A simple, dynamic, hydrological model for mesotidal salt marshes

Abstract

Salt marsh hydrology presents many difficulties from a measurement and modeling standpoint: bi-directional flows of tidal waters, variable water densities due to mixing of fresh and salt water, significant influences from vegetation, and complex stream morphologies. Because of these difficulties, there is still much room for development of a truly mechanistic model of salt marsh groundwater and surface-water hydrology. This in turn creates an obstacle for simulating other marsh processes, such as nutrient cycling, that rely heavily on hydrology as a biogeochemical control and as a mode of nutrient transport. As a solution, we have used water level data collected from a well transect in Winant Slough, a mesotidal salt marsh on the Oregon coast, to create and calibrate a simple, empirical dynamic marsh hydrology model with few parameters. The model predicts the response of a marsh’s water table level to tides and precipitation as a function of surface elevation and distance from tidal channel. Validation was conducted using additional well data from a separate transect in Winant Slough (achieving a standard error of 2.5 cm) and from two other mesotidal marshes in Tillamook Bay, Oregon (achieving standard errors of 3.1 cm and 3.6 cm). Inundation frequencies of the top 10 cm of soil were estimated from model outputs to be 18.3 % of a 14.8-day tidal cycle for the area closest to the tidal creek and 59.3 % for the area furthest from the creek. Model outputs were also used to predict the amount of soil pore space available to receive incoming tide water in Winant Slough, finding the volume available to range from 12.5 % to 24.7 % of the incoming marsh tidal prism volume, depending on the maximum tide height. Incrementally increasing sea level rise scenarios ranging from 15 cm to 75 cm predicted an exponential decrease in soil pore space available to receive incoming tidal water and an approximately linear increase in inundation frequency of the top 10 cm of soil; this substantial change in hydrology would impact the marsh’s ability to process incoming water and could alter the zonation of vegetation. The model is relatively easy to apply to salt marshes and can provide informative hydrology predictions to land managers, ecologists, and biogeochemists who may not have the time or expertise required to apply more complex models.

Graphical Abstract

1. Introduction

The hydrology of a salt marsh is a critical component of its structure, function, and ability to provide services to society and the environment. It governs a marsh’s inflows, outflows, and internal dynamics of water, nutrients, and sediments. Further, it controls water availability, salinity, and aeration dynamics which in turn determines benthic habitat, plant zonation, and soil biogeochemistry (Morris et al., 2002; Silvestri et al., 2005; Wilson et al., 2015). In recent decades, salt marshes have become increasingly recognized for the important role they play within an estuarine landscape by purifying water, sequestering carbon, reducing flooding, and providing habitat (Barbier et al., 2011; Pendleton et al., 2012; Moller et al., 2014). Altering the existing hydrology of a salt marsh can have substantial impact on its potential to deliver these services (Craft et al., 2009; Tempest et al., 2015). Coastal development and rising sea levels are two immediate and continuously increasing threats to the natural hydrology of salt marshes around the world (Craft et al., 2009). The combination of the high value and high vulnerability of salt marsh hydrology necessitates that scientific and management communities be able to model it accurately in order to predict how it may change in various future scenarios.

Salt marsh hydrology models have been developed and applied since the 1980s (Harvey et al., 1987; Hemond and Fifield, 1982; Nuttle, 1988). These models continue to develop in complexity over time as our understanding of soil-water dynamics improves, field data collection methods are refined, and available computing power increases. Modern salt marsh hydrology models such as SUTRA (Voss and Provost, 2002) and MARUN (Boufadel et al., 1999) incorporate temporal and spatial heterogeneity in hydraulic properties of water such as temperature and salinity (Wilson and Morris, 2012). They also consider soil characteristics such as macropores (Xin et al., 2009) and compressibility (Gardner and Wilson, 2006) while also including the effects of vegetation (Ursino et al., 2004; Marani et al., 2006; Xin et al., 2013; Xiao et al., 2017). These models can also output a variety of specific hydrological parameters such as velocity flow fields and groundwater age (Wilson and Gardner, 2006; Xin et al., 2017). However, along with the growing complexity and physical realism of these models have come challenges to their application and calibration due to limited available input data, large parameter spaces, and growing computational resource requirements (Silberstein, 2006; Clark et al., 2017). For example, the model SUTRA has over a hundred user-specified parameters, which can result in large parameter spaces and high input data requirements (Voss and Provost, 2002). The ability of these models to provide insights into system dynamics and output advanced hydrology results is undoubtedly valuable. However, we still see an opportunity to provide alternative, more accessible modeling options that can output relevant hydrological information to be used by land managers, ecologists, and biogeochemists that may not need more complex hydrology outputs.

Our goal was to develop a model that can accurately provide some of these valuable hydrologic outputs while remaining easy to apply, calibrate, and transfer to new sites. While there are many ecologically-relevant aspects of salt marsh hydrology, some stand out as particularly useful for science and management applications. For example, how water flows through marsh soil affects porewater turnover, concentrations of toxic solutes like hydrogen sulfide, and the delivery of water purification services (Portnoy, 1999; Wilson and Gardner, 2006; Taillefert et al., 2007). The model developed in this study can provide predictions of subsurface water levels which influence soil redox potential which in turn affects rates of denitrification and sulfate reduction (Mitsch and Gosselink, 2015; Taillefert et al., 2007). Further, average water table levels and inundation frequencies can be used to predict marsh ecology, classification, and vegetation zonation (Silvestri et al., 2005, Sadro et al., 2007; Mitsch and Gosselink, 2015). Marsh vegetation distributions depend on a combination of factors including salinity levels and soil saturation periods which are governed by subsurface hydrology (Ursino et al., 2004; Silvestri et al., 2005; Wilson et al., 2015).

By including flooding and drainage dynamics, our model is able to predict the aforementioned hydrologic characteristics while also providing other useful hydrologic information that could not be gained using only tidal data and surface elevations. For example, calculating the Soil Saturation Index, an ecologically important parameter defined by Xin et al. (2010) as “the ratio of saturated period to a tidal period at a particular soil depth”, requires knowing how marsh water table levels will change once the tide has receded. The model described in this paper can output this information to the user with the minimal data input of tide levels, precipitation, and marsh surface elevations.

We present in this paper an empirical dynamic model of salt marsh hydrology that is relatively easy to apply and is able to provide relevant hydrology outputs needed for various ecological and biogeochemical applications. Water level data from well transects in a salt marsh on the coast of Oregon were used to develop, calibrate, and partially validate the model, while data from two other marsh sites on the same coast were used to validate the model in different hydrogeological settings. By combining empirical equations in a dynamic way based on the state of the water table, the model is able to capture adequately the nonlinear nature of the system while maintaining a small and relatively easy to calibrate parameter set. To demonstrate the potential utility of the model, multiple sea level rise scenarios were simulated and the results compared to baseline hydrologic characteristics. The advantages and disadvantages of this modeling approach when compared to alternatives are discussed in the context of potential applications. Ultimately, we propose that a simple model with a small parameter set combined with an automated calibration program can provide an effective and easily transferrable hydrology tool to be used by land managers, ecologists, and biogeochemists.

2. Field methods

2.1. Site Descriptions

The field work was conducted in two estuaries on the north-central Oregon (USA) coast (Figure 1). The Yaquina Bay is a 13 km², drowned river estuary with a 658 km² watershed that is 95% forest land. The bay has mixed semi-diurnal tides with a mean range of 1.91 m (https://www.tidesandcurrents.noaa.gov). The Tillamook Bay (33 km²) is also a drowned river estuary but is unusual in that it drains five rivers of similar size and is extremely shallow compared to its areal extent (Komar et al., 2004). The entire watershed covers ca. 1400 km². Similar to Yaquina Bay, the tides are mixed semi-diurnal with a mean range of 1.90 m (https://www.tidesandcurrents.noaa.gov).

