A comprehensive runoff variation evaluation system of the Yarlung Zangbo River based on vague sets Open Access

Natural runoff processes are important for maintaining river environments and aquatic ecosystems (Jardim et al. 2020), and the primary environmental factors include flow, sediment, water temperature, and other essential elements of biogenic substances. Whether river runoff processes are normal is an important standard from which to assess whether river ecosystems can operate healthily. This consideration is not only related to the process involved in river energy and material exchange but also affects the relationships between all types of organisms. However, with the intensification of human activities in recent years, accelerated hydropower development has affected the temporal and spatial evolution of the downstream flow, sediment, and water temperature, resulting in different degrees of variation in runoff processes compared with natural conditions. Approximately half of all river reaches globally have diminished connectivity due to flow regulation by dams and reservoirs. Built river infrastructure can affect riverine connectivity either directly through the impeding effect of the structure itself or indirectly through alterations to the hydrological, thermal, and sediment regimes (Grill et al. 2019). The Yarlung Zangbo River (YZR) basin is located in the hinterlands of the Tibetan Plateau. Due to its special geographical conditions, it has a fragile ecosystem and is highly sensitive to climate change (Yao et al. 2019). In recent years, increasing attention has been given the hydrological variation in the YZR. Studies have shown that the climatic factors and hydrological conditions in the YZR basin have changed (Chen 2012; Li et al. 2015). These studies have preliminarily described the variations in several hydrological elements of the YZR, but the comprehensive effect of runoff change at multiple timescales requires further investigation.

At present, there is no unified definition of runoff variation. Variation in runoff can be recognized when the change in runoff has a significant impact on the ecosystem (Macnaughton et al. 2017). From a broader perspective, variation can be observed when the patterns and characteristic parameters of runoff processes have significantly deviated from the natural situation. As important environmental elements in river systems, the flow process directly reflects the runoff characteristics, the sediment transport process is the major carrier of important biogenic substances, and the water temperature could affect biochemistry and biochemical processes. These three factors form an important system of material and energy transport in rivers. Therefore, it is necessary to establish the relationship between physical flow processes and ecological processes by introducing sediment and water temperature to describe runoff in a more comprehensive way. Regarding the change in the flow process, Richter et al. (1997) proposed the range of variation approach (RVA) in 1997 based on indicators of hydrological alteration (IHA) to evaluate the degree of river hydrological regime change, and this method has been widely used. However, the RVA method has shortcomings and has been improved by some researchers (Zhang et al. 2019). In addition, the RVA method only describes the hydrological situation from the perspective of the flow, ignoring other factors that affect runoff processes, such as sediment and water temperature processes. Moreover, the existing studies on the impact of hydropower development on the water environment (including river runoff, sediment, water temperature and water quality, etc.) are mostly limited to descriptive analysis. Due to the lack of a set of unified quantitative indicators to evaluate the flow, sediment and water temperature processes, it is difficult to understand the environmental effects of cascade reservoir construction systematically (Ji et al. 2017). Therefore, constructing a set of evaluation indicator systems that can comprehensively assess the variability in the flow, sediment and water temperature under runoff regulation is of great value for the sustainable development of water resources.

Investigators have used a variety of statistical methods to study runoff changes (Tian et al. 2019). However, these statistical methods are primarily based on the change in hydrological sequence quantity and occurrence frequency to measure the variation in the indicators, ignoring the fuzziness of hydrological phenomena. There are a large number of fuzzy concepts in hydrological phenomena, such as the definition of the influence of reservoir construction on downstream runoff processes. Gau & Buehrer (1993) proposed the vague sets concept in 1993; because vague sets can express the fuzzy nature of various events well, this method has been widely used in recent years.

