A new model to estimate shallow lake nitrogen removal rate based on satellite derived variables

Lake nitrogen (N) removal, mainly resulting from bacterial denitrification that converts nitrate (NO3 −) to gaseous N (N2), is important for lake water quality and eutrophication control. However, quantifying lake N removal is challenging due to the high background atmosphere N2 concentration and the heavy burden of field surveys, leading to a decoupling of watershed N management and water quality improvement. Here, we developed and validated an innovative nonlinear model for lake N removal rate estimation by linking the N removal rates with remote sensing-derived variables (chlorophyll-a, chromophoric dissolved organic matter, and lake surface water temperature). The model was validated in shallow eutrophic Lake Taihu in the Yangtze River basin and at the global scale. Based on the new N removal model, we estimated that an annual average of 3.21 × 104 t N yr‒1 was removed in Lake Taihu from 2011 to 2020, accounting for 53%–66% of the total lake N loading. The remaining N loading after denitrification removal in Lake Taihu would be approximately 2.37 mg N l‒1, and 0.79 × 104 t N y‒1 of lake N loading still needs to be removed to meet the target of class IV water quality (1.5 mg N l‒1). This is the first study linking lake N removal in sediment microcosm incubations with reach-scale remote sensing derived variables, providing timely-much insights into lake N removal. This approach can be easily applied in other lakes with satellite derived data, to better understand lake N budget, drivers of eutrophication control, and watershed N management.


Introduction
Due to the excessive use of anthropogenic reactive nitrogen (N) (Galloway et al 2008), lake eutrophication has been widely reported over the past century (Sinha et al 2017, Suresh et al 2023).Lake N removal through bacterial denitrification, sediment sorption, and plant uptake can remove a significant proportion of lake N loading and thus bridge watershed management and water quality (e.g.36%-47% of lake N loading in the Mississippi River watershed (Cheng et al 2020)).While other processes offer only temporary N removal (Knights et al 2020), the process of bacterial denitrification in sediment is the primary pathway for permanent reactive N removal, converting nitrate (NO 3 − ) to gaseous nitrogen (N 2 ) (Loeks-Johnson and Cotner 2020).Therefore, quantifying lake N removal through denitrification is critical for watershed N management to improve lake water quality.However, accurately quantifying the magnitude of N removal through denitrification is challenging due to the high background concentrations of atmospheric N 2 , as well as the heavy burden in long-term and large-scale field surveys (Zhang et al 2023).
Traditional measurements for lake N removal in the laboratory either suffer from biased estimation or are labor-intensive regarding time and cost, including incomplete inhibition of the acetylene inhibition (Watts and Seitzinger 2000), potential priming effect of the isotope pairition (Middelburg et al 1996), and complex incubation procedures of the N 2 /Ar method (van Luijn et al 1996).These techniques are mostly only applied to closed incubation or river reach systems, which is challenging to expand to the watershed scale.The estimation of lake N removal rates has increasingly relied on model approaches, as more accessible environmental factors (e.g.NO 3 − , dissolved organic carbon (DOC), dissolved oxygen (DO), and water temperature (WT)) jointly regulate denitrification in aquatic ecosystems (Seitzinger 1988, McMahon et al 2021, Wang et al 2021).For example, Li et al (2013) established an empirical model using water NO 3 − and WT to estimate N removal in the Jurong Reservoir watershed, southeastern China, which could explain 86% of the variability in riverine N removal.We analyzed more than 20 previous studies which demonstrated that lake N removal rate through denitrification can be well estimated from the controlling factors of water NO 3 − and temperature (table S1).However, the reach scale application of these models was also strictly limited by the measurement of NO 3 − , DOC, WT, or/and DO concentration, which are not always available in a large spatial scale and long time series estimation.
In principle, most of the environmental variables that control N removal can be directly or indirectly derived from remote sensing data, providing an approach to estimate lake N removal through remote sensing.For example, we conducted a meta-analysis on the relationship between Chla and N concentration in 39 411 lakes worldwide.The results demonstrate that Chla can serve as a proxy for N concentration, given that N is the limiting nutrient for algal growth (figure S1), especially in shallow lakes where a robust linear correlation between Chla and N concentration existed (Zou et al 2020).Similarly, water DOC can be indirectly quantified by water chromophoric dissolved organic matter (CDOM) for studies of freshwater carbon cycling worldwide (Tehrani et al 2013, Massicotte et al 2017).The WT can be directly monitored by remote sensing with high precision (e.g.within ± 0.5 • C) (Torgersen et al 2001).Highfrequency, continuous, and large-scale data of lake WT, Chla, and CDOM can be accurately provided by remote sensing (e.g.R 2 > 0.90 in Lake Taihu for Chla estimation) (Duan et al 2010, 2012, Qi et al 2014).Therefore, we hypothesize that reachscale and long-term estimations of N removal in shallow eutrophic lakes can be estimated through remote sensing derived variables such as Chla, CDOM, and lake surface WT.
In this study, we aimed to (i) develop and validate a simple and powerful model to estimate shallow lake N removal based on remote sensing derived variables; (ii) apply the new model to a typical shallow eutrophic lake (Lake Taihu) and identify the spatiotemporal variation of Lake Taihu N removal from 2011 to 2020; and (iii) develop a watershed N management strategy for water quality improvement in Lake Taihu basin based on the estimated lake N removal.