Figure 1:

Location of calibration and validation sites on the Oregon Coast. Bayocean Peninsula Park (BPP) and Kilchis Point Reserve (KPR) are both located in Tillamook Bay, while Winant Slough (WS) is located in Yaquina Bay. Black bars on site maps indicate well transect locations. Delineated tidal marsh map source: (Scranton, 2004).

The majority of the data used to develop and parameterize the model were collected in a small, mesohaline marsh along the Yaquina River approximately 11.5 river-km from the ocean. Winant Slough (44°34’55” N 123°59’41” W) is a 2-ha marsh bounded on the upland side by a steep, mixed conifer/alder catchment; the total watershed area is ca. 20 ha. Vegetation in Pacific Northwest salt marshes is a diverse mix of grasses, forbs, rushes, and sedges. Previous studies have described the vegetative species in this area in more detail (Janousek and Folger, 2013; Weilhoefer et al., 2013). Two main sub-catchments supply approximately 50% and 15% of the fresh water, with the remainder from about 20 much smaller sources. The estuary side is constrained by a causeway, and bay water exchanges with the slough under a bridge lined with large boulders (Figure 1).

Data from two marshes along the fringe of Tillamook Bay were used to validate the model under different hydrological conditions (Figure 1). The first site (45°30’16” N 123°52’48” W), on the Kilchis Point Reserve (KPR), is a 2.6 ha marsh on one of the branches of Doty Creek bounded by very flat upland of mixed forest and agricultural land. The marsh system is cut off from the larger agricultural delta by a railroad line and a highway to the northeast, so the freshwater input is very diffuse from a roughly 1 km semi-circular area of little contour to the east. The marsh receives estuarine water from the west by an unconstrained boundary with a mud flat of Tillamook Bay.

The second Tillamook site (45°31’9” N 123°56’37” W) is on a marsh fringing the long, sandy spit called Bayocean Peninsula Park (BPP) that separates the west side of Tillamook Bay from the ocean. In contrast to the other sites, the contour from marsh to estuarine water is much flatter, grading from high marsh (surface elevation above mean high water) to low marsh (surface elevation below mean high water) to sand flat very gradually out into the subtidal zone. The spit at the transect location is approximately 1 km wide and made up of coastal scrub (shore pines, salt grasses, etc.) bisected by a gravel access road and as such, there is very little upland fresh water source to this marsh. The high marsh ranges in width from a few meters near the access road to ca. 120 m along some of the upland scrub.

2.2. Well installation

Two well transects were installed at Winant Slough (Figure 1). One transect spanned a high marsh site that separated the main tidal channel from a subsidiary (3^rd order) channel. Five wells were placed as such: 1 m from each, 3 m from each, and directly in the center of the 17-m span between the two channels, and water level data were gathered from September 2015 to March 2016. A second transect of ten wells was installed at another location in the high marsh from the edge of a 2^nd order tidal channel up to just above the toe of slope at the upland fringe. These were nominally 1, 2, 3, 5, 8, 13, and 21 m from the channel edge, and then 4 m below, 1 m below, and 1 m above the toe of slope, and water level data were gathered from August to November of 2015.

At the Kilchis Point Reserve, several small creeks in the reserve form the northern edge of the Kilchis River delta, and the site chosen for a well transect was on the southernmost of these. Wells were installed 2, 5, 8, and 21 m from the edge of this channel, and water level data were collected from June 2016 to January 2017. There are a few very small tidal channels running through the Bayocean Peninsula Park, but by far the greatest surface drainage of the marsh is directly to the sand flat. As such, wells at this site were installed in a transect line (2, 5, 13, and 34 m) from the low marsh/sand flat boundary instead of from a tidal channel edge, and water level data were gathered during June and July of 2016.

2.2.1. Sediment coring

Sediment cores were collected at the site of each well using a 98 cm long gouge auger with an outer diameter of 6.1cm; in this way, geomorphological data could be determined exactly where the wells were installed. Any compaction of the core was measured by ruler before removing the auger from the ground; typically, compaction was not observed or was measured at 1 cm or less. The soil core was cut into 5 cm sections to 30 cm, and then 10 cm sections to the end of core (typically between 70 and 95 cm). The cross section of the auger was a little more than a half circle; after sectioning, that part of each depth interval outside the auger body was carefully sliced away from the auger with a knife and used for qualitative description (i.e., texture, color, relict organic material, presence of roots, evidence of reduced or oxidized layers, macro-pores, etc.) Sections still within the auger were removed as quantitatively as possible into Whirl-pak® bags and stored in a cooler on ice for transport back to the laboratory.

Once in the laboratory, the bulk wet weight of each section was measured. (The weight of the Whirl-pak® bag was taken as the average weight of at least 5 bags.) The soil was homogenized in the bag and weighed into tared aluminum pans. At least every third sample within a core was run in triplicate; in some cores all sections were run in triplicate. These samples were dried to constant weight (103°−105° C), ashed (500° C for 4 hours), and re-weighed. Soil structural properties were calculated per Elliot et al. (1999). Bulk density of each section was estimated from the wet weight, the section volume and the average wet/dry ratio of the homogenized replicates. The dry and ash weights were used to calculate percent loss on ignition (an estimate of the organic fraction in the soil), and the following equation was used to calculate porosity:

$$\text{Φ}=1-{\rho }_{bulk}\left(\frac{1-LOI}{{\rho }_{min}}+\frac{LOI}{{\rho }_{org}}\right)$$ (1)

where Φ (unitless) is the porosity, ρ_bulk (g cm⁻³) is the soil bulk density, LOI (unitless) is the mass fraction of soil lost on ignition, ρ_org is the density of organic matter, assumed to be 1.0 g cm⁻³ (Skopp, 2000), and ρ_min is the density of mineral particles assumed to be equal to the density of silica, 2.65 g cm⁻³ (Skopp, 2000).

In addition to bulk sediment properties, the grain size distribution of most of the core sections were analyzed using a Horiba laser scattering Particle Size Analyzer. Approximately 30 g of wet sediment were treated over several days with 6% H₂O₂ at 60°C to digest organic material. Data from this instrument were binned into standard volumetric sand/silt/clay designations.

2.2.2. Well construction and installation

Standard water table hydrology wells were constructed from 1–1/4” Schedule 40 PVC well pipe after Minnesota BWSR (2013). After core samples were removed from the soil, wells were immediately installed in corresponding holes so that the top slit was 8±1 cm below grade. The annular space was back-filled with coarse sand up to approximately 5 cm below grade, and the rest of the space filled with bentonite clay (MBWSR, 2013). Water level in the wells was measured with HOBO U-20 titanium water level loggers (Onset Computer Corp.) set to record on 6-minute intervals to correspond to local NOAA tide gauge data (South Beach, OR, for Yaquina Bay and Garibaldi, OR, for Tillamook Bay). In addition, a HOBO U-20 was installed in each marsh so that the pressure transducer was situated at the elevation of the marsh surface allowing a height of overtopping water to be measured. Finally, a HOBO U-20 was installed somewhere at each field site above the highest water level to measure the local air pressure.

2.3. Well data processing

Logger data were processed using the software provided by Onset Computer Corp. (HOBOware Pro ver. 3.7.8.). Water levels for the well, channel, and marsh surface loggers were calculated by subtracting the recorded contemporaneous air pressure from the data and converting the resulting pressure to water height. The water density is calculated using temperature measured by the logger and a salinity assigned by the HOBOware software when the brackish setting is selected.