In this paper, the comprehensive runoff variation system of the YZR was constructed based on the spatiotemporal characteristics of water flow, sediment, and water temperature. The primary objectives were as follows: (1) The variation indicators were identified based on the IHA system and the characteristics of the flow, sediment and water temperature processes. (2) A comprehensive runoff variation evaluation system of the YZR was constructed by determining a reasonable threshold value and the weight of each indicator and by using the improved vague sets to determine the calculation method for each indicator. (3) The comprehensive variability in the flow, water temperature and sediment processes of the YZR during the development period of the Zangmu Hydropower Station was quantified. The findings of this research can help to support the scientific management of the water resource supply in the YZR.

The runoff, sediment, and water temperature data from hydrological stations during 1956–2000 for this study were obtained from the Hydrological Bureau of Tibet. Dongsa, Semai and Mirui are three water quality monitoring sections in the main stream of the YZR, and they are located in the lower reaches of the Nianchu River, Lhasa River and Niyang River, respectively; their geographical distributions are very close to the Yangcun Nugesha and Nuxia hydrological stations. A total of 50 years of measured data from the Lhaze, Nugesha, Yangcun and Nuxia hydrological stations (Figure 1) with long time-series data from 1956 to 2000 and 2009 to 2013 were selected. For a few missing data points, data from adjacent stations with good correlations were used for regression interpolation. These data include daily flow, daily sediment, and monthly water temperature data.

The Yarlung Zangbo River is the highest river in the world, originating on the southwestern Tibetan Plateau, and it is an important international river (Cai et al. 2017). It has a total length of 2,840 km, and the basin area is approximately 935,000 km². This paper addresses the Lazi-Paixiang reaches of the YZR. The elevation of the river is 2,911 m to 3,996 m, and the length of the river is 941 km. The Zangmu Power Station was built in 2010 and began operating at the end of 2014. The region belongs to the temperate semiarid plateau monsoon climate zone and has a low annual average temperature of 6.3 °C to 8.4 °C, and the study area is within one of the three regions with the lowest water temperature in China. The annual average sediment concentrations at the four stations of Lhaze, Nugesha, Yangcun and Nuxia in the primary stream are 0.079 kg/m³, 0.279 kg/m³, 0.19 kg/m³ and 0.184 kg/m³, respectively. From the point of view of the meteorology, water temperature and sediment characteristics, the YZR basin shows significant specificity. In this paper, the Lhaze, Nugesha, Yangcun and Nuxia hydrological stations in the main stream of the YZR were selected as representative stations. These stations are evenly distributed geographically and reflect the changing characteristics of hydrological elements in the main stream of the YZR (Figure 1).

Equation (2) is the vague sets and similarity measure. When ⁠, the larger the value is, the higher the similarity of vague sets A and B.

To reflect the importance of each indicator in the evaluation system more comprehensively and objectively, the combination of the analytic hierarchy process and entropy weight was used to determine the comprehensive weight of each assessment indicator.

The specific steps for using the analytic hierarchy process (AHP) to determine the weight of indicators are generally as follows:

• (1)

  Construction of judgement matrix:

The relative importance of n indicators at the same level can be judged by decision makers in pairs, and the numbers 1–9 and their reciprocal can be used as scales to define the judgement matrix (Table 1), to obtain the quantitative analysis results. Where a_ij is the value of a pairwise comparison of the importance between row index i and column index j in judgement matrix A.

• (2)

  Weight calculation

The geometric average of each line vector for judgement matrix A is calculated and normalized, and the resulting row vector is the weight vector.

Let l_max be the maximum eigenroot of the matrix A and W be its corresponding eigenvector; then, AW = l_maxW. The specific calculation steps are as follows:

① The judgement matrix A is the product of each row⁠.

② Calculate the nth root of Mi⁠.

③ Normalize the vector ⁠, ⁠, where w is the index weight.

④ Calculate the maximum eigenroot of the judgement matrix A,⁠.

• (3)

  Consistency test of the judgement matrix.

To determine whether the judgement matrices of different orders pass the consistency test, it is necessary to introduce the average random consistency index RI value of the judgement matrices (Table 2).

