What sets aeolian dune height?

Aeolian dunes arise wherever loose sand is exposed to sufficiently strong winds, forming at predictable wavelengths and growth rates. As dunes mature and coarsen, their evolution becomes more complex due to nonlinear interactions, sediment supply, wind variability, and geological constraints. A central open question is whether dunes stop growing and, if so, what sets their ultimate size. To address this, the study compiles a global dataset of giant dune topography along with atmospheric forcing and geological constraints, and runs numerical experiments to examine long-term growth trajectories. A previously proposed hypothesis is that dune size is capped by the atmospheric mixed layer height (MLH); this work evaluates that hypothesis and explores alternative controls, including morphology, wind regime directionality, and sand supply.

Prior work proposed that the average depth of the atmospheric boundary (mixed) layer sets a resonance that limits giant dune size, implying dune wavelength scales with MLH. This capping-layer hypothesis assumes a neutrally stratified mixed layer in which interface waves limit dune growth. Other studies have established predictable dune initiation wavelengths and growth behavior, and linked dune morphology (barchanoid/transverse, linear, star) to wind regime directionality and sediment supply. However, the extent to which MLH, wind variability, and sand availability control the maximum size of mature dunes remained unresolved, motivating the present global analysis and modeling.

Global observational analysis and numerical modeling were combined. Observations: Dune geometry was extracted from 2,093 tiles (each 322 km²) of ASTER GDEM v3 topography that overlap mapped dune fields. An autocorrelation-based algorithm identified characteristic planform shapes and yielded short- and long-axis dimensions interpreted as wavelength (x) and width (y); dune height (z) was obtained from local elevation range maps convolved over scales set by x. Automatic measurements were calibrated against manual extractions (n=25) with linear factors x/x_auto/y/y_auto = 1.51 and z/z_auto = 0.85. Sand-flux directionality was computed from ERA5 reanalysis (87,672 hourly 10-m wind records, 2008–2017) by converting winds to sand flux using threshold friction velocity and a standard transport law; directionality is the ratio of resultant flux magnitude to the sum of magnitudes over time. Mixed layer height (H) was derived from CALIPSO V4-20 Level 2 aerosol layer products by identifying the lowest aerosol layer top over regions of interest for each dune field; 34 dune fields were analyzed (coastal fields omitted due to ocean-influenced MLH). Dune-field ages were compiled from the literature (subset of INQUA Dune Atlas), and areas were mapped in Google Earth. Modeling: Six ReSCAL cellular-automaton/lattice-gas experiments simulated dune growth under conserved sand and horizontally periodic boundaries. Two initial sand-bed thicknesses (η=3.5 m and 35 m) represented sediment-starved and saturated conditions. Wind forcing regimes mimicked unidirectional (directionality=1), linear (≈0.5), and star (0) dunes via the number of wind directions (F_N) cycled every 4 months; all runs exceeded 1,600 years (in scaled units) with a fluid box tall enough that domain height did not constrain dunes. Dune morphology at the end of runs verified intended types. Model measurements included dune height time series, wavelength-height scaling, and celerity via cross-correlation. Numerical scaling matched incipient dune wavelength to set grid spacing (l0 ≈ 0.698 m) and used representative sand flux to estimate timestep (≈14.2 h). The model omits secondary topography-induced flows; scaling uncertainties are acknowledged.

• No empirical support for an MLH-imposed size limit: averaged midday MLH varies little across dune fields (≈1–2 km), dune wavelength often exceeds MLH, and there is no correlation between MLH (H) and dune wavelength (x) across 34 dune fields.
• Dune height correlates inversely with flux directionality: dunes in low-directionality (highly variable) wind regimes are relatively taller; star dunes occur only at low directionality.
• Numerical experiments reproduce observed geometric/morphological trends: dune height grows approximately logarithmically with time (z ~ log t); unidirectional dunes show sub-linear z–x scaling (decreasing aspect with size), whereas linear and star dunes exhibit super-linear scaling and are taller for a given wavelength.
• Dune migration slows as dunes grow; star dunes become essentially stationary beyond z ≈ 10 m due to net-zero flux.
• In the absence of MLH control, dunes coarsen indefinitely under constant forcing, but growth rate diminishes with size.
• Dune-field age versus area shows a positive trend consistent with first-order advective growth scaling √A = C_rep T, with a representative celerity C_rep = 0.48 m/yr; many fields exceed this line, implying additional controls such as sand supply on field size.

Findings indicate that Earth’s giant dunes are not generically limited by mixed layer height; instead, they grow ever more slowly with size, with morphology and wind regime directionality exerting strong control on height and aspect. Low-directionality (reversing) winds promote vertical sand stacking, producing taller linear and star dunes that grow faster than unidirectional types. The lack of H–x correlation challenges planetary applications that infer boundary layer height from dune spacing. Nevertheless, the presence of active dune fields constrains atmospheric dynamics: winds must regularly exceed (but not greatly exceed) the threshold for saltation to sustain growth. The apparent upper bound near x ≳ 2 km likely reflects extremely slow coarsening coupled with long-term climatic and geological limitations—particularly the persistence of aridity/windiness and finite sand supply as dunes pile up and scour interdunes. Observed superimposed dunes and variance in recent directionality relative to dune form suggest sluggish responses to changing winds, motivating rate-and-state style frameworks where dune form tracks adjustment history.

A global synthesis and targeted numerical experiments show that aeolian dunes are not capped by atmospheric mixed layer height. Under steady forcing, dunes can in principle grow indefinitely, albeit ever more slowly; ultimate sizes in nature are shaped by wind regime directionality, morphology, and especially sand supply and long-term climatic stability. New empirical relations between dune geometry and morphology provide a means to place dunes within growth trajectories and to interpret dune-field expansion. Future work should quantify sand supply limits, incorporate secondary wind flows and heterogeneous boundary conditions in models, and develop rate-and-state approaches to predict how dunes with different maturities respond to transient climate and wind changes.

• Observations represent a temporal snapshot of dunes; millennial-scale controls (sand supply histories, past wind climates) are unconstrained.
• Flux directionality is derived from a decade of winds, which may not reflect formative conditions for large dunes.
• Sand supply, a key control, is not directly measured and likely varies across fields.
• Numerical model-to-nature scaling carries uncertainty; model omits secondary topography-induced flows that may affect linear and star dunes.
• Given unknown histories and boundary conditions, no quantitative model–data fit was attempted; coastal dune fields were excluded from MLH analysis due to ocean influence.