With respect to the monitoring site, a WWTP in Hangzhou, a megacity in East China, was chosen. This WWTP is a large-scale plant, processing up to 1.5×106t of domestic wastewater daily. The chosen WWTP processes encompass mechanical treatment, biological treatment, sedimentation, advanced treatment, disinfection, and sludge treatment. As illustrated in Fig. 1, we divide the WWTP into 14 functional areas according to treatment processes. Areas associated with primary treatment were labeled as coarse screens and primary sedimentation tanks, whereas those linked to secondary treatment were indicated as aeration tanks and secondary sedimentation tanks. We performed one monitoring experiment per day, with each experiment entailing one to two rounds of mobile measurements along external roads and along internal roads around the functional areas. Additionally, we conducted repeated mobile measurements and fixed measurements on roads with high concentrations to calculate average concentration data. Over 10 d of experiments from June to December 2023, we obtain 8 d of complete monitoring data, including 3 d in summer and 5 d in winter. On the other 2 experimental days, internal facility maintenance restricted access to certain roads, resulting in incomplete monitoring data.

The monitoring instruments consisted of a vehicle-mounted cavity ring-down spectrometer (CRDS) monitoring system (Zhao et al., 2024) and a portable meteorological station. The vehicle-mounted CRDS system was anchored by the CRDS analyzer (Picarro G2201-i, Picarro 2010), accompanied by GPS and meteorological instruments. The volume fraction of CH4 is measured with an accuracy of 5ppb±0.05%. CRDS measurements have the advantages of strong interference resistance and high sensitivity and accuracy, making them widely employed in research focused on monitoring GHG emissions (Rella et al., 2015; Lopez et al., 2017).

In this study, the CRDS analyzer was placed inside the monitoring vehicle to measure CH4 concentrations in the WWTP. The sampling probe was placed near the roof along the window of the car to avoid interference from vehicle exhaust due to the low position. The mobile meteorological instrument was placed on the roof of the vehicle to gather meteorological data. In addition, the GPS unit was integrated to record the location of sampling points during the measurement period. Two portable meteorological stations (SWS-500, Hangzhou Pengpu Technology), capable of measuring meteorological parameters (wind speed, direction, temperature, humidity, and atmospheric pressure), were positioned adjacent to the main entrance and atop the filter tank at the WWTP.

We used the methods suggested by the Intergovernmental Panel on Climate Change (IPCC, 2006) to calculate the CH4 emissions from wastewater. The formula for calculating the CH4 emissions from wastewater is described as follows: 1ECH4=(TOW-S⋅a)⋅EFCH4-RCH4, where ECH4 denotes the direct CH4 emissions from the wastewater treatment plant (tCH4a-1), total organic waste (TOW) is defined as the total organic pollutant load in the influent wastewater (tCODa-1 – chemical oxygen demand per year), S refers to the annual production total of dry sludge (ta-1), the parameter a signifies the organic matter content in the dry sludge (tCODt-1), EFCH4 is the CH4 emission factor (tCH4tCOD-1), and RCH4 quantifies the annual recovery of CH4 from anaerobic treatment processes (ta-1).

Operational data for the WWTP examined in this study were derived from the “Urban Drainage Statistical Yearbook”, an annual publication of the urban water supply and drainage systems in China. This dataset includes details such as the water treatment volume, sludge production, and the concentrations of six pollutants (CODCr, biochemical oxygen demand (BOD), suspended solid (SS), NH3–N, total nitrogen (TN), and total phosphorus (TP)) in both influent and effluent. TOW is calculated using the amount of treated water and the COD influent concentration of the WWTP provided in the yearbook, while the annual sludge production (S) is extracted directly from the yearbook. The organic matter content in dry sludge is estimated at an empirical 40 %, assuming a sludge moisture content of 75 %, leading to a value of 0.1 (Guo et al., 2019). EFCH4 is selected based on the recommended value of 0.0046 for Zhejiang Province (Cai et al., 2015). Given the infrequency of anaerobic treatment in wastewater, RCH4 is set to zero.

