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 .