Evolutionary mechanisms and shifting trends in water circulation patterns in a tributary of the Three Gorges Reservoir, China

The Three Gorges Reservoir (TGR), accomplished in June 2003, is among the largest reservoirs including 40 tributaries, encompassing a watershed area exceeding 100 km (Cao et al. 2012). Distinctive flow patterns exist in all reservoirs and tributaries (Pu et al. 2021; Zhao et al. 2021). The interactive predominant factors of inflows, intrusions, respective morphometries and relative modification among them ultimately define types of flow patterns and their mechanisms of circulation in reservoirs and tributaries (Jin et al. 2019; Sun et al. 2021). Hydrodynamic phenomena and biogeochemical aspects are analyzed by transport mechanisms in a water body, which are ultimately defined by different density driven current patterns and time scales such as water age, flush time or water retention time (Chen 2007; Saadatpour et al. 2017). Inflows and outflows are major causes of flow field and circulation patterns in water bodies including reservoirs and tributaries (Pandey et al. 2018). The spatiotemporal alterations in inflow and outflow volumes, temperatures have valuable implications on hydrodynamics and ecological aspects of these water bodies (Bermúdez et al. 2018; Sun et al. 2021).

It is proven that the reflective tributary bays have lesser mixing, different velocities at different layers and greater temperature stratification as compared to the TGR (Li et al. 2020a; Xu et al. 2021). High flow speed produces intense vertical turbulence and potential buoyancy in the TGR, subsequently, stratification and vertical gradient in water temperature are less likely and least effective for most of the year except in pre-dams spring season when it was evident closer to the TGD (Ma et al. 2015). Eventually, the water density values of the Xiangxi Bay (XXB) like other tributaries would be different from those of the TGR mainstream (Ji et al. 2017; Xu et al. 2021). The mutual differences in water temperature and density profiles are among the predominant causative factors for bidirectional water currents and water exchange between the XXB and the TGR (Ma et al. 2015; Xu et al. 2021). The fall in water level results in weakening of intrusions into the tributary bays (Liu et al. 2012; Niemeyer et al. 2018). Inflow occurs either as overflow density currents or bottom density currents due to difference in temperature with water at the upper reach of the tributary bays (Jin et al. 2019; Li et al. 2020b). More water age and temperature stratification favors eutrophication at surface layer and anoxic conditions in deep water of reservoir (Gao et al. 2018; Xu et al. 2021). A lake having less water age and a well-mixed water column does not offer support to algal growth (Wang et al. 2012; Yang et al. 2017). High flow speed results in increased buoyancy and turbulence and decreased vertical temperature gradients in the TGR (Ma et al. 2015; Long et al. 2016). Consequently, the water density values of the bays would be different from those of the TGR mainstream (Ji et al. 2017; Dutta & Das 2020). The mutual differences in water temperature and density values cause water currents and water exchange between the bays and TGR (Ma et al. 2015; Li et al. 2020a; Xu et al. 2021). Differences in surface area and flow dynamics cause temperature and density differences among bays and the main reservoir (Yang et al. 2018), which leads to thermal strata development in bays through density currents (Dai et al. 2019; Xu et al. 2021).

The hyper-concentrated and dilute-concentrated sediments transport also affect density profiles of mainstream besides inflow and outflow volumes. The hyper concentrated profiles exhibits a clear distinction of lower (bed-load) to upper layer (suspended-load) (Pu et al. 2021). These suspended solids provide medium to microbial transport and affect water quality eutrophication (John et al. 2021). The pressure, velocity variations and mixing increase within a waterbody with increased inflow discharges (Al-Obaidi & Mohammed 2019). The stagnant water gets heated faster than fast flowing water (Al-Obaidi 2019). Inflow discharges act as guide vanes in determining flow field and circulation patterns in water body (Al-Obaidi 2020a). Sediments transport through inflows affects density profiles and water flow field. Moreover, cements and other construction material bring changes in turbulence in the estuary of the reservoir and could play a decisive role in flow patterns (Pandey et al. 2018).

If longitudinal flows and vertical flows occur simultaneously, turbulent kinetic energy increases, and this refers to low susceptibility of water body (Al-Obaidi & Mohammed 2019). Atmospheric and inflow forcing and intra-basin circulations are interdependent which ultimately affect flow patterns, freshening, mixing and distribution of salinity, density, water quality parameters and algal blooms (Holliday et al. 2020). Water circulation, mixing and flow field depend on volume and intruding layers of water (Al-Obaidi 2020b). Urban agglomeration water resources and increased anthropogenic activities due to population density have affected hydrodynamic parameters such as density which influence bio-diversity through altered mixing (Zhao et al. 2021).

Development of temperature stratification in a typical tributary is one of the main changes given rise by difference in water temperature between the main stream and a tributary bay (Cao et al. 2012; Chuo et al. 2019). Flow fields, hydrodynamics and ecological aspects in a tributary bay are governed by intrusions and backwater jacking from the TGR which depend on interactive water levels and temperature difference in two bodies (Li et al. 2020a). Changes in weather or hydrologic variables such as inflows, starting elevations and air temperatures had much larger implications on reservoir thermal profiles, range, vertical gradients, and strtaification (Johnson et al. 2004). Circulation patterns depend on horizontal and vertical velocities of inflows and outflows (Al-Obaidi 2021). Therefore, effects of transport mechanisms directly on density profiles of interacting water bodies and indirectly on hydrodynamics and water quality are indispensable. Spatiotemporal hydrological variations such as altered volumes and temperatures of inflows and outflows can alter reservoir thermal profiles, stratification and water retention time as well as those of other water bodies (Johnson et al. 2004; Zhao et al. 2013; Niemeyer et al. 2018). Driven by the interactive water temperature variations between the water in a tributary bay and the TGR, overflow, upper interflow, interflow, lower interflow and underflow intrusions take place from the TGR into the bays (Lai et al. 2014; Long et al. 2019). Overflow and underflow density currents induced by upstream inflows and five distinctive types of intrusion flows have been observed and simulated, which express cumbersome but discernable evolutionary mechanism and shifting trends over seasonal and yearly scales, especially during post-cascade reservoirs stage. The bidirectional density currents are not only dependent on mutually interactive hydrodynamics of the TGR and the XXB but also influencing water dynamics of both water bodies (Xu et al. 2011; Lai et al. 2014). These findings encourage us to evaluate unexplored consequences of changes in the TGR during stage 1, 2008–2010, stage 2, 2010–2013 and stage 3, 2014–2018 and their respective exclusive and additive impacts on density current patterns in the XXB.

Hydrodynamic and ecological simulation models have been developed to analyze density driven currents and their respective effects on water circulation patterns (Zhenli 1999; Ambrose et al. 2009; Li et al. 2020b). 2-D models are adopted extensively for different types of water bodies worldwide, for providing advantages of much finer resolutions in horizontal and vertical directions and better control over numerical dispersion as compared to 3-D models. 2-D models can simulate and predict over longer scales, even across seasons and years, and are numerically cheaper than 3-D models (Kurup et al. 2000; Long et al. 2019).

Different water flow patterns in XXB were manifested in existing research studies for short periods from pre-cascade reservoirs stage from 2008 to 2013. Since upstream cascade reservoirs were produced by newly built Xiluodu Dam (XLD), Wudongde Dam (WDD), Xiangjiaba Dam (XJB) and have changed thermal and discharge dynamics of mainstream TGR, hence, entire hydrodynamical and water quality parameters of mainstream and bays including XXB are deemed to have been changed. In previous research, no hydrodynamical and water quality model was established to correlate data in XXB obtained after upstream cascade reservoirs became operative in 2014 with those of pre-dams stages. Therefore, dearth of knowledge regarding altered discharge dynamics in TGR during post-dams stage (third stage) and unexplored consequences on intruding layers in XXB across seasons drew our attention to opt data for all three stages and to throughly investigate and correlate density current patterns underlying water circulation. Moreover, details of evolutionary mechanism and shifting trends of density current flow patterns and reasons for shifts on seasonal scales, per annum and over the years before and after the construction of upstream cascade reservoirs were still undefined. No attention had been paid to the comparative investigation of changed hydrodynamics (thermal profiles, stratification and range in the TGR during pre- and post-cascade reservoirs stages and their respective impacts on intruding density currents over seasons and years in a tributary bay (XXB).

