The capacity of mangroves to reduce coastal flood risk resulted in legislation for mandatory widths of mangrove greenbelts in several countries with mangrove presence. Prescribed forest widths vary between 50 and 200 m. Here, we performed 216,000 numerical model runs informed by realistic conditions to quantify confidence in wave reduction capacity of mangroves for wind and swell waves. This analysis highlights that tidal flat areas fronting mangrove forests already account for 70% of reduction in wave heights. Within mangrove forests that are below 500 m wide, wave dissipation is strongly dependent on local water levels, wave characteristics and forest density. For forest widths of over 500 m, which constitute 46% of global coastal mangroves, around 75% or more of the incoming wave energy is dissipated. Hence, for relying on mangroves to dampen shorter waves, a new standard should be adopted that strives for mangrove widths of 500 m or more.

Due to changing climates and rising sea levels, low-lying coastal regions, such as the Netherlands, face increased risks of flooding driven by extreme sea levels. Thus, understanding extreme sea level events and their underlying dynamics is crucial for effective coastal management. This study developed and applied a novel classification framework to investigate historical storm surge events along the Dutch coast and improve the understanding of regional storm surge dynamics. Using 16 sea level records, storm surges were identified with the Peak Over Threshold (POT) method, using the 70th (POT70) and 99th (POT99) percentiles as thresholds. POT70 captured a more comprehensive storm surge activity, including multiple peaks and successive surges that are critical for coastal management. In contrast, POT99 captured surge peaks but missed significant pre- and post-storm surge activities. The POT70-derived surges were classified into 56 event types using clustering methods based on surge values across the whole event time series, and event duration. Event types were then characterised by temporal patterns, peak magnitude, duration, probability of occurrence, yearly frequency, and cumulative surge intensity. Key findings revealed frequent two-peak storm surges and significant variations in storm surge intensity along the coast, with stronger events occurring in northern regions. The results highlight the complexity of storm surge patterns, indicating that while simplified hydrograph models are useful, they may not always capture the full range of surge pattern variations. This novel classification framework offers a more detailed approach to evaluating surge patterns and can be applied to other coastal regions as well.

Understanding and predicting shoreline variability at various temporal and spatial scales is vital for effective, data-driven coastal management. Shoreline position, a reliable indicator of beach morphological changes, has been assessed using complex numerical models. Recently, equilibrium-based shoreline evolution models (EBSEMs) have gained traction for their efficiency in simulating shoreline orientation, including cross-shore and rotational (longshore) changes. However, existing EBSEMs for shoreline rotation have been applied predominantly to microtidal beaches, with limited validation across diverse coastal environments. This study evaluates the performance and scalability of the EBSEM proposed by Jaramillo et al. (2021) in modelling shoreline rotational variability at seven embayed beaches: Narrabeen Beach (Australia), Tairua Beach (New Zealand), Blackpool Beach (United Kingdom), Poniente Beach, Llevant Beach, Cala Millor Beach, and Moncofa Beach (Spain). These sites represent diverse environmental conditions in terms of sediment size, tidal regimes, monitoring frequency, and data types. The model was tested across full monitoring periods, elevation contours, and temporal resolutions. Results show that EBSEM performs well across contrasting beach types, effectively capturing short-term and seasonal shoreline rotation patterns. However, reduced accuracy was observed in environments with high-energy events or human interventions, such as Poniente, Llevant, and Cala Millor beaches. Sensitivity analyses highlight the importance of temporal resolution and intertidal elevation in model performance. While the EBSEM shows significant potential for broader application, further refinement is needed to better capture storm-driven and anthropogenic variability. These improvements would enhance its utility for coastal adaptation planning, hazard mitigation, and long-term shoreline management in the face of climate change.

