## Introduction

Climate change is likely to cause a global sea-level rise (SLR) by 2100 of 0.63–1.01 m based on a high-end greenhouse gas emissions scenario (SSP5-8.5)1. Combined with ambient trends in shoreline dynamics, SLR under this scenario has been projected (using an approach known as the Bruun rule2) to result in a large retreat or loss of almost half of the world’s sandy beaches by the end of this century3. Climate change has also been predicted to drive increases in extreme wave heights along almost three-fifths of the world’s coastline by the end of the century4, but the long-term (>50 years) impact of extreme storms on coastal recession—and its coupling with SLR—is ambiguous. Increased storminess is generally assumed to exacerbate coastal erosion due to SLR; however, short-to-medium term (years–decades) shoreline variability caused by storms is generally considered noise over long time scales when shoreline change is mainly driven by SLR5,6. On the other hand, extreme storms can transport sediment into the nearshore zone from elsewhere, for example from the lower shoreface7, potentially tempering long-term erosion by SLR8,9.

Despite its many assumptions and shortcomings10,11, the Bruun rule has emerged as the most widely used method for predicting shoreline change due to SLR6, for localized coastal hazard assessments12 as well as in global studies3,13. In its most simple and original form, the Bruun rule reduces to R = S/tanβ, where R is shoreline retreat, S is the sea-level rise and tanβ is the upper-shoreface gradient. Application of the Bruun rule involves a simple upward and backward translation of the shoreface profile to a location where the volumetric losses from the upper part of the profile are matched by the gains across the lower part. Sediment gains and losses can be included in the Bruun rule14,15, but their inclusion requires a rigorous insight into the nearshore sediment budget16 as the cross-shore and longshore sediment fluxes, sediment production, and anthropogenic contribution all play a key role in the coastal response. Of particular relevance in this context is the impact of extreme storm activity on the sediment budget, as it is under these forcing conditions that sediment fluxes are maximized and the impact of the sediment budget on long-term shoreline change is potentially greatest.

Coastal erosion and shoreline retreat as a result of extreme storm activity is particularly apparent on the upper beach as storm waves leave beaches depleted and coastal dunes scarped, with typical beach-dune sediment losses of 50–150 m3 per unit meter beach width17,18,19. A suite of cross-shore and longshore sediment transport pathways are responsible for these morphological changes, summarized in Fig. 1. The vast majority of sediment transport pathways during both extreme and non-energetic (i.e., modal) wave conditions merely redistribute sediment across the upper shoreface, i.e., landward of the depth of closure (DoC), defined as the depth beyond which no detectable morphological change occurs over a given timeframe20,21,22. Sediment exchange between the lower and upper shoreface across the DoC can, however, play an important role in long-term shoreline change, and of particular interest here is the wave-driven onshore sediment transport driven by disequilibrium shoreface morphology7,9.

Geological evidence from Australia strongly suggests that low-magnitude onshore sediment transport O (1 m3/m/yr) from the lower shoreface to the beach has been responsible for extensive coastal progradation when sea level was relatively stable throughout the mid to late Holocene23,24,25 (see also examples from Brazil26 and The Netherlands27). Under the influence of rising sea level, this component, which results in a lowering of the lower shoreface as sediment is transported onshore28, has the potential to offset, or even overturn, the impact of sea-level rise14. As the source of this sediment is beyond the DoC, it is highly likely that energetic wave conditions are implicated in this transport, as modal waves are not expected to be able to move sediments at such depths. Onshore-skewed oscillatory motions on the seabed caused by wave nonlinearity are able to act at much greater depths during energetic conditions, providing a mechanism for suspended and bedload sediment transport from the lower to upper shoreface29. Net shoreface sand supply to beaches may be a widespread and common, but little appreciated factor in coastal stability30,31. Likewise, sediment from adjacent beaches and mobilized during extreme storms (e.g., headland sand bypassing) may provide an additional source of sediment to the nearshore region32,33,34.

