Global mangrove distribution on the open coast is controlled by waves

There is a growing global effort towards coastal ecosystem restoration and conservation, with the United Nations Decade on Ecosystem Restoration and the Decade on Ocean Science for Sustainable Development under way. As conservation initiatives expand in response to historical habitat declines and reduce human-driven rates of deforestation⁴, environmental drivers are accounting for an increasing portion of mangrove loss relative to land conversion⁵. This indicates that, although managing direct anthropogenic mangrove loss is a continuing endeavour, understanding and predicting future natural dynamics is an important consideration for mangrove conservation.

Mangroves face an uncertain future because many locations are vulnerable to sea-level rise and shifting weather and climate patterns^6,7,8. Mangroves occurring along open, wave-exposed coasts are of particular interest because they provide unique benefits to adjacent ecosystems and communities, with coastal protection being the second most studied ecosystem service of mangroves⁹. Open-coast mangroves are uniquely susceptible to changes in wave climate, for which changes are projected to be dominated by shifts in wave direction by 5°–10° throughout tropical and extra-tropical regions¹⁰, as well as potential region-specific changes in storm frequency¹¹.

Mature mangrove forests are influenced by the local physical environment and influence the surrounding hydrodynamics through wave attenuation^1,12. However, during the seedling establishment stage the environmental relationship is unidirectional^13,14, with hydrodynamics being one of the key bottlenecks to propagule anchoring and establishment. During this establishment phase, the buoyant propagules of mangrove pioneer species such as Avicennia alba need to anchor quickly to avoid dislodgement¹⁵. Early approaches to modelling mangrove distribution relied on correlating mangrove presence to time-averaged inundation values such as hydroperiod¹⁶. However, this approach does not consider the distinct events leading to establishment or mortality and is limited in environments with strong seasonality. It has been shown that in estuarine environments with different tidal regimes, this approach can lead to inaccurate predictions of extent¹⁷. These limitations have been addressed in recent approaches^17,18,19,20, which use a process-driven approach involving windows of opportunity (WOOs) for mangrove establishment. WOOs are defined as periods in which conditions do not exceed thresholds for seedling survival. These thresholds vary with seedling age because their vulnerability decreases as seedlings mature¹⁹ (Fig. 1).

On the seaward fringe, it is expected that in addition to inundation, waves act as a critical establishment threshold for mangrove seedlings. This relationship has been demonstrated by flume tests on juvenile seedlings of typical mangrove pioneer species^19,21, as well as in situ experiments²². Historically, several studies have used time-averaged correlative approaches^23,24,25,26 to highlight the role of waves in shaping mangrove presence. At the local scale, the relationship between mangrove progradation and temporal periods of low wave forcing has been explored^22,27, confirming that these insights into seedling establishment can be extended to model mangrove extent. These findings are consistent with coastal saltmarsh research, which has suggested that disturbance, rather than inundation thresholds, limits the seaward extent²⁸ and that temporality of hydrodynamic forcing is a key control on establishment and subsequent marsh expansion²⁹. However, the role of waves as a control on mangrove presence has not been explored on a global scale.

Here we predict the presence or absence of coastal mangroves on a global scale by linking biophysical establishment thresholds with spatiotemporal wave forcing. This approach broadens our understanding of mangrove establishment beyond inundation as the primary control on mangrove distribution by exploring waves as a control on distribution. We use a WOO-based approach to predicting mangrove presence on wave-exposed coasts. We propose that this mechanistic approach to predicting mangrove distribution from establishment bottlenecks (Fig. 1) can be applied to open-coast mangrove sites globally. We hypothesize that contiguous periods of low wave energy are an effective predictor of mangrove presence on the coast. These findings provide a mechanistic approach to understanding global mangrove distribution and predicting restoration potential in a changing climate.

