Fire (plus) flood (equals) beach: coastal response to an exceptional river sediment discharge event

Wildfire and post-fire rainfall have resounding effects on hillslope processes and sediment yields of mountainous landscapes. Yet, it remains unclear how fire–flood sequences influence downstream coastal littoral systems. It is timely to examine terrestrial–coastal connections because climate change is increasing the frequency, size, and intensity of wildfires, altering precipitation rates, and accelerating sea-level rise; and these factors can be understood as contrasting accretionary and erosive agents for coastal systems. Here we provide new satellite-derived shoreline measurements of Big Sur, California and show how river sediment discharge significantly influenced shoreline positions during the past several decades. A 2016 wildfire followed by record precipitation increased sediment discharge in the Big Sur River and resulted in almost half of the total river sediment load of the past 50 years (~ 2.2 of ~ 4.8 Mt). Roughly 30% of this river sediment was inferred to be littoral-grade sand and was incorporated into the littoral cell, causing the widest beaches in the 37-year satellite record and spreading downcoast over timescales of years. Hence, the impact of fire–flood events on coastal sediment budgets may be substantial, and these impacts may increase with time considering projected intensification of wildfires and extreme rain events under global warming.

www.nature.com/scientificreports/ Wildfire is common in the Big Sur River watershed and the surrounding mountains owing to steep landscapes, dry summer climate, and mixed vegetation ground cover 4,38 . For example, the 2016 Soberanes wildfire burned 537 km 2 of the Santa Lucia Range, approximately 100 km 2 of which were within Big Sur River watershed (Fig. 1a) 39 . This wildfire burned the headlands of the watershed at moderate to high soil burn severity, resulting in near complete incineration of organic materials and the development of water-repellent layers in soils 39 . Two other large historical wildfires occurred in the Big Sur River watershed: the 1977 Marble Cone and 2008 Basin Complex fires, which burned 109 and 138 km 2 , respectively, of the Big Sur River watershed ( Fig. 2b; see "Methods").
Estimates of sediment discharge from the Big Sur River, which has received negligible sediment monitoring, were generated by transferring detailed pre-and post-wildfire records from the adjacent and similar Arroyo Seco watershed 4 (see "Methods"). These techniques used a simple precipitation-regulated fire response function, the non-dimensional Fire Factor (F f ), which was derived empirically and represents the scale of fire-related effects on sediment yields. Values of F f exceeded 30 following both the 1977 Marble Cone and 2016 Soberanes wildfires (Fig. 2b), and the estimated 1.1 and 2.2 Mt (10 6 tonnes) of sediment discharge, respectively, during these years combine to roughly 70% of the 50-year sediment discharge (4.8 Mt;1971 ; Fig. 2c). These two wildfireaffected winters (1977-1978 and 2016-2017) had greater sediment discharge than following the 2008 Basin Complex wildfire (0.18 Mt over three years) or the 1995-2000 wet interval (0.54 Mt over 6 years; Fig. 2a-c), which was similarly noted in regional studies of these events 4,40 . The increased sediment discharge in 2016-2017 was due in part to record-setting rainfall along coastal California in early 2017, when atmospheric vapor flux to the coast was three standard deviations above normal due to unusual atmospheric-river activity 41 , causing repeated flooding and large increases in regional sediment flux to the coast 42 . During 47 days of January-February 2017 the Big Sur River experienced six peak flows that exceeded the 2-year flood magnitude, including two near the 10-year flood levels: January 10th (144 m 3 /s) and February 20th (140 m 3 /s; see "Methods"). For comparison, the wet season immediately following the 1977 Marble Cone wildfire included the largest recorded flood of the 50-year record (303 m 3 /s), and the winter after the 2008 Basin Complex wildfire had no flows above the 2-year flood magnitude.
