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.