In this study, 400 globally distributed sites were analysed to develop and assess a causality-driven approach to predicting mangrove presence on the open coast (Fig. 2). Sites with mangroves were selected on the basis of susceptibility to wave forcing. Sites without mangroves were selected in marine ecoregions containing mangroves to minimize the effects of other climate factors that might influence mangrove distribution (Methods). The exposure of sites to wave forcing was explored using the effective wave height (EWH), a time-varying parameter defined to account for offshore wave height and wave direction relative to the shore of three swell partitions.

Analysis of the time-varying EWH at the sites found differences in the minimum non-exceedance values of the EWH for consecutive durations (WOOs) of up to one year (Fig. 3a). If a propagule-stranding event occurs during the first WOO of 24 h, co-originating durations of wave action represent the forcing that would be experienced by a mangrove seedling of that age. The non-exceedance values for these durations are therefore the thresholds that cannot be exceeded for successful establishment to occur. Figure 3a depicts the distribution of all calculated non-exceedance values for the EWH at sites with and without mangroves, for durations up to one year. The distributions of the mean non-exceedance values, calculated across all monthly sampling starting points at each site, were significantly different between mangrove (n = 197) and non-mangrove sites (n = 197). The null hypothesis that they arise from identical distributions can be rejected at the 2% significance level after multiple test correction (Methods); this indicates that sites with mangroves experience prolonged low-energy WOOs compared with non-mangrove sites. The discrepancy between index values shows that coastal sites without mangroves typically lack periods of low wave interaction that occur at sites with mangroves. This is important because mangrove establishment requires these periods of low energy (that is, disturbance-free periods)^18,19,20.

The EWH non-exceedance values at sites with mangroves were used to develop thresholds for seedling dislodgement, based on the hypothesis that wave conditions at sites with mangroves are typically suitable for mangrove establishment. Minimum non-exceedance values of the EWH for the first critical duration of 1 day were determined for each month in the dataset, serving as possible propagule-stranding events (Fig. 1). The maximum EWH experienced during co-originated durations of up to one year were then determined, representing the forcing experienced by a mangrove seedling of that age. The 65th percentile of these values for each duration was then used as the establishment thresholds for a seedling of that age (Methods). These calculated thresholds were termed the mangrove establishment zone (Fig. 3b).

Wave establishment thresholds varied with tidal range. Figure 3b shows the overall calculated thresholds, along with those derived when only sites with micro-, meso- or macro-tidal regimes were considered. These results indicate that coastal mangroves in micro-tidal environments typically experience more-energetic wave conditions than those in meso- and macro-tidal regions. This discrepancy is not observed for shorter WOOs, suggesting that similar low-energy periods of up to one week are experienced by all sites regardless of tidal range. Mangrove sites that experience large tides included locations in northern Australia, western India, northern Brazil and several regions throughout Indonesia^30,31. Mangroves in macrotidal regions may be more susceptible to dislodgement from waves than those in meso- or microtidal regions, as they experience greater total flow velocity due to extra tidal currents, which are unaccounted for in this model.

The mangrove establishment zone (Fig. 3b) highlights the increasing tolerance of mangrove seedlings to disturbance as they age, as supported by previous field and laboratory studies^27,32. These studies have used force³², erosion tolerance and/or shear-stress tolerance²⁷ to represent this, in contrast to the present work which uses the EWH. Here we impose a threshold of 1.13 m on the EWH for 12-month-old seedlings (Fig. 3 and Methods). In shallow water, this corresponds to a near-bed wave orbital velocity of u = 1.46 m s⁻¹ (Methods). It has previously been estimated³² that seedlings may become susceptible to uprooting at flow velocities of 1.2 or 1.5 m s⁻¹ (Rhizophora mangle and Avicennia germinans, respectively, in micro-tidal environments), which aligns with the present result. The bed shear stress corresponding to the EWH limit defined in this study is τ_b = 10.88 Nm⁻² (Methods), which lies within 2 s.d. of the shear-stress limit that has previously been used²⁷ in models for Avicennia marina seedlings of the same age in a meso-tidal environment.