We developed an inversion framework for emission fluxes designed for plant-level applications. The framework used mobile measurement data, the locations of emission sources, and initial emission estimates, alongside wind speed and direction data, as inputs to the multi-source Gaussian diffusion models. The preliminary localization of the emission sources was chiefly contingent upon the concentration distribution along the roads within the internal functional areas. Meanwhile, the initial emission estimates for each source were determined by integrating the concentration data from these areas with an improved empirical equation (Weller et al., 2019). Based on the comparison of measurements and model simulation results (Fig. S1 in the Supplement), it is determined that the plant exhibits multiple point sources and line source diffusion patterns. Figure S1 illustrates that the CH4 concentration curve presents distinct peak distributions in point source diffusion patterns, while the CH4 concentration distribution in line source diffusion patterns consistently maintains higher levels. We then used a genetic algorithm to iteratively optimize source emission fluxes and their locations. The inversion framework simulation dictated the placement of 12 main point sources throughout the WWTP, specifically within Aeration Tank ①, ②, ③, ④, and ⑤; Primary Clarifier ③, ④, and ⑤; Screen ①; Secondary Clarifier ① and ②; and Sludge Treatment ② (Fig. 1). Within this study, a uniform line source was established, with the assumed location along the road between Screen ① and Primary Clarifier ① (yellow mark in Fig. 1). This assumption was grounded in the CH4 concentration distribution observed within this road segment and was substantiated through model validation. The remaining emission flux inversion processes followed the same procedure as the point source simulation. Adjustments to the source locations within the model narrow the gap between simulated and measured concentrations, thus enhancing the accuracy of inversion. This section delineates each model incorporated into the inversion framework.

The closed-path mobile measurements were conducted by a vehicle-mounted CRDS monitoring system along the external roads encircling the WWTP, with further monitoring conducted along the internal roads. This strategy depicts the distribution of CH4 concentrations within a WWTP, allowing for the identification of specific CH4 emission sources. Based on 8 d of CH4 experimental monitoring data, the CH4 concentration range on the overall roads was determined to be 1.98–17.13 ppm. The CH4 concentration distribution indicated higher levels downwind, with the highest concentrations consistently recorded at Screen ① throughout the mobile experiments.

Due to the consistency of the concentration measurement methods, we chose 29 June and 13 December as typical examples. Figure 2 illustrates the measured CH4 concentration enhancement distributions on 29 June (summer) and 13 December (winter) 2023 (other days are shown in Figs. S3–S8). The CH4 concentration enhancements depicted were calculated by subtracting the background concentrations from the measured values, with the background determined as the mean of the bottom 10 % of the concentration data. Specifically, the background concentrations register at 1.98 ppm on 29 June and at a slightly elevated 2.11 ppm on 13 December. The analysis indicates that the shallower boundary layer in winter causes CH4 to accumulate near the surface, resulting in a higher background concentration. Moreover, increased concentrations are detected in the regions surrounding Screen ①, Primary Clarifier ④, and Aeration Tank ③ during these 2 d. The complete concentration maps, which include the internal roads, reveal that the experiment on 29 June exhibits heightened concentrations at Screen ①, Secondary Clarifier ②, and Primary Clarifier ② and ④. Screen ① exhibits the highest CH4 concentration, with an enhancement of 14.83 ppm. On 13 December, the concentration enhancements are noted in proximity to Secondary Clarifier ① and Primary Clarifier ②, with Primary Clarifier ② showing the highest CH4 concentration at 4.79 ppm.

The CH4 concentrations in summer surpass those observed in winter, consistent with a previous study on WWTPs (Masuda et al., 2015). The screen, primary clarifier, and aeration tank are identified as sources with notably higher concentrations. Analysis of concentration distributions reveals that Screen ① shows a peak concentration reaching 14.83 ppm, which is 7.5 times the background concentration. The four primary clarifiers record high concentrations of between 4.79 and 10.88 ppm. The high value of 4.60 ppm measured around the aeration tanks is mainly detected at Aeration Tank ③ . The screen in this study includes coarse and fine screens and a grit chamber, constituting preliminary wastewater treatment to capture larger suspended solids and particulates. The anaerobic environment of the sewer network promotes the production of CH4 from organic compounds in municipal wastewater. As this wastewater enters the WWTP, the influent contains dissolved CH4 that originated in the sewer network. During primary treatment, wastewater is elevated through riser mains, facilitating the release of CH4 into the atmosphere (Guisasola et al., 2008; Bao et al., 2016). The flow velocity, hydraulic design, and detention times in these facilities may affect CH4 production and release (Alshboul et al., 2016; Yin et al., 2024). The primary clarifier physically removes suspended solids from wastewater through sedimentation, while organic matter undergoes anaerobic microbial degradation, resulting in the substantial production of CH4 (Masuda et al., 2017). In the aeration tank, operated under anaerobic and anoxic conditions, complex organic compounds are converted to CH4 by facultative and anaerobic bacteria through biological processes (Yoshida et al., 2014). In contrast, Kupper et al. (2018) identified sludge storage tanks as the primary source of CH4 emissions in Swiss WWTPs, accounting for 70 % or more of the total emissions. Stadler et al. (2022) monitored CH4 concentrations inside and around wastewater treatment facilities that ranged from 2.04 to 32.78 ppm, with elevated CH4 levels predominantly measured near a sludge treatment tank, the digesters, and secondary clarifiers. The CH4 emissions from various WWTPs are affected by a range of factors, including specific processes, pipeline design, and equipment aging, and mobile monitoring can better reflect the actual emission distribution.

