**2. Materials and Methods**

The study site was a system of branching gullies located on a hillslope at the East Tennessee State University Valleybrook research facility in northeast Tennessee, USA (+36◦25 36.77", −82◦32 10.63") at an elevation of 530 m (Figure 1). The site was within the Appalachian Valley and Ridge physiographic province and consisted of northeast-southwest trending parallel limestone valleys (Maynardville Formation) and sandstone or shale ridges (Nolichucky Formation) [17]. The 1.5 ha study area was located on a grass and shrub hillslope surrounded by forest (on the ridges) and pasture (in the valleys). Soils were highly erodible fine-grained silt and clay Ultisols (Collegedale-Etowah complex (CeD3)) with an average erodibility factor (RUSLE K-factor) of 0.28, indicating susceptibility to raindrop impact and transport by surface runoff [18]. The region has a humid subtropical climate (Köppen Cfa) with year-round precipitation of 1070 mm (42 in) annually and an average annual temperature range from 1.1 ◦C (34 ◦F) in January to 23.3 ◦C (74 ◦F) in July. The National Oceanic and Atmospheric Administration describe Tennessee's winter precipitation as dominated by the polar front and summer precipitation that results from convectional systems. September and October are the driest months.

**Figure 1.** The study area was located in northeast Tennessee, USA on an actively eroding hillslope.

A detailed description of the site setup can be found in [13,19] and is summarized as following. Steel erosion pins were installed in transects throughout the 100 m × 100 m gullied zone. Each transect spanned interfluves, sidewalls, and the gully channel to assess erosion in these three morphological settings. In total, 105 erosion pins were installed, 34 (1 m × 5 mm) pins in channels, and the remaining (0.5 m × 5 mm) pins in interfluves (29 pins) and sidewalls (42 pins). From 23 May 2012 to 22 August 2018, pin length was recorded approximately weekly for each pin using a folding ruler. Pin attrition occurred periodically over the study period, such that some pins were eroded, damaged, or dislodged by animals. Therefore, in May 2015, 43 new pins were installed and 3 damaged pins were replaced, bringing the total number of pins to 105. The nature of the site surface limited access during and immediately after rain events, and over the six-year period, pin length was recorded 294 times. The difference between the exposed lengths of each pin was calculated between one measurement period and the next, and this dataset of pin change was compared to precipitation data to identify important drivers for erosion in each morphological setting.

For each setting, we created three erosion variables: (1) average of the absolute value of change (Avg|Ch|); (2) average of only positive changes in pin lengths (deposition) from one measurement period to the next (AvgDep), and; (3) average of only negative changes in pin lengths (erosion) from one measurement period to the next (AvgErosion). In prior research, a fourth variable, average change, was generated, however, because of a balance of erosion and deposition, especially in channels, the average change remained near zero and was not a useful parameter to capture weekly and longer-term erosion on-site [13,14,19–21]. Therefore, in this study, we have retained the three variables described above.

A Davis Vantage Pro wireless weather station (KTNJONES12, data available at https://www. wunderground.com/dashboard/pws/KTNJONES12) was located 350 m from the research site, and recorded precipitation, pressure, temperature, and wind data at five-minute intervals. Occasional data gaps were filled with data from a neighboring station 1.6 km away (KTNJONES7, data available at https://www.wunderground.com/dashboard/pws/KTNJONES7), with only 21 of 2282 study days missing weather data. See [19] for a detailed list of weather data gaps and coverage.

From these data, four precipitation parameters were generated for each measurement period: (1) Duration (total minutes of rainfall); (2) Total Accumulation (total precipitation in mm); (3) Average Intensity in mm/min (Total Accumulation/Duration), and; (4) Maximum Intensity in mm/min (the greatest station-reported rain rate during the measurement period). The rain rate is a smoothed function of rain accumulation over time that is calculated using the ratio of the tipping bucket depth-adjusted volume to the time between tips. As rainfall tapers off, the rate drops but does not reach zero immediately upon cessation of precipitation. Instead, it smooths the rate to more accurately represent how precipitation naturally tapers over an area at the end of a rain storm [22].

Prior research has shown that antecedent precipitation may be an important factor in erosion, and therefore a series of antecedent precipitation parameters were generated for the prior eleven measurement periods, for each of Duration, Total Accumulation (TotAcc), Average Intensity (AvgInt), and Maximum Intensity (MaxInt). These antecedent lagged variables were named Duration-1, Duration-2 ... Duration-11, TotAcc-1, TotAcc-2 ... and so-on, a total of 48 precipitation parameters, which we refer to as lagged precipitation parameters.

The relationship between erosion variables and all precipitation parameters was assessed with Spearman correlation coefficients. Ordinary Least Squares (OLS) regression models were created for the nine erosion variables using the set of current and lagged precipitation parameters. Further, because seasonal variability in erosion was observed in prior studies [13,19], the data were partitioned by season: winter (December, January, February); spring (March, April, May); summer (June, July, August); and autumn (September, October, November). OLS regression models were generated for the erosion variables using the precipitation parameters for each of the seasonal datasets.
