Synergistic Regulation of Pollutant Reduction and Carbon Mitigation in Wastewater Treatment Plants under the Rainfall-Induced Inflow and Infiltration in the Sewer Network

Abstract

Rainfall-induced inflow and infiltration (I/I) alter hydraulic loading, dilute influent pollutants, and challenge the operation of the wastewater treatment plant (WWTP). However, limited attention has been paid to its coupled effects on effluent stability, operating cost, and greenhouse gas (GHG) emissions. This study developed an integrated framework combining data-driven I/I identification, mechanism model-based treatment process simulation, and multi-objective optimization for two WWTPs in Northeast China with different sewer systems. Prophet model predicted that rainfall-induced I/I was weak in the strictly separated sewer system but pronounced in the incompletely separated sewer system, where over 90% of identified wet-weather periods coincided with rainfall or occurred within 12 h afterward. Event-scale I/I volume was strongly related to total rainfall depth, with an R² of 0.929 and an I/I increase of 154.7 m³/km² per millimeter of rainfall. SUMO model simulations showed that all effluents met Class IA limits, but nitrogen removal became less stable as I/I intensified. Under heavy-rain and rainstorm scenarios, operating costs increased by 80.5% and 86.4%, while GHG emissions increased by 70.5% and 75.9%, mainly due to higher energy consumption for pumping and recirculation. Multi-objective optimization suggested that low internal recirculation, moderate external recirculation, and appropriate dissolved oxygen can stabilize nitrogen removal while reducing energy use, cost, and GHG emissions under wet-weather conditions.

Graphical abstract

Keywords

Wastewater treatment plant / Inflow and infiltration / Data-driven quantification / Multi-objective optimization / Pollution and carbon mitigation

Highlight

	● Prophet captured BDWF periodicity and enabled rainfall-induced I/I identification.
	● Rainfall depth explained 92.9% of event-scale I/I variation.
	● Nitrogen removal was more sensitive to I/I than COD and TP removal.
	● Heavy rain raised operating cost by 80.5% and GHG emissions by 70.5%.
	● Optimized recycle and DO settings improved wet-weather low-carbon operation.

1 Introduction

Driven by the goals of carbon peaking and carbon neutrality, the wastewater sector is undergoing a transition from conventional pollutant removal toward integrated operation for pollution reduction, carbon mitigation, cost control, and efficiency improvement [1]. Globally, the wastewater sector contributes approximately 2%–3% of total greenhouse gas (GHG) emissions [2]. Although this share is relatively limited, wastewater treatment plants (WWTPs) rely heavily on energy- and resource-intensive processes, including aeration, recirculation, and chemical dosing, and therefore have considerable potential for carbon mitigation. Meanwhile, WWTPs are important sources of GHG emissions, including indirect emissions associated with electricity and chemical consumption, as well as direct methane (CH₄) and nitrous oxide (N₂O) emissions generated during biological treatment [3]. Thus, maintaining effluent compliance while simultaneously controlling operating costs and GHG emissions has become a central challenge for the low-carbon transition of wastewater treatment systems.

In recent years, more frequent extreme rainfall events, together with sewer aging, structural defects, illicit stormwater connections, and elevated groundwater levels, have caused large volumes of extraneous water to enter wastewater collection systems [4−6]. Inflow and infiltration (I/I) refers to the entry of low-strength water other than domestic sewage and industrial wastewater into sewer networks, mainly including stormwater inflow and groundwater infiltration [7]. Previous studies have shown that I/I is a widespread challenge for urban drainage systems worldwide and is strongly affected by climate conditions, hydrogeological characteristics, and sewer network conditions. The I/I fraction in China has been estimated to be approximately 34% [8], and can exceed 50% in areas with high groundwater levels or during rainy seasons [9,10]. In representative regions of the United States, Poland, and Vietnam, reported I/I fractions range from 38% to 79%, with substantial increases during rainfall events [11−13]. I/I can sharply increase influent flow and reduce pollutant concentrations at WWTPs [14], shorten hydraulic retention time, alter the carbon-to-nitrogen ratio, and disturb key processes such as biochemical reactions, sludge settling, and sludge recirculation [15]. These changes may increase the risk of effluent non-compliance, energy consumption, and chemical demand [14,16]. In China, municipal WWTPs commonly experience influent chemical oxygen demand (COD) concentrations substantially below their design values, with sewer I/I identified as an important contributor to wastewater dilution [17]. Therefore, clarifying the coupled effects of I/I on water quality, operating cost, and GHG emissions is essential for achieving stable low-carbon operation of WWTPs.

