Coastal wetlands mitigate storm flooding and associated costs in estuaries

As storm-driven coastal flooding increases under climate change, wetlands such as saltmarshes are held as a nature-based solution. Yet evidence supporting wetlands’ storm protection role in estuaries—where both waves and upstream surge drive coastal flooding—remains scarce. Here we address this gap using numerical hydrodynamic models within eight contextually diverse estuaries, simulating storms of varying intensity and coupling flood predictions to damage valuation. Saltmarshes reduced flooding across all studied estuaries and particularly for the largest—100 year—storms, for which they mitigated average flood extents by 35% and damages by 37% ($8.4 M). Across all storm scenarios, wetlands delivered mean annual damage savings of $2.7 M per estuary, exceeding annualised values of better studied wetland services such as carbon storage. Spatial decomposition of processes revealed flood mitigation arose from both localised wave attenuation and estuary-scale surge attenuation, with the latter process dominating: mean flood reductions were 17% in the sheltered top third of estuaries, compared to 8% near wave-exposed estuary mouths. Saltmarshes therefore play a generalised role in mitigating storm flooding and associated costs in estuaries via multi-scale processes. Ecosystem service modelling must integrate processes operating across scales or risk grossly underestimating the value of nature-based solutions to the growing threat of storm-driven coastal flooding.


Introduction
Coastal communities are increasingly vulnerable to ooding [1][2][3][4] owing to on-going development in ood risk areas [5][6][7] and anthropogenic climate change leading to sea level rise and intensifying storms [8][9][10][11] . Large storms can raise coastal water levels by more than 5m above astronomic tidal levels 12 , causing extensive coastal ooding [13][14][15] , as exempli ed by the devastating impacts of Hurricane Harvey in the USA and Caribbean 14,16 in 2017, Super Typhoon Haiyan in the Philippines in 2013 17 , and the 2013-14 winter storms in the UK and Europe 18,19 . Current predictions suggest that by 2100, annual coastal ooding will directly affect up to 5% of the world's population and cost up to 20% of global gross domestic product per year 4,20 . Although ood risks have traditionally been managed by building seawalls and other hardened defence structures [21][22][23] , the emerging paradigm of nature-based coastal protection holds that resilient, waveand surge-absorbing wetlands such as saltmarshes and mangroves should be integrated into coastal planning and management to more sustainably and effectively mitigate ood risk and impacts [24][25][26][27] . However, quantifying and valuing the contribution of ecosystems to ood mitigation is fraught with uncertainty due to multi-scale interactions between ecological features and hydrodynamic processes [28][29][30][31] . In particular, understanding how ecosystems in uence ood risk in estuaries -physically complex environments of high socioeconomic signi cance -remains a pressing and challenging question.
Unlocking our understanding of nature-based coastal protection within estuaries is vital because these environments are particularly at risk of increased storm-driven surge and wave ooding; estuaries often have low-lying adjacent land 7,32-35 , act as an interface between ood waters from coastal surge and riverine ooding 29,36,37 , and form natural tidal and storm funnels which magnify and transfer surge effects up-stream 36,38 , threatening inland human settlements and infrastructure 39,40 . Yet despite the enhanced ooding risk in estuaries, natural coastal protection features -such as extensive saltmarshes which typify many estuaries worldwide -can moderate the effects of coastal storms on ooding 25,30 and potentially offer signi cant nature based coastal protection services 26,41 . However, there is a growing urgency to understand how estuarine marshes contribute to coastal ood mitigation, as the combined effects of humaninduced pollution, increasing urbanisation and climate change are driving net global losses of these protective coastal wetlands [42][43][44][45] , and could undermine their ability to perform storm defence functions 46 .
