The Daihai Lake (40°32′-40 36′N, 112 37'−112° 45′E) is a typical inland closed saline lake in the central and southern Mongolian Plateau and located in a temperate semi-arid region (Figure 1). The rivers entering the Daihai Lake are seasonal rivers, which flow into the Daihai Lake in rainy summer and cut off in winter. The average annual temperature is 5.1°C.

The state variables in the model are mainly about different nitrogen contents in the lake and plants, which are shown in Figure 1. These state variables are connected to each other by the flow of nitrogen. This model is divided into three parts based on nitrogen state variables and related parameters (Table 1) including nitrogen transformations in water and soil, submerged plant growth processes and the effects of temperature on some processes. The nitrogen transformation module simulates the processes of nitrification, denitrification and the diffusion of nitrogen from the sediment to the water, as well as the effect of exogenous pollution on nitrogen concentrations in water column. The submerged plant growth module described plant growth by its photosynthesis and absorption of nutrients from water and soil. The effects of temperature on a number of nitrogen transformation processes are obtained by the temperature effect module.

The state variables in the model include ammonia nitrogen content in water (Eq 1), nitrate nitrogen content in water (Eq 2), ammonia nitrogen content in soil (Eq 3), nitrate nitrogen content in soil (Eq 4), nitrogen content of plant carcasses located in the above ground portion (Eq 5), nitrogen content of plant carcasses located in the below ground portion (Eq 6), and nitrogen content stored in plants (Eq 7). The parameters that appear in the equations are detailed in Table 1.

The Eq 1 for the state variable representing the amount of ammonia nitrogen in the water is as follows: N H 4 _ W t = N H 4 _ W t − d t + i n 1 + l e + d i 1 − n i w − u p 1 * d t (1) where NH4_W represents the concentration of ammonia in water; in1, le, di1, niw and up1 represent the increase in ammonia concentration in water due to surface pollution, and the leaching rate, diffusion rate, nitrification rate in water, and the rate of ammonia uptake by plants, respectively. The leaching rate, ammonia diffusion rate and nitrification rate are all simulated using first-order reaction kinetics (Martin and Reddy, 1997; van der Peijl and Verhoeven, 1999; Huang et al., 2020; Wang, 2022), as shown in Eqs 1b–d. n i w = N H 4 _ W * K n i t w * θ 1 T W − 20 * r t e m p (1b) l e = N _ L I T T E R _ W * L e a c h i n g r a t e * θ 2 T W − 20 (1c) d i 1 = N H 4 _ S − N H 4 _ W * c _ t u r b d i f * c _ t e p * K d i f * p o r o s i t y p o r o s i t y + 1 d e e p t h d i f (1d)

The Eq 2 for the state variable representing the nitrate-nitrogen content of the water is as follows: N O 3 _ W t = N O 3 _ W t − d t + n i w + i n 2 − u p 2 − d i 2 − d n w * d t (2) where NO3_W is the concentration of nitrate-nitrogen in water; In 2 represents the increase in nitrate-nitrogen concentration in water brought about by surface source pollution, similar to that produced by surface source pollution in Eq 1, with the introduction of a time-step function Tk, which, according to the actual situation in Daihai (Chapter 4.1), reinforces the effect of seasonal changes on the state variables in the model (Zheng and Men, 2020), as detailed in Eq 1a, Eq 2a. i n 1 = n h 4 _ o u t e r * T K (1a) i n 2 = n o 3 _ o u t e r * T K (2a) where up2, di2 and dnw represent the rate of nitrate nitrogen uptake by plants, which are the rate of nitrate nitrogen diffusion and the rate of denitrification (Boyd, 1970; van der Peijl and Verhoeven, 1999; Wang, 2022),respectively. The nitrate diffusion rate and denitrification rate are simulated using first-order reaction kinetics, as detailed in Eqs 2b, c. d i 2 = N O 3 _ S − N O 3 _ W * c _ t u r b d i f * k d i f _ N O 3 * p o r o s i t y p o r o s i t y + 1 d e e p t h d i f (2b) d n w = N O 3 _ W * K d e n * θ 3 T W − 20 (2c)