Accurate and low-cost quantification of I/I is a prerequisite for precise control under I/I-induced disturbances. Existing methods mainly include flow monitoring [10], tracer tests [13,18], water balance analysis [12], characteristic-factor analysis [19], and thermal analysis [18]. These methods can identify I/I sources or estimate I/I fractions, but they often require field investigation, multi-point monitoring, or long-term water-quality and flow datasets, resulting in high cost, long implementation periods, and operational complexity [20]. Recently, model-based approaches have provided new opportunities for rapid I/I identification. Previous studies have assessed intrusion risks using sewer attributes and maintenance records [21], predicted baseline domestic wastewater flow (BDWF) from influent flow time-series characteristics and compared it with measured flow to estimate I/I [22], or simulated rainfall-induced I/I responses using sewer network digital models [23]. However, most existing studies have focused on a single model or a single drainage system. Systematic comparisons of different data-driven models for I/I identification remain limited. Moreover, separate and incompletely separated sewer systems may differ in I/I sources, rainfall response, and intrusion duration, but the influence of these differences on model applicability remains unclear.

More importantly, I/I has often been treated as a sewer diagnosis or influent dilution issue, with emphasis placed on intrusion quantification, influent concentration changes, or the response of individual effluent indicators [14,24]. Its implications for low-carbon WWTP operation and optimization have received much less attention. Data-driven models can identify influent disturbance patterns from historical operation data and improve prediction and early-warning capacity [25], but they provide limited interpretability regarding pollutant transformation and GHG generation processes [26]. In contrast, process-based models can describe treatment processes and carbon-emission responses, but they depend on parameter calibration and have limited capacity for rapid identification of complex influent disturbances [27]. Therefore, an integrated framework combining data-driven identification and process-based simulation is needed to balance predictive efficiency and process interpretability, quantify water-quality, operating-cost, and GHG-emission responses under I/I scenarios, and support multi-objective operational optimization.

In this study, an integrated framework was developed for I/I identification, system-response analysis, and multi-objective operational optimization. Two WWTPs in Northeast China, representing separate and incompletely separated sewer systems, were selected as case studies. Random forest (RF), long short-term memory (LSTM), and Prophet models were compared for BDWF prediction, and the selected model was used to rapidly estimate I/I and reveal the rainfall-induced I/I response relationships under different sewer system types. A SUMO process-based model was then applied to evaluate the dynamic responses of effluent quality, operating cost, and GHG emissions under different I/I intensities. Furthermore, response surface methodology and non-dominated sorting genetic algorithm II (NSGA-II) multi-objective optimization were combined to determine coordinated control ranges for dissolved oxygen, internal recirculation ratio, and external recirculation ratio under a representative heavy-rainfall scenario. By coupling rapid I/I identification with process-based simulation, this study extends I/I impact assessment from single water-quality responses to the coordinated optimization of effluent quality, operating cost, and GHG emissions, providing a quantitative basis for low-carbon WWTP operation under rainfall-induced disturbances.

2 Methods

2.1 Study sites and data collection

This study investigated two representative municipal WWTPs located in the same city in Northeast China. The study area has a temperate continental monsoon climate, with an annual precipitation of approximately 350–1000 mm. Summer rainfall accounts for 60%–70% of the annual total, showing pronounced seasonality and frequent short-duration, high-intensity rainfall events. WWTP A serves an area with a separate sewer system and has a design treatment capacity of 3.0 × 10⁵ m³/d. WWTP B serves an area with an incompletely separate sewer system and has a design treatment capacity of 3.25×10⁵ m³/d; approximately 15% of its service area still receives flow from combined sewer networks in the old urban district. Both WWTPs primarily treat domestic wastewater and do not receive industrial wastewater.

The dataset used in this study comprised operational data provided by the WWTP, including hourly influent flow rates, influent and effluent concentrations of COD, total nitrogen (TN), total phosphorus (TP), and ammonium nitrogen (NH₄⁺-N), as well as pH, chemical dosing rates, and key operational parameters. Hourly rainfall and air temperature data were obtained from the China Meteorological Data Service Centre. Influent flow data covered the entire year of 2022, whereas water quality, chemical dosing, operational parameters, and meteorological data covered the rainy season from May to September 2022. Data preprocessing included outlier removal, missing-value imputation, and harmonization of datasets with different temporal resolutions. Detailed information on data temporal resolution, outlier screening criteria, and missing-value imputation methods is provided in Appendix Text A.1 and Table A1.

2.2 Quantification of rainfall-induced inflow and infiltration

The influent flow of a WWTP can be decomposed into BDWF and I/I [28]. BDWF is primarily governed by residential water use and drainage activities and typically exhibits regular diurnal and weekly patterns [29]. In contrast, I/I is reflected by abnormal increases in influent flow relative to BDWF. Because background groundwater infiltration in the study area is relatively weak, flow increases during the rainy season are mainly caused by rainfall and post-rainfall responses of the sewer network. Therefore, in this study, the increase in influent flow during and after rainfall events relative to BDWF was defined as rainfall-induced I/I.

