therein, as a means to support that saturation was reached in the present study is inappropriate. First, Andreotti et al. reported for their 3.25m long test section that saturation was not reached if the surface pressure was below 300 mbar: “Upon decreasing P, this zone extends downwind, and below 300 hPa it encompasses the entire bed.” Second, there are a number of hints suggesting that many of their experiments might have been quite far from being saturated, as described in section 4.1 of Pahtz & Duran (JFM, 2023, doi: 10.1017/jfm.2023.343).\n\nI am not claiming that my perspective on the matter will turn out to be true. I think there is a good chance that the authors’ experiments were indeed saturated. However, I think there is more than sufficient uncertainty in this regard to be cautious. The solution is pretty simple. Just state your interpretations and conclusions more cautiously and prominently acknowledge that your experiments might not have been fully saturated, and that you can therefore not conclusively rule out the possibility that transport-associated roughness might also dominate in low-pressure conditions.", "reviewer_2": "My concerns and comments raised in the previous version have been mostly corrected in the latest version of the manuscript. I would like to thank the authors for their work in correcting the manuscript."}, "author_response": "Second Response to Reviewers for\n“Aerodynamic Roughness of Rippled Beds Under Active Saltation\nat Earth-to-Mars Atmospheric Pressures”\nby Alvarez et al.\nUnless otherwise noted, all cited line numbers refer to the revised manuscript (without changes\ntracked). All reviewer comments were addressed point by point and in full, as detailed in our\nresponses below.\n---------------------------------------------------------------------------------------------------------------------\nReviewer #1: Anonymous\n---------------------------------------------------------------------------------------------------------------------\nI reiterate what I already stated in my initial report. This is a nice study that deserves publication\nin a prominent journal such as Nature Communication.\n>> We are grateful for the reviewer’s support of our manuscript for publication in Nature\nCommunications and for their additional thoughts on the fetch required to reach flux saturation.\nHowever, I am not satisfied with the authors’ response to my serious concern. The authors\nresponded to my comment on the potentially too short fetch with a small essay on the saturation\nlength and the subscale saturation length.\n>> We regret that our previous response did not fully address the reviewer’s initial comment. The\nreviewer’s detailed discussion of why they still believe saturation might not have been fully\nreached makes conceptual sense, and although we still contend that multiple elements of our\nexperiments point toward a near-saturated sand flux (see below), we (1) recognize that our initial\ndiscussion of saturation length fell short of addressing the concern because it inherently only\nprovides a conservative lower bound of the required fetch to reach saturation from zero flux, and\n(2) agree that some uncertainty remains as sand fluxes were not directly measured. We addressed\nthese two points by (1) explicitly discussing the non-trivial relationship between saturation length\nand the distance required to reach saturation from a zero-flux, (2) acknowledging that the\nextrapolation relies on the assumption of saturated transport in our experiments, and (3) toned\ndown conclusions drawn on our extrapolations to Mars to acknowledge remaining uncertainty.\nFirst, let me say that the subscale saturation length is not relevant for my comment, since my\nconcern was about a potential strong underestimation of z0 associated with transport. The largest\nz0 one expects when transport is fully saturated. So, I will only discuss the authors arguments\nregarding the “actual” saturation length (see below).\n>> We would like to emphasize that our goal was to use two independent approaches to estimating\nthe “regular” saturation length (Durán et al., 2019 and Yizhaq et al., 2024), one of which relies on\nthe calculation of the subscale saturation length as an intermediate step (Yizhaq et al., 2024). Both\nformulations for the regular 𝑙 yield similar values. No arguments were made in our response\nbased on the subscale saturation length alone. That said, we agree with the reviewer that these\n1\ncalculations only partially address their question as longer distances may be needed when the flux\nstarts from zero.