A density-dependent multi-species model to assess groundwater flow and nutrient transport in the coastal Keauhou aquifer, Hawai‘i, USA

Hawai‘i Island is the largest island (10,464 km²) in the Hawaiian archipelago and was built by five shield volcanoes: Kohala, Mauna Kea, Hualālai, Mauna Loa, and Kīlauea (Izuka 2011). Basaltic lava flows from these five volcanoes covered the island’s surface less than 1 million years ago, making Hawai‘i Island the youngest island in the chain (Clague and Dalrymple 1987). The eruption of each volcano was partially simultaneous with its neighboring volcano, so it is likely that lava flows from neighboring volcanoes interfinger with each other, creating complex geologic contacts (Wolfe et al. 1997; Izuka et al. 2018). Basaltic lava typically flows as either pāhoehoe or ‘a‘ā, which differ in viscosity and texture (e.g., DePaolo and Stolper 1996; Lau and Mink 2006; Izuka et al. 2018). For sequences of pāhoehoe, groundwater primarily travels through spaces, tubes, and vesicles that are formed between the multiple layers of lava flows, resulting in higher porosity and permeability. ‘A‘ā are comprised of two general components—clinker beds and massive cores. The ‘a‘ā clinker beds typically demonstrate higher porosity and permeability while the dense ‘a‘ā cores demonstrate lower porosity and permeability and thus impede groundwater flow across layers (Izuka et al. 2018). Because it is common to see alternating pāhoehoe and ‘a‘ā flows in cross section, the hydrogeologic parameters typically represent both flow types (Lau and Mink 2006).

Located in the northern Kona district, the southern flank of Hualālai is defined as the Keauhou aquifer (426 km²; Fig. 1). The Keauhou aquifer is geologically divided into a basal aquifer and a high-level aquifer with a discontinuous head profile characterized by a near abrupt change. Water levels near the coast are approximately 1 m above mean sea level (msl) but dramatically rise to more than 100 m above msl approximately 4–8 km inland (Fig. 1). It is believed that a subsurface geologic structure reduces groundwater flow from the high-level aquifer to the coast (Oki 1999). Efforts to characterize this structure include modeling of gravity survey data that indicate the presence of a dense substructure under Hualālai, located approximately 4 km southwest of the eruptive vents that map Hualālai’s southeast rift zone (Kauahikaua et al. 2000; Flinders et al. 2013). Although the geologic structure has been conceptually hypothesized (Oki 1999, their Fig. 6), the exact nature of the structure is still not well defined, which is beyond the scope of this study. Another significant, yet undefined, geologic feature acts as a confining unit, creating a second, deep freshwater body below the primary basal aquifer (Thomas et al. 1996; Attias et al. 2020). Since this study focuses on the shallow groundwater, however, no attempt was made to simulate such a feature. To avoid such uncertainties, this study instead focuses on the Keauhou basal aquifer (150 km²), with head levels less than 5 m and the eastern boundary coinciding with the geologic structure bordering the high-level aquifer (Fig. 1). The western boundary follows bathymetry and extends beyond the coastline to accurately account for processes at the land-ocean interface.

Rather than modeling the entire Keauhou aquifer, only the basal area was selected as the focus for this study (Figs. 1 and 2a) and the high-level Keauhou aquifer was excluded due to the following factors:

With the exclusion of the high-level aquifer, the eastern model boundary of the basal aquifer was assigned a specified flow condition and the flow rate was estimated by creating a regional, freshwater-only MODFLOW model for West Hawai‘i (Fig. 2b). Since the eastern boundary of this regional area generally follows the rift zones of Mauna Kea and Mauna Loa, groundwater is not believed to flow from the windward to leeward side of the island (Izuka et al. 2018), and thus the boundary can safely be assigned a no-flow condition. Such a regional model would eliminate the concern about inter-aquifer flow. The geologic structure was simulated as a horizontal flow barrier in the regional model and was reasonably calibrated to estimate hydraulic conductivity (K_h) and the barrier conductance. MODFLOW’s zone-budget option was used to estimate the flow into the eastern boundary of the basal aquifer area. The flows through the northern and southern boundaries were negligible and therefore it was reasonable to treat them as no-flow boundaries.