To accurately characterize BDWF under dry-weather conditions, this study compared three data-driven models, namely RF [30], LSTM [31], and Prophet [22]. These models were selected to account for nonlinear relationships, temporal dependencies, and trend-seasonality characteristics [31]. The models were trained using hourly influent flow data under dry-weather conditions. Model performance was evaluated using mean absolute error (MAE) and root mean square error (RMSE), and the best-performing model was selected for I/I quantification. I/I was calculated as follows [22,31]:

(1)Q_{I/I,t}={\text{max}(Q}_{\text{obs},t}-Q_{\text{base},t},0)

where Q_{I/I,t} is the rainfall-induced I/I flow at time t, m³/h; Q_{\text{obs},t} is the observed influent flow at time t, m³/h; and Q_{\text{base},t} is the model-predicted BDWF at time t, m³/h. When the calculated difference was less than zero, it was set to zero to avoid physically unrealistic negative I/I values caused by short-term prediction errors.

The dry-weather identification method, model input variables, training and testing dataset partitioning, hyperparameter settings, and evaluation metric formulas are provided in Appendix Text A.2 and Tables A2–A3.

2.3 Development of the WWTP mechanistic model

To evaluate the effects of rainfall-induced I/I on WWTP performance, WWTP B, which serves an incompletely separated sewer system, was selected for SUMO modeling. Part of its catchment still contains combined sewer segments, representing typical municipal WWTP conditions under rainfall-induced I/I disturbance. In addition, data-driven I/I identification showed a distinct rainfall-related hydraulic response at WWTP B, whereas such a response was not evident at WWTP A (Section 3.1), providing a quantitative basis for subsequent I/I scenario construction.

The model was developed based on the actual treatment process of the plant, which consists of parallel anaerobic–anoxic–oxic (AAO) and anoxic–oxic (AO) treatment lines (Fig. 1). Detailed treatment process layout, plant configuration, and operating conditions are provided in Appendix Text A.3.1 and Tables A4–A5. To improve calibration efficiency, local sensitivity analysis was first performed to identify key parameters affecting effluent COD, TN, TP and NH₄⁺-N, and sensitive parameters were prioritized during calibration [32] (Appendix Text A.3.2 and Table A6). Calibration involved two stages: steady-state calibration using average rainy-season influent conditions to set initial parameters (Appendix Text A.3.3 and Table A7), followed by dynamic calibration with hourly measured data to ensure simulated effluent quality matched observations.

The performance of dynamic calibration was evaluated using relative errors [33], and the results are shown in Fig. 2. The simulation results showed that the relative errors for effluent COD and TN were within 10%, those for TP were within 15%, and those for NH₄⁺-N were within 20%, which are within the acceptable range for engineering practice [34]. The calibrated model was subsequently used to simulate effluent water quality, operating costs, and GHG emissions under different I/I scenarios.

2.4 Scenario-based performance evaluation

2.4.1 GHG emission accounting

The GHG accounting boundary was defined as the WWTP plant boundary, focusing on emissions associated with on-site treatment and operation. The accounting included direct emissions from biological treatment processes and indirect emissions associated with electricity and chemical consumption [35]. Direct emissions included CH₄, N₂O, and carbon dioxide (CO₂) from fossil carbon oxidation simulated by the SUMO-4N model, with the fossil carbon fraction set to 10% of influent total organic carbon [36]. CO₂ emissions from the mineralization of external carbon sources were calculated separately using the emission factor method [36,37]. Indirect emissions from electricity and chemical consumption were also calculated using the emission factor method. Emissions from plant construction and demolition, chemical transportation, off-site sludge transportation and disposal, and downstream emissions in receiving water bodies were excluded. Total GHG emissions were expressed as CO₂ equivalents:

(2)E_{\text{total}}=E_{\text{direct}}+E_{\text{indirect}}

where E_{\text{total}} is the total GHG emissions, kg CO₂-eq; E_{\text{direct}} is the direct emission from wastewater treatment processes, kg CO₂-eq; E_{\text{indirect}} is the indirect emission, kg CO₂-eq. The methods for direct emission simulation, global warming potentials, electricity emission factor, and chemical emission factors are provided in Appendix Text A.4.1 and Table A8.

2.4.2 Operating cost accounting

Operating cost accounting focused on electricity and chemical costs because these two components are directly affected by hydraulic loading and operational adjustment [38]. Other cost components, including labor, maintenance, depreciation, construction, and sludge disposal costs, were not included. Total operating cost was calculated as:

(3)C_{\text{total}}=C_{\text{electricity}}+C_{\text{chemical}}

where C_{\text{total}} is the total operating cost, yuan; C_{\text{electricity}} is the electricity cost, yuan; and C_{\text{chemical}} is the chemical cost, yuan. Unit electricity price, chemical unit prices, and detailed cost accounting methods are provided in Appendix Text A.4.2 and Table A9.

2.4.3 Rainfall-induced I/I scenario setup

Based on the calibrated SUMO model, five rainfall-induced I/I scenarios were defined: no rain, light rain, moderate rain, heavy rain, and rainstorm. The rainfall grades followed the Chinese precipitation grade standard GB/T 28592–2012, using event-total rainfall depth for scenario classification. The rainfall depth ranges were 0 mm for no rain, 1.0–9.9 mm for light rain, 10.0–24.9 mm for moderate rain, 25.0–49.9 mm for heavy rain, and 50.0–99.9 mm for rainstorm.

