An Estimation Method of River Dry Runoff Alteration after Upper New Reservoirs Storage

Abstract

The impact of reservoirs on downstream river hydrological characteristics is always a focal point in relevant studies exploring the relationship between rivers and dams. Anticipating river runoff patterns following the construction of new dams is crucial for the design of riverine engineering projects, particularly during dry periods. This paper presents a semi-theoretical estimation method based on the correlation between hydrological alterations and reservoir operation. The method incorporates differences in runoff increment distribution and the discrepancy between theoretical and practical results. It was validated and applied in the sub-basins of the upper reaches of the Yangtze River, namely the Jinsha River and Min River. The runoff increment during the driest month for the Jinsha River and the Min River is 817 m³/s and 434 m³/s, respectively. The estimated prediction biases were within 30% of the practical runoff increments observed in the Jinsha River and Min River, which is an acceptable range considering the inherent variability in such studies. Since the construction of the Wudongde and Baihetan dams in 2021, the average runoff during the driest month and the navigation assurance runoff at a 95% probability were predicted to be 2866 m³/s and 2174 m³/s, respectively. Therefore, the method developed in this paper provides a reasonable and straightforward tool for researchers, which can help prevent future engineering invalidation and minimize resource costs. Moreover, in the application process, this method requires careful consideration of the characteristics of the studied river section and the operation of the reservoir group. It relies on measured data to determine the differences between theoretical and actual runoff rather than simply generalizing to all watersheds.

1. Introduction

Over the past decades, numerous reservoirs have been constructed in the southwest region of China, leading to significant alterations in the hydraulic characteristics of upstream rivers in China; correspondingly, the upstream river hydraulic character has been seriously altered [1,2,3,4]. However, considering the critical importance of water supply, shipping development, power generation, and ecological conservation, there are plans to construct reservoirs of varying sizes along the mainstream and tributaries of the upper basin of the Yangtze River in the future. The extent of the impact on river hydrology following the construction of reservoirs has consistently been a popular and widely discussed topic, attracting considerable attention from researchers in the field.

It is widely acknowledged that the river flow undergoes alterations on an annual, monthly, and daily basis after upper cascade reservoir storage. The quantitative variations are generally close to the storage capacity but may differ slightly [5,6,7,8,9]. In general, reservoirs can be classified into three types based on their regulating characteristics: multi-annual regulating, annual regulating, and non-annual regulating. Multi-annual regulating reservoirs, such as the Xiluodu-Xiangjiaba reservoirs in the upper Yangtze River, have the capacity to modify water resources on an interannual basis, partially mitigating the impact of basin meteorological variations. Annual regulating reservoirs primarily bring about seasonal changes in river flow, typically resulting in reduced downstream discharge during the flood season and increased discharge during the dry season. The specific alterations depend on the reservoir control mode [10,11].

In recent years, the alteration of river hydrological characteristics has been associated with another significant factor, namely climate variation [12,13]. With the gradual rise in temperature, precipitation and evaporation within larger spatial watersheds occur simultaneously, influencing the processes of runoff yield and concentration. Consequently, researchers have made efforts to isolate the individual impacts of climate variation and reservoir storage. Various hydrological datasets spanning several decades have been utilized, employing different regression models, wavelet methods, and other techniques to analyze the aforementioned impacts [14]. Downstream runoff exhibits close variability with meteorological variables and is significantly influenced by dam construction [15]. However, the long-term average runoff over multiple decades can encompass the combined effects of climate change. Ultimately, the impact of climate change becomes evident over an extended period of time.