Another sediment source to the study area beach is erosion of the sea cliffs south of the river mouth (Fig. 1e). Cliff erosion is approximately 0.3 m/year along the study area 43 , which suggests that approximately 12,500 m 3 / year (~ 25,000 t/year) of cliff erosion occurs from the 1700 m long and ~ 25 m high mixed bedrock and unconsolidated sediment sea cliffs (see "Methods"). Thus, cliff erosion is approximately 4-times less than the average river sediment input, although it may be a primary sediment source during multi-year droughts, and it is the source of several boulders along the coast (Fig. 1d,e). Shoreline responses following the 2016 wildfire. The Big Sur River mouth study area is immediately downcoast (south) of Molera Point headland, and it includes a narrow sandy beach, several areas with rocky nearshore morphology (~ 700, 1000, and 1500 m from the river mouth), and a small headland ~ 1900 m from the river mouth (Fig. 1d,e). The shoreline shape is influenced by these geomorphic features, including shoreline curvature for ~ 500 m downcoast of Molera Point and ~ 10-30 m seaward extension of the shoreline at the rocky areas (Fig. 1d).
Time series of shoreline change between 1984 and 2020 were obtained from the CoastSat toolbox 36 , which maps shoreline positions from publicly available Landsat and Sentinel-2 imagery. Mapped shorelines of the study area were transferred to eighteen 100-m spaced cross-shore transects and corrected for tidal stage during each image ( Fig. 1d; see "Methods"). We have also generated similar transect data for adjacent coastal areas for comparative purposes, as discussed below and presented fully in the Supplemental Materials.
Each transect has over 1000 shoreline measurements during the 37-year satellite record, and these observations were summarized into annual shoreline metrics for Fig. 2d-g (all transects plotted in Supplemental Materials). Overall, transects near the northern and southern ends of the study area have lower annual variability as shown by the interquartile range (blue shading; Fig. 2d-g). This is related to wave-driven seasonality in the shoreline, which is strongest in the central portion of the study area. Perhaps the most distinct patterns in the shoreline data, however, are the accretion patterns that occurred during and after 2017 ( Fig. 2d-g). During the 2017-2020 interval, all transects recorded either the most seaward median and quartile shoreline positions of the entire record or the most seaward positions since 1984. The timing and extent of beach widening differed across the study area, however, as the transects adjacent to the river mouth narrowed significantly after 2017, whereas the downcoast transects continued to widen through 2020 ( Fig. 2d-g).
Raw shoreline measurements provide additional details about the timing and extent of the 2017-2020 beach widening (Fig. 3). Accretion near the river mouth did not occur until after the high river discharge events of 2017, several months after the 2016 Soberanes wildfire (Fig. 3a,b). By March 2017 the shoreline adjacent to the river mouth had accreted over 100 m, but this accretion was ephemeral as the shoreline retreated soon afterward due to longshore spreading of sediment (Fig. 3b). The downcoast shoreline exhibited several different patterns following the 2016-2017 fire-flood event including: (1) lower magnitude and delayed accretion in the shoreline immediately downcoast of the river mouth (e.g., Fig. 3c) and (2) general widening of the beach with an increase variability-including seasonality-at the middle to southern transects ( Fig. 3d-g; all transects plotted in Supplemental Materials). The average accretion in the shorelines over the 2017-2020 interval ranged between 15.2 and 33.3 m (mean = 23.2 m) and variance in the shoreline also increased after the fire-flood event as shown by red boxes in Fig. 3. The increase in mean beach width for all 18 transects were found to be highly statistically significant (p < 0.0001) using Welch's t-tests (see "Methods" for details).
Higher spatial resolution satellite imagery provides additional information about shoreline patterns after the 2016-2017 fire-flood event. Immediately after the 2016 Soberanes wildfire, but before the high river flows of early 2017, the beaches of the study area were relatively narrow (Fig. 4a). These conditions coincided with www.nature.com/scientificreports/ one of the strongest multi-year droughts in California's precipitation records (2012-2015) and some of the narrowest beach conditions of the 1984-2020 satellite-derived shoreline records (Fig. 2). However, after the high river flows of early 2017, a wider sandy beach was observed in the upcoast (northern) portion of the study area (Fig. 4b), which extended south with time ( Fig. 4c,d). This imagery was obtained during summer to early fall seasons when beach widths were generally greatest (cf. Fig. 3). Thus, there is evidence from the transect data and higher-resolution imagery that beach progradation started near the river mouth and spread downcoast (south) over time (Figs. 3, 4).

River sediment supply hypothesis.