Our mechanistic predictive approach (Fig. 1) using the calculated mangrove establishment zone (Fig. 3b) was applied to all sites with valid hydrodynamic data: 197 with mangroves and 197 without. Sites were considered suitable for mangroves if they experienced at least one set of appropriate WOOs (that is, one year without exceeding the thresholds depicted in the mangrove establishment zone; Fig. 3b), during the 20 years of data included. Using only offshore wave data and shoreline geometry, the model achieved an overall predictive accuracy of 78.2% (Table 1) (see Methods for a description of the model accuracy, sensitivity and specificity).

Preliminary analysis demonstrated that the sensitivity and specificity of the model varied with the nearest genus reported on the seaward fringe³³ (Table 1). Although further investigations involving on-site species observations would be required to explore this phenomenon, these results provide an indication that different mangrove genera may respond differently to hydrodynamic forcing. The model accuracy is highest in regions where Sonneratia was reported on the seaward fringe, indicating that wave forcing is a strong predictor of mangrove distribution for this genus. A previous study has demonstrated that Sonneratia alba seedlings are more susceptible to early hydrodynamic dislodgement than are A. alba seedlings¹³, which may justify waves as a primary predictor of establishment of S. alba. By contrast, in regions where Rhizophora species are on the seaward fringe, sensitivity and specificity indicators are lowest. This indicates that there may be a stronger influence from factors other than from waves or that intragenus variations in hydrodynamic tolerance may be influencing the distribution. However, it is feasible that this result is due to the different hydrodynamic climates in regions with different mangrove types, or that the differences in sample size are skewing the results. Further study is needed to explore this phenomenon on a global scale.

The model was applied along the coastline of two case study sites, selected to explore the application of the model at a smaller spatial scale and to demonstrate the different sensitivities to hypothetical future changes in wave climate. These case studies compare mangrove presence and absence under historical wave conditions and for the same time period with artificially decreased and increased wave conditions at sites in the Indian Ocean (Palk Strait, India) and the Pacific Ocean (Gulf of Thailand, Thailand) (Fig. 4a–h). Figure 4c–f includes a 20% decrease or increase to historical EWH values as an example; Fig. 4g,h shows the sensitivity of each case study to a range of changes to the EWH. For each case study, observed versus predicted presence or absence of mangroves was compared at equidistant points roughly 5.5 km (Indian Ocean case study) and 11 km (Pacific Ocean case study) apart. The model correctly identified all but one point (of 11 and 7 points for the Indian Ocean case study and Pacific Ocean case study, respectively) in each of the case studies under historical conditions (Fig. 4a,b). The sites represent different coastal mangrove sensitivities to changing wave climates. For both case studies, a 20% reduction in EWH relative to historical conditions resulted in all sites being deemed suitable for mangrove establishment. This indicates that a reduction in wave exposure at these locations (due to reduced wave heights or shifts in wave direction away from perpendicular to shore) may result in increased mangrove coverage along the coast. However, in the Indian Ocean case study, all sites were deemed unsuitable for mangrove establishment under increased wave conditions. This suggests that a 20% increase in EWH, in comparison to baseline conditions at this location, may result in no suitable WOO for seedling establishment. Although mature forests may persist for some time, no regeneration would occur at these sites and this coastline may eventually become devoid of mangroves, assuming there are no morphodynamic changes to the foreshore. By contrast, in the Pacific Ocean case study, only one point that presently contains mangroves ceased to experience WOOs under increased wave conditions. As such, mangroves at this location are comparatively resilient to increases in wave climate. This analysis was extended across a range of changes to the EWH (Fig. 4g,h). In the Indian Ocean case study, moderate decreases or increases in the EWH make the site wholly suitable or unsuitable for mangrove establishment, respectively. In the Pacific Ocean case study, the modest EWH reductions may lead to increased mangrove area, but significant increases are needed for the site to no longer support establishment.

