Figure 3: Empirical semivariograms of log-transformed stream
Na+ (blue) and NO3-(red) based on the flow-connected distance between sampling points.
Symbol sizes are proportional to the number of data pairs included in
each bin. The grey shaded region represents the 95% confidence interval
from a local polynomial regression of each semivariogram. Semivariograms
show evidence of strong positive autocorrelation in
Na+ (blue) and weak spatial autocorrelation in
NO3- (red).
3.4 Statistical model
performance
The SSN model improved Na+ predictions relative to the
MLR model, as indicated by lower AIC and RMSPE values (Table 4). Leave
one-out-cross validation demonstrated that SSN predictions were closer
to observed values (Figure 4A) and prediction standard errors were lower
(Figure 4C) in the Na+ SSN model compared to the
Na+ MLR model. In the Na+ SSN model,
predictor variables explained 45% of the variance in
log[Na+], flow-connected autocovariance explained
53.1% and only 1.9% was left unexplained (Table 4).
The NO3- SSN model also had a lower
AIC value and RMSPE relative to the
NO3- MLR model (Table 4). SSN
predictions were closer to the observed values (Figure 4B) and
prediction standard error was lower (Figure 4D) in the
NO3- SSN model than the MLR model. In
the NO3- SSN model, predictor
variables (36%) and flow-connected autocovariance (41.5%) explained a
majority of the variation in
log[NO3-], leaving 22.5%
unexplained (Table 4). Based on NO3-SSN model, 81% of the predicted stream NO3 concentrations that fell
within the fire perimeter exceeded the pre-fire mean concentrations of
0.18 mg/L (Rhoades et al., 2011, Supplemental Figure 3).