Submarine springs are dominated by brackish spring flows along the coastline of the study site (Johnson et al. 2008; Duarte et al. 2010; Kelly et al. 2019). In contrast to diffuse SGD, these point-source springs are caused by preferential flow (Taniguchi et al. 2019). Explicitly modeling preferential flow is impractical due to the absence of detailed aquifer information, mostly related to identification of fractures or conduits contributing to preferential flow. As an approximation, springs were simulated as point drains, or head-dependent sinks, at their respective coordinate locations along the coastline. A similar approach was adopted for volcanic aquifers by Oki (2005) and El-Kadi et al. (2014). The approach is motivated by studies that indicated that discharge from springs is directly related to the aquifer’s head gradient (Taniguchi et al. 2002; Duarte et al. 2010). In MODFLOW, the drain flow is estimated through Darcy’s law, utilizing conductance and hydraulic head terms. In this study, with head levels roughly constant near the shoreline, it was reasonable to assume that conductance of each submarine spring was linearly proportional to the respective measured flow rate. Thus, each submarine spring point has a unique conductance value representing the varying degrees of preferential flow that can be encountered across this complex aquifer system. The bottom of the drain was assumed to be 0.5 m below msl, representing the rough depth from which the springs were sampled. The drains were thus located within the top layer of the model.

The study applied SEAWAT, a transient, multispecies density-dependent model (Langevin et al. 2008), which combines MODFLOW (Harbaugh et al. 2000) with MT3DMS (Zheng and Wang 1999). The software package interface GMS (Aquaveo 2021) was used in facilitating the modeling process. Quasi steady-state simulations were utilized by running the models for 30 years to reach near steady-state conditions. The model consists of 21 layers, 82 rows, and 36 columns (totaling 26,323 cells) and is rotated 10° counterclockwise. The model grid covers the Keauhou basal aquifer and extends out into the ocean. The grid’s top elevation follows topography and bathymetry and the bottom of the grid has a flat elevation of 550 m below msl (Fig. 2c). With head levels less than 5 m above msl, and assuming validity of the Ghyben-Herzberg relation, the freshwater–saltwater interface is expected to be located approximately 200 m below msl. The additional model depth was included as a buffer to ensure the flow in the model area is not significantly affected by the bottom boundary condition. Because the bathymetry offshore of Keauhou is highly variable, the model grid extends perpendicularly offshore as far as 12,034 m and as close as 743 m. The bottom of the first layer is set to 1 m below msl to ensure dry cells are not produced if the water table drops below the cells’ bottom. The remaining 20 layers vary gradually in thickness, where the upper layers are the thinnest (Fig. 2c). The horizontal grid spacing is a consistent 490 m × 490 m.

There are numerous ways nutrients are introduced to the groundwater system in the study site, including point-sources such as OSDS and WWTP, and diffusive nonpoint-sources such as LULC (Kendall and Aravena 2000). Because multiple nutrient inputs are located within Keauhou and because their δ¹⁵N and δ¹⁸O of NO₃⁻ composition ranges overlap, it is difficult to identify the relative contribution of each nitrogen source. Relative N contributions from OSDS, WWTP, LULC, and eastern boundary condition (BC) were estimated by assigning different N species to these sources. The model is equipped to simultaneously simulate these as distinct species. Following the principle of superposition, the total N concentration was estimated by summing these individual concentrations (Reilly et al. 1984).