Different projections have suggested that the case study regions may experience reductions³⁴ or increases³⁵ in annual mean significant wave height under climate change. These locations are also projected to experience shifts in mean wave direction^34,35. Although the 20% increase or decrease to the EWH analysed in these case studies exceeds projected changes to wave height¹⁰ under climate change, this parameter is sensitive to changes in wave direction. Therefore, even small directional shifts, in addition to changes in wave height, may lead to EWH increases or decreases of this magnitude.

The mangrove prediction model was reapplied to all global sites that were correctly identified as mangrove or non-mangrove under baseline conditions, with a decrease or increase to EWH of −45% and 45% (Fig. 4i). These results highlight the global sensitivity of mangrove habitats to changes in wave climate. Even under modest changes to wave climate, sites that currently support mangroves may no longer experience establishment windows and vice versa. Notably, these model results indicate that non-mangrove sites may become suitable for seedling establishment under reductions in wave climate of a similar magnitude to increases that may cause mangrove sites to become unsuitable.

Past and future changes to wave climate are uncertain and highly regional^36,37. Therefore, mangrove habitat suitability might shift considerably along coastlines, with both losses and gains occurring. Furthermore, our approach considers that any threshold exceedance in a given year will limit mangrove establishment. As such, periodic storminess that interrupts historically calm seasons may also preclude mangrove regeneration, along with shifting baseline conditions. Similarly, wave stilling or shifts in direction that reduce the exposure of sites may result in more-frequent WOOs for establishment. Although this result demonstrates the sensitivity of the modelled sites to linear decreases or increases in EWH, site-specific climate change and regional sea-level rise projections are needed to delve deeper into local-scale mangrove distribution forecasts.

Our findings show that, although inundation period has generally been considered the key driver of mangrove establishment and species distribution^{7,16,38,39,40}, wave climate is also a crucial control in open-coast settings. In reality, future mangrove distribution will be influenced by many compounding factors including mean sea-level rise^6,41,42,43, changes to extreme sea levels⁴⁴ and other abiotic factors such as changing air temperatures, salinity and sedimentation⁴⁵. Although this research shows that wave climate alone is predictive of mangrove distribution, the modelled index could be further developed to incorporate other drivers. For example, coupling this model to a distribution model that considers tidal inundation regimes¹⁸ may extend it to predicting the vertical extent of coastal mangroves, rather than only their presence. Incorporation of tidal currents, which are further drivers of seedling dislodgement, would improve model performance at sites where currents cause greater shear stresses than do waves. Furthermore, assessing forcing due to locally generated waves by including wind energy may extend the capacity of the modelled index to predict presence or absence at sites that are disconnected from offshore hydrodynamics. This may allow for mechanistic mangrove predictions in reef-protected or lagoonal settings, as well as in estuaries with sufficient fetch for waves to be relevant. Shifts in wave climate and sea levels are also likely to cause morphodynamic changes that will affect the habitable zone of mangroves. Investigation into these effects would benefit the application of this model at a local scale.

Unlike previous research that has assessed the correlation between mangrove distribution and wave parameters²³, this model adopts a process-driven, rather than statistical, approach. As such, it was developed using knowledge that links the establishment thresholds of mangrove seedlings (from 24 h to 1 year of age) with local hydrodynamics. Although time-averaged approaches may be capable of predicting current mangrove presence, they are limited in terms of predicting mangrove progradation or recession under altered conditions because these models collapse the temporal structure. By contrast, process-driven approaches such as ours, are formulated using establishment and mortality events. This means that our model could be extended to simulating the progradation and recession of the seaward fringe. This is essential for predicting mangrove extent under non-stationary conditions and can assist in assessing the suitability of coastal sites for restoration. Comparing the results from our model to historical periods of mangrove area change is an avenue for future research, along with further validation using empirical studies.

