Hydrodynamic modelling and shape optimisation of second-generation coastal reservoirs in consideration of algal bloom occurrence

Abstract

Algal bloom has been a persistent problem for both fresh and marine water, with no exception for a coastal reservoir (CR). Among the algal bloom mitigations for a CR, shape optimisation to reduce algal bloom occurrence has been frequently mentioned. However, there was no literature found on the actual shape optimisation study or process for CR. Thus, this research was done to bridge this gap, particularly for the second-generation CR. Hydrodynamic model of MIKE 21 has been used, with secondary data obtained from published papers and Google Earth. The secondary data of critical velocity corresponding to algal growth were only available for cyanobacteria, chlorella, filamentous algae and phytoplankton. Hence, only these algae species were considered in the algal mapping. All models were simulated for eight idealised cases of second-generation CR at the Yangtze Estuary. These different geometric shapes were analysed and compared, considering several factors including the average velocity in the reservoir, presence of stagnant water, percentage of occurrence for each algae species and so on. From the results, the reservoir model with the shape of “shorter piano key” ranked the highest among all the shapes in terms of proneness to algal bloom, based on the flow velocity within the reservoir. From the findings, further shape optimisation was done on second-generation CRs. From shape optimisation process, the optimised shape of the “little dinosaur” and “little pencil” showed excellent reduction in algal blooming. However, “little dinosaur” was preferred as its location for algal bloom is small and controllable due to the presence of “piano key” structure. Lastly, all the findings were applied to an existing CR at Qingcaosha to see if shape optimisation based on the analysis can reduce areas prone to algal blooming. The optimised model of Qingcaosha showed great reduction on area prone to algal blooming compared to its original shape but the addition of “piano key” structure did not have significant impact on the reduction of algal bloom occurrence since the shape of Qingcaosha is highly dependent on its natural topography. From the study, it was concluded that shape optimisation for topographic-dependent CR should be done on case-by-case basis, following the flow direction in the reservoir. As for second-generation CR without topographical constraints, the shape optimisation can be done by placing inlet perpendicular to the flow direction, minimising corners, implementing piano-key-like structure, optimising shape based on flow direction and refer “little dinosaur” or “little pencil” for the overall shape optimisation design.

1 Introduction

Estuary reservoir, or more commonly called as the coastal reservoir (CR) has emerged to be a potential major freshwater storage solution due to many benefits it offers as compared to an upstream reservoir. The sources of the freshwater for CR are mainly from the river runoff, flood, or groundwater from its catchment. Some of the successful operating CRs include Qingcaosha in Shanghai, Marina Barrage in Singapore, Cardiff Bay and many more.

Since 90 years ago, many CRs have been constructed, starting from the first CR—Zuiderzee-project in Netherland constructed since 1932 (Seven, 1945). Over the years, design considerations have been broadened based on the assessments and observations on the performance of the existing CRs. With that, the evolution gave rise to a few different types of CRs. Currently, there are three generations of CR, categorised based on its location, method of construction and functionalities. The first generation of CR has existed long ago but their presence has caused many environmental issues and water quality problems. To improve its water quality, CRs were then constructed with passages for pollutants, fish and other unwanted water to bypass. These types of CR were categorised as the second generation of CR. Yang (2022) also mentioned that with the second-generation CR, water quality problem can be solved. The third generation of CR is still under research without physical implementation, with the focus on enabling CR to integrate water, food and energy without compromising any of them (Yang & Sivakumar, 2020a). The differences between all generations of CR have been elaborated by Yang and Sivakumar (2020a, b).

1.1 First generation of CR

Most existing CRs in the world were designed and constructed as the first generation of CR such as Marina Barrage, Saemangeum Reservoir in South Korea, Plover Cove Reservoir in Hong Kong and many more. They were categorised as the first generation of CR as the barrage were designed to close up the entire river mouth for the separation of freshwater from the seawater. Yang (2022) also outlined the detailed basic features for a CR to be categorised as first-generation, which include having a straight and solid barrage freshwater-seawater separation, collecting pollutants and having the barrage to be perpendicular to the flow direction.

This type of reservoir had cause numerous environmental issues and water quality problem observed by the local community and many researchers (Lee et al., 2014, 2015, 2018; Seven, 1945). Some examples include the famous Marina Barrage in Singapore. Upon its completion, environmental assessment such as fish survey has been done to evaluate the project’s impact on the marine life by Hui et al. (2010). In the survey, it was concluded that some fishes may survive without access to the sea and some other fishes may survive but would not breed if the access to the marine environment is restricted (Hui et al., 2010). With this, extra consideration should be made for the future CR construction with passage for fishes to access to the sea and to minimise the impact of the reservoir to the natural environment. Another example would be the Korea Saemangeum CR. With the purpose of reclaiming a new land from the sea, the South Korean Government proposed a large seawall construction project with 33 km of length. The seawall project was initiated in year 1991 and complete in year 2006 as the largest man-made dike (Beigel & Christou, 2010). This project has caused public concerns, controversial environmental issue as well as intense political turbulence in the recent history (Koh et al., 2010). With these constructed first generation of CRs, it was concluded that first-generation CR has to improve in order achieve environmental sustainability.

1.2 Second generation of CR

Based on the observation, quality and impact assessments on the existing CRs, amendments have been made to the first-generation CR design to improve its water quality and minimise its impact on the environment. The improvements made then gave rise to the second generation of CR. Unlike the first generation of CR, the barrage built would not close up the river mouth entirely, giving a passage for fishes to access the sea while enabling unwanted polluted water to bypass the freshwater intake of the CR. Without the pollution of the unwanted water, water quality problem would be solved with this second generation of CR (Yang, 2022). An example of the second generation of CR is the Qingcaosha CR in Shanghai.

1.3 Eutrophication problem in CR

Although the implementation of second-generation CR has largely reduced the water quality problem, eutrophication is still a persistent problem (Chen & Zhu, 2018; Gu, 2020; Ji et al., 2017; Sivakumar et al., 2020a, b; Wu et al., 2017; Zhang et al., 2015). Eutrophication is normally caused by nutrient excessiveness in the water and its common effects include oxygen depletion, increasing the growth of phytoplankton as well as algal bloom (Ansari et al., 2011).

Among the harmful algae, Cyanobacteria or blue-green algae are the common cause of algal bloom in the freshwater. This species can growth excessively when the Nitrogen to Phosphorus ratio is low, stable weather as well as in stagnant water when turbulence is low (CSIRO, 2021). The effect of its growth can cause harmful effect to human health, closure of drinking water storage as well as posing higher water treatment cost (CSIRO, 2021). Some of the species of cyanobacteria include Anabaena circinalis, Microcystis aeruginosa, Nodularia and so on (Percival & Williams, 2016). As cyanobacteria thrives in stagnant water, Mitrovic et al. (2003) also identified that the critical flow velocity of 0.05 m/s is sufficient to prevent the growth of Anabaena circinalis for all sites.

As for marine and brackish water, including estuaries, dinoflagellate and diatoms which are different types of phytoplankton that are also categorised as the common harmful algal bloom species (National Oceanic & Atmospheric, 2021a). An example of dinoflagellate is Ceratium blooms which can release odor and taste compound that cause oxygen depletion (Ewerts et al., 2018). To prevent the excessive growth of phytoplankton, Zhang et al. (2015) found that the flow velocity with the highest inhibitory rate to phytoplankton is 0.15 m/s, whereas the flow velocity with the lowest inhibitory rate is 0.06 m/s.