Keeping in view these information gaps, a 2-D CEQUAL W 2 hydrodynamic model was developed to (1) model and simulate the density-driven bidirectional water currents in the XXB, a reflective tributary bay of the TGR; (2) to recognize, calculate, analyze and categorize density-driven water circulation patterns as per varying upstream inflow and mainstream intrusion positions; (3) to define sequence statistics, evolutionary mechanism and shifting trends of water circulation patterns over seasons and years; (4) to analyze the interactive hydrodynamical developments in XXB and TGR to find reasons for shifting trends of water circulation patterns over seasons and years especially during post cascade dams stage; (5) to correlate and compare the variations in magnitude of total duration (days), frequency (times of occurrence) and longest continuous duration at once of all patterns over seasons and years to illustrate overall shifting trends in effectivity; (6) to analyse thermal establishemnt and discharge dynamics of mainstream TGR after the construction of upstream cascade reservoirs; (7) these findings could be helpful in finding threshold values of temperature, inflow and outflow discharges to trigger effective overflow intrusion in XXB such as 10,000 mg/m³ inflow discharge in spring since 2014; (8) these sustainable overflow intrusions could add to water quality control and effectivity of reservoir to deal with eutrophication.

The construction of Three Gorges Dam (TGD) on the Yangtze River was commenced in 1993 and impoundment took place in 2003. The entire structural and operational unit was completed in 2009 and became operative at maximum water level after 2010. The TGD is one of the largest dams in the world. It caused a huge Three Gorges Reservoir (TGR), in the upper reach of Yangtze River between Yichang and Chongqing cities in Hubei Province of China with maximum water level of 175 m ASL, a storage limit of 3.93 × 10¹⁰ m³, watershed area exceeding 1.00 × 10⁶ km² and surface area reaching 1,080 km² (Chuo et al. 2019). The region has a humid subtropical climate, with an average annual temperature of 17.6 °C, average annual precipitation of 1,122.5 mm and average annual wind speed of 1.3 m/s (MEPC 2012). The reservoir is almost 670 km in length, with an average width and depth of 1.1 km and 90 m (in the mainstream), respectively. The total area of the rainwater catchment which is controlled by TGD is known as Three Gorges Catchment (TGC), which measures almost 1.02 million km².

The mainstream of Xiangxi River (XXR) is approximately 94 km long. Elevation of its watershed is about 1,200–2,000 m and encompasses all of Xingshan County, Zigui County and portions of the Shennongjia Forest, with a total area of 3,099 km². The Xiangxi Estuary, which is located 34.5 km upstream from the TGD, has an average gradient of 14.2% (Liu et al. 2012). The XXB, is the largest tributary formulated by the TGR and is deemed as major of all eutrophic tributary bays of the TGR (Ji et al. 2017; Li et al. 2020b). It is the closest tributary to TGD, located in western Hubei Province, north of the Yangtze River in Xiling Gorge (Figure 1(b)). It encompasses a watershed area of 3,095 km² with an average annual discharge of 47.4 m³/s having a highest value of 300 m³/s (Li et al. 2020b). It lies between the Jingshan and Wushan Mountains at 110°25′E to 111°06′E to 30°57′N to 31°34′N (Figure 1). The primary filling of the TGR in June 2003 to water level of 135 m has caused submergence of lowest 24 km by backwater transgression, that led to formation of a huge XXB. This backwater zone was formed from the XXR estuary to a location near Zhaojun Bridge, which is named XXB. The backwater upstream extension reached 40 km once the TGR was filled to a peak value (175 m) (Xu et al. 2021).

The CE-QUAL-W2 model is a 2-D (longitudinal and vertical), laterally averaged, hydrodynamic and water quality model (Jin et al. 2019). It was co-developed by the U.S. Army Corps of Engineers Waterways Experiment Station and Portland State University (Cole & Wells 2013). The model can precisely simulate thermal distribution, hydrodynamic features, and water quality parameters for different water bodies and under extensively varied conditions (Ji et al. 2010; Ma et al. 2015) as shown in Figure 2.

The model was established to simulate comparatively long and narrow water bodies depicting horizontal and vertical hydrodynamical and water quality variations. The model is applicable for stratified aquatic bodies, and has successfully been implemented to lakes, reservoirs, and estuaries (Xu et al. 2021). In this research, CE-QUAL-W2 was adopted to simulate XXB because lateral differences in water velocity and temperature are ignorable as indicated in Figures 5 and 6.

Synchrony between the observed and simulated storage water elevation curves validated the precision of the bathymetry data as exhibited in Figure 3(a) and 3(b). The simulation period for XXB was from January 1, 2008 to December 31, 2018. The upstream inflows and meteorological data including dew point temperature, air temperature, wind speed and direction, and cloud cover (or total incident solar radiation) were obtained from the hydrological station at Xingshan, which is located almost 36 km from TGR mainstream. Field data on the water level were obtained from the China Three Gorges Corporation (http://www.ctg.com.cn/). The upstream boundary conditions for the model include the measured daily inflow discharge and water temperature. The downstream boundary conditions include daily water levels and the measured water temperature. The W2 model for the XXB is solved by the ‘x’ and ‘z’ momentum equations, the continuity equation, and the equation of state, which relates fluid density to water temperature and concentration of dissolved substances in the water body (Cole & Wells 2013). These equations are given in the appendix. The computational grid of the XXB developed from bathymetric and geometric data was 500 m in length and 1 m in thickness, with a total of 64 longitudinal segments and 109 vertical layers. The period between January 1, 2008 and December 31, 2018 was chosen as the simulation period for modeling the XXB.

The measured daily inflow rate and temperature was used as the upstream boundary for the XXB model. The daily eater level (WL) from the China Three Gorges Corporation (http://www.ctgpc.com.cn/) was used as the downstream boundary. Daily meteorological data including air temperature, dew point temperature, wind speed and direction, and cloud cover (or total incident solar radiation), were obtained from the hydrological station at the upstream of the XXB, located approximately 36 km from the TGR mainstream. In addition, the initial WL in the computational domain was specified by field measurements on January 1, 2008, as was the initial water temperature distribution observed section close to the mouth of the XXB. Using the model, the mixed layer depth (Zmix) can be determined using water temperature-based criterion (Chuo et al. 2019), for which, ‘Z_mix’ is defined as the depth at which the water temperature was 0.5 °C lower than that of the surface water. The water age, i.e. the hydraulic retention time, is calculated for each cell of the XXB using an algorithm in W2 (Cole & Wells 2013).

Model calibration is the technique of assessing accuracy of model parameters by comparing the simulated data with the observed data. Based on PIKAIA genetic algorithms (GAs) and OpenMP shared-memory model, the parameters of the XXB model was automatically calibrated (Long et al. 2019). Many parameters affect the features of water flow field and water temperature profiles, including meteorological conditions, inflow, outflow discharges and geomorphology of reservoirs. Among the vital parameters of the CE-QUAL-W2 model, wind sheltering coefficient (WSC) is utilized to adjust wind speeds measured at a given meteorological station to those at the reservoir surface; longitudinal eddy viscosity (A_X), Manning's roughness coefficient (MANN) and the WSC influence the hydrodynamics directly and then influence the transport of heat and contaminants. Solar radiation absorbed in the surface layer (BETA) and extinction coefficient for pure water (EXH₂O) affect the water temperature and hydrodynamics directly and indirectly, respectively. Water temperature is not sensitive to A_X or longitudinal eddy diffusivity (D_X) (Li et al. 2020a), therefore, the default value of 1 m² s⁻¹ is used for both as shown in Table 1.

The selection of exact parameters is vital to get precision of a numerical model. The CE-QUAL-W2 model used some parameters which specify hydraulic and bottom heat exchange coefficients that can be varied during the model calibration (Cole & Wells 2013; Chuo et al. 2019).

