## Abstract

The concept of overall hydrological alteration degree in the traditional range of variability approach is no longer suitable for the requirements of the current changing environment. First, by introducing the analytic hierarchy process and including the concept of deviation in the range of variability approach, the traditional range of variability approach is improved. Second, by using the daily flow data from the Guide gauging station in the lower reaches of Longyangxia reservoir from 1954 to 2017 and by combining the concept of connection degree in set pair analysis, a more comprehensive overall hydrological alteration degree is obtained. Finally, based on the results of overall hydrological alteration degree in each period, a dynamic evaluation model of overall hydrological alteration degree is established based on a set pair analysis–Markov chain method. The results show that the overall hydrological alteration degree of the Longyangxia reservoir in the postimpact period is at the second level; its average is −0.43, but its identity tends to increase. Furthermore, the dynamic evaluation model shows that the overall hydrological alteration degree of its stable state will be 0.1726, its impact flow changes and its stable state will be at the third level. This is a positive developing trend.

## INTRODUCTION

Dam building remains an important means of water resources utilization in modern society. While bringing economic benefits, dams seriously affect the natural flow of riverine water and thus impact the ecological environment of the downstream river (Graf 1999). Due to these concerns, ecological considerations have become more and more influential in the regulation of reservoirs. The range of variability approach (RVA) method can assess the flow changes caused by human disturbance using 32 indicators of hydrological alteration (IHA). Thus, this method is commonly used to study changes in ecological and hydrological indicators before and after dam construction (Alrajoula *et al.* 2016; Sojka *et al.* 2016), and it also has made many great achievements (Mittal *et al.* 2016; Lin *et al.* 2017). Yu *et al.* (2016) proposed a revised RVA method to better reveal the alteration of hydrological characteristics over a hydrological year, thus enhancing the accuracy of estimates of flow regime changes. In addition, these cited studies have mostly focused on changes in each individual indicator, while studies of the overall hydrological alteration degree (OHAD) are rare. In fact, in the traditional RVA method, there is a simple three-level evaluation system that uses a simple average weight for each indicator. This does not accurately reflect flow changes because it fails to fully weigh the degree of influence of each indicator. Furthermore, current research on hydrological regime changes using the RVA method has not considered the temporal uncertainty of hydrological information (Kumar & Sen 2017). As hydrological time series lengthen, studies of changes in flow during preimpact and postimpact periods must consider the uncertainty and dynamics of hydrological data in a changing environment. The analytic hierarchy process (AHP) method is commonly applied to solve the hierarchically structured and complex evaluation and decision problems of hydrology and water resources (Wang *et al.* 2003). By introducing the concept of deviation from the RVA method into the AHP method, the mutual influence of different hydrological indicators can be determined more effectively and the estimation of the OHAD made more reliable and reasonable.

The characteristics of hydrological events become more uncertain in a changing environment, and this will lead to greater uncertainty. After dam construction, consequently altered hydrological indicators will have unpredictable influences on the OHAD. In 1989, the Chinese scholar Zhao (1994, 1997) proposed the set pair analysis (SPA) method to explain the uncertainty between two variables with the identity, discrepancy, and contrary. SPA is widely used and was developed in the field of hydrology, and it makes hydrological studies more objective and effective (Gang *et al.* 2018; Shu *et al.* 2018).

Furthermore, current studies on hydrological regimes influenced by human activities emphasize a static evaluation at a single time: potential future dynamic trends are not evaluated or predicted. A Markov chain (MC) is a stochastic process used to analyze the variation characteristics of time series, and it can be used to project the dynamic transformation of hydrological variables (Dong *et al.* 2012). Using a combination of SPA and MC, the uncertainty and dynamic features of variables can be better displayed. In recent years, the SPA-MC dynamic assessment method has been gradually developed in the field of security risk dynamic assessment, and many scholars have used it in the study of safety status, protection performance status, and safety management ability (Zhang *et al.* 2016; Yang *et al.* 2017) to solve problems involving information uncertainty and the dynamic analysis of data. There are occasional applications in hydrology, but the SPA-MC method is still evaluated as seriously insufficient.

