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Waves erode sea cliffs by various mechanisms, but the influence of wave power on bedrock coastal erosion has not been well quantified, making it difficult to predict how rocky coasts evolve in different environments. Volcanic ocean islands offer a unique opportunity to examine the influence of waves on bedrock coastal erosion because many islands have relatively homogeneous bedrock, well-constrained initial topography, and considerable differences in wave power between shorelines that face different directions and wave regimes. We used lava-flow ages and the morphology of coastal profiles on Maui, Kaho‘olawe, and the Big Island of Hawai‘i (USA) to estimate sea-cliff retreat rates at 11 sites that experience nearly eightfold differences in incident wave power. Using a range of possible sea-level histories that incorporate different trends of subsidence due to volcanic loading, we modeled the evolution of each coastal profile since its formation (12 ka to 1.4 Ma) to find the regionally consistent relative sea-level history and the site-specific sea-cliff retreat rates that best reproduce observed coastal profiles. We found a best-fit relative sea-level history prescribed by an effective elastic lithosphere thickness of 30 km, consistent with estimates from observations of total deflection beneath the Hawaiian Ridge. This suggests that coastal profiles may retain a decipherable record of sea-level change. Comparing the best-fit sea-cliff retreat rates to mean annual wave power at each site, which we calculated from 30 yr hindcast wave data, we found a positive relationship between wave power and sea-cliff erosion, consistent with theoretical predictions and measurements on unlithified coastal bluffs. These comparisons provide field evidence that bedrock coastal erosion scales with wave power, offering a basis for modeling rocky coast evolution in different wave climates.

High-elevation, low-relief surfaces are widespread in many mountain belts. However, the origin of these surfaces has long been debated. In particular, the southeast Tibetan Plateau has extensive low-relief surfaces perched above deep valleys and in the headwaters of three of the world's largest rivers (Salween, Mekong, and Yangtze Rivers). Various geologic data and geodynamic models show that many mountain belts grow first to a certain height and then laterally in an outward propagation sequence. By translating this information into a kinematic propagating uplift function in a landscape evolution model, we propose that the high-elevation, low-relief surfaces in the southeast Tibetan Plateau are simply a consequence of mountain growth and do not require a special process to form. The propagating uplift forms an elongated river network geometry with broad high-elevation, low-relief headwaters and interfluves that persist for tens of millions of years, consistent with the observed geochronology. We suggest that the low-relief interfluves can be long-lived because they lack the drainage networks necessary to keep pace with the rapid incision of the large main-stem rivers. The propagating uplift also produces spatial and temporal exhumation patterns and river profile morphologies that match observations. Our modeling therefore reconciles geomorphic observations with geodynamic models of uplift of the southeast Tibetan Plateau, and it provides a simple mechanism to explain the low-relief surfaces observed in several mountain belts on Earth.

Marine terraces are a cornerstone for the study of paleo sea level and crustal deformation. Commonly, individual erosive marine terraces are attributed to unique sea-level high stands based on the reasoning that marine platforms could only be significantly widened at the beginning of an interglacial. However, this logic implies that wave erosion is insignificant at other times. We postulate that the erosion potential at a given bedrock elevation datum is proportional to the total duration of sea-level occupation at that datum. The total duration of sea-level occupation depends strongly on rock uplift rate. Certain rock uplift rates may promote the generation and preservation of particular terraces while others prevent them. For example, at rock uplift of ~1.2 mm/yr, the Marine Isotope Stage (MIS) 5e (ca. 120 ka) high stand reoccupies the elevation of the MIS 6d–e mid-stand, favoring creation of a wider terrace than at higher or lower rock uplift rates. Thus, misidentification of terraces can occur if each terrace in a sequence is assumed to form uniquely at successive interglacial high stands and to reflect their relative elevations. Developing a graphical proxy for the entire erosion potential of sea-level history allows us to address creation and preservation biases at different rock uplift rates.

Sequences of coral reef terraces result from the interplay between biogenic and clastic sedimentary production, relative sea level (RSL) variations, wave erosion and tectonic forcing. Reefal sequences are gold standard proxies for paleo-sea level and tectonic reconstructions, but their contribution is usually restricted to a bijective approach, correlating the single elevation and age of their inner edge to single sea level stands or coseismic offsets, and reciprocally. The increase of available data, such as coral datings and high resolution topography revealed major deviations from this bijective approach (corals from a single MIS on several terraces, and conversely, or MIS highstands not represented in a sequence).The Cape Laundi sequence, Sumba island, Indonesia, demonstrates such deviations, with outcrops of corals from MIS 5e on as many as three terraces instead of a single terrace as commonly expected. A preliminar numerical model of coral reef terrace profile has been developed, integrating reef growth, wave erosion, RSL variations and tectonic deformation. The interplay between reef growth rate, tectonic displacements and RSL variations provides a plausible explanation for these numerous occurrences. The low growth rate of this reef appears to prevent coral from saturating the accommodation space generated during sea level transgression, leading to the preservation of drowned platforms and reefal construction of similar age during regressions.Preliminary results from numerical modeling reveal complex feedbacks between the processes shaping these morphologies. Tectonic deformation has a major influence on reef development, by favoring reef preservation at high uplift rates and controlling the available accommodation space for reef growth.. By taking into account the numerous feedbacks controlling reef morphology, we can investigate the significance of RSL variations, continuous and punctual rock uplift, biogenic activity, and clastic inputs on coral terrace morphology and chronostratigraphy. Our approach can bring crucial constraints to the rates and frequency of RSL variations. To do so, we further develop our numerical model in order to provide more robust insights on the controls of reefal sequences morphologies.

