Tectonics as a Regulator of Shoreline Retreat and Rocky Coast Evolution Across Timescales

Posted on 10 Sep 2025 — The copyright holder is the author/funder. All rights reserved. No reuse without permission. — https://doi.org/10.22541/au.175753057.71942649/v1 — This is a preprint and has not been peer-reviewed. Data may be preliminary. Tectonics as a Regulator of Shoreline Retreat and Rocky Coast Evolution Across Timescales Cesar Gavrie Lopez 1 and Claire C. Masteller 1 1Washington University in St Louis September 10, 2025 Abstract Rocky coast morphology is shaped by interactions between wave action, sea level, and tectonics over millennial time scales. However, a clear and quantifiable signature of tectonic uplift on decadal to centennial shoreline retreat rates is outstanding. We isolate the contribution of tectonic uplift to setting shoreline retreat and shore platform morphology from other marine and geologic drivers across the West Coast of the USA. Specifically, we find that decadal-scale tectonic uplift, derived from tide gage records, exerts a significant and measurable control on shoreline retreat rates. Additional influences from wave action, shore platform morphology, and tidal range further contribute to the regional patterns in coastal erosion, and together these factors enable accurate prediction of retreat rates using a multivariate model. Our analysis also reveals robust, time-scale dependent relationships between uplift rate, shore platform morphology, and shoreline retreat. On decadal time scales, rapid tectonic uplift acts as a buffer, shielding the shore from wave action, slowing retreat, and corresponding with narrow shore platforms. On millennial time scales, higher uplift rates relate to wider shore platforms, reflecting greater cumulative shoreline retreat. These observations likely reflect the effects of episodic, seismically driven subsidence, which shifts wave action landward, enhancing wave-driven erosion. Through repeated cycles of uplift and subsidence, the seismic cycle amplifies both shore platform development and long-term retreat. Together, these findings highlight the critical role of tectonics in shaping shoreline retreat and driving landscape evolution timescales on active margins. 1 manuscript submitted to AGU Advances Tectonics as a Regulator of Shoreline Retreat and Rocky Coast Evolution Across 1 Timescales 2 3 Cesar G. Lopez1 and Claire C. Masteller1 4 1Department of Earth, Enviormental, and Planetary Sciences, Washington University in St. Louis, 5 St. Louis, MO, 63130 6 Corresponding author: Cesar G. Lopez ([email protected]) 7 8 Key Points: 9 • Marine and tectonic processes jointly shape rocky coast retreat, with uplift, tides and 10 waves as the dominant controls on modern retreat 11 • Uplift limits short-term retreat, but the effects of the seismic cycle drive a positive 12 scaling between uplift and retreat over millenia 13 • Forecasting rocky coast retreat requires accounting for uplift rates to better assess 14 future hazards along tectonically active margins 15 Abstract 16 Rocky coast morphology is shaped by interactions between wave action, sea level, and 17 tectonics over millennial time scales. However, a clear and quantifiable signature of tectonic 18 uplift on decadal to centennial shoreline retreat rates is outstanding. We isolate the 19 contribution of tectonic uplift to setting shoreline retreat and shore platform morphology from 20 other marine and geologic drivers across the West Coast of the USA. Specifically, we find that 21 decadal-scale tectonic uplift, derived from tide gage records, exerts a significant and 22 measurable control on shoreline retreat rates. Additional influences from wave action, shore 23 platform morphology, and tidal range further contribute to the regional patterns in coastal 24 erosion, and together these factors enable accurate prediction of retreat rates using a 25 multivariate model. Our analysis also reveals robust, time-scale dependent relationships 26 between uplift rate, shore platform morphology, and shoreline retreat. On decadal time scales, 27 rapid tectonic uplift acts as a buffer, shielding the shore from wave action, slowing retreat, and 28 corresponding with narrow shore platforms. On millennial time scales, higher uplift rates relate 29 manuscript submitted to AGU Advances to wider shore platforms, reflecting greater cumulative shoreline retreat. These observations 30 likely reflect the effects of episodic, seismically driven subsidence, which shifts wave action 31 landward, enhancing wave-driven erosion. Through repeated cycles of uplift and subsidence, 32 the seismic cycle amplifies both shore platform development and long-term retreat. Together, 33 these findings highlight the critical role of tectonics in shaping shoreline retreat and driving 34 landscape evolution timescales on active margins. 35 Plain Language Summary 36 Over half of the world’s coastlines are rocky, including the dramatic cliffs and wave-battered 37 platforms of the U.S. West Coast, where millions of people live along the shore. These 38 landscapes are shaped by waves, tides, sea level, and tectonics, but the direct influence of uplift 39 on shoreline erosion is not well understood. In this study, we provide the first quantitative 40 evidence that tectonic uplift plays a central role in shaping both short- and long-term rocky 41 coast change. We show that over decades, faster uplift continuously lifts the shore above the 42 zone of active erosion, narrowing wave attack zones, and slowing retreat. But over thousands 43 of years, higher long-term uplift rates are tied to wider platforms and greater cumulative 44 erosion, a signal of repeated cycles of earthquake-driven uplift and subsidence. Our results 45 suggest that coseismic subsidence along the Cascadia Subduction Zone will shift wave attack 46 landward, accelerating coastal retreat and amplifying future coastal hazards. Our findings show 47 that tectonics leave a clear and lasting imprint on shoreline retreat. As sea levels rise and 48 populations expand along tectonically active coasts, accounting for this link between uplift, 49 earthquakes, and erosion is critical for understanding future coastal change and hazards. 50 1 Introduction 51 Rocky coasts, which make up over 50% of the world's shorelines (Young & Carilli, 2019), are 52 shaped by the dynamic interplay of tectonic uplift, fluctuating sea levels, and the erosive power 53 of crashing waves (Adams et al., 2005; Anderson et al., 1999; Huppert et al., 2020). 54 Characterized by steep rock cliffs descending into the ocean, these landscapes archive climatic 55 and tectonic history in sequences of marine terraces formed and preserved during periods of 56 relative sea level change (Malatesta et al., 2022; Simms et al., 2015). Over millennial timescales, 57 manuscript submitted to AGU Advances the generation and preservation of marine terraces is controlled by the interactions between 58 tectonic uplift and oscillating sea level (Anderson et al., 1999; Malatesta et al., 2022). 59 Understanding the relationship between uplift rates and shoreline erosion is therefore critical 60 to interpreting coastal landscape evolution, reconstructing past tectonic activity, and predicting 61 future coastal erosion and hazards in tectonically active regions. 62 63 A preeminent conceptual model (Anderson et al., 1999) posits that the longevity of marine 64 terrace features is controlled by uplift-driven marine terrace generation, which raises coastal 65 bedrock above the area of wave attack, and progressive, wave-driven backwearing of the 66 coastline, which destroys these uplifted features. Thus, the preserved terrace record reflects a 67 balance between the constructive forces of tectonics and the destructive forces of erosion. 68 Malatesta et al., (2022) built on these ideas by demonstrating that relative rates of tectonic 69 uplift and sea level fluctuation jointly govern the duration and spatial extent of coastal 70 exposure to wave action, critically influencing the timing of marine terrace formation. Given 71 this well-established link between tectonics and erosion on geologic timescales, it stands to 72 reason that tectonic processes should also influence shoreline retreat over shorter, decadal to 73 centennial timescales. However, surprisingly little research has quantitatively linked tectonic 74 uplift rates to shoreline retreat rates over these timescales. Recent studies have shown that 75 relatively rapid modern uplift associated with discrete seismic events can almost instantly 76 modulate shoreline erosion by altering shore platform morphology and nearshore bathymetry 77 (Horton et al., 2022; Kennedy & Beban, 2005; Stephenson et al., 2017). Specifically, coseismic 78 uplift elevates the shore platform and shoreline, shifting the zone of wave action seaward and 79 reducing the frequency and intensity of wave impacts at the base of coastal cliffs. Indeed, this 80 mechanism was observed following the 2016 Mw 7.8 Kaikoura Earthquake, where uplifted 81 areas experienced a 30% reduction in wave energy and a corresponding suppression of coastal 82 erosion rates (Horton et al., 2022; Stephenson et al., 2017). While these case studies illustrate 83 the potential for tectonic uplift to affect short-term erosion rates, to our knowledge, no study 84 manuscript submitted to AGU Advances has yet demonstrated a general, quantitative correspondence between tectonic uplift and 85 shoreline retreat rates at decadal to centennial timescales. 86 87 Most studies focusing on shoreline retreat over these timescales emphasize the impacts of 88 marine forcings – including offshore wave climate (Allan & Komar, 2002, 2006; Barkwith et al., 89 2014) and tidal range (Lim et al., 2011; Young et al., 2016). However, the impact of these 90 forcings on erosion is not uniform along the coast; instead, it is filtered by nearshore processes 91 that govern how wave energy is transformed and delivered to the coastline. Offshore wave 92 energy is dissipated by wave shoaling and breaking, which are controlled by the width and 93 gradient of the shore platform (Horton et al., 2022; Marshall & Stephenson, 2011; Stephenson 94 et al., 2017). Waves that break closer to shore lose less energy before reaching the coast, 95 resulting in more effective energy transfer, evidenced by enhanced ground motions recorded 96 by cliff-top seismometers (Thompson et al., 2019) and correspondingly higher rates of cliff 97 erosion (Trenhaile, 2000). However, the relationship between these marine forcings and 98 shoreline retreat can also be obscured by the strength of coastal bedrock, as more resistant 99 material often erodes slowly even under intense wave attack (Benumof et al., 2000). At the 100 same time, tidal range influences the vertical distribution of wave attack on rocky coasts, 101 modulating the spatial extent and cumulative delivery of wave energy (Adams et al., 2005; Lim 102 et al., 2011). This interplay of waves, tides, and cliff lithology, superimposed on a background of 103 spatially variable tectonic uplift, often obscures the relationship between any single driver and 104 observed shoreline retreat across regions. 105 106 The West Coast of the USA provides a valuable natural laboratory for disentangling the imprint 107 of active tectonic uplift on rocky coastlines due to its setting along the North American Plate 108 margin (Figure 1A). Along the southern half of the coastline, the margin is largely within the San 109 Andreas Fault Zone, dominated by strike-slip motion and relatively low uplift rates except 110 within localized zones of transpression near restraining bends (Anderson, 1990; McGregor & 111 Onderdonk, 2021). To the north, uplift rates increase significantly near the Mendocino Triple 112 Junction, where the San Andreas Fault System transitions into the Cascadia Subduction Zone – a 113 manuscript submitted to AGU Advances megathrust fault formed by subduction of the Gorda and Juan de Fuca Plates, characterized by 114 high uplift rates (Furlong & Schwartz, 2004; Walton et al., 2021). In this region, tectonic uplift 115 rates have been previously reported across a range of temporal scales, with millennial uplift 116 rates derived from marine terrace records (Padgett et al., 2019; Simms et al., 2015, 2020), to 117 decadal uplift rates derived from tide gage records (Zervas et al., 2013.) to daily measurements 118 using GNSS measurements (Blackwell et al., 2020; Govorcin et al., 2025; Hammond et al., 2018). 119 Coupled with a well-constrained uplift gradient, strong north-south wave power variability, and 120 extensive lithologic, bathymetric, tidal, and shoreline retreat data (Fig. 1, Methods), this region 121 offers distinct opportunities to evaluate the links between tectonics and coastal erosion. 122 123 This study is further motivated by the need to better understand the role of active tectonics in 124 shaping modern geomorphic processes and to support more direct and accurate incorporation 125 of this influence into coastal hazard assessments. By isolating the effect of tectonics from wave 126 action, lithology, and tidal range, we may both improve predictive models of coastal evolution 127 on active margins and refine interpretations of the geomorphic record preserved in marine 128 terraces and rocky shorelines. This is of particular importance along the USA West Coast, where 129 the intersection of rising sea levels (Ashton et al., 2011; Shadrick et al., 2022), increasingly 130 powerful waves (Reguero et al., 2019), and variable vertical land motion (Dura et al., 2025; 131 Govorcin et al., 2025) presents a complex and evolving coastal hazard landscape. Further, uplift 132 and subsidence linked to seismic deformation can directly drive sea cliff failure, mass wasting 133 (Bloom et al., 2023) and catastrophic inundation (Walton et al., 2021). Given the region’s large 134 population, infrastructure, and economic significance, assessing the effects of tectonic uplift on 135 modern coastal erosion and cliff retreat on decadal is necessary for coastal hazard management 136 and predicting future landscape change (Bird, 1994; Young, 2018). 137 138 manuscript submitted to AGU Advances 139 Figure 1. A) Tectonic setting of the U.S. West Coast with arrows denoting plate motion with 140 virtual buoys (blue) and corresponding rock shore sites (orange); (B) marine-terrace derived 141 uplift rates (mm/yr) binned by latitude; (C) tide gage derived uplift rates (mm/yr); (D) median 142 offshore wave power (kW/m) calculated from virtual buoys; (E) shore platform width (m); (F) 143 median normalized wave power (kW/m2); (G) median tidal range (m); (H) tensile rock strength 144 (MPa); (I) shoreline change rate (m/yr). 