Even though not all algae species are harmful, its growth can act as an indicator of the water quality (National Oceanic & Atmospheric, 2021a). An example of green algae bloom that are non-toxic is the filamentous algae. Although it may not be harmful, it can cause oxygen depletion, odour and fish kills due to its excessive growth (Clemson, 2022). In addition, the presence of chlorella pyrenoidosa will also reflect the flow velocity (Huang et al., 2014) in the water body. Jiao (2007) also found that the critical flow velocities for the growth of filamentous algae and chlorella are 0.01 m/s and 0.05 m/s respectively.

For algal bloom control in CR, Wu et al. (2017) and Yuan and Wu (2020) suggested that the shape, pump, gate layout, together with the operation schedule should be considered to maintain a smooth water flow and optimum residence time. Yuan and Wu (2020) also mentioned that shape and morphology optimisation are the keys to prevent eutrophication. Yang and Sivakumar (2020b) stated that the shape of CR, inlet and outlet locations can reduce algal bloom occurrence but it is a scientific challenge to keep the water inside moving while having minimum detention time. Although algae are the primary food source in the natural environments, some algae comprised the toxic phytoplankton, cyanobacteria, macroalgae or benthic algae can be harmful (National Oceanic & Atmospheric, 2021b).

1.4 Research scope and objectives

Shape optimisation was constantly mentioned to reduce algal bloom occurrence in CR, but there was only minimal research done till date. Therefore, this research aimed to optimise the shape of CR by reducing areas with low flow velocity which contributes to algal blooming, targeting the second-generation CR. This was done by identifying the best shape out of several geometric shapes for an idealised second-generation CR based on their flow velocity within the reservoir. With that, further shape optimisation was done based on the geometry criteria analysed to further reduce the algal bloom occurrence. The list of geometric criteria was then applied to an existing coastal reservoir to examine the reliability of the findings. The shape optimisation study for this research will be applicable for CRs without topographical constraints.

This study summarised the shape optimisation criteria that help to minimise areas prone to algal blooming in CR. This research can be referenced when a new CR is to be designed in the future. With this, partial water quality problem due to algal blooming can be solved. When the shape of the CR is optimised at an early stage, algal bloom can be controlled more effectively with lower cost needed for water treatment in the future.

2 Data and methodology

Hydrodynamic modelling was done to simulate the flow in the estuary and the CRs located there. The flow simulated are based on the water level difference at upstream and downstream boundary, measured by the tidal gauge data obtained from Lu et al. (2015). Eight idealised cases of different geometric shapes for second-generation CRs were simulated for comparison. For each of the reservoir, parameters such as average velocity, minimum current speed, retention time as well as locations with low flow velocity were extracted, studied and compared. The best shape was selected based on a weighted chart that includes all the criteria examined. Then, it was followed by shape optimisation for the second-generation CR. With that, the findings were applied to an existing CR—Qingcaosha CR in China to see if the optimised shape is applicable to them. Mappings of Algae, Chlorella, Filamentous Algae and Phytoplankton were done for each reservoir.

2.1 Site selected

Yangtze River estuary was chosen as the main site for modelling for this research. Yangtze river is not only the third longest river in the world and the largest estuary in Asia, it also houses one of the largest tidal reservoirs in the world. Therefore, the eight idealised case models of second-generation CRs were done at the Yangtze River estuary. After the modelling of the ideal cases to investigate the shape effect on the flow velocity, Qingcaosha CR, an existing second-generation CR was then modelled with its original shape and optimised shape to examine the applicability of the optimised shape on existing CRs that have topographical constraints. Table 1 shows the geographical specification of Yangtze Estuary.

Table 1 Geographical specification of Yangtze Estuary

2.2 Tools and software involved in the numerical modelling

MIKE software powered by DHI such as MIKE 21/3 and MIKE Zero were the main tools utilised for this research. Other than that, AutoCAD was used to design the shapes of the reservoir before generating the meshes on MIKE. Its geolocation online map feature was used to specify the project boundary for the workspace in MIKE. Google Earth was also used to determine some of the survey points for the site in addition to the secondary data obtained from the published papers related to the site.

2.3 Data sets

2.3.1 Water level

The tidal gauge secondary data was obtained to simulate the flow in Yangtze River’s estuary. The water level from the tidal gauge would reflect the tidal elevation, river discharge as well as other residual elevations during that particular time frame, developed using tidal harmonic analysis. Although the tide-river interaction is better account with non-stationary tidal harmonic analysis (Cai et al., 2019; Matte et al., 2013), the least-square harmonic analysis with stationary time series was applied to compute the tidal harmonic constant during the dry season due to the relatively weaker non-stationary characteristic (Lu et al., 2015). With these boundary conditions, a relatively accurate flow velocity can be obtained within the estuary and it is sufficient to be utilised for this research. The tidal gauges referred for this research are BMZ and GQW, which are also the location of the open boundary for this research, namely the North Boundary and the South Boundary respectively. Figure 1 shows the location of tidal gauge referred for each tidal gauge, the tidal harmonic constants of the four major constituents and non-linear constituents are summarised in Table 2

Fig. 1

Location of tidal gauge referred

Table 2 Tidal harmonic constants of the four major constituents for the tidal gauges referred

The water level in both boundaries of Yangtze estuary was predicted using the user-defined constituents obtained from the tidal gauge. Followed by that, the tidal gauge specification was inserted and the prediction period is set from 1/2/2002, 12 a.m. to 31/3/2002, 11 p.m. Institute of Oceanic Sciences (IOS) Method was used to predict the tidal height. In IOS method, the variation of tide is described by the harmonic constituents and it provides detailed description of tide at a particular location. The water level predicted for the north and south boundary were shown in Figs. 2 and 3 respectively. The Time series representation formulated based on the harmonic development are as follows:

Fig. 2

Water level predicted for the north boundary

Fig. 3

Water level predicted for the south boundary

Tidal time series (DHI, 2017)

$$x(t) =\sum_{j=1}^{N}{f}_{j}\left(t\right){a}_{j}\mathrm{cos}({V}_{j}\left(t\right)+{u}_{j}\left(t\right)-{g}_{j}$$

(1)

where ${a}_{j}$ and ${g}_{j}$ are the amplitude, ${f}_{j}\left(t\right)$ and ${u}_{j}\left(t\right)$ are the modulation amplitude of the nodes and phase correction factors, ${V}_{j}\left(t\right)$ is the astronomical argument for constituent j

The Rayleigh Criterion and step-by-step calculation for the analysis can be found in DHI (2017).

2.3.2 Bathymetry

The elevation points of Yangtze estuary were mainly taken from Google Earth and made visual comparison with the bathymetry profile from Zhou et al. (2019). Once the bathymetry generated in this research achieved a great similarity to the bathymetry profile from Zhou et al. (2019), it is sufficient to be utilised in this research together with the water level generated based on the tidal gauge. With a reasonable value of discharge in and out of the estuary, the same modelling conditions will be applied across all the CR shape. Ultimately, the shape of the CR will be the main deciding factor of the flow velocity within the reservoir since all of them will be run under the same bathymetry, water level and any other conditions set. For Qingcaosha CR, the water depth within the reservoir was taken from Liu et al. (2016) and cross-checked with the mean depth from Zhang et al. (2015).

