Simplified Marsh Response Model (SMRM): A Methodological Approach to Quantify the Evolution of Salt Marshes in a Sea-Level Rise Context

Abstract

Salt marshes are highly valued coastal environments for different services: coastline protection, biodiversity, and blue carbon. They are vulnerable to climate changes, particularly to sea-level rise. For this reason, it is essential to project the evolution of marsh areas until the end of the century. This work presents a reduced complexity model to quantify salt marshes’ evolution in a sea-level rise (SLR) context through combining field and remote sensing data: SMRM (Simplified Marsh Response Model). SMRM is a two-dimensional rule-based model that requires four parameters: a digital terrain model (DTM), local tidal levels, a sea-level rise projection, and accretion rates. A MATLAB script completes the process, and the output is a GeoTIFF file. Two test areas were selected in Tróia sandspit (Setúbal, Portugal). Additionally, a sensitivity analysis for each parameter’s influence and a comparison with SLAMM (another rule-based model) were undertaken. The sensitivity analysis indicates that SLR is the most relevant parameter, followed by accretion rates. The comparison of SMRM with SLAMM shows quite similar results for both models. This new model application indicates that the studied salt marshes could be resilient to conservative sea-level rise scenarios but not to more severe sea-level rise projections.

1. Introduction

Salt marshes are vegetated intertidal wetlands with high ecological value because of their biodiversity. They are one of the most productive ecosystems of the biosphere [1]. In addition, salt marshes (and mangroves) are widely recognized as playing a significant role in coastal defense due to their ability to dissipate wave energy and temporarily store floodwater. Moreover, they are a key feature for wildlife conservation, carbon sequestration [2], and a significant source of organic material and nutrients essential for marine communities [3]. Some of the earliest conservation reserves were salt marshes [4].

Anthropic pressure over these delicate systems and climate-driven changes in external forcing, may threaten the services these environments provide. Worldwide, vast areas of salt marshes have been converted into agricultural land, industrial use, or port facilities, despite lesser losses to other uses recently [4].

One of the main consequences of present and future climate changes is the sea-level rise (SLR), which may negatively impact these ecosystems and severely threaten estuarine areas [5]. Expected impacts include the destruction of habitats and the reduction of the protection they afford to the adjacent coastline and land. Salt marsh establishment is intrinsically linked to sea-level and tidal oscillations because flooding is the primary mechanism for sediment delivery to the marsh platforms [6]. Sea level and tidal range control immersion time, a parameter to which marsh vegetation is susceptible. Salt marsh areas are also prone to erosion, generally attributed to decreased sediment supply, and increased magnitude and frequency of extreme events. Both drivers are also indirectly influenced by SLR [7].

Remote sensing is essential to project the evolution of wetlands in a climate-change context [8,9], being a rapid and cost-effective method to obtain relevant data [10]. The increasing number of studies that use remote sensing reflects the access to this tool, e.g., [11,12,13,14].

Studying the future evolution of wetland environments, including salt marshes, is crucial because their reduction or destruction may increase adverse climate change impacts. For instance, the increase in CO₂ emissions to atmosphere related to wetlands’ destruction represents 3–19% of the increase due to deforestation [15]. An increase in CO₂ emissions to the atmosphere is explained by the release of organic carbon sequestered by these environments (known as blue carbon [16]). Furthermore, it is estimated that the carbon stored in European salt marshes represents 4% of all carbon accumulated in coastal areas [17].

Other factors can impact the behavior of these environments in the future. Salt marsh characteristics and dynamics result from complex interactions among hydrodynamics, sediment transport, and biological processes [18]. Changes in salinity, partially dependent on rainfall, affect their stability and local hydrodynamic patterns, ultimately affecting the distribution of accretion rates over different parcels of the salt marsh. Other significant parameters are elevation distribution and accommodation space in the land, neighboring salt marshes. These areas may provide room for landward marsh expansion, which may compensate seaward erosion; thus, maintaining invariance of the total marsh area. In fact, when SLR rates are higher than accretion rates, salt marshes may evolve in space and time following two ways: (1) marsh areas at higher elevations and fringing the coastline will migrate landwards, providing that the three following conditions are met—absence of vertical barriers (avoiding coastal squeeze), existence of accommodation space, and rate of horizontal marsh expansion upland equal or higher than the rate of horizontal progression of the inundation limit; (2) marsh areas at lower elevations will be more frequently flooded, experience larger submersion periods, and are not colonized, or remain colonized by low marsh vegetation [19].

In conceptual terms, if accretion rates closely match SLR rates, salt marshes may grow or maintain their area. However, the acceleration of SLR rates observed recently and projected into the near future suggests that this equilibrium is at risk of being reversed [20]. It is essential to rely on numerical or rule-based models to project and comprehend how salt marshes can evolve until the end of the 21st century. These are powerful predictive tools that incorporate nonlinear feedback between salt marsh ecosystem morphology and sediment transport and deposition processes [21]. Salt marsh evolution models and marsh response to SLR models can be classified as zero-dimensional (a single marsh point within a marsh is modeled), one-dimensional (simulating the evolution of a salt marsh transect), two-dimensional (when applied to a marsh platform), and landscape models (that simulate processes over an entire estuary) [6].

This work aims to present the Simplified Marsh Response Model, which is a rule-based model to quantify the evolution of salt marsh areas until the end of the century, combining remote sensing with data in the field and literature. SMRM considers the balance between SLR and accretion rates. Several models have been proposed recently to project the evolution of these vulnerable environments under a climate-change context [22,23,24,25]. Such models assume that many data are readily available (e.g., salinity, precipitation, wind, storm surge, uplift/subsidence, land use, erosion, and waves). However, this is not always possible (diversity, quality, and quantity of data are common drawbacks), and in many cases, they involve a too high investment regarding the results.