To translate rainfall conditions into rainfall-induced I/I hydraulic loads for scenario simulation, the relationships between rainfall-induced I/I volume and rainfall characteristics, including total rainfall depth, maximum rainfall intensity, and rainfall duration, were analyzed. The derived rainfall-to-I/I response coefficient was applied to the hourly rainfall profile of each representative scenario to estimate hourly I/I increments, which were then superimposed on the BDWF to generate the 24-h influent flow profiles for SUMO simulation. Influent pollutant concentrations were adjusted according to a mass-balance mixing of baseline domestic sewage and the infiltrated water, using representative concentrations of stormwater runoff from the literature [39] (Table A10). To isolate the independent effect of I/I, all process operating parameters (recycle ratios, aeration, chemical dosing) were kept identical to the dry-weather baseline scenario. The WWTP B model was then used to simulate effluent quality, GHG emissions, and operating costs under different I/I intensities.

Extreme rainfall events with rainfall depths ≥ 100 mm were excluded because such events may exceed the stable operating capacity of the drainage—WWTP system and are more likely to trigger flow restriction or bypass discharge rather than normal treatment operation. Details of rainfall event identification, scenario classification, concentration adjustment method, and model input settings are provided in Appendix Text A.4.3.

2.5 Multi-objective optimization method for synergistic reduction of pollutants and GHG emissions

To identify operating strategies that balance effluent stability, GHG mitigation, and cost control under rainfall-induced I/I, the heavy-rain scenario was selected as a representative high-hydraulic-load condition based on the performance evaluation of the five rainfall scenarios (Section 3.2). Dissolved oxygen (DO), internal recirculation ratio (R_{\text{int}}), and external recirculation ratio (R_{\text{ext}}) were selected as decision variables because they directly affect nitrification–denitrification, sludge retention, recirculation energy demand, and process-related GHG emissions. Their ranges were determined according to actual plant operation, engineering experience, and preliminary simulations.

To reduce the computational burden of repeated SUMO simulations, Box-Behnken response surface models were developed as surrogate models. Peak effluent TN and NH₄⁺-N concentrations, total operating cost, and total GHG emissions were selected as model responses. A second-order polynomial was used to describe the linear, quadratic, and interaction effects of the three decision variables, and model adequacy was evaluated using analysis of variance and goodness-of-fit statistics.

Because TN and NH₄⁺-N were the most sensitive water-quality indicators under I/I disturbance (Section 3.2), a comprehensive water-quality (WQ) index was defined to quantify effluent nitrogen-removal stability:

(4)WQ\left(x\right)=\frac{C_{\text{1,eff}}^{max}\left(x\right)}{C_{\text{1,lim}}}+\frac{C_{\text{2,eff}}^{max}\left(x\right)}{C_{\text{2,lim}}}

where C_{\text{1,eff}}^{max}\left(x\right) and C_{\text{2,eff}}^{max}\left(x\right) are the peak effluent TN and NH₄⁺-N concentrations (mg/L), and C_{\text{1,lim}} and C_{\text{2,lim}} are the corresponding Class IA discharge limits (GB 18918–2002). A lower WQ indicates better nitrogen-removal stability.

COD and TP remained within the discharge limits and were less sensitive to the selected operating variables within the investigated design space; therefore, they were not included as surrogate responses or explicit constraints in the multi-objective optimization. NSGA-II was then employed to simultaneously optimize WQ, total GHG emissions (E_{\text{total}}), and total operating cost (C_{\text{total}}):

min\mathbf{F}\left(x\right)=[WQ\left(x\right),E_{\text{total}}\left(x\right),C_{\text{total}}\left(x\right)]

(5)s.t.C_{\text{1,eff}}^{max}\left(x\right)\le C_{\text{1,lim}},C_{\text{2,eff}}^{max}\left(x\right)\le C_{\text{2,lim}}

x_{\text{i}}^{min}\le x_i\le x_i^{max},i=1,2,3.

where the decision vector is x={[DO,R_{\text{int}},R_{\text{ext}}]}^{\mathrm{T}}; WQ\left(x\right), E_{\text{total}}\left(x\right), and C_{\text{total}}\left(x\right) denote the water-quality index, total GHG emissions, and total operating cost, respectively; C_{\text{1,eff}}^{max}\left(x\right) and C_{\text{2,eff}}^{max}\left(x\right) are the peak effluent TN and NH₄⁺-N concentrations (mg/L); C_{\text{1,lim}} and C_{\text{2,lim}} are their corresponding discharge limits; and x_i^{min} and x_i^{max} are the lower and upper bounds of the i-th decision variable. The resulting Pareto front was used to characterize the trade-offs among nitrogen-removal stability, GHG mitigation, and operating cost. Details of the optimization settings, fitted surrogate equations, model performance, and variable significance are provided in Appendix Text A.5 and Tables A11–A12.