CE-QUAL-W2 has several coefficients that may be adjusted in the calibration process. A sensitivity analysis determined that the most sensitive model parameters included the longitudinal eddy viscosity, longitudinal eddy diffusivity, Manning's roughness coefficient, wind sheltering coefficient, dynamic shading coefficient, the fraction of incident solar radiation absorbed at the water surface, and the light extinction for pure water (Ma et al. 2015; Yang et al. 2018). Default values for these parameters are shown in Table 1. Based on water quality and pollution indices these parameters can be varied and system performances can be calculated (Ambrose et al. 2009; Gao et al. 2018). As CE-QUAL-W2 was validated here and system performances and errors were in allowed range as shown in Figure 3(a) and 3(b), but below mentioned parameters need to be adjusted to reduce ME, AME and RMSE (Yang et al. 2013).

WSC, MANN, BETA and EXH₂O deeply affect water temperature and velocity. Water temperature and velocity are major parameters for defining water circulation patterns, hence they need to be calibrated for assuring precision in simulated results. Figure 3(a) and 3(b) indicate calibration results for observed and model simulated tempertaure and flow velocity at XX01, XX06 and XX09 in XXB.

Calibration of the CE-QUAL-W2 model indicated that simulated temperature and velocity were synchronous to field measurements in the XXB as in Figure 3. The overall averaged mean error (ME), averaged absolute mean error (AME), and averaged root mean square error (RMSE) were 0.21 °C, 0.31 °C, and 0.49 °C, respectively, at site XX01; 0.14 °C, 0.34 °C, and 0.42 °C, respectively, at site XX06; and 0.07 °C, 0.47 °C, and 0.61 °C, respectively, at site XX09. As per Cole & Wells (2013), the thermal vertical profiles should have AMEs less than 0.5 °C and RMSEs less than 1 °C for better elucidation of thermal distribution and stratification. All errors were in allowed range making model applicable for XXB.

The simulated data was plotted for variables of temperature, horizontal and vertical velocities and water age. The pictorial display of flow patterns for all Julian days was viewed to identify, categorize and and calculate reflective density current patterns as shown in Figures 4 and 5. Based on acquired, simulated and processed data, numerical and graphical analyses were carried out which constitute emergence, sequence and durations of reflective flow patterns. The total duration, frequency of occurrence, longest duration by once-off reflective patterns were calculated for all Julian days before and after cascade reservoirs. Moreover, transitions and shifting trends among patterns on seasonal time scales, spring (March–May), summer (June–August), autumn (September–November) and winter (December–February) over the years and two stages (2008–2013 and 2014–2018) were also analysed. Hydrodynamic features, especially thermal developments and flow variables in the TGR, were investigated and correlated deeply to figure out reasons underlying shifts in density currents in XXB. The numerical and graphical analyses of seasonal and yearly variations in sensitive dynamic parameters of density current patterns during both stages are carried out in relation to interactive developments in XXB and TGR. Among these sensitive dynamic parameters, variations in thermal distribution and water age, most preferably at the surface layer were illustrated. Effects of reservoir operation at lower water levels on density current patterns in a tributary during transitional stage 2008–2009 were also elaborated under heading prevalence of patterns. Correlation of evolutionary mechanism and variations in total duration, frequency and reflective patterns refer to hydrodynamic conditions prevailing in XXB. Water quality, eutrophication and eco-environmental aspects were predicted from statistics and features associated with all patterns and their combined proportions. Hydrodynamic features like thermal distribution, mixing and water age were verified through pictorial display and were elaborated as shown in Figures 4, 5 and 13. Thresholds of sensitive dynamic parameters like temperature and inflow and outflow discharges in TGR were also predicted to tackle algal regime, especially in spring.

Previous observations and analysis (Cao et al. 2012; Jin et al. 2019) have identified the existence of density currents at the junctions of the TGR mainstream and bays and upstream and bays owing to the integrated impacts of mutual differences in temperature and suspended solids among water layers. As evident from Figures 3–5, overflow and underflow density currents generated by upstream inflows and five types of intrusion flows with different corresponding circulation patterns have been recognized so far.

Ten reflective water circulation patterns were discerned and are portrayed in Figure 3. Reflective vertical/longitudinal portrayals of flow patterns with temperature and flow field (with vertical mixing strength dissemination) were picked from an 11-year period (2008–2018) in the XXB to distinguish the density-driven circulation patterns. Reflective flow patterns simulated by the W2 model are displayed in Figures 4 and 5 which encompass (Patterns 1–5) and (Patterns 6–10), respectively, and are elaborated as follows:

As shown in the Figure 5(a)–5(d), water of the TGR intruded into the XXB along the upper layer, meanwhile upstream inflow also occurred along the upper layer at the termination of the XXB. Driven by law of conservation of momentum, water underneath the TGR intrusion caused anticlockwise circulation at the lower reach. A small clockwise circulation took place at the upper reach of the XXB. Owing to the collision of the overflows, the middle reach mostly had comparatively less but considerable turbulence and mixing as evident from Figure 5(b). However, the sites and strength of mixing rely on the volume of the surface inflow and intrusion (Niemeyer et al. 2018).

As shown in Figure 5(e)–5(h), the mainstream water intrusion into the XXB took place as upper interflow. The upstream inflow occurred along surface layer at the end of the XXB. Water underneath the plunge point was driven to to generate large anticlockwise circulation, whereas water above the confluence induce a feeble, thin, clockwise circulation as in Figure 5(e)–5(h). In this case, the subsurface water underwent less intense vertical mixing thus warmed rapidly as shown in Figure 5(e)–5(h).

As shown in Figure 5(i)–5(l), the upstream inflow into XXB occurred through the upper layer, but the TGR water entered into the XXB through the middle layer. The water beneath and above the plunge point produced anticlockwise circulation, and weaker, clockwise circulation respectively. Local turbulence and vertical mixing were evident in the deep water, and the upper most layer was comparatively stable.

As shown in Figure 5(m)–5(p), the upstream run-off entered through the upper layer of the XXB. Meanwhile, the TGR water plunged into the XXB through the lower-middle layer. The flow of intruding water was directed towards the mouth of the XXB, in the form of a clockwise circulation.

In this particular flow pattern, entire water body even surface layer had reduced water age due to the clockwise circulation. Large-scale turbulence and intense vertical mixing tended to occur especially in the upper reach of the XXB so as to break water thermal stratification.

In Figure 5(q)–5(t) the upstream inflow is still along the surface layer at the end of the XXB. The TGR water intrusion into the XXB took place as underflow. This flow pattern led to a clockwise circulation and turbulence prevailed in the lower reach and a small, clockwise circulation occurred at the termination of the XXB Figure 5(q)–5(t). In this case, the TGR triggered clockwise circulation, enhanced the velocity of deep water layer and the upstream overflow escalated velocity at the upper reach of the XXR, consequently, more speedy water exchange and mixing took place Figure 5(q)–5(t).

The inflow took place along the bottom of the XXB, while the TGR mainstream intrusion took place into the XXB along the upper layer at the mouth of the XXB led to a large, counterclockwise circulation in the lower reach. In this particular flow pattern, both mainstream overflow and upstream underflow had escalated water velocity, inducing more vigorous flow movements Figure 6(a)–6(d). The strong mixing and eddies caused rapid deformation of the temperature stratification as in Figure 6(a)–6(d).

As shown in Figure 6(e)–6(h) the TGR mainstream intrusion and the upstream inflow into the XXB took place as upper interflow and underflow respectively. A large counterclockwise circulation was induced in the lower reach below the intrusion, led to flow movements of subsurface water towards the mouth of the XXB. This large, anticlockwise circulation was quite obvious in the deeper layers of the XXB.

In this particular case, temperature contours extends into the tributary through the depth of intrusion, giving rise to stratification pattern in the XXB having upper thin layer of relatively warmer water especially in summer besides two other distinctive layers Figure 6(e)–6(h).

As shown in Figure 6(g)–6(j), the upstream run-off flowed into the XXB along the bottom and produced counterclockwise circulation which rose up to the subsurface of the upper reach. The TGR mainstream water intrusion into the XXB along the middle layer clockwise and anticlockwise circulations above and below the plunge point respectively. The encounter between the TGR intrusion and the upstream underflow led to generation of eddies in the middle reach. Resembling to Pattern (7), surface thermal stratification was quite evident.