Wave runup observations are important for coastal management providing data to validate predictive models of inundation frequencies and erosion rates, which are vital for assessing the vulnerability of coastal ecosystems and infrastructure. Automated algorithms to extract the instantaneous water line from video imagery struggle under dissipative conditions, where the presence of a seepage face and the lack of contrast between the sand and the swash impede proper extraction, requiring time-intensive data quality control or manual digitization. This study introduces two novel methods, based on color contrast (CC) and machine learning (ML). The CC method combines texture roughness — local entropy — with saturation. Images are first binarized using entropy values and then refined through noise reduction by binarization of the saturation channel. The ML method uses a convolutional neural network (CNN) informed by five channels: the grayscale intensity and its time gradient, the saturation channel, and the entropy and its time gradient. Both methods were validated against nine manually labeled, 80 min video time series. The CC method demonstrated strong agreement with manually digitized water lines (RMSE = 0.12 m, r=0.94 for the vertical runup time series; RMSE = 0.08 m, r=0.97 for the 2% runup exceedance (R_2%); and RMSE = 3.88 s, r=0.70 for the mean period (T_m−1,0)). The ML model compared well with the manually labeled time series (RMSE = 0.10 m, r=0.96 for the vertical runup time series; RMSE = 0.09 m, r=0.97 for R_2%; and RMSE = 3.51 s, r=0.79 for T_m−1,0). Furthermore, the computed R_2% values of both methods show a good agreement with the formula proposed by Stockdon et al. (2006) for extremely dissipative conditions, with RMSE-values lower than 0.13 m and correlations exceeding 0.70 for manual, CC, and ML estimates. While the CC method is deemed applicable for wave-by-wave analysis under similar dissipative conditions with a smooth seepage face and sufficient turbulent swash, the ML method still struggles with new, unseen data. However, it shows promise for a broader application and serves as a viable proof of concept. Together, these methods reduce the need for manual processing and enhance real-time coastal monitoring, contributing to more accurate predictive modeling of runup events and a better understanding of nearshore processes.

Beach groundwater and nearshore hydrodynamic data were collected during a field experiment along two dissipative beach transects on Galveston Island, Texas, in the fall of 2023. The monitored beaches serve as nesting habitat for the critically endangered Kemp’s ridley sea turtle. Conditions ranged from calm to stormy, with two storms occurring during the experiment, inundating the entire beach up to the dune toe. Collected hydrodynamic data include readings from pressure loggers submerged in the foreshore and mounted in groundwater wells in the backshore, data from two wave buoys about 1.5 km offshore, and GoPro timestacks of the instantaneous waterline (wave runup). Other collected data include bathymetry and topography surveys, subsurface temperature and moisture content readings, and sediment characteristics. This comprehensive dataset can be used to (1) study relevant beach inundation and groundwater processes, including their effect on the local ecosystem (e.g., repeated flooding of sea turtle nests), (2) study the propagation of nearshore hydrodynamic processes into the beach matrix and groundwater table, and (3) validate existing beach groundwater models.

Robust and reliable models are needed to understand how coastlines will evolve over the coming decades, driven by both natural variability and climate change. This study evaluated how accurately five popular ‘reduced-complexity’ models replicate multi-decadal shoreline change at Narrabeen-Collaroy Beach, a sandy embayment in Sydney, Australia. Measured shoreline positions derived from approximately monthly field surveys were used for 20-year calibration and 20-year validation periods. The models performed similarly on average but with large variability between transects. The set-up of several models was modified to compensate for their sensitivity to imperfect input wave data, and further site-specific improvements were identified. Capturing interannual to decadal-scale variability in cross-shore and longshore dynamics at this site was challenging for all five models. Models appeared to aggregate key processes at this timescale into parameter values rather than representing them directly. This suggests time-varying parameters or changes to model structure may be necessary for decadal-scale simulations.

Correction to: Communications Earth & Environmenthttps://doi.org/10.1038/s43247-025-02178-4, published online 3 April 2025 In the version of the article initially published, the title and legend for Fig. 5 was duplicated from Fig. 4; the colour descriptions in the legends to Figs. 3 and 4 were incorrect; the zenodo link in the Data Availability section (https://doi.org/10.5281/zenodo.14872179 (2025)) was missing; and the legend to Supplementary Fig. 1 was missing data source citations. The changes are made in the HTML and PDF versions of the article.