145 146 2 Materials and Methods 147 To systematically evaluate the relative contributions of tectonic uplift, wave climate, 148 lithology, and tidal range to coastal morphology and shoreline retreat, we compile a suite of 149 spatial datasets spanning the U.S. West Coast that characterize each of these key controls and 150 allow for their direct comparison with observed erosion rates. Offshore wave power (kW/m) is 151 derived from a 43-year hindcast model record of hourly significant wave heights and periods 152 (SI) from 51 virtual buoys (Wave Information Study), each located within 25 km of shore at 153 depths >20 m in areas containing sea cliffs. We do not consider sites classified as sandy shores 154 or marine bluffs comprising unconsolidated deposits to avoid the complicating effects of littoral 155 sediment transport. 156 To account for local dissipation of wave energy and constrain shore platform 157 morphology, 2 km wide swath profiles are extracted from 1/3 arc-second resolution 158 bathymetric datasets (NOAA National Centers for Environmental Information) extending from 159 each virtual buoy to the shoreline along each buoy-specific dominant wave direction. We then 160 Virtual Buoys Shore Sites 200 2.42.01.6 0.60.40.2510150.00.510030100 200.02.5-2.5 Mendocino Triple Junction -128º-126º-124º-122º -118º-116º-120º 32º 34º 36º 38º 40º 44º 44º44º44º44º44º44º 41º41º41º 41º 41º41º41º41º 39º39º39º39º39º39º39º39º 37º37º37º37º37º37º37º37º 33º33º33º33º33º33º33º 35º35º35º35º35º35º35º35º 33º 1.0 Millennial Uplift Rate (mm/yr) Decadal Uplift Rate (mm/yr) Wave Power (kW/m) Normalized Wave Power (kW/m2) Tidal Range (m) Platform Width (m) Tensile Rock Strength (MPa) Shoreline Change Rate (m/yr) 0.5 42º 46º 44º 44º N Pacific Plate IHGFEDCBA Oregon California North American Plate San Andreas Fault Juan de Fuca Plate Gorda Plate 300 km Cascadia Subduction Zone manuscript submitted to AGU Advances apply linear wave theory to perform nearshore wave transformations on the buoy-reported 161 wave heights along each swath profile to identify where depth-dependent wave breaking 162 criteria is met for the entire distribution of offshore wave measurements (SI). We then 163 determine the surf zone width (m) based on the shoreward and seaward bounds of offshore 164 wave breaking distances. We then normalize offshore wave power by the surf zone width to 165 generate a normalized wave power metric (kW/m2), which implicitly incorporates the effects of 166 local bathymetry on wave energy dissipation and more accurately captures the translation of 167 offshore wave power to the shore. Because the region of wave action is an important constrain 168 on the development of shore platforms (Kennedy, 2015; Sunamura, 1991, 1992), shore 169 platform width is estimated from both topographic breaks and seaward and shoreward bounds 170 of wave breaking at each site. Given that most sites contain type-A platforms, shore platform 171 and surf zone width are equivalent for the majority of sites (SI) 172 Rock strength, representing the resistance of coastal cliffs to wave attack, is estimated 173 for each site from regional geologic maps (“Geologic Maps and Mapping, California Department 174 of natural Resources.; “Oregon Department of Geology and Mineral Industries : Geologic Map 175 of Oregon : Geologic Map : State of Oregon,” n.d.) (California Department of Conservation; 176 Oregon Department of Geology and Mineral Industries) and laboratory measurements of 177 tensile and compressive rock strength for the mapped lithologies (SI, Table S1). Tidal range, 178 which governs the vertical distribution of wave attack, is calculated using NOAA tide gauge 179 records as the mean difference between Mean Higher High Water (MHHW) and Mean Lower 180 Low Water (MLLW), relative to the MLLW over an 18-year epoch (NOAA Tides and Currents) 181 Similarly, mean sea level is the average of hourly sea level heights observed over the same 182 epoch relative to the MLLW. 183 Shoreline retreat rates are estimated from long-term measures of changes in lateral 184 shoreline extent over a period from the late 1800s to the early 2000s for the entire West Coast 185 from a series of USGS reports (Hapke & Reid, 2007; Ruggerio et al., 2013). Each site is assigned 186 a retreat rate (m/yr) based on the mean shoreline change rate of the littoral cell which a given 187 site lies in. 188 manuscript submitted to AGU Advances Long-term, millennial-scale uplift rates are derived from dating marine terraces and 189 corrected for glacial-isostatic adjustment. Uplift rates correspond to MIS 5a terraces as this is 190 the most recent dating stage (Padgett et al., 2019; Simms et al., 2015, 2020). Decadal scale 191 uplift rates are estimated from local sea level trends recorded at tidal gauges, while accounting 192 for eustatic sea level trends (Zervas et al., 2013) and shorter-term, daily uplift rates are 193 compiled from vertical land velocity estimates at GNSS stations (Kreemer et al., 2014; NSF 194 GAGE). 195 Virtual buoy sites are used as anchor points because they offer a spatially extensive 196 dataset while providing important estimates of offshore wave climate and nearshore 197 bathymetry. This allows us to explore how differences in wave power and nearshore geometry 198 interact with more regionally consistent tectonic, marine, and geologic conditions. Other 199 datasets utilized in this study, including tidal range, uplift rates, and shoreline retreat are more 200 spatially sparse, requiring binning by littoral cell or spatial proximity to ensure complete 201 coverage. Similarly, since site-specific rock strength measurements do not exist, estimates are 202 based on binned value ranges from the literature (SI). While this results in a mix of continuous 203 and ordinal variables, this approach enables the most comprehensive, spatially resolved 204 analysis possible. 205 To assess the relative importance and explanatory power of the variables, we first 206 compute variance inflation factors (VIF) to evaluate potential collinearity among input variables 207 and to ensure that each represents an independent potential control on shoreline retreat. We 208 remove or reduce any variables with VIF values exceeding 2. We then use a random forest 209 classification, a machine learning approach that excels in situations where underlying 210 relationships between predictors and response variables may be nonlinear or interactive. This 211 approach does not assume a specific functional form between input variables and the response 212 variable, making it appropriate for elucidating controls on shoreline retreat, where interactions 213 between tectonic, marine, environmental, and lithologic variables are likely to be non-additive 214 and may involve thresholds or nonlinear responses. Random forests provide feature 215 importance rankings, allowing us to identify which predictors most strongly explain observed 216 spatial patterns in shoreline change, without imposing a priori expectations about their roles or 217 manuscript submitted to AGU Advances relationships (Biau & Scornet, 2016). Random forest is implemented through python’s Ski-Learn 218 Random Forest Classifier or Regressor. Each variable’s importance score is determined through 219 the normalized total reduction of Gini Impurity, a measure of how accurately a randomly 220 chosen element is classified (Menze et al., 2009). Higher importance scores indicate reduced 221 Gini impurity and are therefore more important for the model’s decisions and ability to predict 222 the target process or variable. 223 We then use a multivariate linear regression to assess whether the top-ranked features 224 identified by the random forest model reliably predict shoreline retreat. While this approach 225 assumes a linear relationship, it provides an interpretable hypothesis test to quantify the 226 significance and directionality of individual effects. This approach allows us to determine 227 whether a shoreline retreat model incorporating tectonic, marine, and lithologic drivers 228 outperforms simpler approaches considering individual drivers, such as offshore wave power. 229 By first ensuring low collinearity, then agnostically identifying key variables, and finally 230 quantifying their combined predictive power, this approach allows us to rigorously evaluate the 231 extent to which tectonic uplift, wave action, lithology, and tidal range shape rocky coastline 232 evolution across the U.S. West Coast. 233 Finally, we also perform bivariate analyses on our data by utilizing Spearman’s ρ and 234 Kendall’s τ correlation coefficients. We further verify the robustness of these correlations by 235 implementing permutation tests to produce a distribution of correlation coefficients for both ρ 236 and τ, which we then compare to the actual observed correlations to obtain a p-value indicating 237 how extreme the observed correlations are under the null-hypothesis assumption (SI). We find 238 that the actual correlations in the data are in fact significant, affirming their importance as 239 indicators of the controls on coastal retreat and shore morphology on the West Coast. 240 3 Results and Discussion 241 3.1 Modern Drivers of Rocky Coast Erosion 242 Based on compiled datasets, random forest classification reveals that tide gage-derived 243 decadal uplift rate, tidal range, and normalized wave power (offshore wave power divided by 244 surf zone width) are the strongest predictors of shoreline retreat along the West Coast (Figure 245 manuscript submitted to AGU Advances 2A). To ensure robust interpretation of individual predictors, only variables with low 246 multicollinearity, indicated by variance inflation factors (VIF) below 2, were included in 247 classification (Methods). Feature importance scores from random forest classification denote 248 the relative significance of a given variable in predicting shoreline retreat rates, with tidal range 249 holding the highest feature importance score (0.259), followed by tide gage-derived, decadal 250 uplift rates (0.219), and normalized wave power (0.207). Together, these three drivers account 251 for more than 68% of the total model importance, while the remaining predictors of marine 252 terrace-derived millennial uplift (Padgett et al., 2019; Simms et al., 2015, 2020), GNSS-derived 253 vertical velocities, and tensile rock strength, contribute the remaining 32%. These findings are 254 corroborated by a three-variable, multivariate linear regression, in which tidal range, decadal 255 uplift rate, and normalized wave power all yield T-scores greater than 2 and p-values less than 256 0.05, confirming their statistical and predictive significance (Figure 2B, Methods). Notably, tidal 257 range and decadal uplift rate have T-scores exceeding 3, indicating relatively strong predictive 258 power. The resulting multivariate model yields an R2=0.51 between predicted and observed 259 retreat rates, indicating that these three variables explain just over half of the observed 260 variance in retreat rates. Given the geomorphic and tectonic complexity of the U.S. West Coast 261 compared to more spatially focused studies (Benumof et al., 2000; Horton et al., 2022; Huppert 262 et al., 2020), this represents a strong imprint of these factors on patterns of shoreline retreat. It 263 is worth noting here that a multivariate regression including all six variables yields similar 264 results: decadal uplift rate, tidal range, and normalized wave power remain statistically 265 significant predictors, while marine terrace-derived uplift rate, GNSS-derived uplift rate, and 266 tensile rock strength do not significantly improve the model’s explanatory power. 267 Importantly, our analysis identifies tectonic uplift, particularly as captured by decadal 268 tide gage-derived rates, as a previously underrecognized modulator of modern rock coast 269 erosion. The particular predictive strength of tide gage-derived uplift rates relative to marine 270 terrace- and GNSS-derived rates likely reflects the temporal alignment of this metric and the 271 shoreline change records, which are measured over a comparable, multi-decadal period. As 272 such, decadal uplift rates capture the cumulative impact of vertical land motion on the zone of 273 wave action during the same period during which shoreline change is measured. In contrast, 274 manuscript submitted to AGU Advances longer-term uplift proxies like marine terraces or shorter-term, GNSS-derived vertical velocities 275 are as directly representative of the uplift history relevant to measured shoreline response used 276 in this study. 277 278 279 Figure 2. (A) Importance scores for compiled datasets, with scores greater than 0.15 denoted 280 by solid bars; (B) Comparison of predicted (Epred (m/yr)) and reported (E (m/yr)) shoreline 281 retreat rates from multivariate linear regression using variables with importance scores greater 282 than 0.15; (C) Shoreline retreat rate, E (m/yr), as a function of tide-gage derived, decadal uplift 283 rate, UD (mm/yr), overlapping points are jittered for visibility. Inset shows histogram of 284 Spearman’s ρ values from permutation tests compared the observed Spearman’s ρ (pink 285 dashed line). 286 287 We find a significant negative relationship between decadal uplift rate and shoreline 288 retreat rate (Spearman's ρ = -0.3480, Kendall's τ = -0.2783, p<0.05, Fig. 2C), consistent with 289 prior observations of decreased wave energy delivery following coseismic uplift (Horton et al., 290 2022; Wayne J. Stephenson et al., 2017). Rapid uplift continually raises the shore out of the 291 active zone of wave impact, replenishing the cliff base with fresh material and limiting the 292 exposure duration of any rock parcel. This process precludes progressive backwearing (Uesawa 293 & Miyakawa, 2015), undercutting, and the formation of basal notches, which can lead to cliff 294 destabilization and collapse (Kline et al., 2014; Rosser et al., 2013; Trenhaile, 2015). At the same 295 time, uplifting the shore platform reduces nearshore water depth, shifting wave breaking 296 seaward and enhancing energy dissipation in the near shore (Stephenson et al., 2017). 297 Together, these effects act to tectonically buffer the coastline by reducing the efficiency of 298 wave-driven retreat by disrupting the spatial and temporal continuity of wave attack. In 299 contrast, rapid land level fall enhances shoreline retreat (Fig. 2C). Subsidence of the coastline 300 submerges previously wave-sheltered surfaces, expanding the reach of wave action and 301 Importance Score Tensile Rock Strength Millennial Uplift Rate Vertical Land Velocity Normalized Wave Power Decadal Uplift Rate Tidal Range 0.250.200.150.100.050.0 -3 0.7 0.3 1-2 -1 20 0.2 0.5 0.6 0.4 Study sites Linear best-fit & 95% conf. interval 0.2 0.3 0.5 0.6 0.7 0.4 0.1 0.0 Reported Shoreline Retreat Rate, E (m/yr) 0.6 0.70.50.40.3 Variable T-score P-value VIF Normalized Wave Power 2.105 0.0407 1.290 Tidal Range 3.169 0.0027 1.375 Decadal Uplift -3.469 0.0011 1.075 0.2 R2 = 0.51 Predicted Shoreline Retreat Rate, Epred (m/yr) Decadal Uplift Rate, UD (mm/yr) Shoreline Retreat Rate, E (m/yr) ρ = -0.32, p = 0.023 τ = -0.22, p = 0.022 E = -0.05UD + 0.30 A B CTheil-Sen fit Spearman's ρ 0 400 0.40 p=.01 Frequency 800 Spearman's ρ -0.4 manuscript submitted to AGU Advances exposing a larger portion of the shoreline and cliff face to erosion. Land-level lowering also 302 deepens nearshore water depths, narrowing the active surf zone by shifting wave breaking 303 landward, reducing wave energy dissipation and concentrating wave energy delivery. 