Modeling terrestrial drivers

We generated terrestrial drivers’ grid maps (60x60 m) by diffusing the modeled groundwater discharge (m³.yr^-1) and nutrient flux (kg.yr^-1) from each pour point into the coastal zone using ArcGIS (Fig 2E). First, we created a cost-path surface (c) to quantify the least accumulative cost-distance (impedance) of moving planimetrically through each cell from each pour point, using a composite of three marine drivers known to affect diffusion (depth [m], distance from shore [m], and wave power [kW.m^-1]–see ‘Modeling marine divers’ for more details) [26,105]. Then, the spread of groundwater and nutrient values into coastal waters from each pour point was modeled using a decay function (see Eq 3), which assigned a portion of the remaining quantity from the previous cell in all adjacent cells, based on the cost-path surface until a maximum distance of 1 km from the shoreline was reached [49,60,106–108]:

where W = Grid cell value for diffused groundwater (m³.yr^-1) and nutrients flux (kg.yr^-1), L_p = Groundwater (m³.yr^-1) and nutrients (kg.yr^-1) flux at each pour point (obtained from computing the groundwater and nutrient flux by flow tube), c = cost-path surface (unitless), D_c = cost-path surface threshold distance from the shore for each decayed groundwater metrics (equivalent to 1,000 m from the shoreline). This approach to modeling SGD is diffusive, and thus, allows for wrap around coastal features, but did not account for nearshore advection that acts to push the SGD in specific directions [49]. We used these diffusive models to derive conservative estimates of SGD plumes, since the nearshore circulation patterns were unknown for our study sites.

We assumed that the nutrient chemistry of the SGD was similar to that of the groundwater. Biogeochemical reactions that could occur, but were not considered in this study are those associated with denitrification and anammox (anaerobic ammonium oxidation). Given that the biogeochemical conversion of N and P to other species requires reducing conditions, the high dissolved oxygen content (dominantly >80%) in the aquifers around the main Hawaiian Islands results in stable oxidized forms of dissolved N and P, which are the dominant species [84,88,91,109]. Thus there is a possibility that we over- and under-estimated the amount of N and P, respectively, particularly at Ka‘ūpūlehu, where wastewater is disposed of through injection wells [88,109]. Due to the very limited coastal water quality data in our model domains (S3 Table), these modeled terrestrial drivers could only be partially ground-truthed at Ka‘ūpūlehu using linear regression (R² and p-value) (Fig 3D). These SGD models were meant to capture general spatial patterns, which could be refined with future SGD measurements.