Previous studies on open, exposed sections of coastline e.g. [47][48][49] have shown that saltmarsh vegetation increases hydrodynamic drag 31,50,51 , locally attenuating waves 47,48 and surges 49,52 travelling over marshes towards the shoreline. Yet, in estuaries, upstream surge mitigation -whereby marshes cumulatively attenuate surge over large distances along con ned estuary channels -is also likely to act in unison with local processes, mitigating impacts in vulnerable upstream regions [53][54][55] . Despite evidence of both localised and upstream, estuary-scale, dampening of waves and surge in isolation, there remains a lack of knowledge on how these multi-scale processes interact to holistically reduce ood risk and impacts throughout estuaries (Supplementary Table S1) ( Figure 1). Accordingly, the contributions of saltmarshes to storm ood mitigation may be grossly underestimated and economically undervalued 56,57 .
Here we address the current uncertainty in the role of coastal wetlands in ood mitigation within estuaries by integrating both localised attenuation and estuary-scale processes. Speci cally, we investigated the role of marsh vegetation in reducing ooding and ood impacts -at both local and estuary scales -across a range of estuaries which varied in size, morphology, tidal properties, marsh characteristics, and storm exposures, spanning a wide cross-section of global estuary morphologies and environmental contexts 34,58-60 . We used high-resolution hydrodynamic simulations across eight estuaries, examining how vegetation state and storm intensity affects the degree of protection -both from ooding and resulting economic damages -offered by marshes. Our results demonstrate that saltmarshes play a substantial role in mitigating the effects of storm-driven ooding in estuaries through a combination of localised wave attenuation near estuary mouths, and whole-estuary scale reductions in upstream surge.

Estuary-scale ood mitigation
We rst examined the overall role of vegetated saltmarshes in mitigating coastal ooding at the estuary-scale across storm scenarios. Vegetated saltmarshes reduced both the extent and depth of ooding for all estuaries and storm scenarios considered within our study. Ungrazed, vegetated marshes reduced mean terrestrial ood extent by 34.5% (SD±24.1), and grazed marshes by 29.1% (SD±20.6), compared with unvegetated mud ats (Figure 2a, Supplementary  Table S2). While the mean relative contribution of marshes to ood reduction slightly decreased with increasing storm intensity (Supplementary Table S2 Accompanying the reduction in ood extents and depths, vegetated marshes reduced the relative economic costs from damage to residential and commercial properties, infrastructure, and agricultural land, compared with the unvegetated scenarios across all storm events ( Figure 2c, Table S5). However, unlike the depth and relative ood extents, vegetated marshes drove substantially greater savings in relative ood cost as storm magnitude increased. Under the 100-year return level storm events, where the potential for catastrophic ooding was higher, vegetated marshes reduced ood water depth at the terrestrial boundary leading to fewer banks and defences overtopping, mitigating resulting ooding and economic costs. Notwithstanding the general economic savings observed across estuaries, vegetation drove an increase in ood damage in a single estuary, where vegetation slowed the upstream passage of surge (Supplementary Figure S1) during a large (100 year) storm, enhancing localised ooding in particularly low-lying land near the estuary mouth.

Upstream surge mitigation
To investigate the mechanisms underpinning marsh mitigation of coastal ooding, we rst examined how marshes modify indicators of upstream storm surge propagation within sequential 1km estuary sections.  Table S9, illustrated in Figure 4a,b). At the same time vegetated marshes ampli ed surge level close to the estuary mouths, as surge was less able to dissipate by moving upstream. Both phenomena -water level suppression upstream and surge ampli cation towards the mouth -increased with storm intensity, indicating that the relative contribution of marshes to surge mitigation upstream increases with increasing storm magnitude. In line with the reduction in surge current and water levels, vegetated marshes ultimately more strongly reduced ooding with increasing distance upstream: vegetation drove mean reductions in ood extent by 16.7% in the inner estuary areas, compared to 8% in the outer-estuary areas for large storms (Figure 3g-i, Supplementary Table S10). Grazing of the marshes appeared to have very little effect on storm surge attenuation as indicated by both water level and currents.
We also noted that the effect of vegetation on surge propagation to up-stream areas responded to estuary size, with marsh vegetation reducing mean relative channel water levels at the limit of tidal intrusion more in smaller estuaries ( Figure 5, Supplementary Table S11). These scale effects suggest that small estuaries bene t more from surge reduction due to the presence of marsh vegetation than larger estuaries. This effect was independent of the proportion of marsh area within estuaries, and effects on upstream surge water levels were observed for all storm scenarios.