The Eq 3 for the state variable representing the amount of ammonia nitrogen in the sediment is as follows: N H 4 _ S t = N H 4 _ S t − d t + d e c − u p 3 − n i s − d i 1 * d t (3) where NH4_S is the concentration of ammonia nitrogen in the sediment; dec, up3 and nis represent the rate of mineralisation, the rate of ammonia nitrogen uptake by plants, and the rate of nitrification in the sediment, respectively. The mineralization rate was simulated using first-order kinetics (Mayo et al., 2018), and the nitrification in the sediment introduced the effect of dissolved oxygen on the rate (Brown and Barnwell, 1987; Brix et al., 2002). as detailed in Eqs 3a, b n i s = K s n * r t e m p * θ 5 T W − 20 * 1 − e − λ d o * D O * N H 4 _ S (3a) d e c = N _ S O I L _ O M * K d e * θ 4 T W − 20 (3b)

The Eq 4 for the state variable representing the nitrate-nitrogen content of the sediment is as follows: N O 3 _ S t = N O 3 _ S t − d t + d i 2 + n i s − u p 4 − d n s * d t (4)

Where NO3_S is the concentration of nitrate nitrogen in the sediment mg/L; up4 and dns are the rate of nitrate nitrogen uptake by plants and denitrification rate respectively. Denitrification rates were simulated using first-order reaction kinetics (Ying et al., 2009), as detailed in Eq 4a. d n s = N O 3 _ S * K d e n * θ 3 T W − 20 (4a)

The state variables representing the nitrogen content of the plant carcasses were divided into an above-ground and below-ground fraction, with the following Eqs 5, 6. N _ L I T T E R _ W t = N _ L I T T E R _ W t − d t + d e s h − f r w − l e * d t (5) N _ L I T T E R _ S t = N _ L I T T E R _ S t − d t − d e r o − f r s * d t (6) where N_LITTER_S and N_LITTER_W represent plant residues in sediment and water, respectively, and desh, frw, dero and fes represent the rate of nitrogen reduction in submerged plants and the rate of decomposition of submerged plant residues due to submerged plant mortality (van der Peijl and Verhoeven, 1999; Zhang et al., 2003; Gao et al., 2018), respectively, as detailed in Eq 5a, Eq 6a, Eq 5b, Eq 6b f r w = N _ L I T T E R _ W * f r a g w * r t e m p * θ 6 T W (5a) f r s = N _ L I T T E R _ S * f r a g s * r t e m p * θ 6 T W (6a) d e s h = N _ P L A N T * r d r s h (5b) d e r o = N _ P L A N T * r d r r o (6b)

Equation 7 for the state variable representing the nitrogen content of submerged plants per unit area is as follows. N _ p l a n t t = N _ p l a n t t − d t + u p 2 + u p 1 + u p 3 + u p 4 − d e s h − d e r o * d t (7)

Where N_plant represents the nitrogen content of submerged plants (Nmg/L), and up2, up1, up3 and up4 represent the rates at which submerged plants absorb ammonia and nitrate nitrogen from water and soil, respectively. Considering the relationship between plant growth rate and required nutrients, and considering the growth mechanism, the growth rate of a plant can be expressed by the photosynthetic rate of a plant, that is, the rate at which a plant absorbs solar radiation for photosynthesis and converts it into its own biomass (Eqs 8, 9) (Mankin and Fynn, 1996; Ahn and Mitsch, 2002; Brix et al., 2002; McAndrew and Ahn, 2017). The specific equation is as follows: Eqs 7a–d. u p 1 = n _ d e _ w * N O 3 _ W K N O 3 w + N O 3 _ W * N O 3 _ W N O 3 _ W + N H 4 _ W (7a) u p 2 = n _ d e _ w * N H 4 _ W K N H w + N H 4 _ W * N H 4 _ W N H 4 _ W + N O 3 _ 2 (7b) u p 3 = n _ d e _ s * N O 3 _ S K N O 3 s + N O 3 _ S * N O 3 _ S N H 4 _ S + N O 3 _ S (7c) u p 4 = n _ d e _ s * N H 4 _ S K N H s + N H 4 _ S * N H 4 _ S N O 3 _ S + N H 4 _ S (7d) n _ d e _ w = s l o a r * k 1 * k 3 * k 4 * A k 2 (8) n _ d e _ s = s l o a r * k 1 * k 3 * k 5 * A k 2 (9)

