Exploring data quality and seasonal variations of N₂O in wastewater treatment: a modeling perspective

Wastewater treatment plants (WWTPs) are known to produce substantial amounts of nitrous oxide (N₂O) (Law et al. 2012). With a global warming potential 265 times higher than CO₂ for a 100-year period (IPCC 2013), N₂O is a potent greenhouse gas (GHG) and one of the main contributors to climate footprint of WWTPs (Daelman et al. 2013; Delre & Scheutz 2019). N₂O has, therefore, gained focus in the wastewater industry and in the political debate; and the mitigation of N₂O has become a priority for WWTPs (Li et al. 2022).

N₂O has become the topic of several studies, where datasets of varying lengths have been collected from full-scale WWTPs and used for analysis and estimation of the N₂O emission and production (Vasilaki et al. 2018, 2019, 2020; Chen et al. 2019; Hwangbo et al. 2020, 2021; Myers et al. 2021; van Dijk et al. 2021; Li et al. 2022; Valk et al. 2022). Many studies apply data-driven modeling to model N₂O concentrations or emissions (Hwangbo et al. 2020, 2021; Vasilaki et al. 2020; Li et al. 2022); or exploratory data analysis of N₂O and other operational variables to investigate the relationship between those (Vasilaki et al. 2018; Chen et al. 2019; Myers et al. 2021; van Dijk et al. 2021). A monitoring campaign is usually conducted, where operational data are logged only within a predefined period. However, many WWTPs monitor the biochemical processes with several sensors and appertaining surveillance systems to ensure stable operation and minimize the risk of exceeding effluent standards and polluting surface waters. This practice generates tremendous amounts of operational data, which are stored and can be used for research purposes. Furthermore, as political initiatives are being notified (Danish Government 2020), many utilities (especially in Denmark) are installing N₂O sensors to quantify their climate footprint better and to prepare for N₂O production control. This enhances the prospects for data-driven modeling, which in various studies has shown great results for N₂O modeling (Vasilaki et al. 2020; Hwangbo et al. 2021; Li et al. 2022) and modeling of other variables in the activated sludge process (ASP) (Hansen et al. 2022). However, one major challenge regarding data-driven modeling is data quality. The quality of the data used to train and validate mathematical models can greatly affect the performance, since erroneous data can lead to inaccurate or unreliable models (Breck et al. 2019; Budach et al. 2022).

This study aims to build and support the foundation of data-driven model development for N₂O prediction and estimation. To this end, we investigate the feasibility of data-driven modeling using only operational data from four different treatment plants with various process designs. Consequently, the characteristics of the data collected align with that used to analyze or determine control actions for the plant. The acquired data are subject to a quality assessment where challenges associated with the operational data are identified, while examples from the real data are presented. Four quality issues are quantified, and the data quality across different case plants is compared. In addition, we also present a comparison of data quality across different sensor types used in the daily operation. The data from all four cases are profiled and investigated for seasonal variations, and the results for similar plant designs are compared. Furthermore, we investigate the relationship between N₂O and nitrogenous variables by means of a sliding window rank correlation. All statistical methods used are applied as sliding window operations, hence enabling a better understanding of the N₂O dynamics under changing conditions. The methods applied in this work differ from previously published literature, where statistical techniques were applied to entire datasets (Chen et al. 2019) or larger segments (Vasilaki et al. 2018). In addition, this study includes four case studies, where all biological treatment is done using the alternating ASP. As such, the main contributions of this study are the following:

• (1)

  Using operational data from four Danish WWTPs, which combined provide over 8 years of N₂O measurements, we quantify the data quality and, thus, feasibility of data-driven methods for N₂O modeling in the future.

• (2)

  We analyze and present the N₂O profile for the case plants and compare results across similar plant designs.