The upstream inflow was from the bottom of the XXB generated anticlockwise circulation in the upper reach. In this flow pattern, a large, clockwise circulation was initiated from the intruding lower-middle point reaching to the surface layer of the upper reach, led to almost ineffective or no temperature differences in the deep layer water, Figure 6(k)–6(n).

Intense mixing and violent circulation led to a much shorter water residence time in the XXB.

As shown in Figure 6(o)–6(r), the upstream inflow was along the bottom of the XXB generated anticlockwise circulation in the upper reach. The TGR downstream intrusion into the XXB along the bottom produced a clockwise circulation within the middle-lower reach. Eventually, more local mixing and turbulence was generated in the upper reach of the XXB, driven by anticlockwise circulation.

Particulars of the evolutionary mechanism of density current flow patterns on monthly, seasonal scales and over an annual cycle have been simulated, thoroughly investigated and cataloged as shown in the Figure 7. These statistics include the sequence and continuity of flow patterns for each month from 2008 to 2018.

Figures 4–6 depict that upstream underflow dominated through all seasons of the years from 2008 to 2018 in exemption with upstream overflow for a few days especially in March and April for most of the years and for a few days in February as well for a few years. Conversely, mainstream intrusion was varying in terms of five reflective positions giving basis to 10 types of peculiar flow patterns in the XXB.

Prevalence of patterns (1)–(5) were least considerable to describe yearly trends and were considered in spring and winter and are depicted in Figure 6. The total duration and continuity at once of Patterns (1)–(5) in winter were not that much to affect additive impacts and shifting trend of Patterns (6–10) before and after cascade reservoirs. The overall shifting trend in density current patterns remained the same regardless of inclusion or exclusion of the least dominant Patterns (1–5) in winter.

Winter season spans over the period of three months from December to February. Upstream underflow dominated throughout the opted period over winter seasons. Mainstream intrusion in the winter season was dominant as underflow (Pattern 10) and lower interflow (Pattern 9) until 2010. The dominance of underflows and lower interflows were reduced due to alterations with other least dominant patterns from 2010–2013, as simulated and listed in Figure 7. The total duration of overflow (Pattern 6) increased by 35% and dominance of Patterns (9) and (10) was reduced by 11% and 28% respectively since 2014 as evident from Figures 6 and 7(a)–7(c). Patterns (6–10) were 10%, 15%, 11%, 31% and 34% respectively by 2013 and were changed to 45%, 12%, 11%, 22% and 8% respectively since 2014. Percentage prevalence of Pattern (6) was less than 10% by 2010 and was increased to 10% and 45% during 2010–2013 and 2014–2018, respectively.

Total duration (days) and maximum duration at once of Pattern (6) were minimal until 2013 and were obviously increased from 2014 onwards. Aforementioned parameters for Patterns (7) and (8) were minimal in winter until 2009, and hardly increased from 2010 onwards. This alteration is due to thermal modifications in TGR brought about by upstream cascade reservoirs. There was an obvious decrease in total duration (days) and maximum duration at once of Patterns (9) and (10) during post-dams period. Total duration and continuity (maximum duration at once) of Patterns (9) and (10) and Pattern (6) were maximum in winter before and after 2013, respectively, as exhibited in Figure 8(a)–8(c).

Spring season spans over three months from March to May. Upstream underflow also dominated spring season over all years, with some appearances as overflow, especially in March, April and rarely in May. Patterns (9), (10), (4), and (5) were dominant in March with few appearances of Patterns (7), (8), (3) and (2) until 2013. The frequency of uplift of intrusion depth even to the overflow Pattern (6) increased since March 2014. Patterns (6), (7), (1) and (2) were in alterations in April with dominance of Pattern (7) until 2013, the ratio of dominance of pattern (7) especially over pattern (6) was reduced since 2014. Patterns (6), (7), (1) and (2) were found prevalent in alterations in May until 2013 with increase in transformations of patterns and comparative dominance of Pattern (6) since 2014. On the whole, Patterns (7) and (8) were dominant in spring until 2013 due to obvious dominance in April and May. The proportions of dominance of Patterns (9) and (10) in March and patterns (7) and (8) in April and May were reduced since 2014 due to uplift of intruding water Figures 7 and 9(a)–9(c).

The intruding reservoir water in XXB was more frequently uplifted towards the surface and one month earlier (April) since 2014. Results of simulations displayed in Figure 8(a)–8(c) revealed that density currents, circulation patterns and hydrodynamics in a tributary bay underwent obvious changes as triggered by post-dams spring warming.

Patterns (1)–(10) were 5%, 16%, 3%, 4%, 6%, 20%, 35%, 5%, 1% and 5% respectively by 2013 and were changed to 4%, 11%, 31.5%, 1.5%, 0%, 51%, 19%, 7%, 3% and 2%, respectively, since 2014. Percentage prevalence of Pattern (6) was 20% by 2013 and was increased to 51% since 2014, respectively. The total duration of overflow (Pattern (6)) increased by 30% since 2014 as evident from Figures 7 and 9(a)–9(c).

As shown in Figure 8(a)–8(c), total duration and continuity of Pattern (6) were increased after 2013. Meanwhile, maximum duration at once of Patterns (7) and (8) were reduced after 2013.

As depicted in Figure 8, total duration and continuity at once of Patterns (4) and (5) in spring were not that much to affect additive impacts and shifting trend of Patterns (6)–(10) before and after cascade reservoirs. Patterns (2) and (3) were 16% and 3% by 2013 and were altered to 11% and 1.5% since 2014. These patterns mostly occur in alteration with other patterns in April and May.

Summer or flood season spans over three months from June to August. Pattern (7) was dominant until 2010 with some percentage of Pattern (8). Patterns (6) and (7) were found in alterations, with dominance of Pattern (7) and few appearances of Pattern (8) until 2013. As shown in Figure 12, average inflow water temperature at Cuntan (CUT) was reduced by 0.6, but average water temperature at Miaohe station (MIH) was increased by 0.2 in summer since 2014. The TGR water temperature fluctuated and cooled slowly by minimum magnitude but the cooling effects were least dominant and observed in August if there were any. Patterns (6)–(10) were 17%, 61%, 17%, 5%, 0%, respectively, by 2013 and were changed to 39%, 34%, 19%, 8% and 0%, respectively, since 2014. Percentage prevalence of Pattern (6) was 17% by 2013 and was increased to 39% since 2014, respectively. The total duration of overflow (Pattern (6)) increased by 22% since 2014 as evident from Figures 7 and 10(a)–10(c).

Statistics in Figures 6 and 9 are helpful to discern 27% decrease of upper interflow Pattern (7) in summer since 2014. The percentage of prevalence of interflow Pattern (8) increased in August during post-dams period due to minor cooling of the TGR water. By and large, effectivity and mixing were increased due to increase in overflow intrusions.

Total duration and continuity of Pattern (6) was somehow increased during 2014–2018 and became enough in summer to boost effectivity. Pattern (7) was unilaterally dominant in Summer 2008 and 2009 with some reduction from 2010 to 2013. Although Pattern (7) was reduced further after 2013, but susceptibility to eutrophication is still obvious due to enough magnitudes of upper interflows.

Patterns (9) and (10) were almost absent in summer with occasional appearances in August during post-dams stage.

Autumn season spans over three months from September to November. Patterns (9) and (10) dominated the post flood, autumn period from 2008 to 2013, in alterations with least dominant Patterns (6), (7) and (8) which somehow increased during 2010–2013. The total duration, frequency of occurrence and maximum duration (days) at once of Patterns (9) and (10) were reduced during 2014–2018, but not as much as were reduced in winter. Position of intrusion was lifted from underflows and lower interflows to interflows and even to the overflows but lower in percentage than in winter. Therefore, total duration of Pattern (6) increased by 24% since 2014 more than that of any other pattern due to rise in temperature of mainstream by 1.44 °C in autumn as evident from Figures 7 and 10(a)–10(c). Patterns (6)–(10) were 11%, 9%, 20%, 29%, and 32% respectively by 2013 and were changed to 36%, 14%, 21%, 19% and 10% respectively since 2014. Percentage prevalence of Patterns (6) was 11% by 2013 and was increased to 36% since 2014, respectively. The total duration of overflow (Pattern (6)) increased by 25% since 2014 as evident from Figures 11 and Figure 9(a)–9(c).