To validate the modeled source estimates, δ¹⁵N in dissolved NO₃⁻ were used to identify nitrogen sources in the aquifer; however, the analysis is complicated by the fact that each source exhibits overlapping ranges in isotopic composition. Abaya et al. (2018) measured δ¹⁵N from various N sources in Puakō, which is located on the coast north of the study area. The study estimated natural soil δ¹⁵N ranges from approximately 1–4‰. While most δ¹⁵N samples collected within the Keauhou basal aquifer fall within the natural soil δ¹⁵N range (e.g., Kendall and Aravena 2000), elevated NO₃⁻ measurements for some samples suggest N is added by other inputs as well. To test this, a simple isotope mixing equation was used to compute δ¹⁵N values for wells and submarine springs based on simulated relative contributions and δ¹⁵N endmember assumptions.

Since mixing ratios are used for stable isotopes of dissolved components, δ¹⁵N needs to be weighted by the simulated concentrations in the mixing model (Hunt and Rosa 2009). The following mixing equation was used (Hunt and Rosa 2009): where δ¹⁵N_model is the computed δ¹⁵N at wells and submarine springs, f is the simulated fraction of each source component at a well or submarine spring location, C is the simulated concentration in the component, and dN is the δ¹⁵N endmember of each source component. The δ¹⁵N endmembers used for OSDS, WWTP, LULC, and BC were 7‰ (Wiegner et al. 2016), 1‰ (Abaya et al. 2018), 20‰ (Hunt 2014), and 2‰ (Hunt 2014), respectively. Single endmember values were selected to obtain the best match, but as previously mentioned, each source ranges in δ¹⁵N. Wiegner et al. (2016) summarized that δ¹⁵N for sewage in Hawai‘i ranges from 7 to 20‰, while Abaya et al. (2018) narrowed the range to 9–11‰ in Puakō, Hawai‘i Island. Abaya et al. (2018) reported that values for fertilizers range from −2 to 0‰ while soil ranged from 1 to 4‰. Since the modeled LULC coverage contains natural land and urbanized land, both ranges were considered. Hunt (2014) reported that the treated wastewater from Kealakehe had a δ¹⁵N measurement of 12‰ and a water sample from a well within the Kealakehe wastewater plume had a δ¹⁵N measurement of 20‰. Hunt (2014) reported that the Honokōhau well, which is a high-level pumping well in Keauhou, had a δ¹⁵N measurement of 2‰. This is similar to this study’s high-level samples, which ranged from 1 to 2‰.

As previously stated, models overlooking salinity changes in nearshore aquifers are commonly used to assess both water levels and quality. To test applicability of such an approach, a freshwater-only model was simulated to compare to the density-dependent results. The model was easily set by converting SEAWAT to run MODFLOW and MT3DMS in sequence, with MODFLOW set to run in a steady-state condition. The model retained the boundary conditions, coverages, and various input parameters previously described, except K_h, which was recalibrated to obtain a reasonable match for hydraulic head under freshwater-only settings.

To demonstrate the capability of the density-dependent model as a management tool addressing nutrient and salinity distribution in the basal aquifer, the model was tested with example applications. This study therefore focused on two different aspects that are important for water resource management in West Hawai‘i: (1) aquifer salinity and storage changes as a response to future development and climate change, and (2) aquifer response to sea level rise.

Utilizing a heterogeneous K_h distribution, as described in section ‘Calibration approach’, did not lead to a significant improvement in results (section S.4 in the ESM). Accuracy of salinity calibration in wells improved but was accompanied with a slightly reduced accuracy of hydraulic head calibration; additionally, the accuracy of N and P predictions worsened. It was concluded that such an effort is only useful if appropriate representation of various processes is included in the conceptual model. Under scarcity of data, utilizing a simplified K_h distribution is preferred, considering the complications and computational expenses associated with developing a more involved K_h distribution. The results presented from here forward are all for a homogeneous K_h applied to the entire aquifer. The final calibrated parameter values used in the Keauhou basal aquifer model are provided in Table 2.

