## Introduction

Nature-based solutions refer to the aim to work with nature for tackling socio-environmental challenges, such as climate change, food and water security or natural disasters. Among those, the coastal protection benefits of natural ecosystems, often referred to as nature-based coastal defences, are increasingly being recognised within international and national coastal adaptation, resilience and sustainable development plans and strategies1. Based on the latest Nationally Determined Contributions submitted to the United Nations Framework Convention on Climate Change, a few coastal nations already explicitly advocate nature-based solutions for coastal protection, as a means to address future coastal hazards and sea level rise threats, with mangrove restoration as a common adaptation measure to enhance the resilience of local communities to climate change2.

Mangroves are inter-tidal wetlands found along coastlines in much of the tropical, subtropical and warm-temperate world, where they naturally serve as the first line of defence against flooding and erosion. If existing mangroves were lost, 15 million more people would be flooded annually across the world3. Mangrove wetland restoration projects are starting to be widespread in several countries4 for preserving their natural habitat and carbon sink function5. Understanding their value for coastal defence is also crucial for further encouraging their conservation and restoration. For cities located in estuaries or deltas, like many large Asian cities, the creation or restoration of mangrove wetlands between the city and sea could mitigate waves and the landward propagation of storm surges6.

Wave height reduction due to the interaction with coastal salt marshes7 and mangroves8,9,10,11,12,13 is well established in the literature and mostly acts at the local scale of the wetland. Less well understood are the factors that control storm surge reduction by vegetation14, with the majority of observational and modelling studies focusing on storm surge mitigation due to the resistance exerted by salt marshes15,16,17,18,19,20,21,22,23,24 and few studies demonstrating the value of mangroves25,26,27,28,29,30,31.

The effectiveness of the vegetation in dissipating storm surge and inundation is dependent on the density, height, width and fragmentation of the vegetation zones15,16,17,18,19,23,27,29,30, as well as on intensity, duration, forward speed and track of the storm15,16,17,20,22,24,27,28 and the surrounding case-specific larger-scale landscape settings15,17,18,20,21,22,24,27,28,30. The landward attenuation of the additional water level due to storms, referred to as within-wetland surge attenuation, is usually quantified as the rate of vertical reduction in storm surge height per horizontal inland distance over the wetland, ranging from 1.7 to 25 cm per km across salt marsh vegetation14, with higher rates, 18–50 cm per km, across a mangrove forest27,31.

The majority of studies investigating the effectiveness of vegetation for storm surge attenuation tend to address local (within-wetland) effects14, while only few studies18,24 investigated the non-local effects of coastal wetlands in complex estuary environments. Those studies have focused on salt marshes in estuaries in the Netherlands, Belgium and in the United Kingdom (UK) and examined the upstream surge attenuation, which is the contribution of wetlands to the reduction of surges that propagate upstream along an estuary. There is a lack of similar studies addressing the effects of mangrove forests at an estuarine-wide scale. A better understanding of how nature-based coastal defences, and in particular mangroves, interact within estuaries and complex deltas would help to boost the large-scale implementation of nature-based coastal defences, which at present is limited to a few projects in the UK and Belgium6,18 involving the conversion of reclaimed land back to natural coastal wetlands.

Since mangroves cannot fully block the water, they are often combined with traditional flood defence structures like levees or seawalls. Mangrove forests placed in front of coastal protection structures reduce the risk of overtopping and direct wave impact32, allowing for lower structures and, consequently lower construction costs. In the absence of levees or seawalls, mangrove forests may still reduce the extent of flooding, whereas even a small reduction in water level could already greatly reduce the extent of flooding in the low-lying areas behind the mangroves33. As the attenuation of storm surges increases with the width of the mangrove patch, wider mangrove forests could offer better protection for those low-lying areas, provided that enough accommodation space is available34.