2.3.3 Criteria flow velocity for cyanobacteria, chlorella, filamentous algae and phytoplankton mapping

The critical flow velocities for the growth of algae (cyanobacteria), chlorella and filamentous algae were taken from Jiao (2007), the velocity for high and low inhibitory rate of phytoplankton was referred from Zhang et al. (2015) and the defining velocity for stagnant water was obtained from Nguyen et al. (2018). The summary between the flow velocity correlating to cyanobacteria bloom, chlorella, filamentous algae, phytoplankton are shown in Table 3.

Table 3 Critical flow velocity corresponding to the algae species

2.4 Mesh generation

For all the simulation, the triangular mesh specifications were set with 3,900,000 m² as the maximum area, 26 as the smallest allowable angle and maximum number of nodes as 100,000. This specification was from the default setting of the software and is sufficient for the analysis for this research work, since the meshes generated are in a good size range and could accurately simulate the flow velocity at the desired study location. From that, the meshes were smoothened further with 10 iterations to maximise the angle and area. From the mesh file, the boundaries in the mesh were defined. The definition of boundary was done by highlighting the nodes in an anticlockwise direction and the boundary code number was changed to 2 for the north boundary and 3 for the south boundary. Figure 4 shows the grid cells and the boundary code assigned for the model whereas Fig. 5 shows the bathymetry of the estuary generated.

Fig. 4

Grid cells of the model and the boundary code assigned

Fig. 5

Bathymetry generated for Yangtze Estuary

2.5 Modelling of the ideal case reservoirs

2.5.1 Assumptions and constants

As there are multiple factors affecting the flow velocity and algal bloom occurrence in the CR, therefore these factors have to be kept constant for each model. These factors include the inlet and outlet width, depth in the reservoir, type of estuary, tide level from each boundary, bed resistance, eddy viscosity and many others criteria that can affect the flow velocity in the reservoir. Wind forcing, infiltration and precipitation were not considered in the model since lower flow velocity is more critical for this research. Nutrients, salinity, carbon dioxide, temperature and other factors affecting algal bloom occurrence were also not considered. Therefore, the mapping of the algal bloom occurrence was solely based on the flow velocity, controlled by the geometry and shape of the reservoir. Other constants set for this research are shown in Table 4.

Table 4 Constants for reservoir modelling

2.5.2 Geometry and shape determination of the second-generation CRs

The geometry of the reservoirs used in this study were modelled in AutoCAD with dimension shown in Fig. 6. Since rectangular shape reservoirs were regularly seen, 1 generic rectangular reservoir was then first modelled. To study the effect of angles on the flow velocity in the CR, 3 triangular reservoirs with different angles were modelled. This was followed by CR shape without the presence of angles, and hence2 semi-circular reservoirs were modelled to study the circular shape effect on the flow velocity within the reservoir. Finally, two piano key CRs were also modelled as this shape was also regularly used in hydraulic structure design. The length of the reservoir in most cases were set around 10400 m so that the capacity of each reservoir is similar. At first, only two triangular CRs were modelled for comparison. However, to examine if the area is the biggest factor affecting the flow velocity instead of the angles, a controlled triangle—named as ideal case 8 was then modelled with the same area as the 45°–90°–45° triangle but with a different angle.

Fig. 6

Shapes of CRs compared in the research. a Dimension of idealised case 1—rectangular CR. b Dimension of idealised case 2—45°–90°–45° triangular CR. c Dimension of idealised case 3—45°–105°–30° triangular CR. d Dimension of idealised case 4—40°–90°–50° triangular CR. e Dimension of idealised case 5—10,460 D semi-circular CR. f Dimension of Idealised Case 6—12,000 D semi-circular CR. g Dimension of idealised case 7—shorter piano key CR. h Dimension of idealised case 8—longer piano key CR

2.5.3 Simulation of the generated mesh models

The simulation period was set from 24/2/2002, 12 a.m. to 9/3/2009, 1 p.m. which covers one set of spring tides and one set of neap tide variation. The total simulation period is 14 days with time step interval of 90 s. A time step of 90 s was chosen with the consideration of the time needed for the computer to run as well as the CFL number within the model to be maintained below 1. Hydrodynamic model was chosen to simulate the flow in the estuary. Other modules were not chosen to reduce the computational power needed for the simulation.

The solution technique uses Shallow Water Equation for the hydrodynamic modelling. Shallow water equation consists of hyperbolic partial differential equations that can describe the fluid flow. It was derived from the Navier–Stokes equation based on the equation of mass conservation and linear momentum. The critical CFL number is set to be 0.5 for a stable simulation. The allowed minimum water depth in the estuary before it was excluded from the calculation (the drying depth) was set as 0.005 m, whereas the water depth that will be reincluded into the calculation (wetting depth) was set as 0.1 m (DHI, 2017).

The density type is set as barotropic so that the density of the fluid is solely a function of pressure. For the horizontal eddy viscosity, a constant value of 0.28 was chosen based on the Smagorinsky formulation. Coriolis forcing was set to be varying in the domain. For other parameter such as infiltration, precipitation, wind forcing, ice coverage, tidal potential and wave radiation are set as “none” for this research. With that, the flow in the estuary was solely based on the water level recorded by the tidal gauge, reflecting the discharge and the tidal variation at the boundaries. It would be sufficient for this research since a lower flow velocity is more critical for algal blooming.

Once all the setting for the parameters were done, the initial conditions are set with the surface elevation as 0.1743 m for soft-start. At the start of the simulation period, the water level at the north boundary was − 0.3084 m and 0.6565 m at the south boundary. 0.1743 m is obtained by taking the average of the water level from both boundaries at the start of the simulation period. This is to provide a soft-start for the simulation to stabilise the flow and avoid chock effect. After the input of initial condition, the boundary conditions were then set with specified level as water level is to be inserted for both boundaries. The water level was set to be varying in time and constant along the boundary and the water level prediction file was then inserted in to the data file. The same procedure was applied for the other boundary but with different water level file generated previously. The soft start was set with a time interval of 1800s and the reference value was set to be the same as the initial condition of 0.1743 m as mentioned earlier.

For time step, the frequency was input as 40 Hz for the time step to be in hourly basis. 40 Hz is obtained by:

$$\begin{aligned} & {1}\;{\text{hour/Time}}\;{\text{step}}\;{\text{interval}} \\ & = { 36}00\;{\text{seconds}}/{9}0{\text{s}} \\ & = { 4}0\;{\text{Hz}} \\ \end{aligned}$$

13,000 was the initial number of time steps input into the simulation, with 90 s of interval for each time step, as this will speed up the simulation process. To express the time step in the output in an hourly manner, it was then divided with the frequency of 40 Hz. Therefore, in the output file, there was only 13,000/40 = 325 time steps which each of them representing an hour.

2.6 Model stability

The Courant–Friedrichs–Lewy (CFL) reflects the stability of the unstable numerical methods, plays a primary role in computational fluid dynamics and it is essential to solve partial differential equation. For model stability, the CFL condition should be lesser than 1 so that the solution will not blow up. Hence, the model was checked against the CFL number before the data extraction to ensure stability and result validity. Figure 7 shows the CFL condition of the model at timestep 34, in which the CFL condition of the flow simulated in the hydrodynamic model was lesser than 1 and stable.