Moreover, the assumption that adding more detail and variables to models always leads to better results is questionable. Adding too many parameters can result in a situation where neither the studied systems nor the model are understandable [26]. In contrast, reduced complexity models are distinguished by a high degree of simplification, incorporating only the fundamental parameters to describe the processes or trends characterizing a particular coastal system at given time and spatial scales, leaving out as many processes as possible [27,28]. The Simplified Marsh Response Model (SMRM) is a reduced-complexity, two-dimensional rule-based model. The motivation to present this simplified model is that the complexity of the coastal systems often challenges the ability of complex models to forecast timely and accurately the meso to macro-scale evolution of marsh environments [29]. SMRM needs only four parameters to run and departs from a digital terrain model (DTM) of the studied marsh area. Using a DTM is the basis for modeling the evolution of salt marshes, a fundamental application of remote sensing to coastal areas. In order to evaluate its performance, SMRM was applied to two test areas in Portugal. The results were compared to those obtained by modeling marsh changes in the same areas for the same period of time with SLAMM (Sea Level Affecting Marsh Model) (Warren Pinnacle Consulting, Inc., Warren, VT, USA; Washington, DC, USA), a more complex rule-based model. In addition, a sensitivity analysis was performed to evaluate the influence of each input parameter on the final results.

2. Test Areas

Almost 50% of Portugal’s mainland perimeter corresponds to the Atlantic coast [30] (950 km) (Figure 1A) and about ¾ of the population lives in coastal municipalities [31]. The Portuguese coast hosts several estuarine/lagoonal areas featuring salt marshes. Atlantic estuaries occur north of Mondego River (central Portugal), and Mediterranean estuaries occur on the south and west (southward of Mondego River) coasts of Portugal [32]. The salinity and biodiversity are higher in the latter than the former, particularly in the high marsh. Although both types are anthropically modified, the Mediterranean estuaries are the best-preserved [33].

Sado estuary, with an area of 23,560 ha [34], is a Mediterranean estuary located 40 km south of Lisbon at the mouth of a river with the same name (Figure 1B). Sado river’s headwaters is located in “Serra da Vigia” (Ourique, Portugal) at 230 m of elevation [35]. Sado features the largest Portuguese watershed, with an area of circa 764,000 ha [36]. The climate (dry–subhumid [37] or subtropical [38]) can be described as uniform along the watershed, where the mean annual precipitation is 650 mm [35]. The river is classified as Mediterranean [39] and the flow ranges are between 1 m³/s in the dry season and 80 m³/s in the wet season [36]. The circulation and drainage within the estuary are essentially controlled by tides [40] because wind (which mainly blows from the north) only affects the surface water layer [35] and the river flow is too low. Ocean swell from the Atlantic Ocean cannot pass through the inlet, so the waves are usually smaller than 1 m inside the estuary.

Sado estuary is separated from the Atlantic Ocean by Tróia sandspit, a 25 km-long barrier trending NNW–SSE. Five growing phases were identified in Tróia sandspit, dated from 6500 years to present (Figure 1C) [41]. Two test areas featuring salt marshes were selected on the estuarine margin of this spit (Figure 1C–E) to apply the SMRM and the SLAMM. They are located in the NNW tip of Tróia sandspit, at Caldeira de Tróia (C. Tróia), which was further subdivided into two marsh expansions: north (C. Tróia (N)—Figure 1D) and south (C. Tróia (S)—Figure 1E) sectors. C. Tróia (S) was formed during the fourth growing phase of the sandspit (1870–1100 years before present), while C. Tróia (N) was installed during the most recent (fifth) growing phase (1100 years–present).

C. Tróia (N) salt marsh extends over 4.3 ha and consists mainly of a high marsh, with small areas of a low marsh at lower heights. Adjacent to the salt marsh, there are two different environments: dunes of moderate slope (landwards) and tidal mudflats (seawards). C. Tróia (S) has similar characteristics to the northern sector, even though it displays a larger area (10.5 ha) and a larger proportion of low marsh vegetation.

3. Models

3.1. Simplified Marsh Response Model (SMRM)

The SMRM is a reduced complexity and two-dimensional rule-based model of marsh response to SLR that only requires the input of four parameters: (1) a high-resolution DTM, representing both the target marsh area and the adjacent surfaces (e.g., tidal flats, backbarrier flats, dunes, alluvial plains), with an acceptable spatial range, resolution, and quality to allow the simulation of marsh expansion; (2) critical tidal levels, representing a transition between main intertidal environments and vegetation sensitive to submersion time; in the test-cases addressed herein, the model considers mean high-water neap elevation (MHWN) as the critical boundary between the tidal flat and low marsh, mean high-water (MHW) as the transition between the low and high marsh, and mean high-water spring (MHWS) as the upper growth limit of the high marsh [42]; (3) at least one SLR projection, including an initial rate and an optional SLR acceleration value; (4) representative accretion/sedimentation rates for high marsh, low marsh, and tidal flat domains, which can remain invariant over time or change throughout the century (in this last case, acceleration values of accretion rates must be introduced). The SMRM works with several data sources, joining the results obtained from fieldwork and laboratory (accretion rates), monitoring equipment (tidal levels and SLR), physical models (SLR), and remote sensing (DTM).

The model was built considering the premises that present-day tidal amplitudes will not change significantly in future decades and that the salt marsh surface’s signal and rate of evolution result from the balance between SLR rates and accretion rates (

Table 1. Possible results for the evolution of salt marsh areas, considering the balance between SLR rates and accretion (Acc.) rates.

Situation	Possible Result
SLR rates < Acc. rates	Expansion
SLR rates ≈ Acc. rates	Stability
SLR rates > Acc. rates	Inundation

).

The process starts by comparing the elevation of each DTM cell with the elevation thresholds (as previously defined) at the reference time (2020). This step automatically classifies each cell as terrestrial environment, high marsh, low marsh, or tidal flat (subtidal areas are not discriminated). Next, the accretion rate characterizing each type of intertidal environment for each year is applied to the discretized surface and a new DTM is generated, corresponding to the next year’s (2021) morphology. This process is repeated each year, and the transition levels are also adjusted yearly according to projected changes in sea level (Figure 2). The iteration sequence ends in the selected year as an output (2100 is the example shown herein, although decadal iterations were also performed).

