Across the globe, people have settled and established communities beside estuaries and river deltas that have proven to be ideal habitats for humans, flora, and fauna [1
]. Estuaries are unique habitats in a myriad of ways—they are the location where tidal influence extends into the riverine landscape, where saline seawater and fresh river water mix, and where geomorphic effects from marine processes meet fluvial erosion and deposition. All of these factors produce an ecosystem that is specially adapted to growth and success in this confluence of conditions. Even though estuaries support a large diversity of species, they are threatened habitats [2
]. Numerous anthropogenic effects have impacted the quality of estuarine habitat [4
]. For example, pollutants and anthropogenic inputs in the form of chemicals, human and agricultural wastes, and sediment have been introduced into the watersheds along their reaches [5
]. Projected sea level rise [7
] and massive diversions from natural riverine inputs [8
] have impacted salinity dynamics, affecting ecosystem health [9
]. Entire landscapes have been shifted from land to sea [10
], affecting numerous processes from the headwaters of tributaries down to their deltas, all impacting the health of the estuary.
To combat these problems, humans have sought ways to balance their needs for the natural resources provided by estuaries with the long-term survival and fitness of those habitats. Better practices have been established to control pollution into rivers, estuaries, and marine environments. Furthermore, restoration efforts have been made in order to address the degradation of physical habitat surrounding river deltas and estuaries. Combinations of these efforts have been undertaken in order to produce multi-pronged benefits within these habitats. Often, the goal of restoration and management actions are to allow for the physical and biological processes important in estuaries to resume functioning. For instance, the restoration of off-channel habitat in the tributaries leading into an estuary provides the physical parameters (such as turbidity, dissolved oxygen, temperature, and light availability) to generate primary and secondary producers (phyto- and zoo-plankton) [12
]. With proper connectivity, that productivity can flow into riverine habitat and be transported downstream throughout the estuary. Following the overall impacts of estuarine restoration is complicated, however, because of the complex physical properties of deltas and estuaries, such as reconnecting or braided river networks, tidal pumping effects [13
], and salinity gradients.
Understanding where water flows and where it originates is useful for understanding what impacts a restoration project has as well as what the character of water is coming into a potential restoration site. Identifying source water fraction (SWF) of a river network addresses the spatiotemporal distribution of source waters and allows the investigation of tributary water fate. The properties of tributaries, such as the stable isotope compositions of water, have been used to identify source water distribution, but these studies have typically been applied to lakes or groundwater [14
]. Other studies have used isotope signatures to identify which tributaries have dominant effects on geochemical properties of the mainstem [18
], to investigate snowmelt versus rainfall contribution [19
], and to identify water origin [20
]. Our study aimed to use two methods to find the SWF at each location within the study area over time; one method used is similar to that of Halder et al. [21
] and Marchina et al. [20
], which evaluates stable hydrogen (2
and oxygen (18
isotopes at sample locations and compares those to the tributary source waters of interest.. Another direct application of using physical properties of tributary water to find the distribution of source waters in a river network was presented by Peter et al. [22
] in a physically modeled hypothetical watershed. In the study, high-resolution mass spectrometry of organic contaminants was used to confirm the source hydrology of a hypothetical river system with known flows, and thus known mixtures. This physical model study demonstrated the potential of using physical and chemical signatures in water to identify source water, but was limited to systems with an exact knowledge of tributary discharge and mixing patterns, limiting the study to a discussion of methodology instead of an application of a real-world scenario in a river network. We address this limitation using a separate method to investigate the hydraulics and transport processes of a system in order to provide estimated flows and mixing patterns.
Hydrodynamic models are numerical tools that solve equations of motion in fluid mechanics and are widely used to replicate flood events and complex physical processes in river networks. Sridharan et al. [23
] used a one-dimensional streamline-following junction model to evaluate particle paths through the Sacramento–San Joaquin Delta of California (Delta), giving insight to source-water fate at a large and broad scale. Bai et al. [24
] used a three-dimensional hydrodynamic and water quality model to source-apportion different tributary contributions to nitrogen and phosphorous loads. The source-apportionment indicates the chemical impact of tributaries, but not their relative volume at any particular location. In order to test the validity of a field-based approach to identifying SWF in a river network, we developed a hydrodynamic model coupled with a transport model. This study’s comparison of methods can help address limitations of stable isotope methods of finding the SWF of a particular site, as well as demonstrating a field validation of source water tracking using hydrodynamic models.
This study centered on the McCormack-Williamson Tract (MWT), an island protected by a ring levee in the Delta, and the surrounding area. Slated for restoration, the site lies downstream of several other floodplain restoration sites along the Cosumnes River and Dry Creek, making understanding the distribution of incoming source waters helpful to improve the overall efficacy of the MWT restoration. Specifically, water that has had access to floodplains would likely carry more allochtonous material, providing more carbon and nutrients to kickstart in situ production at the study site. In this paper, we characterize the spatiotemporal distribution of SWF at different sites in and around the island while it was flooded. In the absence of measurements of individual tributary flows into the study area, indirect methods must be applied to estimate source water distribution. Our study aimed to evaluate the utility of the two methods discussed, to compare hydrodynamically derived values to in situ data, and to discuss the implication of these approaches to the Delta, as well as other riverine systems.