Fig. 7

CFL condition for timestep 34 of the hydrodynamic simulation

2.7 Data extraction

Since there are 325 h in the output, only a few should be chosen for the research study. The choice of the time step is mainly depending on the flow direction. Since there is no gate set for the reservoir in the model, therefore selecting a time step that enables the flow to move from inlet to outlet direction is important. Otherwise, the current direction will be reversed when there is a high tide from the south boundary that enables water to go into the outlet and exit from the inlet. For an operating CR, there will be gates to control the movement of water, that is from inlet to the outlet. Therefore, 5 sets of water level were chosen, with all of them having negative value to simulate low tide condition at the south boundary for the water to move from the inlet to outlet, without any primary or secondary flow of water moving from outlet towards the inlet direction. Table 5 shows the 5 sets of data used for data extraction.

Table 5 Five sets of data used for data extraction

After the determination of the time step to be used for the preliminary data extraction, the surface elevation in the reservoir as well as the u-velocity at the inlet and outlet with their respective surface elevation were tabulated for the computation of residence time and residence time per unit volume. u-velocity is the depth-average velocity in the horizontal axis whereas v-velocity is the depth-average velocity at the vertical axis. In reservoirs with outlet located towards the y-axis, y-velocity data at the outlet was then taken since the v-velocity dominates over v-velocity in that case. The dominating depth-average velocities were normally similar to the current velocity at that particular point.

2.8 Model validation

A simple model validation was also done to validate the flow velocity at Yangtze River by taking the water level at the north boundary which is − 0.333 m, with time step 34 as an example. The average elevation of the north boundary is − 4 m, the current speed at the middle of the boundary from the model as 0.63 m/s, width of the channel as 14890 m, and hence the discharge from the north boundary was 3.667 m × 14,890 × 0.63 m/s = 34,399 m³/s. This is about the average discharge of 28,630 m³ of Yangtze river (Lu et al., 2015). Other validation includes the comparison of water level and flow velocity with the secondary data from Lu et al. (2015) to ensure they are in a good agreement. Therefore, the flow velocity simulate in the model is valid and it is sufficient to conduct this research.

Once the data is extracted, the retention time for each reservoir from each tidal data set were then calculated.

To eliminate the effect of volume in examining the retention time due to the geometry effect, retention time per unit volume was then calculated by dividing the retention over the reservoir volume. Followed by that, the retention time per unit volume for each reservoir was then compared with the reservoir with the highest retention time/volume. These percentage errors should be similar across all the 5 tidal data set since within the data set, the reservoirs are compared among each other. Hence, a regression model was developed to choose the most accurate tidal data to be used for further study.

The percentage difference calculation for each reservoir was done by:

$${\text{Percentage}}\;{\text{Difference }}\left( \% \right) \, = \frac{{{\text{Residence }}\;{\text{Time }}\;{\text{Per }}\;{\text{Unit }}\;{\text{Volume }}\;{\text{of }}\;{\text{the }}\;{\text{Reservoir}}}}{{{\text{The}}\;{\text{ Highest }}\;{\text{Residence }}\;{\text{Time }}\;{\text{Per}}\;{\text{ Unit }}\;{\text{Volume}}\;{\text{ in}}\;{\text{ the}}\;{\text{ respective}}\;{\text{ tidal}}\;{\text{ set}}}}*{1}00\%$$

(2)

Followed by that, the percentage difference of one reservoir was then compared with the percentage difference from the same reservoir from different tidal data set. The trend should be similar and with minimal differences between the percentage difference. Hence, a graph was generated comparing all the percentage differences for all tidal data sets shown in the supplementary material.

By graphical comparison, the percentage difference for tidal data set 1 was slightly higher than the rest of the tidal data set, as well as for tidal data set 3. Hence, leaving tidal set 2, 4 and 5 for obtaining the average line. With a closer observation, tidal set 5 has a high fluctuation towards the end of the graph and hence it was also omitted from the averaging process. With that, the values from tidal set 2 and 4 were averaged to be used in the regression model. With that, each tidal data set is then compared with the average data to obtain the R² value. The tidal data set with the highest R² value was chosen for algal mapping, shape optimisation and other studies. Table 6 shows the R² value obtained from the Excel Regression Data Analysis for each tidal set.

Table 6 R² value of each tidal data set compared against the average value

From the analysis, TH2 is then chosen since it has the highest R² value. Though TH4 might also be a good fit but TH2 was preferred since the average residence time for all reservoirs in the data set was higher than in TH4 which is more critical for the study. Despite that, since TH2 is at a lower time step value, hence taking TH2 to be analysed would be a great choice for a hot start as it required lesser simulation period and computational power.

Time step 34 was chosen for the average velocity calculation, mapping of cyanobacteria, chlorella, filamentous, phytoplankton and stagnant water in the reservoir. A general colour pallete with velocity interval of 0.01 m/s was used for average velocity calculation whereas the colour palette used for the mapping was set based on the critical velocity. After the general colour pallete was set, the image was exported to AutoCAD to determine the area between each isolines. The result was then tabulated and analysed.

2.9 Critical velocity correlation and the percentage of occurrence

Based on the critical velocity correlation, the colour palette was set based on them to identify the areas in CR prone to algal blooming. The areas of potential algal bloom were totaled and compared among each shape. The colour palette used for average velocity calculation, stagnant water mapping, cyanobacteria and chlorella mapping, filamentous algae mapping and lastly mapping for area with low inhibitory rate to phytoplankton can be found in the supplementary material.

The percentage of occurrence will be shown in the cyanobacteria and chlorella mapping. The formula for the percentage of occurrence for any algae species is:

$${\text{Percentage}}\;{\text{of}}\;{\text{Occurrence}}\left( \% \right) = \frac{{\left( {{\text{Critical}}\;{\text{Velocity}}\;{\text{of}}\;{\text{any}}\;{\text{algal}}\;{\text{bloom}}} \right) - \left( {{\text{the}}\;{\text{midpoint}}\;{\text{of}}\;{\text{the}}\;{\text{velocity}}\;{\text{interval}}} \right)}}{{{\text{Critical}}\;{\text{Velocity}}\;{\text{of}}\;{\text{any}}\;{\text{algal}}\;{\text{bloom}}}}*100\%$$

(3)

For the other algae species, indication of 0% means no occurrence, whereas those in colours are indications of algal bloom. The result of the algal mapping can be seen in the supplementary material.

3 Results and discussion

3.1 Rectangular CR

At time-step 34, this 10,400 × 5230 m² Rectangular CR stored a total of 1.78953661 × 108 m³ of water with inlet and outlet discharge of 557.775 m³/s and 795.24 m³/s of water respectively. The inlet and outlet discharge were not controlled by the operational setting but due to the geometrical position of the dike set-up, which eventually affects the position of the inlet and surface elevation of water in the reservoir. Since the left and right dike of the reservoir were placed perpendicular to the shore and perpendicular to the water flow direction, the water flow from the estuary can enter the reservoir with minimal turns and bending. Based on the Work-Energy Theorem by James Joule, where “the sum of all forces acting on a particle is equal to the change in the kinetic energy of the particle”, with lesser distance travelled by the water to the inlet, lesser work was done and hence more kinetic energy were preserved. Thus, the water can enter the inlet at a speed of 1.1 ms⁻¹ which is the second fastest, and exit with a speed of 1.88 ms⁻¹, which is the highest among the other shape of reservoir models covered under this research as shown in Figs. 8 and 9.