304 While the influence of tectonic uplift emerges as particularly important driver of 305 modern shoreline retreat, our results also highlight the importance of both tidal range and 306 normalized wave power in shaping how much wave energy reaches the coastline and the 307 spatial footprint over which it is delivered. The high importance of tidal range reinforces the 308 role of vertical wave reach in governing coastal erosion (Ruggiero et al., 2001; Trenhaile, 2000). 309 Larger tidal range expands the elevation band subject to wave attack, intensifying cliff ground 310 motions and increasing the likelihood of retreat (Adams et al., 2002; Lim et al., 2011; Trenhaile, 311 2019; Young et al., 2011, 2016). Our multivariate model confirms a positive correlation 312 between tidal range and shoreline retreat, such that areas with greater tidal range generally 313 result in more rapid retreat rates. These findings are consistent with previous field and 314 modeling studies that find that higher tide levels drive greater sea cliff erosion (Matsumoto et 315 al., 2016; Trenhaile, 2000; Vann Jones et al., 2015). 316 Our analysis also shows that normalized wave power, calculated as offshore wave 317 energy divided by local surf zone width, is a strong predictor of rocky coastline retreat and 318 highlights the importance of nearshore wave transformation in shaping erosion patterns. This 319 metric incorporates both the magnitude of offshore wave energy and the degree of energy 320 dissipation across the active surf zone, which we estimate using a depth-based wave breaking 321 criterion and site-specific bathymetry (Methods). By accounting for variations in both offshore 322 forcing and local morphology, normalized wave power captures how efficiently wave energy 323 reaches the shoreline. Our multivariate model reveals a strong positive relationship between 324 normalized wave power and shoreline retreat, consistent with previous observational and 325 modeling studies (Alessio & Keller, 2020; Huppert et al., 2020; Limber et al., 2014; Thompson et 326 al., 2019). Increases in normalized wave power can result either from a more energetic offshore 327 wave climate or a narrower surf zone. In both cases, more wave energy is retained and 328 delivered to the shoreline, increasing the erosive potential of incident waves and accelerating 329 retreat. The significance of this predictor reinforces the notion that shoreline retreat is not 330 manuscript submitted to AGU Advances governed by wave climate alone, but also by local shore platform morphology (Lim et al., 2013; 331 Vann Jones et al., 2018). This morphology-dependent dissipation strongly influences the energy 332 retention of incident waves, which in turn modulates their erosive power (Horton et al., 2022; 333 Stephenson et al., 2017). 334 Despite past studies finding a primary role of rock strength in modulating cliff retreat 335 rates (Benumof et al., 2000), in our analysis, rock strength emerges as a surprisingly weak 336 predictor of shoreline retreat. Tensile rock strength holds the lowest importance score in the 337 random forest classification (Figure 2A). Further, while bivariate correlations show a positive 338 relationship between both tensile and compressive rock strength and retreat rates (Spearman’s 339 ρ = 0.43–0.44, Kendall's τ = 0.38-0.39, p < 0.05), this contrasts with prior work suggesting 340 stronger rocks are more resistant to erosion (Benumof et al., 2000; Budetta et al., 2000; 341 Thornton & Stephenson, 2006). This finding reinforces the dominant role of marine forcings and 342 tectonic uplift over lithologic resistance in shaping modern rock coast evolution across the U.S. 343 West Coast. 344 The combined influence of normalized wave power and tidal range captures how both 345 the horizontal and vertical extent of wave attack shape shoreline retreat, reinforcing the central 346 roles of coastal morphology and marine forcings in focusing or diffusing wave energy. This 347 finding agrees with field observations and key elements of process-based models for rocky 348 coast retreat (Dornbusch et al., 2008; Trenhaile, 2000). Our study reveals that decadal tectonic 349 uplift acts as a powerful modulator of these marine forcings by governing the persistence of 350 wave attack at any given elevation and shifting the locus of erosion on or offshore. Together, 351 these findings demonstrate that rocky coast erosion reflects the combined influence of vertical 352 land motion, wave energy delivery, and tidal forcing, each shaped by the evolving coastal 353 morphology. To our knowledge, this is the first study to quantify the relative contribution of 354 decadal-scale tectonic uplift to shoreline retreat rates on rocky coastlines, highlighting tectonics 355 manuscript submitted to AGU Advances not just as a passive backdrop but as an important governor that can amplify or buffer the 356 effects of changing marine conditions. 357 3.2 Shore Platform Evolution and the Seismic Memory of Rocky Coasts 358 Our results demonstrate that modern shoreline retreat rates are partially governed by 359 decadal uplift rates. Additionally, the high relative importance and predictive power of 360 normalized wave power highlights the fundamental role of wave transformation and dissipation 361 within the surf zone. Wave dissipation is primarily controlled by shore platform morphology, 362 especially platform width, which governs where waves break relative to the coastline (Vann 363 Jones et al., 2018). In turn, the width of the shore platform also reflects the longer-term effects 364 of cliff erosion, driven by progressive backwearing over thousands of years (Clow et al., 2023; 365 De Lange & Moon, 2005; Payo et al., 2015). In this context, the shore platform serves as a 366 cumulative record of coastal retreat prior to abandonment, after which the platform is 367 preserved as a marine terrace (Anderson et al., 1999). 368 Because uplift and erosion are coupled over modern timescales (Fig. 2), we expect 369 platform width, which preserves this erosive history, to also relate to uplift rate. Indeed, we 370 find a significant, negative correlation between decadal uplift rate and shore platform width 371 (Spearman’s ρ = -0.3714, Kendall's τ = -0.2673, p<0.05; Fig 3A), directly reflecting the observed 372 modern relationship between shoreline retreat and decadal uplift (Spearman's ρ = -0.3480, 373 Kendall's τ = -0.2783, p<0.05; Fig. 2C), further supporting the interpretation that tectonic uplift 374 buffers coastal backwearing and limits shore platform development (Horton et al., 2022; 375 Stephenson et al., 2017). 376 In contrast, modern shore platform widths exhibit a significant, positive correlation with 377 marine-terrace derived, millennial uplift rates (Spearman’s ρ = 0.3550, Kendall's τ = 0.2464, 378 p<0.05; Fig. 3B), similarly reflected by a positive correlation between modern retreat rates and 379 millennial scale uplift (Spearman's ρ = 0.3199, Kendall's τ = 0.2461, p<0.05). These uplift rates, 380 derived from Marine Isotope Stage (MIS) 5a terraces, represent the last interglacial highstand 381 (Simms et al., 2015). Because these terraces reflect the last surfaces abandoned by wave action, 382 the width of the underlying modern shore platform likely records the cumulative erosion that 383 manuscript submitted to AGU Advances has occurred since their uplift. The observed positive correlation suggests that, over millennia, 384 higher uplift rates are associated with the development and preservation of wider shore 385 platforms, implying more efficient cumulative shoreline retreat and coastal erosion over these 386 timescales. 387 388 389 Figure 3. (A) Shore platform width, W (m) as a function of tide gage-derived decadal uplift rate, 390 UD (mm/yr); (B) Shore platform width, W (m) as a function of marine terraced-derived, 391 millennial uplift rate, UM (mm/yr). Insets show histogram of Spearman’s ρ values from 392 permutation tests relative to the observed Spearman’s ρ (teal dashed line). 393 394 The positive correlation revealed in our analysis directly contrasts predictions from 395 models of marine terrace formation, which suggest that higher uplift rates should lead to 396 narrower terraces due to the vertical smearing of wave attack and reduced backwearing as cliff 397 rock is rapidly removed from the cliff base and replaced by fresh, uneroded material (Anderson 398 et al., 1999; Uesawa & Miyakawa, 2015). However, these models typically consider constant 399 uplift rates superimposed on either constant sea level (Uesawa & Miyakawa, 2015) or a 400 fluctuating sea level curve spanning multiple glacial-interglacial cycles (Anderson et al., 1999). 401 By doing so, they represent time-averaged, net uplift rates, when in reality, uplift along much of 402 West Coast – especially in Cascadia – is not steady. Instead, vertical motion is temporally 403 variable and driven by cyclic land-level rise and fall driven by the earthquake deformation cycle. 404 Taken together, our observations suggest that the contrasting relationships between shore 405 0 400 1000 600 200 800 Frequency 0.4 0 400 1000 600 200 800 Frequency -0.2 0.20.0 0.25-0.25-0.4 Spearman's ρ p = 0.0073 0.0 0.5 p = 0.0108 -0.5 Spearman's ρ W = -18.57UD + 76.02 Decadal Uplift Rate, UD (mm/yr) Shore Platform Width, W (m) Shore Platform Width, W (m) Millennial Uplift Rate, UM (mm/yr) BA Theil–Sen Fit Cascadia San Andreas Spearman's ρ W = 48.78UM + 48.83 manuscript submitted to AGU Advances platform width and shoreline retreat rates across timescales reflect how both the style and 406 relative magnitude of uplift and erosion vary through time, shaping coastal morphology in 407 different ways depending on the temporal scale of analysis. 408 On decadal timescales, tectonic uplift along the U.S. West Coast primarily reflects 409 interseismic strain accumulation. In the Cascadia Subduction Zone vertical motion is driven by 410 the gradual elastic deformation of the overriding plate between megathrust earthquakes 411 (Walton et al., 2021). Along the San Andreas Fault Zone, interseismic strain is driven by fault 412 locking at depth, resulting in more localized differences in uplift rate (Smith & Sandwell, 2006; 413 Smith-Konter et al., 2014). While the style of interseismic deformation differs between these 414 tectonic settings, regional elastic shortening in Cascadia versus localized uplift or subsidence 415 and flexure along the San Andreas, the tide gage-derived uplift rates span a similar range across 416 both regions (Fig. 3A). The main exceptions are two rapidly subsiding sites in central Oregon, 417 associated with localized forearc subsidence near the downdip end of the locked megathrust 418 (Malatesta et al., 2021; Oryan et al., 2024). Despite the differences in tectonic style and 419 structure between these two major faults, decadal uplift rates correspond closely with regional 420 patterns in shoreline retreat and shore platform width, reinforcing the role of interseismic 421 strain as a dominant short-term control on rocky coast erosion. 422 On the millennial times scales, marine terrace-derived uplift rates integrate multiple 423 seismic cycles and longer-term deformation patterns, reflecting the net vertical displacement of 424 the coastline over thousands of years (Fig. 4A). In Cascadia, these millennial scale, terrace-425 derived uplift rates include cycles of interseismic uplift followed by abrupt coseismic subsidence 426 (Leonard et al., 2010; Walton et al., 2021). Building on our modern analysis of the quantitative 427 relationship between uplift and shoreline retreat (Fig. 2C), we infer that rapid coseismic 428 subsidence amplifies erosion by abruptly shifting the wave attack zone landward and exposing 429 previously protected surfaces to direct wave impact. While interseismic uplift can buffer 430 erosion, this protective effect is episodically undone by subsidence. In Cascadia, more rapid 431 interseismic uplift is often paired with more pronounced subsidence (Chapman & Melbourne, 432 2009; Stanton et al., 2024), thus the net effect across seismic cycles favors enhanced 433 backwearing and the horizontal expansion of the shore platform. This process-based 434 manuscript submitted to AGU Advances interpretation aligns with the positive correlation we observe between terrace-derived uplift 435 rates and shore platform width (Fig. 3B), supporting the idea that, over millennial timescales, 436 coastal landscape evolution is predominately shaped by the cumulative effects of shoreline 437 backwearing during repeated periods of enhanced wave attack. 438 This effect is recorded not only in the width of the modern shore platform (Fig. 1E) but 439 also preserved in relatively wide marine terraces of Cascadia (SI; Fig. S2). These morphologic 440 patterns are also consistent with broader-scale submarine topography. Along the Cascadia 441 margin, the location of the continental shelf break consistently aligns with the downdip limit of 442 megathrust coupling, a pattern attributed to a long-term balance between permanent 443 interseismic uplift and wave erosion over hundreds of seismic cycles (Malatesta et al., 2021). By 444 isolating the modern relationship between uplift and rock coast retreat rates, our results offer a 445 mechanistic basis linking these processes to the morphologic signatures of enhanced shore 446 platform development over geologic timescales (Fig. 3B, 6) and highlighting the critical role of 447 the seismic cycle that is often overlooked in conventional coastal landscape evolution models 448 (Fig. 4). 449 In the predominantly strike-slip San Andreas Fault Zone, time-variable uplift driven by 450 interseismic strain and localized fault geometry (Grove et al., 2010), coseismic rupture 451 influenced by local compressional or extensional regimes (Smith-Konter et al., 2014), and fault 452 creep (Johnson & Segall, 2004; Lindsey et al., 2014) produce a comparable range of millennial 453 uplift rates to Cascadia (Fig. 1B, Fig. 3B). However, unlike Cascadia, where coseismic subsidence 454 commonly lowers the coastline, the San Andreas Fault Zone can experience localized coseismic 455 uplift depending on the local stresses present (55; Fig 4B), especially in regions of transpression 456 along restraining bends in the fault (Anderson, 1990; Anderson & Menking, 1994; Mueller & 457 Suppe, 1997). Because retreat rates peak during subsidence or more gradual uplift phases, the 458 coastlines across these regions respond differently following earthquakes: Cascadia’s rapid 459 coseismic subsidence accelerates coastal retreat, whereas San Andreas’ coseismic uplift rapidly 460 slows it. Though the timing and magnitude of backwearing peak at different stages of the 461 earthquake cycle in each tectonic setting (Fig. 4), the integrated effect of repeated uplift and 462 erosion over many seismic cycles produces a consistent geomorphic outcome. This is reflected 463 manuscript submitted to AGU Advances in the robust correlation between millennial uplift rates, shoreline retreat, and shore platform 464 width, emphasizing cumulative backwearing during periods of slow uplift or subsidence as the 465 primary long-term driver of coastal morphology (Fig. 3B, 4). 