This paper presents three unique coastal morphological datasets from three different continents (Australia, Europe, and North America, refer Fig. 2) that each encompasses a sequence of an extreme storm or extended storm cluster followed by a milder period of beach recovery. Despite the morphological data being collected beyond the theoretical DoC, sediment budget analysis unequivocally points towards unbalanced sediment budgets at all three sites, demonstrating in these cases large sediment gains within the upper shoreface over the storm-recovery sequence. We show that these short time-scale events can have important implications for long-term coastal evolution and, when placed in the context of projections undertaken using the common Bruun-rule approach, can theoretically offset decades of predicted shoreline retreat due to SLR, even under a high-range greenhouse gas emissions scenario (SSP5-8.5). Our results highlight major limitations of the Bruun-rule approach for long-term coastal projections and emphasize the need for enhanced shoreface monitoring worldwide to better quantify changes in sediment budgets due to climate change.

## Results

Figures 35 summarize long-term and extreme storm sequence results at three high-resolution coastal monitoring locations in Australia, the UK, and Mexico. These three locations are: (1) the 3.6 km-long Narrabeen embayment in SE Australia (Fig. 3), comprising one of the longest (>40 years, monthly) subaerial beach survey programs worldwide;35 (2) the 3.5 km-long Perranporth embayment in SW England (Fig. 4), where monthly subaerial beach surveys have been undertaken monthly since 2006;36 and (3) the open-coast La Misión Beach in NW Mexico (Fig. 5), where a 2.2-km stretch of sandy coast has been monitored monthly since 2015. Each site is characterized as wave-dominated (average Hs ≈ 1.6 m at all three sites), sandy (D50 ≈ 0.3–0.4 mm), and of moderate upper-shoreface steepness (tanβ, ≈ 0.03–0.04). The tidal regimes at Narrabeen and La Misión are microtidal (spring tidal range = 1.3 and 2.3 m, respectively), whereas Perranporth is macrotidal (spring tidal range = 6.3 m).

Complementing the continuous subaerial beach measurement records (including dune systems if present) were detailed three-dimensional surveys of the entire upper shoreface at time intervals prior to, immediately following and ~12 months after an extreme storm event or extended storm cluster. At Narrabeen, an extreme east coast low storm impacted the coast in June 2016 that resulted in the largest subaerial beach erosion (average = 121 m3/m) over four decades19. At Perranporth, a cluster of extratropical cyclones over successive boreal winters between 2013 and 2016 caused an average of 212 m3/m of subaerial beach erosion, with the 2013/2014 winter period in particular considered the most energetic winter period since at least 194818. At La Misión, a similar sequence of extratropical storms concentrated over the 2018/2019 boreal winter caused the most severe winter erosion (average = 208 m3/m) since measurements at the site began (Fig. 5b). Each three-dimensional survey extended from the upper beach to beyond the theoretical DoC over the respective storm sequences, calculated (see Methods) as −11.6 m (Narrabeen), −19.3 m (Perranporth), and −9.1 m (La Misión), all referenced to mean sea level (MSL).

The morphological response from all three storm sequences indicates patterns of extensive erosion along the subaerial beach coupled with adjacent sediment deposition in the shallow subaqueous zone. Representative cross-shore transects (Figs. 3g, 4e, and 5e) show these deposition zones are characterized by pronounced storm bar morphology with bar crests between approximately 200 m offshore for the microtidal Narrabeen site and 700 m for the macrotidal Perranporth site. Pivot points separating areas of upper-shoreface storm erosion and deposition are observed at depths relative to MSL of ~−2.9 m (Narrabeen), −5.8 m (Perranporth), and −1.2 m (La Misión). In the subsequent recovery phase, eroded sediment stored in the storm bar returns under more modal wave conditions, and the patterns of storm erosion and deposition are mostly reversed. At lower depths, profile variability displays the characteristic “pinching” toward the theoretical DoC that is typical of the upper shoreface, although seabed variability outside of the survey error (~0.14 m) is still evident at these lower depths.