2.6 Overall technical framework

The overall technical framework is shown in Fig. 3. First, WWTP operational and meteorological data were integrated and preprocessed (outlier removal, missing-value imputation, temporal harmonization). Second, machine-learning models were trained on dry-weather influent flow to predict BDWF, and rainfall-induced I/I was quantified as the difference between measured and predicted flow during rainfall events. The I/I responses of separate and incompletely separated sewer systems were then compared, and the relationship between rainfall and rainfall-induced I/I was further quantified to support wet-weather scenario construction. A SUMO mechanistic model was developed and calibrated for WWTP B to simulate effluent quality, GHG emissions, and operating cost under different I/I scenarios. Finally, a representative heavy-rain scenario was selected, and response surface methodology and NSGA-II were combined to determine operating parameters that balance effluent stability, GHG emissions, and operating cost.

3 Results

3.1 Data-driven quantification of inflow and infiltration

Influent flow at WWTPs is largely governed by domestic water-use behavior and therefore exhibits regular temporal fluctuations. Analysis of hourly influent flow under dry-weather conditions showed a pronounced diurnal pattern but weak weekly variation (Figs. A1 and A2). The diurnal profile generally decreased first and then increased, with the minimum flow occurring at 9:00–10:00. This pattern was likely associated with the delayed transport of nighttime domestic wastewater through the sewer network and its superposition with wastewater generated during morning residential activities. Therefore, the key requirement for rainfall-induced I/I quantification is not merely achieving the highest short-term fitting accuracy, but constructing a BDWF that can represent the intrinsic periodicity of domestic sewage.

To select a suitable data-driven model for BDWF construction, RF, LSTM, and Prophet models were compared. As shown in Fig. 4A, all three models achieved acceptable prediction errors. LSTM produced the lowest RMSE and MAE values, at 664.74 and 431.56 m³/h, respectively, followed by RF. Prophet showed slightly higher errors, with RMSE and MAE values of 705.44 and 521.26 m³/h, respectively. However, the lag-correlation analysis indicated that the predictions from random forest and LSTM were more strongly correlated with the observed flow lagged by 1 h than with the synchronous observations, suggesting that these two models mainly reproduced the previous-hour flow and showed an evident lag-copying tendency (Appendix Table A13). In contrast, Prophet showed no clear preference for lagged observations and explicitly decomposed the diurnal and weekly components of influent flow. The identified diurnal minimum was also consistent with the statistical pattern derived from measured data (Fig. 4B). Therefore, although Prophet did not provide the lowest fitting error, it was more appropriate for constructing BDWF in this study. Prophet was therefore used for subsequent rainfall-induced I/I quantification.

Based on the BDWF generated by Prophet, rainfall-induced I/I was defined as the abnormal increment of observed influent flow above the BDWF. Continuous wet-weather periods were identified using iterative residual filtering and a sliding-window voting procedure. In the strictly separated sewer system, no persistent deviation was observed between the measured influent flow and the BDWF (Fig. 4C). The suspected I/I periods identified by the model showed limited agreement with rainfall events, and only approximately 60% of the identified wet periods coincided with rainfall (Fig. A3). The estimated I/I flow was mainly scattered within 0–2200 m³/h, which was largely within the normal daily fluctuation range of the plant influent flow. In addition, no significant linear correlation was found between hourly rainfall intensity and the estimated I/I flow (P > 0.05). These results indicate that rainfall-induced responses caused by manhole inflow, pipe defects, or local infiltration were weak in the strictly separate sewer system and did not cause substantial disturbance to the influent hydraulic loading of the WWTP.

In contrast, the incompletely separated sewer system showed a clear rainfall response. Approximately 15% of the sewage collection flow in this catchment originated from combined sewer segments in the old urban area, with a combined drainage area of approximately 17.5 km². The Prophet model effectively captured the smooth periodic fluctuations under dry-weather conditions and identified the flow increments substantially exceeding the BDWF during heavy rainfall as rainfall-induced I/I (Fig. 4D). The identified wet periods were highly consistent with rainfall events, with more than 90% of the wet periods either coinciding with rainfall or occurring within 12 h after rainfall (Fig. A4). Rainfall events that were not detected were mostly characterized by small rainfall depth, short duration, weak rainfall at the early stage of continuous events, or abnormally low post-rainfall flow responses. This suggests that the proposed method is more sensitive to continuous and relatively intense rainfall events.

Event-scale analysis was conducted using 51 rainfall events with total rainfall depth greater than 1 mm. As shown in Fig. 5, rainfall-induced I/I volume generally increased with total rainfall depth, maximum rainfall intensity, and rainfall duration, with total rainfall depth showing the strongest apparent association. Partial correlation analysis further confirmed that total rainfall depth was the dominant driver. After controlling for rainfall duration and maximum rainfall intensity, total rainfall depth remained strongly correlated with rainfall-induced I/I volume (r = 0.857, P < 0.01), whereas rainfall duration was not significant and maximum rainfall intensity showed a weak negative correlation (r = −0.287, P < 0.05). This suggests that excessive short-term rainfall intensity may overload combined sewer segments or trigger local overflow, thereby limiting the amount of extraneous water conveyed to the WWTP.

