2.4 Cumulative sum charts
We used the cumulative sum (CUSUM) to demonstrate graphically long phases of the suspended sediment discharges. The CUSUM charts section with an ascending trend indicated a period in which the values were above the overall average. Similarly, the section with a descending trend showed a period in which the values were below the overall average.
This approach is relatively robust compared to other tests (Buishand, 1982) for a change-point that occurs toward the time series center (Kundzewicz and Robson, 2004). We used the techniques developed by Taylor (2000) that combine CUSUM charts and bootstrapping to compute 10000 iterations of the CUSUM chart. This approach is widely used in hydroclimatic studies (e.g., Mavromatis and Stathis, 2011; Fischeret al. , 2012; Salerno et al. , 2012; Liuzzo et al. , 2017). We did all computations in R using the ChangePointTaylor package (Marks, 2020).
For each change, this change-point analysis approach estimates (1) a confidence level, indicating the likelihood (with a confidence level of ≥80%) of that change and (2) a confidence interval (with a confidence level of ≥95%), indicating the time of the specific change occurred. This method also controls the change-wise error rate and is robust to outliers. More regarding this approach can be found in Taylor (2000).
We also applied a Pettitt (1979) test for single-point detection, another widely used technique (Zhang et al. , 2008; Gao et al. , 2011; Rets et al. , 2020). This rank-based nonparametric technique can be more robust as it is distribution-free and insensitive to outliers and data skewness. It tests the time series for a single change in the mean with an exact unknown time of transition.
Multiple regression models were used to impute missing values in mean annual suspended sediment discharges. Models explained 68% of the variance in SSD on average. They included as predictors an annual sum of liquid precipitation (P , mm), number of wet days in a year (n_rain , days), simple precipitation intensity index (SDII ), mean annual air temperature (Tav , °C), number of warm days (with the average daily air temperature above 5°C) in a year (Tsum , days). These parameters were estimated based on meteorological observations at seven meteorological stations: Kluhorskij pereval, Gudermes, Vladikavkaz, Kazbek mountain, Nalchik, Shadzhatmaz, and Oni (see Fig. 1 for their location). Model description and performance metrics are presented in Supplementary 2.
Daily summaries of air temperature and precipitation were provided by the NOAA Global Historical Climate Network from their website https://www.ncdc.noaa.gov/cdo-web/. We used a +2.0 °C rain-snow temperature threshold (i.e., the 50% rain-snow air temperature threshold estimated by Jennings et al. (2018)) to estimate P andSDII .