Only when CR<0.10 is the judgement matrix considered to have satisfactory consistency; otherwise, the judgement matrix should be adjusted appropriately.

The specific calculation steps are as follows:

The Mann-Kendall trend test method was used to analyse whether the trend in each indicator was significant.

At a given confidence level a, if ⁠, the null hypothesis is not valid, and the sequence at a confidence level has significant trends. If Z > 0, the sequence has a significant upward trend; if Z < 0, the sequence shows a significant downward trend. However, if ⁠, the original hypothesis is true, and the sequence has no significant change trend. If Z > 0, then the sequence has no significant upward trend; and if Z < 0, then the sequence shows no significant downward trend. In this paper, we took a = 0.05, then ⁠.

The idea for constructing the evaluation system was as follows: first, based on the IHA system, the PCA was primarily adopted to select indicators of flow, the sediment and water temperature indicators were established based on the analysis of hydrological characteristics, and the quantile method was used to determine the threshold of the indicators. The AHP and the EWM were used to determine various indicators of empowerment, and the improvement of vague sets was used to determine the indicators of the membership function. The difference in the vague value of each indicator under natural conditions and runoff regulation can be calculated by using the indicator membership function, and the comprehensive runoff variability before and after runoff regulation can be calculated from the degree of variation and the weight of the indicator to complete the construction of the runoff variation evaluation system in the YZR. Figure 2 shows a summary on the construction of the evaluation system.

Based on the principles of mutual independence, representativeness and systematicness among the indicators, the selection of assessment indicators in this paper was primarily divided into three categories: flow indicators, sediment transport indicators and water temperature indicators.

Based on the IHA system and using the measured water flow of the Nuxia Hydrological Station of the YZR from 1956 to 2000, the specific values of 32 hydrological indicators (Table S2-1 of supplementary material (2)) in each year are obtained, and Pearson correlation analysis is carried out. As shown in Figure 3(a), the absolute value of the correlation coefficients among these 32 hydrological indicators ranged from 0 to 1, and some hydrological indicators were significantly correlated. The November to May (dry season) flow indicator had a strong correlation. The correlation between the annual maximum 1-day, 3-day, 7-day, 30-day and 90-day flows was strongest, with an average of 0.97. According to Figure 3(b), the absolute value of the correlation coefficient between most indicators and other indicators can reach 0.75 or even 0.9. Among the 23 indicators, 25% of the absolute value of correlation coefficients with other indicators was greater than 0.5, and among the 9 indicators, 50% of the absolute value of correlation coefficients with other indicators was greater than 0.5.

In conclusion, the correlations between the 32 IHA indicators were high, and the problem of information redundancy was clear. Therefore, it is particularly important to screen the metrics on this basis.

As shown in Figure 4, the eigenvalues of 32 principal components (PCs) showed a precipitous decline. Starting from the first principal component, the eigenvalues declined rapidly; the decline then became slightly gentle and finally tended to a straight line. The eigenvalue of PC1 was 15.65, and the contribution rate was 48.92%. The eigenvalue of PC2 was 4.54, and the contribution rate was 14.19%. The eigenvalues of PC1 to PC5 were all greater than 1, and the cumulative contribution rate reached 82.46%. According to the principle of the PC extraction, PC1-PC5 were identified as the required PCs.

The load values of PC1-PC5 are listed in Table 3. The IHA indicators with similar load values in each PC formed small clusters (as marked by shadows in the table). These cluster groups indicated which set of IHA indicators were dominant in a particular PC and could be used to further explain the PC axis. In PC1, the flow for December (Q_Dec) had the highest load value. The indicators related to PC2 were primarily I_Qbase and the time of occurrence of annual extreme flow. In PC3, the indicators were primarily the D_Qlow, flow change rate and frequency. The indicators related to PC4 were primarily Q_May and the frequency and duration of low flow in a year (N_Qlow, D_Qlow). The main correlation with PC5 was June water flow (Q_Jun). Because the variables with the highest load value can be selected from each PC to replace the PC (Yu et al. 2010), the explanatory variables for PC1-PC5 as selected in this study were Q_Dec, I_Qbase, D_Qlow, N_Qlow and Q_June, which were relatively independent from one another.