The script to execute this set of steps was written in MATLAB R2018a (and updated to MATLAB R2020a) [43,44]. The output is a GeoTIFF file, which preserves the georeference of the original DTM. The final step is the generation of final maps and the determination of the new areas (high marsh, low marsh, and total area), based on tidal levels for the considered output year, which can be completed through any GIS software. In this work, this step was undertaken using ArcGIS Pro [45]. The SMRM script is available online [46].

In addition to the previous metrics, it is possible to obtain a parameter to estimate the maturity of the marsh, which depends on the ratio between high and low marsh areas and indicates the robustness of the salt marsh as a whole. In agreement with [42], a salt marsh is classified as young if the low marsh area is larger than the high marsh; intermediate, if both areas are broadly equivalent; and mature, if the high marsh is dominant over the low marsh area [42]. In order to obtain a quantitative indicator, an HM/LM (High Marsh/Low Marsh) ratio was established by the authors (HM/LM < 0.9 → young; HM/LM = [0.9–1.1] → intermediate; HM/LM > 1.1 → mature).

3.2. Sea Level Affecting Marsh Model (SLAMM)

The SLAMM model (version 6.7, Warren Pinnacle Consulting, Inc., Warren, VT, USA; Washington, DC, USA) [47,48] is also a two-dimensional rule-based model. It was initially developed to project the evolution of North American salt marsh areas until the end of the 21st century. However, SLAMM has not been widely applied to the Mediterranean–Atlantic salt marshes due to marked differences in vegetation, extent, and structure, although its application seems acceptable [49]. SLAMM works in a complex relation among six processes: inundation, accretion, erosion, overwash, saturation, wind, and salinity.

In order to apply SLAMM to Portuguese test areas, spatial and site-specific parameters (which are detailed further below) are mandatory: digital terrain model (DTM), slopes, wetland category maps, tidal levels, diurnal tidal range, direction offshore, salt elevation, accretion rates, and at least one SLR scenario. To compare the obtained results with the results provided by SMRM, no more than the mandatory parameters were considered.

4. Parameters

The parameters considered to project the evolution of the test areas are local tidal levels, DTM, SLR, and accretion rates. Other parameters such as wind and waves are not used in SMRM and were not considered in SLAMM. Although sometimes these parameters seem relevant [50], they are not significant in the Sado estuary, as explained in Section 2 of this work. In addition, salinity can be considered uniform in a small area such as C. Tróia.

4.1. Local Tidal Levels

The first parameter considers the threshold limits to automatically classify each DTM cell as dune, high marsh, low marsh, and tidal flat. This work considers tidal levels because they correctly identify the transitions among the environments. However, other data can be considered for other areas, which can be chosen by the model’s user.

Local tidal levels used in this study were modeled using harmonic analysis and based on data acquired by the Setúbal-Tróia tide gauge (years 1977, 1978, 1993, 1998, and 2005), located 2 km north of the study site (Figure 1B). Tide tables of 2000–2016 were computed from the harmonic model, mean values were evaluated, and a correction for the 2020 local mean sea level was applied (NMM1938, Cascais—the datum considered for all the heights presented in this study) [51,52].

SMRM and SLAMM use different tidal levels. SMRM considers the MHWN, MHW, and MHWS, whereas SLAMM uses heights of 30/60/90 days annual inundation periods. Furthermore, SLAMM also requires the introduction of the great diurnal tidal range (equivalent to the difference between mean highest high water and mean lowest low water levels) and the salt elevation (often defined as the elevation that is inundated by saltwater less than every 30 days in a year) [48]. These parameters were computed from the harmonic tidal model (

Table 2. Tidal levels for SMRM and SLAMM in 2020.

SMRM
MSL	MHWN	MHW	MHWS
0.19 m	0.90 m	1.26 m	1.61 m
SLAMM
MSL	90 days	60 days	30 days
0.19 m	1.32 m	1.47 m	1.62 m
SLAMM site-specific parameters
Great Diurnal Tidal Range		Salt Elevation
2.14 m		1.62 m

).

4.2. Digital Terrain Model

The colonization of new marsh areas depends on the annual inundation periods, governed mainly by topography. The latter is a fundamental parameter since it influences many processes determining coastal change [53]. To evaluate the uncertainty of the inundation, it is essential to consider a remote sensing technique that accurately represents the studied area: a high-resolution DTM.

A DTM was obtained by interpolating a 2011 LiDAR survey performed by Agência Portuguesa do Ambiente (APA) and Direção Geral do Território (DGT), both Portuguese public institutions. The horizontal resolution of the LiDAR varies between 1 and 2 m (2 m for intertidal environments such as salt marshes), and its vertical precision varies from 8 to 24 cm [30]. The LiDAR survey used topographic and bathymetric sensors, guaranteeing the data quality regardless of the surface type. Significant factors were also considered (topography and hydrography, temperature, humidity, precipitation, wind, water turbidity, pollution, flora, and fauna) to produce the final DTM [30].

The studied salt marshes display many tidal channels less than 2 m wide, matching the horizontal resolution of the considered DTM. Consequently, some of these channels are not well represented and generate sinks. Considering that tidal channels were not separately represented in simulations produced by both models, these artifacts (sinks) were leveled with the surrounding surface elements using the fill tool provided by ArcGIS Pro.

Heights of homologous points measured in the field using a DGPS-RTK (Leica Viva NetRover GS08) and yielded by the DTM were compared to validate the accuracy of the terrain model. In total, 2722 points distributed over the high marsh, low marsh, and tidal flat of both C. Tróia (N) (1844 points) and C. Tróia (S) (878 points) were measured (Figure 3,

Table A1. Statistical parameters of high marsh, low marsh, and tidal flat heights for C. Tróia (N) and C. Tróia (S), considering DGPS and DTM.