Marine terraces are a cornerstone for the study of paleo sea level and crustal deformation. Commonly, individual erosive marine terraces are attributed to unique sea level high-stands. This stems from early reasoning that marine platforms could only be significantly widened under moderate rates of sea level rise as at the beginning of an interglacial and preserved onshore by subsequent sea level fall. However, if marine terraces are only created during brief windows at the start of interglacials, this implies that terraces are unchanged over the vast majority of their evolution, despite an often complex submergence history during which waves are constantly acting on the coastline, regardless of the sea level stand. Here, we question the basic assumption that individual marine terraces are uniquely linked to distinct sea level high stands and highlight how a single marine terrace can be created By reoccupation of the same uplifting platform by successive sea level stands. We then identify the biases that such polygenetic terraces can introduce into relative sea level reconstructions and inferences of rock uplift rates from marine terrace chronostratigraphy.Over time, a terrace’s cumulative exposure to wave erosion depends on the local rock uplift rate. Faster rock uplift rates lead to less frequent (fewer reoccupations) or even single episodes of wave erosion of an uplifting terrace and the generation and preservation of numerous terraces. Whereas slower rock uplift rates lead to repeated erosion of a smaller number of polygenetic terraces. The frequency and duration of terrace exposure to wave erosion at sea level depend strongly on rock uplift rate.Certain rock uplift rates may therefore promote the generation and preservation of particular terraces (e.g. those eroded during recent interglacials). For example, under a rock uplift rate of ca. 1.2 mm/yr, Marine Isotope Stage (MIS) 5e (ca. 120 ka) would resubmerge a terrace eroded ca. 50 kyr earlier for tens of kyr during MIS 6d–e stages (ca. 190–170 ka) and expose it to further wave erosion at sea level. This reoccupation could accordingly promote the formation of a particularly wide or well planed terrace associated with MIS 5e with a greater chance of being preserved and identified. This effect is potentially illustrated by a global compilation of rock uplift rates derived from MIS 5e terraces. It shows an unusual abundance of marine terraces documenting uplift rates between 0.8 and 1.2 mm/yr, supporting the hypothesis that these uplift rates promote exposure of the same terrace to wave erosion during multiple sea level stands.Hence, the elevations and widths of terraces eroded during specific sea level stands vary widely from site-to-site and depend on local rock uplift rate. Terraces do not necessarily correspond to an elevation close to that of the latest sea level high-stand but may reflect the elevation of an older, longer-lived, occupation. This leads to potential misidentification of terraces if each terrace in a sequence is assumed to form uniquely at successive interglacial high stands and to reflect their elevations.

Geologic evidence of island uplift and subsidence can provide important observational constraints on the rheology, thermal evolution, and dynamics of the lithosphere and mantle – all of which have implications for understanding Earth’s heat budget, the styles of deformation that develop at plate boundaries, and the surface expression of mantle convection. Hotspot ocean islands, like the Hawaiian Islands, result from mantle plumes, which may originate as deep as the core-mantle boundary. They often host paleoshorelines, which preserve a geologic record of surface deformation, and they can also be situated far from complex plate boundaries that obscure evidence of dynamic topography – long wavelength, low amplitude topography resulting from mantle flow. Ocean islands therefore provide a unique window to deep earth processes operating today and in the geologic past.We examine the relative contribution of lithosphere and mantle processes to surface deflection at ocean hotspots. The seafloor surrounding ocean hotspots is typically 0.5 - 2 km shallower than expected for its age over areas hundreds to >1000 km wide, but the processes generating these bathymetric swells are uncertain. Swells may result from reheating and thinning of the lithosphere and the isostatic effect of replacing colder, denser lithosphere with hotter, less dense upper mantle. Alternately, they may be supported by upward flow of ascending mantle plumes and/or hot, buoyant plume material ponded beneath the lithosphere. Because these two end-member models predict different patterns of seafloor and island subsidence, swell morphology and the geologic record of island drowning may reveal which of these mechanisms dominates the process of swell uplift. We examine swell bathymetry and island drowning at 14 hotspots and find a correspondence between island lifespan and residence time atop swell bathymetry, implying that islands drown as tectonic plate motion transports them past mantle sources of uplift. This correspondence argues strongly for dynamic uplift of the lithosphere at ocean hotspots. Our results also explain global variations in island lifespan on fast- and slow-moving tectonic plates (e.g. drowned islands in the Galápagos 20 Myr old above sea level in the Canary Islands), which strongly influence island topography, biodiversity, and climate.Over shorter timescales, paleoshorelines on hotspot ocean islands may constrain transient changes in local swell morphology. Accounting for flexural isostatic adjustment of the lithosphere to volcanic loading, we also examine patterns in the residual deflection of paleoshorelines across the Hawaiian Islands that might correspond to non-steady state behavior of the Hawaiian plume. Together, these analyses highlight the unique constraints that island paleoshorelines and topo-bathymetry can place on plume-plate interactions at ocean hotspots.