Flooding is the natural hazard most likely to affect individuals and can be driven by rainfall, river discharge, storm surge, tides, and waves. Compound floods result from their co-occurrence and can generate a larger flood hazard when compared to the synthetic flood hazard generated by the respective flood drivers occurring in isolation from one another. Current state-of-the-art stochastic compound flood risk assessments are based on statistical, hydrodynamic, and impact simulations. However, the stochastic nature of some key variables in the flooding process is often not accounted for as adding stochastic variables exponentially increases the computational costs (i.e., the curse of dimensionality). These simplifications (e.g., a constant flood driver duration or a constant time lag between flood drivers) may lead to a mis-quantification of the flood risk. This study develops a conceptual framework that allows for a better representation of compound flood risk while limiting the increase in the overall computational time. After generating synthetic events from a statistical model fitted to the selected flood drivers, the proposed framework applies a treed Gaussian process (TGP). A TGP uses active learning to explore the uncertainty associated with the response of damages to synthetic events. Thereby, it informs regarding the best choice of hydrodynamic and impact simulations to run to reduce uncertainty in the damages. Once the TGP predicts the damage of all synthetic events within a tolerated uncertainty range, the flood risk is calculated. As a proof of concept, the proposed framework was applied to the case study of Charleston County (South Carolina, USA) and compared with a state-of-the-art stochastic compound flood risk model, which used equidistant sampling with linear scatter interpolation. The proposed framework decreased the overall computational time by a factor of 4 and decreased the root mean square error in damages by a factor of 8. With a reduction in overall computational time and errors, additional stochastic variables such as the drivers' duration and time lag were included in the compound flood risk assessment. Not accounting for these resulted in an underestimation of 11.6 % (USD 25.47 million) in the expected annual damage (EAD). Thus, by accelerating compound flood risk assessments with active learning, the framework presented here allows for more comprehensive assessments as it loosens constraints imposed by the curse of dimensionality.

The bimodal wave climate of the semi-protected shallow Gulf St Vincent in South Australia has been analyzed through a forty-year (1980-2020) wave hindcast and an investigation into the climatic drivers of wave climate anomalies is presented. The sea and swell partitions of the wave climate were modelled independently as well as using an integrated model with both partitions represented. The wave hindcast was validated against two wave buoys located off the coast of Adelaide’s metropolitan beaches and key wave parameter anomalies were calculated across the gulf. Teleconnections were investigated, and the Southern Annular Mode is found to have the strongest correlations to wave parameter anomalies while the Southern Oscillation Index and the Dipole Mode Index fluctuations are found to correlate seasonally with wave parameter anomalies. Projected future trends of these climate drivers from literature have been related to the teleconnections found in this study to inform future trends of bimodal wave conditions in the gulf. The Southern Annular Mode is projected to trend positive which will reduce wave height and the westerly component of waves in the gulf, while the Southern Oscillation Index is projected to become more variable in the future which will lead to more extreme winter and spring wave conditions. An understanding of these trends allows coastal managers to pre-emptively manage the impacts of waves on the coastline at a seasonal to annual basis and provides insight into future wave conditions beyond these time periods.

Climate change and human activity threaten sea turtle nesting beaches through increased flooding and erosion. Understanding the environmental characteristics that enable nesting can aid to preserve and expand these habitats. While numerous local studies exist, a comprehensive global analysis of environmental influences on the distribution of sea turtle nesting habitats remains largely unexplored. Here, we relate the distribution of global sea turtle nesting to 22 coastal indicators, spanning hydrodynamic, atmospheric, geophysical, habitat, and human processes. Using state-of-the-art global datasets and a novel 50-km-resolution hexagonal coastline grid (Coastgons), we employ machine learning to identify spatially homogeneous patterns in the indicators and correlate these to the occurrence of nesting grounds. Our findings suggest sea surface temperature, tidal range, extreme surges, and proximity to coral and seagrass habitats significantly influence global nesting distribution. Low tidal ranges and low extreme surges appear to be particularly favorable for individual species, likely due to reduced nest flooding. Other indicators, previously reported as influential (e.g., precipitation and wind speed), were not as important in our global-scale analysis. Finally, we identify new, potentially suitable nesting regions for each species. On average, 23 % of global coastal regions between - 39 ^∘ and 48 ^∘ latitude could be suitable for nesting, while only 7 % is currently used by turtles, showing that the realized niche is significantly smaller than the fundamental niche, and that there is potential for sea turtles to expand their nesting habitat. Our results help identify suitable nesting conditions, quantify potential hazards to global nesting habitats, and lay a foundation for nature-based solutions to preserve and potentially expand these habitats.