Development of the conceptual model
Based on previous studies, we hypothesize that the dynamic response of N removal to Chla, CDOM, and WT in lakes follows the multivariate quadratic polynomial pattern (figure 1).First, Chla drives N removal with the increase of Chla concentration, but high Chla concentration inhibits N removal (Zhu et al 2020).It is likely the processes of denitrification and nitrification often couple together to achieve effective N removal under low Chla concentration (Zhu et al 2020).The decomposition of a small amount of algal under low Chla concentration not only provides carbon and N but also decreases the penetration depth of DO into sediments, creating favorable conditions for sediment nitrification and denitrification (Small et al 2014).However, the decay of excessive algal biomass, which results in high Chla concentration, can deplete DO and potentially disrupt the coupling of nitrification and denitrification in sediments (Zhu et al 2020).This mechanism leads to a quadratic polynomial response of N removal to Chla.Second, many studies have reported that the denitrification rate was positively related to the content of carbon (proxy of CDOM) in worldwide freshwaters because carbon enhanced microbial metabolism and provided electron donors for denitrification (Chen and MacQuarrie 2004, Qin et al 2007, Zhou et al 2020).This evidence recognized the linear relationship between the N removal rate and CDOM.Third, it has been widely accepted that warmer temperatures tend to increase denitrification linearly by enhancing microbial respiration rates, consuming oxygen and creating anaerobic conditions (McCutchan and Lewis 2008, Zhao et al 2015, Gardner et al 2016).To sum up, a final additive conceptual model that includes a quadratic polynomial term and two linear terms is proposed to link the dynamic lake N removal to Chla, CDOM, and WT (figure 1).

Model validation at a typical shallow lake 2.2.1. Lake description and data collection
We chose Lake Taihu in the lower reaches of the Yangtze River Basin to parameterize and validate the model because Lake Taihu has been well studied, varied N removal rates, and has longterm remote sensing data for N removal estimation (supporting information text S1).Lake Taihu is the third-largest freshwater lake in China and has been severely impacted by eutrophication.Although extensive efforts have been implemented to reduce N pollution, the N concentrations in the lake remain high (Paerl et al 2011).It is crucial to accurately quantify N removal in Lake Taihu to develop more effective mitigation strategies.Lake Taihu covers a surface area of 2338 km 2 and has a catchment area of 36 500 km 2 .Its mean water residence time is 284 d and the mean depth is 1.9 m.The lake experiences a subtropical monsoon climate, with an average annual precipitation of 1050 mm and a WT of 15 • C (Qin et al 2007).
In this study, we conducted six sampling campaigns from June 2020 to January 2021 in Lake Taihu.Each sampling campaign included eight sampling sites; thus, a total of 48 sampling sites in the six sampling campaigns were evenly distributed in Lake Taihu (figure 2).At each sampling site, the N removal rate was determined by measuring net N 2 fluxes using intact sediment cores (Zhao et al 2015).The methods of N removal, water and sediment characteristics measurements were provided in supporting information text S2.The analysis of the variability and controlling factors of N removal in Lake Taihu can be found in supporting information text S3.