466 The strong correspondence between shore platform width and millennial-scale uplift is 467 likely also informed by relative differences in coastal backwearing rates and time-averaged 468 uplift rates. Modern shoreline retreat rates exceed terrace-derived uplift rates by over an order 469 of magnitude (Fig. 1B, SI), meaning that over geologic timescales, lateral cliff retreat is likely to 470 far outpace net uplift rates. It’s also worth emphasizing that backwearing rates outpace 471 measured shore platform downwearing rates (Stephenson et al., 2010; Trenhaile & Porter, 472 2018) because the shear stresses exerted on the seabed and shore platform are weaker than 473 the forces at the water surface (Stephenson & Kirk, 2000; Trenhaile & Kanyaya, 2007). This 474 imbalance means that erosion is primarily expressed through the landward retreat of the 475 coastline, rather than the vertical lowering of the platform. Because backwearing rates exceed 476 both uplift and downwearing rates, platform widening will continue as long as wave energy can 477 reach the shore. This suggests that a horizontal, steady state equilibrium profile is likely not 478 attainable for shore platforms (Dickson et al., 2013) without invoking changes in sea level. 479 However, backwearing rates may decrease over time due to increasing wave energy dissipation 480 as the platform continues to broaden. While shore platform width is a record and manifestation 481 of cliff backwearing (De Lange & Moon, 2005; Payo et al., 2015) we find no strong correlation 482 between decadal erosion rates and platform width - highlighting the importance of legacy 483 processes and cumulative effects over longer timescales. Cosmogenic dating across shore 484 platforms could further constrain the decadal versus millennial trends we identify in this study 485 manuscript submitted to AGU Advances and bolster the relationship between retreat rates and platform width (Clow et al., 2023; Hurst 486 et al., 2017). 487 488 489 Figure 4. Conceptual diagrams for the (A) Cascadia Subduction Zone (orange) and (B) San 490 Andreas Fault Zone (blue), depicting the relationship between tectonic uplift (top) and both 491 short-serm shoreline retreat rate (bottom, gray) and cumulative, long-term retreat (bottom, 492 orange and blue), across multiple seismic cycles. Uplift curves are based on observed and 493 theoretical deformation patterns (Beavan & Litchfield, 2012; Sea-Level Rise for the Coasts of 494 California, Oregon, and Washington, 2012; Wesson et al., 2015). 495 496 3.3 Forecasting Rocky Shoreline Retreat and The Diminishing Tectonic Buffer 497 Our results demonstrate that tectonic uplift exerts a significant, timescale-dependent 498 control on rocky coast morphology and shoreline retreat along the U.S. West Coast. Over 499 decadal time scales, tectonic uplift buffers to shoreline retreat by enhancing nearshore 500 dissipation of wave energy and inhibiting basal notch development. However, this protective 501 tectonic buffering effect is likely to be increasingly offset by accelerating sea level rise. In many 502 locations, global sea level rise is already outpacing vertical land motion, effectively reducing 503 tectonic uplift rates (Sweet et al., 2017, 2022). As sea level rises faster than the land surface, 504 Coseismic Subsidence Net Uplift Interseismic Uplift A Uplift (m) EQEQ Cascadia Subduction Zone Time Retreat Rate (m/yr) Time Net Uplift B Uplift (m) Coseismic Uplift Intereismic Subsidence Time EQ Cumulative Retreat (m) Time Retreat Rate (m/yr) Cumulative Retreat (m) San Andreas Fault Zone EQ manuscript submitted to AGU Advances even tectonically uplifting coasts will experience a net relative fall in elevation, shifting wave 505 action landward, increasing the potential for cliff erosion. The loss of this natural buffer, 506 combined with intensifying wave climate (Reguero et al., 2019; Young et al., 2011), stands to 507 significantly amplify shoreline retreat rates across coastlines on active margins. Yet, most 508 existing rock coast erosion models that focus on short-term morphodynamics do not directly 509 incorporate vertical land motion, including uplift or subsidence (Matsumoto et al., 2016; 510 Trenhaile, 2000; Walkden & Hall, 2005). While sea level rise has been linked to enhanced cliff 511 erosion in soft rock environments (Ashton et al., 2011; Dickson et al., 2007; Shadrick et al., 512 2022), the capacity of tectonic deformation to mediate or intensify these effects remains poorly 513 integrated into forecasts of future rocky coast erosion (Govorcin et al., 2025). Incorporating 514 vertical land motion into rocky coast evolution models may help to improve coastal hazard 515 assessments and guide long-term adaptation strategies in tectonically active regions. 516 Despite the well-recognized role of tectonic deformation in modulating relative sea-517 level change (Harvey et al., 2021; Wöppelmann & Marcos, 2016), its influence on the mechanics 518 and rates of cliff retreat, distinct from the problem of inundation, remains poorly understood. 519 Our analysis isolates the influence of tectonic uplift on modern shoreline retreat rates, 520 providing an empirical, process-based framework to guide future forecasts of wave-driven 521 erosion on tectonically active coasts. It also establishes a link between shore platform 522 development and the cumulative effects of repeated seismic deformation. These findings are 523 particularly consequential along the Cascadia Subduction Zone, and other regions of the West 524 Coast, where vertical land motion is governed by the earthquake deformation cycle. In 525 Cascadia, future megathrust earthquakes are expected to generate 0.5–2 meters of coseismic 526 subsidence within minutes, abruptly increasing coastal inundation and flood exposure (Dura et 527 al., 2025). This rapid coseismic subsidence will also dramatically affect nearshore wave 528 dynamics. In contrast to observations of coseismic uplift during the Kaikōura earthquake in New 529 Zealand, which shifted the surf zone seaward, enhanced energy dissipation and slowing coastal 530 erosion (Horton et al., 2022; Stephenson et al., 2017), coseismic subsidence in Cascadia will 531 instead concentrate wave energy at the shoreline, intensifying cliff erosion. To our knowledge, 532 no existing forecasts of accelerating wave-driven coastal erosion in Cascadia fully account for 533 manuscript submitted to AGU Advances the geomorphic consequences of rapid coseismic subsidence and its effects on wave energy 534 delivery. 535 More broadly, forecasting wave-driven erosion and cliff retreat along the tectonically 536 active U.S. West Coast remains limited by fundamental uncertainties in how wave energy is 537 transformed and dissipated across the nearshore. Addressing this gap is critical as cliff collapse, 538 unlike gradual inundation, is abrupt, destructive, and difficult to anticipate (Bird, 1994; Rosser 539 et al., 2013). Emerging tools, including cliff-top seismometers capable of directly recording 540 nearshore wave energy delivery (Thompson et al., 2019) and coastal cliff response (Adams et 541 al., 2002, 2005; Young et al., 2013), offer promising new approaches to constrain these 542 processes in real time. These effects, when integrated with existing coastal models, could 543 substantially improve our ability to predict and plan for future cliff failure hazards. This is 544 especially important along the West Coast of the U.S. where people, critical infrastructure, and 545 transportation corridors are situated along eroding cliffs (Young, 2018). Understanding how 546 tectonics modulate both long-term landform evolution and short-term shoreline stability is 547 essential for anticipating future change and developing more effective coastal hazard planning 548 strategies. 549 4 Conclusions 550 Our findings demonstrate that rocky coast evolution along the U.S. West Coast is not 551 shaped by waves and tides alone, but by the repeated rise and fall of the Earth’s surface driven 552 by the earthquake deformation cycle. By integrating datasets accounting for major rock coast 553 processes and employing a range of statistical techniques and analyses, we identify decadal-554 scale uplift, tidal range, and normalized wave power as the dominant drivers of modern 555 shoreline retreat. Among these, tide gage–derived uplift emerges as a previously 556 underrecognized control, such that when uplift is more rapid, it continuously lifts the coastline 557 out of the reach of waves, slowing retreat, and producing narrow shore platforms. However, 558 this tectonic buffer is temporary. Over millennia, earthquake-driven cycles of uplift and 559 subsidence reshape the coastline in the opposite direction. Coseismic or interseismic 560 subsidence shifts wave action landward, accelerating erosion and driving the cumulative retreat 561 manuscript submitted to AGU Advances recorded in wide shore platforms and marine terraces. This seismic “memory” highlights 562 tectonics as a governing force that amplifies or damps the effects of marine processes 563 depending on the timescale. 564 These findings have important implications for future coastal hazards along the West 565 Coast of the USA. Rising sea level and intensifying wave climate will continuously diminish this 566 tectonically-drive coastal buffer. Further, our results strongly suggest that future coseismic 567 subsidence during the next Cascadia megathrust earthquake will further accelerate wave-568 driven coastal erosion and retreat. Current coastal erosion forecasts rarely account for the 569 geomorphic consequences of rapid land-level change, leaving hazard assessments incomplete. 570 Our results provide a process-based framework for linking tectonics, wave dynamics, and 571 shoreline evolution, which should integrated into future models of rocky coast change and 572 coastal risk. 573 Acknowledgments 574 Funding for this project was provided by National Science Foundation grant 2339542 to CCM. 575 We thank Kimberly Huppert, Roger Michaelides, and Doug Wiens for insightful discussions that 576 helped shape the ideas presented in this work. 577 Conflicts of Interest 578 The authors declare no conflicts of interest relevant to this study. 579 Open Research 580 The dataset containing the values for each coastal parameter at each site as well as a python 581 script for shallow-water wave transformations (Methods, SI) are available at Zenodo via 582 10.5281/zenodo.16780888. 583 584 References 585 Adams, P. 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Masteller1 4 1Department of Earth, Enviormental, and Planetary Sciences, Washington University in St. Louis, 5 St. Louis, MO, 63130 6 Corresponding author: Cesar G. Lopez ([email protected]) 7 8 Key Points: 9 • Marine and tectonic processes jointly shape rocky coast retreat, with uplift, tides and 10 waves as the dominant controls on modern retreat 11 • Uplift limits short-term retreat, but the effects of the seismic cycle drive a positive 12 scaling between uplift and retreat over millenia 13 • Forecasting rocky coast retreat requires accounting for uplift rates to better assess 14 future hazards along tectonically active margins 15 Abstract 16 Rocky coast morphology is shaped by interactions between wave action, sea level, and 17 tectonics over millennial time scales. However, a clear and quantifiable signature of tectonic 18 uplift on decadal to centennial shoreline retreat rates is outstanding. We isolate the 19 contribution of tectonic uplift to setting shoreline retreat and shore platform morphology from 20 other marine and geologic drivers across the West Coast of the USA. Specifically, we find that 21 decadal-scale tectonic uplift, derived from tide gage records, exerts a significant and 22 measurable control on shoreline retreat rates. Additional influences from wave action, shore 23 platform morphology, and tidal range further contribute to the regional patterns in coastal 24 erosion, and together these factors enable accurate prediction of retreat rates using a 25 multivariate model. Our analysis also reveals robust, time-scale dependent relationships 26 between uplift rate, shore platform morphology, and shoreline retreat. On decadal time scales, 27 rapid tectonic uplift acts as a buffer, shielding the shore from wave action, slowing retreat, and 28 corresponding with narrow shore platforms. On millennial time scales, higher uplift rates relate 29 manuscript submitted to AGU Advances to wider shore platforms, reflecting greater cumulative shoreline retreat. These observations 30 likely reflect the effects of episodic, seismically driven subsidence, which shifts wave action 31 landward, enhancing wave-driven erosion. Through repeated cycles of uplift and subsidence, 32 the seismic cycle amplifies both shore platform development and long-term retreat. Together, 33 these findings highlight the critical role of tectonics in shaping shoreline retreat and driving 34 landscape evolution timescales on active margins. 35 Plain Language Summary 36 Over half of the world’s coastlines are rocky, including the dramatic cliffs and wave-battered 37 platforms of the U.S. West Coast, where millions of people live along the shore. These 38 landscapes are shaped by waves, tides, sea level, and tectonics, but the direct influence of uplift 39 on shoreline erosion is not well understood. In this study, we provide the first quantitative 40 evidence that tectonic uplift plays a central role in shaping both short- and long-term rocky 41 coast change. We show that over decades, faster uplift continuously lifts the shore above the 42 zone of active erosion, narrowing wave attack zones, and slowing retreat. But over thousands 43 of years, higher long-term uplift rates are tied to wider platforms and greater cumulative 44 erosion, a signal of repeated cycles of earthquake-driven uplift and subsidence. Our results 45 suggest that coseismic subsidence along the Cascadia Subduction Zone will shift wave attack 46 landward, accelerating coastal retreat and amplifying future coastal hazards. Our findings show 47 that tectonics leave a clear and lasting imprint on shoreline retreat. As sea levels rise and 48 populations expand along tectonically active coasts, accounting for this link between uplift, 49 earthquakes, and erosion is critical for understanding future coastal change and hazards. 