Regarding the hydrological factors influenced by reservoir operations, considerable attention has been focused on downstream river discharge and sediment load [16,17,18,19]. Regardless of whether the reservoir operates on a multi-annual, annual, or daily basis, the total runoff volume in a year is relatively less adjusted, except for climate variations. However, the construction of dams has led to a significant reduction in sediment load by intercepting the entire river flow [20,21,22,23]. As a result of these pronounced alterations, various aspects of river functioning have been extensively studied, including riverbed regime, riverbank stability, waterway hydraulic conditions, and ecosystem health [24]. Consequently, to mitigate these impacts, different recommendations for adjusting reservoir operation schedules have been proposed. For example, downstream river flood processes have become more subdued, with fewer multi-peak natural floods occurring after reservoir storage, and the seasonal water temperature cycle has experienced slight delays [25,26]. These new variations have directly impacted the reproductive process of Chinese carp following the construction of the Three Gorges Dam, prompting the development and practical utilization of optimized scheduling to simulate a more natural flood pattern since 2011.

Due to their importance as crucial waterways and their significant roles in the Chinese Southwest communication nets, the mainstream and certain tributaries of the upper Yangtze River have drawn increasing attention to their impact on channel hydraulic conditions. This attention has particularly focused on the cascade reservoirs of the Three Gorges, Xijiangba, and Xiluodu in the mainstream, as well as Pubugou and Zipingpu in the Min River tributary. The accumulation of sand sediment in the upper reservoirs has resulted in the discharged flow carrying less sand than during natural stages, disrupting the original balance of erosion and deposition in the downstream riverbed. This disruption has led to intense scouring, water level decline, and insufficient depth in critical waterways. Conversely, in certain instances, the waterway depth has significantly improved in the upper reservoir regions, and there has been an increase in dry season runoff to some extent. In summary, the impact of cascade reservoir construction cannot be simply defined as good or bad; rather, it involves complex aspects, processes, and extents that continue to attract ongoing research and investigation.

However, previous research has predominantly focused on the impact of downstream river hydrological changes after dam construction, while giving little attention to the prediction of river attributes. To date, nearly no theoretical method has been reported for accurately estimating future river runoff, despite its importance for river regulation and waterway construction. In the past, artificial values or additional designs were often employed to compensate for this lack of prediction, resulting in wasteful practices and potential engineering invalidation. For instance, if the previous runoff was underestimated, downstream waterway regulations would require deeper channel dredging, consuming additional resources and potentially causing excessive water level declines in the navigation locks of the dam. It is therefore crucial to develop a reliable method for predicting river runoff alterations to avoid unnecessary costs and ensure the effectiveness of engineering projects.

This paper aims to develop an estimation method for calculating the alteration of river dry runoff after the construction of new upper reservoirs. The method is based on an analysis of the relationship between reservoir storage capacity, regulation schedule, and historical river runoff changes in the upper watershed of the Yangtze River. As a rank-based non-parametric test for detecting monotonic trends in time series, the Mann-Kendall (M-K) test is suitable for trend test of hydrological data [27,28,29,30]. The long-term hydrological data from multiple key measurement stations were systematically analyzed using methods such as the Mann-Kendall test, dividing them into different periods corresponding to the construction of the dam.

The hydrological data alterations were then resolved considering the regulated schedules of relevant cascade reservoirs, resulting in the development of a theoretical estimation method. The validity of the method was assessed using hydrological data from the Jinsha River and Min River basins over the past decade. Furthermore, the method was utilized to predict future river runoff based on the designed adjustive storage capacity of the reservoir.

2. Background and Methodology

2.1. Study Area Background

The Yangtze River, with a length of 6397 km, is the largest river in Asia. It flows from west to east, ultimately reaching the East China Sea at Shanghai. The river’s geographic coordinates range from E90° to E122° longitude and from N25° to N35° latitude. The upper reach of the river is divided at Yichang, and it encompasses several major tributaries, including the Yalong River, Min River, Tuo River, and Jialing River. The segment of the mainstream that is upstream of YiBin is also known as the Jinsha River.

This paper proposes a river runoff estimation method primarily based on historical hydrological data from the Jinsha River and Min River basins, which converge at YinBin to form the Yangtze River. The Jinsha River spans a length of 2136 km, with a watershed area of 473,200 km². Its largest tributary, the Yalong River, is located approximately 550 km upstream of YinBin. Xiangjiaba has served as the control hydrological station for the Jinsha River since the construction of the Xiangjiaba dam in 2012. Prior to that, the control station was Pingshan, situated around 30 km upstream of Xiangjiaba. The Min River, on the other hand, stretches for 735 km, with a watershed area of 135,800 km². Its largest tributary is the Dadu River, located 135 km upstream of YinBin. Gaochang serves as the control hydrological station for the Min River, situated 25 km upstream of YinBin.