To examine the hypothesis that the sediment comprising the new beach widening in 2017 was derived from the Big Sur River, we evaluated three elements: a simple sediment budget, patterns in remote sensing imagery, and CoastSat data from other regional beaches without river sedi-  www.nature.com/scientificreports/ ment inputs. First, a sediment budget was derived from estimates of river discharge and beach sedimentation. As noted above, the 2016-2017 suspended-sediment discharge was estimated to be 2.2 Mt. Only a portion of this sediment was coarse enough to be compatible with the littoral cell, as finer-grained sediment will be transported offshore 44 . The sand content (> 63 µm) of the post-fire river discharge was estimated to be 67.5% from the two highest discharge rates sampled by the USGS for suspended-sediment in the Arroyo Seco following the Marble Cone wildfire. Limber et al. 44 suggested only approximately 45% of this total sand will be coarser than the typical littoral cutoff diameter of 120-µm for California rivers and beach settings. Thus, only ~ 30% of the total sediment discharge, or approximately 0.66 Mt, was estimated to have compatible grain sizes with the littoral cell. Assuming a bulk density of 1500 kg/m 3 , an estimated 440,000 m 3 of beach-compatible sand was discharged by the Big Sur River during the 2016-2017 winter. The total sedimentation within the littoral cell was estimated by assuming that the new sand uniformly covered the littoral profile from the upper beach (~ 2 m elevation) to the estimated depth of closure (~ 13 m water depth from standard formulations 45,46 ). By May 2017, there was ~ 50 m of progradation along 600 m of the beach and using the full-profile assumption across the 15 m of the active littoral height, the total volume of new beach sand was estimated to be 450,000 m 3 . Although the two elements of the sediment budget differ by only ~ 2%, there is likely up to 50% uncertainty in each value. Regardless, the simple sediment budget suggests that the volume of sand discharged by the river and the volume of new beach sand are of the same magnitude, thereby allowing for the possibility of river sediment causing the coast changes.
Observations of imagery from the Sentinel-2 and Landsat sensors provide additional support for a river source of sediment (Fig. 5). This imagery clearly shows negligible shoreline change after the largest and most sustained high flows in the river during January 2017 (Fig. 5a-c). However, several weeks after the high river www.nature.com/scientificreports/ discharge, a new bar was observed immediately offshore of the river mouth as seen from wave breaking (Fig. 5c), and several weeks later the beach showed accretion near the location of the former bar (Fig. 5d). The final pulse of flooding in February 2017 did not coincide with additional beach accretion (Fig. 5e), although accretion was measured during the weeks after this event (Fig. 5f,g). These observations are consistent with observations and theory of how river sand is integrated into littoral cells: sand deposition initially occurs in the submarine region offshore of the river mouth and is reworked by waves toward land to form a subaerial beach as the beach profile is reestablished 47,48 . Lastly, it is valuable to examine other beaches in the region to see if they responded similarly to the Big Sur River mouth. Two beaches immediately north of the Big Sur River have no direct river sediment inputs and were chosen for this task. A complete presentation of this comparison is provided in the Supplemental Materials. We found that unlike the Big Sur River study area, the two beaches did not show widening during the fire-flood interval of 2017-2020. Those beaches also had correlation patterns with sediment inputs that were inverse to those by the Big Sur River mouth. In total, these factors suggest that the Big Sur River mouth shoreline exhibited different temporal patterns to regional beaches. Combined these results support a conclusion that fluvial sediment inputs were responsible for beach widening near the Big Sur River mouth.
Alongshore sediment spreading. Once in the littoral cell, sediment spread from the river mouth toward the south. To examine this spreading of sediment, changes in the 2016-to-2020 annual median shoreline positions were compared for each transect (Fig. 6a-e). These data reveal that the largest shoreline responses during 2016-2017 were within 600 m of the river mouth, where median accretion was 29-45 m (Fig. 6a). However, this same area exhibited 10-27 m of erosion in the subsequent year, while the remaining transects south of 600 m experienced up to 31 m of accretion (Fig. 6b). Thus, the annual shoreline position data provide evidence that accretion started near the river mouth and spread downcoast over the following year. After tens of meters of shoreline change during the first two years, annual shoreline change was less during the subsequent years (Fig. 6c,d). These changes included 2018-to-2019 erosion and 2019-to-2020 rotation, each of which occurred under different storm-season (Oct.-Mar.) wave conditions. Overall, the net shoreline changes between 2016 and 2020 revealed that accretion was greatest toward the southern portion of the study area, where up to 45 m of accretion occurred by 2020, not the river mouth (Fig. 6e).