Furthermore, investigations into the distribution of mangroves have noted that sea-level rise and net gains in surface elevation will have competing roles in determining the future habitable range^6,7. However, complex impacts of climate change may also lead to altered coastal hydrodynamic climates¹⁰, the effects of which are poorly understood. The development of causality-based distribution models that include wave forcing, rather than correlative models that use geospatial distribution mapping, is essential to accurately forecast the response of mangroves in a changing climate. Here the suitability of sites for mangroves was assessed using the EWH, which considers wave height and direction. A takeaway from this research, therefore, is that wave climate shifts involving altered wave directions will also influence mangrove establishment on open coasts. A global review of wind–wave climate change projections¹⁰ noted that in tropical and extra-tropical regions (comprising the habitable latitudes of mangroves) the primary change expected in 2100 (representative concentration pathway 8.5; ref. ⁴⁶) comprises shifts in mean wave direction of 5°–10°. These directional shifts may contribute to mangrove habitat changes alongside other key stressors to mangroves such as sea-level rise, increased cyclonic activity and changes to hydrodynamic energy⁴⁷.

This research highlights the role of waves in shaping the global distribution of coastal mangroves. With our process-driven model, we highlight that mangrove establishment and therefore distribution along the coast will change in line with wind–wave climate changes globally. This knowledge can be used to better understand current distribution patterns, inform coastal restoration and conservation practices and enable improved projections of future mangrove habitat. Our findings have important implications for coastal management and mangrove ecosystems globally because we must understand why locations may transition from having favourable to unfavourable conditions for mangrove habitat, or vice versa, if we are to plan for future resilient coastlines.

Site selection

This study is based on 20 years of data (3-h temporal resolution) from 400 globally distributed sites. Sites were selected from all continents containing mangroves (Africa, Asia, North America, Oceania and South America) and chosen to extend to their latitudinal boundaries, therefore encompassing a broad range of genera and climates. The selected sites included 200 with mangroves on the open coast and 200 sites without mangroves (Fig. 2). Sites with and without mangroves were identified on the basis of distribution data from Global Mangrove Watch⁵⁰ and were cross-referenced with Google Earth satellite imagery from 2025. Sites with mangroves present were selected only where mangroves seemed to be exposed to waves, based on visual inspection of the satellite imagery. As such, back-barrier mangroves protected from offshore wave conditions due to the presence of a dune or reef were not included in the dataset. Sites protected by a barrier reef or an island at an offshore distance greater than the resolution of the mesh of the wave model (about 20 km) were permitted in the analysis (for example, sites near the Great Barrier Reef). Embayed sites were permitted where the body of water (for example, bay or gulf) had a width greater than 20 km.

To reduce the influence of climate factors on mangrove distribution, non-mangrove sites were selected in marine ecoregions that contain mangroves. These non-mangrove sites were identified using 2025 Google Earth satellite imagery in coastal environments that seem to comprise sand or mud (rocky headlands, for example, were excluded). Sites with any visible development in the satellite imagery that could preclude mangrove growth such as hardened shorelines and seawalls were not selected for the analysis.

Data collection

This study was conducted using wave data from the Global Ocean Waves Reanalysis⁴⁸ (https://doi.org/10.48670/moi-00022) of the EU Copernicus Marine Service Information. This dataset contains spectral wave data at 0.2° × 0.2° spatial resolution globally and 3-h temporal resolution. The product is based on MFWAM, a third-generation spectral wave model. This model calculates the wave spectrum using ERA5 climatological winds⁵¹, GLORYS12V1 currents⁵² and ETOPO2 bathymetry⁵³. Twenty years of wave data from 1 January 2003 to 1 January 2023 were used in the analysis. Three swell partitions were considered: the primary, secondary and wind components of the spectrum. The bearing of the coastline at each site was measured to the nearest 5° in QGIS with Google Earth basemap (map data 2025 Google).