The variation in the annual average flow and suspended sediment transport rate at Nuxia Station in the main stream of the YZR (Figure 5) showed that the annual variation trends in the suspended sediment transport rate and flow were basically the same. Based on the linear fitting of the annual sediment transport and annual runoff of the YZR, a good linear relationship between water and sediment was found (Figure 6), and the Pearson correlation coefficient between the two variables is 0.936 (⁠⁠). Thus, the variation in annual sediment transport in the main stream of the YZR under runoff regulation can be revealed indirectly through the variation in annual runoff. In addition, considering the importance of the impact of flood passage on sediment transport in maintaining riparian biodiversity, it is particularly important to characterize the hydrological indicators of flood duration in rivers driven by meltwater from ice and snow (Grams et al. 2020). According to statistics, the annual average sediment transport of Nuxia Hydrological Station was 16.398 million tons, and the sediment transport accounted for 85.4% of the annual sediment transport during the primary precipitation period from June to September, which showed that the flood peak discharge had an important influence on sediment transport. As a further supplement, the monthly or seasonal duration of a high sediment transport rate (S_30max, S_90max) and the occurrence time of extreme sediment transport were selected as sediment indicators. Because the correlation between the annual maximum 30-day suspended sediment transport rate (S_30max) and the selected flow indicators was relatively low, the occurrence time of the maximum sediment transport rate (Date_Smax) had greater ecological significance than the minimum-time transport rate (Date_Smin). As a result, the final choices of sediment indicators were S_30max and Date_Smax.

To evaluate the energy transport in the river system and the change in the basic conditions of biochemical reactions comprehensively, a specific water temperature indicator was introduced in this paper. Based on the evaluation indicators of water temperature change proposed by Tang et al. (2013), we established indicators to represent water temperature change from the perspectives of the amplitude, phase and extreme value.

• (1)

  Water temperature amplitude indicator

Lastly, 10 runoff variation assessment indicators were selected: Q_Jun, Q_Dec, I_Qbase, D_Qlow, N_Qlow, S_30max, Date_Smax, I_TA, I_TP and I_TE. (Table S2–2 of supplementary material (2)).

The AHP and EWM were used to calculate the weight coefficients of each indicator, and the results are shown in Table 4. Among them, the weight coefficient of S_30max is the greatest, at 0.22, and that of Q_Jun is the lowest, at 0.04. In addition, I_Qbase and D_Qlow have high weight coefficients. The weight coefficients of other indicators are low, at not more than 0.1.

Based on the analysis of the interannual variation trend in each assessment indicator, we determined the threshold with quantiles according to the length and integrity of the sequence to eliminate the extreme values. The reasonable thresholds of the flow indicators in this study were determined by the 95% and 5% quantiles of the historical hydrological series (1956–2000), the sediment indicators were determined by the 90% and 10% quantiles, and the reasonable thresholds of the water temperature indicators were determined by the extreme value. As seen in Figure 7, except for a few extreme years, each indicator basically fluctuated within the defined upper and lower limits, and the extreme values were clearly eliminated in this limit range. The number of low-flow years (N_Qlow) was not high (1–4 times), but the low-flow years (D_Qlow) had a reasonable threshold value of up to 156 days. The indicator of great value that appeared in 1970 reached 278 days. Compared to the Yichang gauging station of the Yangtze River basin hydrological sequence (Li et al. 2007), which had low flow over 9.8–91 days at the extreme value of the lower limit, the annual duration of low flow in the middle reaches of the YZR was longer and had specificity (Table 5).

In referring to the standard measure of change in river hydrological indicators (the RVA) proposed by Richter et al. (1997), the comprehensive evaluation standard for evaluating the degree of variation in runoff in the main stream of the YZR was constructed (Table 6).