Due to the objectives of water supply and electricity generation, numerous dams have been constructed since 2000. As of 2020, there were four major dams in the Jinsha River watershed: Xiajiaba, Xiluodu, Ertan, and Jinping 1st, with the former two located along the mainstream. According to the latest cascaded reservoir plan, two additional dams, Baihetan and Wudongde, will be added along the mainstream in the next two years, while Lianghekou will be constructed on the Yalong River, a tributary of the Jinsha River. Similarly, as of 2020, four major dams have been built in the Min River watershed: Zipingpu, located on the mainstream, and Pubugou, Houziyan, and Changheba, situated on its largest tributary, the Daduhe. In the next five years, an additional major dam, Shuangjiangkou, is planned for the Daduhe. Detailed information and the distribution of the aforementioned dams are shown in

Table 1. Designed information of the studied reservoirs.

River	Reservoir	Storage Time	Adjustable Volume (Billion m3)	Adjustable Capacity
Min River	Zipingpu	2006	0.8	Non-annual regulating
Dadu River	Pubugou	2010	3.9	Non-annual regulating
	Houziyan	2018	0.4	Non-annual regulating
	Changheba	2018	0.4	Non-annual regulating
Jinsha River	Xiangjiaba	2014	0.9	Annual regulation of the combine
	Xiluodu	2014	6.5
	Baihetan	2021	10.4	Multi-annual regulating
	Wudongde	2021	3.0	Annual regulating
Yalong River	Ertan	2000	3.4	Annual regulating
	Jinping 1st	2014	4.9	Multi-annual regulating

and Figure 1.

2.2. Hydrological Characteristics Alteration

To analyze the impact of dam storage on the downstream river hydrological characteristics, long-term historical datasets of the Jinsha River (Pingshan hydrological station, 1956–2011 and Xiangjiaba hydrological station, 2012–2020) and Min River (Gaochang hydrological station, 1980–2020) were collected from the Hydrologic Data Year Book of the People’s Republic of China (P.R.C.). The hydrological data officially released has undergone error analysis and corrective measures during the compilation process, resulting in high data accuracy, thus making it directly suitable for analyzing the hydrological characteristics of rivers.

2.2.1. Jinsha River

According to the hydrologic data statistics during 1956–2020, the muti-annual average discharge of Jinsha River was 4483 m³/s, the maximum annual average runoff was 6205 m³/s (occurring in 1988), and the minimum one was 3190 m³/s (occurring in 2011). The total tendency of the annual average runoff was not sharp but fluctuated, and the maximum variable amplitude was 1700 m³/s, which indicated that the climate of the upper basin of the Yangtze River had not changed much. Just like other monsoon climate watersheds, the average month was seriously different in a year; the flood period was from June to October, during which the total runoff was 65.1% of water volumes in a whole year. Accordingly, only 14.6% of water volumes in a whole year were distributed in the dry period from December to April of the next year.

In light of the significance of dry discharge for ship navigation, urban water consumption, and ecological maintenance, the trend in dry discharge variation was further analyzed using the Theil-Sen median trend method combined with the Mann-Kendall [30,31] test. As a robust trend calculation method, the Theil-Sen median trend method is frequently employed alongside the MK test to identify trend variations in long-term sequential data [32,33]. Through trend test analysis of the monthly average flow of the Jinsha River in February and March from 1956 to 2020, the Theil-Sen median value was calculated as 10.53, with a normalized test statistic Z of 4.48, exceeding the 95% confidence level of 1.96. This indicates a clear increasing trend in the monthly average discharge during the dry period. However, the time series variation process can be divided into three stages, and this paper adopts the M-K mutation detection method, as shown in Figure 2a. The UF and UB are calculated sequence test statistics. Since 2000, the sequential test statistic UF has consistently been positive, indicating that the dry discharge has continued to increase. The point at which the UF and UB curves intersect within the confidence interval represents the computed breakpoint. The curves of Mann-Kendall test statistic UF and UB intersected in 2014, although this intersection was not within the confidence zone but only approached it.