Integrating these observations over the upper shoreface and beach, whilst carefully considering survey error (refer “Methods”), reveals that the overall sediment balances are not closed and all three locations record large net sediment gains over the storm-recovery sequence (Fig. 6). Average net gains per unit meter beach width range from +59 m3/m (La Misión) to +140 m3/m (Perranporth), which are comparable in magnitude to the extreme erosion observed over the subaerial beach during each storm sequence. In absolute terms, within the three-dimensional survey areas spanning several kilometers, these sediment gains equate to +130,000 m3 of sediment (La Misión), +400,000 m3 (Narrabeen), and +420,000 m3 (Perranporth). While the direct source of these sediment gains cannot be conclusively ascertained without detailed process-based measurements and tracer experiments, the alongshore variability and phasing of these net gains provide some insight into the sediment pathways (using Fig. 1 for reference). At Narrabeen, sediment gains occurred primarily in the storm phase and are strongly skewed towards the southern half of the embayment (max. net gain = +392 m3/m). This is consistent with likely counter-clockwise beach rotation (Transport Pathway 3 in Fig. 1) caused by this anomalous easterly storm19,37, but also coincides with the region of the rocky embayment where lower shoreface sand bodies (i.e., beyond the DoC) are more abundant38, suggesting onshore sediment transport from the lower to upper shoreface (Pathway 6). At Perranporth, sediment gains occurred instead primarily over the recovery phase and particularly at the southern half (max. net gain = +271 m3/m), which might be related to alongshore headland sand bypassing input at the southern extremity (Pathway 1) under less-extreme winter periods that have been shown to enhance beach recovery32. Similar to Narrabeen, sediment gains at La Misión occur primarily over the storm phase, but unlike the embayed Narrabeen and Perranporth sites, shows no obvious alongshore bias (max. gain = +309 m3/m). Possible sediment sources for these net gains include onshore sediment transport from lower shoreface sand storages (Pathway 6), as well as winter fluvial discharges from the nearby tidal inlet (Pathway 7).

The observed sediment gains over the entire upper shoreface and beach are subsequently characterized in terms of equivalent years of theoretical shoreline retreat predicted by the Bruun rule under various emission scenarios1, thereby evaluating the potential for substantial errors in shoreline predictions due to SLR using the Bruun-rule approach14. Figure 6b shows that the annual rate of sediment input required to theoretically offset 21st Century (2000–2100) SLR recession as predicted by the Bruun rule (Qoffset) is a function of the upper shoreface width W*, defined as the horizontal distance from the subaerial beach berm to the DoC. Here we use the long-term DoC derived from 41 years of wave reanalysis data (see “Methods”), rather than over the DoC calculated over the shorter-term storm sequence as above28. For Narrabeen, the narrower upper-shoreface width (long-term DoC = −14.3 m, W* = 480 m) means that this offset rate equates to 3.7 m3/m/year for SLR estimated under an upper SSP5-8.5 emissions scenario between 2000 and 2100, compared to 6.2 and 8.4 m3/m/year for the deeper and wider La Misión and Perranporth upper shorefaces (long-term DoC = −18.2 m and −20.2 m, W* = 810 m, and 1090 m for La Misión and Perranporth, respectively). Based on these annual rates, the observed sediment gains over the extreme storm-recovery sequence at Narrabeen are equivalent to 25 years of SLR recession predicted by the Bruun rule that may be theoretically offset at the upper SSP5-8.5 scenario, or 43 years for the more sustainable SSP1-2.6 emissions scenario. At Perranporth and La Misión, these sediment gains equate to 18 and 10 years for SSP5-8.5, or 31 and 17 years for SSP1-2.6, respectively.

## Discussion

Our results based on unique high-resolution field measurements over three extreme storm-recovery sequences from three different continents highlight the present major challenges of predicting long-term coastal evolution over planning horizons of decades to centuries. Whereas long-term modeling approaches typically assume short-term sediment losses on the subaerial beach and dune caused by extreme storm sequences are balanced by sediment gains in the subaqueous zone (resulting in zero net change in the sediment budget), our results indicate large net positive sediment gains integrated over the entire upper shoreface. Furthermore, the magnitude of these observed net gains—which primarily manifest at depths from MSL down to the DoC—are commensurate (O(100 m3/m)) to the extreme erosion that is highly visible (and widely-reported18,19) on the subaerial beach and dune during these extreme events. Likewise, these magnitudes equate to typical volumes undertaken for artificial beach nourishment projects39 and, when expressed in terms of Bruun-rule predicted shoreline change, are equivalent to offsetting decades of predicted shoreline retreat, even under an upper-range emissions scenario (SSP5-8.5). This highlights the potential for a cascading of model prediction error using the Bruun rule and other simplified approaches9,23 that do not implicitly include storm-driven sediment fluxes, placing additional concern10,11 regarding their validity for long-term prediction. This is particularly in light of robust projections pointing towards an increase in extreme waves along almost three-fifths of the world coastline4, implying an exacerbation of episodic major sediment exchange between the lower and upper shoreface, and/or alongshore adjacent embayments, in the coming decades that could significantly alter long-term coastal evolution.