In using the hydrological data of Nuxia Hydrological Station in the main stream of the YZR before 2000 as the reference group under natural conditions (reference group), the variation assessment was performed according to the river conditions from 2010 to 2013 (assessment group), during the development period of the Zangmu Hydropower Station, which was the first hydropower station on the main stream of the YZR. The hydrological years from 1956 to 2000 that were closest to the annual runoff rate from 2010 to 2013 were selected to form four groups of ‘reference assessment groups’ to measure the comprehensive variability in the flow, water temperature and sediment processes in the main stream of the YZR during the development of the Zangmu Power Station. Figure 8 is a schematic diagram of the variation in annual hydrological indicators, and most of the assessment indicators for each hydrological year were within the reasonable range of variation. In 2010 and 2011, only one indicator exhibited low variation, namely, D_Qlow and I_TP, respectively. In 2012, I_TA and I_TE exhibited low and moderate variation, respectively. In 2013, I_TE and S_30max exhibited low and moderate variation, respectively. In addition, the differences in water temperature extremes in 2012 and 2013 were 11.3 °C and 11.8 °C, respectively, which was indeed small compared with the range of 13.8–14.9 °C in the reference group (1956–2000), with given variation. The comprehensive variation degrees of runoff during the hydrological years from 2010 to 2013 were 0.20, 0.16, 0.15 and 0.17, respectively, none of which exceeded 0.33, and all of which were within a reasonable range (Table 6). The detailed comprehensive variability results on annual hydrological runoff from 2010 to 2013 are shown in Tables S2–3 ∼ S2–6 of the supplementary material (2).

In summary, compared with the situation of the main stream of the YZR before 2000, the comprehensive variation degree of runoff in the YZR from 2010 to 2013 was within the reasonable variation range (Table 6). This result may be attributed to the restoration and improvement of vegetation cover in the region, resulting in a more uniform distribution of maximum runoff during the year (Li et al. 2021).

Compared with similar research results (Table 7), due to the different hydrological characteristics of different rivers, the assessment indicators screened out here were not the same, but they reflected some commonalities. For example, all the results in the table included indicators such as the annual extreme flow and duration and the occurrence frequency and duration of high and low flow, indicating that these two indicators are of great importance for describing river hydrological regimes. The five indicators selected in this study covered three types of indicators in the IHA system: monthly flow, annual extreme flow and duration, and occurrence frequency and duration of high and low flow; however, they did not include indicators of the occurrence time and rate of change for annual extreme flow. Minckley & Meffe (1987) noted that the indicator of the change rate was necessary to describe seasonal rivers (intermittent rivers). However, the main stream of the YZR never stops flowing, and the lack of a change rate indicator will not have a great impact on the comprehensiveness of the description of the river. In view of the above analysis, the flow indicators screened according to the PCA not only greatly reduced the data redundancy but also retained the information from the original data.

The rationalities of this study were analysed as follows: (1) We selected flow indicators compared with other similar research results (Table 7). Due to different river hydrological features, the assessment indicators screened out here were not the same, but they reflected some commonalities and showed that the flow indicators screened according to the PCA not only greatly reduced the data redundancy but also well retained the information from the original data. For the sediment indicators, the analysis in Section 3.1.2 showed that there was a good linear water-sediment relationship between the annual sediment transport and the annual runoff. In addition, considering that the sediment specificity of the YZR, S_30max and Date_Smax were ultimately obtained, they were of extremely representative importance. The water temperature indicators were established from the three factors of amplitude, phase and extreme value, which revealed the basic conditions of energy transport and biochemical reaction in the river system. (2) The subjective AHP and the objective EWM were combined to determine the comprehensive weight of each assessment indicator, which reflects the importance of each indicator in the measurement index system more comprehensively and objectively. (3) The Mann-Kendall trend test was used to analyse each indicator (Table 8). I_Qbase showed a significant downward trend, which was caused by the decrease in annual runoff. Both S_30max and Date_Smax showed a downward trend, while I_TP and I_TE showed no significant decline. The test results were consistent with the evaluation results of various indicators. (4) An analysis of the precipitation and air temperature before 2000 and 2010–2013, revealed that the extreme values of precipitation and air temperature appeared before 2000 (Table 9), in which the maximum value of precipitation appeared in 1998, at 291.3 mm, and the maximum value of air temperature appeared in 1983, at 16.3. Compared with the data from before 2000, the coefficient of variation (Cv) for precipitation from 2010 to 2013 was 0.14, and the Cv of the air temperature was 0.04. Compared with that before 2000, the climate changes in precipitation and air temperature from 2010 to 2013 were not significant. The climate change characteristics of precipitation and air temperature are shown in Figure S2–1 of the supplementary material (2).