These water levels were further corrected to account for logger-to-logger inconsistencies. Each deployment (80–90 days) was carried out whenever possible with a complete set of loggers (well string, marsh surface, channel, and air). The loggers were launched so that each set was left undisturbed in air for at least an hour prior to traveling to the field site. Upon retrieval, they were brought back to the lab and left together undisturbed for at least an hour before they were stopped and the data downloaded. Thus, at least ten air pressure readings before and ten after were recorded by all the loggers in a set when they were in a stable, undisturbed location. Ten “before” and ten “after” water levels (that is, zeroes) were averaged (overall average offset was 0.5 cm), and this logger-to-logger offset was subtracted from all the water level readings.

2.3.1. Elevation measurements

Water level data were also used to estimate elevation of the marsh at each well site by comparing the well data to that from the marsh surface logger during overtopping tides. First, the high-water delay between the appropriate NOAA tide gauge and the marsh surface data was estimated to the nearest 6-minute interval. Then the NOAA data (lagged by the appropriate tidal delay) relative to mean lower low water (MLLW) were plotted vs. those surface logger data that were >0.05 m. The intercept of the best-fit line through these points gave a good elevation estimate of the marsh surface loggers in MLLW. This method relies on the assumption a given high water at the marsh in question is the same elevation as high water at the associated NOAA tide gauge site. This was validated by using RTK-GPS on three surface logger sites at Winant Slough; elevations calculated using the water level loggers agreed with RTK-measured elevations to within 2 cm in all cases at Winant Slough. The other sites were similar or shorter distances from their associated NOAA tide gauge (5.1 km for BPP, and 6.3 km for KPR compared to 6.4 km for Winant) which gave us confidence to apply this method at those sites.

The same technique was used to estimate the elevation at each well relative to the surface logger associated with a given transect. Water level data for each well was plotted vs. data from the nearest marsh surface logger, using only time points when the tide overtopped the marsh (i.e., surface logger data >0.05 m). The best-fit line through these points gave an intercept that was the negative of the elevation of the well site relative to the surface logger. This technique relies on the assumption, borne out by the data, that the water in the wells and the water above the marsh surface were hydrologically connected and moved in concert quickly on the 6-minute time scale.

Finally, these elevations were converted to the NAVD88 reference frame in order to have the water table, marsh surface, and tidal data on the same datum. For Winant Slough, NAVD88 elevations were 0.225 m less than MLLW values based on the South Beach, OR, Station Datums (available at: https://www.tidesandcurrents.noaa.gov). For the marshes in Tillamook Bay, NAVD88 elevations were 0.124 m above MLLW values. This conversion between NAVD88 and MLLW at Garibaldi was taken from Brown et al. (2016), who measured the elevations of tidal datums near Garibaldi tide gauge with high precision RTK-GPS because NOAA does not provide this conversion for Garibaldi.

2.4. Precipitation measurements

Precipitation was measured in Winant slough from October 2010 until April 2015 using a Texas Electronics model TR-525i tipping bucket rain gauge which tips once per 0.01 inches of rain. Data were recorded using an Onset Computer Corp. “Pendant” event logger every 15 minutes and processed by aggregating the data into either hourly or daily totals. For model runs in Tillamook Bay, precipitation data were downloaded from the Tillamook Airport weather station (TMKO3), located less than 15 km from both sites, through wunderground.com.

3. Field sampling results

Analyzing the water level data gathered from Winant Slough revealed several types of hydrologic phenomena that informed model development. When comparing water level changes during and after overtopping high tides, a recurring ‘drainage curve’ was observed (Figure 2A). First, water levels across the marsh were very similar and matched the bay tidal patterns when tides were above the surface of the marsh. Once the tide receded below the marsh surface, wells in close proximity to the tidal creek started draining quickly while water levels in wells further inland remained near the surface for some time. Next, the drainage of the near-creek wells began to slow, and the more inland wells started to drain. Eventually the drainage of the more inland wells also began to slow, and the water levels across the marsh steadily declined until the next precipitation or tidal event. This recurring drainage pattern results in the soil water nearer the creek having a substantially higher turnover rate than soil water further inland that is less connected to the tidal hydrology.

Figure 2:

Sample water level data for five wells in Transect 1 located in Winant Slough. Tidal creek water levels approximately follow the water levels of Yaquina Bay. The dashed horizontal line shows the mean surface elevation across well locations. Specific well location elevations (NAVD88) are: 2.36 m (2 m), 2.40 (5 m), 2.41 m (8 m), 2.42 m (13 m), 2.43 m (21 m). Plot A demonstrates overtopping and non-overtopping tide effects, while plot B shows water levels during neap-tide periods and effects of precipitation.

High tides that did not overtop the marsh surface sometimes influenced water levels in the wells closer to the tidal creek, depending on their height and the height of the well’s water level at the time (Figure 2A). Precipitation events increased the well water levels to a similar degree across the marsh as a function of rainfall intensity, or the amount of rainfall per unit of time (Figure 2B). Precipitation did not noticeably affect well water levels if they were already above the marsh surface, a phenomenon observed in previous studies (Carr and Blackley, 1986; Montalto et al., 2006). In other words, if the marsh is flooded, precipitation has little effect on the hydrodynamics as the majority of it simply flows off the surface back into the creek with the rest of the floodwaters.

Water levels in the validation sites of KPR and BPP followed similar patterns to those in Winant Slough, but with markedly different drainage rates (Figure 3). The 2-m well at KPR drained much faster than the other three wells, and all wells drained faster than their counterparts in Winant Slough (Figure 3A). At BPP, surface elevations were lower than other sites, causing most high tides to overtop the marsh surface. Wells at BPP drained faster than comparable wells at other sites, with wells closer to the marsh edge (2-m, 5-m, and 13-m) even tracking bay water levels for a short period of time after they dropped below the surface (Figure 3B). Additionally, both KPR and BPP sites did not demonstrate the delay in drainage in more inland wells that was observed in Winant Slough after an overtopping tide receded.

Figure 3:

Sample water level data for the same time period in validation wells located in Kilchis Point Reserve (Plot A) and Bayocean Peninsula Park (Plot B). The dashed horizontal line shows the mean surface elevation across well locations for KPR (omitted from BPP due to significant elevation range). Specific well location elevations (NAVD88) for KPR are: 2.47 m (2 m), 2.43 m (5 m), 2.44 m (8 m), 2.42 m (13 m). Specific well location elevations for BPP are: 1.58 m (2 m), 1.75 (5 m), 2.13 (13 m), 2.10 (34 m). Note the different vertical scales between plots.

A summary of soil analyses results for the top 30 cm of the soil column reveals several points of distinction between each field site (Table 1). Winant Slough had a relatively low average bulk density (0.28 g cm⁻³) and high porosity (0.84), attributable to the high amount of organic matter (32.1% mass lost on ignition) found there. The KPR site had similar bulk density (0.33 g cm⁻³) and porosity values (0.83) to Winant Slough, but had relatively lower % mass lost on ignition (21.7), lower % clay (5.8 compared to 20.4), and an associated higher % silt (81.9 compared to 67.7). The BPP soil characteristics varied greatly from the other two sites in almost every regard: bulk density was much higher (1.28), porosity lower (0.49), % mass lost on ignition was much lower (3.1), and % sand was much higher (80.5) with an associated drop in % clay (2.2) and % silt (17.4).

Table 1:

Measured soil parameters (Average ± Standard Deviation of all sections above 30 cm) from the three marshes in this study. Winant Slough (WS) averages include bulk density, porosity, and % loss on ignition values from Transect 1 and % clay/silt/sand from Transect 2, as well as data from four other cores taken in the high marsh.