In this study, we investigate how coastal mangrove wetlands can modify the hydrodynamics of a complex delta coastal plain during extreme events, at both the local wetland scales and, more broadly, at the delta scales. The study focuses on the Pearl River Delta (Fig. 1a, b), a site containing complex river systems, with several bifurcating and coalescing river branches, where water levels are influenced by the interaction of the river runoff, tides and storm surges from the South China Sea. The Pearl River Delta flood plain is also home to several very large cities (‘mega-cities’), including Hong Kong, Shenzhen and Guangzhou (Fig. 1b), that are experiencing an exponential population and economic growth, and thus an expansion of areas vulnerable to coastal flooding35.

Estuarine mangroves within the broader Guangdong—Hong Kong—Macao Greater Bay Area, where the Pearl River Delta is located, have first undergone a loss and then a gain of the area over the last 30 years. Nearly 40% of mangrove areas were lost during the 1990s, mainly resulting from human exploitation of the coastal landscape (conversion to built-up area and aquaculture ponds), but from 2000 to 2018, the mangrove area has increased thanks to the establishment of nature reserves36. In the Pearl River Delta only, a net loss of 11.73 km2 (45%) of mangroves during the period between 1985–2015 has been detected in the analysis of satellite imagery37. While these studies demonstrate the dramatic reduction in mangrove extent and subsequent degradation of the ecological function of these habitats, the previous range indicates that the coastal areas investigated are suitable mangrove habitats. Thus re-vegetation of coastal areas by mangroves is a potentially viable ecosystem-based coastal adaptation measure. The remaining few small patches of mangroves in the Pearl River Delta are found in the lower estuary, along the coast of Qiao Island, Shenzhen Bay and Lingding Bay36 and in the upper estuary close to Guangzhou, along the river channels of the Nansha and the Panyu district38. Guangzhou is crossed by several urban channels, most of which directly connect to the South China Sea, increasing the city’s exposure to coastal flood risks. Guangzhou has been identified as the most vulnerable city in the world in terms of annual economic losses due to flooding39. Shenzhen is presently ranked as the ninth most vulnerable city to sea level rise, but it is projected to rise to the fourth most vulnerable by 205039. The vulnerability of these two cities to coastal hazards motivated the present modelling investigations. In this study, we numerically modelled the protection capability of the mangrove wetlands in Shenzhen Bay (Fig. 1c) and in the upper estuary river branches close to Guangzhou (Fig. 1d) to determine their ability to mitigate coastal flooding. In Shenzhen Bay, the presence of mangroves located in two natural reserves (Futian Nature Reserve and Mai Poi Nature Reserve), where mangrove conservation and restoration effort have been conducted36, was simulated (Fig. 1c). The Shenzhen Municipal Government has also initiated a large coastal reclamation project for some areas in the Futian coastal wetland35, which could interact and alter its function as flood-storage area. For the upper delta location, we simulated two hypothetical mangrove forests, which are an expansion of the existing small mangrove plantations located in one of the river channels just downstream of Guangzhou (Fig. 1d). To explore the effects of vegetation on storm surge dynamics and currents, we used a Finite Volume Community Ocean Model (FVCOM) implementation for the South China Sea and the Pearl River Delta (model domain in Fig. 1a and model bathymetry in Fig. 2a, c) and simulated Typhoon Hato (2017) one of the strongest typhoons to affect the coastal areas of the Pearl River Delta in recent decades40. Additionally, we analyzed how the effectiveness of mangroves changes under different sea level rise (SLR) scenarios.

In this work, we show that water level attenuation by mangroves varies in space and in time and cannot be summarised into a single linear reduction factor. The vegetation properties and the location of the mangroves within the delta play an important role. In general, if mangroves are located in open bays and open coastlines they will affect the water levels mostly locally (within-wetland), instead if located in the delta river channels, they will also influence non-local water levels (upstream water level attenuation). Both within-wetland and upstream attenuation are at their highest during extreme water levels, like those experienced during strong typhoons.