The Pettitt change point test and cumulative anomaly method were employed to further analyze the aforementioned catastrophic events. The Pettitt change point test is based on non-parametric analysis and can identify a single change point in a sequence. However, it is limited to detecting only one change point and is often used in combination with other methods. The cumulative anomaly method entails plotting a cumulative series displaying the differences between each value in a time series and the series’ mean value. By scrutinizing the inflection points on the resultant cumulative anomaly curve, this method identifies breakpoints or change points. The results demonstrated that significant inflection points occurred in 1998 and 2012. Consequently, the construction of the Ertan, Xiluodu, Xiangjiaba, and Jinping 1st dams took place in 1998 and 2012, respectively. It is evident that the dam construction in the Jinsha River had a notable impact on alterations in dry discharge. As a result, catastrophic alterations were observed with the construction of Ertan in 2000, and Xiluodu and Jinping 1st in 2014. During the first stage, spanning from 1955 to 2000 the monthly average discharge amounted to 1343 m³/s. Following the completion of the Ertan Reservoir, the average discharge increased to 1718 m³/s during the second stage from 2001 to 2014. With the completion of the Xiluodu, Xiangjiaba, and Jinping 1st Dams in 2014, the average discharge further increased to 2379 m³/s, as shown in Figure 2b.

After the construction of the first major dam, Ertan, in the Jinsha River basin, which began impounding in 2000, as mentioned earlier, a noticeable increase in monthly average runoff was observed during the dry period, ranging from 12 to 423 m³/s, with the highest values occurring in March. Conversely, a slight attenuation was observed during the flood period, ranging from 157 to 465 m³/s, with the highest values in October. Subsequently, with the completion of the Xiluodu, Xiangjiaba, and Jinping 1st dams in 2014, a greater increase in monthly average runoff was observed during the dry period, ranging from 234 to 1253 m³/s. Additionally, a more significant attenuation was observed during the flood period, ranging from 547 to 1574 m³/s, compared to the situation before 2000, when no dam construction had taken place, as shown in Figure 3b. It highlights the substantial impact on downstream river hydraulic characteristics resulting from the implementation of cascade reservoirs.

2.2.2. Min River

Based on the hydrologic data analysis during 1980–2020, the muti-annual average runoff discharge of Min River was 2697 m³/s; the maximum annual averaged runoff was 3430 m³/s in 2020; and the minimum one was 2010 m³/s in 2006. The total tendency of the annual averaged runoff of the Min River was more moderate than that of the Jinsha River, and the maximum was only 733 m³/s of negligible fluctuation. Because of the vicinage of the basins of the Min River and Jinsha River, the variable character of monthly average runoff alteration was basically similar in a year, namely, the flood period from June to October and the dry period from December to April of the next year. The percentage of the whole-year water volume of the flood period and dry period was 60.4% and 14.0%, respectively.

The dry discharge variation trend of the Min River was also further analyzed by the Theil-Sen median trend method combined with the Mann-Kendall test. Through the trend test analysis of monthly average discharge of Min River in January and March. during 2006–2020, the Theil-Sen median value was calculated as 28.3, with a normalized test statistic Z of 4.48, exceeding the 95% confidence level of 1.96, which indicted that the monthly average discharge increased significantly in the dry, as seen in Figure 4a. And the M-K mutation shows that UF has always been positive since 2010, namely that dry discharge has still increased. The curves of UF and UB intersected in 2010, which was located in the confidence zone. Therefore, the mutation time was preliminarily determined to be 2010.

