Figure 2 : Pearson correlation matrix between all potential predictor and response variables. The black box highlights correlations between the predictor variables and stream Na+ and NO3-, both of which were log-transformed. Everything beyond the black box represents correlations among predictor variables.
Note: Area is watershed area, Slope is mean watershed slope, Elev is mean watershed elevation; Rip is riparian extent, TWI is mean topographic wetness index, Tree is mean tree cover (%), Shrub is mean shrub cover (%), Bare is mean bare ground cover (%), NDMI is mean normalized differenced moisture index, NDVI is mean normalized vegetation index, EVI is mean enhanced vegetation index, Burn is burn extent (%), dNBR is mean differenced normalized burn ratio, and both stream NO3- and stream Na+ concentrations are log-transformed (mg/L).
To build SSN models, stream sampling locations were incorporated into a landscape network (LSN) to characterize network geometry (Peterson & Ver Hoef, 2014) using the openSTARS package (Kattwinkel & Szöcs, 2020). The additive function quantified the proportional influence of each stream segment (Ver Hoef & Peterson, 2020) and calculated distance matrices between all sampling points. We used a tail-up autocovariance structure to restrict our modeling to flow-connected distance, which is only measured between points with an upstream-to-downstream connection (Isaak et al., 2014; Peterson & Ver Hoef, 2010). This distance metric is better suited for stream network studies than straight-line Euclidean distance because it characterizes downstream transport and longitudinal connectivity of dissolved solutes (Peterson & Ver Hoef, 2010). We then modeled an empirical semivariogram and derived 3 associated parameters – the nugget, sill, and range. Empirical semivariograms quantify the variation between samples (i.e., stream Na+ or NO3- concentrations) as a function of distance between sampling points (Ganio et al., 2005). Positive autocorrelation occurs when semivariance is smaller (i.e., measurements are more similar) near the origin and increases at greater lag distances. In some cases, the semivariogram will reach an inflection point at a given lag distance (‘range’) where semivariance begins to flatten out (‘sill’). Samples are considered uncorrelated at distances greater than the range and the sill represents the dissimilarity of the uncorrelated data (Isaak et al., 2014). The nugget describes spatial variation at scales smaller than the minimum sampling interval (i.e., ≤52 m in our study).

2.5 Longitudinal patterns across two watersheds with inverse burn patterns

Finally, we used kriging to interpolate stream NO3- concentrations along the mainstems of two paired watersheds and compared spatial NO3- patterns to continuous measures (i.e., every 10 m) of hydrologic inputs and the vegetation condition of those inputs. These two watersheds had similar contributing areas (6.1 and 9.3 km2, Table 1) and were extensively burned (i.e., >50% of UAA burned). For both watersheds, patch density was high and fire severity was mixed equally among burn severity classes (Table 2). However, the headwaters were severely burned in Brush Creek and unburned in Pine Creek (Figure 1). We distributed 3,000 equally spaced prediction points along the geomorphic channel networks of each watershed, delineated the contributing area of each prediction point, and calculated topographic, vegetation, and fire predictor variables (see section 2.3). We also calculated the flow-connected distance between all observed and prediction locations. The NO3- SSN model then predicted NO3- concentration and standard error at each location based on both landscape characteristics (i.e., watershed area, riparian extent, mean TWI, and mean NDMI) and flow-connected distance. We then calculated the relative lateral input (LI) as the incremental downstream increase in contributing area relative to the total contributing area (i.e., Relative LI =\(\frac{(\text{UAA}_{\text{cell}\left(n\right)}\ \ \text{UAA}_{\text{cell}\left(n-1\right)})}{\text{UAA}_{cell(n)}}\)). Because stream discharge scales with contributing area (Bergstrom et al., 2016), this metric reflects the contribution of hillslope water relative to mainstem flow. Finally, mean NDMI was calculated for the discrete lateral input (LI) contributing to each 10-m stream cell using the same June 2018 NDMI image described in section 2.3. We also resampled the paired watersheds in June of 2019 at a 300 m resolution to assess the accuracy of our NO3- SSN predictions with observed values.