Head, salinity, N and P concentration calibration results are shown in Fig. 3. Head was reasonably calibrated with a relatively low RMSE (<0.5 m; Fig. 3a). Under density-dependent conditions, the calibration process is complicated by the nonlinear relationship between the hydraulic head and salinity. Attempts to improve on the accuracy of salinity calibrations resulted in less precise head calibrations. The reasonable accuracy of head prediction, nonetheless, implies validity of the continuum approach via Darcy’s law (e.g., Bear 1972) for simulating the hydraulic head for this complex domain. However, lower accuracy and the scatter regarding salinity and nutrients are likely attributed to the complexities in geological characteristics of the field such as the potential existence of preferential flow, which would naturally affect various simulation processes. The simulated salinity in submarine springs exhibit lower accuracy due to the nature of sampling location. Submarine springs are simulated along the shoreline and are positioned at the interface between fresh groundwater exiting the aquifer and saline ocean water moving inland. Thus, most of the submarine springs have a simulated salinity confined within a narrow range in comparison to the wide range of salinities measured in the field (Fig. 3b). This mismatch is possibly caused by the model’s inability to simulate a very precise spring point location. The field-based submarine spring salinity measurements were assessed from the freshest terrestrial water that could be detected at the coast; thus, they are expected to be biased towards lower values. In contrast, the modeled salinity was averaged over an entire cell, and therefore falls within a mid-salinity range.

The N simulations produce reasonable calibration results (Fig. 3c,d). In contrast, many of the observed P measurements fall within a small range that is not well represented in the model results (Fig. 3e,f). The imprecise results for P should be expected considering that the assumption of a conservative behavior is not valid (Delevaux et al. 2018); however, the results can be useful while applying the model for screening purposes. In contrast to salinity, the relatively better correlation between simulated and measured N and P for submarine springs is due to the fact that these species are primarily sourced from terrestrial sources located in freshwater zones and not drastically influenced by marine processes at the land-ocean interface.

Modeling submarine springs as drain points with varying conductance produced accurate results (RMSE = 1,237 m³/day, r² = 0.98). Under such conditions, the model simulated 107,673 m³/day of groundwater discharging at point-source submarine springs, closely matching the observed values. The model also simulated an additional 1,230,000 m³/day of fresh and saline water diffusively discharging along the coast and offshore. However, accurately simulated flux rates combined with lower accuracy of salinity, N, and P concentrations emphasize the fact that a continuum approach for flow modeling can be acceptable for preferential flow but fails to simulate solute transport.

Although comparable head accuracy was obtained for the freshwater-only model and the density-dependent model (Fig. 3a), a significantly lower K_h of 300 m/day was required to calibrate the hydraulic head. Compared to a value of 2,500 m/day for the density-dependent model, such a value is not realistic for a young basalt, as documented in previous modeling and other studies (Oki 1999; Izuka 2011). Hence, such a value can simply be considered as a fitting parameter that is not physically based. It is of interest to note that K_h appears to be a process-based parameter, thus it depends on the nature of the conceptual model and processes simulated. Saltwater circulation clearly affects the estimated effective aquifer thickness, which cannot be accurately estimated by a freshwater-only model. RMSE of submarine spring flux also increased from 1,237 m/day to 3,273 m/day. Although the submarine spring drains retained the same conductance values, the lower K_h assigned to the freshwater-only model reduced overall flow fields (Fig. 4b) and resulted in lower discharge at the submarine springs.