Parameterization and validation of the model
We first validated the measured relationships between the lake N removal and remote sensing variables.Consistent with the theoretical relationships proposed in the conceptual model, the measured lake N removal rate was related to Chla concentration quadratic polynomially, while linearly related to the absorption coefficient of CDOM, and WT (figure S2).Then, random 36 of 48 sampling sites with in situ measured data in this study were selected to parameterize the models for N removal.The model from Chla, CDOM, and WT (named as 'CCW' model) led to the following equation: where y is the lake N removal rate (µmol N 2 m −2 h −1 ), Chla is the concentration of chlorophyll-a (µg l −1 ), CDOM is the absorption coefficient of CDOM (m −1 ), and WT is the lake surface WT ( • C).This model accounted for 71% of the observed variability in N removal rates (figure 3(a)).
It should be noted that organic carbon may not be a limiting factor for the N removal rate in many eutrophic lakes with relatively high contents of organic carbon (Zhao et al 2013(Zhao et al , 2015)).Therefore, we also proposed another conceptual model that only incorporates Chla and WT to estimate N removal in Lake Taihu (named as 'CW' model), which led to the following equation: (2) This model accounted for 64% of the observed variability in N removal rates (figure 3(b)).
Finally, we validate how well the developed models using the remaining 12 of 48 independent sampling sites in situ measured data.The CCW model accounted for 71% of the variability in the observed lake N removal rates, while the CW model accounted for 70% of the variability in the observed N removal rates in Lake Taihu (figure 3).These results suggest the two models can be well validated with the independently measured data.In addition, Monte Carlo simulation also showed that the remote sensing model can be used to estimate N removal with low uncertainties (supporting information text S4).

Model validation at the global scale
We validated our model by comparing the global 4483 lakes N removal estimates with the RivR-N model based on global remote sensing derived data of Chla and WT (supporting information text S5).The RivR-N model was empirically derived from water residence time and depth for lake N removal fraction estimations across America and Europe (Seitzinger et al 2002).Here, the N removal fraction is defined as the proportion of lake N loading that can be permanently removed through denitrification.As the N removal rates measured in Lake Taihu can cover nearly 90% variation range of the global lake N removal rates (figure S3), we directly adopt the model parameter in Lake Taihu for the preliminary validation.More detailed information about the model validation can be found in supporting information text S5.
In general, our estimations fit well with the results of the RivR-N model (slope = 1.002,R 2 = 0.46, red line in figure 4).However, our model would provide a lower estimate than the RivR-N model at   the low-value predictions, and a higher estimate than the RivR-N model at the high-value predictions (blue line in figure 4).This may be because the influence of substrate concentration on lake N removal rate was included in our model.In fact, following the Michaelis-Menten equation, the Lake N removal rate slowly increases and approaches saturation with the increased substrate concentration due to limitations in enzyme activity.Thus, N removal processes are characterized by a biological saturation effect under high N levels (Penn et al 2010, Cheng and Basu 2017).This biological saturation effect leads to a decreasing lake N removal fraction with the increased substrate concentration.However, the RivR-N model, which only considers the effect of water residence time and depth on lake N removal while focusing on physical effects, fails to account for this biological saturation effect.Hence, our remote sensing model, incorporating the effect of substrate concentration on lake N removal, provides a more realistic estimation of lake N removal.