In order to make the rate of most of the reactions in the model change with the season, temp_airK, which can describe the annual temperature, is introduced in the model. The relationship between temperature and process rate used in the model (Eq 10) is based on the absolute reaction rate theory, but some parameter values are verified in this paper, so that the change of reaction rate is more in tune with the seasonal change (Schoolfield et al., 1981; van der Peijl and Verhoeven, 1999). r t e m p = r h o 25 * t e m p _ a i r K 298 * 10 H a r * 1 298 − 1 t e m p _ a i r K 1 + 10 H i r 1 T i − 1 t e m p _ a i r K + 10 H h r * 1 T h − 1 t e m p _ a i r K (10)

In 2019, 118 sampling sites were set up and corresponding samples were collected in the Daihai (Figure 2), which covered the entire lake area as much as possible in order to study the exogenous pollution in summer. Submerged plant samples were collected by a submerged plant collection rake and weighed on site. After returning to the laboratory, the samples were weighed after over-dried at 105°C for about 30 min and then dried to constant weight at 70°C, and grinded into powder for detection of total nitrogen, ammonia nitrogen and nitrate nitrogen contents. Water samples with a 0.5 m water depth were collected by using a water sample collector and a total of five indicators in them were measured: Turbidity, PH, dissolved oxygen content, and nitrate nitrogen, ammonia nitrogen and total nitrogen concentration. The total nitrogen, the ammonia nitrogen and the nitrate nitrogen concentrations were measured by SKALAR Continuous Flow Analyzer. Dissolved oxygen, Turbidity and PH were measured on site with a portable instrument. All measurements were made in accordance with standard methods (Rice et al., 2012). In addition, the area of submerged plants in the Daihai Lake used in this study were obtained from “Concluding Report on the Construction of Water Ecological Security Assessment and Management Decision Support System of One Lake and Two Seas”, and the meteorological data used were collected from the local meteorological stations.

The calculation of the total nitrogen pollution load into Daihai Lake is divided into five main components: Rural living, livestock breeding, agricultural cultivation, atmospheric deposition, and soil erosion (Zheng and Men, 2020). According to the statistics of the Daihai watershed and related research literature, the rural population of the Daihai watershed in 2019 was 94,000 and the rural arable land was 63,000 hm2; and the livestock stock was 559,000, including 53,000 cattle, 500,000 sheep as well as 0.6 million pigs (Tang, 2021).

The formulae for calculating the total nitrogen pollution load for rural living, livestock breeding and agricultural cultivation is shown in Eq 11. W 1 = N * α 1 * β 1 (11)

Where, W₁ is the total nitrogen load into the lake, N₁ is the quantity in the region (all livestock stock is converted into pigs for calculation, such that one cow is converted into five pigs, three sheep are converted into one pig). α₁ is pollution production coefficient with 1.5g/(person*d) in rural domestic pollution, 1.27kg/(n*a) in livestock and 2.64 kg/(hm²*a) in farmland (Council, 2009). β₁ is lake input coefficient with 0.15% for rural household pollution, 10% for livestock breeding pollution, and 7% for farmland pollution (Zhu, 2011).

The formula for calculating the total nitrogen pollution load from atmospheric deposition is expressed in Eq 12. W 2 = A * α 2 (12)

Where W₂ is the total nitrogen load to the lake, A is the total area of the Daihai Lake, α₂ is the atmospheric nitrogen deposition flux with 532.53kg/(km²*a) (Lu et al., 2015).

The formula for calculating the total nitrogen pollution load for soil erosion is described in Eq 13. W 3 = S D R * X * C * η * α 3 (13)

Where W₃ is the total nitrogen load into the lake from soil erosion. SDR is the sediment transport ratio, which in China varies little between 0.1 and 0.4, and is taken as 0.25 (Jiang and Xi, 2011). X is the amount of soil erosion. C is the background content of nitrogen and phosphorus in the soil at 0.9 g/kg (Kalin and Hantush, 2006). η is the soil enrichment ratio of nitrogen (dimensionless). α₃ is the coefficient of entry into the lake with 0.7% (Zhu, 2011).