Wave and localised surge transformation
In addition to the estuary-scale surge attenuation, we observed vegetated marshes also drove localised decreases in ooding extent and depth, with effects particularly pronounced in wave-exposed outer-estuary areas (see Figure 4 for illustration) suggesting an important dual role of wave attenuation. To begin further investigating the mechanisms of storm wave attenuation in our study estuaries, we examined how saltmarshes in uence wave heights in the estuary channel. Our focal metric was wave height relative to the maximum observed within an estuary sector to control for differences in absolute wave height across estuaries and with distance upstream (see Methods).  Table S12). These results indicate that, compared with unvegetated scenarios, vegetated saltmarsh reduced up-stream propagation of waves through estuary channels, particularly under the largest storms. However, vegetated marshes also tended to amplify wave heights in channels towards the estuary mouths for all storm scenarios, increasing water depth over shallow estuary mouth structures and in turn allowing higher energy waves to propagate into estuaries 61,62 . Yet, at these outer-estuary locations, the aforementioned increases in surge height (Figure 3d-f), as well as these now described ampli ed wave heights, generally did not translate into increases in terrestrial ooding (Figure 3g-i). Instead, marsh vegetation offset increases in surge and wave height within estuary channels via localised transformation of waves and surge travelling landward over the marshes, ultimately decreasing ooding.
Indeed, examination of wave and surge transformation along transects perpendicular to the shoreline revealed vegetated marshes -particularly wide marshes characteristic of the lower-reaches of estuaries -reduced relative wave height and ood depth at the terrestrial boundary and these bene ts increased with marsh width (Figure 6d-f). Smaller, narrower marshes also provided local ood reduction bene ts through direct attenuation of landward wave and surge but these bene ts were more variable, depending on the hydrodynamic and topographical context of their location. Unlike the estuary-scale effects of vegetation on water level and currents, grazing consistently and negatively impacted on marsh ability to attenuate incoming waves (Figure 6d-f) leading to greater ooding adjacent to the marshes, particularly for wide marshes. The relative impact of grazing on wave-attenuation appeared to be most pronounced for smaller storms but was also evident for the larger storms.

Discussion
The utility of nature-based coastal ood protection strategies has been extensively supported along open coastlines but remains uncertain within estuarine systems due to the complex, multiscale interactions at play in these socially and economically vital environments. Using high resolution modelling across a set of eight diverse estuaries we reveal the general importance of vegetated saltmarshes -regardless of grazing management -in mitigating ooding and associated economic costs across a range of storm scenarios. Crucially, while our models con rm the local scale wave attenuating effects of saltmarshes, they also reveal a far less quanti ed or appreciated effect of large-scale ood mitigation via surge attenuation, with bene ts magnifying up-stream, under more extreme storm scenarios, and with greater proportion of marsh area within an estuary. Furthermore, bene cial effects of marshes appear strongest within the smallest estuaries. Collectively, our results demonstrate that the role of marsh vegetation is more critical for reducing ood impacts -particularly in small estuaries -than previously assumed.