50 1 Introduction 51 Rocky coasts, which make up over 50% of the world's shorelines (Young & Carilli, 2019), are 52 shaped by the dynamic interplay of tectonic uplift, fluctuating sea levels, and the erosive power 53 of crashing waves (Adams et al., 2005; Anderson et al., 1999; Huppert et al., 2020). 54 Characterized by steep rock cliffs descending into the ocean, these landscapes archive climatic 55 and tectonic history in sequences of marine terraces formed and preserved during periods of 56 relative sea level change (Malatesta et al., 2022; Simms et al., 2015). Over millennial timescales, 57 manuscript submitted to AGU Advances the generation and preservation of marine terraces is controlled by the interactions between 58 tectonic uplift and oscillating sea level (Anderson et al., 1999; Malatesta et al., 2022). 59 Understanding the relationship between uplift rates and shoreline erosion is therefore critical 60 to interpreting coastal landscape evolution, reconstructing past tectonic activity, and predicting 61 future coastal erosion and hazards in tectonically active regions. 62 63 A preeminent conceptual model (Anderson et al., 1999) posits that the longevity of marine 64 terrace features is controlled by uplift-driven marine terrace generation, which raises coastal 65 bedrock above the area of wave attack, and progressive, wave-driven backwearing of the 66 coastline, which destroys these uplifted features. Thus, the preserved terrace record reflects a 67 balance between the constructive forces of tectonics and the destructive forces of erosion. 68 Malatesta et al., (2022) built on these ideas by demonstrating that relative rates of tectonic 69 uplift and sea level fluctuation jointly govern the duration and spatial extent of coastal 70 exposure to wave action, critically influencing the timing of marine terrace formation. Given 71 this well-established link between tectonics and erosion on geologic timescales, it stands to 72 reason that tectonic processes should also influence shoreline retreat over shorter, decadal to 73 centennial timescales. However, surprisingly little research has quantitatively linked tectonic 74 uplift rates to shoreline retreat rates over these timescales. Recent studies have shown that 75 relatively rapid modern uplift associated with discrete seismic events can almost instantly 76 modulate shoreline erosion by altering shore platform morphology and nearshore bathymetry 77 (Horton et al., 2022; Kennedy & Beban, 2005; Stephenson et al., 2017). Specifically, coseismic 78 uplift elevates the shore platform and shoreline, shifting the zone of wave action seaward and 79 reducing the frequency and intensity of wave impacts at the base of coastal cliffs. Indeed, this 80 mechanism was observed following the 2016 Mw 7.8 Kaikoura Earthquake, where uplifted 81 areas experienced a 30% reduction in wave energy and a corresponding suppression of coastal 82 erosion rates (Horton et al., 2022; Stephenson et al., 2017). While these case studies illustrate 83 the potential for tectonic uplift to affect short-term erosion rates, to our knowledge, no study 84 manuscript submitted to AGU Advances has yet demonstrated a general, quantitative correspondence between tectonic uplift and 85 shoreline retreat rates at decadal to centennial timescales. 86 87 Most studies focusing on shoreline retreat over these timescales emphasize the impacts of 88 marine forcings – including offshore wave climate (Allan & Komar, 2002, 2006; Barkwith et al., 89 2014) and tidal range (Lim et al., 2011; Young et al., 2016). However, the impact of these 90 forcings on erosion is not uniform along the coast; instead, it is filtered by nearshore processes 91 that govern how wave energy is transformed and delivered to the coastline. Offshore wave 92 energy is dissipated by wave shoaling and breaking, which are controlled by the width and 93 gradient of the shore platform (Horton et al., 2022; Marshall & Stephenson, 2011; Stephenson 94 et al., 2017). Waves that break closer to shore lose less energy before reaching the coast, 95 resulting in more effective energy transfer, evidenced by enhanced ground motions recorded 96 by cliff-top seismometers (Thompson et al., 2019) and correspondingly higher rates of cliff 97 erosion (Trenhaile, 2000). However, the relationship between these marine forcings and 98 shoreline retreat can also be obscured by the strength of coastal bedrock, as more resistant 99 material often erodes slowly even under intense wave attack (Benumof et al., 2000). At the 100 same time, tidal range influences the vertical distribution of wave attack on rocky coasts, 101 modulating the spatial extent and cumulative delivery of wave energy (Adams et al., 2005; Lim 102 et al., 2011). This interplay of waves, tides, and cliff lithology, superimposed on a background of 103 spatially variable tectonic uplift, often obscures the relationship between any single driver and 104 observed shoreline retreat across regions. 105 106 The West Coast of the USA provides a valuable natural laboratory for disentangling the imprint 107 of active tectonic uplift on rocky coastlines due to its setting along the North American Plate 108 margin (Figure 1A). Along the southern half of the coastline, the margin is largely within the San 109 Andreas Fault Zone, dominated by strike-slip motion and relatively low uplift rates except 110 within localized zones of transpression near restraining bends (Anderson, 1990; McGregor & 111 Onderdonk, 2021). To the north, uplift rates increase significantly near the Mendocino Triple 112 Junction, where the San Andreas Fault System transitions into the Cascadia Subduction Zone – a 113 manuscript submitted to AGU Advances megathrust fault formed by subduction of the Gorda and Juan de Fuca Plates, characterized by 114 high uplift rates (Furlong & Schwartz, 2004; Walton et al., 2021). In this region, tectonic uplift 115 rates have been previously reported across a range of temporal scales, with millennial uplift 116 rates derived from marine terrace records (Padgett et al., 2019; Simms et al., 2015, 2020), to 117 decadal uplift rates derived from tide gage records (Zervas et al., 2013.) to daily measurements 118 using GNSS measurements (Blackwell et al., 2020; Govorcin et al., 2025; Hammond et al., 2018). 119 Coupled with a well-constrained uplift gradient, strong north-south wave power variability, and 120 extensive lithologic, bathymetric, tidal, and shoreline retreat data (Fig. 1, Methods), this region 121 offers distinct opportunities to evaluate the links between tectonics and coastal erosion. 122 123 This study is further motivated by the need to better understand the role of active tectonics in 124 shaping modern geomorphic processes and to support more direct and accurate incorporation 125 of this influence into coastal hazard assessments. By isolating the effect of tectonics from wave 126 action, lithology, and tidal range, we may both improve predictive models of coastal evolution 127 on active margins and refine interpretations of the geomorphic record preserved in marine 128 terraces and rocky shorelines. This is of particular importance along the USA West Coast, where 129 the intersection of rising sea levels (Ashton et al., 2011; Shadrick et al., 2022), increasingly 130 powerful waves (Reguero et al., 2019), and variable vertical land motion (Dura et al., 2025; 131 Govorcin et al., 2025) presents a complex and evolving coastal hazard landscape. Further, uplift 132 and subsidence linked to seismic deformation can directly drive sea cliff failure, mass wasting 133 (Bloom et al., 2023) and catastrophic inundation (Walton et al., 2021). Given the region’s large 134 population, infrastructure, and economic significance, assessing the effects of tectonic uplift on 135 modern coastal erosion and cliff retreat on decadal is necessary for coastal hazard management 136 and predicting future landscape change (Bird, 1994; Young, 2018). 137 138 manuscript submitted to AGU Advances 139 Figure 1. A) Tectonic setting of the U.S. West Coast with arrows denoting plate motion with 140 virtual buoys (blue) and corresponding rock shore sites (orange); (B) marine-terrace derived 141 uplift rates (mm/yr) binned by latitude; (C) tide gage derived uplift rates (mm/yr); (D) median 142 offshore wave power (kW/m) calculated from virtual buoys; (E) shore platform width (m); (F) 143 median normalized wave power (kW/m2); (G) median tidal range (m); (H) tensile rock strength 144 (MPa); (I) shoreline change rate (m/yr). 145 146 2 Materials and Methods 147 To systematically evaluate the relative contributions of tectonic uplift, wave climate, 148 lithology, and tidal range to coastal morphology and shoreline retreat, we compile a suite of 149 spatial datasets spanning the U.S. West Coast that characterize each of these key controls and 150 allow for their direct comparison with observed erosion rates. Offshore wave power (kW/m) is 151 derived from a 43-year hindcast model record of hourly significant wave heights and periods 152 (SI) from 51 virtual buoys (Wave Information Study), each located within 25 km of shore at 153 depths >20 m in areas containing sea cliffs. We do not consider sites classified as sandy shores 154 or marine bluffs comprising unconsolidated deposits to avoid the complicating effects of littoral 155 sediment transport. 156 To account for local dissipation of wave energy and constrain shore platform 157 morphology, 2 km wide swath profiles are extracted from 1/3 arc-second resolution 158 bathymetric datasets (NOAA National Centers for Environmental Information) extending from 159 each virtual buoy to the shoreline along each buoy-specific dominant wave direction. We then 160 Virtual Buoys Shore Sites 200 2.42.01.6 0.60.40.2510150.00.510030100 200.02.5-2.5 Mendocino Triple Junction -128º-126º-124º-122º -118º-116º-120º 32º 34º 36º 38º 40º 44º 44º44º44º44º44º44º 41º41º41º 41º 41º41º41º41º 39º39º39º39º39º39º39º39º 37º37º37º37º37º37º37º37º 33º33º33º33º33º33º33º 35º35º35º35º35º35º35º35º 33º 1.0 Millennial Uplift Rate (mm/yr) Decadal Uplift Rate (mm/yr) Wave Power (kW/m) Normalized Wave Power (kW/m2) Tidal Range (m) Platform Width (m) Tensile Rock Strength (MPa) Shoreline Change Rate (m/yr) 0.5 42º 46º 44º 44º N Pacific Plate IHGFEDCBA Oregon California North American Plate San Andreas Fault Juan de Fuca Plate Gorda Plate 300 km Cascadia Subduction Zone manuscript submitted to AGU Advances apply linear wave theory to perform nearshore wave transformations on the buoy-reported 161 wave heights along each swath profile to identify where depth-dependent wave breaking 162 criteria is met for the entire distribution of offshore wave measurements (SI). We then 163 determine the surf zone width (m) based on the shoreward and seaward bounds of offshore 164 wave breaking distances. We then normalize offshore wave power by the surf zone width to 165 generate a normalized wave power metric (kW/m2), which implicitly incorporates the effects of 166 local bathymetry on wave energy dissipation and more accurately captures the translation of 167 offshore wave power to the shore. Because the region of wave action is an important constrain 168 on the development of shore platforms (Kennedy, 2015; Sunamura, 1991, 1992), shore 169 platform width is estimated from both topographic breaks and seaward and shoreward bounds 170 of wave breaking at each site. Given that most sites contain type-A platforms, shore platform 171 and surf zone width are equivalent for the majority of sites (SI) 172 Rock strength, representing the resistance of coastal cliffs to wave attack, is estimated 173 for each site from regional geologic maps (“Geologic Maps and Mapping, California Department 174 of natural Resources.; “Oregon Department of Geology and Mineral Industries : Geologic Map 175 of Oregon : Geologic Map : State of Oregon,” n.d.) (California Department of Conservation; 176 Oregon Department of Geology and Mineral Industries) and laboratory measurements of 177 tensile and compressive rock strength for the mapped lithologies (SI, Table S1). Tidal range, 178 which governs the vertical distribution of wave attack, is calculated using NOAA tide gauge 179 records as the mean difference between Mean Higher High Water (MHHW) and Mean Lower 180 Low Water (MLLW), relative to the MLLW over an 18-year epoch (NOAA Tides and Currents) 181 Similarly, mean sea level is the average of hourly sea level heights observed over the same 182 epoch relative to the MLLW. 183 Shoreline retreat rates are estimated from long-term measures of changes in lateral 184 shoreline extent over a period from the late 1800s to the early 2000s for the entire West Coast 185 from a series of USGS reports (Hapke & Reid, 2007; Ruggerio et al., 2013). Each site is assigned 186 a retreat rate (m/yr) based on the mean shoreline change rate of the littoral cell which a given 187 site lies in. 188 manuscript submitted to AGU Advances Long-term, millennial-scale uplift rates are derived from dating marine terraces and 189 corrected for glacial-isostatic adjustment. Uplift rates correspond to MIS 5a terraces as this is 190 the most recent dating stage (Padgett et al., 2019; Simms et al., 2015, 2020). Decadal scale 191 uplift rates are estimated from local sea level trends recorded at tidal gauges, while accounting 192 for eustatic sea level trends (Zervas et al., 2013) and shorter-term, daily uplift rates are 193 compiled from vertical land velocity estimates at GNSS stations (Kreemer et al., 2014; NSF 194 GAGE). 195 Virtual buoy sites are used as anchor points because they offer a spatially extensive 196 dataset while providing important estimates of offshore wave climate and nearshore 197 bathymetry. This allows us to explore how differences in wave power and nearshore geometry 198 interact with more regionally consistent tectonic, marine, and geologic conditions. Other 199 datasets utilized in this study, including tidal range, uplift rates, and shoreline retreat are more 200 spatially sparse, requiring binning by littoral cell or spatial proximity to ensure complete 201 coverage. Similarly, since site-specific rock strength measurements do not exist, estimates are 202 based on binned value ranges from the literature (SI). While this results in a mix of continuous 203 and ordinal variables, this approach enables the most comprehensive, spatially resolved 204 analysis possible. 