Total duration and continuity of Patterns (7) and (8) in autumn were more than enough to enhance eutrophication since reservoir started operating at high water level in 2010. Overall, percentage of prevalence of Patterns (7) and (8) were somehow increased during post-cascade reservoirs stage.

The thermal structure and stratifications in reservoirs could be mitigated by several methods, such as selective withdrawals, calculated and controlled inflow and outflow discharges (Niemeyer et al. 2018). The combined impacts of functional cascade reservoirs add to the complications of the correlation of hydrodynamics of reservoirs and resultant bays (Ouyang et al. 2011; Bem et al. 2021).

The water temperature of mainstream varies seasonally; the average temperature per annum is 17.6 °C (Sun et al. 2021). A noteworthy difference in thermal distributions of the TGR has been discovered after 2013, since the newly built upstream cascade reservoirs were operated. The numerical and graphical analyses of temperature evolutions as shown in Figure 12 and Figure 15 are helpful in justifying shifting trends of density current patterns over seasons and years. In general, nature of bidirectional intrusive density currents from mainstream and flow field in tributary bay heavily rely on thermal distributions in the mainstream (TGR) and tributary (XXB) (Niemeyer et al. 2018).

Temperature differences (warming or cooling) can prompt vertical density gradients leading to stratification in lakes and reservoirs. In stratified reservoirs, metalimnion, the middle layer acts as an obstacle and does not let the relatively warmer surface layer (epilimnion) and the colder deep water layer (hypolimnion) get mixed (Xu et al. 2021). Prevalence of the large temperature gradient (75 m) in TGR was evaluated below the elevation of the reservoir intake (110 m) in spring (Cao et al. 2012; Jin et al. 2019).

The Figure 11 has manifested the increase of inflow water temperature at Cuntan by (+1.2 °C) in winter, (+0.2 °C) in spring, and (+0.8 °C) in autumn and decreased by (0.6 °C) in summer since 2014 owing to the operational upstream cascade reservoirs. The observed and simulated data at MIH in the TGR mainstream also figured out that water temperature of TGR rose by (+1.01 °C) in winter, (+2.0 °C) in spring, (0.6 °C) in summer with little cooling in August and (+1.56 °C) in autumn since 2014. The post dams much warmer TGR water in spring, autumn and winter uplifted the probability of position of intrusion in the XXB even to the surface, eventually contributed to the shifting trends of intrusive density currents and circulation patterns in respective seasons in the XXB.

In consonance with changes brought about by cascade reservoirs in the TGR, model simulation of density currents revealed that post dams warming of the TGR mainstream during spring triggered a steady uplift of the intruding water from the TGR as underflow (March 2008–2013) to middle flow (March 2014–2018), the middle flow (April 2008–2013) to overflow (April 2014–2018) and eventually as upper interflow and overflow (May 2008–13), to dominant and long lasting overflow (May 2014–2018), respectively (Figures 6 and 8). Therefore, warming-induced uplift of the intruding reservoir water took place in spring since 2014 as in Figures 7 and 9.

Consistent with relative increase in the TGR water temperature in winter, uplift of intrusion took place from lower middle and middle flow in December 2008–2013 to overflow in December 2014–2018 as evident from Figure 7. Pattern (7) occurred for 24 days and Pattern (8) occurred for 7 days in December 2015. Pattern (6) appeared thrice in December 2016 which reflected the warming of mainstream in winter. Pattern (6) appeared thrice for 7 days, 8 days and 10 days in December 2017 whereas Patterns (8) and (9) appeared once each for 2 and 4 days, respectively. Appearance of pattern (6) twice in December, thrice in January and for 13 days in February 2018 were in compliance with changing trends since 2014 as in Figure 7.

The qualitative and quantitative interpretation of simulated density currents data were in synchrony with significant findings of recent temperature differences in the TGR, Figures 7 and 12. Similarly, percentage of prevalence of overflows and underflows in the XXB had been increased and decreased respectively, due to increase in temperature of TGR in autumn by 1.56 °C since 2014. Patterns (7), (8) and (9) continued for early 11 days and Pattern (6) appeared for late 20 days in October 2014. Pattern (6) appeared in alterations with other patterns in September 2016. Pattern (6) appeared twice for 5 and 10 days in October 2016. Pattern (6) appeared thrice in November 2016.

The intrusion position of TGR in summer did not get affected much after 2013, but there is mixed trend of alterations among patterns (6) and (7) due to minor fluctuations in temperature. The lowering of intrusion depth in August indicated slow cooling of the TGR in late summer. In June 2015, Pattern (6) spanned over an entire month, which indicated frequently occurring uplift of intrusion. Slow and little cooling in summer made its impacts evident in August in terms of increased replacement of overflow and upper interflow by interflow. In August 2016, Patterns (6), (7) and (8) appeared twice each, Pattern (8) lasted for 2 and 10 days, respectively. Pattern (8) was also evident in August 2017.

The specifications of flow patterns in bays rely on interactive hydrodynamics of bays and TGR (Ji et al. 2017). The upstream recently built reservoirs on Yangtze River have not only modified water temperature build out of the TGR, but also caused changes in discharge at Cuntan (CUT) and total inflow and outflow volumes of the TGR as shown in Figure 13(a)–13(c). Increased post dams volume of water was traced to be associated with variations in inflow and outflow water temperatures and thermal structure in the TGR.

Coldest water in dry season was identified to be flowing downstream of the TGR and mixing with warm water (Sun et al. 2021).

Like other hydrodynamic features, position of intruding water layer in the XXB also relies on thermal profiles, temperature range and stratification in main reservoir. Due to reduced air temperature in autumn and winter, hypolimnion in reservoirs gets cooler and stratification becomes unlikely (Long et al. 2016).

High inflow and reduced retention time as usually observed in flood periods prompt rigorous vertical mixing to make the reservoir behave like a river through inhibiting stratification. Stratification can thus be shattered by reduced retention time during the flood period. Reservoirs located in a subtropical zone like the TGR is always vulnerable to stratification in some part of the year (Dai et al. 2019; Posada-Bedoya et al. 2021).

Thermal stratification is determined by duration of stratified water column, vertical temperature gradient, maximum temperature difference from surface layer to bottom layer (MTD) and water retention time (WRT). Aforementioned governing parameters of temperature stratification are strongly interdependent. Reliance of these influential factors on discharge at CUT, and total inflow and outflow of the TGR as in Figure 13(b)–13(d), besides inflow discharge temperature made discharge dynamics of the TGR noteworthy (Johnson et al. 2004). Previous analysis of data from pre-cascade reservoirs stage has already verified that modifications of WRT triggered by flow changes led to the severe changes of stratification in the TGR (Cao et al. 2012). A mathematical derivation implying proportional reliance between inflow discharge and duration of stratified water column have confirmed the emergence of potential buoyancy and extinction of stratification if inflow discharge approaches to 6,000 m³ s⁻¹ (Bermúdez et al. 2018).

A vital increase in inflow discharge in spring, autumn and winter at Cuntan (CUT) and the TGR was noted since 2014. The inflow discharge at Cuntan (CUT) was increased by 1,385.7 m³ s⁻¹, 1,367.39 m³ s^−1, and 708.14 m³ s⁻¹ in spring, autumn and winter, respectively, and decreased by 2,017.85 m³ s⁻¹ in summer. The total inflow discharge along the TGR was increased by 1,855 m³ s⁻¹, 2,197 m³ s⁻¹ and 2,167 m³ s⁻¹ in spring, autumn and winter, respectively, and decreased by 1,418.48 m³ s⁻¹ in summer. The outflow discharge of the TGR increased by 2,209 m³ s⁻¹, 2,140 m^3/s, and 912 m^3/s in spring, autumn and winter but reduced by 1,706.77 m^3/s in summer. At first, stratification in the TGR appeared in spring 2006 followed by more strength in terms of enhanced maximum temperature difference of 10.2 °C and vertical gradient of 0.43 °C m⁻¹ during spring 2008–2010. (Sun et al. 2021).