Tropical-cyclone impacts can have devastating effects on the population, infrastructure, and natural habitats. However, predicting these impacts is difficult due to the inherent uncertainties in the storm track and intensity. In addition, due to computational constraints, both the relevant ocean physics and the uncertainties in meteorological forcing are only partly accounted for. This paper presents a new method, called the Tropical Cyclone Forecasting Framework (TC-FF), to probabilistically forecast compound flooding induced by tropical cyclones, considering uncertainties in track, forward speed, and wind speed and/or intensity. The open-source method accounts for all major relevant physical drivers, including tide, surge, and rainfall, and considers TC uncertainties through Gaussian error distributions and autoregressive techniques. The tool creates temporally and spatially varying wind fields to force a computationally efficient compound-flood model, allowing for the computation of probabilistic wind and flood hazard maps for any oceanic basin in the world as it does not require detailed information on the distribution of historical errors. A comparison of TC-FF and JTWC operational ensembles, both based on DeMaria et al. (2009), revealed minor differences of <10 %, suggesting that TC-FF can be employed as an alternative, for example, in data-scarce environments. The method was applied to Cyclone Idai in Mozambique. The underlying physical model showed reliable skill in terms of tidal propagation, reproducing the storm surge generation during landfall and flooding near the city of Beira (success index of 0.59). The method was successfully applied to forecasting the impact of Idai with different lead times. The case study analyzed needed at least 200 ensemble members to get reliable water levels and flood results 3 d before landfall (<1 % flood probability error and <20 cm sampling errors). Results showed the sensitivity of forecasting, especially with increasing lead times, highlighting the importance of accounting for cyclone variability in decision-making and risk management.

Low-lying, tropical, coral-reef-lined coastlines are becoming increasingly vulnerable to wave-driven flooding due to population growth, coral reef degradation, and sea-level rise. Early-warning systems (EWSs) are needed to enable coastal authorities to issue timely alerts and coordinate preparedness and evacuation measures for their coastal communities. At longer timescales, risk management and adaptation planning require robust assessments of future flooding hazard considering uncertainties. However, due to diversity in reef morphologies and complex reef hydrodynamics compared to sandy shorelines, there have been no robust analytical solutions for wave runup to allow for the development of large-scale coastal wave-driven flooding EWSs and risk assessment frameworks for reef-lined coasts. To address the need for fast, robust predictions of runup that account for the natural variability in coral reef morphologies, we constructed the BEWARE-2 (Broad-range Estimator of Wave Attack in Reef Environments) meta-process modeling system. We developed this meta-process model using a training dataset of hydrodynamics and wave runup computed by the XBeach Non-Hydrostatic process-based hydrodynamic model for 440 combinations of water level, wave height, and wave period with 195 representative reef profiles that encompass the natural diversity in real-world fringing coral reef systems. Through this innovation, BEWARE-2 can be applied in a larger range of coastal settings than meta-models that rely on a parametric description of the coral reef geometry. In the validation stage, the BEWARE-2 modeling system produced runup results that had a relative root mean square error of 13 % and relative bias of 5 % relative to runup simulated by XBeach Non-Hydrostatic for a large range of oceanographic forcing conditions and for diverse reef morphologies (root mean square error and bias 0.63 and 0.26 m, respectively, relative to mean simulated wave runup of 4.85 m). Incorporating parametric modifications in the modeling system to account for variations in reef roughness and beach slope allows for systematic errors (relative bias) in BEWARE-2 predictions to be reduced by a factor of 1.5–6.5 for relatively coarse or smooth reefs and mild or steep beach slopes. This prediction provided by the BEWARE-2 modeling system is faster by 4–5 orders of magnitude than the full, process-based hydrodynamic model and could therefore be integrated into large-scale EWSs for tropical, reef-lined coasts and used for large-scale flood risk assessments.

Sandy beach-dune systems make up a large part of coastal areas world wide. Their function as an eco-system as well as a protective barrier for human and natural habitat is under increased threat due to climate change. A thorough understanding of change processes at the sediment surface is essential to facilitate prediction of future development and management strategies to maintain their function. Especially slow and small scale processes happening over several days up to weeks at cm level, such as aeolian sand transport are difficult to identify and analyse. Permanent laser scanning (PLS) is a useful tool in the study and analysis of coastal processes as it captures a data representation of the evolution of the sediment surface over extended periods of time (up to several years) with high detail (at cm-dm level). The PLS data set considered for this study, consists of hourly acquired 3D point clouds representing the surface evolution of a section of the Dutch coast during three years. However, it is challenging to extract concrete information on specific change processes from the large and complex PLS data set. We use multiple hypothesis testing in order to reduce the PLS data set to a so-called inventory of trends, consisting of 12.8 million partial time series with associated rate of change and elevation. The inventory of trends proofs to be a suitable tool to identify natural processes such as storms and aeolian sand transport in our test area in the aeolian zone of a sandy beach-dune system on the Dutch coast. We identify these processes and provide a tool to derive summarising data from the complex PLS data set. We find that all partial time series identified as most likely representing aeolian sand transport, result in 1354 m³ of sand deposition in our study area over the course of three years. We also show a comparison with transects from JarKus data and find a correlation between anthropogenic activities and erosion in our test area with a correlation coefficient of 0.3.