The overall accuracy of N and P concentrations are comparable for the two models at wells (Fig. 3c,e), in contrast to the values in the submarine springs (Fig. 3d,f). The freshwater-only model overestimates nutrient concentrations in the springs due to the fact that water circulation is not simulated in the nearshore area, where in reality, nutrient-poor saltwater intrudes into the aquifer. As should be expected, the influence of circulation diminishes far from the shoreline, leading to better accuracy for wells. Flow fields for the two models are compared in Fig. 4, showing a significant contrast in the nearshore area. It should be noted that salinity does not directly affect nutrient concentrations, considering that they are treated as conservative species. The case can be different for reactive chemicals such as contaminants of emerging concern (CECs), where salinity can directly play a role (e.g., Patel et al. 2019; McKenzie et al. 2020). It can be concluded that, not only does the freshwater-only model overlook salinity, but it also ignores the significant water circulation in the nearshore environment, leading to unacceptable errors in water quality assessment. Salinity is an important factor regarding water sustainability concerning different water uses, such as reducing estimates of aquifer sustainable yield and causing damage to anchialine ponds. Fresh groundwater in Hawai‘i is considered to have less than 1,000 mg/L of dissolved solids (Yee 1987), while the USGS also classifies water as “slightly saline” with concentration less than 3,000 mg/L (Swenson and Baldwin 1965). If it is assumed that salinity measurements directly correspond to dissolved solid concentrations, then 45% of the 20 wells used in the Keauhou basal aquifer model had salinity measurements that exceed the “slightly saline” water standard, while 75% of the simulated salinity measurements exceed the threshold. Such an assessment clearly indicates the need for a density-dependent model to accurately assess water sustainability and estimate aquifer sustainable yield.

Based on simulated N mass loadings entering the Keauhou basal aquifer, the majority of N is sourced from OSDS (54%), while urban development LULC contributed 10%, the Kealakehe WWTP contributed 9%, and groundwater applied at the eastern boundary contributed 26% (Fig. 5). It is clear that OSDS have the greatest impact on nutrient contribution to the groundwater system. Areas with urban development, where there are significant clusters of OSDS, experience plumes of higher nutrient concentrations, which travel with groundwater flow to the coast (Fig. 5b). The results can be useful for managing water quality issues such as efforts to meet Federal regulations regarding the total maximum daily load and identifying major contributor sources where upgrade efforts should be directed. For this study, it is important to recognize the significant nutrient mass load that is sourced from the eastern boundary condition (Fig. 5e), especially while considering the boundary uncertainties previously discussed. The mass load that enters through the boundary was dependent on the assigned nutrient concentrations and water flux.

Based on simulated N concentrations in wells and submarine springs, relative N source contributions were also estimated at each sample location (Fig. 6). Overall, minimal amounts of LULC-sourced N were detected in simulated samples, with an average contribution of 0.13 mg/L (13% of total concentration). The N sourced from the WWTP contributed a significant amount of N to a few submarine springs. An estimated 57–71% of WWTP-sourced N was simulated in the two submarine springs (HHA and HHB) located directly downgradient of the WWTP. This was also validated by the enriched δ¹⁵N measured at these submarine springs (Fig. 6). Simulated N sourced from OSDS and the eastern boundary were both significantly detected in most wells and submarine springs. Of importance is to note that OSDS-sourced N appears in all but one sample across the aquifer, demonstrating the widespread effect of wastewater on groundwater quality. Eight of the 25 simulated samples had at least 50% of the simulated N concentration sourced from OSDS, while 11 samples had at least 50% of N sourced from the eastern boundary (Fig. 6). Conversely, the average OSDS-sourced N concentration was 0.6 mg/L, while the average boundary-sourced N concentration was 0.4 mg/L.