Downcoast sediment spreading was also evaluated by arrival dates of measurable accretion at each transect. Because accretion occurred over intervals of weeks to years, we took an approach of identifying the initial dates of specific proportions of the maximum progradation (see "Methods"). This technique revealed that the initiation of accretion started next to the river mouth and proceeded systematically downcoast (red circles; Fig. 3b-g). Accretion initiation was clearly related to seasonal shoreline cycles, especially for transects in the middle of the study area. A compilation of these data for all transects reveals three distinct accretion intervals: (1) an initial interval during early 2017 near the river mouth (100-600 m), (2) a relatively uniform interval in summer 2017 for the middle of the study area (700-1400 m), and (3) the Sep.-Dec. 2017 accretion along the most downcoast region (1500-1800 m; Fig. 6f). These measurements suggest an arrival time of ~ 310 days between the river mouth and the 1800-m transect (equivalent to an average speed of 5.8 m/day). We hypothesize that the near uniform initial arrival of sediment in the central area may be related to sediment spreading to this region within the shallow subtidal regions and onshore transport during the seasonal widening of the beach.
Thus, shoreline positions provide evidence that sediment was introduced at the river mouth in early 2017 and spread downcoast in a manner that was influenced by the morphology of the coast, the wave conditions, and the seasonality of shorelines. Thus, large river sediment inputs can influence local and downcoast shoreline widths for many years as dictated by the littoral transport. In the next section we use records of sediment discharge and wave conditions to evaluate how these factors are related to the region's shoreline positions over decadal scales.

Evaluation of factors influencing shoreline positions.
To examine factors influencing shoreline positions near the Big Sur River, correlation analyses were made with annual measurements of sediment discharge and wave conditions for the coincidental 1984-2020 records (see "Methods"). Correlations between these variables and shoreline positions were generally weak, however, suggesting that no one external variable explained the majority of variance in the shoreline positions (Fig. 6g,h). An exception was found for transects near the river mouth (100-600 m), which had positive correlations (r = 0.56-0.72) with river sediment discharge ( Fig. 6g; see Supplemental Materials for additional correlation information). If a delayed response to sediment discharge is considered, for example by including a 1-year lag for the shoreline response, we found weak, positively correlated relationships (r = 0.12-0.52) across the entire study area (Fig. 6g).
Wave effects were examined by considering the wave energy flux during the Oct.-Mar. storm season and the average direction of the most powerful wave conditions of each year, factors that drive shoreline change within the broader region 17 (see "Methods"). However, these correlations were also weak (r = − 0.41 to 0.33 and − 0.23 to 0.53, respectively), although they did reveal transitions in the sign of correlation at 500-700 m from the river mouth (Fig. 6h). These results suggest that steeper (more northerly) winter wave angles resulted in somewhat narrower beaches in the north and wider beaches in the south. Additionally, the results suggest that higher waveenergy fluxes were generally related to wider beaches in the north and narrower beaches in the south (Fig. 6h).
Although the single-variable correlation results were consistently weak across the study area, they provided evidence that multiple factors contributed to influence shoreline positions. To test this hypothesis, we conducted a stepwise multiple regression for each transect with the variables described above and one additional variable, the preceding year's shoreline position (see "Methods"). Results suggest that the combination of factors explained an average of 57% (and up to 78%) of the shoreline position variance, which far exceeded the single-variable correlations (Fig. 6i) www.nature.com/scientificreports/ whereas the previous shoreline position and wave direction were generally important variables in the middle and southern portion of the study area (Fig. 6i). On the southern end (1500-1800 m), wave energy flux and the 1-year lagged sediment input became significant variables. Thus, shoreline position patterns in the study area were shown to be related to multiple factors, and the importance of these factors changed with distance along the beach.