Fig. 8

Comparison of CR discharge at inlet and outlet

Fig. 9

Comparison of CR flow velocity at inlet and outlet

From Fig. 10, it is seen that all 4 corners are filled with stagnant water–water with velocities lesser than 0.03 m/s and the area of the stagnant water in the left corners are relatively bigger than the ones at the right side of the dike. This observation can be explained based on the Work—Energy Theorem as well and is directly affected by the direction of water flow in the reservoir. To reach the corners of the reservoir, a large work has to be done by water and hence kinetic energy is lost during the process. As shown in Fig. 11, there are also eddies formed at the left and right side of the inlet due to sudden channel constriction.

Fig. 10

Flow Velocity Direction in the Rectangular CR with indication of stagnant water

Fig. 11

Eddies formation at left and right side of the inlet

When comparing the area of the stagnant water on the right upper and bottom corners, the area of the stagnant water at the lower right corner is smaller when compared to the upper right corner. This observation is due to the to the presence of Coriolis effect that drove the motion of water to the south-east direction, as examined by Li et al. (2010).

3.2 Triangular CRs

Three triangular CRs were modelled and each of them have their unique percentage of stagnant water as well as inlet and outlet velocity. The inlet and outlet velocity were mainly affected by the rotational angle of the water flow, thus the work done and kinetic energy. From the Work-Energy Theorem, the resultant work done is equal to the change in the rotational kinetic energy.

$$W_{{{\text{net}}}} = \, \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \, I\omega_{{\text{f}}}^{2} {-} \, \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \, I\omega_{{\text{i}}}^{2}$$

(4)

where I is the rotational inertia, W_net is the net work done and ω is the angular velocity.

Work done is expressed as W = Fθ, and for a net torque in a rotation,

$$W_{{{\text{net}}}} = \, F_{{{\text{net}}}} \theta \, = \, I\alpha \theta$$

(5)

where α is the angular acceleration.

With this, the work done by the rotational motion is therefore

$$w_{f}^{2} = \, w_{i}^{2} + 2\alpha \theta$$

(6)

In short, the larger the angular displacement, the larger the work done, and hence the larger the change in the kinetic energy.

The bending angles or angular displacements for the water to enter each of the triangular CRs were illustrated in Figs. 12, 13 and 14. Ideal case 2, 3 and 8 are termed as triangle 1, 2 and 3 respectively in the figure. Triangle 1 and 2 have the same angular displacement of water entering the inlet whereas Triangle 3 has the largest angular displacement of water entering the inlet compared to Triangle 1 and 2. The angular displacement of Triangular CRs 1, 2 and 3 is 45°, 45° and 50° respectively. Hence, the work done by the water flow entering triangle 3 is higher as compared to triangle 1 and 2, and the kinetic energy loss should be higher. When comparing the inlet velocity of three of the triangular CRs, the inlet velocity of third triangular CR was indeed the lowest due to its greater work done and hence greater loss in kinetic energy. Whereas the first and second triangular CR have similar inlet velocity since their angular displacement were the same. The inlet velocity difference in this case is not due to channel constriction since the distance between the obstacle to Triangular CR 1 is 1000 m larger than of Triangular CR 3 but the inlet velocity of Triangular CR 1 is still higher. Whereas for the outlet velocity comparison, the incidence angle of the water hitting the top boundary for all the triangular reservoirs are compared. Since the water entered the inlet with an angle, therefore the water needs to travel with a certain angular displacement to be discharged out of the reservoirs. The angular displacements for triangular CR 1,3 are the same, which is 90°, whereas as the angular displacement is 75° for triangular CR 2 for water from the top surface to bend towards the outlet. With a smaller angular displacement, Triangular CR 2 should have the highest outlet velocity and discharge, whereas Triangular CR 1 and 3 should have a similar outlet velocity but lower than triangular CR 2. The result from the numerical modelling proved that the theory was correct as triangular CR 2 has the highest outlet velocity. Since the travelling distance for the water from the upper boundary of triangular CR 3 is longer compared to triangular CR 1, 4014 m for Triangular CR 3 and 3677 m for Triangular CR 1, therefore more kinetic energy was lost in between due to work done and friction. Hence, the outlet velocity of Triangular CR 3 is lower than Triangular CR 1.

Fig. 12

Motion of the water flow in and out Ideal case 2—the first triangular CR

Fig. 13

Motion of the water flow in and out Ideal case 3—the second triangular CR

Fig. 14

Motion of the water flow in and out Ideal case 8—the third triangular CR

For the percentage of stagnant water in each of the triangular reservoir, triangular CR 3 has the lowest percentage of stagnant water and triangular CR 1 has the highest percentage of stagnant water in the reservoir. The area of stagnant water in the top left and bottom corners of all the reservoirs are similar, since a maximum of 90° of angular displacement is needed to reach these corners. Therefore, the percentage difference of stagnant water was mainly affected by the angular displacement of the water travelling towards the right corner. As illustrated earlier, the angular displacements for the water from the top boundary to travel to the right corner are 45°, 60° and 40° for triangular CR 1, 2 and 3 respectively. The modelling result is in agreement to the prediction in which the triangular CR 3 has the lowest percentage of stagnant water. The area of the stagnant water at the right corner of triangular CR 2 is indeed larger than in triangular CR 1 but because of the of the higher discharge rate of triangular CR2, the average velocity in the reservoir is increased. With this, the percentage of stagnant water in triangular CR 2 is slightly lower than triangular CR 1 by 0.23%.

3.3 Semi-circular CRs

2 semi-circular CRs with different diameter were modelled with one having a diameter of 10460 m and 12000 m for the other. The location of the stagnant water in the reservoir is shown in the supplementary material.

Due to the larger size of the second semi-circular CR, the reservoir constricts the flow channel more as compared to the first semi-circular CR with the smaller diameter. From the continuity equation, where the flow is constant, the velocity of the water is increased when the width of the channel is decreased at a constant depth. In which

$$Q_{1} = \, Q_{2}$$

$$V_{1} A_{1} = V_{2} A_{2}$$

$$V_{1} B_{1} D \, = \, V_{2} B_{2} D$$

As D is constant, hence they are cancelled out from the equation, leaving:

$$V_{1} B_{1} = \, V_{2} B_{2}$$

(7)

To maintain the flow as V₁B₁, V₂ has to increase when B₂ decreases. Since, the tangent gradient is the same for both semi-circular CR, thus the velocity increase due to channel constriction is the main explanation to the higher inlet velocity for semi-circular CR2 compared to semi-circular CR1.