Calculated δ¹⁵N values were used to validate simulated N contributions. Results from the described isotope mixing model (section ‘δ¹⁵N model validation’) produced a reasonable fit between the measured and computed δ¹⁵N values (r² = 0.76), where 14 of the 25 samples matched within ±1‰ (Fig. 7). Considering that δ¹⁵N values vary over a range within each source, the mixing results are influenced by uncertainties associated with endmember designations. Since relative N contributions from LULC and WWTP were minimal, variations in δ¹⁵N_LULC and δ¹⁵N_WWTP endmembers did not drastically affect overall δ¹⁵N_model results (Fig. 7a,b). Although the N contribution from the BC was relatively high, the δ¹⁵N_BC range was not large enough to significantly affect δ¹⁵N_model results (Fig. 7c). Since the BC is an ambiguous endmember with mixed water sources, the most reliable δ¹⁵N reference were water samples from high-level pumping wells, which showed very little variation. Modeling results show that OSDS serves as the most significant N source, thus changes in the δ¹⁵N_OSDS endmember exhibited the greatest variation (Fig. 7d). An enriched δ¹⁵N_OSDS endmember would potentially enrich δ¹⁵N_model results and thus skew relative contributions. There is a large range of OSDS δ¹⁵N measurements because of the different individual units, but this approach is limited to assigning one OSDS endmember. Therefore, differences between measured and modeled δ¹⁵N is to be expected; nonetheless, a reasonable fit was obtained with a δ¹⁵N_OSDS value of 7‰. Although this endmember is slightly depleted compared to previously published values from other areas in Hawai‘i (e.g., Wiegner et al. 2016), findings from previous studies (e.g., Abaya et al. 2018) already demonstrate that δ¹⁵N measurements in West Hawai‘i are isotopically depleted compared to universal ranges typically found in literature (e.g., Kendall and Aravena 2000). These results therefore emphasize the importance of site-specific measurements, suggesting that more sampling from varying conditions is required and an approach acknowledging wider ranges should be considered. With these limitations in mind, the model captured overall δ¹⁵N ranges. These results validate the simulated N transport results and show that mixing between N from various sources can be constrained; hence, the model can be used as a tool to estimate relative contributions of multiple nitrogen sources.

The model developed for this study simulates groundwater flow and nutrient transport through the Keauhou basal aquifer, calibrated with measured head, salinity, N and P concentrations, and submarine spring fluxes. The major assumption in the approaches adopted concerns validity of the continuum approach (e.g., Bear 1972) for simulating density-dependent flow and transport in a domain that is highly complex with apparent preferential flow. Results suggest that such a concept, as the basis of Darcy’s law, is applicable with good calibration accuracy for hydraulic head and submarine spring flows. Some scatter obtained for the results of salinity and nutrient calibration is mainly due to effects of local hydrogeologic medium variability. Use of models that account for small-scale variability such as accounting for preferential flow, is impractical due to the related extensive data needs. Another assumption concerns the treatment of N and P as conservative chemicals based on the justifications presented by Delevaux et al. (2018). Additionally, measurements of NO₃⁻ + NO₂⁻ and PO₄³⁻ were used as major chemical species of N and P, respectively, due to well oxygenated aquifer conditions (Richardson et al. 2017). Considering that a relatively high fraction of TN was represented by NO₃⁻ in this groundwater, it was assumed that these measurements could serve as representative values for model calibration.

Another model uncertainty is related to the estimation of flow through the eastern boundary of the model. Occurrence of such a flow is confirmed by Fackrell et al. (2020). A reasonable estimate was utilized in this study by a simplified regional model. Since calibration accuracy is sensitive to the eastern boundary condition (section S.3 of the ESM), such an estimate can significantly impact results. There is also an uncertainty regarding the flow condition at such a boundary regarding an assumed vertical flow distribution, considering that the actual hydrogeologic nature of this interflow aquifer boundary is not well understood. In addition, the model did not account for deep offshore freshwater discharge that exists off the coast of Keauhou (Attias et al. 2020).

The model has limitations due to the relatively coarse grid resolution that reduces accuracy of results regarding the spatial distribution of OSDS and LULC. These variables were averaged and assigned as a single lumped value to the corresponding modeling grid since it is certainly impractical to design the grid on an individual OSDS scale. However, numerical accuracy was not impacted by the spatial resolution and mass conservation for water flow and constituent transport was maintained by the model under all applications.

Finally, model calibration is affected by the lack of continuous head records, which is a serious drawback that hinders researchers’ efforts in Hawai‘i and other similar areas. Available data normally include initial head values measured during the drilling process. Most pumping wells are not continuously monitored, and the initial head measurements were therefore collected at different times. However, the assessment here indicated that the values used for model calibration are within the average fluctuations in water level measurements (section S.1 of the ESM). Fluctuations are not drastic due to the large K_h values associated with volcanic rock materials.