Marsh Site	Bulk Density (g cm −3)	Porosity	% Loss on Ignition	% Clay	% Silt	% Sand
WS	0.28 ± 0.09	0.84 ± 0.04	32.1 ± 11.9	20.4 ± 2.3	67.7 ± 3.8	11.8 ± 5.0
KPR	0.33 ± 0.04	0.83 ± 0.02	21.7 ± 1.5	5.8 ± 0.5	81.9 ± 2.9	12.4 ± 3.4
BPP	1.28 ± 0.17	0.49 ± 0.05	3.1 ± 2.3	2.2 ± 1.1	17.4 ± 8.1	80.5 ± 9.1

4. Model description

The model was built in the visual dynamic modeling program, Simile, that runs models constructed within it as compiled C++ programs (Muetzelfeldt and Massheder, 2003). The model is structured as a dynamic combination of several empirical sub-models that are best expressed as different ‘states’ of the water level dynamics. Empirical dynamic models are beneficial for explaining non-linear relationships in time-series data, particularly when the relationships change depending on the state of the system (Chang et al., 2017). The model switches between these different states when specific conditions involving model outputs or inputs are met. The four modeled states are described in detail in the following four sections. To capture spatial heterogeneity in the marsh water level dynamics, the model can be applied separately to different subsections of the marsh. The structure of this spatial component and the influences between each subsection is further described in Section 4.6. Measured or predicted values for marsh surface elevations, bay tide levels, and precipitation rates are needed to drive the model. Along with these driver inputs, a total of eight parameters need to be calibrated for each simulated subsection of the marsh.

4.1. Overtop State

The Overtop State is based on the observation that during periods when the bay tide level is above the marsh surface, water levels across the marsh are all approximately equal to the bay tide level (Figure 2A). The condition required for the model to be in this state is simply the tide level being greater than the surface elevation (H_T > H_S), and when true, supersedes all other states. With tide level being a required data input and driver for the model, there is no need to create a tidal sub-model, so the water level output for this state is made equal to the tide level input data (H_W = H_T).

4.2. Surface State

Once the tide level recedes below the surface of the marsh, the model transitions to the Surface State. For the model to enter this state, the tide level of the previous time-step must be above the surface elevation and the tide level of the current time-step below the surface elevation. (H_{T, t-1} > H_S and H_T,t < H_S). This state is characterized by the marsh water level maintaining an elevation approximately equal to the surface until sections nearer the tidal channel drain enough to allow for lateral drainage of the more distant sections. This dynamic is simulated as a threshold elevation (surface drainage elevation, H_D) to which the water in adjacent marsh sections nearer the creek must fall before lateral drainage can occur in the more inland section (H_W,nearer < H_D, where H_W,nearer is the water level in the adjacent section closer to the tidal creek). In sections adjacent to the creek and at sites with generally quick drainage, this state may not be observed on the time scale of the model time step and can be easily disabled. In this case the model will proceed from the Overtop State to the Lateral Drainage State.

4.3. Lateral Drainage State

In this state, water levels drop in a manner resembling exponential decay, likely due to lateral drainage driven by substantial differences in head between the tide channel and the inner-marsh water table. The equation to simulate water level in this state is as follows:

$$H_W=\left(H_S-H_L\right)e^{-K_E{t}_E}+H_L$$ (2)

where H_W (m) is the water level elevation, H_S (m) is the surface elevation and H_L (m) is the linear drainage elevation (explained below), K_E (h⁻¹) is the exponential rate of water level decline, and t_E (h) is time elapsed since entering the Lateral Drainage State. This equation is similar to what would be expected under Darcian Flow dynamics: flowrate decreases with the decreasing difference in pressure head between two locations. The result is an exponential decay in the water level between the surface elevation, and the elevation (H_L) at which water level transitions to a more linear function. Due to the nature of the exponential decay equation, the simulated water level will never actually reach H_L. To remedy this and initiate transition to the next drainage state, the water level must instead reach a predetermined height (state switch height, S) above H_L (H_W < H_{L +} S). During model development we found that a value of 0.01 m works adequately for this ‘state switch height’ in all situations to which the model was applied.

4.4. Vertical Drainage State

This state of linear water level decrease occurs once lateral drainage rates have been substantially reduced in magnitude due to decreasing differences in head between the marsh water table and the tidal creek. As a result, the relatively slower ‘flows’ of evapotranspiration and vertical drainage begin to dominate the local groundwater hydrodynamics. The water level in this state is simulated by the following equation:

$$H_W=H_L-K_L{t}_L$$ (3)

where H_W (m) is the water level elevation, H_L (m) is the linear drainage elevation, K_L (m h⁻¹) is the linear rate of water level decline, and t_L (h) is the time elapsed since entering the linear drainage state. This state can persist for long periods of time, but is transitioned out of when either tides or precipitation increase the water level to an elevation above the surface (Overtop or Surface States) or to an elevation where large differences in head cause lateral drainage to again dominate the hydrodynamics (Lateral Drainage State).

4.5. Precipitation and non-overtopping high tides

The effect of precipitation events on the water level of the marsh was modeled with a linear response based on the rainfall intensity (m hr⁻¹) of each hourly time-step. Following what was observed in the well data, precipitation only has a noticeable effect on water levels when the water table is below the surface. The equation for subsurface water level change as a result of precipitation is as follows:

$$\text{Δ}{H}_{W,P}=K_{P}P$$ (4)

where ΔH_W,P (m) is the change in water level elevation due to precipitation, K_P (unitless) the coefficient of the precipitation effect, and P is the total precipitation (m) that occurred during the current time-step. While this equation is a simplification of the physical process, it works adequately while requiring only one calibrated parameter (K_P) per marsh subsection.

Tides that rise above the surface of the marsh ‘reset’ the water table across the marsh to a similar state; however, those that do not rise above the surface were observed to affect the water table differently in two ways. First, the water table nearer the tidal creek is more influenced by these tides than the water table further inland. Second, the water table is raised to a certain elevation as a function of how high the tide was relative to the current water level. Accordingly, to raise the marsh water level in the model, the tide level must be higher than the current water level and also higher than a calibrated-for minimum elevation parameter (H_N). The non-overtopping high tide effect on water level is thus simulated with the following equation:

$$\text{if }{H}_S>H_T>H_N\text{ and }{H}_T>H_W\text{ then Δ}{H}_{W,T}=K_T\left(H_T-H_W\right)$$ (5)

where ΔH_W,T (m) is the change in water level elevation due to a non-overtopping tide, K_T (unitless) is the non-overtopping tide coefficient, and H_T is the elevation of the non-overtopping high tide (m). If precipitation and a non-overtopping tide occur simultaneously, the model sums the two effects to determine the cumulative effect on the water level.

4.6. Spatial component

It is clear from the measured hydrology data that the water table behaves differently in different parts of the marsh. These variations largely appear due to distance from the tidal creek, with closer areas draining faster between high tides than areas further from the creek. Because of this, one set of parameters is not sufficient for an entire marsh, so a spatial component was implemented in our model to capture the heterogeneity of the marsh water table dynamics. The model divides the marsh into a number of subsections (the number of needed subsections will vary by marsh and can be altered in the model set up), each identical in model structure, but with different hydrologic parameters. The subsections largely run independently of each other with one exception: the duration each section stays in the Surface State is dependent on the water level of the next-nearest subsection to the tidal creek as described in Section 4.2.