Our results show that local-scale surge and wave attenuation work together with larger-scale upstream surge attenuation to deliver substantial mitigation of coastal ooding, and subsequent ood damages, under a range of storm scenarios and estuary contexts. We found that, by attenuating waves and surge travelling perpendicular to the shoreline, marshes have the strongest localised dampening effects close to the estuary mouths where marsh widths and wave energy are highest, in-line with previous results from exposed coastlines 48,52,63 . However, larger, and more consistent ood extent and water level reductions were observed at wave-sheltered upstream locations. Observed strong and progressive divergence between vegetated and unvegetated scenarios with distance upstream clearly indicates that upstream ood reduction is driven by cumulative estuary-scale surge attenuation, suggesting that vulnerable up-stream human settlements rely heavily on downstream marshes in mitigating surge-driven ooding. Furthermore, the greatest reductions in localised wave attenuation occur across wide marshes, while the strongest large-scale surge attenuation occurs in estuaries with extensive marsh areas, indicating that greater relative marsh area has both local and large-scale ood mitigation bene ts. Within estuaries, this interplay between the role of long-distance surge mitigation, and limited local wave and surge reduction in our study adds to previous work emphasising direct local wave-and surgeattenuation along exposed coastlines e.g. 53,64,65 , to reveal the under-appreciated role of marshes within typically wavesheltered small estuaries. Furthermore, within the size ranges of estuaries (3-108km²) in our study, the role of marsh vegetation in attenuating upstream surge was stronger in the smallest estuaries, consistent with previous evidence of scale-dependence of surge mitigation along creeks 54 , as well as theoretical work on the morphology and con guration of estuary channels [66][67][68] , and is supported by smaller surge reductions observed in the much larger Scheldt estuary 69 (~370km²). The extension of the coastal protection paradigm to estuaries, and the suggestion these services may be even stronger in the smallest estuaries, is globally signi cant because small to medium sized estuaries are most common across many countries 34,[58][59][60]70 while also being particularly vulnerable to ampli cation of surges driven by sea level rise 38,71 .
Marsh mitigation of storm ooding has accompanying economic bene ts, reducing ood damage costs by an average of 37% for large storms across the estuaries within our study. Savings from ungrazed and grazed marsh vegetation scaled exponentially with storm intensity, with the relative marsh-driven cost savings considerably higher than the 1-16% savings previously predicted for similar signi cant tropical storms along open coastlines dominated by extensive fringing or back-barrier marshes 41,57,72 . The estimated absolute ood damage savings within estuaries are similar to those previously estimated for hurricane-exposed US coastlines 73,74 , and considerably greater than the value of other saltmarsh services such as carbon storage 75,76 or livestock grazing 77,78 . Indeed, in our study average ood mitigation from marshes -per hectare per year -was valued at between 22-75 times that of carbon storage, and 117 times that of grazing (Supplementary Table S7). Accordingly, our new estimates serve as a tool to generate greater public and policymaker recognition of the nature-based ood mitigation services in these deceptively sheltered environments, and substantially enhances the economic case for saltmarsh conservation and restoration. Even so, as our reported estimates relate exclusively to ood mitigation, they will underestimate the total value of marshes for coastal protection, including the role of vegetation in reducing shoreline erosion 79,80 , and maintaining wave and surge attenuating raised marsh platforms 26 . In our study, ood-mitigation economic bene ts of marshes can be considered general, with vegetation driven reductions in ood cost occurring in 7 of the 8 estuaries, but not universal: in one heavily modi ed estuary, extensive high-crested channelisation prevented ooding upstream while vegetation enhanced surge water levels in downstream, densely populated areas, leading to a modest increase in ood damages when vegetation was present. Yet despite this inevitable context dependency, arising from interactions between physical, ecological and anthropogenic features, we nd strong evidence for general patterns of marsh-driven reductions in economic costs from storm ood events.
Our results have important implications for marsh management for ecosystem services. Previous valuation and ecosystem service mapping approaches have considered the more direct effects of marshes on coastal protectionemphasising marshes in wave-exposed locations and fronting valuable infrastructure 56,56,81,82 . Clearly, it is vital that tools used for valuation of coastal protection services evolve to include the dominant process of long-distance surge mitigation, in addition to the better integrated direct contributions of marshes and other coastal systems to ood mitigation. Accordingly, marsh conservation and restoration must be treated at the whole estuary scale, with an understanding that marshes in highly wave-sheltered locations, or fronting areas with low ood vulnerability, may still be providing essential ood mitigation services further upstream. Importantly, our results suggest that marshes can be managed for multiple bene ts, with grazing generally having only small in uences on wave attenuation and surge mitigation -indicating that maintaining or enhancing marsh extent, rather than grazing pressure, should be a priority for ood mitigation management. Looking ahead, as climate change is predicted to bring increasing frequencies 3 , and magnitudes 10,14,83 of large storms, with current 1 in 100 year storm water level events expected annually by 2100 84 , our results indicate that appropriate valuation and effective management of marshes is paramount to mitigate rising risks of ooding and its social and economic impacts.
