There exists a significant risk of water blooms during the utilization of recycled water in landscape environments. The nitrogen and phosphorus discharge standards of sewage treatment plants are very low. Controlling hydraulic retention time (HRT) is currently the most effective means to control water bloom. This article proposes a new method for determining the HRT threshold based on water transparency as a control indicator. The following results were obtained: (1) with the nitrogen and phosphorus concentrations of 15 and 0.5 mg/L, respectively, the threshold for HRT under high temperature and strong light is 4.6 days, while the threshold under low temperature and low light is 11.5 days. (2) With the nitrogen and phosphorus concentrations of 10 and 0.3 mg/L, respectively, the threshold for HRT under high temperature and strong light is 5 days, while the threshold under low temperature and low light conditions is 12.3 days. (3) The HRT threshold obtained under high temperature and strong light is lower than that obtained under low temperature and low light conditions. (4) The higher the concentrations of nitrogen and phosphorus, the smaller the HRT threshold obtained. (5) Blue algae have stronger adaptability than green algae and diatoms.

  • A new method for determining the hydraulic retention time (HRT) threshold based on water transparency was proposed.

  • Cyanobacteria have stronger adaptability than green algae and diatoms.

  • Light and temperature have a significant impact on the determination of the HRT threshold.

  • The higher the concentrations of nitrogen and phosphorus, the smaller the threshold value of HRT obtained.

With the increasing human population and the development of urbanization, the extensive use of water resources is leading to a lack of surface water (Zaibel et al. 2016; Ao et al. 2018; Leong & Mukhtarov 2018; Li et al. 2020). Urban sewage has the characteristics of stable water quantity, controllable water quality, and nearby availability. Therefore, sewage recycling has become an effective way to solve water resource shortages (Chu et al. 2004; Marks 2006; Qu et al. 2019; Chen et al. 2020; Xie et al. 2021). Currently, recycled water is widely used in supplementing landscape water bodies (Li et al. 2015), which can meet the demand for landscape water bodies in water-scarce cities. The use of reclaimed water for landscaping can also achieve ecological storage, providing a stable and reliable water source for the further utilization of reclaimed water. In addition, the utilization of reclaimed water landscapes can achieve the best method of natural restoration of the urban ecological water cycle (Mitsch 1995). In 2020, the recycled water used for the landscape environment in Beijing accounted for 92.5% of the total recycled water use.

The dilution and self-purification capacity of urban landscape water bodies are worse than natural water bodies, and the water depth is generally shallow, usually 1–2 m. In addition, the high concentration of nitrogen and phosphorus nutrients in the reclaimed water can easily lead to the excessive growth of microalgae in the landscape water that is recharged by reclaimed water (Ao et al. 2018; Song et al. 2022a), even resulting in water blooms (Muhid et al. 2013).

The growth and movement of algae in landscape water bodies are closely related to hydrodynamic conditions. Many studies have shown that when the intensity of hydraulic scouring increases or the flow velocity increases, the growth rate of algae will slow down (Lung & Paerl 1988). A critical flow velocity is found under hydrodynamic conditions, and when the flow velocity of the water body is greater than the critical flow velocity, the growth of algae can be suppressed to some extent, thus controlling the outbreak of water blooms. For a given landscape water body, hydraulic retention time (HRT) has a significant impact on the accumulation of nutrients and the growth of algae in the water body (Huang et al. 2018). The HRT is too short, and oxygen-consuming organic pollutants cannot be fully degraded, resulting in high operating costs. Excessive HRT greatly increases the possibility of algae overpopulation. Therefore, the study of the hydraulic retention threshold in the utilization of reclaimed water landscape environment is of great significance for controlling the outbreak of algal blooms in water bodies (Huang et al. 2018).

As we all know, the perception of water landscapes significantly affects the aesthetic and recreational value of these underwater parks. The perception of water landscapes is influenced by visual factors, particularly the physical characteristics of urban landscape water, which encompass water transparency, hue, and turbidity (Liu et al. 2013). The transparency of water is typically assessed using the Secchi depth (SD), a metric that is intricately linked to water landscapes. When members of the public evaluate whether a body of water is suitable for recreation, they often rely on SD as a guiding factor (Lee & Lee 2015; Smith et al. 2015). The correlation between the public perception of water quality and SD is both positive and robust, with SD exhibiting a predictive power of 74.2% (Lee 2016). Therefore, SD serves as an intuitive indicator of landscape impact, making it easily comprehensible. To bridge the communication gap in landscape water quality between scientists and the general public, the use of SD is essential (Chang et al. 2020).

In this study, the article introduces a novel approach for establishing the threshold value of HRT using SD as the primary indicator. It also provides corresponding HRT threshold values for various sewage discharge standards. This approach is pivotal in preventing and managing the risk of water blooms in the reuse of reclaimed water for urban landscape water bodies.

In this study, the following formulas will be used.