To quantify the relationship between rainfall characteristics and rainfall-induced I/I at the event scale, stepwise multiple linear regression was performed using the three rainfall variables as candidate predictors. Only total rainfall depth was retained in the final model:

(6)Q_{\text{mathrm}}=2707.5P

where Q_{\text{mathrm}} is the event-scale rainfall-induced I/I volume (m³), and P is the total rainfall depth of a single rainfall event (mm). The model explained 92.9% of the variation in rainfall-induced I/I volume (R² = 0.929), indicating an average increase of 2707.5 m³ in rainfall-induced I/I volume per 1 mm increase in event-total rainfall depth. This rainfall-to-I/I response coefficient was subsequently used for wet-weather scenario construction.

3.2 Effects of inflow and infiltration on pollutant removal and GHG–cost performance

Based on the calibrated SUMO model, five rainfall-induced I/I scenarios, namely no rain, light rain, moderate rain, heavy rain, and rainstorm (Section 2.4.3), were simulated to evaluate pollutant removal, operating cost, and GHG emissions under wet-weather disturbances. Based on the event-scale analysis in Section 3.1, the rainfall-to-I/I response coefficient was set to 2707.5 m³/mm and applied to the hourly rainfall profiles of representative scenarios to estimate hourly I/I increments. These increments were then superimposed on the corresponding BDWF to generate the 24-h influent flow profiles. The rainfall depths and hourly rainfall-influent flow profiles are provided in Appendix Text A.7, Table A14 and Fig. A5, respectively. The results showed that effluent COD, TN, TP, and NH₄⁺-N concentrations met the Class IA discharge limits under all scenarios (Fig. 6), indicating that the plant retained a certain hydraulic shock resistance within the investigated range [40]. However, rainfall-induced I/I did not simply lead to effluent non-compliance. Instead, it weakened the stability of synergistic pollution and carbon reduction by increasing hydraulic loading, shortening hydraulic retention time, and raising conveyance-related energy demand [41].

The water-quality responses differed substantially among pollutants. COD and TP generally decreased with increasing rainfall-induced I/I intensity, suggesting that dilution dominated over hydraulic disturbance for these indicators (Figs. 6A and 6C). Under the no-rain scenario, effluent COD remained stable at 23.86–25.14 mg/L, with a daily fluctuation of only 5.1%. As I/I intensified, the COD fluctuation increased from 9.9% under light rain to 29.2% under the rainstorm scenario, although the overall concentration still declined. In contrast, nitrogen removal was more sensitive to I/I (Figs. 6B and 6D). The fluctuation of TN was strongly correlated with total rainfall depth, with a correlation coefficient of 0.98. NH₄⁺-N exhibited a pronounced peak under short-duration intense rainfall, and its peak concentration was highly correlated with maximum rainfall intensity, with a correlation coefficient of 0.97. These results indicate that the main wet-weather water-quality risk was not insufficient organic matter removal, but reduced stability of nitrogen removal. High hydraulic loading shortened the reaction time and intensified hydraulic disturbance in the secondary clarifier, which may have caused partial activated sludge washout. Meanwhile, nitrifiers have a relatively long generation time and cannot rapidly recover their activity under short-term shock loading, ultimately limiting NH₄⁺-N oxidation and increasing TN variability [42].

Operating cost and GHG emissions showed highly consistent responses to rainfall-induced I/I (Fig. 7). Under the no-rain scenario, the total operating cost was 158,182 yuan, and total GHG emissions were 155.98 t CO₂-eq. Under light and moderate rain, both indicators increased slowly, with operating costs rising by 10.8% and 20.9%, and GHG emissions by 9.7% and 18.4%, respectively. This suggests that low-to-moderate I/I could still be absorbed by the system. When rainfall intensity increased to heavy rain and rainstorm levels, the plant entered a high-hydraulic-load state. The operating costs increased to 285,453 and 294,860 yuan, corresponding to increases of 80.5% and 86.4%, respectively. Total GHG emissions also increased sharply, by 70.5% and 75.9%. Both the unit treatment cost and unit GHG emission reached their maximum values under the heavy-rain scenario, at 0.71 yuan/m³ and 0.65 kg CO₂-eq/m³, respectively. This indicates that heavy rainfall represents a critical condition under which the synergistic efficiency of pollution and carbon reduction declines markedly.

The synchronous increase in operating cost and GHG emissions was mainly driven by electricity consumption. As rainfall-induced I/I intensified, the dominant system burden shifted from biochemical reaction demand to hydraulic conveyance demand, making pumping and recirculation the primary energy-consuming units. Their share of total electricity consumption increased from 68.9% under the no-rain scenario to 88.1% under the rainstorm scenario, while electricity consumption by pumping units increased by approximately 250%. By contrast, aeration energy increased only slightly, from 18,541.08 to 19,639.36 kWh, and mixing energy remained nearly unchanged. Chemical consumption also increased only marginally, mainly due to higher disinfectant and flocculant dosing. Therefore, the increase in operational burden under I/I was not primarily caused by higher biochemical treatment energy, but by the nonlinear increase in hydraulic conveyance energy. Electricity-related indirect GHG emissions increased from 61.21 to 168.36 t CO₂-eq, representing a 175% increase and becoming the dominant contributor to total GHG emission growth. Direct emissions showed a weaker response: CO₂ and CH₄ varied by less than 5%, whereas N₂O increased from 11.77 to 15.47 t CO₂-eq, corresponding to a 31.5% increase. This suggests that high hydraulic loading may disturb nitrification-denitrification processes and increase the risk of N₂O release.