Spatial and temporal patterns of N removal estimation in Lake Taihu
We chose Lake Taihu as a case study to simulate spatial and temporal patterns of N removal.The monthly detailed N removal rate of Lake Taihu from 2011-2020 was reconstructed based on the CW model and satellite-derived Chla and WT at 250 m resolution.Specifically, the CW model including Chla and WT was used to map the N removal of Lake Taihu, as CDOM does not help explain more of the variation in N removal in lakes with high contents of organic carbon (figure 3).The satellite-derived data of Chla concentrations and WT data was obtained from the National Earth System Science Data Center (www.geodata.cn)(National Earth System Science Data Center 2024).The Chla and WT were derived from Moderate-Resolution Imaging Spectroradiometer (MODIS) image data using a rigorous processing approach, which included cloud removal, geometric correction, model inversion, and validation using field measurements (Qi et al 2020).Generally, long-term in situ measured Chla concentration data in 75 stations suggested that the three Chla algorithms based on MODIS image (band-ratio, nested band-ratio, and three-band) provided highly accurate Chla estimates in Lake Taihu (R 2 > 0.90) (Duan et al 2012).More detailed satellite data acquisition and processing can be found in supporting information text S6.
In figure 5, we first estimated the monthly detailed N removal rate of Lake Taihu in 2019.The highest monthly N removal rate was predicted in July, with a rate of 64.62 ± 17.56 µmol N 2 m −2 h −1 .The lowest monthly N removal rate was predicted in October, with a rate of 54.55 ± 11.92 µmol N 2 m −2 h −1 .The predicted mean lake N removal rate in 2019 was 59.53 ± 6.20 µmol N 2 m −2 h −1 .These estimated N removal rates were within the range of previously reported rates in a meta-analysis for global lake denitrification rates (11.42-424.66µmol N 2 m −2 h −1 ) (Seitzinger et al 2006).Similar results were also reported by Zhao et al (2017), with N 2 flux rates ranging from 26.3 to 71.3 µmol N 2 m −2 h −1 for the Taihu River networks using 15 N-isotope pairing combined with the N 2 /Ar technique.More detailed information about the monthly N removal rates of Lake Taihu in 2019 can be found in figure S4.
Total annual N removal through denitrification in Lake Taihu from 2011 to 2020 was further calculated by extrapolating the estimated annual mean N removal rate to the area of Lake Taihu (2338 km 2 ) (figure 6).The predicted annual mean N removal rate from 2011 to 2020 ranged from 47.92 to 59.53 µmol N 2 m −2 h −1 , with a mean value of 55.92 µmol N 2 m −2 h −1 .Therefore, the estimated total annual N removal through N 2 emissions in Lake Taihu ranged from 2.74 × 10 4 to 3.42 × 10 4 t yr −1 , with a mean value of 3.21 × 10 4 t yr −1 .Our estimation of annual N removal was approximately 51%-68% of the reported 5-5.37 × 10 4 kt N yr −1 of N inflow to Lake Taihu from surrounding rivers and underground loads (Zhao et al 2015, Zhang et al 2016).This estimation fell well in estimations from the monitoring data and mass balance method, in which the average N removal percentage was 54% for Lake Taihu during 2005-2018 (Xu et al 2021).Similarly, when we fitted the depth (1.9 m) and water residence time (284 d) of Lake Taihu to the RivR-N model (Seitzinger et al 2002), the model estimated that the N removed in Lake Taihu would be 64%.These results are close to the value predicted by our model and further indicate that our estimation is appropriate.

Implications to watershed N management
Based on the model estimated N removal in Lake Taihu, more accurate N mitigation strategies can be implemented to control N pollution.A previous study reported that 5.37 × 10 4 t yr −1 of total N would be exported to Lake Taihu from the sounding river network (Zhao et al 2015).Our study estimated that the mean N removal in Lake Taihu from 2011 to 2020 was 3.21 × 10 4 t yr −1 .Given that the remaining 2.16 × 10 4 t yr −1 of total N loading and the inflow water flux discharging into Lake Taihu was 91.15 × 10 8 m 3 (Ji et al 2019), we estimated that the average N concentration in Lake Taihu reached approximately 2.37 mg N l −1 , which was much greater than the target grade IV standard (National Surface Water Quality Standard GB3838-2002, [TN] ⩽ 1.5 mg l −1 ).To achieve the water quality goal of 1.5 mg N l −1 , the maximum N loading allowed to flow into Lake Taihu can be calculated by adding the N removal capacity to the N loading allowed in the lake.In the present study, we estimated that the maximum N loading allowed to flow into Lake Taihu was 4.58 × 10 4 t yr −1 based on 3.21 × 10 4 t yr −1 of N removed and 1.37 × 10 4 t yr −1 of N loading allowed in Lake Taihu (calculated by water quality standard × inflow water flux).Thus, another reduction of 0.79 × 10 4 t yr −1 N loading is required to meet the target of IV standard in Lake Taihu (1.5 mg l −1 ).Therefore, it is necessary to reduce the N originating in this region, including human excreta, runoff from farmland, and domestic sewage (Qin et al 2019, Zhong et al 2021).
By taking advantage of the estimated lake N removal, more defined spatiotemporal hotspots of N mitigation strategies can be developed in Lake Taihu.The large-scale estimated N removal showed that the N removal rates in northwest Lake Taihu are higher than in other areas of Lake Taihu (figure 5).This suggests that the northwest of Lake Taihu receives a higher influx of riverine N (Xing et al 2001, Liu et al 2011, Wang et al 2019), emphasizing the necessity of implementing additional control strategies in the northwest of the Lake Taihu basin.In addition, the reconstructed long-term N removal suggests that different pollution control strategies are required in different seasons of Lake Taihu.In the periods without severe algal existence, only external lake N loading reduction is required for eutrophication control, as the lake has a relatively strong capacity for lake N removal.However, in bloom maintenance periods, the N removal rate is considerably low in Lake Taihu (e.g.extremely low in August, figure S4), because the decay of excessive algal biomass likely depleting DO and thus could have broken the coupled nitrificationdenitrification in sediments (Zhu et al 2020).Given that decreased N removal can make more nutrients retained in the lake, thereby promoting algal proliferation, it becomes imperative to implement strategies for not only reducing external N loading but also enhancing the frequency of algal harvesting to improve N removal.These measures are essential for effective eutrophication control during periods of bloom maintenance in Lake Taihu.