Theil’s Inequality Coefficient (TIC) is used as the evaluation index of the calibration results of the evaluation model, which can be used to quantitatively describe the degree of coincidence between model simulation results and measured data and shown in Eq 14 (Min et al., 2010). TIC is generally between 0 and 1 and 0 represents a perfect fitting with the actual monitoring value. In general, when TIC is less than 0.5, it can be considered that the simulation value is in good agreement with the monitoring value. The concentrations of NO₃ and NH₄ in water were verified in our study. T I C = 1 n ∑ i = 1 n C i , s i m − C i , o b s 2 1 n ∑ i = 1 n C i , s i m 2 − 1 n ∑ i = 1 n C i . o b s 2 (14)

C_i,sim is the model simulation value at time i; C_i,obs is the actual monitoring value at time i; n is the number of data points used for model verification.

The final calculated TIC of NH₄ is 0.018 and TIC of NO₃ is 0.25. This shows that the simulated values of the model are in good agreement with the measured values, and the calibration of the model is successful.

It was calculated that the N pollution load in the Daihai Lake in 2019 was 107.895t (Figure 3), which were mainly contributed by soil erosion, atmospheric deposition, agricultural cultivation, livestock breeding and rural living and carried by rivers into the lake. Among the pollution source, livestock raising was the largest contributor of the total N pollution load, which produced 52.44 tN pollution load accounting for 48.6% of the total annual N pollution load. Rural life was the least contributor of the total N pollution load with 0.055t, which only occupied 0.05% of the annual total N. These implied that external pollution would being the main pressures in the lake ecosystem health.

Based on Figure 4A, it can be seen that the NH₄ ⁺-N and NO₃ ⁻-N contents in the water column of the Daihai Lake increased more rapidly after July, reached a maximum and then decreased after October, which was confirmed by the measured data, because of exogenous pollution entering the lake by rivers in summer. NH₄ ⁺-N and NO₃ ⁻-N contents in the soil column of the Daihai Lake were higher in the dry season than in the wet season, and this was possible for N absorption by plants in the wet season.

The N content of submerged plants relied on nutrient uptake from the water and soil. The N content of submerged plants per unit area could to some extent reflect the growth and quantity of submerged plants. According to Figure 4B, the area of the Daihai decreased continuously and the area of submerged plants increased constantly. By comparison, the nitrogen uptake rate of submerged plants was highest from May to July, with the rate gradually decreasing towards the end of August and gradually ceasing to grow from November.

In this study, the purification amount of submerged plants referred to the difference between the amount absorbed by submerged plants and released by the decomposition of death plant residues in water. Based on Figure 5A, the N absorption amount of submerged plants mainly occurred during the growing season from May to October. Due to a relatively simple mortality rate being positively correlated with the biomass of submerged plants, the N release amount of submerged plants was almost always in an increasing state except for the time of winter growth stagnation (Figure 5B). The variation trend of the N purification amount of submerged plants was almost similar to that of the N absorption amount of submerged plants, as gradually decreased from October to January and then gradually increased. And this N purification amount was negative in January because the N release amount was greater than the N absorption amount for submerged plants (Figure 5C). Therefore, the N purification capacity of submerged plants depended on the biomass of the submerged plants in this lake.

In this study, the expansion of submerged plant area and the decrease of turbidity in the Daihai Lake caused by increased submerged plant area were mainly considered in the ecological restoration of submerged plants in the Daihai Lake. In this model, the area of submerged plant restored from 4.95 km² to 9.91 km², and light utilization increased from 0.02 to 0.022. The variation trend of NO₃ ⁻ concentration in water column was similar before and after recovery, while the NO₃ ⁻ concentration after recovery was significantly lower than before recovery (Figure 6A). The concentrations of NH₄ ⁺ before and after recovery gradually kept stable after the third year, and the NH₄ ⁺ concentrations after recovery were lower than before recovery (Figure 6B).

In order to better compare the purification capacity of submerged plants before and after restoration, when the external non-point source N pollution load is only 107.895t, it can be seen that the restored submerged plants will spend 12 years on purifying 107.895t of N pollution load (Figure 6C). However, the purification speed of submerged plants before recovery is very slow, and the time required before recovery is much longer than after restoration. Under the two conditions, the annual purification amount of submerged plants decrease basically with time, which is basically consistent with the variations of N concentration in water column.