Discussion
We have shown that a burned California watershed generated elevated fluvial sediment discharge to the coast after post-fire storms that, in turn, expanded beach widths and resupplied the littoral cell with sand. However, it is also clear that not all wildfires exhibited similar responses. For example, consider the differences between the 2008 Basin Complex fire and the 2016 Soberanes fire (Fig. 2). Although the 2008 wildfire burned a larger www.nature.com/scientificreports/ portion of the Big Sur River watershed, it was followed by moderate rainfall conditions and only ~0.18 Mt of suspended-sediment discharge over three years (tenfold less than the event studied here), and the shoreline response was considerably muted compared to 2016-2020 (Fig. 2). Thus, similar wildfires can result in markedly different sediment yield and coastal responses. The added effects of wildfire on watershed sediment yield during 2016-2017 were estimated to be a factor of 30-fold over what was expected given the year's hydrologic conditions (Fig. 2). Without these wildfire effects, annual suspended-sediment discharge would have been only ~ 0.07 Mt, which is approximately the mean annual sediment discharge of the 50-year record. Over the actual 50-year record, however, the two years with the greatest wildfires effects combined to contribute 70% of the total river sediment discharge (Fig. 2). Thus, wildfire has the potential to be a dominating factor for sediment budgets for coastal watersheds like the Big Sur River, but only if the post-wildfire hydrologic conditions are adequately wet to induce enhanced erosion processes throughout the landscape 1,4,14,49 .
In addition to the implications of new sediment discharged to the coast, it is also important to note that the lack of sediment discharge during drought conditions, such as during 2012-2015, corresponded with some of the narrowest beach conditions on record (Fig. 2). As such, it appears that the lack of sediment during dry intervals can be similarly important to beach widths as the abundance of sediment after massive inputs. We hypothesize that these sediment-supply-dictated responses of the beach occur because sediment is transferred downcoast through the littoral system by northwesterly waves over time scales of one to several years ( Fig. 4 and Fig. 6f-i).
A simple event-response conceptual model for the Big Sur River study site was constructed to summarize these findings (Fig. 7). For the Big Sur River setting, the seasonality in waves-larger, northwesterly waves in the winter and smaller waves with a southern component in the summer-provides fundamental forcing on this coast (Fig. 7a). This generally transports beach sand toward the south, where multiple rocky areas and a small headland interrupt sediment transport and form several ~ 400 m shoreline cuspate features. Additionally, seasonality in wave conditions causes seasonality in shoreline positions, especially in the central and southernmost section of the beach (Fig. 7a).
During fire-flood event sequences, the majority of newly introduced fluvial sediment will be deposited immediately offshore of the river mouth 47 , and much of it will move back inshore toward the beach and spread downcoast over weeks to months (Fig. 7b,c). Although the longshore spreading of this new sediment is initially slowed by the first rocky coastal section, it passes into the ~ 2-km littoral cell over the coming years as sediment is transported in the downcoast direction (Fig. 7d). This downcoast spreading of sediment occurs coincidentally with erosion of the broad beach at the river mouth, a geomorphic pattern that is conceptually similar to patterns found at many deltas worldwide that redistribute sediment from the river mouth toward distal regions of the delta 50 . It is likely that sediment is transported around the southern headland, and presumably lost to downcoast littoral systems, although we did not evaluate this hypothesis with our data (Fig. 7d).
Over the years following a fire-flood event, two endmember shoreline conditions are observed (Fig. 7e,f). During winters with more direct (westerly) wave approach, the beach is generally wider in the north and narrower in the south (Fig. 7e). The widening may be a function of differences in littoral sediment exchanges 51 or from additional river inputs of sediment. Precipitation is notably increased during storms from more westerly directions 52,53 , suggesting that increased fluvial sediment discharge likely coincides with winters with more direct waves (Fig. 7e). Other winters are dominated by more northerly, or "steep" winter waves, which will cause the beach to be narrower in the north and wider in the south (Fig. 7f). Both of these post-event scenarios are hypothesized to transport littoral sediment around the southern headland, resulting in a gradual loss of sediment from the littoral system-and an overall narrowing of beach-over time (Fig. 7e,f).
Combined, these observations and models can be used to hypothesize how similar coastal systems will respond to climate change. For example, climate change will alter the distributions of many of the forcing factors found to be important to the system studied here, including the size, intensity, and frequency of wildfire, precipitation intensity during wet conditions, and the prolongation and intensification of drought between wet years 2,11,12,54 . In general, these changes are expected to increase sediment production to fluvial systems in the U.S. West 11 , which may result in more river sediment discharge events such as those detailed here and by others 42,47 . However, these fire and flood events will likely be separated by more intense drought conditions with negligible river sediment discharge 9,54 . Combined, this would lead to increased variability in fluvial sediment supply, and our observations suggest that this may result in increases in shoreline variability, such as during 2010-2020 at the study site (Fig. 2).