The interactive relationship between the specific growth rate μ (d−1) of algae with the dissolved total nitrogen or phosphorus is described by the Monod model (Yang et al. 2011; Song et al. 2022b).
formula
(1)

In Equation (1), μmax,N(P) (d−1) is the maximum specific algal growth rate when the solution was saturated with nitrogen or phosphorus, CN(P) (mg/L) is the nitrogen or phosphorus concentration in the medium, and KN(P) (mg/L) is the half-saturation constant of nitrogen or phosphorus.

The Steele model (Equation (3)) was used to describe the relationship between the specific algal growth rate and the light intensity (Benson & Rusch 2006).
formula
(2)

In Equation (3), I (lx) is the light intensity, μ (d−1) is the specific algal growth rate at the light intensity I, μmax is the maximum specific algal growth rate at the optimal light intensity, and Iopt (lx) is the optimal light intensity.

At typical environmental temperatures, the relationship between the specific algal growth rate μ in the logarithmic phase and the thermodynamic temperature T (K) can be described using the Arrhenius model (Eppley 1972).
formula
(3)
In Equation (4), Ar is a constant, R is the ideal gas constant (8.3 J/(mol·K)), and Ea is the algal growth activation energy. The relationship between μ and the culture temperature T can be described using Equation (5) (Song et al. 2022b).
formula
(4)
The multiplicative model principle was used to include all possible parameters affecting the algal growth rate (Lee et al. 2015). Combining Equations (2) and (4), the following comprehensive model of the specific algal growth rate was constructed (Song et al. 2022b).
formula
(5)
A control model of the effect of HRT on algal blooms in reclaimed water landscape systems was developed by Song et al. (2022b).
formula
(6)
where X (mg/L) is the dry weight of algae; KN (mg/L) is the half-saturation constant of nitrogen; KP (mg/L) is the half-saturation constant of phosphorus; YX|N is the yield coefficient for algal cells based on nitrogen; YX|P is the yield coefficient for algal cells based on phosphorus; C0N (mg/L) is the nitrogen concentration in the reclaimed water; C0P (mg/L) is the phosphorus concentration in the reclaimed water.

Derivation of the HRT model based on SD

It is well known that Lambert–Beer's law was used to describe the relationship between SD and the attenuation coefficient of light as follows (Imboden 1974):
formula
(7)
From Equation (7), we can further obtain
formula
(8)
The influence of other impurities in the water on light attenuation is ignored. k0 represents the optical attenuation coefficient related to algal cell biomass, and its expression with respect to algal cell biomass X is as follows:
formula
(9)
where kb is the biomass-light attenuation coefficient (m2g−1) determined by the algal species, kw is the water-light attenuation coefficient (m−1), and X is the algal cell biomass (g m−3).
It can be obtained from Equation (9).
formula
(10)
That is,
formula
(11)
Substituting Equation (8) into Equation (5) yields
formula
(12)
Substituting Equations (11) and (12) into Equation (6) yields
formula
(13)
The control model (13) describes the interaction between temperature, light, transparency, nitrogen concentration, phosphorus concentration, and HRT. For specific effluent nitrogen and phosphorus concentrations from sewage treatment plants, it provides a method for determining the threshold value of HRT for receiving water bodies. Additionally, model (13) can be used to determine the water quality of effluent from reclaimed water plants based on the condition of the receiving water body. The method proposed in this study for determining the threshold value of HRT can be extended to determine the water quality thresholds for reclaimed water. This approach is based on the conditions of actual water bodies and provides a certain reference significance for setting effluent water quality standards for reclaimed water.

Simulations

In this section, two types of green algae (Chlorella vulgaris and Scendesmus quadricauda), two types of cyanobacteria (Microcystis aeruginosa and Oscillatoria planctonica), and Synedra sp. will be the choice to research the threshold of HRT. The water-light attenuation coefficient kw = 1.97 m (Gutierrez-Wing et al. 2012). The values of the unstated model parameters are taken from Song et al. (2022b). The model parameters of these algae have been listed in Table 1.

Table 1

Parameters used in the control model for model (13)

Algae speciesYX|NYX|PKN (mg/L)KP (mg/L)μmax (d−1)Iopt (lx)Ea (kJ/mol)kb (m2g−1)
C. vulgaris 32.5 219.0 5.5 0.3 0.52 2,621 76.5 0.08 (Sirisansaneeyakul et al. 2011
S. quadricauda 25.0 207.7 9.8 0.2 0.70 2,880 49.9 0.10 (Cabello et al. 2014
M. aeruginosa 24.7 224.2 18.6 0.4 0.61 1,920 38.7 0.03 (Wu et al. 2005
O. planctonica 37.7 247.2 20.0 0.4 1.01 2,411 124.3 0.18 (Lee et al. 1987
Synedra sp. 3.0 48.8 7.6 0.3 0.95 5,085 99.7 0.27 (Slegers et al. 2013
Algae speciesYX|NYX|PKN (mg/L)KP (mg/L)μmax (d−1)Iopt (lx)Ea (kJ/mol)kb (m2g−1)
C. vulgaris 32.5 219.0 5.5 0.3 0.52 2,621 76.5 0.08 (Sirisansaneeyakul et al. 2011
S. quadricauda 25.0 207.7 9.8 0.2 0.70 2,880 49.9 0.10 (Cabello et al. 2014
M. aeruginosa 24.7 224.2 18.6 0.4 0.61 1,920 38.7 0.03 (Wu et al. 2005
O. planctonica 37.7 247.2 20.0 0.4 1.01 2,411 124.3 0.18 (Lee et al. 1987
Synedra sp. 3.0 48.8 7.6 0.3 0.95 5,085 99.7 0.27 (Slegers et al. 2013

Based on differences in light intensity, temperature, and nitrogen and phosphorus concentrations in reclaimed water makeup, this section will discuss four typical conditions (HA, HB, LA, and LB) (see Table 2).