Further, combined with the Pettitt change point test and cumulative anomaly method, it could be seen that the main inflection points emerged in 2010, consistent with the Pettitt test results. Therefore, the catastrophic time of the dry discharge was in 2010, which was just the construction time of Pubugou in the Dadu River. Hence, the construction of the dam in the Min River Basin had a significant impact on the dry discharge. Monthly average discharge in the first stage during 2006–2010 was 918 m³/s, and after the completion of the reservoir of Pubugou, the discharge in the second stage during 2011–2020 was incremented to 1223 m³/s, as seen in Figure 4b.

Similar to the above mentioned, when the cascade reservoir conduction, Zipingpu, in Min River was built in 2006, some increment of monthly average runoff during the dry period occurred by 51–128 m³/s, and attenuation of average runoff during the flood period was 607–1676 m³/s monthly. Subsequently, when a series of dams along the Dadu River were built from 2010 to 2018 in Pubugou, Houziyan, and Changheba, the monthly average runoff variation became more obvious. The increment during the dry period was 157–541 m³/s compared with the situation of no dam construction before 2006; accordingly, the attenuation during the flood period was 441–856 m³/s, as seen in Figure 5b.

2.3. Estimation Method Development

2.3.1. Correlation of Hydrological Alteration and Reservoir Operation

The cascade reservoirs in the upper reaches of the Yangtze River serve multiple functions, including flood prevention, water supply, electricity generation, ecology conservation, and ship navigation. Consequently, the operational principle of these reservoirs is focused on peak clipping during the main flood period and compensation during the dry period, as depicted in Figure 2b and Figure 3b, considering the observed alterations in river runoff discussed in Section 2.2.1 and Section 2.2.2. It is important to highlight that the magnitude of downstream river runoff alteration is highly dependent on the regulation capacity of the cascade reservoirs.

For the gap between flood month and dry month, i.e., May in the pre-flood period and October in the post-flood period, the alteration of monthly average runoff was relatively complex. The reservoir would be declined to maintain a relatively low water level in advance of the main flood, resulting in an increase of 764 m³/s in the Jinsha River in May. However, the virtual increment was close to the succedent flood climate prediction, and more obvious alteration always emerged in a large basin, e.g., a little attenuation of 220 m³/s in Min River, oppositely.

During the post-flood period, reservoirs typically store water to ensure sufficient supply for water and electricity generation in the subsequent dry season. As a result, a relative attenuation of river runoff is observed in October. Before 2014, this attenuation was evident in Jinsha River (465 m³/s) and Min River (607 m³/s), with Min River experiencing a more pronounced decrease due to its smaller basin size. However, the significant decline in downstream river runoff has been mitigated due to efforts in ecology restoration. In recent years, the decrease in Min River’s runoff has been reduced to only 157 m³/s.

Although there is an obvious increase in river runoff during the dry season, the presence of dams also introduces a notable difference. The highest increments typically occur in February to March, which were the months with the lowest runoff before the construction of dams. For example, in the Jinsha River, the increment ranged from 817 to 1254 m³/s. However, after the implementation of compensation measures for the driest month, the variation of the monthly average runoff during the dry period becomes smaller. In the Jinsha River, the runoff was 849 m³/s in the absence of dams before 2000, and it reduced to 384 m³/s between 2014 and 2020 with the presence of multiple dams. Similarly, a similar change from 398 to 324 m³/s was observed in Min River.

2.3.2. Method of River Runoff Increment Estimation during the Dry Season

Based on the correlation between downstream river hydrological alterations and reservoir operation during the dry period, an estimation method was developed to predict the increment of river runoff in the dry season when additional dams are constructed in the future. The framework of this estimation method is illustrated in Figure 6.

To address the concerns regarding ship navigation and ecology restoration, the estimation method focused on the minimum runoff. The following steps outline the details of the estimation method, using the month with the minimum runoff as an example:

Firstly, based on the observed alterations during the dry period after the construction of previous dams, the percentage increment of the driest month within the total increment during the dry period (P₀) can be calculated by

$$P_0=\Delta Q_{driest Month }^0/\Delta Q_{dryPeriod }^0$$

(1)

where $\Delta Q_{driest Month }^0$ is the practical increment of the driest monthly average runoff and $\Delta Q_{dryPeriod }^0$ is the sum of the monthly average runoff increment during the dry period.