So the innovation of this study is to construct a dynamic evaluation model of overall hydrological alteration degree with the SPA-MC method to reveal the uncertainty and dynamic features, and also to represent the river flow change trend affected by the reservoir in the future. Based on the daily flow data of the preimpact period (1954–1985) and the postimpact period (1988–2017) from the Guide gauging station, 32 IHA indicators are considered. First, the relative weights of the indicators are determined. Second, their hydrological alterations are calculated. Third, the OHAD of the hydrological flow is estimated by the SPA method. Finally, combining the RVA and SPA-MC methods, the dynamic evaluation model of OHAD is used to analyze and predict hydrological changes and trends in the reservoir.

## MATHEMATICAL METHODS

### Outline of the mathematical methods

The dynamic evaluation model of the overall hydrological alteration degree includes the following steps: (1) data series are collected and prepared to be analyzed; (2) the RVA method is applied to show the hydrological alteration degree; (3) using the AHP method, the objective weighting indicators system is established and using the SPA method, the uncertain relations (including the identity, the discrepancy and the contrary) of OHAD are exhibited; and (4) with the SPA-MC method, the dynamic evaluation model of OHAD is shown. Figure 1 shows the outline of the mathematical methods.

### RVA

Richter *et al.* (1998) proposed using the RVA method to assess changes in natural flow affected by human activities, considering 32 indicators called IHA. IHA can be classified into five groups (as shown in Table 1), which display the annual flow changes, the time, frequency, duration, and change rate of extreme hydrological conditions.

IHA statistics group | Regime characteristics | Hydrological parameters |
---|---|---|

Magnitude of monthly water conditions | magnitude timing | mean value for each calendar month |

Magnitude and duration of annual extreme water conditions | magnitude duration | annual minima 1-day means |

annual maxima 1-day means | ||

annual minima 3-day means | ||

annual maxima 3-day means | ||

annual minima 7-day means | ||

annual maxima 7-day means | ||

annual minima 30-day means | ||

annual maxima 30-day means | ||

annual minima 90-day means | ||

annual maxima 90-day means | ||

number of zero-flow days | ||

base flow index: 7-day minimum flow/mean flow for year | ||

Timing of annual extreme water conditions | timing | Julian date of each annual 1-day maximum |

Julian date of each annual 1-day minimum | ||

Frequency and duration of high and low pulses | magnitude frequency duration | number of low pulses within each water year |

mean or median duration of low pulses (days) | ||

number of high pulses within each water year | ||

mean or median duration of high pulses (days) | ||

Rate and frequency of water condition changes | frequency rate of change | rise rates |

fall rates | ||

number of hydrological reversals |

IHA statistics group | Regime characteristics | Hydrological parameters |
---|---|---|

Magnitude of monthly water conditions | magnitude timing | mean value for each calendar month |

Magnitude and duration of annual extreme water conditions | magnitude duration | annual minima 1-day means |

annual maxima 1-day means | ||

annual minima 3-day means | ||

annual maxima 3-day means | ||

annual minima 7-day means | ||

annual maxima 7-day means | ||

annual minima 30-day means | ||

annual maxima 30-day means | ||

annual minima 90-day means | ||

annual maxima 90-day means | ||

number of zero-flow days | ||

base flow index: 7-day minimum flow/mean flow for year | ||

Timing of annual extreme water conditions | timing | Julian date of each annual 1-day maximum |

Julian date of each annual 1-day minimum | ||

Frequency and duration of high and low pulses | magnitude frequency duration | number of low pulses within each water year |

mean or median duration of low pulses (days) | ||

number of high pulses within each water year | ||

mean or median duration of high pulses (days) | ||

Rate and frequency of water condition changes | frequency rate of change | rise rates |

fall rates | ||

number of hydrological reversals |

*i*-th IHA, is the number of years in which the

*i*-th IHA falls within the RVA target range in the postimpact period, is the expected number years falling within the RVA target range in the postimpact period, and is the proportion of IHAs falling within the RVA in the preimpact period. If the RVA target range includes the 25th and 75th percentiles values, ; is the total number of years in the postimpact period.

indicates no alteration or low HAD, indicates moderate HAD, and indicates high HAD.