The SE Tibetan Plateau has extensive broad, low-relief, high-elevation surfaces perched above deep valleys, as well as in the headwaters of the three rivers (the Salween, the Mekong, and the Yangtze). However, understanding the presence of these low-relief surfaces is a long-standing challenge because their formation process remains highly debated. While alternate mechanisms have been proposed to explain the low-relief surface formation in this setting (e.g., drainage-area loss mechanism due to horizontal advection; Yang et al., 2015, Nature), a long-standing hypothesis for the formation of low-relief surfaces is by a step change in uplift and incision into a pre-existing, low-relief surface (Clark et al., 2006, JGR; Whipple et al., 2017, Geology).The morphology of low-relief surfaces in the SE Tibetan Plateau is largely consistent with formation by a step change in uplift, but one problem with this model is that low-relief surfaces formed by a step change in uplift are relatively short-lived, since they are incised and steepened by erosion, which sweeps upstream at the response time of mountain ranges (in the order of several million years). Using a landscape evolution model that combines erosion, sediment transport and deposition processes (Yuan et al., 2019, JGR), we demonstrate that propagating uplift form large parallel rivers, with broad low-relief, high-elevation interfluves that persist for tens to hundreds of million years, consistent with various dated ages. These low-relief surfaces can be long-lived because the drainage areas in these interfluves are insufficient to keep up with rapid incision of the large parallel mainstem rivers. Our simulated features match various observations in the SE Tibetan Plateau: (i) low-relief surfaces are approximately co-planar in headwaters, and decrease in elevation smoothly from northwest to southeast across the plateau margin; (ii) χ-elevation plots of the mainstem rivers are convex; (iii) low-relief surfaces have low erosion rates; and (iv) erosion rates are high in the mainstem rivers at the propagating margin.

Symmetric sand ripples formed by water waves are common features on modern coasts and in sedimentary rocks. The size and spacing of wave ripples generally scale with water depth and wave conditions, and are widely used to reconstruct coastal environments of the geologic past. Interpretations based on average ripple dimensions and assumed constant wave conditions are informative, but many rippled beds contain striking patterns involving defects—deviations from straight, evenly spaced ripple crests—that suggest more dynamic flow regimes. We report a set of laboratory experiments that reveal how these patterns form in rippled beds adjusting to a change in wave conditions. As the ripples in our experiments evolved toward a new spacing, they developed defects that are widely observed in modern environments and in the rock record. The dominant defect type depends on the sign and magnitude of the adjustment in ripple spacing and the number of wave periods since the change in wave conditions. A regime diagram summarizing these associations quantitatively links ripple defects to transient flow conditions. Our experiments reveal the origin of previously unexplained ripple patterns and add a new dimension to paleoenvironmental interpretations.

Wave-generated ripples are macroscopic roughness elements that influence fluid flow and sediment transport. For a major group of ripples (orbital ripples), morphology (height and wavelength) is set by the wave conditions. In natural conditions, where wave forcing is highly variable, ripple morphology is frequently changing. We investigate the rate of morphological change after changes in wave conditions (i.e., wave height and period), using laboratory experiments with a step-change in wave forcing. The adjustment time of ripple morphology to new conditions –– the hysteresis time scale (hereafter referred to simply as hysteresis) –– is proportional to changes in wave orbital diameter, and the coefficient of proportionality differs for decreasing and increasing orbital diameter. When the Shields parameter is lower than a threshold (0.043), there is no change in ripple morphology (or changes are extremely slow). In addition, we find the presence of defects (irregularities from straight parallel crestlines) reduces the hysteresis time scale. The dependence of hysteresis on defect density implies that a larger density of defects results in faster ripple adjustment, confirming previous theoretical and numerical model results.