Secondly, the theoretical increment of the driest monthly average runoff after the previous dams were built ($\Delta Q_{driest Month}^0$) can be calculated by

$$\Delta Q_{driest Month }^{0\prime }=P_0\times {\displaystyle \sum V_{adjustable}^0}/(D_{driestMonth}\times 24\times 3600)$$

(2)

where ${\displaystyle \sum V_{adjustable}^0}$ is the sum of the adjustable capacity of upstream cascade reservoirs and $D_{driestMonth}$ is the total days in the driest month.

Then, the $De{v}_0$, which is the bias between the practical runoff increments and the theoretical in the driest month, can be expressed as

$$De{v}_0=(\Delta Q_{driest Month }^{0 }- \Delta Q_{driest Month}^0)/\Delta Q_{driest Month }^0$$

(3)

Thirdly, according to Equation (2), the theoretical increment of the driest monthly average runoff after the future dams are built ($\Delta Q_{driest Month }^{1\prime }$) can be obtained by

$$\Delta Q_{driest Month }^{1\prime }=P_0\times {\displaystyle \sum V_{adjustable}^1}/(D_{driestMonth}\times 24\times 3600)$$

(4)

where ${\displaystyle \sum V_{adjustable}^1}$ is the sum of the adjustable capacity of upstream cascade reservoirs in the future.

By following the above steps, the predicted increment of the driest monthly average runoff after the future dams built, $\Delta Q_{driest Month}^1$, can be obtained by

$$\Delta Q_{driest Month }^1=\Delta Q_{driest Month }^{1\prime }\times (1-De{v}_0)$$

(5)

3. Results and Discussion

3.1. Method Validation

To account for inter-annual climate fluctuations, the long-term effects of cascaded reservoirs’ operation were utilized to validate the proposed estimation method in this study. The historical hydrological data was divided into two periods based on the commencement of major reservoirs’ storage. The first period represents the purely natural condition without any dams, while the second period represents the regulated situation after the completion of the main reservoirs’ construction. This division provides suitable validation data for evaluating the performance of the estimation method.

3.1.1. Jinsha River

In the Jinsha River basin, a total of four major reservoirs were constructed between 2003 and 2014, with a combined adjustable capacity of 15.7 billion m³. Analysis of the historical recorded data from 2014 to 2020 revealed that the runoff increment mainly occurred during the period from November to May of the following year. Specifically, the majority of the increments took place from January to May, accounting for approximately 90% of the total increments.

The runoff increment in the driest month, i.e., February, was 817 m³/s, which was 16% among the total increments. Thus, based on Equation (2), the theoretical increment of the driest month could be calculated.

The runoff increment in the driest month, specifically February, was determined to be 817 m³/s, accounting for approximately 16% of the total increments. Therefore, based on Equation (2), the theoretical runoff increment for the driest month can be calculated as 1028 m³/s.

Compared with the practical increment of 817 m³/s, the bias, $De{v}_0$, was 26%, as seen in

Table 2. Increase in downstream river flow due to the construction of key projects in the Jinsha River Basin.

Reservoir		Monthly Average Runoff Increase in February
Name	Adjustable Volume (Billion m3)	Theoretical (m3/s)	Deviation
Ertan + Xiluodu + Jinping 1st + Xiangjiaba	15.7	1028	26%

. The reason for this deviation was probably that the theoretical increment was the ideal status and the entire utilization of the adjustive capacity of upstream cascade reservoirs. However, the operation mode of reservoirs was so explicated that it could not exactly be considered in the estimation. Moreover, the studied reservoir was located widely; the farthest one was about 900 km upstream from Xiangjiaba station, so there were water inflow and evaporation along the river in all probability.