## Results

The level of protection offered by a vegetation patch located in the natural reserves in Shenzhen Bay with a width of 600 m, which is about the width of the vegetation patch actually present, is shown in Fig. 3. The same figure demonstrates the loss in protection if the mangroves decrease in size to 300 m or disappear completely, as well as the changes in protection with a wider mangrove forest (900 m) (see Fig. 2b). Figure 3 analyses the total, tide and surge water levels along the coast, with and without the mangroves, for 24 h, spanning before and after the water level peaks driven by Typhoon Hato. The temporal trends represent the average value among all the mangrove patch coastal nodes (blue squares in Fig. 2b). Each experiment is performed twice (see Experiments 01–06 in Table 1): fully forced (panel a) and tide-only (panel b). Tide and surge contribute to the total water level. The surge is calculated as the difference in water levels between the tide-only and the fully forced runs (panel c). We refer hereafter as ‘high-drag vegetation’ to the experiments (see a full description of experiments in the section ‘Method’) with drag coefficient CD = 4 and flow-facing area per tree A = 3 m2 (mangroves with leaves), and as ‘low-drag vegetation’ to those with CD = 2 and A = 1 m2 (mangroves without leaves). The drag coefficient and flow-facing area depend on the mangrove species, age and presence/absence of leaves.

The maximum total water level at the coast (on 23 August 2017 at 06:00 UTC (Coordinated Universal Time), the time Typhoon Hato passed closest to the Pearl River Delta) is overall reduced from 3.3 to 2.1 m by the vegetation patch of 600 m (the width of the vegetation patch actually present) when a high-drag vegetation is applied (green solid line in Fig. 3a). A 600 m patch with a low-drag vegetation and a narrower vegetation patch (300 m) with high-drag vegetation (dashed green and light green lines in Fig. 3a) are effective in reducing the total water level in the hours before reaching the peak, but not in reducing the peak itself. A wider vegetation patch (900 m) with high-drag vegetation would instead greatly reduce the total water level, which then reaches only 0.5 m at the coast (orange solid line in Fig. 3a); the same width but low-drag vegetation leads instead to a reduction of 0.8 m at the coast (dashed orange line in Fig. 3a).

The maximum tidal elevation (on 23 August 2017 at 03:00 UTC) is changed only by the 900 m vegetation patch with high-drag vegetation, showing a 0.1 m decrease in the maximum tidal height (orange solid line in Fig. 3b). However, the tides are delayed in all experiments. This time delay becomes more evident with high-drag vegetation 600 and 900 m patches: half hour delay and 1 h delay, respectively (Fig. 3b). This shift leads to an apparent increase (of about 0.1–0.3 m) in tidal elevation when the tide is falling, which contributes in reducing further the surge when the total water level peaks (surge is calculated as the difference between total water level and tidal elevation, thus if the tidal elevation increases the surge decreases).

The maximum surge level (on 23 August 2017 at 06:00 UTC) along the coast is halved (from 2.8 to 1.4 m) by the 600 m vegetation patch with high-drag vegetation (green solid line in Fig. 3c). As observed for the total water level, there is an apparent big surge reduction before reaching the peak with the low-drag vegetation 600 m and high-drag vegetation 300 m patches (dashed and light green lines in Fig. 3c), however when reaching the peak the surge at the coast is not reduced or only slightly reduced (5 cm). This can be explained as a delay of the currents bringing water from the open ocean toward the coast, pushed toward the shore by the force of the wind, similar to the delay observed for the tides. A wider vegetation patch (900 m) with high-drag vegetation leads instead to a total suppression of the surge at the coast (−0.3 m) (orange solid line in Fig. 3c), the same width but low-drag vegetation leads instead to a reduction of 1 m (dashed orange line in Fig. 3c).

Before the passage of Typhoon Hato (before 23 August 2017 04:00 UTC), the total water level and the surge both increased when vegetation is present in the model, 0.3 m for the total water level and 0.6 m for the surge (for the high-drag vegetation 600 m patch). The time delay in tides leads to an apparent decrease/increase in tides of about 0.3–0.5 m, that could affect the water depth and have consequences on the surge. However, an increase in the surge before the peak has been observed in a run without tides too (see Supplementary Fig. S.1), this means it cannot be fully attributed to the changes in the tidal modulation of the surge.