Thus, if the 32 IHA indicators are given specific weights, the OHAD can be obtained by summing them.

### SPA

*N*characteristics of the setting pair (A, B) and then to sort these characteristics into three classes: identity characteristics, discrepancy characteristics, and contrary characteristics. Thus, the connection degree of the set pair (A, B) can be expressed as: where is the connection degree,

*O*is the number of identity characteristics,

*P*is the number of discrepancy characteristics,

*Q*is the number of contrary characteristics, and

*N*is the total number of characteristics.

*j*is specified as −1.

### MC

is called the MC. The MC explores the observation that the value of at time is only related to the value at time and has no relation to the observation value of earlier times. is the conditional probability, also called the state transition probability.

## DYNAMIC EVALUATION MODEL OF THE OHAD

### Evaluation indicator system and indicator weight

The evaluation indicator system of the OHAD is defined by five groups of hydrological parameters and 32 secondary IHA indicators in the RVA method (as shown in Table 1).

*i*-th IHA in the preimpact and postimpact periods as follows: where is the deviation of the

*i*-th IHA, is the

*i*-th IHA in the preimpact period, and is the

*i*-th IHA in the postimpact period.

Using the actual calculated and the classification of each indicator on the judgment matrix 1–9 scale range, as determined by experts, the weights of the secondary indicators are finally achieved.

### Determination of OHAD

*A*and indicator change degree is set

*B*. The indicator system and indicator alteration degree can form a set pair for OHAD evaluation; then, the indicator weights are introduced into the SPA method. Assuming that at time

*t*, within the total of 32 hydrological indicators, indicators have a high change degree, indicators have a moderate change degree, indicators have a low change degree, and, all together, the indicators satisfy . Thus, the connection degree of set

*A*and set

*B*can be expressed as: where is the weight of the secondary indicators in different states,

_{,}

_{,}, and is the connection degree. The connection degree is the OHAD.

The values of OHAD can be divided into five classes using the equipartition method and are expressed from high to low as fifth level, fourth level, third level, second level and first level. Therefore, represents fifth level; represents fourth level; represents third level; represents second level; represents first level.

## DYNAMIC EVALUATION MODEL ESTABLISHMENT OF THE OHAD

### State transition probability matrix

*t*show high alteration and that after time , there are IHA indicators still showing high alteration, IHA indicators showing moderate alteration, IHA indicators showing low alteration, and , the state transition probability matrix of IHA indicators in the time interval is: where and .

### Establishment of dynamic evaluation model

*E*is the identity matrix, and is the average state transition probability matrix.

### Study area and data

The Longyangxia reservoir is located on the main stream of the Yellow River in Republic County and Guide County of Qinghai Province. This reservoir is the first large-scale hydropower station in the upper reaches of the Yellow River and is the leading reservoir of the Yellow River Main Reservoir Group. The Guide gauging station is the first gauging station in the lower reaches of the Longyangxia reservoir (as shown in Figure 2). In October 1986, the Longyangxia reservoir began to store water, which greatly changed the river's flow conditions and had an important influence on the river basin ecosystem.

To analyze the flow variations impacted by reservoir operation clearly, the 1986 and 1987 flow data from the Guide gauging station are removed because 1986.10–1987.02 is the reservoir storage period. Thus, the daily flow data from the Guide gauging station is divided into two periods: the preimpact period (1954–1985) and the postimpact period (1988–2017).

## RESULTS AND DISCUSSION

### Weights of the 32 IHA indicators

According to the adjustment matrix, the weights of the 32 IHA indicators at the Guide gauging station are shown in Table 2.