Innovations and potential applications
This is the first study linking N removal in sediment microcosm incubations with reach-scale remote sensing derived variables, thus offering accessible estimation in timely much-needed lake N removal.
Presently, N removal estimations in lakes are limited by low spatiotemporal resolution due to the difficulties in N 2 emission measurement and large spatiotemporal heterogeneity of N removal, as well as the heavy burden in long-term and large-scale field surveys (Small et al 2016, Cheng and Basu 2017, Heiss et al 2020).These difficulties limit our comprehensive understanding of lake N budgets and the underlying mechanisms of eutrophication control.By leveraging the remote sensing empirical equation, large-scale and long-term estimations of N removal can be achieved through satellite-derived variables.This approach facilitates the calculation of wholelake N removal with a superior resolution compared to conventional field surveys and mathematical models.Recent literature has witnessed a burgeoning body of support for utilizing remote sensing techniques to estimate the non-optical rates of biogeochemical cycle processes.For example, researchers have successfully reconstructed spatially explicit dissolved CO 2 concentrations (cCO 2 ) in lakes and coastal oceans using MODIS-derived variables (Bai et al 2015, Chen et al 2019, Qi et al 2020).Other studies have used remote sensing derived variables to image lake CH 4 ebullition and create ebullition-flux maps for 5143 Alaskan lakes at whole-lake and regional scales (Engram et al 2020).While numerous studies have employed satellitederived variables or optical indicators to directly or indirectly measure control factors of N removal, such as Chla, NO 3 − , DOC, WT, and DO concentrations (Torgersen et al 2001, Liu et al 2020, Zou et al 2020), none have directly estimated lake N removal using these satellite-derived variables.This research contributes to the first landscape of remote sensing applications in understanding lake N removal processes.
The estimated lake N removal from remote sensing has great potential to strengthen our understanding of watershed N management for water quality improvement.Presently, despite widespread efforts, such as wastewater treatment, planting of cover crops, and riparian buffer construction, aimed at reducing lake N loading, the correlation between watershed N management and water quality improvement remains unclear (Van Meter et al 2016, Yin et al 2023).In certain lakes where substantial initiatives have been undertaken to reduce watershed N input, achieving water quality improvement proves challenging, underscoring the ineffectiveness of current strategies in these specific aquatic environments (Bianchi et al 2010, Costa et al 2021).Conversely, in some lakes with a high capacity for lake N removal, the cost associated with N reduction is too much, suggesting that implementing these strategies might not be economically feasible in these particular contexts (Small et al 2016, Xia et al 2016).One of the key reasons for these uncertainties is the limited knowledge about lake N removal through denitrification, which links watershed N input and lake water quality (Seitzinger et al 2006, Maringanti et al 2009).Our remote sensing model, characterized by its cost-effectiveness and adaptability, enables the quantification of lake N removal, empowering the development of more nuanced watershed N management strategies.By enhancing efficiency and reducing the cost of water quality restoration, this methodology contributes to a more informed and targeted approach, aligning with the broader goal of advancing sustainable water resource management.