The surge reduction offered by mangroves changes under different SLR scenarios. Figure 4 shows how the effectiveness of the high-drag vegetation 600 m patch changes under three SLR scenarios (30, 50, and 90 cm). With 30 cm SLR, the vegetation will reduce the surge, however, the surge will reach 2.2 m, which is higher than what was simulated without SLR. The mangroves will be even less effective with 50 cm SLR and 90 cm SLR, when the surge will reach roughly 2.5 m (dashed and dotted red lines in Fig. 4). The friction of mangroves will be less effective in dissipating the surge with SLR due to the vegetation being placed in a deeper water column. This is because in the model simulations, we are assuming the coastline is fully protected and mangroves are placed in front of a seawall and no extra land gets inundated. At the same time, under the different SLR scenarios, the surge will also decrease with SLR (purple lines in Fig. 4). This is due to the wind stress being less effective in pushing a deeper water column, leading to a reduction of the maximum surge during extreme events41. This means that with 90 cm SLR, the surge reduction due to mangroves is nearly zero (dotted red line and dotted purple line in Fig. 4), although there is a reduction in the hours before the peak is reached.

Figure 5 shows how the surge (a–d) and current speed (e–h) change during extreme water level conditions in Shenzhen Bay (from 04:00 to 07:00 on 23 August 2017) due to the presence of the high-drag vegetation 600 m patch (Experiment 03 in Table 1). The other experiments show similar patterns but lower values (Experiments 02 and 04, see Supplementary Figs. S.2,  S.3) or more intensity of changes (Experiments 05 and 06, see Supplementary Figs. S.4, S.5). One hour before the total water level peaks along the coast of Shenzhen Bay (on the 23 August 2017 at 05:00 UTC), there is a decrease of the surge in the vegetation patch and an increase in the surge in the rest of the bay. This pattern is connected to a decrease in the current speed in the vegetation patch, which is driven by the local vegetation friction, and a decrease in speed in the bay in the same location where the surge increases. When the water travelling from the open ocean into the bay, pushed toward the shore by the force of the wind, feels the friction of the vegetation, this causes a decrease in the speed of the currents bringing water toward the coast (i.e. slow down of the surge propagation speed) and consequently a temporary increase in a surge in the middle of the bay (i.e water piling up in the bay). When all the water pushed by the force of the winds reaches the shore on 23 August 2017 at 06:00 UTC, the changes are a local (in the vegetation patch) decrease in surge and current speed due to the vegetation friction. The vegetation effect of decreasing the current speed in such extreme events is relevant for reducing erosion along the coast, while local increases in current speed are visible outside of the vegetation patch.

The Shenzhen Bay mangrove forest experiments have shown that mangroves can locally attenuate the surge travelling over the vegetation towards the shoreline. In estuaries, upstream surge attenuation, i.e. the cumulative surge reduction over large distances along confined estuary channels, is also likely to mitigate extreme water levels in vulnerable upper delta regions, like the Guangzhou area. Here, we show how hypothetical mangrove forests, located in the river channels in the upper delta areas (Fig. 2c), change the water levels upstream, where Guangzhou is located. We show here the results with different patch lengths (see Fig. 2d) and vegetation drag coefficients (we did not test varying patch width because the channels are too narrow to accommodate mangrove forests wider than 300 m). The effect of vegetation is maximum just before and when the surge peaks in the area, between 07:00 and 09:00 on 23 August 2017. Figure 6 shows the effect of the 16 km patch from Hualong to Lianhuashan (Experiment 08 in Table 1). Cumulative mangrove drag first delays and then overall reduces the surge level in the upstream delta channels close to Guangzhou, at the same time, the vegetation patch (Fig. 6a, b) amplifies the surge level downstream of the mangrove forest (towards the estuary mouth) and in the eastern river channels, as the surge is less able to propagate upstream of the mangrove forest (blockage effect). The vegetation patch has the largest blockage effect when the surge is reaching the area between 07:00 and 08:00 on 23 August 2017, acting as a solid obstacle rather than dissipating energy, diverting some water into the eastern channels and increasing the water level downstream of the vegetation patch (Fig. 6a, b). This downstream water level increase is dissipated when the surge has peaked in the area (Fig. 6c), and as a consequence, the blockage effect is reduced too. While the large surge reduction (>0.3 m), visible at 07:00 and 08:00 on 23 August 2017 (Fig. 6a, b), can be attributed to a delay (induced by the vegetation) of the surge travelling up in the estuary, when the surge peaks in the area at 09:00 on the 23 August 2017 (Fig. 6c), the cumulative mangrove drag overall reduces the surge level upstream. The change in the maximum surge at any time (Fig. 6d) is a more meaningful measure, i.e. not affected by shifts in time, to understand how effective, or disruptive, the vegetation is. It shows indeed, a surge reduction exceeding 0.2 m in the upstream delta channels close to Guangzhou, while the increase in the eastern river channels is nearly negligible.