IHA indicators | Sequence number | Weight | IHA indicators | Sequence number | Weight |
---|---|---|---|---|---|

Jan | ω_{1} | 0.0077 | 90-day min | ω_{17} | 0.0156 |

Feb | ω_{2} | 0.00844 | 1-day max | ω_{18} | 0.0344 |

Mar | ω_{3} | 0.01286 | 3-day max | ω_{19} | 0.02072 |

Apr | ω_{4} | 0.05113 | 7-day max | ω_{20} | 0.01797 |

May | ω_{5} | 0.07783 | 30-day max | ω_{21} | 0.0156 |

Jun | ω_{6} | 0.06273 | 90-day max | ω_{22} | 0.0156 |

Jul | ω_{7} | 0.03942 | Base flow | ω_{23} | 0.02736 |

Aug | ω_{8} | 0.0503 | Date min | ω_{24} | 0.03942 |

Sep | ω_{9} | 0.0344 | Date max | ω_{25} | 0.07235 |

Oct | ω_{10} | 0.03942 | Low pulse count | ω_{26} | 0.00328 |

Nov | ω_{11} | 0.08799 | Low pulse duration | ω_{27} | 0.0231 |

Dec | ω_{12} | 0.02025 | High pulse count | ω_{28} | 0.00518 |

1-day min | ω_{13} | 0.06273 | High pulse duration | ω_{29} | 0.0181 |

3-day min | ω_{14} | 0.04634 | Rise rate | ω_{30} | 0.01286 |

7-day min | ω_{15} | 0.02519 | Fall rate | ω_{31} | 0.00481 |

30-day min | ω_{16} | 0.0181 | No. of reversals | ω_{32} | 0.0288 |

IHA indicators | Sequence number | Weight | IHA indicators | Sequence number | Weight |
---|---|---|---|---|---|

Jan | ω_{1} | 0.0077 | 90-day min | ω_{17} | 0.0156 |

Feb | ω_{2} | 0.00844 | 1-day max | ω_{18} | 0.0344 |

Mar | ω_{3} | 0.01286 | 3-day max | ω_{19} | 0.02072 |

Apr | ω_{4} | 0.05113 | 7-day max | ω_{20} | 0.01797 |

May | ω_{5} | 0.07783 | 30-day max | ω_{21} | 0.0156 |

Jun | ω_{6} | 0.06273 | 90-day max | ω_{22} | 0.0156 |

Jul | ω_{7} | 0.03942 | Base flow | ω_{23} | 0.02736 |

Aug | ω_{8} | 0.0503 | Date min | ω_{24} | 0.03942 |

Sep | ω_{9} | 0.0344 | Date max | ω_{25} | 0.07235 |

Oct | ω_{10} | 0.03942 | Low pulse count | ω_{26} | 0.00328 |

Nov | ω_{11} | 0.08799 | Low pulse duration | ω_{27} | 0.0231 |

Dec | ω_{12} | 0.02025 | High pulse count | ω_{28} | 0.00518 |

1-day min | ω_{13} | 0.06273 | High pulse duration | ω_{29} | 0.0181 |

3-day min | ω_{14} | 0.04634 | Rise rate | ω_{30} | 0.01286 |

7-day min | ω_{15} | 0.02519 | Fall rate | ω_{31} | 0.00481 |

30-day min | ω_{16} | 0.0181 | No. of reversals | ω_{32} | 0.0288 |

It can be seen from Table 2 that after the beginning of reservoir operation, the deviations in the mean monthly flows in January, February, and March, as well as the low pulse count, high pulse count, rise rate, and fall rate, have been larger. Except for the mean monthly flows of May and November, which are 1-day maximum flows, the deviations are generally greater. Therefore, just estimating from the deviations, it can be roughly seen that the hydrological flow of the postimpact period is in a state of high alteration.