Parameters	C. Tróia (N)						C. Tróia (S)
	High Marsh		Low Marsh		Tidal Flat		High Marsh		Low Marsh		Tidal Flat
	DGPS	DTM	DGPS	DTM	DGPS	DTM	DGPS	DTM	DGPS	DTM	DGPS	DTM
Min. (m)	1.05	0.77	0.66	0.42	−0.04	0.09	0.91	0.58	0.50	0.40	−0.21	−0.38
Q1 (m)	1.28	1.35	0.94	0.91	0.48	0.38	1.14	1.27	0.91	0.89	0.48	0.52
Median (m)	1.39	1.47	1.02	1.00	0.57	0.48	1.21	1.42	0.99	1.05	0.54	0.67
Q3 (m)	1.46	1.55	1.08	1.12	0.66	0.61	1.31	1.54	1.05	1.14	0.62	0.92
Max. (m)	1.76	1.77	1.31	1.42	0.96	1.04	1.85	2.13	1.21	1.53	1.29	1.69
IQR (m)	0.19	0.20	0.15	0.22	0.18	0.23	0.17	0.27	0.14	0.25	0.14	0.40
Mean (m)	1.37	1.43	1.00	1.00	0.57	0.52	1.24	1.40	0.97	1.01	0.57	0.74
Points	678		928		238		489		191		198

) between 2016 and 2021. Although there is a gap of at least five years between the LiDAR survey and DGPS records, the difference should only correspond to the sedimentation that occurred in this period, because the erosion of marshes is not laminar and usually occurs at the edges [54].

In general, each environment is distributed between the theoretical tidal limits, so the SMRM will correctly classify each pixel of the DTM. On average, heights extracted from the DTM are higher than those obtained in the field, which can be justified by the salt marsh vegetation or water, even though these parameters were considered during the survey and data processing. C. Tróia (N) high marsh is higher than the high marsh in the southern sector. Although there are natural differences between the two data sources, the DTM is considered a reasonable morphologic representation of the study areas.

Besides the DTM, SLAMM requires a slope file and a *.txt file with each pixel’s SLAMM wetland categories. The slope file was obtained from the original DTM, and the categorization was completed manually according to the classification provided by this model’s Technical Documentation [47]. SLAMM does not clearly differentiate high and low marsh. Instead, it considers “regularly flooded marsh” and “irregularly flooded marsh”, which was associated with low and high marsh, respectively, in agreement with other authors [49]. Dunes were classified as undeveloped dry land since they are vulnerable to inundation and colonization by marsh vegetation.

A statistical evaluation of the DTM accuracy was performed in addition to the comparison between the DGPS and DTM data. The root mean square error (RMSE) was determined, considering both data sources (Equation (1),

Table 3. RMSE and L.E. of C. Tróia (N) and (S) salt marshes DTM.

C. Tróia (N)
	Global	Dune	High marsh	Low marsh	Tidal flat
RMSE	17 cm	29 cm	13 cm	18 cm	14 cm
L.E.	33 cm	57 cm	25 cm	36 cm	27 cm
C. Tróia (S)
	Global	Dune	High marsh	Low marsh	Tidal flat
RMSE	22 cm	39 cm	21 cm	15 cm	31 cm
L.E.	43 cm	76 cm	41 cm	29 cm	60 cm

). The RMSE is a metric widely used to express the vertical accuracy of elevation datasets [55].

$$RMSE=\sqrt{\frac{\sum {\left(Z_{DTM i}-Z_{DGPS i}\right)}^2}{n}}$$

(1)

Z_DTM is the height of each point in the DTM, Z_DGPS is the height of each homologous point measured with the DGPS, n is the number of points being checked, and i is an integer from 1 to n. Besides the RMSE, the linear error (L.E.) was also determined at a confidence level of 95% (the metric used by the National Standard for Spatial Data Accuracy (Federal Geographic Data Committee, 1998)) (Equation (2), Table 3).

$$L.E{.}_{\left(95\%\right)}=1.96\times RMSE$$

(2)

A global RMSE of 17 cm for C. Tróia (N) was obtained, which is compatible with the vertical accuracy of the DTM. The error is higher on dunes, probably because the DGPS data were measured between 2016 and 2021 and the DTM corresponds to a survey of 2011. The RMSE of the C. Tróia (S) salt marsh is globally higher. However, the global value is within the accuracy limits of the DTM. An RMSE of 17 cm was considered in the sensitivity analysis of the model performed in C. Tróia (N).

In this study, the DTM is considered static until the end of the century due to negligible vertical land motion (either isostatic or tectonic driven) compared with the magnitude of sea level changes. However, changes can occur due to land motion, and if that is the case, they can be added to the DTM error or to SLR.

A combination of data on absolute mean sea level derived from satellite observations with high-precision GPS data of vertical ground motion measured near tide gauges and relative mean sea level data measured at those tide gauges may be used to decouple eustatic from vertical land movements at shorter timescales and evaluate uncertainty. The magnitude of vertical land movement in the Cascais region (some 50 km north of Sado estuary) has been assessed by [52], comparing the 1990–2019 relative sea level data, retrieved from Cascais tide gauge, with 1993–2016 data on absolute sea level derived from satellite altimetry. He inferred vertical uplift rates from 0.08 to 0.28 mm/year. Different results have been obtained by [56]. These authors computed vertical land motions along the Iberian Atlantic coast using GPS time series with more than 8 years of observations. GPS-derived estimates of the vertical land movement were further used to correct data on sea level obtained at tide gauges. The latter was compared with satellite altimetry absolute sea level. In Cascais region, tide gauge results suggest small subsidence (−0.40 ± 0.08 mm/year) over 1997–2020. Another recent study [57] analyzed a global database of high-precision GPS data acquired after 2002 to set up an interpolated field of vertical land movement rates, from which median rates at the location of tide gauges in the Permanent Service for Global Mean Sea Level may be obtained ([57] provides methodological details). Vertical land movements shown in this study for Cascais and Setúbal-Tróia tide gauges indicate low subsidence at both stations, at rates of −0.766 ± 0.238 and −0.766 ± 0.320 mm/year, respectively. As correctly pointed out by [56,57], the above estimates should be taken with caution, given that different studies use different methodological approaches, contrasting lengths of the data series, heterogeneity in the spatial distribution of GPS source stations, and possible undocumented problems affecting both GPS and tide-gauge stations, and differences in data analysis and correction.