Limitations and potential improvements
The main limitation of the model application is the uncertain relationship between the N removal rate and Chla concentration.In deep lakes where P is the limiting nutrient for algal growth, Chla can not represent N concentrations and therefore may not be appropriate for lake N removal estimates.Previous studies suggested deep lakes are usually characterized by higher N:P ratios because deep lakes are usually distributed in a hilly region with high vegetation coverage, and they receive N and P from natural sources, which export much less P than N (Downing andMcCauley 1992, Zou et al 2020).Thus, high N:P indicates that P, not N, likely limited algal growth in deep lakes.Although we restrict our model in application in shallow lakes, we would also suggest that special care should be taken when applying the model to lakes with P limiting the growth of algal.
Despite the maturity of the technology for deriving Chla and CDOM using remote sensing data with high accuracy (e.g.R 2 > 0.90 in Lake Taihu for Chla estimation) (Duan et al 2010, 2012, Qi et al 2014), it is important to highlight the uncertainties associated with this process.The challenges associated with using satellite-derived variables, such as unavailable regions covered by algal blooms or cloud cover, can introduce uncertainty when estimating N removal rates.Algal blooms that cover the water surface can hinder satellite sensors from accurately capturing information about CDOM and surface temperature in the water column.Additionally, satellite observations cannot collect reflectance data from lake areas obscured by clouds.However, studies have shown that partially missing satellite data has minimal impact on overall lake estimations (Shi et al 2015, Qi et al 2020).This is because algal blooms and clouds are dynamic, and a significant amount of satellite data can compensate for these gaps.Despite these challenges, satellite data offers significant advantages in estimating lake Chla concentrations over large areas without the need for extensive field measurements.In this study, our main focus is to utilize remote sensing to infer the biogeochemical cycle process involved in N removal.
Our model can be further improved by model refitting with the global data of lake N removal.In this study, the parameter of our model was obtained based on the measured removal rates in Lake Taihu.This is because the data of lake N removals measured with the N 2 flux method (the best method for N removal measurement) are rarely reported due to the limitation of the expensive mass spectrometry and complex incubation procedure (e.g.only 1% N removal was measured by N 2 flux method reported by a metaanalysis (Qi and Liu 2023)).Moreover, the data that simultaneously measure N removal rate and remote sensing factors are rarely reported in lakes, which is insufficient to support the model construction.Fortunately, the data measured in Lake Taihu can cover nearly 90% variation range of the global lake N removal rates (figure S3), and the estimated global lake N removal can be well validated by other model (figure 4), suggesting our estimations are also reasonable for other lakes.Nonetheless, more research on how Chla affects lake N removal rates should be conducted in the future to help reduce model uncertainty and construct a global dataset.This will enable us to more accurately estimate global lake N removal using the remote sensing approach employed in this study.

Conclusion
By correlating the lake N removal rate with remotely sensed variables, we established the feasibility of X Yan et al estimating N removal via remote sensing and validated the model in a shallow eutrophic Lake Taihu in the Yangtze River basin and at the global scale.Utilizing the model to estimate long-term N removal (2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020) in Lake Taihu, we propose that 53%-66% of the lake's N loading can be effectively removed, with an additional 0.79 × 10 4 t N y −1 removal required to meet the class IV water quality target (1.5 mg N l −1 ).This is the first study that links lake N removal in sediment microcosm incubations with reach-scale remote sensing variables, offering valuable insights into lake N removal dynamics.Applying a similar approach to other lakes allows for the reconstruction of historical N removal dynamics through satellite data, facilitating a comprehensive understanding of lake N budgets, eutrophication control, and watershed N management.

Figure 1 .
Figure 1.Conceptual model linking lake N removal with remote sensing derived chlorophyll-a (Chla), chromophoric dissolved organic matter (CDOM), and water temperature (WT) concluded from previous studies.

Figure 2 .
Figure2.Sampling sites and a heatmap of in situ measured N removal rates in Lake Taihu, China.In the heat of N removal rates, the different colored dots represent different N removal rates in these sampling sites of Lake Taihu.

Figure 3 .
Figure 3. Relationships between in situ measured lake N removal rates versus remote sensing estimated lake N removal rates.(a) Shows the model that incorporated lake chlorophyll-a (Chla), the absorption coefficient of chromophoric dissolved organic matter (CDOM), and water temperature (WT).(b) Shows the model that only incorporated lake Chla and WT.The red squares represent in situ measured samples for model parameterization and the green circles represent independent measured samples for model validation.

Figure 4 .
Figure 4.The relationship between the estimated global lake N removal by our model and the RivR-N model (Seitzinger et al 2002).The RivR-N model was empirically derived from water residence time and depth for lake N removal fraction estimations across America and Europe.The blue line represents the fitting of the power function, and the red line represents the linear regression.