\n1. I disagree with the notion that, if the test section length exceeds the saturation length, transport\ncan be considered as saturated. The reason is twofold: First, the saturation length refers, roughly\nspeaking, to the length sand transport needs to go back to the saturated state after a small\ndisturbance of the saturated state. The processes governing this response may be substantially\ndifferent from those that govern the transition from zero towards the saturated state. For example,\nin my opinion, the main limiting factor when going from zero to saturation in low-pressure\nconditions is to accelerate grains mobilized by wind or splash towards quasi-steady attractor\ntrajectories. Especially the beginning of this transient process, when grains hops are small, can\npotentially be very slow. However, the higher a grain hops, the longer will it be exposed to the\nflow and the more energy it will gain during its hop, creating a positive feedback loop, making the\ntransient process quicker and quicker the higher the grain hops. So, clearly, from this simple picture\nalone, there is a possibility that the saturation length (grains are already close to the final hop\nheight) is much smaller than the fetch length. Second, even on Earth, where a saturation length of\n0.5m-1m is quite well established, it can take up to 6m to reach saturation. This is because the\nsaturation length is just a characteristic length in a differential equation, not the actual length to\nreach saturation. For example, see Selmani et al. (GRL, 2018, doi: 10.1002/2017GL076937).\n>> We thank the reviewer for this clarification and for pointing us to the work of Selmani et al.,\n2018. We envisioned the length required to reach saturation from a zero flux to scale with the\nsaturation length (and their “scaling factor” to be a function of u /u ). To a first order, this indeed\nappears to be the case in the work of Selmani et al. (2018); however, it is clear that this factor is\ngreater than 1. Furthermore, the work of Selmani et al. (2018) was conducted at Earth pressure,\nsuch that uncertainty remains as to how the relationship between both length scales is affected by\nlower pressure conditions. We now explicitly discuss this point, cite the work of Selmani et al.\n(2018), and acknowledge the uncertainty associated with the assumption that saturated transport\nconditions were reached at l. 269-282.\n2. Using the study by Andreotti et al. (2021), or a scaling reported therein, as a means to support\nthat saturation was reached in the present study is inappropriate. First, Andreotti et al. reported for\ntheir 3.25m long test section that saturation was not reached if the surface pressure was below 300\nmbar: “Upon decreasing P, this zone extends downwind, and below 300 hPa it encompasses the\nentire bed.” Second, there are a number of hints suggesting that many of their experiments might\nhave been quite far from being saturated, as described in section 4.1 of Pahtz & Duran (JFM, 2023,\ndoi: 10.1017/jfm.2023.343).\n>> Our reference to the Andreotti et al. (2021) study was confusing as it is not the source of the\nrelationship used; it was removed to avoid any ambiguity. The expression used by Andreotti et al.\n(2021) to calculate ripple celerity was originally proposed in Durán et al. (2014) based on\nexperimental and field data as well as numerical simulations (the experimental and field data are\nthose of Andreotti et al., 2006 in the Physical Review Letters). The field measurements used to\ncalibrate that relationship were performed under saturated flux conditions (Andreotti et al., 2006).\nThus, the expression we use is not affected by the fact that Andreotti (2021)’s wind-tunnel\nexperiments may not have reached saturated flux conditions.\ndistinct instabilities and that the observed celerity of impact ripples aligns with those predicted\nunder transport at capacity. However, we recognize that this scaling relationship also involves a\npre-factor that could very well be affected by low-pressure conditions. Therefore, we opted to\nbetter acknowledge that our experiments may not have reached fully saturated sediment transport\nconditions and toned down our conclusions.\nAnother encouraging observation, which may hint at a near-saturated flux, is the good quantitative\nagreement between our inverted focal-height parameter values (alpha and beta) and those of\nAndreotti et al. (2004), calculated from the experiments of Rasmussen et al. (1996). However\nagain, we acknowledge that truly saturated flux conditions may not have been reached in those\nexperiments.\nOur revised section on the extrapolation to Mars conditions now provides a better account of these\npoints, and explicitly acknowledges assumptions and uncertainties.\nI am not claiming that my perspective on the matter will turn out to be true. I think there is a good\nchance that the authors’ experiments were indeed saturated. However, I think there is more than\nsufficient uncertainty in this regard to be cautious. The solution is pretty simple. Just state your\ninterpretations and conclusions more cautiously and prominently acknowledge that your\nexperiments might not have been fully saturated, and that you can therefore not conclusively rule\nout the possibility that transport-associated roughness might also dominate in low-pressure\nconditions.\n>> We are thankful for the reviewer’s reiteration of this important point. It helped us give a better\naccount of remaining uncertainties and in doing so, strengthen our manuscript.\n---------------------------------------------------------------------------------------------------------------------\nReviewer #2: Anonymous\n---------------------------------------------------------------------------------------------------------------------\nMy concerns and comments raised in the previous version have been mostly corrected in the\nlatest version of the manuscript. I would like to thank the authors for their work in correcting the\nmanuscript.\n>> We are thankful for the reviewer’s initial comments and questions, as these helped enhance\nboth the clarity of impact of our paper.\n3"}]

Decision letter