The contrast between the magnitude of vertical land motion (in the order of 10⁻¹ mm/year) affecting the study area recently and coeval multi-decadal changes in relative sea level (in the order of 10⁰ mm/year) indicates that eustatic components have largely dominated the latter. The future increase in sea level rise rate (in the order of 10¹ mm/year by the end of the 21st century) will enhance this contrast. It is reasonable to disregard the influence of vertical land motions in relative sea-level patterns, and marsh inundation projected until the end of the 21st century for Sado salt marshes, considering the objectives and timescale of this study.

4.3. Sea-Level Rise Scenarios

This study considers four SLR scenarios: IPCC RCP4.5 and RCP8.5 [58], Mod.FC_2b [52], and NOAA Extreme [59]. IPCC SLR scenarios were chosen to consider global projections, MOD.FC_2b is an empirical projection based on the Cascais (Portugal) tide gauge, and NOAA Extreme is a high-end SLR projection, which can be useful for land management measures.

SMRM requires an initial SLR rate and an acceleration value. These parameters are published for MOD.FC_2b, but only decadal absolute mean sea-level values are available for IPCC RCP4.5/RCP8.5 and NOAA Extreme. The provided values were plotted, and a polynomial function was calculated. The initial SLR rate (2020) and the acceleration were obtained through the first and second derivates of the functions, respectively (

Table A2. SLR rates for 2020, acceleration and SLR values for 2050 and 2100 for the considered SLR scenarios: IPCC RCP2.6/RCP4.5/RCP8.5, MOD.FC_2b, and NOAA Extreme.

SLR Scenario	Rate 2020	Acceleration	SLR (cm)
	mm/year	mm/year2	2050	2100
IPCC RCP2.6	4.463	0.000	33	55
IPCC RCP4.5	4.449	0.030	35	65
IPCC RCP8.5	4.340	0.097	37	86
MOD.FC_2b	5.260	0.152	43	111
NOAA Extreme	9.506	0.505	74	261

). All the SLR projections were adjusted to the Portuguese datum to be concordant with other parameters (Figure 4). A remark must be made on the NOAA Extreme projection since the 2020 SLR rate inferred from the respective model gives a much higher rate than the most recent observed SLR rate [52]. In 2100, such SLR would be only possible through an exponential model, related to a disruptive process, that could respect the actual SLR rates and the final sea level. However, the model and respective values of SLR and rates were used as presented by the report’s authors [59].

In addition to the previous scenarios, the IPCC RCP2.6 SLR projection was also included to perform a sensitivity analysis, since it can be described as a scenario with an almost linear behavior.

Many different scenarios can be incorporated in models of marsh response to SLR. It is fundamental to select a wide range of scenarios, to obtain different results. The previously presented scenarios include rises in sea level from 55 (IPCC RCP2.6) to 261 cm (NOAA Extreme) until 2100, and intermediate values (111 cm—MOD.FC_2b). Other SLR scenarios, e.g., [60], are within the presented set of values.

SLAMM allows the user to introduce a specific SLR projection or to select an SLR scenario from a list (mainly from IPCC). However, the included SLR projections are from the outdated IPCC 4th Assessment Report [61].

4.4. Accretion Rates

Sediment availability is fundamental for the survival of saltmarsh areas [62]; thus, any models trying to predict how these areas will evolve need to include this parameter. In this paper, sedimentation and accretion are used interchangeably to mean “the vertical increase in surface elevation (in mm) relative to a specific layer of soil” [63].

Vertical accretion combines the deposition and erosion of sediments, the accumulation of dead biomass on the marsh surface, and a certain amount of local subsidence (also called settlement or autocompaction) [63]. Many factors can influence the vertical accretion rate (e.g., sediment availability, presence of vegetation, tidal dynamics). The advantage of using radiochronology (e.g., ¹³⁷Cs and ²¹⁰Pb dating) to derive sedimentation rates is that the results already incorporate most of these factors [63].

In C. Tróia (N), accretion rates derived from the ²¹⁰Pb dating method are 2.9 mm/year in the high marsh, 3.0 mm/year in the low marsh, and 2.5 mm/year in the tidal flat. From the ¹³⁷Cs measurements and considering 1963 maximum atmospheric fallouts as the time marker, the sedimentation rates are 2.9, 2.9, and 3.3 mm/year, respectively. Appendix B presents the results from the ¹³⁷Cs and ²¹⁰Pb determination, and a detailed explanation of the used methods. The obtained values represent the last century’s sedimentation pattern and are suitable for integrating a model that will not exceed 2100 in its projections. We assume that accretion rates will not vary until the end of the century. Regarding the proximity of the two study sites and their similarities, the same accretion rates were also assumed for C. Tróia (S) marsh. Furthermore, other studies performed nearby found values of sedimentation rates ranging from 2.80 to 4.40 mm/year (depending on the technique) in the marshes of Malha da Costa (38°25′58″N, 8°49′31″W) and Faralhão (38°31′04″N, 8°47′03″W), both on the Sado estuary [64]. The similarity of the results demonstrates how consistent sedimentation is in this region, implying that, in the absence of new measurements, the obtained accretion rates in one marsh can be applied when modeling others located nearby.

Both SMRM and SLAMM consider one accretion rate for each environment, which is a simplification, since there are many aspects not considered: accretion rates will usually decrease with the increase in height, accretion rates tend to be higher near the tidal creeks, and others. Furthermore, changes in SLR could potentially affect sediment availability in the entire estuary. Investigating this aspect is, in itself, an entirely separate work. It might be possible to identify different accretion rates in areas with very high sedimentation rates over time. SMRM considers the possibility of working under nonlinear accretion rates. This is done by introducing a positive or negative acceleration value that affects the initial rates.