All around the world, deltas are among the most densely populated and heavily utilised regions, where crucial functions, such as freshwater availability and safety against flooding, strongly relate to the natural dynamics of the system. Therefore, a thorough understanding of the estuarine system is crucial, especially when developing nature-based solutions for safeguarding these essential functions for today’s society as well as future generations. To better understand the effect of different estuarine parameters on salt intrusion, an extensive sensitivity analysis has been executed based on an idealised estuary layout. The idealised estuary is parametrically designed using thirteen parameters that represent both boundary conditions and geometric features, such as river discharge and water depth. Subsequently, the Delft3D Flexible Mesh (DFM) model has been used to determine the salt intrusion, allowing the exploration of a wide range of estuary layouts.

This study unravels 58-years (1961–2018) of wind-waves in the Mediterranean Sea (MS). A wave dataset was developed using the wave model WAVEWATCH III forced with the high-resolution (5.5 km) UERRA-MESCAN-SURFEX downscaled wind fields which better contain the imprint of the local geomorphology compared to other, coarser wind datasets used in previous studies. Thus, improving the reliability and characterization of the wind-wave climate in the basin. Validation results revealed a higher performance than previous datasets, particularly on the wave direction (θ_m), with a bias<1°. Climate variability at seasonal and interannual scales, wind-seas and swells distribution, and long-term trends in storminess and in the mean and extreme regimes were analysed. Results show a slight swell influence over the wind-sea in the hourly spectra at a large portion of the basin, excluding the wave generation areas. We detected that the western MS is the most storminess region with an average of three storms/year. Moreover, the anomalies of the seasonal mean wave direction relative to θ_m are large (∼60°), with opposing behaviours between the winter and summer. Finally, the long-term trends in the mean and extreme conditions and in storminess are mild with values reaching 6 cm/decade and less than 2% in the absolute value, respectively.

In the coming decades, coastal flooding will become more frequent due to sea-level rise and potential changes in storms. To produce global storm surge projections from 1950 to 2050, we force the Global Tide and Surge Model with a ∼25-km resolution climate model ensemble from the Coupled Model Intercomparison Project Phase 6 High Resolution Model Intercomparison Project (HighResMIP). This is the first time that such a high-resolution ensemble is used to assess changes in future storm surges across the globe. We validate the present epoch (1985–2014) against the ERA5 climate reanalysis, which shows a good overall agreement. However, there is a clear spatial bias with generally a positive bias in coastal areas along semi-enclosed seas and negative bias in equatorial regions. Comparing the future epoch (2021–2050) against the historical epoch (1951–1980), we project ensemble-median changes up to 0.1 (or 20%) in the 1 in 10-year storm surge levels. These changes are not uniform across the globe with decreases along the coast of Mediterranean and northern Africa and southern Australia and increases along the south coast of Australia and Alaska. There are also increases along (parts) of the coasts of northern Caribbean, eastern Africa, China and the Korean peninsula, but with less agreement among the HighResMIP ensemble. Information resulting from this study can be used to inform broad-scale assessment of coastal impacts under future climate change.

Changing (wind) climate might influence the magnitude, direction, and frequency of wave systems (Lobeto et al., 2021). However, in coastal engineering applications, generalized wave parameters are commonly used in climate change assessments with the risk of, for example, misrepresenting the nearshore transformation of wind-driven wave climates (Hegermiller et al., 2017). In consequence, these uncertainties in the nearshore (wind) climate will affect, amongst others, ship navigation, the implementation of marine renewable energy farms, the feasibility of coastal infrastructure and defences, or the efficiency of sandy coastal maintenance, and thus the decision-making of long-term, multidecadal coastal strategies (Rijksoverheid, 2013), especially when they are designed accounting for the Building with Nature concept (de Vriend et al., 2015). This study analyses the importance and application of considering multiple coexisting wave trains on the Dutch shoreface.