Whether these observed major short-term net sediment gains to the upper shoreface and beach are relatively common, or indicative of the extreme nature of these particular storm sequences, is presently difficult to ascertain. Each storm sequence is characterized by extreme subaerial beach erosion that equates to the largest short-term erosion volumes observed in this upper part of the beach over their respective measurement records (refer Figs. 3c, 4b, and 5b). At lower depths, however, the potential for major wave-driven sediment transport across the DoC (i.e., Pathway 6 in Fig. 1) can be evaluated by estimating wave orbital velocities (Urms) at the seabed corresponding to the long-term DoC (see “Methods”). This simple approach provides a first-order assessment of sediment transport potential, while recognizing that processes such as longshore sediment transport and headland bypassing (Pathway 1), upwelling and/or tidal currents (Pathway 9) and estuarine/fluvial inputs (Pathway 7) may all play a key role22,29. Figure 7 indicates that for the three respective storm sequences, wave orbital velocities at these depths are estimated to have reached up to 1.2 m/s (Perranporth), 1.0 m/s (Narrabeen) and 0.6 m/s (La Misión), which are well above the typical threshold of motion for shoreface sediment (Ucrit ≈ 0.2 m/s, see Methods) and suggest large sediment transport potential. Over the longer-term (1979–2020) dataset, these equivalent wave orbital velocities are estimated to occur only rarely at Perranporth and Narrabeen where the largest net sediment gains were observed (∆V = + 140 m3/m and +91 m3/m, respectively), having been exceeded just 9 h over the 41-year record at Perranporth (i.e., Urms > 1.2 m/s) and 91 h at Narrabeen (Urms > 1.0 m/s). At La Misión, where observed net sediment gains were the smaller of the three sites (∆V = + 59 m3/m), equivalent wave orbital velocities are estimated to occur more frequently over the historical record (636 h over the 41 years, Urms > 0.6 m/s). This suggests a potential scaling between sediment transport potential (estimated by the wave orbital velocity at the DoC) and the magnitude of short-term net sediment gains caused by storm-recovery sequences, with less-frequent events potentially resulting in a larger sediment influx. A notable example evident in the historical dataset at La Misión is the January 1988 storm (maximum Urms = 1.4 m/s, Fig. 7c) that resulted in extreme coastal impacts at nearby Southern California, including reported in situ observations40 of large seabed changes extending down to depths of −25 m.

Further evidence as to the historical frequency of these major short-term net sediment gains can be garnered from the long-term subaerial volume measurements. Considering the Narrabeen beach monitoring program that spans 44 years of continuous subaerial beach measurements35, the subaerial beach volume data (Fig. 3c) indicate no significant long-term erosion or accretion trend (linear regression trend = −0.08 ± 0.11 m3/m/year). Similar to the wave orbital velocity analysis above, this suggests that similar short-term sediment gains as observed over the 2016–2017 storm-recovery sequence at this site have either: (1) occurred very rarely; (2) do not have a noticeable subaerial beach signature (i.e., sediment gains do not move sufficiently onshore to be observed on the subaerial beach); have been balanced by equivalent sediment losses (e.g., Pathways 1, 7, 8, and 9 in Fig. 1); or (3) have possibly contributed to offsetting the approximately 0.10 m of relative SLR that has occurred over this 44-year record41. At Perranporth and La Misión, the subaerial beach volume data suggest a slight erosional trend at Perranporth (linear regression trend = −5.3 ± 2.9 m3/m/year) and a relatively strong accretionary trend at La Misión (linear regression trend = 23.3 ± 16.8 m3/m/year), although it is likely that these shorter-term records are biased by the storm sequences themselves.