205 To assess the relative importance and explanatory power of the variables, we first 206 compute variance inflation factors (VIF) to evaluate potential collinearity among input variables 207 and to ensure that each represents an independent potential control on shoreline retreat. We 208 remove or reduce any variables with VIF values exceeding 2. We then use a random forest 209 classification, a machine learning approach that excels in situations where underlying 210 relationships between predictors and response variables may be nonlinear or interactive. This 211 approach does not assume a specific functional form between input variables and the response 212 variable, making it appropriate for elucidating controls on shoreline retreat, where interactions 213 between tectonic, marine, environmental, and lithologic variables are likely to be non-additive 214 and may involve thresholds or nonlinear responses. Random forests provide feature 215 importance rankings, allowing us to identify which predictors most strongly explain observed 216 spatial patterns in shoreline change, without imposing a priori expectations about their roles or 217 manuscript submitted to AGU Advances relationships (Biau & Scornet, 2016). Random forest is implemented through python’s Ski-Learn 218 Random Forest Classifier or Regressor. Each variable’s importance score is determined through 219 the normalized total reduction of Gini Impurity, a measure of how accurately a randomly 220 chosen element is classified (Menze et al., 2009). Higher importance scores indicate reduced 221 Gini impurity and are therefore more important for the model’s decisions and ability to predict 222 the target process or variable. 223 We then use a multivariate linear regression to assess whether the top-ranked features 224 identified by the random forest model reliably predict shoreline retreat. While this approach 225 assumes a linear relationship, it provides an interpretable hypothesis test to quantify the 226 significance and directionality of individual effects. This approach allows us to determine 227 whether a shoreline retreat model incorporating tectonic, marine, and lithologic drivers 228 outperforms simpler approaches considering individual drivers, such as offshore wave power. 229 By first ensuring low collinearity, then agnostically identifying key variables, and finally 230 quantifying their combined predictive power, this approach allows us to rigorously evaluate the 231 extent to which tectonic uplift, wave action, lithology, and tidal range shape rocky coastline 232 evolution across the U.S. West Coast. 233 Finally, we also perform bivariate analyses on our data by utilizing Spearman’s ρ and 234 Kendall’s τ correlation coefficients. We further verify the robustness of these correlations by 235 implementing permutation tests to produce a distribution of correlation coefficients for both ρ 236 and τ, which we then compare to the actual observed correlations to obtain a p-value indicating 237 how extreme the observed correlations are under the null-hypothesis assumption (SI). We find 238 that the actual correlations in the data are in fact significant, affirming their importance as 239 indicators of the controls on coastal retreat and shore morphology on the West Coast. 240 3 Results and Discussion 241 3.1 Modern Drivers of Rocky Coast Erosion 242 Based on compiled datasets, random forest classification reveals that tide gage-derived 243 decadal uplift rate, tidal range, and normalized wave power (offshore wave power divided by 244 surf zone width) are the strongest predictors of shoreline retreat along the West Coast (Figure 245 manuscript submitted to AGU Advances 2A). To ensure robust interpretation of individual predictors, only variables with low 246 multicollinearity, indicated by variance inflation factors (VIF) below 2, were included in 247 classification (Methods). Feature importance scores from random forest classification denote 248 the relative significance of a given variable in predicting shoreline retreat rates, with tidal range 249 holding the highest feature importance score (0.259), followed by tide gage-derived, decadal 250 uplift rates (0.219), and normalized wave power (0.207). Together, these three drivers account 251 for more than 68% of the total model importance, while the remaining predictors of marine 252 terrace-derived millennial uplift (Padgett et al., 2019; Simms et al., 2015, 2020), GNSS-derived 253 vertical velocities, and tensile rock strength, contribute the remaining 32%. These findings are 254 corroborated by a three-variable, multivariate linear regression, in which tidal range, decadal 255 uplift rate, and normalized wave power all yield T-scores greater than 2 and p-values less than 256 0.05, confirming their statistical and predictive significance (Figure 2B, Methods). Notably, tidal 257 range and decadal uplift rate have T-scores exceeding 3, indicating relatively strong predictive 258 power. The resulting multivariate model yields an R2=0.51 between predicted and observed 259 retreat rates, indicating that these three variables explain just over half of the observed 260 variance in retreat rates. Given the geomorphic and tectonic complexity of the U.S. West Coast 261 compared to more spatially focused studies (Benumof et al., 2000; Horton et al., 2022; Huppert 262 et al., 2020), this represents a strong imprint of these factors on patterns of shoreline retreat. It 263 is worth noting here that a multivariate regression including all six variables yields similar 264 results: decadal uplift rate, tidal range, and normalized wave power remain statistically 265 significant predictors, while marine terrace-derived uplift rate, GNSS-derived uplift rate, and 266 tensile rock strength do not significantly improve the model’s explanatory power. 267 Importantly, our analysis identifies tectonic uplift, particularly as captured by decadal 268 tide gage-derived rates, as a previously underrecognized modulator of modern rock coast 269 erosion. The particular predictive strength of tide gage-derived uplift rates relative to marine 270 terrace- and GNSS-derived rates likely reflects the temporal alignment of this metric and the 271 shoreline change records, which are measured over a comparable, multi-decadal period. As 272 such, decadal uplift rates capture the cumulative impact of vertical land motion on the zone of 273 wave action during the same period during which shoreline change is measured. In contrast, 274 manuscript submitted to AGU Advances longer-term uplift proxies like marine terraces or shorter-term, GNSS-derived vertical velocities 275 are as directly representative of the uplift history relevant to measured shoreline response used 276 in this study. 277 278 279 Figure 2. (A) Importance scores for compiled datasets, with scores greater than 0.15 denoted 280 by solid bars; (B) Comparison of predicted (Epred (m/yr)) and reported (E (m/yr)) shoreline 281 retreat rates from multivariate linear regression using variables with importance scores greater 282 than 0.15; (C) Shoreline retreat rate, E (m/yr), as a function of tide-gage derived, decadal uplift 283 rate, UD (mm/yr), overlapping points are jittered for visibility. Inset shows histogram of 284 Spearman’s ρ values from permutation tests compared the observed Spearman’s ρ (pink 285 dashed line). 286 287 We find a significant negative relationship between decadal uplift rate and shoreline 288 retreat rate (Spearman's ρ = -0.3480, Kendall's τ = -0.2783, p<0.05, Fig. 2C), consistent with 289 prior observations of decreased wave energy delivery following coseismic uplift (Horton et al., 290 2022; Wayne J. Stephenson et al., 2017). Rapid uplift continually raises the shore out of the 291 active zone of wave impact, replenishing the cliff base with fresh material and limiting the 292 exposure duration of any rock parcel. This process precludes progressive backwearing (Uesawa 293 & Miyakawa, 2015), undercutting, and the formation of basal notches, which can lead to cliff 294 destabilization and collapse (Kline et al., 2014; Rosser et al., 2013; Trenhaile, 2015). At the same 295 time, uplifting the shore platform reduces nearshore water depth, shifting wave breaking 296 seaward and enhancing energy dissipation in the near shore (Stephenson et al., 2017). 297 Together, these effects act to tectonically buffer the coastline by reducing the efficiency of 298 wave-driven retreat by disrupting the spatial and temporal continuity of wave attack. In 299 contrast, rapid land level fall enhances shoreline retreat (Fig. 2C). Subsidence of the coastline 300 submerges previously wave-sheltered surfaces, expanding the reach of wave action and 301 Importance Score Tensile Rock Strength Millennial Uplift Rate Vertical Land Velocity Normalized Wave Power Decadal Uplift Rate Tidal Range 0.250.200.150.100.050.0 -3 0.7 0.3 1-2 -1 20 0.2 0.5 0.6 0.4 Study sites Linear best-fit & 95% conf. interval 0.2 0.3 0.5 0.6 0.7 0.4 0.1 0.0 Reported Shoreline Retreat Rate, E (m/yr) 0.6 0.70.50.40.3 Variable T-score P-value VIF Normalized Wave Power 2.105 0.0407 1.290 Tidal Range 3.169 0.0027 1.375 Decadal Uplift -3.469 0.0011 1.075 0.2 R2 = 0.51 Predicted Shoreline Retreat Rate, Epred (m/yr) Decadal Uplift Rate, UD (mm/yr) Shoreline Retreat Rate, E (m/yr) ρ = -0.32, p = 0.023 τ = -0.22, p = 0.022 E = -0.05UD + 0.30 A B CTheil-Sen fit Spearman's ρ 0 400 0.40 p=.01 Frequency 800 Spearman's ρ -0.4 manuscript submitted to AGU Advances exposing a larger portion of the shoreline and cliff face to erosion. Land-level lowering also 302 deepens nearshore water depths, narrowing the active surf zone by shifting wave breaking 303 landward, reducing wave energy dissipation and concentrating wave energy delivery. 304 While the influence of tectonic uplift emerges as particularly important driver of 305 modern shoreline retreat, our results also highlight the importance of both tidal range and 306 normalized wave power in shaping how much wave energy reaches the coastline and the 307 spatial footprint over which it is delivered. The high importance of tidal range reinforces the 308 role of vertical wave reach in governing coastal erosion (Ruggiero et al., 2001; Trenhaile, 2000). 309 Larger tidal range expands the elevation band subject to wave attack, intensifying cliff ground 310 motions and increasing the likelihood of retreat (Adams et al., 2002; Lim et al., 2011; Trenhaile, 311 2019; Young et al., 2011, 2016). Our multivariate model confirms a positive correlation 312 between tidal range and shoreline retreat, such that areas with greater tidal range generally 313 result in more rapid retreat rates. These findings are consistent with previous field and 314 modeling studies that find that higher tide levels drive greater sea cliff erosion (Matsumoto et 315 al., 2016; Trenhaile, 2000; Vann Jones et al., 2015). 316 Our analysis also shows that normalized wave power, calculated as offshore wave 317 energy divided by local surf zone width, is a strong predictor of rocky coastline retreat and 318 highlights the importance of nearshore wave transformation in shaping erosion patterns. This 319 metric incorporates both the magnitude of offshore wave energy and the degree of energy 320 dissipation across the active surf zone, which we estimate using a depth-based wave breaking 321 criterion and site-specific bathymetry (Methods). By accounting for variations in both offshore 322 forcing and local morphology, normalized wave power captures how efficiently wave energy 323 reaches the shoreline. Our multivariate model reveals a strong positive relationship between 324 normalized wave power and shoreline retreat, consistent with previous observational and 325 modeling studies (Alessio & Keller, 2020; Huppert et al., 2020; Limber et al., 2014; Thompson et 326 al., 2019). Increases in normalized wave power can result either from a more energetic offshore 327 wave climate or a narrower surf zone. In both cases, more wave energy is retained and 328 delivered to the shoreline, increasing the erosive potential of incident waves and accelerating 329 retreat. The significance of this predictor reinforces the notion that shoreline retreat is not 330 manuscript submitted to AGU Advances governed by wave climate alone, but also by local shore platform morphology (Lim et al., 2013; 331 Vann Jones et al., 2018). This morphology-dependent dissipation strongly influences the energy 332 retention of incident waves, which in turn modulates their erosive power (Horton et al., 2022; 333 Stephenson et al., 2017). 334 Despite past studies finding a primary role of rock strength in modulating cliff retreat 335 rates (Benumof et al., 2000), in our analysis, rock strength emerges as a surprisingly weak 336 predictor of shoreline retreat. Tensile rock strength holds the lowest importance score in the 337 random forest classification (Figure 2A). Further, while bivariate correlations show a positive 338 relationship between both tensile and compressive rock strength and retreat rates (Spearman’s 339 ρ = 0.43–0.44, Kendall's τ = 0.38-0.39, p < 0.05), this contrasts with prior work suggesting 340 stronger rocks are more resistant to erosion (Benumof et al., 2000; Budetta et al., 2000; 341 Thornton & Stephenson, 2006). This finding reinforces the dominant role of marine forcings and 342 tectonic uplift over lithologic resistance in shaping modern rock coast evolution across the U.S. 343 West Coast. 344 The combined influence of normalized wave power and tidal range captures how both 345 the horizontal and vertical extent of wave attack shape shoreline retreat, reinforcing the central 346 roles of coastal morphology and marine forcings in focusing or diffusing wave energy. This 347 finding agrees with field observations and key elements of process-based models for rocky 348 coast retreat (Dornbusch et al., 2008; Trenhaile, 2000). Our study reveals that decadal tectonic 349 uplift acts as a powerful modulator of these marine forcings by governing the persistence of 350 wave attack at any given elevation and shifting the locus of erosion on or offshore. Together, 351 these findings demonstrate that rocky coast erosion reflects the combined influence of vertical 352 land motion, wave energy delivery, and tidal forcing, each shaped by the evolving coastal 353 morphology. To our knowledge, this is the first study to quantify the relative contribution of 354 decadal-scale tectonic uplift to shoreline retreat rates on rocky coastlines, highlighting tectonics 355 manuscript submitted to AGU Advances not just as a passive backdrop but as an important governor that can amplify or buffer the 356 effects of changing marine conditions. 357 3.2 Shore Platform Evolution and the Seismic Memory of Rocky Coasts 358 Our results demonstrate that modern shoreline retreat rates are partially governed by 359 decadal uplift rates. Additionally, the high relative importance and predictive power of 360 normalized wave power highlights the fundamental role of wave transformation and dissipation 361 within the surf zone. Wave dissipation is primarily controlled by shore platform morphology, 362 especially platform width, which governs where waves break relative to the coastline (Vann 363 Jones et al., 2018). In turn, the width of the shore platform also reflects the longer-term effects 364 of cliff erosion, driven by progressive backwearing over thousands of years (Clow et al., 2023; 365 De Lange & Moon, 2005; Payo et al., 2015). In this context, the shore platform serves as a 366 cumulative record of coastal retreat prior to abandonment, after which the platform is 367 preserved as a marine terrace (Anderson et al., 1999). 