Because beaches provide important habitats, recreational opportunities, and storm hazard mitigation, it is crucial to better understand changes to these systems 23,26,55 . To encourage these studies, we note that publicly available satellite imagery collected during the past four decades was exceptionally useful for characterizing changes in this small littoral system with narrow beaches. This finding suggests that these tools can be applied broadly to develop a greater understanding of coastal morphodynamics and the physical factors that control marginscale coastlines. Furthermore, broader application of satellite-based observations will allow for more examples of sediment supply events to coastal systems-from both fire-flood events and other events such as floods and landslides 42 -to expand the understanding of how landscape disturbances influence the world's shorelines. www.nature.com/scientificreports/ with a standard deviation of 1.1 m, suggesting that differences in excess of 4-8 m were greater than the sampling uncertainty.

Methods
To examine the shoreline response to the 2016-2017 fire-flood event, the 2014-2020 data were divided into 'before' and 'after' intervals by a separation date of Mar. 1, 2017 and renormalized by subtracting the mean position of the 'before' interval. Mean and standard deviation positions for the intervals were compared with Welch's t-tests, all of which indicated that the beach was significantly wider after the fire-flood event (all p < 0.0001).
To examine the initial timing of accretion, the 2014-2020 data were fit with locally estimated scatterplot smoothing (LOESS) 57 functions using a fitting value (f) of 0.1. The maximum difference in the LOESS values was found for each transect, and the initiation of accretion was defined as the first date that a specific percentage of this difference occurred. Values from 33 to 90% showed similar patterns, so for simplicity the timing of the 50% values, which are referred to as the midpoints, are shown in the paper.
Hydrologic data. Precipitation data were obtained from the monthly National Weather Service rainfall gauge at Big Sur (station BGS; Fig. 1), which are available at the California Data Exchange Center (CDEC; http:// cdec. water. ca. gov/). Monthly data from the BGS station were summarized into water year increments. River discharge data were obtained from the15-min observations from USGS streamgage 11143000 (Fig. 1) available from the USGS NWIS system 58 . Additionally, the annual peak flow vales from 1950 to 2020 were used to compute annual exceedance probabilities of 0.5 and 0.1 (2-and 10-year recurrence values).
Fluvial sediment discharge estimates were derived by extrapolating from an adjacent watershed, the Arroyo Seco, because the Big Sur River does not have a suspended-sediment sampling program. The Arroyo Seco drains a similarly steep and forested landscape and shares over 16 km of ridgeline with the Big Sur River. River suspended-sediment monitoring on the Arroyo Seco includes years without wildfire impacts and two watershedscale wildfires (1977 and 2008), which burned 100 and 93% of the watershed drainage area, respectively. From these data, Warrick et al. (2013) developed an annual sediment yield model based on precipitation, wildfire extent and time since wildfire 4 : where Q ss is the annual suspended-sediment discharge (Mt/year), P is the annual precipitation at station BGS (cm/year), m and n are coefficients derived from least-squares regression for years without wildfires effects (m = 7.52 × 10 −13 ; n = 4.96, r 2 = 0.80), F f is termed the 'Fire Factor' and represents the increase in suspendedsediment discharge that occurs from the cumulative wildfire effects in the watershed during year, t. The F f is computed annually by summing the effects of previous wildfires: where, A i is the area burned for fire i, A ws is the total watershed area, C is a non-dimensional sediment yield increase factor that includes precipitation enhancement based on regression analyses 4 : and the exponential function in Eq. (2) represents the decay in the wildfire effects with time from the year of the wildfire (t i ). The decay coefficient (k) was found to be equivalent to a 1.4-year half-life (k = 0.5062) using post-fire records 4 . After 8 years transpire after a wildfire, it is excluded from Eq. (2), and F f are not allowed to drop below values of unity, even during the driest conditions. The standard deviation of the lognormal output of this model is a factor of 2; that is, 68% of the estimates fall within approximately one half to two times the measured values.