Sensitivity analysis further identified the key response pathways of the WWTP under I/I disturbance (Appendix Text A.7 and Table A15). COD, TN, and TP showed low-sensitivity negative responses, confirming that dilution dominated their effluent behavior. In contrast, NH₄⁺-N showed a high-sensitivity positive response, with a sensitivity coefficient of 1.52, making it the most vulnerable water-quality indicator under I/I. For resource consumption and GHG emissions, the sensitivity coefficients of electricity cost and electricity-related indirect GHG emissions were both 3.85, far exceeding those of chemical cost, chemical-related emissions, and direct emissions. These results indicate that electricity consumption is the decisive factor driving the increase in operational burden. Overall, the impact of I/I on the WWTP can be summarized as “effluent compliance with reduced synergistic efficiency”. The key pathway can be summarized as a chain: higher influent flow leads to unstable nitrogen removal, which then drives up pumping energy, and finally pushes both operating cost and indirect GHG emissions higher [43]. Therefore, wet-weather operation should shift from a single compliance-oriented strategy toward coordinated optimization focused on NH₄⁺-N stability, pumping energy reduction, and electricity-related GHG emission control.

3.3 Optimization of synergistic pollution and carbon reduction under I/I disturbance

Rainfall-induced I/I did not directly cause effluent non-compliance, but it weakened the stability of nitrogen removal and simultaneously increased energy consumption and GHG emissions. Under heavy rain and rainstorm conditions, nitrogen-removal fluctuations intensified, while pumping and recirculation became the main energy burdens. Heavy rain, with the highest unit treatment cost and unit GHG emission (Section 3.2), was therefore selected for subsequent multi-objective optimization. Wet-weather operation should not simply rely on stronger aeration or higher recirculation. Instead, it should maintain a sufficient safety margin for nitrogen removal while avoiding unnecessary recirculation-related energy use.

Based on this response pattern, DO, internal recirculation ratio, and external recirculation ratio were selected as the decision variables for multi-objective optimization because they link nitrogen-removal stability with nitrification, nitrate return, sludge retention, and recirculation-pump energy use [44]. Their relative effects on water quality, operating cost, and GHG emissions are summarized in Appendix Text A.8 and Table A16. In contrast, COD and TP were mainly governed by dilution under I/I disturbance and were less sensitive to these operational adjustments. Therefore, the optimization focused on the trade-offs among nitrogen-removal stability (WQ), operating cost, and GHG emissions.

The response surface surrogate models showed good fitting performance, with R² values ranging from 0.9670 to 1.0000. The predicted R² values ranged from 0.7471 to 1.0000, with relatively lower values for TN than for the other responses (Table A12), supporting their use for subsequent multi-objective optimization.

The multi-objective optimization results revealed clear nonlinear trade-offs among WQ, operating cost, and GHG emissions (Fig. 8). For the AAO process, operating cost and GHG emissions generally increased as WQ decreased. When WQ decreased from approximately 1.9 to 1.5, TN and NH₄⁺-N control improved substantially, whereas cost and emissions increased only slightly. However, when WQ further decreased below 1.2, the marginal benefit of water-quality improvement declined rapidly, and small additional improvements caused marked increases in cost and emissions. This indicates that the AAO process should not pursue an excessively low WQ under I/I disturbance, but should instead maintain an appropriate compliance safety margin. Considering effluent stability, operating cost, and GHG emissions together, the recommended operating ranges for the AAO process were 1.8–3.3 mg/L for DO, 100%–140% for internal recirculation, and 58%–94% for external recirculation. Within these ranges, a relatively low internal recirculation ratio can reduce pumping energy and indirect GHG emissions, while a moderate increase in external recirculation can help maintain sludge concentration and reduce nitrogen fluctuation.

The AO process showed a more distinct synergistic optimization window. When WQ was 0.4–1.0, and the operating cost was approximately 7.8 × 10⁴–8.2 × 10⁴ yuan, GHG emissions remained low at 76.7–77.9 t CO₂-eq, while the peak TN and NH₄⁺-N concentrations remained stable and compliant. Further strengthening of water-quality control increased both operating cost and GHG emissions. Conversely, insufficient operating intensity reduced nitrogen-removal stability and also led to a rebound in GHG emissions. These results indicate that higher operational intensity is not always beneficial for the AO process. Instead, a specific operating window exists in which low energy use, low carbon emissions, and stable nitrogen removal can be achieved simultaneously. The recommended ranges were 1.0–2.4 mg/L for DO, 100%–117% for internal recirculation, and 74%–100% for external recirculation. Within this range, the internal recirculation ratio should be maintained at a relatively low level; external recirculation can serve as the main control parameter for stabilizing sludge concentration and nitrogen removal, and DO can be adjusted to sustain nitrification and suppress NH₄⁺-N peaks.