• (3)

  To investigate the N₂O dynamics over time and over changing environmental conditions; we apply the sliding window rank correlation, which highlights the changing relationship between N₂O and nitrogenous variables. The outcomes of this analysis are evaluated within the context of the data quality investigation, considering potential significant interactions.

Dissolved N₂O concentrations were measured using the liquid-phase Clark-type electro-chemical N₂O sensor from Unisense Environment, Denmark (Unisense Environment A/S 2022). The sensor has a replaceable sensor head for which the manufacturer guarantees a lifetime of 4 months from the date of receipt but expects a lifetime of 6 months. Before deploying the sensor, it is calibrated using a two-point calibration at the same temperature as the wastewater in which the sensor will be placed in. The measurements will then be valid with an uncertainty of within of the calibration temperature; hence, it is recommended to perform a two-point calibration every 2 months to comply with seasonal variations in the wastewater temperature (Unisense Environment A/S 2022). In its default configuration, the sensor is designed to measure within the range of 0–1.5 mg N₂O-N/L with a resolution of 0.005 mg N₂O-N/L. Nevertheless, there is an option to calibrate the sensor to accommodate a working range tailored to the anticipated N₂O concentration at a particular plant. It is important to note that calibrating the sensor to a nonstandard range will necessitate a trade-off with resolution, leading to increased increments in sensor values. The response time of the sensor is 65 s for temperatures between 10 and 30⁠. At lower temperatures, the sensor response will be slower. Information about the sensor is acquired from the sensor manual and through personal communication with the manufacturer.

This work is based on operational data collected from four Danish WWTPs from 2018 to early 2023. All plants involved in this study have permanent N₂O sensors installed in the biological reactors and collect N₂O data on the same terms as other measured operational variables (dissolved oxygen, nitrogen component concentrations, flow rates, temperature, etc.). Due to the warned political initiatives (Danish Government 2020), more Danish WWTPs are installing N₂O sensors for permanent use as part of the operation surveillance. However, few plants have collected data from 2022 or earlier, meaning that datasets of at least 1 year are difficult to obtain. The four datasets are of various sizes depending on the time of installation of the N₂O sensor(s) and the number of measured operational variables. Table 1 provides an overview of the individual dataset characteristics, where the following are specified: sample time (TS), temporal length of the dataset, the period in which the data were collected, number of installed N₂O sensors, plant design, and the population equivalent (PE) capacity.

Table 1

Characteristics of the available data

.	Dataset characteristics .			Plant characteristics .
.	Resolution .	Length .	Period .	Plant design .	sensors .	Lines .	Capacity (PE) .
Avedøre	2 min	4 years	2018–2022	Biodenitro (Bundgaard et al. 1989)	4	6	350,000
Fredericia	5 min	3 years	2019–2022	Single tanks	1	4	420,000
Køge	2 min	10 months	2022	Biodenitro (Bundgaard et al. 1989)	2	3	100,000
Skanderborg	5 min	1 year	2021–2022	Single tanks	2	2	41,500

.	Dataset characteristics .			Plant characteristics .
.	Resolution .	Length .	Period .	Plant design .	sensors .	Lines .	Capacity (PE) .
Avedøre	2 min	4 years	2018–2022	Biodenitro (Bundgaard et al. 1989)	4	6	350,000
Fredericia	5 min	3 years	2019–2022	Single tanks	1	4	420,000
Køge	2 min	10 months	2022	Biodenitro (Bundgaard et al. 1989)	2	3	100,000
Skanderborg	5 min	1 year	2021–2022	Single tanks	2	2	41,500

Note: All plants run the biological treatment using alternating ASP.

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High-quality data are a precondition for analysis, development, and implementation of data-driven methods in any framework (Cai & Zhu 2015). Although several studies concern data-driven modeling of wastewater treatment processes (Ni et al. 2013; Chen et al. 2019; Hwangbo et al. 2020, 2021; Li et al. 2022; Valk et al. 2022), none address the quality of the collected data.