When comparing the practical increment of 817 m³/s with the theoretical increment, a bias ($De{v}_0$) of 26% was observed. This discrepancy can be attributed to the fact that the theoretical increment represents an ideal scenario, assuming the full utilization of the adjustable capacity of upstream cascade reservoirs. However, the actual operation mode of the reservoirs is more complex and may not align precisely with the ideal conditions considered in the estimation. Additionally, the studied reservoirs are located over a wide area, with the furthest one positioned approximately 900 km upstream of the Xiangjiaba station. Along such a long stretch of the river, there are other factors to consider, including water intake and evaporation, which can further contribute to the deviation between the theoretical and practical increments.

3.1.2. Min River

The runoff increment in the driest month, i.e., February, was 434 m³/s, which was a proportion of 21.8% among the total increments. Similarly, the theoretical runoff increment of the Min River in the driest month was calculated.

In the Min River basin, four cascade reservoirs with a total adjustable capacity of 5.5 billion m³ have also been constructed since 2006. According to the hydrologically recorded data from 2011 to 2020, it was observed that the runoff increment during the dry period ranged from 157 m³/s to 541 m³/s. This dry period runoff increment accounted for approximately 99% of the total increments in the river.

Focusing on the driest month, February, the runoff increment was measured at 434 m³/s, which constituted around 21.8% of the total increments. Based on this information, the theoretical runoff increment for the driest month in the Min River can be calculated as 492 m³/s using the previously mentioned equation.

Compared to the practical increment of 434 m³/s, the bias $De{v}_0$ in the calculated result for the Min River was 13%, which was lower than the deviation observed in the Jinsha River estimation, as seen in

Table 3. Increase in downstream river flow due to the construction of key projects in the Min River Basin.

Reservoir		Monthly Average Runoff Increase in February
Name	Adjustable Volume (Billion m3)	Theoretical (m3/s)	Deviation
Zipingpu + Pubugou + Houziyan + Changheba	5.5	492	13%

. This could be attributed to the fact that in a smaller basin, the influence of other factors on the runoff increment was relatively smaller compared to the impact of dam operations. Additionally, the calculated result falling within an acceptable deviation of less than 30% further validates the estimation method proposed in this paper. It is important to note that a certain level of bias is a common occurrence in studies related to climate variation and hydrological alteration.

3.2. Runoff Prediction

In practice, the construction of the Baihetan and Wudongde dams was completed in 2021. However, it should be noted that the full impact of these dams on river runoff will take several years to manifest. Additionally, the recorded hydrological data for the most recent year has not yet been published. Therefore, the runoff increments in the driest month, February, after the implementation of these two dam projects, were predicted using the estimation method proposed in this paper.

According to the designed parameters of the dams, the additional adjustable capacity was 13.5 billion m³. Similarly, the theoretical increment of the driest month could be calculated as 893 m³/s. Given the practical bias of the theoretical result at 26%, a more precise increment of 654 m³/s could be calculated using Equation (5), as seen in

Table 4. Prediction of downstream river flow increase due to hydropower development in the Jinsha River Basin.

Reservoir		Monthly Average Runoff Increase in February
Name	Adjustable Volume (Billion m3)	Theoretical (m3/s)	Deviation
Ertan + Xiluodu + Jinping 1st + Xiangjiaba	15.7	1028	26%
Wudongde + Baihetan	13.4	654 (Deduction deviation)

.

In other words, the predicted result suggests that the monthly average runoff in February is expected to increase from 2212 m³/s to 2866 m³/s following the construction of the Baihetan and Wudongde dams.

The differences in the regulating storage capacity and operational scheduling methods of reservoir groups in various basins, along with factors such as in-stream water withdrawals and evaporation, result in variations in the increase of dry season flow caused by the addition of the same adjustable storage capacity in the Jinsha River and Min River, as depicted in Figure 7.

For channel regulation engineering, the assurance runoff is a critical parameter in the design process. Currently, the design standard for the channel from YinBin to Chongqing aims to ensure that ships with a loading capacity of 2000 t can navigate 95% of the time throughout the year. This corresponds to a 95% assurance runoff. Based on the recorded data of the Jinsha River, the assurance runoff since 2014, when the Xiluodu and other dams were constructed, has been measured at 1749 m³/s. This represents an increase of 527 m³/s compared to the period prior to the construction of any dams before the year 2000.