From the kinetic energy formula, where

$${\text{K}}{\text{.E }} = \, \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} {\text{ mv}}^{2}$$

(8)

and the centripetal force energy as

$$F_{{\text{c}}} = {\text{ mv}}^{2} {\text{/r}}$$

(9)

When the radius of the reservoir, r increases, velocity will increase according and hence the kinetic energy of the flow. With that, the semi-circular CR with the larger radius had a higher outlet velocity and also a lesser percentage of stagnant water. A simple calculation can be demonstrated in the following to estimate the outlet velocity from the centripetal formula:

In semicircle 1, where radius is 5230 m, assume m is 1 kg and v is 1.5 m/s from the modelling result,

$$F_{{\text{c}}} = \, \left( 1 \right)\left( {1.5} \right)^{2} {/}5230 = 4.3021 \, \times 10^{ - 4} {\text{N}}$$

To estimate v in the second semicircle with radius of 6000 m, take

$${4}.{3}0{21 } \times { 1}0^{{ - {4}}} = \, \left( {1} \right)\left( {\text{v}} \right)^{{2}} /{6}000$$

v is therefore 1.6 m/s as shown in the numerical modelling result

3.4 Piano keys CRs

The inspiration of idea of implementing piano-key reservoir was from the piano key weirs due to its high spillway capacity (Abhash & Pandey, 2022). However, the performance of piano-key-like structure in CR is yet to be known. Two piano keys CRs were modelled and they outperformed the other CR with different shape in terms of average velocity, percentage of stagnant water as well as the inhibitory rate of algal bloom occurrence. One of the notable observations is that the average velocity for both piano keys are relatively higher than all the other CRs of different. This is mainly due to the sudden enlargement and constriction of the reservoir design. For the shorter piano key CR, the distance travelled by the water to reach the right boundary is the shortest among all the reservoir shape and hence more kinetic energy is conserved. In short, more kinetic energy can be concentrated on travelling onto the upper portion of the reservoir and to the outlet.

At the first piano key of the shorter piano key reservoir, a reversed circulation pattern was observed. As the jet of water came in from the inlet, the water flow that is diverting towards the piano key hits all the boundary of the piano key in a short time since the distance to reach the piano key is short. However, due to the angular displacement as mentioned in the triangular reservoir section, it is relatively easier for the water to hit the right boundary of the piano key due to lesser work done, resulting in a higher momentum. Since the angular displacement for the water to reach the left boundary of the piano key is larger, therefore the kinetic energy is lesser for water travelling from the left boundary to the right boundary and out of the piano key to the outlet direction. With that, the water with higher momentum from the right boundary pushes the water towards the left, forming a negative circulation. Hence, there is a presence of water with turbulence at the first piano key amidst the stagnant water as shown in Fig. 15. This helps to increase the minimum velocity in the reservoir due to better water circulation. For the longer piano key CR, the average velocity is lower than of the shorter piano key CR as the distance needed for the water to travel to the bottom boundary of the piano key is longer.

Fig. 15

Water circulation pattern at the first piano key of the first piano key CR

As for the comparison of the inlet velocity of both the piano key CR, the inlet velocity of the longer piano key CR is higher compared to the piano key CR with shorter length. Same as the cause of velocity difference in the semi-circular CRs, the piano key CR with the longer causes the channel to be narrower and hence increasing the flow velocity based on continuity equation, Q1 = Q2 as explained earlier.

For the piano key CR with shorter length and more extended keys, more water flow was diverted into the keys and hence more kinetic energy was lost. Therefore, the piano key CR with longer length but fewer keys has a slightly higher outlet velocity as compared to the shorter piano key CR.

3.5 Comparison of CRs with the highest inlet velocity from each category

Three shapes with the highest inlet velocity were chosen for further comparison. Among all the shapes, the semicircle with the larger radius has the highest velocity, followed by the rectangular CR, the smaller semi-circular CR and finally the piano key with the longer key. The velocity difference among all these CRs from each shape category is mainly due to the area of the CR as well as the distance from its width to the nearest obstacle. Indeed, CR 1, 4, 5 and 7 have the largest area compared to the other CR shown in Fig. 16. Although the area of the piano key CR is larger, the inlet velocity is still the same as the smaller semi-circular CR. That is because the area of the piano key CR is arranged in such a way, it enlarge and then constrict the channel flow. Therefore, when the water is travelling to the extended piano key, which is a constricted channel, the velocity increase by in a short distance the channel enlarge again and the water would move upwards to a further distance until it hit the boundary between the piano keys. With this sudden angular displacement, the work done for the water flow is higher and hence more kinetic energy is lost. As flow velocity increases when channel constriction is higher, therefore the channel constriction caused by the CR 1, 4, 5 and 7 is therefore examined. The average channel gap from the obstacle to the reservoir is calculated by taking the average of the channel gap at 5 different points. From the measurement, the gap from the obstacle to the reservoir is indeed inversely proportional to the inlet velocity, in which the smaller the gap, the larger the velocity flowing around the reservoir and hence a larger inlet velocity.

Fig. 16

Area comparison among all the CR shapes

3.6 Comparison of the percentage of stagnant water and the number of stagnant water location of all shapes

The top three CRs with the least percentage of stagnant water is the piano key with longer length, followed by the semi-circular CR with the larger diameter and the piano key with the shorter length. Therefore, it shows that the water circulations in the piano keys CRs are good due to the absence of angular displacement at the inlet. Other than that, having shorter distance between the inlet to the reservoir boundary can help to increase the overall average velocity, and having reservoir with a larger radius would be good to improve the overall circulation of water. When comparing the number of stagnant water location, the piano key with the shorter length has more stagnant water location. The stagnant water locations are determined based on the geometry of the reservoir, whereby those with more corners would have more stagnant water location.

3.7 Comparison of the minimum velocity, average velocity and the retention time

The average velocity was calculated based on the colour palette set in the 0.01 m/s interval with the formula of Average velocity = Velocity midpoint between the isoline * area between the isoline/the sum of the total area from all the isolines:

$$V_{{{\text{avg}}}} = \, \Sigma \left( {V_{{\text{i}}} *A_{{\text{i}}} /A_{{\text{T}}} } \right)$$

(9)

where V = midpoint of the range of velocity between the isoline. I = 1, 2, 3, 4, 5…16 from the highest of 0.2 m/s to the lowest -0.05 m/s at an interval of 0.01 m/s. A = area between the respective isoline.

From the result shown in Fig. 17, the piano key with the shorter length showed the highest overall velocity due to the factors discussed. The 40°–90°–50° triangular CR has the highest minimum velocity due to having a smaller angular displacement for water to travel towards the right corner as explained earlier. For the retention time, 45°–90°–45° triangle has the lowest retention time since its volume is the smallest, as retention time is calculated by the formula, Retention time = volume/outlet discharge. Further calculation was done by diving the retention time over the volume to omit the factor of volume in examining the retention time, the rectangular reservoir showed the lowest retention time/volume. Despite reflecting a higher natural outlet discharge by the rectangular CR, it also reflects that the rectangular reservoir has an effective shape of not impounding the water inside for too long due to the presence of corners and difficult path for water to travel.

Fig. 17

Average velocity comparison for the CRs

3.8 Discussion of cyanobacteria and Chlorella bloom mapping

Cyanobacteria and Chlorella was mapped based on the 0.05 m/s as the critical velocity obtained. From the numerical modelling result as tabulated in Table 7, most of the CR shape showed more than 70% of area with velocity lesser than 0.05 m/s which are prone to cyanobacteria and Chlorella occurrence. The reservoir shape with the least percentage of area with velocity lesser than 0.05 m/s are the piano keys reservoir, with the shorter piano key having 31.2% and the longer piano key reservoir having 50.6% of area prone to algal and chlorella blooming. Due to the piano key geometry explained, the velocity in the most of area of the piano key CR is 0.085 m/s, and thus, less prone to algae and chlorella blooming in terms of its flow velocity. The algae and chlorella mapping for each of the CR shape can be found in the supplementary material.