Rates of island vertical motion above intra-plate hotspots record the processes that arise from interactions between lithospheric plates and mantle plumes. To assess the contribution of mantle and lithospheric processes to surface motion above the Hawaiian hotspot, we compare simple models of lithospheric deformation to vertical motion rates measured from dated paleoshorelines and tide gauge records in the Hawaiian Islands. Our analysis shows that observed uplift and subsidence rates mainly record the flexural response of the lithosphere to volcanic loads. The effective elastic plate thickness that best fits the spatial distribution of subsidence and uplift rates is ∼40 km, consistent with previous estimates based on total vertical deflection. Because volcanic loading dominates the vertical motion signal, Hawaiian Islands appear to follow a predictable trajectory of vertical motion when they reside within one flexural half-wavelength of the active volcanic center. Islands initially subside at rapid and decreasing rates in the first ∼1 Myr following their construction, uplift relatively slowly ∼1–2.5 Myr following their construction, and eventually subside again, but at slow rates, within ∼5 Myr of their construction. This observed pattern of uplift and subsidence is consistent with the pattern of vertical motion predicted to result from volcanic loading at the Hawaiian hotspot. Lithospheric migration over the long-wavelength topographic swell associated with the Hawaiian hotspot has a comparatively minor influence on island uplift and subsidence. Its contribution to island vertical motion is not readily observed in our data, with the possible exception of some uplift observed in the past ∼500 kyr on O‘ahu that might correspond to non-steady state behavior of the Hawaiian plume.

Erosion of volcanic ocean islands creates dramatic landscapes, modulates Earth’s carbon cycle, and delivers sediment to coasts and reefs. Because many volcanic islands have large climate gradients and minimal variations in lithology and tectonic history, they are excellent natural laboratories for studying climatic effects on the evolution of topography. Despite concerns that modern sediment fluxes to island coasts may exceed long-term fluxes, little is known about how erosion rates and processes vary across island interiors, how erosion rates are influenced by the strong climate gradients on many islands, and how modern island erosion rates compare to long-term rates. Here, we present new measurements of erosion rates over 5 yr to 5 m.y. timescales on the Hawaiian island of Kaua‘i, across which mean annual precipitation ranges from 0.5 to 9.5 m/yr. Eroded rock volumes from basins across Kaua‘i indicate that million-year-scale erosion rates are correlated with modern mean annual precipitation and range from 8 to 335 t km[superscript –2] yr[superscript –1]. In Kaua‘i’s Hanalei River basin, [superscript 3]He concentrations in detrital olivines imply millennial-scale erosion rates of >126 to >390 t km[superscript –2] yr[superscript –1] from olivine-bearing hillslopes, while fluvial suspended sediment fluxes measured from 2004 to 2009 plus estimates of chemical and bed-load fluxes imply basin-averaged erosion rates of 545 ± 128 t km[superscript –2] yr[superscript –1]. Mapping of landslide scars in satellite imagery of the Hanalei basin from 2004 and 2010 implies landslide-driven erosion rates of 30–47 t km[superscript –2] yr[superscript –1]. These measurements imply that modern erosion rates in the Hanalei basin are no more than 2.3 ± 0.6 times faster than millennial-scale erosion rates, and, to the extent that modern precipitation patterns resemble long-term patterns, they are consistent with a link between precipitation rates and long-term erosion rates.

Bedrock river incision drives the development of much of Earth's surface topography, and thereby shapes the structure of mountain belts and modulates Earth's habitability through its effects on soil erosion, nutrient fluxes and global climate. Although it has long been expected that river incision rates should depend strongly on precipitation rates, quantifying the effects of precipitation rates on bedrock river incision rates has proved difficult, partly because river incision rates are difficult to measure and partly because non-climatic factors can obscure climatic effects at sites where river incision rates have been measured. Here we present measurements of river incision rates across one of Earth's steepest rainfall gradients, which show that precipitation rates do indeed influence long-term bedrock river incision rates. We apply a widely used empirical law for bedrock river incision to a series of rivers on the Hawaiian island of Kaua'i, where mean annual precipitation ranges from 0.5 metres to 9.5 metres (ref. 12)-over 70 per cent of the global range-and river incision rates averaged over millions of years can be inferred from the depth of river canyons and the age of the volcanic bedrock. Both a time-averaged analysis and numerical modelling of transient river incision reveal that the long-term efficiency of bedrock river incision across Kaua'i is positively correlated with upstream-averaged mean annual precipitation rates. We provide theoretical context for this result by demonstrating that our measurements are consistent with a linear dependence of river incision rates on stream power, the rate of energy expenditure by the flow on the riverbed. These observations provide rare empirical evidence for the long-proposed coupling between climate and river incision, suggesting that previously proposed feedbacks among topography, climate and tectonics may occur.