The CH4 concentrations measured via mobile monitoring were employed in combination with the inversion framework to achieve the quantification of CH4 emissions and localization of the emission sources within the WWTP. Figures 3 and 4 show the locations of identified point sources and the comparison between the measured and simulated concentration distribution. The experiment conducted on 29 June finds Screen ① to be the most significant contributor to CH4 point source emissions at 18.26 kgh-1, whereas Secondary Clarifier ② is classified as the least significant at 1.23 kgh-1. The correlation coefficient R2 for the measured and simulated concentrations is 0.63, with a root-mean-square error (RMSE) of 0.70 mgm-3. On 13 December, Aeration Tank ⑤ is the largest point source of CH4 emissions at 3.93 kgh-1, whereas Primary Clarifier ⑤ is the smallest source at 0.55 kgh-1, with a correlation coefficient R2 of 0.70 and an RMSE of 0.28 mgm-3. The enhanced correlation between the winter measurement and simulation data, as well as the improved fit of the measurement and simulation value curves, is attributed to the shorter monitoring cycle and more stable meteorological conditions.

In addition, when employing the multi-source Gaussian diffusion model combined with a genetic algorithm framework for iterative optimization to pinpoint point sources, we were able to locate external sources. As shown in Fig. S2a and c, external sources are primarily located along the main roadway to the south of the WWTP. Moreover, the estimated emissions vary across different days, which indicates that external source emissions are influenced by vehicle traffic. Figure S2b and d compare measured and simulated CH4 concentrations before and after accounting for external sources, demonstrating that simulations are significantly closer to the measurements when external sources are included.

Table 1 displays the CH4 emission fluxes (Q), wind speed and direction data (Ws and Wd, respectively), the horizontal diffusion coefficient (γ1, α1), and the vertical diffusion coefficient (γ2, α2) from the 8 d monitoring experiment. Wind speed and direction data are the average wind speed and direction during the monitoring time, and the CH4 emission fluxes are obtained by the inversion of the average concentration and wind speed and direction data as input to the inversion framework. The emission flux values of CH4 emission sources (12 point sources and 1 line source) for all experimental days are detailed in Tables S1 and S2 in the Supplement. It is observed that the summer average CH4 emission flux (68.78±17.40kgh-1) surpasses the winter average CH4 emission flux (47.76±21.39kgh-1). This seasonal disparity in emissions is primarily attributed to the aeration tank, followed by the screen and primary clarifier. The activated sludge in the aeration tank contains a higher population of methanogens, whose CH4 production capability intensifies with rising temperatures (Vítěz et al., 2020). Notably, the seasonal variance in the aeration tank is predominantly driven by the performance of Aeration Tank ④. However, the substantial variation in the emissions from the three summer experiments of Aeration Tank ④ suggests a degree of emission instability. Conversely, the uniformity in the low emissions from the five winter experiments might be associated with the meteorological conditions and the actual operational status of the plant on those days. At lower wind speeds, the CH4 emissions show only slight differences when compared to emissions on days with higher wind speeds. This suggests that the inversion results are less influenced by wind speed and are primarily associated with seasonal variations.

The screen and primary clarifier are the predominant emission sources at the WWTP. Specifically, these sources emit 37.50 kgh-1 in the summer and 31.92 kgh-1 in the winter, accounting for 55 % and 67 % of the total emissions. Pipeline leaks near the screen and primary clarifier led to the CH4 release. Previous research has similarly examined major emission sources at WWTPs. Yin et al. (2024) conducted offline monitoring of WWTPs in Beijing and Guiyang, identifying the primary treatment zone as the primary source of CH4, accounting for 60.1 % and 35.8 % of the respective total emissions. Masuda et al. (2017) analyzed CH4 emissions from different processes at three WWTPs in Japan, concluding that primary clarifiers are one of the major sources of CH4 emissions. He et al. (2023) compiled CH4 emission proportions for different processes in WWTPs based on reported data, finding percentages of 7 %–12 % for the grit chamber, 8.2 %–68.1 % for the primary clarifier, and 18.3 %–86.4 % for the aeration tank.

An alternative top-down approach, known as the tracer gas dispersion method (TDM), has been applied to estimate CH4 emissions from city streets (von Fischer et al., 2017; Weller et al., 2018), WWTPs (Yoshida et al., 2014; Delre et al., 2017, 2018), biogas plants (Reinelt et al., 2017; Scheutz and Kjeldsen, 2019; Fredenslund et al., 2023), and landfills (Rees-White et al., 2019; Kissas et al., 2022). TDM involves releasing tracer gases like nitrous oxide and acetylene near the source and measuring their concentrations along with CH4 downwind using a mobile platform. The similar diffusion patterns of CH4 and the tracer gases result in a stable concentration ratio after atmospheric mixing, enabling the calculation of CH4 emission rates with a better accuracy (Mønster et al., 2014).