In conclusion, our study demonstrates that coastal wetlands strongly reduce storm ooding and its economic consequences through both local and estuary-scale processes. Our research demonstrates that current valuation tools based on local-scale interactions oversimplify and underestimate contributions by coastal marshes to ood mitigation in estuaries where storm ooding threatens homes, industry, and infrastructure. Furthermore, we show that marshes mitigate ooding across a range of estuarine and environmental contexts, suggesting that our results will also apply to many other estuaries worldwide. Ecosystem service modelling and decision making in estuarine socio-ecological systems must now move towards integrating multi-scale processes or risk underestimating the value of wetlands and their conservation for protecting communities in the face of rising ood risk.

Site characteristics
To investigate the role of saltmarsh vegetation in reducing storm ood risk we examine eight case study estuaries along the coast of Wales, UK (Supplementary Figure S5) which explicitly differed in their size, morphology, marsh extents and exposure to storm events, re ecting the inherent morphological and environmental variability of estuaries 34,[58][59][60]70 . These differences, and differences in prevailing conditions, allowed us to explore the role marshes play irrespective of environmental context, and investigate potential interactions between marsh vegetation and estuary characteristics in moderating ooding. The properties of each estuary summarised in Table 1. (Delft/SWAN-VEG) on both waves and ow. This approach has been successfully applied in recent numerical modelling studies which include vegetation 89,90 , and has been found to be more consistent across contexts than xed Manning's n friction approaches 91 . The hydrodynamic processes within Delft3D were calculated using a 2-dimensional depthaveraged form of the unsteady shallow water equations 92 which has been extensively utilised and validated across a variety of applications and timescales [93][94][95] , including for investigating the role of saltmarsh systems 89,90 .
Models were run on high resolution structured grids. Offshore areas were typically represented as 150x50m grids, and grid sizes became progressively smaller towards the estuary mouth and the upstream areas. Grids within estuary boundaries were high resolution and uniform, with 10x10m cell sizes giving good resolution to resolve hydrodynamics in up-stream river channels and marsh creeks. The model domain extended into the terrestrial zone to 3m elevation above the height of the terrestrial-estuary boundary to characterise terrestrial ood extents and depths. Models were validated To understand the roles and potential interactions of vegetation and storms, we used a fully crossed factorial design, covarying the vegetation state and storm magnitude over the 8 estuaries, creating 72 individual scenarios. We suspected that in estuaries, ood risk would be dictated by different processes operating at different spatial scales, and so we analysed depths, ood extents, current velocities and signi cant wave heights for each estuary and scenario at three different spatial grains; local (transect level), segment (1km segments) and whole estuary levels.
Previous studies have indicated that over-marsh transformation of waves and surge is the most important pathway for reducing ooding in open-coastline systems 26,49,63 . To assess whether this also applies in estuarine environments we employed transect sampling to look at wave and surge transformation across individual marshes to examine the importance of marsh vegetation for preventing ooding from local wave and surge overtopping of banks and defences.
Transects were created in QGIS and were mapped onto model output data at 250m intervals, and sampling points were equally spaced at 10m intervals from the marsh/channel edge until the terrestrial boundary. At each transect point we measured maximum water level, signi cant wave height and current velocity. From this data, we then examined the total reduction and proportional reduction in water level and wave height driven by the vegetation from the channel to terrestrial boundary as an indicator of the effectiveness of marshes in reducing local storm ooding.
