2.6 Uncertainty assessment
Uncertainties on suspended sediment load values were simulated by considering the most critical sources of measuring errors. More specifically, other potential SSL values were simulated using the following equation, modified from Vanmaercke et al. (2015):
\(\text{SS}L_{\text{sim}}=SSL\times U_{\text{ME}}+SSL\times U_{\text{FF}}\), (4)
where SSLsim is another potentially true value ofSSL after considering the various sources of uncertainty.UME reflects the uncertainties associated with measuring errors, UFF represents the uncertainty associated with the unmeasured finer fraction. In the original equation from Vanmaercke et al. (2015), two more potential sources of uncertainty are discussed: low sampling frequency and length of measuring period. The latter is not applicable for our data as we are dealing with annual values. We also assumed that sampling frequency might not be a source of uncertainty in our case, as with daily sampling intervals, both bias and imprecision tend to zero (Moatar et al. , 2006).
UME reflects the integrated effect of errors on individual runoff discharge measurements, suspended sediment concentration measurements, and uncertainties due to intra-daily variation in runoff and sediment concentrations not captured by the measurements. Previous studies reported that these errors are commonly 20-30% (Steegen and Govers, 2001; Harmel et al. , 2006; Vanmaercke et al. , 2015). We, therefore, expected that 30% provides a realistic and relatively conservative estimate of the uncertainty on SY-values associated with measuring errors. Hence,UME was simulated as a random number from a normal distribution with a mean of 1 and a standard deviation of 0.30.
However, SSL values derived from measurements at gauging stations in Russia are subject to additional uncertainties associated with filter type and may underestimate the actual suspended sediment load (Chalovet al. , 2019). At Russian gauging stations, suspended sediment concentration is measured by the gravimetric method using paper filters with pore sizes ranging from 2 to 3 µm (so-called «blue tape», de-ashed filters, «ТУ 6-09-1678-86» specification) according to Handbook. One may argue that our results are incomparable with other findings (Kasperet al. , 2018). However, from previous studies (Bogen, 1989; Williams and Rosgen, 1989), we know that the > 5 µm fraction constitutes most of the suspended load in the glacierized and mountainous catchments. Therefore, we assume that our sediment data may be a good indicator of the total sediment output from the study catchments.
To estimate how pore size can impact total suspended sediment concentration, we performed a brief exploratory data analysis of particle size distribution from Williams and Rosgen (1989). We selected only nine mountainous rivers flowing in similar environmental conditions as those presented in this study from their dataset. We found that out of 216 samples mean percent by weight finer than 4 µm is 24.7%, with a corresponding standard deviation of 9.5%. The proportion of finer fraction can vary from 8% to 43% (i.e., the 2.5% and 97.5% quantile) depending on the season and river. Hence, UFF was simulated as a random number from a normal distribution with a mean of 0.247 and a standard deviation equal to 0.095. Evidently,UFF values were restricted to values between 0.08 and 0.43.
Equation 4 was used to simulate respectively 1000 alternative SSLfor every year and every gauging station. From these values, we calculated 95% confidence intervals on every SSL value (i.e., the difference between the 97.5% and 2.5% quantile of the 1000 simulated values).
Buchner et al. (2020) reported that the overall accuracy of the cropland change map is 75.7%, of the forest change map is 90.2 %. Therefore, uncertainties of the landcover change associated with measuring errors were simulated as a random number from a normal distribution with a mean of 1 and a standard deviation of 0.24 for cropland and 0.1 for a forest.
Various data sources (global satellite imagery, aerial photos, and topographic maps) were used to create the Greater Caucasus glacier inventory (Tielidze and Wheate, 2018), so the glacier area error varies through time and between methods from 4.4% to 7.9%. We assumed that an 8% error provides a realistic estimate of the glacier area uncertainty. In the result, the uncertainty was simulated as a random number from a normal distribution with a mean of 1 and a standard deviation of 0.08.