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).