WOOs

Significant wave height and direction were chosen to represent the magnitude of wave interaction at the shoreline. The physical mechanisms leading to mangrove mortality as a result of waves are forces due to near-bed orbital flow velocity and erosion due to bed shear stress¹⁹. For mangrove seedlings (which have diameters D ≪ 1 m), inertial forces due to near-bed flow acceleration can be considered negligible. The drag force F_D due to flow velocity (u) acting on a submerged structure is given by

where C_D is a drag coefficient, A is the projected area and ρ is seawater density in this case.

Mean bed shear stress is given by

where f_w is the wave friction factor. Both physical mechanisms for mangrove seedling dislodgement—drag forces and erosion—are therefore driven largely by the bed flow velocity.

The maximum horizontal component of the bed flow velocity due to waves is given by

where H is the wave height, ω is the wave angular frequency ((omega equiv frac{2pi }{T})), T is the wave period, h is the water depth and k is the wavenumber ((kequiv frac{2pi }{lambda })). In shallow water, where wavelengths (λ) are approximated by (lambda approx Tsqrt{{gh}}) and (sinh (kh)approx kh), this simplifies to

where g is gravitational acceleration. This approximation is used to justify the choice of the significant wave height H_s as the offshore wave property most appropriate to represent mangrove seedling establishment thresholds.

As an offshore wave approaches the coast, it is transformed by refraction. The refracted wave height H_r is given by

where H₀ is the incident wave height and K_r is the refraction coefficient given by

and ({theta }_{0,perp }) is the angle relative to shore normal of the offshore wave and ({theta }_{perp }) is that of the refracted wave.

It was assumed that waves at the shoreline travel perpendicular to the shore, so that the wave height near the shore can be expressed as

To capture the component of the wave spectrum most impactful to the coastline for each 3-h timestep, the EWH at time t was therefore defined as

where H_s is the offshore significant wave height and ({theta }_{perp }) is the mean wave direction relative to the beach normal for each of the spectrum partitions considered. This represents the component of the wave spectrum that is expected to have the most impact at the site at time t. The maximum of the swell partitions was used, rather than bulk wave statistics of the whole spectrum, to better capture scenarios in which the spectral mean wave direction would result in a low value of EWH (({theta }_{perp ,m}approx pm {90}^{^circ })), but a particular swell partition is approaching at an angle that is more impactful at the shore (({theta }_{m}approx {0}^{^circ })). A diagram demonstrating the calculation of this parameter is shown in Extended Data Fig. 1. This defined parameter accounts for the incidence of non-locally generated swell and is temporal, enabling the identification of low-energy windows key to mangrove establishment.

Twenty years of spectral wave data were extracted from the nearest offshore non-null node of the wave dataset⁴⁸ for each of the 400 analysis sites. Wave nodes were classified as offshore if the bearing between the node and the analysis site approached the shore at an angle between −90° and 90° relative to shore normal. In doing so, three mangrove and three non-mangrove sites were removed from the datasets as a result of the surrounding offshore nodes all being null. At each site for each 3-h timestep, the EWH was calculated.

A deterministic model to predict mangrove presence was then created using only the training sites. The establishment thresholds for mangrove seedlings were calculated on the basis of wave data from the sites with mangroves, using the following process. Time periods representing mangrove seedling establishment up to 1 year were defined as D_s = {1 day, 2 days, 5 days, 10 days, 2 weeks, 4 weeks, 8 weeks, 12 weeks, …, 52 weeks}. These increasing durations were selected to represent the increasing tolerance of mangrove seedlings to disturbance as they grow³². This set was defined with higher resolution for smaller durations to capture the rapid initial anchoring of seedlings²² and durations up to 1 year were considered to capture the seasonality of sites. At each site, the minimum thresholds that have a period of non-exceedance for the first critical duration of 1 day (1d)—were determined for each month (M) in the dataset. These thresholds C_M,1d were defined as

where EWH_M(t) includes all values of the EWH for the given month at the site. Each of these durations was then considered a possible candidate for the early establishment of a mangrove propagule. The maximum value of the EWH for co-originating durations (Din {D}_{{rm{s}}}) was then determined. These durations represent the windows in which hydrodynamic thresholds for a seedling of that age should not be exceeded, for successful establishment. The non-exceedance threshold for each duration D following the 1-day threshold C_M,1d for each month M was defined as C_M,D and calculated as