For the Big Sur River watershed, values for F f (t) were derived from the wildfire perimeter maps provided by the California Department of Forestry and Fire Protection's Fire and Resource Assessment Program (FRAP; https:// frap. fire. ca. gov/ mappi ng/), which provides data for all fires greater than at least 0.4 km 2 . The computed annual sediment discharge estimates from Eq. (1) were scaled from the Arroyo Seco (293 km 2 ) to the Big Sur River watershed (151 km 2 ) using the watershed area ratio (0.515).

Cliff erosion.
Cliff erosion is another primary sediment source to California beaches, including the study area (Fig. 1e). To estimate the volume of sediment contributed by cliff erosion, we utilized cliff erosion measurements for the study area from the USGS National Assessment Project, which suggest that approximately 0.3 m/ year of cliff erosion occurred between 1933 and 1998 43 . For the study area, approximately 1700 m of the shoreline is backed by cliffs, and the cliff ranges from 20 m high in the north to 30 m high in the south. Using an average cliff height of 25 m, the average volumetric erosion can be estimated by the product of the three terms (height, length and erosion rate) to be approximately 12,500 m 3 /year. The lower half of the cliff material is weak metasedimentary rock from the Franciscan Formation, and the upper half is unconsolidated Quaternary materials, so an average bulk density of 2000 kg/m 3 is assumed. Combined, this calculation suggests that about 25,000 t/year of rock and sediment are eroded from the cliff to the beach. We can compare the cliff sediment flux with the average river input (4.8 Mt over 50 years, or 96,000 t/year). Thus, using average rates, the Big Sur River provides ~ 80% of the sediment input to the study area, whereas cliff erosion provides ~ 20%.
Oceanographic data. Wave (Fig. 1) were derived from hourly directional wave (1) Q ss = mP n F f (t), www.nature.com/scientificreports/ measurements during 1983-2020 of significant wave height (H s ) and direction from which the dominant period was derived (Dir). Unfortunately, wave measurements were not continuous for the 1984-2020 satellite records. Thus, we utilized hindcast data from the ERA5 of the Copernicus Climate Change Service (C3S) to provide a continuous wave record to compare with the satellite-derived shorelines. Wave data were interpreted from the ERA5 records for the location of NDBC 46028 for all annual indices generated as noted below.
Regression analyses. Annual median shoreline positions were used in single and stepwise multiple regressions to evaluate whether environmental factors may have influenced shoreline positions. Several independent variables were evaluated. For river sediment discharge, we utilized the annual data in two manners: (1) sediment discharge during the same year as the shoreline measurement, and (2) sediment discharge during the previous year. Other time lags were used (2-5 years) to see if the dominant shoreline response was longer than 1 year, but all resulted in lower correlation coefficients. Regressions were conducted with raw and log-transformed sediment discharge data, and both produced similar correlation coefficients. We present the log-transformed data owing to the likelihood of a non-linear response and to the strong skew in the sediment discharge data. For waves, we used a similar approach as Barnard et al. 59 , who found that shoreline change in the broader region was related to winter storm wave energy flux and direction. Thus, we calculated the wave energy flux (F wave ) from each hourly ERA5 hindcast value: where ρ is the density of seawater (1025 kg m −3 ) and g is the acceleration of gravity. The fall-to-winter F wave was calculated by summing over Oct. 1 to Mar. 30 59 , which was normalized by dividing by the average of all annual values. Because the direction of the most powerful waves also plays an important role in shoreline position 60,61 , we computed an average storm-season Dir by considering hourly records within the top 5% of each annual F wave value. A compilation of these wave variables are presented in the Supplemental Materials.
Variables were tested independently in single variable linear regressions with the annual shoreline positions for each transect. The stepwise multiple regression was run with an additional independent variable, the median position of the shoreline during the previous year, to incorporate the potential for year-to-year 'memory' in shoreline position. Stepwise analyses were conducted in a forward manner for which the most significant variable was added by selecting the lowest p value at each step and limiting variables to p < 0.05.

Data availability
All data are publicly and freely available as noted in the "Methods" section and the references cited therein. The satellite-derived shorelines data for the Big Sur region can be visualized at http:// coast sat. wrl. unsw. edu. au/ (sites usa_CA_0163 and usa_CA_0162).