At somehow larger but less than critical discharges, the inflowing or outflowing layer is likely to interact with the thermocline, and at critical or larger than critical discharges, the buoyancy becomes dominant and water flow reaches its potential. Outflow dynamics evaluated through transition number also verified the increase in mixing through enhanced discharges (Bermúdez et al. 2018).

Increase in outflow discharge of water, especially from the bottom layers, was verified to be the most impactful in strengthening the mixing of the stratified water columns (Dai et al. 2019), thus post dams increased discharge from the TGR in spring accounts for reduced thermal stratification and emergence of enhanced as evident from Figure 13(c)–13(e).

In spite of high magnitude of average inflow discharge at Cuntan and the TGR, the exact values were less than a critical value to completely break thermal stratification from late April to May in spring until 2013 as shown in Figure 13(b)–13(d). Therefore, thermal stratification was observed and simulated in the TGR in spring during pre-cascade reservoirs stage, especially during late April and May (Long et al. 2016). As shown in Figure 12, graphical analysis has proven, that increased average discharge by 1,855.79 in April, May, and shorter residence time in spring have reduced the duration of stratification from 57 days in 2010 to 20 days in 2015 and maximum vertical temperature difference between surface and bottom from 7 °C in 2010 to 2.0 °C in 2015 as shown in Figure 13(b)–13(d).

Excess energy caused by increased inflows has been proven to account for high vertical mixing and weak thermal stratification (Jin et al. 2019).

Due to reduced water retention time (WRT), maximum temperature difference (MTD) and duration of stratification after 2013, the buoyancy became potential and stratification got weakened and disappeared in spring even in May as shown in Figure 13(b)–13(d). In the presence of long-lasting thermal stratification with high vertical temperature gradient in the TGR until 2013, the mainstream relatively cold bottom layer affected intrusion position. The warm, less or not stratified, rapidly flowing and more vibrantly mixing post dams spring water had intruded into the XXB from upper layers with more strength and volume. Hence, the post dams stratification breakdown resulted in a change in thermal profiles, range of the TGR and subsequent uplift of intruding water in spring a month ahead.

Thermal stratification is mostly established in spring and summer when intense solar radiations and high air temperature heats upper layers more than deep water layers (Dai et al. 2019). Reduced water level in summer can lessen water retention time, supports mixing and eventually reduces thermal stratification in the TGR, therefore it has only been considered in spring here (Dai et al. 2019).

Figures 7 and 9 justify the impacts of foregoing ultimate changes in thermal developments of the TGR on density current patterns in the XXB in all seasons and in spring, respectively. Reduced post-dams water age and broken thermal stratifications in TGR have caused increase in overflow intrusions by 30% in XXB.

Through the simulation outcomes, the average water age in XXB in the upper reach (0–4,000 m) away from upstream, was 8 days and was increased to 46 days in middle and lower reaches (4,000–30,000 m) away from upstream during late March. It was 8,44,53,44 and 26 days at 0–8,000, 8,000–13,000, 13,000–20,000, 20,000–25,000 and 25,000–30,000 m away from upstream, respectively, during early April as shown in Figure 14(c) and 14(d). The average water age in XXB remained the same (8 days) in the upper reach at 0–4,000 m and was altered to 17 days at 4,000–10,000 m and 50 days at 10,000–30,000 m during mid April. It was 9 days in the upper reach at 0–10,000 m away from upstream, 26 days at 10,000–15,000 m and 50 days at 15,000–30,000 during late April. In early May, water age was increased to 18 days in upper reach at 0–10,000 m, 26 days at 10,000–130,000 m, increased to 53 days in middle reach at 13,000–20,000 m from upstram. It was highest (80) days at 20,000–30,000 m in the lower reach. Reasonably, higher vaues of 9,54,62, and 70 days at 0–2,000 m, 2,000–15,000 m, 15,000–24,000 m and 24,000–30,000 m, respectively, are evident from Figure 14(f). The water age in XXB was still high in late May as 9,53,63,70 and 52 days at 0–2,000 m, 2,000–8,000 m, 8,000–14,000 m, 14,000–20,000 m and 20,000–30,000 m from the upper reach, respectively, as exhibited in Figure 14(f).

The average water age in XXB in upper to middle reach at 0–14,000 m away from upstream was 14 days and was decreased to 6 days in the middle and lower reaches at 14,000–30,000 m during late March 2015. It was 3, 14 and 2 days at 0–4,000, 4,000–21,000 and 21,000–30,000 m away from upstream, respectively, during early April as shown in Figure 14(b)–14(d). The average water age in XXB was high (20 days) in upper reach at 0–2,000 m and was decreased to 14 days at 2,000–6,000 m and 5 days at 6,000–30,000 m during mid April. It was 13 days in upper reach at 0–3,000 m away from upstream and 5 days at 3,000–30,000 m during late April. In early May, water age was 10 days at 0–26,000 m and was reduced to 5 days at 26,000 m–300,000 m away from upstram. It was 4 days at 0–2,000 m in upper, 20 days in 2,000–19,000 m, 10 days at 20,000–26,000 m and 3 days at 26,000–30,000 m during mid May as evident from Figure 14(b) and 14(g). The water age in XXB was lower in late May 2015 as 3 days at 0–5,000 m, 20 days at 5,000–1,000 m and 4 days at 10,000–30,000 m away from upper reach as exhibited in Figure 14(b) and 14(f).

Furthermore, Figure 13 exhibits the impacts of hydrological variations in the TGR on hydrodynamic parameters like water age and vertical mixing of circulation patterns in the XXB in spring 2010 and 2015. The decreased post-dams water age in XXB with respect to thresholds or critical values of inflow and outflow discharges and temperatures in XXB give deep insight to reservoir operators. Average inflow water temperature of more than 14 °C at CUT and 15 °C at MIH were effective in triggering overflow intrusions in XXB during the most vulnerable season spring. However, these values are to be maintained in accordance with those in XXB, because increased difference among them trigger overflow intrusions with more travel distance as depicted in Figure 6(a)–6(d). Induced overflow intrusion through selective thermal and discharge dynamics is highly recommended. However, integrated strategies of hydrological management, nutrient and sediments concentration control and biological predation could serve to counter seriously threatening algal regime.

Through statistical analyses as in Figure 6, it is obvious that Patterns (1) to (5) merely appeared for a few days in late February to April each year provided with warmer inflow water or comparable to that at confluence with XXB. This condition and Patterns (1) to (5) were observed in late February, March and April in 2009, 2010 and 2015, and in March to April for rest of the years. The total duration (days) of the Patterns (1) to (5) were only 53, 149, 26, 44, 53 days in these 11 years, respectively, and are less effective because of lack of continuity for longer at once.

Percentage, exact total duration (days), total duration at once (days) and frequency of prevalent patterns per annum are shown in Figure 15(a)–15(e), respectively, and in supplementary material file S3: year wise stats of all patterns. Total duration of Pattern (6) from 2008 to 2018 was 1,100 days. Total duration (days) of Pattern (6) year wise are 30 (4, 19, 0 and 7 in winter spring, summer and autumn, respectively), 10 (0, 5, 2 and 3 in winter, spring, summer and autumn, respectively), 69 (0, 27, 20 and 17 in winter, spring, summer and autumn, respectively), 58 (0, 27, 25 and 6 in winter, spring, summer and autumn, respectively), 71 (17, 23, 22 and 7 in winter, spring, summer and autumn, respectively), 72 (15, 15, 22, and 20 in winter, spring, summer and autumn, respectively), 144 (34, 42, 32 and 36 in winter, spring, summer and autumn, respectively), 189 (40, 68, 52 and 29 in winter, spring, summer and autumn, respectively), 150 (42, 44, 30 and 34 in winter, spring, summer and autumn, respectively), 159 (40, 45, 35 and 29 in winter, spring, summer and autumn, respectively), 152 (40, 47, 36 and 26 in winter, spring, summer and autumn, respectively) from 2008 to 2018, respectively. Pattern (6) was observed six times, four times, 15 times, 15 times, 16 times, 12 times, 12 times, 13 times, 20 times, 20 times and 20 times from 2008 to 2018, respectively, showing a significant increase in terms of frequency of occurrence after 2014. Appearance of Pattern (6) (overflow) has been simulated in all seasons but not been continuous for more days in any season before the cascade reservoirs became functional.