As the initial thresholds C_M,1d were calculated from the beginning of each month, this resulted in 12 sets of non-exceedance values (each containing one threshold per duration (Din {D}_{{rm{s}}})) per year at each site. Each of these sets was then considered a candidate for a seedling establishment event. In reality, propagule availability is a bottleneck to establishment in many environments¹⁵. However, global trends have shown that propagule abundance is typically minimal during winter⁵⁴ when time waves are more energetic. This suggests that, globally, optimal establishment events in terms of wave forcing will typically occur when propagules are available. There are, however, exceptions to this trend and future site-specific studies should therefore take local propagule seasonality into account.

The sites allocated for training the model (all sites excluding the one on which the model is being assessed, as per the leave-one-out cross-validation (LOOCV) method; see ‘Model performance’) were used to determine the establishment thresholds of mangroves. Sites with and without mangroves had different distributions of non-exceedance values (Fig. 3a). A series of Anderson–Darling k-sample tests (see ‘Model performance’) were conducted to compare these distributions for each duration, with the results shown in Extended Data Table 1. To ensure data independence, the average non-exceedance value for each duration at each site was used (n₁ = n₂ = 197). The tests indicate that the null hypothesis that mangrove and non-mangrove sites are drawn from the same distribution can be rejected for all durations at the 2% significance level after Bonferroni correction for 18 tests (as P < 0.0011 for all tests and α_corrected = 0.11% is the per-test significance level corresponding to a family-wise error rate of 2%; see ‘Model performance’).

The 65th percentile of the threshold values at sites with mangroves for each duration were selected as the upper limits of establishment for a seedling of that age. This percentile was chosen by determining the value that optimized (≈1) the ratio of exceedance at the non-mangrove sites and non-exceedance at the mangrove sites (that is, the values that resulted in the best performance for specificity and sensitivity). This resulted in a hydrodynamic habitat threshold C_D corresponding to each duration (Din {D}_{{rm{s}}}) (Fig. 3b). These thresholds were then recalculated using only sites in micro-, meso- and macro-tidal environments to determine how tidal range may affect hydrodynamic tolerance (tidal classification from a dataset³⁰ based on the FES2014 global tide model³¹).

The alignment of these calculated thresholds with previous empirical studies^27,32 was then assessed. The present work suggests a threshold of 1.13 m for the EWH for 12-month-old seedlings (Fig. 3; see ‘WOOs’, Methods for calculation). If the shallow water depth breaking limit is taken to be (frac{H}{h}=0.78) (ref. ⁵⁵) (where H is wave height and h is water depth), this wave can be assumed to be broken when the depth becomes shallower than 1.44 m, beyond which linear wave equations will no longer apply. In shallow water, the resulting near-bed wave orbital velocity will be u = 1.46 m s⁻¹ (equation (4)). It has previously been estimated³² that seedlings (less than 1 year old) may become susceptible to uprooting at flow velocities 1.2–1.5 ms⁻¹; this aligns with the present result.

If a standard friction factor of f_w = 0.01 (ref. ⁵⁶) and saltwater density of ρ = 1,025 kg m⁻³ are used, the bed shear stress corresponding to this EWH limit is τ_b = 10.88 Nm⁻² (equation (2)). This lies within 2 s.d. of the shear-stress limit that has been imposed previously²⁷ in models for seedlings of the same age.

The following predictive approach was then applied to all sites (197 with and 197 without mangroves). It was asserted that, for a mangrove seedling to establish in a particular year, all hydrodynamic habitat thresholds should be satisfied. Thus, if the following condition is satisfied at a given site for a particular year, that year is considered suitable for mangrove establishment.