Table 7 Percentage of area in the CR with velocity lesser than 0.05 m/s

3.9 Discussion of filamentous algae bloom mapping

Filamentous mapping was based on the 0.01 m/s as the critical velocity for filamentous algae bloom occurrence. From the numerical modelling result as tabulated in Table 8, the piano key with the longer showed the highest percentage of area with velocity lesser than 0.01 m/s and the smaller semi-circular CR showed the smallest percentage of area with velocity lesser than 0.01 m/s. This is mostly due to the effective of shape in enabling water mobility within the reservoir as earlier. As the longer piano key reservoir has more a long extended piano key, therefore the further distance the water needs to travel down to the piano key boundary and move back up again, resulting in a low velocity flow. The filamentous algae mapping for each of the CR shape can be found in the supplementary material.

Table 8 Percentage of area with velocity lesser than 0.01 m/s in the CRs

3.10 Discussion on phytoplankton mapping

0.06 m/s is the velocity for low inhibitory to phytoplankton occurrence and thus phytoplankton mapping was done based on this velocity. From the numerical modelling result as tabulated in Table 9, most of the CR shape showed about 90% of area with velocity lesser than 0.06 m/s which has low inhibitory to the growth of phytoplankton. The reservoir shape with the least percentage of area with velocity lesser than 0.06 m/s are the piano keys reservoir, with the shorter piano key having 45.0% and the longer piano key reservoir having 54.8% of area with low inhibitory to phytoplankton occurrence. Due to the piano key geometry, the velocity in the most of area of the piano key CR is 0.085 m/s, and thus, having a high inhibitory rate to phytoplankton occurrence in terms of its flow velocity. The mapping for area with low inhibitory to phytoplankton in each of the CR shape can be found in the supplementary material.

Table 9 Percentage of area with velocity lesser than 0.06 m/s in the CRs

3.11 Discussion on the chart selection and ranking

As there are multiple factors to be considered when selecting the best reservoir shape for minimal algae bloom occurrence, a weightage chart was developed shown in the supplementary material. The weightage chart took account of all the important performance keys discussed in the previous section to see the overall performance of each CR. Since not all the performance keys have the same weightage, adjustment was made to select the best weightage for each criterion based on its importance in minimising the algal bloom occurrence. The CR shape with the highest mark would be selected as the best shape for minimising the algal bloom occurrence.

For each of the criteria, the lowest mark is 1 and the highest mark is 8, except for the location of stagnant water since many of the shapes would have the same number of locations. Therefore, for the location of stagnant water criteria, the lowest mark is 1 and the highest mark 3. Table 10 shows the unweighted mark allocation for each CR shape.

Table 10 Unweighted mark allocation for each CR shape

From the unweighted mark, the weightage developed previously was factored inside the score and Table 11 showed the final weighted mark for each of the CR shape.

Table 11 Final weighted mark for each CR shape

From the result, the shorter piano key is selected as the best shape among other reservoir shape, followed by the smaller semi-circular CR. The shape with the least mark is the 40°–90°–50° triangular CR. The ranking shown is not because of the area of the CR but due to its geometrical arrangement. The reason the shorter piano key CR outperformed reservoirs with other shape is simply due to the distance of the inlet to the bottom boundary as explained in the previous sections. Indeed, there are still areas with low velocity which are prone to algal bloom but these areas are seen to be only at the extended keys. Therefore, this is particularly useful when the design requires a large area but still require a good flow mobility within the reservoir, as the potential occurrence of algal bloom is only at a small area stored in the extended keys. With this, further actions can be taken targeting only the area of the extended piano keys to increase the flow velocity there instead of involving a higher cost to treat the freshwater in the whole reservoir. However, the best shape here in this given condition is only applicable for the future second-generation CR with the same setting, whereby one boundary is attached to the shore and the boundary at the other sides are free to change. For CR designs that are to be constructed with other obstacles near the inlet or outlet, or it is to be attached onto an island, the best shape from this finding would not be too relevant since the CR that are to be constructed are topography-dependent. For such cases, the geometry concept from this research can be applied and the shape should be optimised based on the location of inlet and outlet, as well as the flow of water in the reservoir based on the bathymetry.

3.12 Shape optimisation

From the shape comparison and analysis done based on the effect of the geometry to the water flow, further shape optimisation was done to further minimise the stagnant water in the CR under the same condition and setting. The algae mapping in the previous CR shapes was referred to minimise the location that are prone to stagnant water. Below are the geometry considerations to generate the optimised shape:

• a. The distance from the inlet to its left and right boundary

• b. The direction of water entering the reservoir

• c. Channel within the reservoir with constrictions to simulate a fast flow

• d. Minimising the angular displacement for the flow to travel

• e. Circular path from the top boundary for water to travel down the outlet smoothly

• f. Presence of piano key geometry for algal control

With the above considerations, an optimised shape called the “little dinosaur” is then formed, with the inlet as the “tail” and outlet as the “head”. It has an area slightly higher than the 45°–90°–45° and 40°–90°–50° triangular CRs. A series of simulations was then done to this optimised shape to see its effectiveness in reducing the area prone to algal bloom. Figure 18a shows the location of stagnant water in the optimise shape. Compared to the other shapes, the area of stagnant water has greatly reduced and they are all stored in the “leg” or the extended structure of the reservoir. This is the same for algae, chlorella and phytoplankton mapping, showing a great reduction in the area with these algal occurrences, shown in Fig. 18b–d. All and all, the best thing of this optimised shape is that all flow with low velocities are kept inside one specific location, which is in the “leg”. With that, algal control would be relatively easier since the location with potential occurrence of algal bloom are easily pinpointed and controlled. Other than the leg, the other part of the reservoir showed a good flow mobility with no algal occurrence based on its velocity.

Fig. 18

Algal bloom mapping for the optimised shape—the little dinosaur. a Stagnant water in the little dinosaur optimised shape reservoir. b Algae and Chlorella mapping in the little dinosaur optimised shape reservoir. c Filamentous Algae mapping in the little dinosaur optimised shape reservoir. d Phytoplankton mapping in the little dinosaur optimised shape reservoir

After the formation of “little dinosaur” as the first optimised shape, it is seen that the “body” part of the reservoir is free of any algae occurrence. With that, the top part of the shape is then mirrored to observe the flow in the modified “little dinosaur”, which then named as the “little pencil”. The area of this modified shape is slightly bigger than the short piano key reservoir and all the triangular reservoirs.

With this modified shape—the “little pencil”, the percentage of stagnant water in the reservoir is close to zero percent and there is no sign of filamentous algae bloom based on the velocity in the reservoir as shown in Fig. 19a, b respectively. However, there’s a large area in the reservoir prone to algae, chlorella and phytoplankton blooming due to the absence of constrictive area shown in Fig. 19c, d. Therefore, it would be hard to control since the spread occurred over a large area of the reservoir unlike “little dinosaur”, which only occur inside the “leg” of the “little dinosaur”. Therefore, this proved that the presence of piano key-like structure is important to increase the overall flow of the reservoir and for easier algal bloom management as mentioned earlier.