According to the analysis of the daily averaged runoff distribution throughout the year, it is observed that the period with daily averaged runoff below the 95% assurance runoff threshold is primarily concentrated in the driest month, which is February. It is likely that the runoff increments will also occur for most of the month of February. Therefore, we can estimate the predicted increment of the 95% assurance runoff by considering the ratio of the assurance runoff increment to the monthly average runoff increment in February, which has been found to be approximately 0.65. By utilizing this ratio, we can estimate the future 95% assurance runoff after the construction of dams in the Jinsha River using the following equation:

$$Q_{P=95\%}^1=Q_{P=95\%}^0+\Delta Q_{driest Month}^1\times (\Delta Q_{P=95\%}^0/\Delta Q_{driest Month}^0)$$

(6)

where, $Q_{P=95\% }^1$ is the predicted assurance runoff of 95%, $Q_{P=95\% }^0$ is the practical assurance runoff of 95%, and $\Delta Q_{P=95\% }^0$ is the practical assurance runoff increment of 95%. Thus, the predict value of the assurance runoff of 95% was 2174 m³/s, which is obtained by

$$Q_{P=95\% }^1=1749+654\times 0.65=2174 {\mathrm{m}}^3/\mathrm{s}$$

(7)

Recently, there has been little relevant reporting on runoff estimation after the construction of reservoir clusters. The method developed in this paper provides a reasonable and straightforward tool for researchers, which can help prevent future engineering invalidation and minimize resource costs. However, this method requires careful consideration of the characteristics of the studied river reach and the management of reservoir clusters during its application. It is crucial to determine the disparities between theoretical and actual runoff based on available measured data rather than simply generalizing these findings to all river channels.

4. Conclusions

Previous studies have primarily focused on the practical impacts of cascade reservoirs on downstream river hydrological characteristics, with limited attention given to the prediction of these impacts when dams are built in the future. Particularly, the estimation of runoff, a crucial factor for future engineering design, has received little attention. This paper addresses this gap by proposing an estimation method for predicting river runoff during the dry period based on the correlation between hydrological alterations and reservoir operations. The method is validated and applied using relevant datasets from the Jinsha River and Min River basins. The developed method takes into account the differences in the increment distribution of monthly average runoff during the dry period and the bias between theoretical and practical results. By considering these factors, the method provides a comprehensive approach for predicting the impacts of dam construction on river runoff.

Due to the primary objectives of reservoir operation, including flood control, water supply, electricity generation, and ecological conservation, downstream river runoff exhibited a decrease during the flood period and an increase during the dry period. The M-K trend tests and catastrophic analysis conducted on the Jinsha River and Min River demonstrated that the mutation times of monthly average discharge during the dry period corresponded to the construction of dams in the river basins. In both the Jinsha River and Min River basins, over 90% of the runoff increment was concentrated between January and May, resulting in respective runoff increments of 234–1253 m³/s and 157–541 m³/s. The proposed method was validated with deviations of 26% for the Jinsha River and 13% for the Min River, which are relatively common in studies concerning climate variations and hydrological alterations. Considering the recent construction of Baihetan and Wudongde dams in 2021, the predicted values for the average runoff during the driest month and the 95% navigation assurance runoff were 2866 m³/s and 2174 m³/s, respectively.

The developed method presented in this paper offers a practical and efficient tool for researchers in the field, ensuring the avoidance of engineering invalidation and unnecessary resource costs in the future. The method requires careful consideration of the characteristics of the studied river section and the operation of the reservoir group in the application process. It relies on measured data to determine the differences between theoretical and actual runoff, rather than simply generalizing to all basins. Further research could utilize coupling models and similar approaches to refining the correlation between hydrological changes and reservoir operations, expanding the temporal scale to daily or ten-day intervals. Additionally, investigating the proportion of dry months among the total runoff increments based on the long-term impact of dams using methods such as trend analysis will provide valuable insights. This will contribute to a more comprehensive understanding of the effects of reservoir operation on hydrological patterns and enable better predictions and management strategies for water resource systems.