Figure 5 .
Figure 5. Spatial and temporal distribution of model estimated monthly N removal rates in 2019 of Lake Taihu.These N removal rates were estimated by the CW model, which comprises variables of chlorophyll-a (Chla) and water temperature (WT).

Figure 6 .
Figure 6.Spatial and temporal distribution of estimated annual N removal rates in Lake Taihu from 2011 to 2020.The 12 month N removal rate in each year was averaged as the annual N removal rate.

X
Yan et al matter in lakes along the Yangtze River Water Res.168 115132 Liu X, Lu X and Chen Y 2011 The effects of temperature and nutrient ratios on Microcystis blooms in Lake Taihu, China: an 11-year investigation Harmful Algae 10 337-43 Loeks-Johnson B M and Cotner J B 2020 Upper midwest lakes are supersaturated with N2 Proc.Natl Acad.Sci.USA Tang T, van Vliet M T H, Bierkens M F P, Strokal M, Sorger-Domenigg F and Wada Y 2023 Recent advancement in water quality indicators for eutrophication in global freshwater lakes Environ.Res.Lett.18 063004 Tehrani N C, Sa E J, Osburn C L, Bianchi T S and Schaeffer B A 2013 Chromophoric dissolved organic matter and dissolved organic carbon from sea-viewing wide field-of-view sensor (SeaWiFS), Moderate Resolution Imaging Spectroradiometer (MODIS) and MERIS sensors: case study for the Northern Gulf of Mexico Remote Sens. 5 1439-64 Torgersen C E, Faux R N, McIntosh B A, Poage N J and Norton D J 2001 Airborne thermal remote sensing for water temperature assessment in rivers and streams Remote Sens. Environ.76 386-98 van Luijn F, Boers P C M and Lijklema L 1996 Comparison of denitrification rates in lake sediments obtained by the N2 flux method, the 15 N isotope pairing technique and the mass balance approach Water Res. 30 893-900 Van Meter K J, Basu N B, Veenstra J J and Burras C L 2016 The nitrogen legacy: emerging evidence of nitrogen accumulation in anthropogenic landscapes Environ.Res.Lett.11 035014 Wang J, Fu Z, Qiao H and Liu F 2019 Assessment of eutrophication and water quality in the estuarine area of Lake Wuli, Lake Taihu, China Sci.Total Environ.650 1392-402 Wang Y, Li Q, Zhang W, Wang S and Peng H 2021 Pollutants removal efficiency assessment of constructed subsurface flow wetlands in lakes with numerical models J. Hydrol.598 126289 Watts S H and Seitzinger S P 2000 Denitrification rates in organic and mineral soils from riparian sites: a comparison of N2 flux and acetylene inhibition methods Soil Biol.Biochem.32 1383-92 Xia Y, Weller D E, Williams M N, Jordan T E and Yan X 2016 Using Bayesian hierarchical models to better understand nitrate sources and sinks in agricultural watersheds Water Res.105 527-39 Xing G, Cao Y, Shi S, Sun G, Du L and Zhu J 2001 N pollution sources and denitrification in waterbodies in Taihu Lake region Sci.China Ser.B 44 304-14 Xu H et al 2021 Contributions of external nutrient loading and internal cycling to cyanobacterial bloom dynamics in Lake Taihu, China: implications for nutrient management Limnol.Oceanogr.66 1492-509 Yin S, Gao G, Li Y, Xu Y J, Turner R E, Ran L, Wang X and Fu B 2023 Long-term trends of streamflow, sediment load and nutrient fluxes from the Mississippi River Basin: impacts of climate change and human activities J. Hydrol.616 128822 Zhang L, Yao X, Tang C, Xu H, Jiang X and Zhang Y 2016 Influence of long-term inundation and nutrient addition on denitrification in sandy wetland sediments from Poyang Lake, a large shallow subtropical lake in China Environ.Pollut.219 440-9 Zhang W, Li H and Li B 2023 Whole-system estimation of hourly denitrification in a flow-through riverine wetland J. Hydrol.618 129132 Zhao Y, Wu Y and Jiang L 2017 Nitrogen removal by denitrification and anammox processes in freshwater rivers of high nitrogen loading region of China Glob.Nest J. 19 650-7