For Winant Slough, the marsh was divided into five subsections (2-m, 5-m, 8-m, 13-m, and 21-m) based on breakpoints in differences in observed well data. The boundaries of these subsections bisect the distance in between specific wells such that the wells are located in the ‘center’ of these subsections with regards to distance from the creek. The areas of these subsections were determined using marsh and creek delineations in ArcMap, allowing for the conversion of our water level data into volumetric values. The two validation sites in Tillamook Bay were both divided into four subsections in a similar way, based on well locations.

4.7. Calibration process

Water level data measured from August to November of 2015 in Transect 1 wells in Winant Slough that corresponded to each marsh subsection were used in the development and initial calibration of the model (Figure 1). Model performance in the calibration and validation stages was assessed with multiple measures of accuracy. First, the coefficient of determination (R²) was calculated for the linear regression created from observed data being the independent variable and model output being the dependent variable. Second, the standard error (SE) was also calculated using the following formula:

$$SE=\sqrt{\frac{\sum {\left(H_{o,t}-H_{m,t}\right)}^2}{n-2}}$$ (6)

Where H_o,t is the observed water level at time, t; H_m,t is the modeled water level at time, t; $\overline{{\text{H}}_0}$ is the average of all observed water levels, and n is the number of observations (Montalto et al., 2007). Observed and modeled data from times when the tide level was above the surface of the marsh (Overtop State) were not included in the calculations of these values; we felt they resulted in an overestimation of model performance since the output water levels were set equal to input tide levels and were very similar to measured well data during overtop.

Calibration of the model was conducted for each subsection of Winant Slough using a combination of the automated calibration program, PEST, and manual parameter adjustments. PEST uses incremental parameter adjustments and iterative model runs to calibrate parameter sets (Doherty and Hunt, 2010). This tool was particularly effective due to the short runtime of our model. The resulting parameter sets from PEST calibration were not always ideal, but usually gave good approximations that could be further refined manually. The direct and easily understandable effects of parameters on water level dynamics aided manual calibration efforts. If manual calibration was needed, the parameters for the section closest to the creek were adjusted first, then increasingly distant sections were subsequently adjusted, following the chain of influence built in to the spatial model structure.

4.8. Validation process

Two types of validation were performed with this model; one used data from a different time interval and location within Winant Slough that involved no parameter adjustment and one was from different times and in different marshes that involved some parameter adjustments.

The validation within Winant Slough used the same calibrated parameters from Transect 1 and applied them to Transect 2. The number of subsections was changed from five to two as there were fewer needed for the shorter transect. Parameters used for the subsection 2 m from the creek in Transect 1 were used for a comparable subsection 3 m from the creek in Transect 2, and parameters from the subsection 8 m from the creek in Transect 1 were used for a subsection that was 8.5 m from the creek in Transect 2. For validation, the outputs from the 8.5 m subsection in Transect 2 were compared to the well water levels measured at that location from November 2015 to March 2016.

The validation outside of Winant Slough was performed at two different marshes bordering Tillamook Bay. The marsh located at KPR was similar in structure to Winant Slough but had different soil characteristics (Table 1). Data gathered from June to August of 2016 at KPR was compared to model outputs for validation calculations. The other marsh located at BPP, a sandy spit between the bay and ocean with no tidal creek, was markedly different from Winant Slough in marsh structure and soil composition. Data gathered from June to July of 2016 at BPP was compared to model outputs for validation calculations. These sites were chosen to validate the performance of the model in different substrates and marsh types with similar tide ranges and precipitation patterns.

4.9. Hydrology metric calculations

There are several important hydrologic metrics that can be derived from the model’s water level outputs with the application of additional data and equations. One that is important to ecosystem services is how much soil pore space is available within the marsh to process incoming tidal bay water. The following equation was used to determine available marsh pore space for each marsh subsection:

$$V_P=A_X\Phi \left(H_S-H_{W,0}\right)$$ (7)

Where V_P (m³) is the potential pore space available before tidal inundation, A_X (m²) is the subsection area, H_S (m) is the surface elevation, H_W,0 is the marsh water level just before it is increased by tidal inflows, and Φ (unitless) is the average soil porosity calculated for the top 30 cm of soil (Eq. 1). The result was calculated for each simulated subsection and summed to find the value for the entire marsh.

These values can also be converted to a percentage of the total tidal prism entering the marsh using the total marsh area, and estimates of the full tidal creek volume using the following equations:

$$V_T=V_P+A_C\left(H_T-H_C\right)+\sum A_X\left(H_T-H_{S,X}\right)$$ (8)

$$PercentageofTidalPrismEnteringSoil=\frac{V_P}{V_T}\ast 100$$ (9)

where V_T (m³) is the total tidal prism flowing into a marsh on a given high tide of elevation (H_T), A_C (m²) is the area of the tidal channel, H_C (m) is the average elevation of the bottom of the tidal channel, A_X (m²) is the area of a subsection of marsh, and H_S,X is the surface elevation of that subsection of marsh. Because the result can vary depending on the tide height, two different tide heights were selected to capture a range of possible results: a tide that just floods the surface of the marsh, and a typical spring high tide. This calculation could be further refined if higher resolution elevation maps are available, but these can be difficult to create for densely-vegetated marshes, and the current formulation provides an adequate estimate.

The hydroperiod of Winant Slough and its Soil Saturation Index (SSI) as defined by Xin et al. (2010) across a spring-neap tide cycle of 14.8 days were also calculated and compared using measured and modeled data. The equation used is as follows:

$$SS{I}_{(x)}=\frac{{\displaystyle {\sum }_{i=1}^m{S}_{xi}\text{Δ}t}}{P_T}$$ (10)

where SSI_(x) is the Soil Saturation Index at distance x (m) from the tidal creek, m is the number of model timesteps that occur over the tidal period (P_T), defined here as 14.8 days, Δt is the model timestep (1 h), and S_xi is equal to 1 when the water level is above a specified soil depth and 0 when the water level is below that depth. A depth of 10 cm below the marsh surface was used for our calculation of SSI and the calculation of hydroperiod is simply this equation with the specified depth equal to zero.

4.10. Scenario implementation

The model was used to simulate a range of sea level rise scenarios in Winant Slough to demonstrate its utility in providing hydrology predictions and to analyze how sea level rise may influence important marsh hydrology parameters. Scenarios were implemented by adding 15, 30, 45, 60, and 75 cm to input tide levels used for the calibration period. These increases are based on estimates of relative sea level rise for the nearby coastal city of Newport, Oregon for the years 2050 and 2100 (Dalton et al., 2013). The estimates by Dalton et al. (2013) account for the vertical uplift of land associated with the Northwest’s active subduction zone but do not take into consideration the potential for marshes to mitigate sea level rise effects through accretion (Morris et al., 2002). Model outputs were used to calculate hydrology parameters which were compared between scenarios and to baseline conditions.

5. Model results

5.1. Calibration and validation results

The model calibration in Winant Slough achieved a satisfactory level of accuracy, with R² values above 0.8 and SE values of 3.0 cm or less for all marsh subsections when compared to corresponding observed well data (Figures 4 and 5). The R² was lowest (0.82) and SE highest (3.0 cm) in the subsection nearest the creek (2-m). The R² steadily increased and the SE decreased (indicating improved model performance) with increasing distance from the channel until leveling off with R² values of approximately 0.95, and SEs of approximately 2.1 cm in the 8-m, 13-m, and 21-m subsections. In general, data for lower water elevations fit the 1:1 line better indicating that model accuracy improved lower in the soil column. The horizontal arrangement of data in the upper portion of all the graphs is because the Surface State sub-model holds the water at the surface for either too long or too short of a time period.

Figure 4:

Calibrated model outputs and measured water levels for wells 2 m (Plot A), 8 m (Plot B), and 21 m (Plot C) from the tidal creek in Winant Slough. Dashed horizontal lines show surface elevations at each well location.