Table 2

The four typical conditions

ConditionsC0N (mg/L)C0P (mg/L)T (°C)Ios (lx)
HA 15 0.5 25 5,000 
HB 10 0.3 25 5,000 
LA 15 0.5 12 1,000 
LB 10 0.3 12 1,000 
ConditionsC0N (mg/L)C0P (mg/L)T (°C)Ios (lx)
HA 15 0.5 25 5,000 
HB 10 0.3 25 5,000 
LA 15 0.5 12 1,000 
LB 10 0.3 12 1,000 

Based on the control model (13), the curve of HRT–SD is given under the conditions HA and HB for the five algal species in Figure 1. The warning line for water blooms in landscape water bodies is an SD of 0.4 m. As can be seen from Figure 1, under high temperature and high light conditions, when the nitrogen and phosphorus concentrations are 15 and 0.5 mg/L, respectively, the HRT threshold corresponding to the bloom warning line SD = 0.4 m is approximately 4.6 days; when the nitrogen and phosphorus concentrations are 10 and 0.3 mg/L, respectively, the HRT threshold corresponding to the bloom warning line SD = 0.4 m is approximately 5 days. Under the conditions of HA and HB, the minimum HRT threshold is determined by M. aeruginosa. This also shows that under high temperature and high light conditions, M. aeruginosa has a growth advantage over other algal species.
Figure 1

The control curve of HRT–SD under HA and HB for the five algal species.

Figure 1

The control curve of HRT–SD under HA and HB for the five algal species.

Close modal
Based on the control model (13), the curve of HRT–SD is given under the conditions LA and LB for the five algal species in Figure 2. As can be seen from Figure 2, under low temperature and low light conditions, when the nitrogen and phosphorus concentrations are 15 and 0.5 mg/L, respectively, the HRT threshold corresponding to the bloom warning line SD = 0.4 m is approximately 11.5 days; when the nitrogen and phosphorus concentrations are 10 and 0.3 mg/L, respectively, the HRT threshold is approximately 12.3 days. Under the conditions of LA and LB, the minimum HRT threshold is still determined by M. aeruginosa. This also shows that under low temperature and low light conditions, M. aeruginosa has a growth advantage over other algal species.
Figure 2

The control curve of HRT–SD under LA and LB for the five algal species.

Figure 2

The control curve of HRT–SD under LA and LB for the five algal species.

Close modal

As can be seen from Figures 1 and 2, light and temperature have a significant impact on the determination of the HRT threshold; the threshold value of HRT under high temperature and high light conditions is approximately 5 days, while the threshold value under low temperature and low light conditions is approximately 12 days. In addition, M. aeruginosa has a growth advantage over other algal species. Therefore, under certain conditions, M. aeruginosa may be used to determine relevant water quality thresholds.

In this study, a determination method for the threshold of HRT was proposed employing transparency as a control indicator. The control model (13) can directly calculate the reasonable HRT threshold of water bodies through the growth data of specific algae species and the environmental conditions of landscape water bodies. The main conclusions obtained in this article are as follows.

  • (1) With the nitrogen and phosphorus concentrations of 15 and 0.5 mg/L, respectively, and the bloom warning line SD = 0.4 m, the threshold for HRT under high temperature and strong light conditions is 4.6 days, while the threshold under low temperature and low light conditions is 11.5 days.

  • (2) With the nitrogen and phosphorus concentrations of 10 and 0.3 mg/L, respectively, and the bloom warning line SD = 0.4 m, the threshold for HRT under high temperature and strong light conditions is 5 days, while the threshold under low temperature and low light conditions is 12.3 days.

  • (3) The threshold value of HRT obtained under high temperature and strong light conditions is lower than that obtained under low temperature and low light conditions; therefore, the threshold value of HRT suitable for local conditions should be determined based on the temperature and light conditions in different regions.

  • (4) The higher the concentrations of nitrogen and phosphorus, the smaller the threshold value of HRT obtained.

  • (5) Cyanobacteria have stronger adaptability than green algae and diatoms and can be used to determine the HRT threshold.

In addition, for a given water body with a certain concentration of nitrogen and phosphorus, it is feasible to determine the HRT of the landscape water body through transparency.

This work was supported by the Major Program of the National Natural Science Foundation of China (Nos. 52293440, 52293442, and 52270044).

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

The authors declare there is no conflict.

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