Current speed (Fig. 6e–h) is decreased locally in the vegetation patch and in one of the river branches, likely reducing erosion along the coast. However, it is increased in the river branch further upstream where Guangzhou is located, thus likely increasing erosion there. The spatial changes in surge and current speed induced by the low-drag vegetation long patch (Experiment 10 in Table 1) and the high- and low-drag vegetation short patch (6 km, Hualong) are not shown here (Experiments 07 and 09 in Table 1), they have a similar pattern but less intensity than the high-drag vegetation long patch (see Supplementary Figs. S.6S.8).

Figure 7 shows how the 300 m high-drag and low-drag vegetation patches of different lengths (6 and 16 km) change the maximum total water level and surge at any time during the passage of Typhoon Hato, starting from the southernmost edge of the mangrove patch and going upstream along the west shore (Fig. 7a, c) and along the east shore up to the channel where Guangzhou is located (Fig. 7b, d) (start and end points of the coastal sections are the pink squares in Fig. 6d). The maximum total water level and surge are reduced by the cumulative drag of the mangrove forest. The reduction gets larger going upstream in the vegetation patch (the location of the mangrove patch along the coastal section is identified by green and orange circles in Fig. 7a, c) and it is sustained further upstream outside of the vegetation patch. The largest reductions in total water level (0.3 m) and surge (0.2 m) are achieved with the high-drag vegetation longest patch, along the west shore (Fig. 7a, c), where the mangrove forest is actually located. Along the east shore of the upstream river channel where Guangzhou is located, the maximum reduction is obtained with the high-drag vegetation longest patch and it is 0.2–0.3 m for the total water level and 0.1–0.2 m for the surge. With the shorter vegetation patch the maximum reduction, in both total water level and surge, is <0.1 m along both the west and east shore. For both the long and short patches the high-drag vegetation patch is slightly more effective than the low-drag vegetation patch.

We have analyzed how the effectiveness of the high-drag vegetation patch from Hualong to Lianhuashan change under different SLR scenarios (30, 50 and 90 cm), and we found the vegetation will be still able to reduce the total water level in the upstream river channels where Guangzhou is located, with similar spatial changes as the ones simulated with no SLR (see Supplementary Fig. S.9). Differently from the Shenzhen Bay mangrove patch experiments, where the mean total water level uniformly increases by the SLR amount, in the upstream river channels SLR will interact with the river discharge and tides in a complex way. As described in a previous study41, SLR will not increase the total water level by the same amount everywhere in the Pearl River Delta. The western river channels will be influenced by the interaction of SLR, river discharge and tides. While tides will see an amplification due to SLR-induced depth changes and consequently reduced bottom friction, the river discharge will halve the increase in mean water level due to SLR.