The definition of data quality depends on the perspective of, e.g., data users, producers, and custodians and the different use contexts (Fürber 2015). A very general definition could be ‘data is of high quality if it is fit for use by data consumers’ (Wang 1996). Now the question arises, of whether the data are fit for use, and to answer that question, one may consider various different dimensions. Wang (1996) identified 15 important dimensions of data quality; however, several modern publications summarize the important aspects into fewer dimensions (Herzog et al. 2007; Cai & Zhu 2015; Fleckenstein & Fellows 2018), some with several elements in each dimension. In this study, the data quality was evaluated in six dimensions as inspired by several existing formulations (Wang 1996; Herzog et al. 2007; Cai & Zhu 2015; Fleckenstein & Fellows 2018), and those are the following:

• •

  Relevance

• •

  Accuracy

• •

  Completeness

• •

  Consistency, coherence, and clarity

• •

  Comparability

• •

  Accessibility

These dimensions were examined to evaluate the quality of operational data and its applicability in data-driven analysis and modeling. Challenges specific to WWTP data were identified and elucidated through examples drawn from operational data, with certain issues quantified. The evaluated variables encompass N₂O (nitrous oxide), NH₄ (ammonium), NO₃ (nitrate), DO (dissolved oxygen), temperature, influent flow rate, and airflow to the biological process. Note that certain challenges can be associated with multiple dimensions of data quality, highlighting the complexity of data quality assessment. In the following, we will define the six dimensions briefly. However, the full theoretical background is presented in Section S2 in the Supplementary Material along with visual examples of data quality issues from the four case plants.

The relevance of the data refers to which extent the data is applicable and useful for the intended task (Herzog et al. 2007). Given that we aim to determine the amount and quality of information possible to extract from operational data in this study, the relevance of the collected datasets is high. The relevance is a data quality dimension that is contextual; hence, a given dataset might be less relevant in different use-cases, for instance, due to missing variables.

Accuracy is a data quality dimension, which may partly rely on instinct (Wang 1996; Fürber 2015), but can also be assessed scientifically by comparing the data to a reference. However, when dealing with operational data, a reference measurement is rarely available since the operators are interested in low maintenance and operational costs, which avoids performing multiple measurements of the same variable when one is sufficient. Instead, a more accessible evaluation of data accuracy can be provided by the sensor manufacturers. Accuracy for the chemical sensors measuring, i.e., DO NH₄, NO₃, etc., is often provided with a percent-wise deviation from the true value. Other issues related to accuracy is the tendency of sensor drift or bias in the measurements. Both phenomena are visualized in Section S2 in the Supplementary material. Visual inspections of all chemical variables were performed using time series plots. Chemical variables that realistically cannot become negative involve N₂O, NH₄, NO₃, and DO. Hence, when encountering negative values for those variables, it indicates bias, drift, or another sensor fault. Similarly, the measurements for N₂O and DO are known to have cycles that drop to 0, meaning that drift can be clearly observed if the minimum of DO and N₂O never reaches 0. The number of variables that are identified to have drift or bias were identified. In addition, a more general quantification of negative values in the data was performed by calculating the number of negative values over the entire dataset and comparing it to the total number of measurements.

Completeness is tied to the SCADA system and operator philosophy. Incompleteness can arise from missing temporal data, excluded variables, or missing metadata (such as undocumented units). Incomplete data introduce uncertainties, often addressed by replacing missing values with the last available measurement. This practice, though, may create a misleading impression of stability in dynamic periods, emphasizing the need for comprehensive data practices and collection of metadata. An evaluation of completeness was performed by detecting missing and constant values in operational variables. Variables with missing or constant values for more than 30 min, were identified as having bad quality for the given period. Variables such as N₂O, DO, airflow, and flow of influent frequently measure 0 (mg/L or m/h), and periods longer than 30 min with a value of 0 were, hence, not identified as inaccurate for those specific variables. The accumulated duration of periods with incomplete data was compared to the total length of each dataset, providing a percentage of low-quality data in the dataset.