5. Application of SMRM to the Test Areas and Comparison with SLAMM

This section presents the results of SMRM application to both sectors of C. Tróia (the output datasets are available in [65]). They are similar in the two test areas, although the southern sector is less resilient to SLR. In addition, the obtained results are compared with SLAMM simulations for C. Tróia (N). The comparison is presented according to each SLR scenario’s severity (IPCC RCP4.5/8.5, MOD.FC_2b, and NOAA Extreme). In line with each SLR projection, the obtained results are quite different (

Table 4. Area and HM/LM ratio values for 2020, 2050, and 2100 for C. Tróia (N) and C. Tróia (S) salt marshes, considering IPCC RCP4.5/RCP8.5, MOD.FC_2b, and NOAA Extreme SLR scenarios using SMRM and SLAMM.

	Scenario		SMRM						SLAMM
			2020		2050		2100		2020		2050		2100
			Area (ha)	HM/LM	Area (ha)	HM/LM	Area (ha)	HM/LM	Area (ha)	HM/LM	Area (ha)	HM/LM	Area (ha)	HM/LM
C. Tróia (N)	IPCC	RCP4.5	4.48	2.9	4.49	2.3	4.33	1.0	4.31	2.8	4.30	2.2	3.99	0.8
		RCP8.5			4.45	2.1	3.79	0.4			4.27	2.0	3.63	0.3
	MOD.FC_2b				4.36	1.4	1.89	0.7			4.17	1.3	1.67	0.5
	NOAA Extreme				3.42	0.3	1.25	1.2			3.25	0.2	1.03	0.8
C. Tróia (S)	IPCC	RCP4.5	10.29	1.4	10.12	1.2	9.10	0.8	10.31	1.4	9.93	1.2	8.60	0.7
		RCP8.5			9.95	1.2	6.65	0.4			9.74	1.1	6.37	0.4
	MOD.FC_2b				9.44	1.0	4.39	1.1			9.22	0.9	4.01	0.8
	NOAA Extreme				5.98	0.3	5.40	1.5			5.71	0.3	3.81	1.0

).

The results are very similar for both models. However, some differences should be noted. The initial area is manually defined based on field and satellite imagery observation. Nevertheless, each model adjusts the initial area according to the local tidal levels (SMRM) or other relevant parameters (slope, salt elevation, great diurnal tidal range—SLAMM). For this reason, in 2020, the area is not precisely the same for both models. Thus, in the C. Tróia (N) salt marsh, the initial area is overestimated by 3% with SMRM and 1% with SLAMM (Figure 5A,B). In the case of C. Tróia (S), the real limits coincide with the local tidal levels (Figure 5C,D).

Considering IPCC RCP4.5 (SLR of 65 cm until 2100), SMRM projects that C. Tróia (N) will maintain its area until 2050 and a loss of only 3% is expected until 2100 (4.33 ha) (Figure 6A). The HM/LM ratio will decrease to 2.3 and to 1.0 by 2050 and 2100, respectively, which is clear in the morphological maps (Figure 7A,C). C. Tróia (S) will lose 2% (10.12 ha) and 12% (9.10 ha) of its area (Figure 8A) and the HM/LM ratio will be 1.2 and 0.8 in 2050 and 2100 (Figure 9A,C). The losses are greater with SLAMM: in C. Tróia (N), there will be no losses in the area until 2050 and a loss of 7% (Figure 6B) (HM/LM = 2.2/0.8 for 2050/2100—Figure 7B,D) is expected until 2100. In C. Tróia (S), the area will be reduced by 4% and 17% until 2050 and 2100 (Figure 8B) (HM/LM = 1.2/0.7 for 2050/2100—Figure 9B,D).

With IPCC RCP8.5 (SLR of 86 cm until 2011), SMRM projects 1% (4.45 ha) and 15% (3.79 ha) losses until 2050 and 2100 for C. Tróia (N) (Figure 6C). The HM/LM ratio will decrease to 2.1 and 0.4 for these reference dates, respectively (Figure 7E,G). In C. Tróia (S), the area will be reduced by 3 and 35% (Figure 8C) and the HM/LM ratio will be 1.2 and 0.4 in 2050 and 2100 (Figure 9E,G). With SLAMM, C. Tróia (N) area will decrease by 1% and 16% (Figure 6D) (HM/LM = 2.0/0.3 for 2050/2100—Figure 7F,H) and C. Tróia (S) will decrease by 6% and 38% until 2050 and 2100 (Figure 8D), respectively (HM/LM = 1.1/0.4 for 2050/2100—Figure 9F,H).

The SMRM with the MOD.FC_2b SLR scenario (111 cm until 2100) produces major changes until the end of the century. In C. Tróia (N), the area will be reduced by 3% (4.36 ha) and 58% (1.89 ha) (Figure 6E) and the HM/LM ratio will be 1.4 and 0.7 until 2050 and 2100 (Figure 7I,K). For C. Tróia (S), the losses will be almost identical: the area will be reduced by 8% (9.44 ha) and 57% (4.39 ha) in 2050 and 2100 (Figure 8E). However, the HM/LM ratio will be 1.0 and 1.1, respectively (Figure 9I,K). SLAMM produces area losses of 3% and 61% for C. Tróia (N) (Figure 6F) (HM/LM = 1.3/0.5 for 2050/2100—Figure 7J,L) and of 11% and 61% for C. Tróia (S) for the reference dates (Figure 8F) (HM/LM = 0.9/0.8 for 2050/2100—Figure 9J,L).