Previous studies^17,18 have indicated that a single set of WOOs is sufficient to initiate mangrove establishment, meaning that mangrove stands may be present at sites despite experiencing unsuitable conditions outside the WOO. It was therefore asserted that, if the previous condition was met for any of the years considered, the site could be considered suitable for mangroves. The resulting model output is a binary result predicting the presence or absence of mangroves at each site. The model results were first assessed for all sites collectively, then for sites with Avicennia, Rhizophora or Sonneratia reported on the seaward fringe³³ to determine how different mangrove genera may respond to hydrodynamic forcing.

Model performance

The performance of the predictive model developed in this work is assessed using accuracy, sensitivity and specificity. These quantities were calculated as described in the following expressions.

True positives are defined as points that are predicted to have mangroves and do, whereas false positives are defined as points that are predicted to have mangroves but do not. True negatives are those predicted to be without mangroves that do not, whereas false negatives are those predicted to be without mangroves that do have mangroves.

The model performance was validated using the LOOCV method⁵⁷. LOOCV involves assessing the model prediction at all sites in the study. For each point, all other points are used to train the model, and the trained model is then used to predict the outcome (mangrove or non-mangrove) for the remaining point. In this case, the training of the model means that the 65th percentile of the non-exceedance value of EWH at all other sites was used as the establishment threshold to predict mangrove establishment at the remaining site.

The statistical significance of the difference between distributions of non-exceedance values of the EWH at sites with and without mangroves was assessed using the Anderson–Darling k-sample test and corrected for several tests using the Bonferroni correction. The Anderson–Darling k-sample test⁵⁸ is a modification of the Anderson–Darling test⁵⁹ and is a non-parametric statistical test to evaluate the null hypothesis that two or more groups are drawn from the same underlying distribution. This test was selected because it does not require specification of the underlying population distribution and it is sensitive to differences across the entire distribution. To ensure data independence, the mean non-exceedance value (calculated across all sampled monthly starting points) for each duration at each site was used. This test computes the test statistic (A²), which can be compared with a critical value to determine whether the null hypothesis can be rejected at the corresponding significance level. When conducting several statistical tests, the probability of a type-I error (incorrect rejection of a true null hypothesis) occurring in at least one of the tests is greater than the probability of this error occurring in any one test individually. To adjust for this, a Bonferroni correction was applied, which defines the adjusted significance level as⁶⁰

where m is the number of tests. In this study, tests were considered statistically significant at the Bonferroni-adjusted significance level corresponding to a family-wise error rate of 2%. This corresponds to a significance level for each test of α_corrected= 0.11%.

Case studies

Two case study sites were chosen that had a coastline with both mangrove and non-mangrove regions. The first was selected in the Palk Strait of the Indian Ocean (9.599069° N, 78.911753° E; 9.238059° N, 79.286306° E); the second in the Gulf of Thailand of the Pacific Ocean (9.342269° N, 99.187294° E; 9.221632° N, 99.352620° E). Equidistant points (0.05° and 0.1° spacing) were created along the coastline selected for the case study. The shoreline at each of the points was then visually classified as mangrove, non-mangrove or developed. Mangrove sites were classified as described previously (‘Site selection’, Methods) and points were classed as developed where houses or structures were built along the shoreline. The model was then applied as described previously (‘WOOs’, Methods), using thresholds calculated using all valid mangrove sites in the global analysis (197). Each of the points was then classed as mangrove suitable or unsuitable. This was repeated using the historical values of EWH decreased and increased across a range of percentages.

Global sensitivity to wave climate

The sites that were correctly identified by the model (as described in ‘WOOs’, Methods) as mangrove or non-mangrove were reassessed under altered conditions to assess their sensitivity to changes in wave climate. The 20 years of historical data used to predict current presence were multiplied by factors from 55% to 145% (changes of −45% to +45%). The suitability of the sites for mangroves was then reassessed using these data.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.