While each of the three datasets shows net positive sediment contributions, equally plausible on sandy coastlines more generally are extreme storm sequences that cause major losses to the overall sediment budget (e.g., imbalances in Pathways 1, 7, 8, and 9 in Fig. 1). Short-term sediment fluxes between the lower and upper shoreface (across the DoC) and from adjacent beaches reflect complex interactions between sediment transport processes, sediment storage (both on the lower shoreface and at adjacent beaches), and accommodation space between the lower and upper shoreface. As outlined in two recent reviews of shoreface morphodynamics29,42, the present conceptual understanding of sediment transport on the lower shoreface is extremely limited. This is due to a combination of many factors, including subtle imbalances between onshore and offshore-directed sediment fluxes; the dominance of bedload and gravity flows at these depths; the presence of migrating bedforms; a paucity of field data measurements beyond the surf zone; and uncertainties associated with upscaling short-term measurements and process understanding to longer time scales. These limitations are compounded by the severe lack of any knowledge of the seabed composition on the lower shoreface, with estimates suggesting that 71% of ocean depths between the MSL and −200 m depth contours remain completely uncharted43.

Predicting the potential fate of coastal environments out to the year 2100 and beyond, i.e., forecasting the 2100 coastline, is one of the most pressing challenges facing coastal science today. While it is unlikely that a step-change in our ability to model sediment transport at and between the lower and upper shoreface will be achieved in the near future, significant improvements in long-term predictions can be realized through: (1) a major upscaling of seabed mapping efforts (e.g. refs. 44,45) to evaluate the magnitude of sediment presently stored on the lower shoreface; and (2) a significantly greater number of routine monitoring efforts of entire nearshore systems appropriate for quantifying sediment fluxes. These two steps can greatly help identify both short and long-term changes to sediment budgets and their connectivity between lower and upper shoreface (including dunes), and between adjacent embayments, as well as provide early warning for coastal communities of any large-scale sediment shifts to SLR in the coming decades. The latter is particularly important considering potential coastal barrier overstepping and dramatic shoreline change under very rapid sea-level rise scenarios, as has been observed in the mid-Holocene46. Improvements in remote sensing technology (e.g., satellite-derived bathymetry47) are also likely to complement shoreface monitoring efforts, by providing regional perspectives on entire sediment compartments and their linkages48. However, the vertical accuracies of these technologies are still limited (σv > 0.4 m), re-emphasizing the need for enhanced traditional in situ monitoring strategies49.

## Methods

### Multimethod morphological surveys

Morphological surveys at each of the three locations were undertaken using a combination of survey methods to ensure seamless digital elevation models (DEMs) spanning the subaerial and subaqueous beach system. At Narrabeen, subaerial beach surveys were undertaken using Airborne Lidar and Uncrewed Aerial Vehicles (UAVs), with vertical uncertainty (σv) quantified for this site and equipment as 0.11 m and 0.07 m, respectively50,51. At Perranporth, subaerial beach surveys were undertaken using a combination of Airborne Lidar (σv = 0.15 m) and either UAV (σv = 0.06 m at this site) or RTK-GNSS mounted to an ATV (σv = 0.05 m)32. At La Misión, subaerial beach surveys were undertaken by walking RTK-GNSS (σv = 0.05 m) at 50-m spaced cross-shore transects. At all three sites, subaqueous surveys were undertaken using a single-beam echosounder mounted on a boat (Perranporth, σv = 0.05 m) or jetski (Narrabeen and La Misión, σv = 0.10 m). These depth soundings were collected near-continuously along cross-shore transects spaced every 50 m at Narrabeen and Perranporth, or every 150 m at La Misión. At Perranporth, surveys were also complemented in deeper water (<−10 m) by multibeam echosounder (σv = 0.06–0.30 m)32. Seamless DEMs were subsequently created from the multimethod surveys using cubic interpolation. This method was found to best represent natural beach variability (e.g., intertidal bars) in the small data gaps (<30 m cross-shore) between subaerial and subaqueous measurements found at the microtidal Narrabeen and La Misión sites.