Finally, considering SMRM with NOAA Extreme (261 cm of SLR until 2100), the area will be reduced by 24% (3.42 ha) and 72% (1.24 ha) in 2050 and 2100 in C. Tróia (N) (Figure 6G). The HM/LM will be 0.3 and 1.2, showing a recovery by the end of the century (Figure 7M,O). In C. Tróia (S), the losses in the area will be almost the same in 2050 and 2100: 42% (5.98 ha) and 48% (5.40 ha) (Figure 8G). The HM/LM ratio decreases to 0.3 in 2050 and increases to 1.5 in 2100 (Figure 9M,O). SLAMM produces area losses of 25% and 76% in C. Tróia (N) (Figure 6H) (HM/LM = 0.2/0.8 for 2050/2100—Figure 7N,P) and 45% and 63% in C. Tróia (S) until 2050 and 2100 (Figure 8H) (HM/LM = 0.3/1.0 for 2050/2100—Figure 9N,P).

In general terms, the results obtained with the two considered models are similar for both study areas.

6. Sensitivity Analysis

6.1. Methodology

A sensitivity analysis was performed on the C. Tróia (N) salt marsh to evaluate the influence of each parameter on the result of SMRM, establishing three risk levels: low, medium, and high (

Table 5. Risk levels for the sensitivity analysis performed with SMRM to the C. Tróia (N) marsh.

Risk	DTM	SLR	Acc. Rates
		IPCC RCP2.6
Low	SLR − RMSE	IPCC RCP4.5	5.46/5.84 mm/year (tidal flat/marsh)
Medium	-	MOD.FC_2b	2.73/2.92 mm/year (tidal flat/marsh)
High	SLR + RMSE	NOAA Extreme	0 mm/year

). For each level, each parameter (DTM, SLR, and accretion rates) was combined in all the available possibilities. In total, 36 different combinations were considered in this exercise and the results were plotted in boxplots (Figure 10).

Each risk level includes different values for each evaluated parameter (DTM, SLR, and Accretion Rates). The three risk levels of the DTM were formed through the inundation heights, adding or subtracting the RMSE to the SLR [53]. Four SLR scenarios were considered: the conservative one (low risk—IPCC RCP4.6), the intermediate (medium risk—MOD.FC_2b), and the high-end (high risk—NOAA Extreme). In addition, IPCC RCP2.6 was also considered since it is a scenario with an almost linear behavior. Lastly, the determined accretion rates were used for the medium-risk scenario. For the low risk, accretion rates were doubled (5.8 mm/year for high and low marsh; 5.5 mm/year for tidal flat) and eliminated (0 mm/year) for the high-risk scenario. The evaluated results were the change in the global area as well as the inundation area (which is the new area colonized by marsh that is currently terrestrial area) until 2100.

Results yielded by SMRM are contained in a GeoTIFF file. Therefore, it is possible to determine the total addressed area, partial high and low marsh areas in the simulated time horizon, and the inundation area (which is the area now colonized by marsh vegetation). Therefore, both the changes in total and inundation areas in 2100 were used in the sensitivity analysis.

6.2. Results

The sensitivity analysis results show that SLR is the most critical parameter to consider in the evolution of the marsh areas, because each SLR scenario produces a different set of results. For instance, when the NOAA Extreme scenario is considered, C. Tróia (N) marsh will lose between 70% and 80% of its original area until the end of the 21st century, no matter which risk level is selected for the remaining parameters. An exception is made for IPCC RCP2.6 and RCP4.5, which may produce similar results. Accretion rates are also a fundamental input for the model (as other authors have reported [66,67]). Double rates (low risk) may produce lower variations in the global area than the medium risk level. However, the most significant impacts are observed when no accretion rates are considered (high risk). Thus, it is possible to infer that accretion rates are an essential parameter to consider, even if an increase in the value does not produce proportionally different results. The RMSE of the DTM seems to have an impact on the global area that is proportional to the size of the error.

Regarding the inundation area, SLR is also the most relevant parameter, although only NOAA Extreme (high risk) produces a very significant change in the result. As in the global area evolution, the RMSE of the DTM also impacts the inundation area proportionally to the error’s size. Lastly, accretion rates do not influence the inundation area, which is only controlled by the inundation height, which is different according to the chosen SLR scenario and RMSE of the DTM.

7. Discussion

The discussion of this work is based on three topics: the advantages and drawbacks of applying SMRM to marsh areas; the projection of the evolution of the test areas; and the possibility of extrapolating the results to other areas.

Using a reduced-complexity model allows for obtaining projections of marsh evolution considering only the fundamental data. This case includes tidal levels, SLR, accretion rates, and the local morphology. Using as few parameters as possible without compromising the reliability of the results is essential to study many areas where there are not sufficient available data or to perform quick preliminary projections. Furthermore, these advantages are crucial to undertake the correct land management of these areas (e.g., to define which areas should remain free of occupation).

In order to evaluate the reliability of the produced results, a comparison with SLAMM was performed. Besides the SMRM inputs, SLAMM also requires at least the following additional parameters: slopes, wetland categories map (spatial parameters), great diurnal tidal range, and salt elevation (site-specific parameters). SLAMM also allows the user to choose among predefined SLR scenarios, which are outdated. The alternative is to input the mean sea-level position for each year until the end of the century. The results obtained with SMRM are quite similar to those obtained with SLAMM regarding the global area, HM/LM, and marsh distribution. For the initial year, both models recalculate the marsh area, which is the basis for the simulations performed until the end of the century. SLAMM seems more accurate in representing the initial salt marsh area, although the differences are not significant. Differences between models are always related to the maximum inundation line—the behavior of seaward limits is always similar in both models.

The sensitivity analysis shows that the parameter that most significantly controls the evolution of marsh areas with SMRM is the SLR—the result is clearly different according to the chosen scenario. It is the most powerful parameter regarding both the evolution of the marsh area and the inundation area. Conservative and intermediate scenarios produce comparable results, but the high-end scenario can project an almost complete inundation of these areas. The other two parameters are relevant in different ways. When the RMSE of the DTM is considered, a proportional change in the evolution of the marsh is identified (i.e., the greater the error, the larger the expected inundation, e.g., [53,68,69]). Accretion rates are crucial for estimating the marsh area in the future, but they are not relevant to determining the inundation area, since it only depends on the DTM and SLR. On the one hand, if the accretion rates double, it seems that the results are hardly affected. On the other hand, considering no accretion rates, a major difference in the results can be produced.