By comparison, the N pollution load of the Daihai Basin in 2019 calculated in this study was similar to that in 2017 referenced from the study of (Wu and Zhao, 2015). This indicated that non-point source pollution has been reduced to some extent in rural life, atmospheric subsidence and soil erosion. We found that the loss of population in the villages and towns around the Daihai Lake led to the reduction of N pollution load brought by rural life (Zheng and Men, 2020; Tang, 2021), with the decreasing of the Daihai Lake’s area year by year, the N pollution load caused by atmospheric subsidence would become reduction, and N pollution load caused by soil erosion also reduced for the depletion of river channels and the decrease of rainfall. However, because of increasing in farmland and livestock raised in the countryside, N pollution load from both agricultural cultivation and livestock raising would increase obviously (Tang, 2021), which was proved by our conclusion, too. Therefore, how to controlling N pollution load from both agricultural cultivation and livestock raising was important for the management of the Daihai Lake ecosystem.

In this study, due to the impact factors being complex and difficult to simulate perfectly in the model, we adopted some parameters from some references such that the growth of submerged plants was expressed by using the plant growth coefficient (Guan, 2021; Li et al., 2021), and a relatively simple mortality rate was used to calculate the N release amount of submerged plants (van der Peijl and Verhoeven, 1999). Therefore, the N release amount of submerged plants was positively correlated with the biomass of submerged plants, which would have a certain impact on annual purification amount of submerged plants. This also led to the amount of purification in the front growing season being higher than that in the back growing season.

The restoration of submerged plants would be realized by changing their area and light utilization efficiency. In this model, the area of submerged plants will affect the total amount of light absorbed by submerged plants, and the light utilization efficiency will affect the N absorption efficiency of submerged plants, which was very important for restoration of submerged plants. Because the growth of submerged plants was largely restricted by the water depth (Li et al., 2021), and the area suitable for submerged plant growth during the water depth less than 2.5 m in the Daihai Lake accounted for 23% of the lake area (Zhao et al., 2020), we chose 20 percent of the Daihai area (9.91 km²) to restore submerged plants. In addition, the turbidity of lake water in Daihai Lake would decrease due to the expansion of submerged plants, and the light utilization efficiency would be further improved due to the decrease of turbidity. According to the influence of turbidity on photosynthesis, the photosynthetic rate increased by about 5%–10% when turbidity recovered from 60NTU to 30NTU (Li et al., 2006; Xue et al., 2007). According to the field investigation, the turbidity in the whole Daihai Lake was between 15.6–75.8NTU, and between 40–70NTU in most of the areas where submerged plants grew, which need to increase photosynthesis rates to reduced turbidity by submerged plants (Li et al., 2006; Xue et al., 2007). Ultimately, the simulation results showed that an increase in the area of submerged plants in Daihai Lake can significantly increase the total amount and rate of N uptake by submerged plant.

Liu et al. (2020) found that the assemblage of three or more submerged macrophyte species only significantly improved water clarity, but not water quality. Our findings were that it can be seen that annual N purification amount in the water of the Daihai Lake before and after restoration was different, the purification speed of submerged plants before recovery was very slow, and the recovery time required before recovery was much longer than after restoration. This also proved that small area submerged plant could not improve water quality obviously and only restoration of large area submerged plant benefited for the nutrient N absorption of submerged plants.

In addition, the death parameters of submerged plants used in the model only generally calculated the normal death and loss of each part of submerged plants in the natural growth process, and other biomass of submerged plants would be not considered next year, which indicated that most submerged plants would be removed from the lake and not re-pollute the lake water. Therefore, it is necessary to carry out the salvage work of plant residues in winter every year to maintain normal plant growth and prevent from submerged plant nutrient N releasing into the water.

Endogenous pollution was also one of the main reasons for the deterioration of water quality in Daihai Lake (Zheng and Men, 2020). Submerged plants could fix and absorb various types of N in the sediment, which was an effective means to control endogenous pollution in the lake (Jingbo et al., 2007; Huang et al., 2019). In this study, because the N in the sediment lacked exogenous recharge, it was found that the concentration of various types of N in the sediment continuously decreased, which was continuously consumed by submerged plants. As the N concentration in the sediment decreased, the nitrogen concentration in the water would also decrease accordingly, which was the main reason why the model simulated a gradual decrease in purification capacity before reaching stability. Therefore, the restoration of submerged plants in the Daihai Sea could effectively slow down the release of endogenous N pollutants to water, which was of a great important role in N purification in sediments.