368 Because uplift and erosion are coupled over modern timescales (Fig. 2), we expect 369 platform width, which preserves this erosive history, to also relate to uplift rate. Indeed, we 370 find a significant, negative correlation between decadal uplift rate and shore platform width 371 (Spearman’s ρ = -0.3714, Kendall's τ = -0.2673, p<0.05; Fig 3A), directly reflecting the observed 372 modern relationship between shoreline retreat and decadal uplift (Spearman's ρ = -0.3480, 373 Kendall's τ = -0.2783, p<0.05; Fig. 2C), further supporting the interpretation that tectonic uplift 374 buffers coastal backwearing and limits shore platform development (Horton et al., 2022; 375 Stephenson et al., 2017). 376 In contrast, modern shore platform widths exhibit a significant, positive correlation with 377 marine-terrace derived, millennial uplift rates (Spearman’s ρ = 0.3550, Kendall's τ = 0.2464, 378 p<0.05; Fig. 3B), similarly reflected by a positive correlation between modern retreat rates and 379 millennial scale uplift (Spearman's ρ = 0.3199, Kendall's τ = 0.2461, p<0.05). These uplift rates, 380 derived from Marine Isotope Stage (MIS) 5a terraces, represent the last interglacial highstand 381 (Simms et al., 2015). Because these terraces reflect the last surfaces abandoned by wave action, 382 the width of the underlying modern shore platform likely records the cumulative erosion that 383 manuscript submitted to AGU Advances has occurred since their uplift. The observed positive correlation suggests that, over millennia, 384 higher uplift rates are associated with the development and preservation of wider shore 385 platforms, implying more efficient cumulative shoreline retreat and coastal erosion over these 386 timescales. 387 388 389 Figure 3. (A) Shore platform width, W (m) as a function of tide gage-derived decadal uplift rate, 390 UD (mm/yr); (B) Shore platform width, W (m) as a function of marine terraced-derived, 391 millennial uplift rate, UM (mm/yr). Insets show histogram of Spearman’s ρ values from 392 permutation tests relative to the observed Spearman’s ρ (teal dashed line). 393 394 The positive correlation revealed in our analysis directly contrasts predictions from 395 models of marine terrace formation, which suggest that higher uplift rates should lead to 396 narrower terraces due to the vertical smearing of wave attack and reduced backwearing as cliff 397 rock is rapidly removed from the cliff base and replaced by fresh, uneroded material (Anderson 398 et al., 1999; Uesawa & Miyakawa, 2015). However, these models typically consider constant 399 uplift rates superimposed on either constant sea level (Uesawa & Miyakawa, 2015) or a 400 fluctuating sea level curve spanning multiple glacial-interglacial cycles (Anderson et al., 1999). 401 By doing so, they represent time-averaged, net uplift rates, when in reality, uplift along much of 402 West Coast – especially in Cascadia – is not steady. Instead, vertical motion is temporally 403 variable and driven by cyclic land-level rise and fall driven by the earthquake deformation cycle. 404 Taken together, our observations suggest that the contrasting relationships between shore 405 0 400 1000 600 200 800 Frequency 0.4 0 400 1000 600 200 800 Frequency -0.2 0.20.0 0.25-0.25-0.4 Spearman's ρ p = 0.0073 0.0 0.5 p = 0.0108 -0.5 Spearman's ρ W = -18.57UD + 76.02 Decadal Uplift Rate, UD (mm/yr) Shore Platform Width, W (m) Shore Platform Width, W (m) Millennial Uplift Rate, UM (mm/yr) BA Theil–Sen Fit Cascadia San Andreas Spearman's ρ W = 48.78UM + 48.83 manuscript submitted to AGU Advances platform width and shoreline retreat rates across timescales reflect how both the style and 406 relative magnitude of uplift and erosion vary through time, shaping coastal morphology in 407 different ways depending on the temporal scale of analysis. 408 On decadal timescales, tectonic uplift along the U.S. West Coast primarily reflects 409 interseismic strain accumulation. In the Cascadia Subduction Zone vertical motion is driven by 410 the gradual elastic deformation of the overriding plate between megathrust earthquakes 411 (Walton et al., 2021). Along the San Andreas Fault Zone, interseismic strain is driven by fault 412 locking at depth, resulting in more localized differences in uplift rate (Smith & Sandwell, 2006; 413 Smith-Konter et al., 2014). While the style of interseismic deformation differs between these 414 tectonic settings, regional elastic shortening in Cascadia versus localized uplift or subsidence 415 and flexure along the San Andreas, the tide gage-derived uplift rates span a similar range across 416 both regions (Fig. 3A). The main exceptions are two rapidly subsiding sites in central Oregon, 417 associated with localized forearc subsidence near the downdip end of the locked megathrust 418 (Malatesta et al., 2021; Oryan et al., 2024). Despite the differences in tectonic style and 419 structure between these two major faults, decadal uplift rates correspond closely with regional 420 patterns in shoreline retreat and shore platform width, reinforcing the role of interseismic 421 strain as a dominant short-term control on rocky coast erosion. 422 On the millennial times scales, marine terrace-derived uplift rates integrate multiple 423 seismic cycles and longer-term deformation patterns, reflecting the net vertical displacement of 424 the coastline over thousands of years (Fig. 4A). In Cascadia, these millennial scale, terrace-425 derived uplift rates include cycles of interseismic uplift followed by abrupt coseismic subsidence 426 (Leonard et al., 2010; Walton et al., 2021). Building on our modern analysis of the quantitative 427 relationship between uplift and shoreline retreat (Fig. 2C), we infer that rapid coseismic 428 subsidence amplifies erosion by abruptly shifting the wave attack zone landward and exposing 429 previously protected surfaces to direct wave impact. While interseismic uplift can buffer 430 erosion, this protective effect is episodically undone by subsidence. In Cascadia, more rapid 431 interseismic uplift is often paired with more pronounced subsidence (Chapman & Melbourne, 432 2009; Stanton et al., 2024), thus the net effect across seismic cycles favors enhanced 433 backwearing and the horizontal expansion of the shore platform. This process-based 434 manuscript submitted to AGU Advances interpretation aligns with the positive correlation we observe between terrace-derived uplift 435 rates and shore platform width (Fig. 3B), supporting the idea that, over millennial timescales, 436 coastal landscape evolution is predominately shaped by the cumulative effects of shoreline 437 backwearing during repeated periods of enhanced wave attack. 438 This effect is recorded not only in the width of the modern shore platform (Fig. 1E) but 439 also preserved in relatively wide marine terraces of Cascadia (SI; Fig. S2). These morphologic 440 patterns are also consistent with broader-scale submarine topography. Along the Cascadia 441 margin, the location of the continental shelf break consistently aligns with the downdip limit of 442 megathrust coupling, a pattern attributed to a long-term balance between permanent 443 interseismic uplift and wave erosion over hundreds of seismic cycles (Malatesta et al., 2021). By 444 isolating the modern relationship between uplift and rock coast retreat rates, our results offer a 445 mechanistic basis linking these processes to the morphologic signatures of enhanced shore 446 platform development over geologic timescales (Fig. 3B, 6) and highlighting the critical role of 447 the seismic cycle that is often overlooked in conventional coastal landscape evolution models 448 (Fig. 4). 449 In the predominantly strike-slip San Andreas Fault Zone, time-variable uplift driven by 450 interseismic strain and localized fault geometry (Grove et al., 2010), coseismic rupture 451 influenced by local compressional or extensional regimes (Smith-Konter et al., 2014), and fault 452 creep (Johnson & Segall, 2004; Lindsey et al., 2014) produce a comparable range of millennial 453 uplift rates to Cascadia (Fig. 1B, Fig. 3B). However, unlike Cascadia, where coseismic subsidence 454 commonly lowers the coastline, the San Andreas Fault Zone can experience localized coseismic 455 uplift depending on the local stresses present (55; Fig 4B), especially in regions of transpression 456 along restraining bends in the fault (Anderson, 1990; Anderson & Menking, 1994; Mueller & 457 Suppe, 1997). Because retreat rates peak during subsidence or more gradual uplift phases, the 458 coastlines across these regions respond differently following earthquakes: Cascadia’s rapid 459 coseismic subsidence accelerates coastal retreat, whereas San Andreas’ coseismic uplift rapidly 460 slows it. Though the timing and magnitude of backwearing peak at different stages of the 461 earthquake cycle in each tectonic setting (Fig. 4), the integrated effect of repeated uplift and 462 erosion over many seismic cycles produces a consistent geomorphic outcome. This is reflected 463 manuscript submitted to AGU Advances in the robust correlation between millennial uplift rates, shoreline retreat, and shore platform 464 width, emphasizing cumulative backwearing during periods of slow uplift or subsidence as the 465 primary long-term driver of coastal morphology (Fig. 3B, 4). 466 The strong correspondence between shore platform width and millennial-scale uplift is 467 likely also informed by relative differences in coastal backwearing rates and time-averaged 468 uplift rates. Modern shoreline retreat rates exceed terrace-derived uplift rates by over an order 469 of magnitude (Fig. 1B, SI), meaning that over geologic timescales, lateral cliff retreat is likely to 470 far outpace net uplift rates. It’s also worth emphasizing that backwearing rates outpace 471 measured shore platform downwearing rates (Stephenson et al., 2010; Trenhaile & Porter, 472 2018) because the shear stresses exerted on the seabed and shore platform are weaker than 473 the forces at the water surface (Stephenson & Kirk, 2000; Trenhaile & Kanyaya, 2007). This 474 imbalance means that erosion is primarily expressed through the landward retreat of the 475 coastline, rather than the vertical lowering of the platform. Because backwearing rates exceed 476 both uplift and downwearing rates, platform widening will continue as long as wave energy can 477 reach the shore. This suggests that a horizontal, steady state equilibrium profile is likely not 478 attainable for shore platforms (Dickson et al., 2013) without invoking changes in sea level. 479 However, backwearing rates may decrease over time due to increasing wave energy dissipation 480 as the platform continues to broaden. While shore platform width is a record and manifestation 481 of cliff backwearing (De Lange & Moon, 2005; Payo et al., 2015) we find no strong correlation 482 between decadal erosion rates and platform width - highlighting the importance of legacy 483 processes and cumulative effects over longer timescales. Cosmogenic dating across shore 484 platforms could further constrain the decadal versus millennial trends we identify in this study 485 manuscript submitted to AGU Advances and bolster the relationship between retreat rates and platform width (Clow et al., 2023; Hurst 486 et al., 2017). 487 488 489 Figure 4. Conceptual diagrams for the (A) Cascadia Subduction Zone (orange) and (B) San 490 Andreas Fault Zone (blue), depicting the relationship between tectonic uplift (top) and both 491 short-serm shoreline retreat rate (bottom, gray) and cumulative, long-term retreat (bottom, 492 orange and blue), across multiple seismic cycles. Uplift curves are based on observed and 493 theoretical deformation patterns (Beavan & Litchfield, 2012; Sea-Level Rise for the Coasts of 494 California, Oregon, and Washington, 2012; Wesson et al., 2015). 495 496 3.3 Forecasting Rocky Shoreline Retreat and The Diminishing Tectonic Buffer 497 Our results demonstrate that tectonic uplift exerts a significant, timescale-dependent 498 control on rocky coast morphology and shoreline retreat along the U.S. West Coast. Over 499 decadal time scales, tectonic uplift buffers to shoreline retreat by enhancing nearshore 500 dissipation of wave energy and inhibiting basal notch development. However, this protective 501 tectonic buffering effect is likely to be increasingly offset by accelerating sea level rise. In many 502 locations, global sea level rise is already outpacing vertical land motion, effectively reducing 503 tectonic uplift rates (Sweet et al., 2017, 2022). As sea level rises faster than the land surface, 504 Coseismic Subsidence Net Uplift Interseismic Uplift A Uplift (m) EQEQ Cascadia Subduction Zone Time Retreat Rate (m/yr) Time Net Uplift B Uplift (m) Coseismic Uplift Intereismic Subsidence Time EQ Cumulative Retreat (m) Time Retreat Rate (m/yr) Cumulative Retreat (m) San Andreas Fault Zone EQ manuscript submitted to AGU Advances even tectonically uplifting coasts will experience a net relative fall in elevation, shifting wave 505 action landward, increasing the potential for cliff erosion. The loss of this natural buffer, 506 combined with intensifying wave climate (Reguero et al., 2019; Young et al., 2011), stands to 507 significantly amplify shoreline retreat rates across coastlines on active margins. Yet, most 508 existing rock coast erosion models that focus on short-term morphodynamics do not directly 509 incorporate vertical land motion, including uplift or subsidence (Matsumoto et al., 2016; 510 Trenhaile, 2000; Walkden & Hall, 2005). While sea level rise has been linked to enhanced cliff 511 erosion in soft rock environments (Ashton et al., 2011; Dickson et al., 2007; Shadrick et al., 512 2022), the capacity of tectonic deformation to mediate or intensify these effects remains poorly 513 integrated into forecasts of future rocky coast erosion (Govorcin et al., 2025). Incorporating 514 vertical land motion into rocky coast evolution models may help to improve coastal hazard 515 assessments and guide long-term adaptation strategies in tectonically active regions. 516 Despite the well-recognized role of tectonic deformation in modulating relative sea-517 level change (Harvey et al., 2021; Wöppelmann & Marcos, 2016), its influence on the mechanics 518 and rates of cliff retreat, distinct from the problem of inundation, remains poorly understood. 