## Discussion

The Pearl River Delta is a coastal region with a large population, projected to be more than 120 million people by 2050, that has become a global economic hub, dominated by the manufacturing, logistic, tourism and finance industries35. Traditional hard-engineered flood protection measures remain a favourite option, but less than 4% of Guangzhou is protected to at least the 1-in-100-year flood frequency and most flood-prone areas are protected only for the 1-in-20-year flood frequency or below35. The current urbanisation and industrialisation rate means also that more areas are becoming vulnerable to flooding and need to be protected. Flood defences by hard-engineered approaches alone are, therefore, unlikely to be economically sustainable under current rates of climate change and urban expansion. Nature-based coastal defences could be used in conjunction with hard-engineered defences to reduce their cost42. To the contrary, in some areas of the Pearl River Delta, land reclamation has extended the coastline 1 km seawards in the last decade, and most reclaimed land has been converted from mangrove coastal wetlands35,36, which originally acted as a buffer to extreme water level.

In 2017, the State Forestry Administration of China released a 10-year plan called ‘The Planning of Establishing National Coastal Shelter Forests’ (2016–2025), in which the ‘Mangrove Forest Restoration Project’ is listed as a key project43. The local (behind the wetland) protection offered by nature-based coastal defences has been demonstrated14. However, large-scale implementation of mangrove restoration for coastal protection, in a physically complex area like the Pearl River Delta, with major outlets of three main tributaries of the Pearl River and several river branches connected with the South China Sea, requires a full understanding of the local and non-local effects of vegetation in a deltaic area. The latter can be achieved with location-specific modelling of the complex deltas dynamics and their interactions with mangroves, as we did in the present study for the Pearl River Delta. The obtained knowledge is of value to the management of the spatial planning of mangrove-based coastal defence in the Pearl River Delta. Similar studies are necessary for the real-life implementation of nature-based coastal defences in other urban deltas worldwide.

In Shenzhen Bay, where mangroves are present, they attenuate the water level during extreme water conditions, while a slight amplification is observed during calm conditions, however, flood risks are not exacerbated since amplification rates are very small. The local, within-wetland, attenuation of extreme water level (total) can vary from 0 to 2.8 m, depending on the width of the patch and the mangrove forest properties. Hypothetical 300 m wide mangrove forests located in the upper estuary (where some mangrove plantations exist) contribute to the reduction of surges that propagate upstream where Guangzhou is located. Thus, narrow vegetation patches (up to 300 m) can be effective if located in estuarine/deltaic settings as they can provide upstream (total) water level attenuation, which in Guangzhou is about 0.1–0.3 m, depending on the length of the patch and the mangrove forest properties. Mangroves in the upper river channels can also create blockage effects, thus complex deltas need accurate modelling of specific interventions to understand which are the areas that can eventually see an amplification of water levels and under which conditions.

While empirical data and modelling studies are available for within-wetland surge attenuation by salt marshes14, there are only a few observational studies about surge attenuation rates observed in mangrove forests27,29 and none of them are in deltas, where some of the largest mangrove trees in the world are located. We found that a 600 m patch could provide a surge attenuation up to 1.4 m (233 cm per km) with the high-drag vegetation. These values are larger than the attenuation rates for salt marshes, showing that, to offer coastal protection, a narrower wetland is needed with mangroves compared to the width required with salt marshes (at least 10 km wide14). Our simulations are based on the drag coefficients of mangrove branches sampled in the Pearl Delta and measured in flume experiments44. A comparison with measurements in situ would be desirable to validate our results. However, the surge attenuation rates discussed in this study are during typhoon conditions, which are inherently rare events (and it is dangerous to collect data under such conditions), thus it is not surprising that no field data exist.

In this work, the upstream water level attenuation that we observed in Guangzhou is due only to cumulative vegetation drag and not to a water storage effect of additional inundated land, as in other studies18, because it is not realistic in a highly urbanised region like the Pearl River Delta where the coastline and river shores are ‘fixed’, i.e. protected. A nature-based coastal defence scenario, where coastal societies retreat from the coast, is more likely in rural, sparsely-populated areas45, where more space is available for accommodating an expansion of coastal wetlands. However, future-proofing schemes of urban areas could also opt for the accommodation of flood buffer areas depending on the specific settings and socio-economic circumstances.