Figure 5:

Modeled versus measured water levels at the 5 well sites at Winant Slough along Transect 1 used for calibration, and the well site along Transect 2 used for validation. Dashed lines represent the theoretical 1:1 line of modeled data matching observed data exactly. The Coefficient of Determination (R²) and Standard Error (SE) are displayed for each well.

The validation of the model using data gathered at a different time and at a different well transect than used for the calibration demonstrated its ability to transfer calibrated parameters to a similar setting (Figure 5 and 6). Parameters from the subsection 8 m from the creek in Transect 1 were applied to a subsection 8.5 m from the creek in Transect 2, with only the surface elevation being adjusted. The performance of the model for this within-site validation was comparable to that in the calibration transect, with an R² of 0.88 and SE of 2.5 cm (Figure 5).

Figure 6:

Calibrated model outputs and measured water levels for validation wells 8.5 m from the tidal creek in Winant Slough (Plot A), 8 m from the tidal creek in Kilchis Point Reserve (Plot B), and 13 m from the marsh edge in Bayocean Peninsula Park (Plot C). Dashed horizontal lines show surface elevations at each well location.

The validation at the Kilchis Point Reserve (KPR) site that was similar to Winant Slough in structure demonstrated the model’s ability to be transferred to other marshes (Figures 6 and 7). The parameters of the model were first manually adjusted to account for the different elevations and soil characteristics of KPR, and then PEST was used to further improve the calibration. Key parameter adjustments include a higher non-overtopping tide effect coefficient (K_T) in all marsh sections, indicating an increased connectivity of the marsh soil water levels to those in the tidal creek (Table 2). Additionally, the Surface State sub-model was disabled since there were no observations of water being held at the surface for extended periods of time after the tide had receded, as had been observed at Winant Slough. The average exponential soil drainage rates (0.16 h⁻¹) and linear soil drainage rates (1.53 × 10⁻³ h⁻¹) of KPR subsections were both greater than the average values used in Winant Slough (0.12 h⁻¹ and 8.30 × 10⁻⁴ h⁻¹, respectively). Similar to Winant Slough, the accuracy of the KPR simulations varied by marsh subsection (Figure 7). The model performed well overall, with the lowest accuracy being in the section nearest the creek with an R² of 0.83 and SE of 4.5 cm, and higher accuracy in the three more inland subsections, with R² values ranging from 0.91 to 0.94 and SEs ranging from 2.3 cm to 3.4 cm.

Figure 7:

Modeled versus measured water levels at the 4 well sites at the Kilchis Point Reserve (KPR) validation site. Dashed lines represent the theoretical 1:1 line of modeled data matching observed data exactly. The Coefficient of Determination (R²) and Standard Error (SE) are displayed for each well.

Table 2:

Calibrated parameters for each subsection of each site. No H_D values exist for KPR and BPP as this part of the model was disabled for these sites. Likewise, the 2 m section in WS does not need an H_D value as it is adjacent to the creek and drains first.

Distance from Creek/Edge	HS (m)	HD (m)	HL (m)	HN (m)	KE (hr−1)	KL (m hr−1)	KP (−)	KT (−)
WS Avg.	2.40	1.90	2.25	2.23	0.125	8.14E-04	0.20	0.22
2 m	2.36	n/a	2.20	2.00	0.270	1.18E-03	0.20	0.40
5 m	2.40	2.32	2.25	2.19	0.164	8.81E-04	0.20	0.22
8 m	2.41	2.36	2.27	2.23	0.098	8.06E-04	0.24	0.10
13 m	2.42	2.41	2.26	2.35	0.060	6.55E-04	0.15	0.24
21 m	2.43	2.40	2.27	2.40	0.035	5.51E-04	0.20	0.16
KPR Avg.	2.44	n/a	2.25	2.26	0.161	1.53E-03	0.21	0.61
2 m	2.47	n/a	2.22	2.17	0.406	2.26E-03	0.20	0.32
5 m	2.43	n/a	2.25	2.28	0.081	1.62E-03	0.21	0.46
8 m	2.44	n/a	2.28	2.28	0.108	1.37E-03	0.24	0.72
21 m	2.42	n/a	2.24	2.32	0.048	8.87E-04	0.18	0.96
BPP Avg.	1.88	n/a	1.65	1.50	0.647	8.31E-03	0.28	3.19
2 m	1.58	n/a	1.53	1.50	0.519	3.36E-03	0.15	4.00
5 m	1.75	n/a	1.57	1.50	0.933	4.90E-03	0.36	4.00
13 m	2.13	n/a	1.66	1.50	0.658	8.32E-03	0.26	3.00
34 m	2.06	n/a	1.83	1.50	0.477	1.67E-02	0.33	1.75

The validation at the BPP site was a test of the model’s ability to perform in a site with different structure (no significant tidal creeks) and soil characteristics (sandy as opposed to silty). As with the KPR site, parameters were adjusted to account for the site’s different elevations and soil characteristics. Notable parameter adjustments included a substantial lowering of the non-overtopping tide effect elevation (H_N), indicating that almost all high tides noticeably influenced the marsh water level, regardless of height. Additional adjustments included increasing the non-overtopping tide effect coefficient (K_T), exponential drainage rate, and linear drainage rate (Table 2). Also, as with the KPR validation, disabling the Surface State sub-model was necessary as water was not observed to be held at the surface for extended periods of time after the tide receded.

The initial validation run at BPP did not perform as well as others, presumably because the model did not capture the rapid dynamics of the sandy system. Specifically, the water level transitioned between states faster than the 1-hour time-step of model could simulate. This provided an opportunity to assess the flexibility and transferability of the model; in attempt to capture these faster transitions, the model time-step was simply reduced from 60 minutes to 30 minutes. Two relatively easy adjustments had to be made to achieve this: the model drivers of tide level and rainfall data had to be changed in frequency from every 60 minutes to every 30 minutes, and the values of the two calibrated drainage rate parameters (exponential and linear) were halved to account for the halving of the time-step length. This time-step adjustment substantially improved the model’s performance, increasing the R² values and reducing the SE in each section of BPP (Figures 6 and 8). With the 30-minute time-step, the subsection 2 m from the marsh edge had a moderate R² of 0.62 (0.57 before time-step change), but also had a low SE of 1.4 cm (1.8 cm before time-step change) indicating low variation in measured data. The subsection 5 m from the marsh edge was the least accurate overall with an R² of 0.63 (0.47 before time-step change) and a moderate SE of 3.3 cm (4.4 cm before time-step change). Moving inland, the R² values improved with 0.86 (0.62 before time-step change) and 0.79 (0.68 before time-step change) for the 13-m and 34-m subsections. These sections also had moderate SEs of 4.9 cm (8.5 cm before time-step change) and 4.8 cm (5.9 cm before time-step change), respectively (Figure 8).

Figure 8:

Modeled versus measured water levels at the 4 well sites at the Bayocean Peninsula Park (BPP) validation site. Note that axes scales are not the same for each site due to differing data ranges. Dashed lines represent the theoretical 1:1 line of modeled data matching observed data exactly. The Coefficient of Determination (R²) and Standard Error (SE) are displayed for each well.

5.2. Hydrology metrics and sea level rise simulations

Model outputs from Winant Slough simulations were used to calculate informative hydrology metrics, then sea level rise simulations were run to evaluate potential changes to these metrics. The soil pore space available to process the tidal water entering the marsh was calculated (Eqs. 7, 8, 9) for two different high tide heights and is presented as a percent of the tidal prism volume (Figure 9, Plot A). In the baseline model, these values ranged from 12.5% for a typical spring high tide (2.58 m) to 24.7% for a high tide that just overtops the marsh (2.46 m). As sea levels rose in simulated scenarios, these values decreased exponentially due to the combined increase in tidal prism volume and elevated soil water levels before tidal inundation causing a smaller percentage of the tidal prism able to be processed through the marsh soil.