Overall, synergistic pollution and carbon reduction under I/I disturbance should follow the principle of “low internal recirculation for energy control, moderate external recirculation for effluent stability, and appropriate DO for nitrification.” Under light- to moderate-rain scenarios, I/I loading is limited, and conventional operation can be maintained with enhanced online monitoring of TN and NH₄⁺-N. Under the heavy-rain scenario, the system enters a high-hydraulic-load state and becomes a key target for operational optimization. In this stage, excessive internal recirculation should be reduced to control pumping energy, while external recirculation and DO should be adjusted to stabilize nitrogen removal. When rainfall exceeds the system’s carrying capacity, the priority should shift to maintaining biological-process stability through sewer-flow restriction, storage regulation, online early warning, and emergency control. These results demonstrate that low-carbon operation under I/I disturbance cannot be achieved by intensifying a single parameter but requires coordinated control of recirculation, aeration, and effluent-quality safety margins.

3.4 Research limitations and future directions

Although the event-scale regression quantified the relationship between rainfall and rainfall-induced I/I, the I/I estimates used for regression were derived from model-estimated BDWF and therefore remain subject to prediction uncertainty. Previous studies have shown that uncertainties in dry-weather flow characterization and influent conditions can affect I/I estimation and subsequent WWTP model predictions [45,46]. In this study, overestimation of BDWF may lead to underestimation of rainfall-induced I/I, and vice versa, thereby affecting the rainfall-to-I/I response coefficient and the hydraulic loads assigned to wet-weather scenarios. Based on the sensitivity analysis, the resulting uncertainty may be particularly relevant to NH₄⁺-N, electricity consumption, and electricity-related GHG emissions, which showed relatively strong responses to I/I disturbance. These effects may further propagate to the evaluation of nitrogen-removal stability and energy–carbon performance, and ultimately influence the Pareto front and recommended operating ranges. Future work should therefore quantify uncertainty propagation from BDWF estimation through scenario simulation and optimization and assess the robustness of the resulting operational recommendations.

In addition, scenario analysis involved several simplifying assumptions, including representative stormwater pollutant concentrations and fixed operating parameters, and the multi-objective optimization was conducted for one WWTP under the heavy-rain scenario. Because nitrogen-removal and energy responses vary with I/I intensity, the resulting operating windows are scenario-specific and may shift under other wet-weather conditions. The GHG assessment was limited to operational emissions within the WWTP plant boundary; exclusion of off-site sludge management and downstream emissions may result in lower estimates than those based on a broader system boundary. Future studies should evaluate the optimization across different I/I intensities and WWTP configurations and incorporate relevant off-site emission pathways to assess the robustness and broader applicability of the operational strategies.

4 Conclusions

To support stable and low-carbon wastewater treatment plant (WWTP) operation under rainfall-induced inflow and infiltration (I/I) disturbances, this study developed an integrated framework combining data-driven I/I identification, SUMO-based process simulation, and multi-objective optimization.

Prophet was more suitable than random forest and long short-term memory models for baseline domestic wastewater flow estimation because it captured the intrinsic periodicity of influent flow and avoided lag-copying behavior. Based on this model, rainfall-induced I/I was found to be limited in the strictly separated sewer system but pronounced in the incompletely separated system, where more than 90% of the identified wet-weather periods coincided with rainfall or occurred within 12 h after rainfall. Event-scale analysis further identified total rainfall depth as the dominant driver of I/I volume.

The calibrated SUMO model showed that I/I did not cause effluent non-compliance within the investigated range, but it weakened the stability of synergistic pollution and carbon control. COD and TP were mainly governed by dilution, whereas nitrogen removal was more vulnerable to hydraulic disturbance. TN fluctuations increased with rainfall depth, while NH₄⁺-N peaks were closely related to maximum rainfall intensity, indicating that nitrogen-removal instability was the primary wet-weather risk. Rainfall-induced I/I also shifted the operational burden from biochemical treatment to hydraulic conveyance, leading to substantial increases in operating cost and greenhouse gas (GHG) emissions. Under heavy rain and rainstorm scenarios, operating costs increased by 80.5% and 86.4%, respectively, while GHG emissions increased by 70.5% and 75.9%. Pumping and recirculation of electricity became the dominant contributor to indirect carbon emissions.

Multi-objective optimization indicated that wet-weather operation should avoid excessive aeration and recirculation. Instead, a coordinated strategy of low internal recirculation, moderate external recirculation, and appropriate dissolved oxygen can stabilize nitrogen removal while reducing energy use, operating cost, and GHG emissions. These findings provide a quantitative basis for shifting WWTP operation from compliance-oriented control to coordinated pollutant removal and GHG mitigation under I/I disturbances.

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