### Sediment budget error analysis

DEMs of Difference (DoD), characterizing spatial variability in beach elevation change at each site, were calculated from the individual DEMs described above. Sediment budget error analyses were calculated following the approach of52, by first considering the limit of detection (LoD) for each DEM grid point:

$${LoD}=\sqrt{{{\sigma }_{{{{{{\rm{DEM}}}}}}1}}^{2}+{{\sigma }_{{{{{{\rm{DEM}}}}}}2}}^{2}}$$

where $${\sigma }_{{{{{{\rm{DEM}}}}}}}$$ is the vertical uncertainty at each grid point depending on the localized survey method. The overall volume change ∆V and associated uncertainty for each DoD were then calculated by considering only statistically significant (95% confidence level) morphological change above the limit of detection ($$\left|{Z}_{{{{{{\rm{DEM}}}}}}1}-{Z}_{{{{{{\rm{DEM}}}}}}2}\right|$$ > LoD). These overall volume changes ∆V were then normalized per unit beach width based on the number of cross-shore transects in the survey region.

### Equivalent years of SLR recession theoretically offset using the Bruun rule

Volumetric changes to the sediment budget caused by the three storm sequences were converted to equivalent years of SLR recession that may be theoretically offset over the 21st Century when estimated using the Bruun rule, in order to evaluate the potential for large error using this simple approach. Upper-shoreface widths W* were calculated at each site considering the alongshore-averaged horizontal distance between the subaerial beach berm and the long-term DoC, which is calculated relative to mean low water as:21,53

$${DoC}=2.28{H}_{{{{{{\rm{s}}}}}},Y}-68.5\left(\frac{{{H}_{{{{{{\rm{s}}}}}},Y}}^{2}}{g{{T}_{{{{{{\rm{p}}}}}},Y}}^{2}}\right)$$

where Hs,Y is the significant wave height exceeded 12 h every Y years, g is gravity and Tp,Y the associated peak wave period. Following other SLR estimates using the Bruun rule3,13, ERA5 wave reanalysis data54 spanning 41 years (1979–2020) was used to calculate the long-term DoC at each site. These values relative to mean low water were then converted to MSL considering the tidal range. The annual rate of sediment input required to theoretically offset SLR recession using the Bruun rule (Qoffset) is subsequently calculated by:

$${Q}_{{offset}}=\frac{S}{Y}{W}^{* }$$

where S is the predicted median change in sea level over the 21st Century1 (S = 0.44 m and 0.77 m for SSP1-2.6 and SSP5-8.5 scenarios for 2000–2100, respectively) and Y the time period in years (Y = 100 years). The equivalent years of SLR recession that may be theoretically offset is then calculated by dividing the volumetric changes ∆V by Qoffset.

### Orbital wave velocities at the depth of closure

Orbital wave velocities (Urms) at the DoC for each of the three sites were estimated to assess sediment transport potential at these depths from the historical ERA5 wave reanalysis between 1970 and 2020. The wave orbital velocity can be estimated from random waves (assuming a JONSWAP spectrum) by an explicit solution defined by:55

$${U}_{{{{{{\rm{rms}}}}}}}=\frac{0.25{H}_{{{{{{\rm{s}}}}}}}}{{T}_{n}{(1+A{t}^{2})}^{3}}$$
$$A={\left[6500+{\left(0.56+15.54t\right)}^{6}\right]}^{\frac{1}{6}}$$
$${T}_{n}={\left(\frac{{Z}_{{{{{{\rm{DoC}}}}}}}}{g}\right)}^{\frac{1}{2}}$$
$$t=\frac{{T}_{n}}{{T}_{{{{{{\rm{z}}}}}}}}$$

where ZDoC is the seabed depth corresponding to the long-term DoC (Narrabeen = −14.3 m, Perranporth = −20.2 m, La Misión = −18.2 m), Hs the significant wave height (from ERA5 reanalysis) and Tz the zero-crossing wave period. Tz is calculated from the ERA5 peak wave period Tp using the spectral approximation Tz ≈ 0.78Tp. The typical threshold of motion for shoreface sediment resulting from wave orbitals at the seabed is estimated based on a characteristic wave period of 10 s and shoreface sediment in the range D50 = 0.2–0.7 mm (refer Figure 19 in ref. 56).