We also suspected that vegetation may play a wider role in estuaries, creating a cumulative drag effect at the estuary scale which could reduce ood extents further upstream 69 . To investigate whether cumulative drag had a strong effect on ood potential, we decomposed the model outputs into 1km sections along main estuary channels, and measured averaged peak current velocity, averaged peak water level, and averaged peak signi cant wave height within the estuary area sections, and ood extents and depths in adjacent terrestrial areas using zonal statistics. These 1km sections extended from the estuary/coastal boundary, up until the limit of tidal intrusion (LTI). Because of the high degree of variability in absolute area and topography within estuaries, we calculated ood extents, water levels and depth within each block as a proportion of the maximum observed ood extent, levels or depth respectively within each estuary to look at the relative role of marsh vegetation independent of estuary context. We also applied this to the distance of sections upstream, as the estuaries varied considerably in length, with distance being represented as a proportion of distance of each section upstream from the estuary mouth (0) to the LTI (1). At the whole estuary level, we quanti ed average peak water level, mean peak current velocity ( ood and ebb) and mean peak signi cant wave height using zonal statistics within the boundaries of the whole estuary. Additional information on model speci cation is available in the supplementary materials (section 3.1 to 3.2).

Economic Analysis
In addition to examining the hydrodynamic consequences of vegetation, we assessed the economic costs associated with ood events based on the extents and depths of ood waters from the hydrodynamic models. We compared the ood damages experienced in each estuary when marshes have no vegetation to those with full or grazed vegetation, and for different storm return levels (1 in 1, 1 in 10, 1 in 100 year). Our calculations aggregated ood damage estimates for residential, commercial, industrial and agricultural properties, as well as to public buildings and water and electricity utility installations using ood cost estimates for saltwater inundation damages (to building fabric, household inventory and domestic clean-up) from cost tables in the 2018 update of the Multi-Coloured Manual (MCM) 100 . Properties in atrisk areas were identi ed using OS Mastermap layers 101 , assigned a building type (e.g. terraced, detached, retail properties etc.) and property age using a systematic visual assessment in Google StreetView©, and segmented by neighbourhood for socioeconomic status (UK Census Data 102 ) to calculate economic cost values (in GBP(£)).
We also accounted for losses in agricultural output on ooded farmland, osses from disruption to travel arising from ooded roads, and from restrictions in outdoor recreation activity resulting from the ooding of parks and countryside paths. Roads were identi ed using the Ordinance Survey Integrated Transport Network 103 data layer, and assigned a value for the average number of vehicles using them per hour from Department for Transport road tra c statistics data (DfT, 2020 104 ). To calculate economic costs from ooding we applied a 'diversion-value method' 100 , whereby vehicles were assumed to have to divert to avoid ooding. For the sake of simplicity, we assumed that diversion to extend the journey by a distance equal to the length of road made impassable by the ood water for a period of 12 hours. Travel disruption costs were then calculated by multiplying the costs per kilometre of additional travel -provided in the MCM cost tables 100 -by the number of vehicles affected during the ooding event. Estimates of ood losses arising in agriculture and outdoor recreation activity were also calculated, following established repair and disruption values in the Green Book (Central government guidance on appraisal and evaluation) 105 .
We calculated absolute ood damage costs for single storms for each return-level event, as well as an annualised cost based on the Net Present Value (NPV) 100 , and these values (in £GBP) were subsequently converted into $USD (at exchange rate of USD$1.36 to GBP£1; December 20 th , 2020). As the exposure of assets varied between estuaries, we also recalculated these absolute values as proportional reductions, comparing the cost for each scenario with the maximum observed ood cost for each estuary. This allowed us to compare the relative ood protection value of marshes across estuaries, independently of population density and asset exposure. Further details on the economic analysis are available in the supplementary materials (Section 3.3)

Statistical analysis
Analysis of model outputs was conducted in the R statistical computing environment 106 . To analyse relative extent, water level and wave reduction (relative ood effects) data (proportional data) we employed mixed effects beta regression models using the glmmTMB package 107 with the estuary as a random factor to account for unquanti ed environmental differences in prevailing conditions between estuaries. We assessed effects of a range of different predictors on ood effects at three different scales: Transect level (within marshes), up-stream zone, and whole estuary level. The proportional upstream distance and marsh width predictors were log10 transformed -at the estuary scale and marsh transect levels respectively -to account for non-linearity, and model diagnostics performed to ensure adequate model t. Results were then visualised using the GGplot2 108 , Coefplot 109 and Visreg 110 packages.