Similarly, the SLR scenarios presented in the paper show what will happen with mangroves placed in front of a fully protected coastline. However, in the absence of seawalls and where inland areas are accessible and suitable for the establishment, mangroves could shift inland. Additionally, under the right circumstances, mangroves may respond to relative SLR by shifting vertically, if the accumulation of sediments (not modelled in this work) raises the forest floor at a pace similar to SLR46.

In general, we found that the effective design of nature-based coastal defences requires location-specific realistic predictions to be done prior to extensive restoration efforts. This should be done in conjunction with an understanding of the survivability of mangroves in that specific setting. We keep this as a question for future studies to understand what the minimal level of surge reduction that would make an extensive restoration effort a successful investment for flood mitigation, which should also take into consideration other ecosystem services offered by mangroves, i.e. carbon storage, biodiversity, prevention of coastal erosion, fisheries, water quality.

## Method

We used an FVCOM47 implementation for the South China Sea and Pearl River Delta, with an unstructured grid that extends from a coarse grid (>10 km) in the open ocean to an appropriately high resolution (100 m) in the delta distributary channels, with 25 uniform σ (terrain following) vertical layers. The model has been previously validated and used to explore future interactions between sea level rise, tides and storm surges41,48. Water level time series have been validated against observed data from four coastal stations (root mean square error <20 cm) and average tidal range levels have been also validated using 23 tide gauges located in the river branches41. Comparison between the total water level modelled and observed at the Hong Kong tide gauge during typhoons Hato is also presented in a previous study41.

To understand what is controlling the effectiveness of mangroves, we modelled several scenarios with different locations of mangroves (in Shenzhen Bay and in the upper estuary) and mangrove properties. In Shenzhen Bay, we have simulated a mangrove forest of 600 m, which is about the width of the vegetation patch actually present (Fig. 1c) and the loss in protection if the mangrove forest decreases in size to 300 m or disappears completely, as well as the changes in protection with a wider mangrove forest (900 m) (Table 1 and Fig. 2b). For the upper delta location, we have analyzed the level of protection which would be provided by two hypothetical mangrove forests of 300 m width and of different length. These hypothetical patches include some existing mangrove plantations: the short patch (6 km) includes the mangrove plantation in Hualong and the long patch (16 km) encompasses the Hualong and Lianhuashan mangrove plantations (Panyu District) (Figs. 1d,  2d). In the upper estuary, we did not test the sensitivity to the width of the mangrove patch because the channels are too narrow to accommodate mangrove patches wider than 300 m, and we did not test varying lengths in Shenzhen Bay because we wanted to reproduce the length of the mangrove patch that is actually present.

The resistance created by vegetation has been previously modelled by increasing the bottom friction15,19,20,22,23,24,27,28,30. A more accurate approach, used in this study, is to consider the vegetative drag within the water column using a momentum sink approach, i.e. adding an additional drag force in the three-dimensional momentum equation. This same approach has been used for modelling other underwater features, including kelp vegetation49, tidal turbines50,51, wind farm pylons52 and aquaculture farms53. We do not consider any turbulence generation/dissipation induced by vegetation, as done in other studies16,17,21. The vegetation-induced resistance horizontal force, F, has been implemented in FVCOM as a quadratic drag law in the form54:

$${{{{{{{\bf{F}}}}}}}}=-\frac{1}{2}\rho {C}_{D}A| {{{{{{{\bf{u}}}}}}}}| {{{{{{{\bf{u}}}}}}}}N$$
(1)