Moreover, TDM was employed to validate and compare other model inversion methods. Moore et al. (2023) proposed that Gaussian dispersion modeling demands less experimental equipment, site access, and personnel than TDM, thereby allowing for swifter data gathering. Yacovitch et al. (2015) utilized a 5 d dataset of tracer gas release in the Barnett Shale region to evaluate the Gaussian dispersion flux quantification method. The results indicated a 95 % confidence interval, with a lower-bound factor of 0.334 and an upper-bound factor of 3.34.The work of von Fischer et al. (2017) presented three controlled release experiments to validate the reliability of a leak rate algorithm in Fort Collins, CO, which indicated a very significant correlation between known and estimated leak rates (p<0.0001, r2=0.43). Compared with the method employed in the study, TDM offers advantages such as simpler formula calculations. Nonetheless, it also presents several drawbacks, including complex experimental procedures and safety hazards associated with the release of tracer gases, which requires access permits from industrial facilities.

The CH4 emissions were also calculated using the IPCC method, with data sourced from the Urban Drainage Statistical Yearbook of 2017. The emission flux of 213.95±128.37ta-1 was determined, with the uncertainty (60 %) derived from the data summarized in the research (Lin et al., 2021). Figure 5 shows the contrast between the emission inversion results from the monitoring experiment and the emission inventory. The uncertainty in the inversion results was determined by accounting for the uncertainties in wind speed, wind direction, and instrument measurements, following the method presented in Sect. 2.4.5. The uncertainties in the emission flux inversion ranged from 33 % to 63 % on individual days. Notably, the uncertainty associated with wind speed contributes approximately 44 %–94 % of the uncertainty range. The summer average inversion emission flux (603.33±152.66ta-1) was calculated to be 2.8 times that of the inventory, and the winter average (418.95±187.59ta-1) was twice as much. It is posited that the discrepancy may stem from significant uncertainties in the emission factors associated with the WWTPs or the lack of updated activity level data, as the statistical yearbook provided data only up to 2017; therefore, the emission inventory might have underestimated the actual emissions.

Furthermore, other studies have also investigated the comparison between CH4 emissions obtained from different measurement methods at WWTPs and the IPCC inventory estimates. The majority of these studies have indicated that the measured values exceed the inventory values. Wang et al. (2021) conducted a measurement-based assessment of CH4 emissions (46.58 ta-1) in Wuhu City, revealing emission values 46.71 % higher than those calculated using the IPCC method. Moore et al. (2023) employed mobile monitoring to evaluate CH4 emissions at 63 WWTPs across the USA. Specifically, CH4 emissions from centrally treated domestic wastewater in the USA amount to 4.64×105ta-1, which is 1.9 times greater than the Environmental Protection Agency inventory. Song et al. (2023) investigated CH4 emissions from municipal wastewater treatment in the USA and reported a value of (4.36±2.8)×105ta-1. This value was approximately twice the estimates provided by the IPCC. Our estimated results are generally consistent with previous studies. The lower estimated results provided by the IPCC method can be attributed to the neglect of certain potential emission sources from the emission inventories, including emissions from equipment in sludge treatment facilities and leaks from pressure relief valves.

In this section, we evaluate the stability of the inversion framework through sensitivity analysis and explore the impact of different point source locations on the inversion of emission concentrations. The precise identification of emission sources can enhance the accuracy of emission flux inversion, making a sensitivity analysis of the source location essential. We applied the method of controlling variables to perform a sensitivity analysis on the location of a single point source. The central position of the plant was taken as the reference origin, and the positions of 12 emission sources were determined to analyze the variation in error between measured and simulated concentrations within a 200m×200m range around each emission source. We sequentially modified the source position parameters in the model input to analyze the congruence between the simulated concentrations and the observed measurements, quantifying the fit using the RMSE. The change in concentration error serves as an indicator of the accuracy of the emission source localization.

Figures 6 and 7 describe the error variation between monitored and simulated concentrations when the point source location is subject to change within a 200m×200m range from the monitoring experiment on 29 June and 13 December. The error variation in the remaining days can be seen in Figs. S9–S14. The point source locations simulated based on the inversion framework are mostly in areas with minor relative concentration errors, which can be considered to have a high reliability in simulating point source locations. The emission source location errors for the two experiments are within the ranges of 0.7–1.3 and 0.2–0.3 mgm-3. The winter emission source locations exhibit greater stability and accuracy in the inversion results than the summer ones.