Fig. 19

Algal bloom mapping for the optimised shape—the little pencil. a Stagnant water in the little pencil modified optimised shape reservoir. b Filamentous algae mapping in the little pencil modified optimised shape reservoir. c Algae and chlorella mapping in the little pencil modified optimised shape reservoir. d Phytoplankton mapping in the little pencil modified optimised shape reservoir

Hence, this summarised how shape optimisation is done based on the flow of the water in and out of the reservoir as well as its topography. As mentioned earlier, the optimised shape would not be same at sites which has obstacle constraining the shape of the reservoir. For that particular situation, the flow must be re-analysed to choose the best shape that suit that particular topography. Otherwise, this optimised shape can be applied to any sites that have similar setting and topography, in which the shape of the reservoir is free for engineers to decide without site constraints.

3.13 Application to existing CR at Qingcaosha

As an example of shape optimisation for CRs that are topography-dependent, Qingcaosha CR was used as an example since it is also constructed at Yangtze River. The reservoir is attached to an existing island called the Changxing Island, and within the reservoir there is Chongming Island. Therefore, the shape of Qingcaosha is largely dependent to the topography of the island. Qingcaosha in this case is simulated with the existing depth of the reservoir as well as the discharge and tidal effect at Yangtze River, with the same setting used for the idealised shape simulation. Therefore, there is no account on the salinity, nutrients, carbon dioxide and other factors that are affecting the growth of algae. Hence, the result shown are the mapping of algae, chlorella, filamentous and phytoplankton occurrence solely due to the shape of the reservoir as well as the depth in the reservoir. Table 12 showed the result summary for the percentage of area in the reservoir with velocity lesser than 0.06 m/s, 0.05 m/s and 0.01 m/s and its respective percentage of algae, chlorella, phytoplankton and filamentous algae bloom occurrence.

Table 12 Result summary showing the percentage of area in the reservoir with velocity lesser than 0.06 m/s, 0.05 m/s and 0.01 m/s and its respective percentage of algae, chlorella, phytoplankton and filamentous algae bloom occurrence

From the percentages, especially on the total percentage of area with low inhibitory rate, it is in agreement to Ren et al. (2015) stating that Qingcaosha Reservoir is an ideal environment for phytoplankton to proliferate.

Based on the topography, an attempt of shape optimisation was made to Qingcaosha to minimise the areas prone to algal blooming. The attempt was made based on the direction of water flow within the reservoir. The changes made for the shape optimisation include:

• a. Filling up the locations behind the sharp bends to reduce stagnant water behind corners

• b. Changing the location of the inlet to direct water into the reservoir to ensure a straight flow of water from the inlet

• c. Smoothen the island to ensure a smooth water flow

After the changes made, an addition effort to increase the area of the reservoir was made by adding the piano keys at the filled area from the optimised shape. Graphical comparisons were made to examine if the optimised shape has reduced the areas prone to algal blooming shown in the supplementary material.

By graphical comparison, it is seen that the area of stagnant water has greatly reduced after shape optimisation based on the water flow. There are areas with stagnant water even after shape optimisation as some are located behind the Chongming island and most stagnant water gathered at the end of the reservoir before exiting to the outlet. This also reflects the ineffectiveness of the location of outlet in the reservoir which could be due to topographical constraints when designing. Since the area of the reservoir has been greatly reduced to suit optimise its shape, there will be reduction in the storage area and hence the supply. Therefore “piano keys” are added to the optimise shape to increase the storage area. However, the area of stagnant water increased and therefore, piano keys under these topography constraints would only help to increase storage area but would not help to increase the overall velocity in the reservoir.

The same observation is applied to the algae, chlorella, filamentous algae and phytoplankton mapping, whereby the optimised shape has reduced the area prone to algal blooming.

As a summary from this application, shape optimisation based on the water flow does help to improve the flow mobility in the reservoir. However, the addition of piano key does not improve the overall flow mobility but just aided to provide extra storage area for more water supply. Therefore, the best shape determined from the previous topographical setting do not apply here but the geometrical effect on the flow mobility studied in the previous section still applies. However, the shape optimisation for Qingcaosha reservoir done in this research is based on idealised condition, whereby the location of inlet can be changed and there is permission to alter the land owned by the island’s authority. In reality, there are most constraints related to the land authority, government, the local community, finance and so on. Therefore, when shape optimisation of an existing CR or is not possible, dredging could be a quick solution to increase the flow velocity in the reservoir. This is so as flow speed would increase at a greater depth, and vice versa.

An attempt to increase the flow velocity in Qingcaosha reservoir was made by SOGREAH (2008) by dredging. The model shows water renewal in zones that were static before dredging. Thus, dredging would be a good way to improve the mobility of water in the reservoir when shape optimisation is not possible.

4 Conclusion

The shape of a CR is high depending on the location of its construction, especially for second-generation CRs that are attached to existing islands and for all the first-generation CRs. However, if there are no topography constraints, the shape of the CR can be optimised to reduce algal bloom occurrence.

Since the second-generation CR can be constructed in any location of the estuary, therefore the shape of the reservoir is easier to be controlled during the design phase. For second-generation CRs without any topographical constraints such as attaching to islands or any kind of existing landforms, the following geometry criteria can be implemented to reduce algal bloom occurrence:

• a. Location of inlet should be placed perpendicular to the flow direction

• b. Minimal corners within the reservoir

• c. Shape optimised based on water flow direction with minimal angular displacement

• d. Implement piano-key-like structure for effective algal bloom control and provide additional storage of freshwater

• e. Incorporate the “little dinosaur” or “little pencil” reservoir model which is the optimised shape for CR for minimal algal bloom occurrence

For second-generation CR with topographical constraints, the shape can be optimised based on the flow of water in the CR, with minimal corners to reduce angular displacement. However, if shape optimisation is not possible due to land use permission, the other method should be adopted to reduce the occurrence of algal bloom.

More extensive research can be done in the future with the incorporation of practical experiments, real-life application, implementation Artificial Intelligence technology for shape optimisation and so on. As only hydrodynamic modelling using one software was done, therefore the result is reliant to the accuracy of the particular software. Therefore, if extensive research is to be done, physical modelling with different shape prototypes can be incorporated to compare the result from the numerical modelling with the physical modelling result. For this research, improvements can also be done on the orientation of the North boundary to be perpendicular to the water movement. Therefore, it is encouraged that the future researchers or engineers can perform the numerical modelling again with the data from real site measurement if future researches are to be carried out on this topic. In addition to that, the simulation period can be increased to 28 days instead of 14 days to increase the stability of the hydrodynamic model, which is limited in this research due to time and the need for high computational power due to the repetitive run of all the CR shapes with a long period. However, these slight adjustments would not affect the outcome for this research since all the CR shapes were run under the same condition and hence the ultimate dependent factor would be the shape of the CR itself.

Since the shape comparison and shape optimisation were done only on one hydrodynamic software, field measurement can be done to validate its capability in reducing algal bloom occurrence based on the flow velocity. The optimised shape should be observed for a longer period to examine its performance. If there are occurrence of algal bloom in the optimised shape, they should be mapped on the real reservoir to compare the mapping on the numerical model, even though it might be caused by other algal growth factor since it is subjected to real life conditions.