Figure 9:

Calculated effects of 15, 30, 45, 60, and 75 cm sea level scenarios on the incoming tidal prism able to be processed through soil pore space (Plot A), and inundation frequencies (over a 14.8-day tidal period) of the marsh surface (Plot B) and top 10 cm (Plot C). Zero on the x-axis of all plots refers to the baseline model results with no sea level rise considered.

The hydroperiod (presented as a percentage of a 14.8-day tidal period that the marsh surface was inundated) and SSI (for a depth of 10 cm) were also calculated (Figure 9, Plots B & C). In the baseline model, the hydroperiod increased from the subsection nearest the creek (10.7%) to the subsection furthest from the creek (28.1%). The SSI similarly increased in the baseline model as distance from the creek increased, ranging from 18.3% to 59.3%. This trend is due to the water table being held at the surface longer, and draining slower after a tide recedes, in areas further from the creek (Figure 2). In simulated scenarios of increasing sea levels, the hydroperiod increased approximately linearly across all sections, with the surface of the marsh 21 m inland from the creek being inundated 93.5% of the time in the 75 cm scenario. Additionally, sections further from the creek saw a more dramatic increase in inundation time per sea level rise increment. For example, the hydroperiod 2 m from the creek saw an increase of 11.0% from the baseline to the 30 cm sea level rise scenario, while the section 13 m from the creek saw an increase of 20.8%. The SSI calculations had similar trends to those for surface inundation but with more pronounced effects per sea level rise increment: at the 45 cm sea level rise scenario, the water table 21 m from the creek was already above 10 cm deep in the soil 100% of the time (Figure 9, Plot C).

6. Discussion

6.1. Model performance

Using a combination of the automated calibration program, PEST, and manual parameter adjustments, an adequate calibration of the model was achieved for water levels in each subsection of Winant Slough. The standard errors of the model at the calibration site ranged from 1.9 to 3.0 cm, a similar result to a comparable marsh water table model developed by Montalto et al. (2007), which achieved standard errors of 3 cm. The difference in the model’s performance between subsections within the same site during calibration is likely due to the sections nearer the creek being more dynamic and more impacted by non-overtopping tides than sections further inland (Figures 2 through 8). A similar trend is seen with changes in water level: the model is more accurate at lower water elevations than higher elevations, likely due to the relatively less dynamic nature of the water level during periods of neap tides and minimal precipitation (Figures 5, 7, and 8). The model showed an impressive ability to maintain reasonable accuracy through the wet season when tidal and precipitation effects were co-occurring (Figure 4, 11/7–11/16). The consistent effects of precipitation on water level as a function of rainfall intensity enabled a relatively simple equation (Eq. 4) to be sufficiently accurate.

There were certain periods when model accuracy was relatively lower than others, such as during non-overtopping high tides. The increases in water level and subsequent drainage rates due to non-overtopping high tides were less consistent than those caused by overtopping tides (Figures 4 and 6). The single parameter (K_T) in Equation 5 was not always able to accurately predict how high a non-overtopping tide would raise the water level, indicating a non-linearity in this effect not fully captured in the model. Underpredicting or overpredicting this water level increase can then cause the model to calculate inaccurate drainage rates for subsequent timesteps since they are essentially functions of the predicted water level at the current timestep (Eq. 2 and 3). This feedback effect can cause model error to propagate over time, however, the occurrence of an overtopping tide will effectively ‘reset’ the state of the model and end this feedback loop. This feedback effect can also impact the initial water level predictions at the start of a model run before an overtopping tide occurs, making the period right before a flooding tide the best time to start a model run.

The model also does not capture the small height that the water level stayed above the marsh surface after an overtopping tide recedes, a phenomenon only observed at Winant Slough (Figures 2 and 4). This phenomenon is likely due to the tortuous drainage path created by vegetation, microtopography, and surface roughness that water needs to follow to flow off the marsh surface. We considered adding another parameter to account for this but did not feel it was worth increasing the parameter space. Further issues with accuracy may be attributable to variations in conditions that were not explicitly simulated in the model such as regional water table levels, and vegetative or meteorological influences on evapotranspiration. Future model development will likely focus on refining or expanding the model’s function in regard to these issues.

6.2. Viability of empirical dynamic modeling for marsh hydrology

Empirical dynamic models like the one presented here can be considered part of a ‘top-down’ approach to simulating marsh hydrology (Hrachowitz and Clark, 2017). This type of approach relies on robust datasets to iteratively test different models of system function. It is in contrast to the ‘bottom-up’ approach which estimates large-scale processes by aggregating small-scale observations (Hrachowitz and Clark, 2017). While our integration of many hydrologic characteristics into a limited number of parameters may oversimplify the physical mechanisms at work, if model performance remains satisfactory, the reduction in parameter space can prove beneficial. Additionally, salt marsh systems are so spatially heterogeneous in their soil characteristics and temporally heterogeneous in their water characteristics, even the most comprehensive models must make many simplifying assumptions (Wilson and Morris, 2012; Xiao et al., 2017). A smaller parameter space reduces data and computational needs, increases transferability, and decreases risk of equifinality (multiple parameter sets that achieve similar results) (Hrachowitz and Clark, 2017). The result is a tool that is more readily applied by land managers and scientists to obtain the hydrologic predictions they need.

The model’s performance at the validation sites demonstrated its ability to be transferred to new locations (Figures 5, 7, and 8). Differences in drainage parameters between calibration and validation sites were likely due to varying soil characteristics (Tables 1 and 2). While drainage rates K_L and K_E are calibrated parameters, as this model is applied in more locations and soil types, better pre-calibration predictions of their value may be possible using known soil characteristics. The relative simplicity and flexibility provided by the empirical dynamic structure of the model greatly aided the processes of model transfer and calibration (Chang et al., 2017). The small number of parameters enabled PEST to be an effective calibration tool for applying the model to new marsh sites.

Additionally, any modifications to the model structure that were needed to transfer it to new sites were relatively easy to make. The state-based structure of the model allowed for the modification or removal of a state if it was not observed at a site (as was done with the Surface State at the KPR and BPP sites), without impacting the rest of the model’s functions. Changing the time step to 30 minutes was another modification shown to be effective when applying the model to sites with sandy soils, assuming the higher temporal resolution of input data is available (Figures 6 and 8). We tried adjusting the time-step to 30 minutes at other sites to test for similar improved accuracy like that seen at BPP, but there was not a substantial improvement: for the 5-m section in Winant Slough, R² was only improved from 0.87 to 0.89. At any site, if maximum accuracy is desired, reducing the time step may be an option, but minimal improvements in accuracy may not always be worth the associated increase in data needs and simulation time.