4. Discussion and Conclusions
This study compared two techniques from two fields of study in order to arrive at estimates of source water fraction (SWF) within a natural system. The hydrodynamic model provided estimated flows and mixing patterns to complement a field-based isotope approach that would otherwise be unsubstantiated (as opposed to previous field-based studies [21
]). Similarly, the isotope findings act as a field-validation for a numerically-based method of finding SWF in surface-water systems. Both methodologies can be applied to other riverine systems. In order to confidently use the isotope mixing model approach, one would want to ensure that the system is fluvially dominated, that each source tributary has a distinct isotopic signature, and that some stationarity exists in the isotope composition of those source waters [33
]. Both methods provide insight to the larger issue of tracing the composition of water in a system in order to better understand the larger mixing processes and patterns in a complex river network. Inherent in the methods are a few assumptions.
Throughout the course of the 2017 sampling done for this paper, our river system was dominated by fluvial processes, unlike typical conditions in which the study area experiences a tidal signal. To compare to 2017, which was a wet year, we briefly compared the two SWF methods in 2018 and 2019 floods, which were below normal years, and found there was little agreement, likely because of the flows not being strong or persistent enough to maintain a fluvial character to the study site. During the 2017 period of this study, the two methods outlined produced similar results, despite the major assumption in the isotope mixing model () being imprecise due to widespread overland flow and the high “Other” fractions modeled at the sample sites. Presumably, an increased spatial extent for isotopic sampling could partially alleviate this limitation, although when the number of sources exceeds two, solutions to an expanded Equations (1), (8) and (9) become non-unique. There are additional limitations to the methodologies that may affect the validity of results.
The assumption that endpoint (C1 and M1) samples are representative of cross-sectional averaged isotopic composition may also be imprecise. At each of these locations one sample was collected at one location in the cross-section per sampling date. To evaluate the impacts of this limitation in single-sample field locations, we evaluated model output for all cells across the channel for sites M2, M3, and IA2 and found that the Cosumnes and Mokelumne River waters were well-mixed laterally at the time of sampling, indicating that the lack of replicate samples in the lateral did not necessarily present errors when compared to the model results. However, because this study was performed using a depth-averaged model we cannot investigate sensitivity to the water sample being taken near the top of the water column, but we can assume that the vertical mixing past the confluence is thorough [13
]. Although the model accurately predicts cross-sectional flows and stage, the same issue arises as in the study on the model watershed by Peter et al. [22
]: the exact flow and mixing patterns are unknown.
The calibrated hydrodynamic model coupled with a transport model provides more spatiotemporally specific output that has proven to be reliable within the bounds of the field data approach this study used. Additionally, the number of water sources traced is unlimited, unlike the isotope-based approach that is limited to two source tributaries. Another advantage of the hydrodynamic model approach over the isotope mixing model is there is no necessity for the source waters to be isotopically distinct. Lastly, the hydrodynamic model predicts additional variables such as depth and velocity that could provide habitat characteristic values (e.g., Pasternack et al. 2004 [39
], Whipple 2018 [40
]) to be combined with SWF results to further evaluate restoration potential.
Before exploring the significance of applications to other systems, let us explore the significance to the McCormack-Williamson Tract (MWT). There have been a few examples of multiple restoration sites along a river having cumulative benefits as one moves downstream. These have been demonstrated in gravel restoration sites along rivers in the Sacramento–San Joaquin River system [39
], and the multitude of restoration sites across freshwater tributaries of the Chesapeake Bay [43
] where restored sites along a river continuum act as a “string of pearls” of aquatic habitat. Ultimately, as water moves through rehabilitated habitat its ecological value or potential cumulatively improves [44
] It follows that the restoration-laden Cosumnes River carries with it the potential to boost restoration value within the MWT restoration: the last “pearl” in the string. Understanding the spatiotemporal patterns of SWF allows us to identify regions that retain source waters from the Cosumnes, and thus water that has a higher likelihood to contain nutrients or productivity from upstream restoration sites [31
]. Being downstream of completed and ongoing restoration projects is not a unique trait of the MWT within the Delta. Many restoration sites are slated or under construction in the Delta [48
]. Understanding how these sites are connected and how they can be synergistic may help to better understand how a single site can have regional ecosystem benefits.
Given that the hydrodynamic method of finding SWF discussed in this paper could be applied to any river network, insights on riverine restoration potential can be gained in any system. For simple fluvial systems that satisfy the assumptions of the isotope mixing model method of finding SWF, isotope samples could suffice in place of developing hydrodynamic models. With careful regard for the limitations discussed, the implications for understanding SWF distribution can be further explored in any river network, and perhaps other connections to aquatic ecology or water quality processes can be found. For instance, Farly et al. used an isotope mixing model to investigate fish diet composition in terms of floodplain-produced or channel-produced resources [49
]. This could be coupled with hydrodynamic models to investigate possible effects of drift versus autochthonous production. These methods (hydrodynamic tracers and isotope mixing models) can also be used to investigate habitat quality and its linkages to SWF, using a number of biological or water quality data.