519 Our analysis isolates the influence of tectonic uplift on modern shoreline retreat rates, 520 providing an empirical, process-based framework to guide future forecasts of wave-driven 521 erosion on tectonically active coasts. It also establishes a link between shore platform 522 development and the cumulative effects of repeated seismic deformation. These findings are 523 particularly consequential along the Cascadia Subduction Zone, and other regions of the West 524 Coast, where vertical land motion is governed by the earthquake deformation cycle. In 525 Cascadia, future megathrust earthquakes are expected to generate 0.5–2 meters of coseismic 526 subsidence within minutes, abruptly increasing coastal inundation and flood exposure (Dura et 527 al., 2025). This rapid coseismic subsidence will also dramatically affect nearshore wave 528 dynamics. In contrast to observations of coseismic uplift during the Kaikōura earthquake in New 529 Zealand, which shifted the surf zone seaward, enhanced energy dissipation and slowing coastal 530 erosion (Horton et al., 2022; Stephenson et al., 2017), coseismic subsidence in Cascadia will 531 instead concentrate wave energy at the shoreline, intensifying cliff erosion. To our knowledge, 532 no existing forecasts of accelerating wave-driven coastal erosion in Cascadia fully account for 533 manuscript submitted to AGU Advances the geomorphic consequences of rapid coseismic subsidence and its effects on wave energy 534 delivery. 535 More broadly, forecasting wave-driven erosion and cliff retreat along the tectonically 536 active U.S. West Coast remains limited by fundamental uncertainties in how wave energy is 537 transformed and dissipated across the nearshore. Addressing this gap is critical as cliff collapse, 538 unlike gradual inundation, is abrupt, destructive, and difficult to anticipate (Bird, 1994; Rosser 539 et al., 2013). Emerging tools, including cliff-top seismometers capable of directly recording 540 nearshore wave energy delivery (Thompson et al., 2019) and coastal cliff response (Adams et 541 al., 2002, 2005; Young et al., 2013), offer promising new approaches to constrain these 542 processes in real time. These effects, when integrated with existing coastal models, could 543 substantially improve our ability to predict and plan for future cliff failure hazards. This is 544 especially important along the West Coast of the U.S. where people, critical infrastructure, and 545 transportation corridors are situated along eroding cliffs (Young, 2018). Understanding how 546 tectonics modulate both long-term landform evolution and short-term shoreline stability is 547 essential for anticipating future change and developing more effective coastal hazard planning 548 strategies. 549 4 Conclusions 550 Our findings demonstrate that rocky coast evolution along the U.S. West Coast is not 551 shaped by waves and tides alone, but by the repeated rise and fall of the Earth’s surface driven 552 by the earthquake deformation cycle. By integrating datasets accounting for major rock coast 553 processes and employing a range of statistical techniques and analyses, we identify decadal-554 scale uplift, tidal range, and normalized wave power as the dominant drivers of modern 555 shoreline retreat. Among these, tide gage–derived uplift emerges as a previously 556 underrecognized control, such that when uplift is more rapid, it continuously lifts the coastline 557 out of the reach of waves, slowing retreat, and producing narrow shore platforms. However, 558 this tectonic buffer is temporary. Over millennia, earthquake-driven cycles of uplift and 559 subsidence reshape the coastline in the opposite direction. Coseismic or interseismic 560 subsidence shifts wave action landward, accelerating erosion and driving the cumulative retreat 561 manuscript submitted to AGU Advances recorded in wide shore platforms and marine terraces. This seismic “memory” highlights 562 tectonics as a governing force that amplifies or damps the effects of marine processes 563 depending on the timescale. 564 These findings have important implications for future coastal hazards along the West 565 Coast of the USA. Rising sea level and intensifying wave climate will continuously diminish this 566 tectonically-drive coastal buffer. Further, our results strongly suggest that future coseismic 567 subsidence during the next Cascadia megathrust earthquake will further accelerate wave-568 driven coastal erosion and retreat. Current coastal erosion forecasts rarely account for the 569 geomorphic consequences of rapid land-level change, leaving hazard assessments incomplete. 570 Our results provide a process-based framework for linking tectonics, wave dynamics, and 571 shoreline evolution, which should integrated into future models of rocky coast change and 572 coastal risk. 573 Acknowledgments 574 Funding for this project was provided by National Science Foundation grant 2339542 to CCM. 575 We thank Kimberly Huppert, Roger Michaelides, and Doug Wiens for insightful discussions that 576 helped shape the ideas presented in this work. 577 Conflicts of Interest 578 The authors declare no conflicts of interest relevant to this study. 579 Open Research 580 The dataset containing the values for each coastal parameter at each site as well as a python 581 script for shallow-water wave transformations (Methods, SI) are available at Zenodo via 582 10.5281/zenodo.16780888. 583 584 References 585 Adams, P. 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Journal of Geophysical 872 Research: Oceans, 118(12), 6590–6602. https://doi.org/10.1002/2013JC008883 873 Young, A. P., Guza, R. T., O’Reilly, W. C., Burvingt, O., & Flick, R. E. (2016). Observations of 874 coastal cliff base waves, sand levels, and cliff top shaking. Earth Surface Processes and 875 Landforms, 41(11), 1564–1573. https://doi.org/10.1002/esp.3928 876 Zervas, C. E., Gill, S. K., & Sweet, W. (William V. (n.d.). Estimating vertical land motion from 877 long-term tide gauge records. Retrieved from 878 https://repository.library.noaa.gov/view/noaa/14751 879 880 881 882 883 SI References 884 Fenton, J. D., & Mckee, W. D. (1990). On calculating the lengths of water waves. Coastal 885 Engineering 14(6), 499-513. https://doi.org/10.1016/0378-3839(90)90032-R 886 Flavio, L., Johnan, O., & Fredriksson, A. (2006). Rock mechanics modelling of rock mass 887 properties - summary of primary data. Preliminary site description Laxemar subarea - 888 version 1.2. Swedish Nuclear Fuel and Waste Management Co. 889 Goodman, R. E. (1989). Introduction to Rock Mechanics, Wiley. 890 Holton, C. A., & Sulivan, S. P. (2023). Permutation tests for experimental data. Experimental 891 Economics 26, 775–812. https://doi.org/10.1007/s10683-023-09799-6 892 Johnson, R. B., & DeGraff, J. V. (1988). Principles of engineering geology, Wiley. 893 Lucca, A., Ogata, K., Balsamo, F., Borsani, A., Clemenzi, L., Hatushika, R., Tinterri, R., & Storti, F. 894 (2024). Sedimentary facies control on fracture and mechanical stratigraphy in 895 siliciclastics: Marnoso-arenacea formation, Northern Apennines, Italy. Marine and 896 Petroleum Geology 167, https://doi.org/10.1016/j.marpetgeo.2024.106927. 897 McNamara, D. D., Faulkner, D. R., & McCarney, E. (2011). Rock Properties of Greywacke 898 Basement Hosting Geothermal Reservoirs, New Zealand: Preliminary Results” in 39th 899 Workshop on Geothermal Reservoir Engineering Stanford University. 900 manuscript submitted to AGU Advances Melia, A., Faulkner, D. R., & McNamara, D. D. (2022). Physical property characterization of the 901 Waipapa greywacke: an important geothermal reservoir basement rock in New Zealand, 902 Geothermal Energy 10(11). https://doi.org/10.1186/s40517-022-00218-2 903 Perras, M. A., & Diederichs, M. S. (2014). A Review of the Tensile Strength of Rock: Concepts 904 and Testing. Geotechnical and Geologic Engineering 32, 525–546. 905 https://doi.org/10.1007/s10706-014-9732-0 906 Rahn, P. H. (1996). Engineering geology an environmental approach, Prentice Hall. 907 Rybacki, E., Reinicke, A., Meier, ., T., Makasi, M., & Dresen, G. (2015). What controls the 908 mechanical properties of shale rocks? – Part I: Strength and Young's modulus. Journal of 909 Petroleum Science and Engineering 135, 702-722. 910 https://doi.org/10.1016/j.marpetgeo.2024.106927 911 Schultz, R. A. (1993). Brittle strength of basaltic rock masses with applications to Venus, Journal 912 of Geophysical Research 98(E6), 10883–10895. https://doi.org/10.1029/93JE00691 913 Schultz, R. A & Watters, T. R. (1995). Elastic buckling of fractured basalts on the Columbia 914 Plateau, Washington State” in 35th U.S. Symposium on Rock Mechanics, pp. 885-860 915 Yu, H., & Hutson, A. D. (2022). A robust Spearman correlation coefficient permutation test. 916 Communications in Statistics - Theory and Methods 53(6) 2141–2153. 917 https://doi.org/10.1080/03610926.2022.2121144 918 1 AGU Advances Supporting Information for Tectonics as a Regulator of Shoreline Retreat and Rocky Coast Evolution Across Timescales Cesar G. Lopez and Claire C. Masteller Department of Earth, Environmental, and Planetary Sciences, Washington University in St. Louis Contents of this file Supporting Text Table S1 Figure S1 2 Wave Calculations Peak wave period, 𝑇! or 𝑇 [T], and deep-water significant wave height, 𝐻" [L], are initial measurements retrieved from the offshore virtual buoys. We also incorporate measurements of mean wave direction, to determine the dominant wave direction and angle of incidence with the coast. Acceleration due to gravity, 𝑔 [LT-2] (9.81 ms-2) is a constant and r [ML-3] (1000 kgm-3) is the density of water. Offshore wave energy density 𝐸, [ML3T-2] is calculated using equation 1 in units of Jm-2: 𝐸= 116 r𝑔𝐻"# Offshore wave energy flux or wave power, 𝑃 [ML3T-3] is determined using equation 2 in units of Wm-1, where 𝑐𝑔 is the group velocity (equation 11): 𝑃=𝐸∗𝑐𝑔= 𝜌𝑔#𝐻"#𝑇64𝜋 Depth, 𝑑 [L], is inputted as a vector of depths ranging from 0.1 to 30 meters at intervals of 0.1 m. First, the angular frequency of the wave, 𝜔 [radT-1], is calculated using equation 3: w=2𝜋𝑇 and the initial deep-water wavelength, 𝐿" [L], is calculated with equation 4: 𝐿"=𝑔𝑇2𝜋 These two parameters are then used to find the wavelength 𝐿 [L] utilizing equation 5 (Fenton & Mckee, 1990) where tanh is the hyperbolic tangent: 𝐿=𝐿"[tanh8𝜔#𝑑𝑔9$%]#$ Next, deep-water wave celerity, 𝑐" [LT-1], is calculated using equation 6: 𝑐"= 𝐿"𝑇 and wave celerity, 𝑐 [LT-1], is computed using equation 7: 𝑐= 𝑔𝑇2𝜋 tanh;2𝜋𝑑𝐿1+4𝜋𝑑𝐿sinh (4𝜋𝑑𝐿)D Next, the initial deep-water group velocity, 𝑐&! [LT-1], is determined with equation 9: 𝑐&!= 12𝑐" and the group velocity, 𝑐& [LT-1], is found using equation 10: 𝑐&=𝑛𝑐 The dimensionless shoaling coefficient 𝐾' is computed using equation 11: 𝐾'=F𝑐&!𝑐& The transformed, shallow water wave height, 𝐻 [L] is found using equation 12: 𝐻= 𝐾'𝐻" Finally, the breaking depth 𝑑( [L] can be found using equation 13, where 𝐻( is the breaking wave height and 𝛾 is the breaking criterion, with a value of 0.8: 𝛾= 𝐻(𝑑(=0.8 The breaking (𝑑() and shoaling (𝑑') depths are then used to find the corresponding offshore distances from the extracted swath profiles for the entire distribution of wave measurements. 4 Permutation Tests A distribution of correlation coefficients is produced after 10,000 permutations, which are compared to the observed correlation to obtain a p-value indicating how extreme the observed correlations are under the null-hypothesis assumption using equation 14 (Holt & Sullivan, 2023; Yu & Hutson, 2022): 𝑝= (L𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝜌 𝑜𝑟 𝜏!)*+,-).L≥|𝜌 𝑜𝑟 𝜏/0-,/1|)10000 Coastal Lithology We Incorporate laboratory measurements of tensile and uniaxial compressive strength (MPa) for the rock type present at each site. For large ranges, we used the median values reported in the literature or those that most closely matched the specific unit or formation at each site. Lithology Tensile Strength (MPa) Compressive Strength (MPa) References Basalt 14 260 (Shultz, 1993) (Shultz & Watters, 1995) Graywacke 15 200 (McNamara et al., 2011) (Melia et al., 2022) Gneiss 15 160 (Johnson & DeGraff, 1988) (Perras & Diederichs, 2014) Tonalite 15 156 (Flavio et al., 2006) Volcanics 15 150 (Goodman, 1989) (Rahn, 1996) Sandstone 10 70 (Perras & Diederichs, 2014) (Goodman, 1989) Blue Schist 10 60 (Johnson & DeGraff, 1988) (Perras & Diederichs, 2014) Turbidite 10 70 (Lucca et al., 2024) Shale 4 44 (Perras & Diederichs, 2014) (Rybacki et al., 2015) Mudstone 5.4 41 (Perras & Diederichs, 2014) Table S1. Tensile and compressive rock strength values used for the different lithologies in the study region. For specific types and values at each site, see the data repository. 5 Figure S1. Boxplots of shore platform widths within the Cascadia Subduction Zone (left) and along the San Andreas Fault Zone (right). The gray line in each box denotes the median and box bounds denote the interquartile range. Whiskers denote the minimum and maximum values and outliers are plotted as individual points. 6 SI References Fenton, J. D., & Mckee, W. D. (1990). On calculating the lengths of water waves. Coastal Engineering 14(6), 499-513. https://doi.org/10.1016/0378-3839(90)90032-R Flavio, L., Johnan, O., & Fredriksson, A. (2006). Rock mechanics modelling of rock mass properties - summary of primary data. Preliminary site description Laxemar subarea - version 1.2. Swedish Nuclear Fuel and Waste Management Co. Goodman, R. E. (1989). Introduction to Rock Mechanics, Wiley. Holton, C. A., & Sulivan, S. P. (2023). Permutation tests for experimental data. Experimental Economics 26, 775–812. https://doi.org/10.1007/s10683-023-09799-6 Johnson, R. B., & DeGraff, J. V. (1988). Principles of engineering geology, Wiley. Lucca, A., Ogata, K., Balsamo, F., Borsani, A., Clemenzi, L., Hatushika, R., Tinterri, R., & Storti, F. (2024). Sedimentary facies control on fracture and mechanical stratigraphy in siliciclastics: Marnoso-arenacea formation, Northern Apennines, Italy. Marine and Petroleum Geology 167, https://doi.org/10.1016/j.marpetgeo.2024.106927. McNamara, D. D., Faulkner, D. R., & McCarney, E. (2011). Rock Properties of Greywacke Basement Hosting Geothermal Reservoirs, New Zealand: Preliminary Results” in 39th Workshop on Geothermal Reservoir Engineering Stanford University. Melia, A., Faulkner, D. R., & McNamara, D. D. (2022). Physical property characterization of the Waipapa greywacke: an important geothermal reservoir basement rock in New Zealand, Geothermal Energy 10(11). https://doi.org/10.1186/s40517-022-00218-2 Perras, M. A., & Diederichs, M. S. (2014). A Review of the Tensile Strength of Rock: Concepts and Testing. Geotechnical and Geologic Engineering 32, 525–546. https://doi.org/10.1007/s10706-014-9732-0 Rahn, P. H. (1996). Engineering geology an environmental approach, Prentice Hall. Rybacki, E., Reinicke, A., Meier, ., T., Makasi, M., & Dresen, G. (2015). What controls the mechanical properties of shale rocks? – Part I: Strength and Young's modulus. Journal of Petroleum Science and Engineering 135, 702-722. https://doi.org/10.1016/j.marpetgeo.2024.106927 Schultz, R. A. (1993). Brittle strength of basaltic rock masses with applications to Venus, Journal of Geophysical Research 98(E6), 10883–10895. https://doi.org/10.1029/93JE00691 7 Schultz, R. A & Watters, T. R. (1995). Elastic buckling of fractured basalts on the Columbia Plateau, Washington State” in 35th U.S. Symposium on Rock Mechanics, pp. 885-860 Yu, H., & Hutson, A. D. (2022). A robust Spearman correlation coefficient permutation test. Communications in Statistics - Theory and Methods 53(6) 2141–2153. https://doi.org/10.1080/03610926.2022.2121144