6.3. Hydrology metrics and sea level rise scenario

The ability for a salt marsh to deliver the ecosystem services of water purification and flood mitigation relies on the marsh soil capacity to receive and chemically process incoming water. While previous studies have attempted to quantify the purification service by measuring nutrient concentrations on the inflowing and outflowing tides (Drake et al., 2009), our calculation of available pore space demonstrates an alternative method to predict a marsh’s relative potential to deliver this service. The model’s predicted range of 12.5 – 24.7% of an incoming tidal prism volume that is able to be processed through the pore space provides an upper bound on the purification service. There is a caveat in this calculation in that it does not consider the degree of soil saturation above the water table. From field measurements made during low tide and from modeled literature values we can estimate this soil saturation before tidal flooding to range from approximately 50% to 85% of soil pore volume depending on the location in the marsh and the time since the last flooding tide (Wilson and Gardner, 2006; Xin et al, 2017). However, much of the water associated with soil particles in the unsaturated zone (and likely some of the pore water at the top of the saturated zone) could be replaced with the water entering on an overtopping tide and thus can be considered as part of the water volume that is processed in the marsh soil. Tidewater brings with it dissolved oxygen, salinity, nutrients, and other cations that diffuse through the soil pore spaces, shifting the pore water chemistry and altering microbial biogeochemical pathways (Eriksson et al., 2003; Silvestri et al., 2005; Herbert et al., 2018). It is the subsequent and continuous changes in these pore water constituents that controls a salt marsh’s ecology and its associated nutrient cycling capabilities. Other hydrologic characteristics that influence water purification and flood mitigations services include the velocity and residence time of water in the marsh soil. While accurately estimating these parameters has proven difficult in salt marshes, researchers have made progress in this area by applying more complex hydrology models (Wilson and Gardner, 2006; Xin et al., 2017).

The multiple scenarios of increasing sea level rise show possible impacts to marsh hydrology not captured by surface inundation calculations alone. Some existing models have simulated the effects of sea level rise on marsh surface inundation (Craft et al., 2009; Wu et al., 2017), but subsurface water table dynamics are also ecologically important, and only provided by a model that can simulate drainage (Eriksson et al., 2003; Xin et al., 2010). Sea level rise can also have differing effects on subsurface inundation frequencies: our simulated results show that while the surface inundation frequency of the marsh section nearest the tidal creek had an absolute increase of 11.0 % for the 30 cm sea level rise scenario, the same value for the top 10 cm of soil had a greater absolute increase of 16.9 % (Figure 9). The sections further from the creek saw even greater increases in inundation frequency with each incremental increase in sea level (Figure 9). As increased inundation eventually causes parts of the marsh to become permanently submerged, the result would be the development of pools of water in marsh areas further from the creek; a phenomenon observed in submerging marshes like those along Blackwater River in Maryland (Schepers et al., 2017) As a marsh becomes inundated more frequently with increasing sea level rise, our simulations also predict that the available soil pore space to receive incoming water will decline, limiting the marsh’s ability to deliver water purification and flood mitigation services. While salt marshes can potentially accrete soil to reduce impacts of sea level rise (Morris et al., 2002), we did not attempt to incorporate this effect into these simulations and instead presented a range of potential sea level rise scenarios.

6.4. Potential model applications

We see a variety of uses for its outputs and the hydrology values that can be calculated from them. The primary benefit the model provides is the substantial reduction in resources, time, and effort required to gain spatially explicit marsh water level time series. While some field data should be collected for the calibration of the model (ideally during a period with rain and overtopping tides), once the model is sufficiently calibrated, water level predictions can be made for any time period for which the user has measured or predicted tide and precipitation data. The time and resources required to maintain a transect of wells within a marsh for long periods is significant, and our model provides a means to reduce these costs while achieving similar results.

The utility of our model is expanded when water level outputs are linked to biogeochemical models that require them. For instance, some marsh denitrification models need inundation patterns to determine the occurrence of aerobic and anaerobic soil conditions (Ensign et al., 2008; Ensign et al., 2013). In their salt marsh denitrification study, Ensign et al. (2013) were able to develop a three-parameter sigmoid model that relates N₂ efflux to the average daily water level. A study by Grant et al. (2012) describes relationships in wetlands between water table depth and ecosystem productivity, an important ecological function that influences delivery of ecosystem services such as nutrient cycling and carbon sequestration (Bouchard and Lefeuvre, 2000; Kirwan and Mudd, 2012). Further, Pavelka et al. (2016) established a connection in marshes between water level and CO₂ efflux, a value needed to estimate the carbon budget of a marsh. In all of these cases, water level data made available from a model like ours would allow the prediction of these ecosystem functions over longer periods of time and under various future scenarios.

Vegetation zonation is another important characteristic of marshes and has been shown to be largely controlled by hydrology (Silvestri et al., 2005; Wilson et al., 2015). Different vegetation types in marshes influence nutrient cycling, carbon sequestration, and even hydrology (Sousa et al., 2010; Townend et al., 2011). Outputs from our model could be used in zonation studies, providing water level data and the ability to predict how it may change under various scenarios. As previous studies have shown, salt marsh vegetation zonation is a factor of more than just inundation duration (Ursino et al., 2004; Silvestri et al., 2005); subsurface hydrology is also important in zonation as it controls concentrations of oxygen, nutrients, and toxic solutes such as hydrogen sulfide (Silvestri et al., 2005; Taillefert et al., 2007). Two sites could have the same inundation depth and frequency of overtopping tides, but as our model results show, have vastly different soil saturation durations based on their distance from the channel. Moffett et al. (2012) demonstrate this concept by using outputs from a hydrology model to delineate a salt marsh’s “ecohydrological zones”. Being able to predict vegetation zonation with hydrology information elucidates the potential impacts of environmental change on a marsh’s ecology.

The sea level rise simulations only demonstrate one type of scenario that may be run in the model. Similar scenarios that could be run by altering input data include erosion/accretion scenarios that impact the surface elevation, or predicting the impacts of a restoration or development project that alters the tidal patterns or prisms in the marsh. Simulations could also be run for changes in the future timing and amount of precipitation as Mote and Salathe (2010) concluded may occur in the Pacific Northwest. The effect on model parameters due to changes in soil characteristics can be seen between the silty (Winant and KPR) and sandy (BPP) sites (Table 2). Assessing these types of effects in various marsh soil types could enable simulations of altered soil characteristics to be tested such as in a recently restored marsh where organic matter in the top soil layers increases steadily over time (Craft et al., 2002).

7. Conclusions

Salt marsh ecosystems are hydrologically and ecologically complex. The empirical data gathered in this paper provided insight into the hydrology of several mesotidal marshes in the Pacific Northwest and established a base for the development of a dynamic hydrology model. The empirical dynamic modeling approach used here proved relatively easy to calibrate and transfer between marshes. This model can be a useful tool for scientists or land managers needing more hydrologic information than can be gathered from tide data alone, particularly those lacking the time, resources or expertise required to apply a more complex hydrology model. Utilizing the model will also reduce the amount of field work and resources needed to establish long-term water level time series. The potential applications of the model are numerous in the fields of ecology, biogeochemistry, and ecosystem services.

The calculation of the pore space available to process tidal water is likely a necessary component of any estuary-scale mechanistic model of nitrogen dynamics or other estuarine chemical cycling. Expanding this model to the estuary scale should be feasible without a substantial increase in field data requirements. The variability of marsh types within the estuary is unlikely to exceed the range of conditions for which this model was validated. The model has also been validated in marsh areas with multiple flow paths (see 8.5 m Winant well in Figures 5 and 6 which was located equidistant between the main creek channel and a branch of the creek), but a marsh with particularly unusual flow paths may require model adjustments. With accurate maps of marsh areas and tidal creeks, along with knowledge of the types of soils in each marsh, volumetric estimates of tidal processing at the estuary scale should be achievable and is a potential future direction of this research effort.

With further development, the model may be transferred to a more diverse range of salt marsh types (e.g. microtidal, culverted, etc.). The simple, modular structure of the model allows for changes to be made to core model components such as time steps and governing equations with relative ease. The Simile file of the model along with a user guide is provided in the supplemental materials and can be run in the Evaluation Version of Simile that can be downloaded for free from www.simulistics.com. We welcome any party to undertake the calibration and validation of the model at a new study site. Making modifications to the model to better suit a new setting may be necessary and is encouraged.