*3.2. Erosion*

Mean erosion by measurement period (assessed using the average absolute change variables CAvg|Ch|, IAvg|Ch|, and SAvg|Ch|, where C, I, and S, refer to channels, interfluves, and sidewalls, respectively) was greater in winter and spring than the overall mean for all three geomorphic areas (Table 2). Notably, in winter months, CAvg|Ch| was 16.8 mm compared to 9.9 mm overall and SAvg|Ch| was 8.0 mm compared to 5.0 mm overall. Seasonal effects on interfluves were less pronounced, with IAvg|Ch| in winter at 4.8 mm compared to the overall mean of 3.5 mm. As with precipitation parameters, autumn was the season with the lowest mean erosion by measurement period for all geomorphic areas at 4.8 mm for channels, 3.5 mm for sidewalls, and 2.8 mm for interfluves.

**Table 2.** Descriptive statistics for erosion variables by measurement period. All values measured in millimeters. C, channel I, interfluve; S, sidewall.


Seasonally, erosion variables show the most variability during winter months (Figure 3). Winter of 2016–2017 experienced less erosion than other years for all geomorphic areas, however, the study area received high rainfall accumulation during two weekly measurement periods.

**Figure 3.** Comparison of erosion variables by geomorphic area. The top three graphs show erosion in channels (C, top), interfluves (I, middle), and sidewalls (S, lower), bottom graph shows precipitation. Columns mark seasons (Su = summer, A = autumn, W = winter, and Sp = spring).

#### *3.3. Statistical Modeling*

Erosion variables were significantly correlated with total accumulation and duration parameters for all variables except interfluve erosion (IErosion) (Table 3). Concordant with prior studies, erosion in channels was most strongly correlated with total accumulation (r = 0.467, r = 0.352, and r = −0.469 for CAvg|Ch|, CDep, and CErosion, respectively) and duration (r = 0.470, r = 0.367, and r = −0.447 for CAvg|Ch|, CDep, and CErosion, respectively). Note that all correlation coefficients for erosion variables (CErosion, IErosion, and SErosion) are negative because these variables are values below zero.

Spearman's correlation between the four precipitation parameters was compared to assess the potential for multicollinearity in statistical models, and total accumulation shows a very strong positive correlation with duration (r = 0.903) and a moderately strong positive correlation with average intensity (r = 0.591) and maximum intensity (r = 0.657). Likewise, average and maximum intensity were strongly and positively correlated (r = 0.794).

**Table 3.** Spearman's correlation coefficients for erosion variables and precipitation parameters. C, channel; I, interfluve; S, sidewall. Only significant correlations are shown (\* significant at α = 0.05, \*\* significant at α = 0.01).


Before modeling erosion by season, OLS regression models were developed for the annual dataset (all measurement periods) using the four precipitation parameters from the current period, plus lagged variables for up to 11 prior periods (weeks). Table 4 summarizes output from models for each erosion variable in columns, with the variable name and R2 value at the head of the column, and retained parameters marked by \*. Retained parameters (independent variables) were those with statistically significant coefficients in each OLS model output. Nine models are represented in Table 4, one for each erosion variable. Model coefficients are not presented (only significance) here because the purpose of the modeling was to identify the precipitation parameters that were universally important, which was completed through frequency analyses. All model linear equations are, however, presented in Table A1 in Appendix A. Duration and total accumulation were the most important variables for channel erosion, while average intensity was important for erosion in interfluves and sidewalls. Also notable is the influence of antecedent precipitation at lags of up to 11 weeks for some variables.



Seasonal OLS regression models clearly indicate the importance of precipitation intensity, which was, in prior studies, not retained in annual models of erosion (Table 5). Note that seasonal models for IAvg|Ch| were omitted from Table 5 because only one viable model was generated, and its coefficient of determination was extremely low (R2 = 0.064).

Interestingly, in summer and winter, average and maximum intensity were important explanatory parameters both during the current period, but also in prior periods. Precipitation intensity was not often retained in models of erosion during spring and autumn. It is also important to note that viable OLS regression models were generated for all erosion variables for summer and winter, with coefficients of determination ranging from R<sup>2</sup> = 0.245 to R<sup>2</sup> = 0.49 (except for IErosion in summer at R<sup>2</sup> = 0.131 and SDep in winter at R<sup>2</sup> = 0.087), suggesting that precipitation is an important driver for erosion in these months, no matter the metric used. Moreover, these results show that the character of the precipitation is an important driver for erosion; antecedent precipitation has an influence on erosion in the following weeks and months and it varies with season.

**Table 5.** Parameters retained (indicated by \*) in seasonal Ordinary Least Squares regression models of erosion variables (dependent variables) using lagged precipitation parameters (independent variables) Duration (min), Total Accumulation (TotAcc (mm)), and Average and Maximum Intensity (AvgInt and MaxInt, respectively (mm/min)). C, channel; I, interfluve; S, sidewall. Each column represents a separate model.