In recent years, coastal management has been facing new challenges: socio-economic growth and consequent climate change impose new boundary conditions pushing coastal systems towards unseen states. For adaptation and mitigation strategies as well as risk management, the resilience of systems to these projected changes must be tested and quantified using predictive tools, given the scarcity of observations. Process-based models, which limit the number of assumptions, are the preferred tools. However, these models are computationally expensive and therefore unattractive for global sensitivity and uncertainty analyses. Input and model reduction techniques, as well as behavioural empirical models, have been widely used to overcome these computational difficulties. In this paper, we propose a process-based hybrid workflow—that combines statistical and machine learning with a process-based numerical model—to provide sensitivity analyses on complex systems. As an example we explore salt intrusion in estuaries. The novelty of the method presented is the implementation of an adaptive sampling technique of numerical experiments with a process-based hydrodynamic model, and the training of a neural network to augment the set of numerical runs executed. The first uses predictive uncertainty to automatically explore the response of the complex system to varying environmental boundary conditions and geomorphological configurations. The second is trained to provide system responses around the sampled points. This exploration is closed by simulating the extremes in the output space as found by a genetic algorithm. This scheme is shown to be highly efficient in non-linear, heteroscedastic, and highly non-stationary systems.

In this study four experiments were conducted to investigate uncertainty in future longshore sediment transport (LST) projections due to: working with continuous time series of CSIRO CMIP6-driven waves (experiment #1) or sliced time series of waves from CSIRO-CMIP6-Ws and CSIRO-CMIP5-Ws (experiment #2); different wave-model-parametrization pairs to generate wave projections (experiment #3); and the inclusion/exclusion of sea level rise (SLR) for wave transformation (experiment #4). For each experiment, a weighted ensemble consisting of offshore wave forcing conditions, a surrogate model for nearshore wave transformation and eight LST models was used. The results of experiment # 1 indicated that the annual LST rates obtained from a continuous time series of waves were influenced by climate variability acting on timescales of 20-30 years. Uncertainty decomposition clearly reveals that for near-future coastal planning, a large part of the uncertainty arises from model selection and natural variability of the system (e.g., on average, 4% scenario, 57% model, and 39% internal variability). For the far future, the total uncertainty consists of 25% scenario, 54% model and 21% internal variability. Experiment #2 indicates that CMIP6 driven wave climatology yield similar outcomes to CMIP5 driven wave climatology in that LST rates decrease along the study area’s coast by less than 10%. The results of experiment #3 indicate that intra- and inter-annual variability of LST rates are influenced by the parameterization schemes of the wave simulations. This can increase the range of uncertainty in the LST projections and at the same time can limit the robustness of the projections. The inclusion of SLR (experiment #4) in wave transformation, under SSP1-2.6 and SSP5-8.5 scenarios, yields only meagre changes in the LST projections, compared to the case no SLR. However, it is noted that future research on SLR influence should include potential changes in nearshore profile shapes.

Estuaries are among the most densely populated and heavily utilised regions in the world, where crucial functions – e.g., freshwater availability and water safety – strongly relate to the natural dynamics of the system. When developing nature-based solutions to safeguard these essential functions, a thorough understanding of estuarine dynamics is required. This study describes an elaborate sensitivity analysis on the salt intrusion length using an idealised estuary, which is parametrically designed using key estuary-scale parameters – e.g., river discharge and tidal flats – to cover a wide range of estuary classes. We were able to systematically investigate such a wide range of estuary classes due to the combination of (1) state-of-the-art hydrodynamic modelling software, (2) high performance computing, and (3) reduction and analysis techniques using machine learning. The results show that the extent of the estuarine salt intrusion length is largely determined by four estuarine features: (1) river discharge; (2) cross-sectional area (especially water depth); (3) tidal damping/amplification; and (4) tidal asymmetry. In general, the salt intrusion length shows clear correlations with (a combination of) estuary-scale parameters, which all put an upper limit on the salt intrusion length. These relations provide crucial insights for successful development of nature-based solutions to mitigate salt intrusion in estuarine environments.