As far as maximum duration by once of Pattern (6) is concerned, it lasted for 14 days in 2008 in April, 4 days in 2009 in April, 22 days in 2010 as 7 days in September and 15 days in October, 11 days in 2011 as 5 days in May and 6 days in June, 16 days in 2012 in May, 17 days in 2013 in November, 22 days in 2014 in October, 45 days in 2015 as 25 days in April and 20 days in May, 18 days in 2016 as 10 days in February and 8 days in March, 13 days in 2017 in December and 15 days in 2018 in April.

As shown in Figure 15, total duration of Pattern (7) from 2008 to 2018 was 940 days. Total duration (days) of Pattern (7) year-wise are 116 (40, 64,12 in spring, summer and autumn, respectively), 119 (33, 71 and 15 in spring, summer and autumn, respectively), 82 (28, 50 and 4 in spring, summer and autumn, respectively), 79 (5, 34, 29 and 11 in winter, spring, summer and autumn, respectively), 106 (18, 36, 52 spring, summer and autumn, respectively), 111 (12, 28, 64 and 7 in winter, spring, summer and autumn, respectively), 88 (15, 18, 45, 16 in winter, spring, summer and autumn, respectively), 51 (15, 11, 18 and 11 in winter, spring, summer and autumn, respectively), 79 (8, 26, 39 and 5 in winter, spring, summer and autumn, respectively), 57 (9, 16, 27 and 5 in winter, spring, summer and autumn, respectively), 62 (12, 13, 24, and 13 in winter, spring, summer and autumn, respectively) days from 2008 to 2018.

Pattern (7) appeared six times in 2008, six times in 2009, 15 times in 2010, 18 times in 2011, 16 times in 2012, 13 times in 2013, 11 times in 2014, 12 times in 2015, 10 times in 2016, 6 times in 2017 and 7 times in 2018.

As far as maximum duration at once for Pattern (7) is concerned, it lasted for 62 days in 2008 in April, May and June, 64 days in 2009 in June, July and August, 27 days in 2010 in July, 8 in 2011 in August, 18 in 2012 in July and August, 37 days in 2013 in late July, August and early September, 16 days in 2014 in July, 11 days in 2015 in summer (July and August), 25 days in 2016 in July, 9 days in 2017 in August and 16 days in 2018 in May.

Total duration of Pattern (8) from 2008 to 2018 was 535 days. Total duration of Pattern 8 year-wise are 55 (10, 3, 21 and 21 winter, spring, summer and autumn, respectively), 18 (0, 0, 8, 10 winter, spring, summer and autumn, respectively), 38 (7, 4, 19 and 12 winter, spring, summer and autumn, respectively), 93 (20, 0, 37 and 35 winter, spring, summer and autumn, respectively), 40 (13, 0, 6 and 21 winter, spring, summer and autumn, respectively), 48 (16, 11, 4 and 17 winter, spring, summer and autumn, respectively), 42 (12, 2, 4 and 23 winter, spring, summer and autumn, respectively), 20 (5, 0, 5, 10 winter, spring, summer and autumn, respectively), 60 (13, 3, 20 and 24 winter, spring, summer and autumn respectively), 67 (11, 10, 23 and 25 winter, spring, summer and autumn, respectively), 51 (12, 5, 20 and 13 winter, spring, summer and autumn, respectively) days for these 11 years. Pattern (8) appeared seven times, five times, 15 times, 10 times, eight times, nine times, nine times, five times, nine times, seven times and six times in 2008–2018, respectively, as in Figure 15.

As far as maximum duration at once of Pattern (8) is concerned, it lasted 19 days in 2008 in September, 5 days in 2009 in August, 10 days in 2010 in July and August, 21 days in 2011 in September and October, 10 days in 2012 in November, 10 days in 2013 in October, 9 days in 2014 in September, 3 days in 2015 in February, 22 days in 2016 in August, 14 days in 2017 in October and 17 days in 2018 in June.

Total duration of Pattern (9) from 2008 to 2018 was 704 days. Total duration per annum of Pattern (9) from 2008 to 2018 are 103 (61, 4, 7 and 31 in winter, spring, summer and autumn, respectively), 70 (27, 0, 11 and 32 in winter, spring, summer and autumn, respectively), 60 (36, 0, 0 and 24 in winter, spring, summer and autumn, respectively), 35 (8, 0, 1 and 27 in winter, spring, summer and autumn, respectively), 62 (25, 8, 7 and 22 in winter, spring, summer and autumn, respectively), 45 (18, 2, 2 and 23 in winter, spring, summer and autumn, respectively), 38 (17, 5, 2 and 13 in winter, spring, summer and autumn, respectively), 60 (16, 0, 17 and 27 in winter, spring, summer and autumn, respectively), 36 (19, 3, 0 and 14 in winter, spring, summer and autumn, respectively), 43 (17, 2, 3 and 21 in winter spring, summer and autumn, respectively), 53 (24, 0, 12 and 17 in winter, spring, summer and autumn, respectively) days for these 11 years, with increase in magnitude since 2014.

Pattern (9) appeared seven times, seven times, eight times, four times, nine times, six times, eight times, nine times, six times, seven times and eight times from 2008 to 2018, respectively, being more frequent after 2008 and 2009 (when it respectively appeared thrice and five times) until 2013 and less recurrent since 2014.

As far as maximum duration at once for Pattern (9) is concerned, it lasted for 14 days in 2008 in April, 4 days in 2009 in April, 22 days in 2010 as 7 days in September and 15 days in October, 9 days in 2011 as 5 days in May and 6 days in June, 16 days in 2012 in May, 17 days in 2013 in November, 14 days in 2014 in October, 16 days in 2015 in April, 11 days in 2016 in February, 11 days in 2017 in December and 10 days in 2018 in April.

Total duration of Pattern (10) from 2008 to 2018 was 513 days. Total duration (days) of Pattern (10) year wise are 39 (15, 1, 0 and 23 in winter, spring, summer and autumn, respectively) days, 67 days (36, 0, 0 and 31 in winter, spring, summer and autumn, respectively), 83 days (39, 9, 0 and 35 winter, spring, summer and autumn, respectively), 81 days, 75 days (57, 6, 0 and 12 in winter, spring, summer and autumn, respectively), 70 days (17, 12, 0 and 41 winter, spring, summer and autumn, respectively), 54 days (30, 0, 0 and 24 in winter, spring, summer and autumn, respectively), 12 days (12, 0, 0 and 0 in winter, spring, summer and autumn, respectively) 21 days (11, 0, 0 and 10 in winter, spring, summer and autumn, respectively), 21 days (5, 6, 0 and 10 in winter, spring, summer and autumn, respectively), 18 (2, 7, 0 and 9 in winter, spring, summer and autumn, respectively), and 26 (2, 6, 3 and 15 in winter, spring, summer and autumn, respectively) for these 11 years. Pattern (10) appeared thrice, five times, seven times, six times, seven times, six times from 2008 to 2013. Pattern (10) is more prevalent in autumn and winter periods, especially before cascade reservoirs became functional.

Pattern (10) appeared once in 2014, in February for 10 days, four times, six times, five times and five times in 2014–2018, being less recurrent per annum after 2013.

Maximum duration by once of Pattern (10) per annum was 24 days in 2008 in November, 46 days in 2009 in the entire month of November and 16 days of December, 21 days in 2010 in February, 51 days in 2011 (17 days in January, 28 days in February, and 6 days in March), 31 days in 2012 (for 28 days in October and for 3 days in November), 13 days in 2013 for 10 days in September and 2 days in October, 12 days in 2014 in February, 10 days in 2015 in September, 8 days in 2016 in October, 7 days in 2017 in November, 12 days in 2018 in October, respectively, getting lesser after 2013.