where ρ is the water density, CD is the mangrove drag coefficient, u is the fluid velocity, A is the flow-facing area per mangrove tree and N is the number of mangrove plants in the model element. Since the mangroves can span multiple model vertical σ layers, a fraction of the resistance force (proportionally to the layer thickness) is exerted in each model layer occupied by the mangroves. To obtain an estimate of N we assumed a homogeneous dense mature tall forest with a mangrove density of 0.5 plant per m255. The drag properties for five different mangrove species sampled across several sites in the delta have been measured in flume experiments44, with CD ranging from 1.85 to 14.47 (with currents of 0.15 m s−1) depending on the mangrove species and presence/absence of leaves. We are looking at both with/without leaves, because mangroves can lose leaves during a storm56. We chose to use the lower threshold of CD values among the five species common in the Pearl River Delta: CD = 2 for mangroves without leaves and CD = 4 for mangroves with leaves (see description of experiments in Table 1). We use the same drag coefficients for both Shenzhen Bay and the upper delta locations, thus not considering the specific type of mangroves present (or possibly present) in each specific area. To calculate the projected frontal surface area per tree A, we considered a trunk diameter of about 10 cm, which is the average value for the Pearl River Delta species44. By assuming that trees grow like a fractal57, where each subsequent branch looks like a smaller version of the previous branch, we calculated the projected area using the empirical relationships for branch-projected area valid for mangrove species common in the Pearl River Delta44. This gives 2 m2 for a projected area A without leaves and 6.04 m2 with leaves. However, this estimate has to be reduced because of branch realignment, which can result in a 50% reduction in the projected area58. Thus, we consider a maximum projected frontal surface area per tree of 3 m2 (with leaves) and 1 m2 (no leaves) (see description of experiments in Table 1). In the mangrove parameterisation we implemented in FVCOM, the projected area is not constant, it is further reduced considering that in inter-tidal areas, the plants are not always fully submerged. When the water level is less than the height of the plant, which on average for a dense tall mature mangrove forest in the Pearl River Delta we assumed to be 3 m44, the projected frontal surface area is reduced proportionally to the water level height.

To reproduce Typhoon Hato (2017), we forced the FVCOM Pearl River Delta model with wind velocity and air pressure calculated using the Holland parametric model59,60, which uses observed maximum wind speed and radius of maximum winds to calculate radial profiles of sea level pressure and winds in a tropical cyclone. Observations were obtained from 3-hourly data provided by the International Best Track Archive for Climate Stewardship (IBTrACS) Version 4. This approach was preferred to the usage of atmospheric model reanalysis, where the peaks in wind velocity (and thus in water levels) can be underestimated41. Although the track of Typhoon Hato is along a very typical track followed by tropical cyclones near the Pearl River Delta61, further research is needed to address how storm properties, such as duration and intensity, or a different storm track, would modulate the attenuation offered by mangroves.

Additionally, we have investigated how the effectiveness of mangroves could change with SLR. We have repeated the high-drag experiments for the 600 m patch in Shenzhen Bay and for the patch from Hualong to Lianhuashan in the upper river channels with an increase in mean sea level imposed at the boundary of the model domain (as done in a previous study41). The three future SLR scenarios chosen are 30, 50 and 90 cm (Experiments 11–19 in Table 1). These correspond to the median (50th percentile) and upper limit (95th percentile) by 2050 (30 and 50 cm, respectively) and 90 cm is the median by 2100 of the regional (specific for the Pearl River Delta area) sea level projections62 for the ‘High-end’ Representative Concentration Pathway (RCP) 8.5 future climate scenario. However, the model experiments do not necessarily correspond to water levels for a specific climate scenario or time horizon. The applicability of our results is much broader, for example, 30 cm is the RCP 8.5 scenario in 2040 (95th percentile) and 50 cm could equally apply to the RCP 4.5 scenario in 2060 (95th percentile) or in 2090 (50th percentile), while 90 cm is the upper limit in 2100 for the RCP 4.5 scenario62. We did not simulate any SLR scenario higher than 1 m. In our model setup, we are simulating a fully protected coastline with mangroves placed in front of a seawall, no extra land can get inundated and no sediment accretion will happen. In this case, the mangroves will be drowned and ineffective with SLR higher than 1 m.