Many studies have been published regarding the evolution of wetlands, trying to find a global tendency of evolution, even if each wetland can have its behavior in the future [31]. Recently, marsh areas have kept pace with SLR [70], with small area losses [71]. However, there are different results (from different studies) on the future of salt marshes. Some authors project that in the future, these areas will survive with conservative SLR scenarios [72] or even if high-end scenarios are considered [73], but other studies always project a significant loss in area in these environments [74]. The results of SMRM indicate that the accommodation space landwards will be fundamental to the survival of wetlands, as other authors previously suggested [75]. Even so, it is reasonable to assume that the stability of marsh areas should be guaranteed in the first half of the century, mainly when conservative or intermediate SLR scenarios are considered. However, the HM/LM ratio reduction seems inevitable in all projections for both study areas, mainly in the second half of the century. This reduction occurs because, when sea level rises, the tidal limits that define each environment’s existence also increase in height. If accretion rates are not high enough to compensate for the SLR rates, areas currently colonized by high-salt marsh vegetation will suffer longer periods of annual flooding. Consequently, these areas will be colonized by vegetation more tolerant to inundation than high marsh vegetation. If sea level continues to rise, the annual inundation periods in these areas will also continue to increase. They may reach values that will be no longer compatible with low marsh vegetation. As a result, these areas will not keep any vegetation type, and will become non-vegetated areas (tidal flats). The consequences of these losses are reflected in the diminishing of the ecosystem’s services, such as physical protection or carbon sequestration [76]. In fact, the loss of marsh areas due to SLR could imply an emission of CO₂ to the atmosphere equivalent to the increase in global greenhouse emissions [77]. That is why the preservation of marshes is seen as a natural climate solution to climate changes [78,79].

In this work, four theoretical phases in the evolution of salt marsh areas until the end of the 21st century were identified (Figure 11): (I) stability, (II) significant loss of maturity, (III) significant loss of area and, in cases, (IV) a partial area recovery. High-end SLR scenarios tend to generate more evolution phases than conservative projections (this is always visible in Figure 7 and Figure 8). The behavior is similar in all cases, which is different in the timing of each evolution phase occurrence.

Regarding the two test areas, they have many common characteristics. However, some key differences motivate different responses to climate change, particularly, to SLR. The marsh in C. Tróia (N) is more mature than C. Tróia (S), which is reflected in the resilience to its response. Therefore, the same behavior can be observed in both sites but at different paces. The northern sector of C. Tróia is the most resilient to the consequences of SLR. Furthermore, although dunes with moderate slopes exist in both areas, the southern sector has more flattened adjacent areas, improving the ability for landward colonization of these new areas. These factors influence the pace at which each evolution phase occurs.

The above-described sequence of evolution indicates that many salt marsh areas will probably disappear in the future. However, there are landward areas adjacent to the present salt marsh limits that, in turn, will be flooded frequently enough to establish new high and low marsh areas. The increase in the annual inundation periods may also promote the deposition of sediments transported in suspension by tides, further facilitating the colonization of these supratidal areas by marsh vegetation. A consequence of these dynamics would be the formation of new salt marsh areas that may minimize (although not compensate) the projected losses in the remaining marsh or even lead to a partial recovery of the global area.

These assumptions are valid if there is no direct anthropogenic destruction of marsh areas until the end of the century and if there is a constant flux of sedimentation. However, this is not necessarily true, because these environments are increasingly threatened by anthropogenic factors and sediment deficits [80]. In addition, it is also assumed that the increase in storm intensity in the future [81,82] will not increase the impact on these areas, which is likely true for the tested marshes, since they occur in a very sheltered area.

8. Conclusions

The SMRM is a reduced complexity model that aims to compromise between complex models and simplistic approaches to quantify the evolution of salt marsh areas in a climate-change context. SMRM does not consider as many parameters as other more complex numerical and rule-based models and the number of required inputs to perform a simulation greatly simplifies the process. In fact, the results obtained with SMRM are quite similar to those obtained with SLAMM. The use of only four parameters makes its application as universal as possible, allowing comparing the results among several environments in different places.

The sensitivity analysis showed that the most relevant parameter to the results (global area change and inundation area) is the SLR. Accretion rates also significantly impact the variation in the total area. However, their influence is not proportional to their value and does not affect the inundation area. This observation supports applying the same accretion rates for more than one study area if they are close enough to each other and have common characteristics. Finally, the RMSE of the DTM causes a variation in the results, which is approximately proportional to the error’s size.

In conclusion, there are four critical parameters to consider in order to estimate the evolution of salt marsh areas until the end of the present century: (1) SLR, (2) accretion rates, (3) the morphology of each salt marsh (heights and maturity), and (4) the availability of colonizable landward space. SMRM is presented in this work as a compromise between accuracy and complexity, which allows a simple way to evaluate the behavior of intertidal areas in the context of SLR, a fundamental analysis to address coastal risk and land management policies and practices. This work also showed that the field data (obtained through cores and monitoring equipment) could be an excellent complement to remote sensing data. Finally, the combination of these parameters from different sources allowed the establishment of a simplified model to quantify the evolution of marsh areas in the future.

The test areas seem to be resilient to moderate SLR scenarios, particularly in the first half of the century (losses between 1 and 7% in the area until 2050, except for NOAA Extreme SLR scenario, with losses of 36%). Only in the second half of the century will the survival of these areas be compromised (losses between 15 and 67% in the area until 2100). Combining the results of the test areas and the sensitivity analysis, it is also possible to assume that marsh areas could positively respond to SLR if conservative scenarios were considered and if there is sediment available to compensate for the SLR. Four evolution phases were identified in these environments: stability, loss of maturity, loss of area, and recovery.