Total duration, continuity (maximum duration at once) and frequency of all 10 representative circulation patterns, on seasonal and yearly scales are expressed in Figures 8–11 and 15. It is very important to evaluate and analyze variations in magnitudes of total duration, continuity (maximum duration at once) and frequency of these circulation patterns because variation in none of the patterns can solely define the evolution and shifting trends of density current patterns over seasons and years. Total duration, continuity (maximum duration at once) and frequency of Pattern (6) per annum were less as compared to those of other patterns until 2010, and magnitudes were increased annually and in spring, autumn and winter until 2013 and even more after cascade reservoirs started operating in 2014.

Figures 7, 9–11 and 15 depict decreasing trend of total duration (days), frequency of occurrence and maximum duration at once of Pattern (7) per annum and in spring, summer and winter since 2014 due to increased chances of uplifted intrusion. Patterns (7) and (8) were found less recurrent after 2009 until 2013 and total duration and frequency of occurrence had further been reduced since 2014.

Total duration (days), frequency of occurrence and maximum duration at once of Pattern (9) were maximum in autumn and winter during 2008 and 2009. The prevalence of Pattern (9) per year remained the same from 2010 to 2013. Figures 7 and 15 justify an obvious decrease in existing annual magnitudes of total duration (days), frequency of occurrence and maximum duration at once of Pattern (9) since 2014 after cascade reservoirs got operated. This happened because warming of the TGR water in spring, autumn and winter since 2014 have uplifted intruding water from TGR as evident from Figure 14. The total duration (days) by year, frequency of occurrence and continuity of Pattern (10) were greater in magnitude in autumn and winter, enough in spring and were absent in summer until 2013. Prevalence of Pattern (10) decreased per annum and in all seasons after cascade reservoirs became operative due to obvious uplift of intruding water since 2014. Patterns (9) and (10) are more prevalent in impoundment and dry period, especially before cascade reservoirs became functional as in Figure 6.

Total duration and continuity of Pattern (6) were less than those of Patterns (7) and (8) per year and in spring, summer, autumn and winter by obvious magnitude before cascade reservoirs started operating and vice versa.

Total duration and continuity of Pattern (6) were less than those of Patterns (9) and (10) per year and in spring, autumn and winter by obvious magnitude before cascade reservoirs started operating and vice versa.

Total duration and continuity of Patterns (9) and (10) were less than those of Patterns (7) and (8) annually and in spring and summer, and were more in autumn and winter before cascade reservoirs started operating and vice versa, as shown in Figure 15. However, susceptibility to occurrence of any pattern from Patterns (6)–(10) in any season is still more than enough, except in summer, when Patterns (9) and (10) are almost missing before and after 2013.

Based on above results from numerical simulations and graphical analysis of seasonal and yearly variations in evolution (sequence, total duration, continuity and frequency) of 10 reflective density driven patterns with reasons following noteworthy conclusions are drawn. As all previously published work deals with data (boundary conditions) for short periods and particularly before cascade reservoirs became operative, especially regarding density currents in XXB. So findings during post-cascade dams stage and comparative investigation and correlation of patterns in both stages add to the knowledge of hydrodynamics and water quality indicators so as to suggest thresholds for hydrodynamic parameters. The following points clearly refer to new findings.

• (1)

  Inflow density currents in upstream and intrusion density current in downstream of the XXB cause 10 reflective circulation patterns in the XXB. Variations in these circulation patterns affect sensitive dynamic parameters like thermal distribution, mixing and water age in XXB and are significant to trigger and mitigate algal and other water environment threats. Efficiency of circulation patterns depend on intensity of intrusion and inflows.

• (2)

  Total duration (days) of Patterns (6) to (10) were 1,100,940,535,605,513 days in these 11 years, respectively.

• (3)

  The continuity of density current patterns for longer or shorter duration cannot solely declare hydrodynamics of waterbody (XXB) irrespective of the types of intrusion and density current patterns, which really matter.

• (4)

  Phenomenon underlying definite seasonal and annual changes of the backwater intrusion depths across pre- and post-dams stages were post-dams modified thermal and discharge dynamics of the TGR since 2014.

• (5)

  Post-dams increased temperature in the TGR triggered increased overflow intrusion in the XXB.

• (6)

  Post-dams increased inflow discharge have broken thermal stratification and resulted in more overflow intrusions.

• (7)

  Foregoing recent developments in TGR have caused increased travel distance of intruding water and effectivity in major overflow cases.

• (8)

  The total duration of overflow (Pattern (6)) increased by 35% and dominance of Patterns (9) and (10) was reduced by 11% and 28% respectively in winter since 2014.

• (9)

  The total duration of overflow (Pattern (6)) increased by 26%, 30%, 22%, 25% and 35% per annum and in spring, summer, autumn and winter, respectively, since 2014.

• (10)

  Based on distinctive hydrodynamic features attributed to reflective patterns, increased post-dams overflow intrusion refers to increased potency of density-driven exchange and mixing phenomena, less water age and less eutrophication at surface of XXB.

• (11)

  Transformations among reflective patterns across seasons refer to their sensitivity towards thermal developments and discharge dynamics in the TGR mainstream and a tributary bay XXB

• (12)

  Short-term changes have led to some irregular, unsystematized and non-sequential transformations during some part of all seasons prior to as well as after completed cascade reservoirs as shown in Figure 6. Therefore, the precise sequence of reflective patterns in any season of the year is not predictable. However, average total duration, frequency and continuity of all patterns were quite systematic and predictable in all seasons.

• (13)

  The quantitative effects of transitions and shifting trends among effective and ineffective circulation patterns on water quality parameters such as chlorophyll-A distribution, total nitrogen, total phosphorus, dissolved oxygen, dissolved silicate and algal biomass are required to be simulated through modelling.

• (14)

  Dearth of knowledge regarding correlation of sediments transports and density currents could harm best optimization of hydrodynamical parameters. Models like line coupled model, the Environmental Fluid Dynamics Code (EFDC) model and 3D hydrodynamic and water quality models could correlate and investigate other possible reasons for shifts in density currents including hyper concentrated sediment flow to make adjustments.

• (15)

  Controlled reservoir operation at thresholds or more inflow and outflow volumes and temperature triggering overflow intrusion in XXB is recommended to inhibit eutrophication. Average inflow and outflow discharges of more than 8,500 m³ s⁻¹ and 10,000m³ s⁻¹ in TGR during spring was found to be effective in triggering overflow intrusion in XXB. Sensitive dynamic parameters in TGR depend on combined effects on inflow and outflow discharges besides inflow and outflow temperature.

• (16)

  Techniques to control thermal developments like selective withdrawals are beyond the scope of this research but are highly recommended to be tested, applied and validated. Average inflow water temperature of more than 14 °C at CUT and 15 °C at MIH were effective in triggering overflow intrusions in XXB during most vulnerable season spring. However, these values are maintained in accordance with those in XXB, because increased differnce among them trigger overflow intrusions with more travel distance as depicted in Figure 6(a)–6(d).

• (17)

  Water elevation ranges are specific to every season, but effects of water level fluctuations in TGR across different seasons with different temperatures, sedimentary and water quality parameters on XXB need to investigated in recent years.

• (18)

  Reasons underlying unsystematic, random and short term changes in circulation patterns and also behind possibility of occcurrence of all patterns in spring, autumn and winter are still undefined and worth-seeking.

• (19)

  Hydrodynamic and water quality model of XXB coupled with TGR could reveal more interactive hydrodynamics, respective of exclusive and additive effects on density currents, water quality and thresholds to advantageous patterns.

• (20)

  Induced overflow intrusion through selective thermal and discharge dynamics is higly recommended. However, integrated strategies of hydrological management, nutrient and sediments concentration control, biological predation and selective reservoir operation could help controlling eutrophication and maintaining water quality. While aiming at such goals, correlation among all methods and involved interactive parameters need to be carried out.

• (21)

  Hydrodynamic parameters like turbulent kinetic energy (TKE), turbulent mixing (Az), horizontal (Vx) and vertical velocities (Vz), buoyancy frequency (N²) and variations in Z_eup and Z_mix with respect to shifts in density current patterns need to be evaluated and analyzed quantitatively. These features could draw a true picture of hydrodynamic conditions in XXB.

All relevant data are included in the paper or its Supplementary Information.