Due to the limitations of the basic data and the selected research methods, there may be some uncertainties in the research, primarily including the following points: (1) Due to the different accuracies of the flow, sediment and water temperature sequences of the YZR obtained in this study, different methods were adopted for the screening of various indicators, primarily based on the PCA, namely the water sediment relationship, amplitude, phase and extreme value. When river and lake assessments are made for different basins or different screening methods are used for specific concerns and conservation objectives, the resulting evaluation system may change. For example, regarding concern about how much the spawning of a particular fish is disturbed by runoff regulation, the time frame of concern can be narrowed to a specific period of its normal spawning, and the target can be reset according to the conditions (flow rate, water temperature, etc.) required to address concerns about spawning. (2) Due to the relative lack of sediment and water temperature data of the Nuxia Station master series of the YZR, there are some limitations in the representativeness of the sediment and water temperature data and the accuracy of the reasonable threshold values of the sediment and water temperature indicators determined in accordance with the principle of eliminating extreme data. This approach may need to be refined in the future with more observational data. (3) Due to the randomness of hydrological series, we defined the variation interval of [0.00,0.33] as a reasonable variation range, with specific uncertainty, by referring to the RVA standard of the river hydrological indicator proposed by Richter et al. (1997). (4) In determining the indicator weights, the combination of subjective AHP and objective EWM was adopted, and there was subjective uncertainty. (5) Using 1956–2000 as the natural runoff state of the YZR, a comprehensive runoff variation evaluation system was constructed, and used to evaluate the comprehensive runoff variability of the YZR during the construction period of the Zangmu Power Station, focusing on the impact of human activities on the runoff. No single system distinguished the effects of climate change, such as precipitation and air temperature, and there was some uncertainty.

The comprehensive evaluation system of the runoff variation in the YZR constructed in this paper is a preliminary framework of the evaluation system, which provides a new approach for measuring runoff variation. In future research, further improvements could include measuring the cumulative effect of the cascade development of hydropower resources on runoff to provide a reference for establishing guiding principles and an optimization model for the adaptive use of water resources.

To quantify the comprehensive variation degree of runoff under runoff regulation in the main stream of the YZR, we formulated a comprehensive runoff variation evaluation system and the primary results are as follows:

• (1)

  The flow, sediment transport and water temperature processes were considered to describe the river runoff processes. Compared with the IHA system, the variation in sediment and water temperature was considered, and reduced the flow indicator redundancy, which was beneficial for the application in practical management.

• (2)

  A comprehensive evaluation system for runoff variation was developed based on vague sets. This study can provide a new approach for evaluating runoff variability in other basins or in the case of specific conservation targets.

• (3)

  The variation index of Nuxia Station on the YZR from 2010 to 2013 was 0.15–0.20 compared with the situation before 2000, which was within the reasonable variation range, indicating that the YZR was not greatly disturbed by human activities such as reservoir construction.

This work was supported by the National Natural Science Foundation of China (grant nos. 51909176 and 52079083).

Data cannot be made publicly available; readers should contact the corresponding author for details.