### Hydrological alteration of the 32 IHA indicators

The postimpact period is divided into six periods: 1988–1992, 1993–1997, 1998–2002, 2003–2007, 2008–2012, and 2013–2017. According to the RHA method, the hydrological alteration of the 32 IHAs in these six periods can be calculated as shown in Figure 3. Number 3 represents high HAD, number 2 represents moderate HAD, and number 1 represents low HAD.

### OHAD

If the IHA indicators in Table 2 are used to define A, the HA in Figure 3 defines B, and the connection degree of pair (A, B) is then calculated, the OHAD of the hydrological flow is determined as shown in Table 3.

Periods | 1988–1992 | 1993–1997 | 1998–2002 | 2003–2007 | 2008–2012 | 2013–2017 | Average |
---|---|---|---|---|---|---|---|

0.204 | 0.153 | 0.023 | 0.265 | 0.072 | 0.153 | 0.145 | |

0.385 | 0.159 | 0.246 | 0.215 | 0.387 | 0.303 | 0.283 | |

0.411 | 0.688 | 0.731 | 0.520 | 0.541 | 0.544 | 0.572 | |

μ | −0.207 | −0.535 | −0.708 | −0.254 | −0.468 | −0.391 | |

OHAD | second level | second level | first level | second level | second level | second level |

Periods | 1988–1992 | 1993–1997 | 1998–2002 | 2003–2007 | 2008–2012 | 2013–2017 | Average |
---|---|---|---|---|---|---|---|

0.204 | 0.153 | 0.023 | 0.265 | 0.072 | 0.153 | 0.145 | |

0.385 | 0.159 | 0.246 | 0.215 | 0.387 | 0.303 | 0.283 | |

0.411 | 0.688 | 0.731 | 0.520 | 0.541 | 0.544 | 0.572 | |

μ | −0.207 | −0.535 | −0.708 | −0.254 | −0.468 | −0.391 | |

OHAD | second level | second level | first level | second level | second level | second level |

Analyzing the trend characteristics of *a* and *c* (as shown in Figure 4), these trends will increase *μ* and improve the OHAD.

### Predictions of the dynamic evaluation model

Thus, , , and the OHAD still displays the third level.

## CONCLUSIONS

Based on the RVA method and the SPA-MC method, a dynamic evaluation model of the OHAD caused by the Longyangxia reservoir is proposed. The main conclusions are drawn as follows:

- (1)
The HADs of 32 IHA indicators in six periods during the postimpact period are variously different: some indicators have always been highly variable, while others change frequently between high, moderate and low states. Except for during the period of annual maximum flow, the reservoir has a strong impact on riverine flow conditions, especially for the IHA indicators in group 1 and group 2; thus, operation of the reservoir can worsen the original river habitat to some extent, and future operations should pay more attention to the hydrological parameters in these two groups to achieve greater ecological benefits.

- (2)
By introducing the deviation in IHA indicators of the RVA into the AHP method, a more objective system of weighting indicators is established. Moreover, using the combined SPA and MC method, a dynamic evaluation model of HAD is built to provide a new procedure for evaluating reservoir management and guiding reasonable reservoir operation. This paper shows that the OHAD in the Longyangxia reservoir has been greater, and the contrary has always been greater than the identity in the past six periods. The contrary and the identity have a favorable trend in the mid and late periods.

- (3)
Riverine flow changes caused by the Longyangxia reservoir show a good development trend, and the connection degree of its stable state is 0.1276, and the OHAD of its stable state is at third level.

## ACKNOWLEDGEMENTS

This research is supported by the National Key R&D Program of China (Grant No. 2018YFC0406501), the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research (Grant No. IWHR-SKL-KF201802), Outstanding Young Talent Research Fund of Zhengzhou University (Grant No. 1521323002), Program for Innovative Talents (in Science and Technology) at University of Henan Province (Grant No. 18HASTIT014), State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University (Grant No. HESS-1717), Dissertation Foundation for Institute of Water Resources and Environment by Zhengzhou University of China in 2018 and Foundation for University Key Teacher by Henan Province of China in 2017.