Consistency is a representational dimension of data quality, which refers to consistent representation and interpretation of data (Wang 1996; Fleckenstein & Fellows 2018). Changing, e.g., the sensor type, frequency of the measurements, sensor range, or unit of the measurement induces poor data quality in relation to consistency. Consistency can, despite its representational aspect, be difficult to quantify without metadata to support the questionable periods of data identified through process understanding and expert knowledge. More information and examples are available in Section S2 in the Supplementary material. Similar to bias and drift, the datasets were investigated visually for consistency issues. More specifically, the variables were inspected for changes in sensor ranges. Due to the lack of metadata (which is also related to completeness), the changes in sensor characteristics are difficult to quantify. Yet, one simple method is to examine visually whether the maximum sensor range changes over the dataset.

Comparability relates to the extent to which the dataset can be compared or perhaps merged with other data. Data used in this work show high comparability as all datasets are (1) from a real plant, (2) with a similar sampling rate (2 or 5 min), and (3) with analogous variables collected in the view of Danish standards. The plant designs differ from each other, but for the purpose of data-driven modeling and exploratory analysis, this aspect increases the data quality as the aim is to cover several different plant designs and compare results.

Data availability involves challenges in collecting, storing, and retrieving data. High availability ensures quick access, but latency can impact data usefulness. Timeliness considers the appropriateness of data age, which, for offline methods (as done in this study), is usually not an issue unless processes change post-collection. Metadata is the most useful tool to determine the availability of the data; however, statistical and time series analysis may provide insight as well. Through personal communication with plant operators, the authors of this work have been informed that the data resolution is reduced in some systems. This is commonly done by down-sampling the time series or aggregation into periodic averages, and those methods are ways of lossy data compression. For data-driven modeling and system dynamics investigation, lossy compression may remove critical information, compromising data quality.

Quantification was performed on the dimensions of accuracy, completeness, and consistency, as these dimensions have aspects that are concrete, as opposed to the abstract and instinctive nature of for instance relevance.

The DO concentration is effectively controlled by adjusting the airflow, and there are approximately 10–20 cycles per day. The N₂O concentration is not controlled; thus, the number of cycles per day varies in the range of 0.25–20 (as shown in Figure 1). The length of the batches in this study is 4 days to ensure there is at least one cycle per batch.

The N₂O and DO are measurements that repeatedly take values of zero; hence, the minimum concentration over a period that includes several cycles is always known. These measurements are, therefore, simple to correct for bias and drift. On the other hand, it is more difficult to correct variables such as NH₄, NO₃ and PO₄, as these measurements do not necessarily fall to zero over several cycles.

The first step after data preprocessing is to determine whether trend or seasonal patterns are present (Chatfield 2003). Understanding the profile and seasonal variations of N₂O within a specific plant is crucial for drawing meaningful conclusions and contextualizing results when conducting inter plant comparisons. Extrapolating findings related to N₂O from one plant to another may not be straightforward, particularly when the profiles exhibit significant differences. Furthermore, seasonal analysis may reveal issues such as data outliers or inconsistencies that can impact the overall quality of the time series data.

The seasonal variations of N₂O were investigated using a centered moving mean, ⁠, and standard deviation, ⁠, over a window of 30 days. Comparison of the N₂O seasonal variations to the nitrogenous variables is performed using a scaled-centered moving mean and moving standard deviation of the compared variables. Scaling, using the min-max-scaling, enables comparison on a common axis as NH₄ and NO₃ endure up to 10 times higher concentrations (in mg/L) compared to N₂O.

As opposed to the linear correlation coefficient, the rank correlation does not assume normally distributed variables, and the method is a measure of the monotonicity of the relationship between two variables. -values lower than 0.01 were considered significant.

In Table 2, the total number of investigated variables is shown alongside the number of alternating sensors (number of variables, where the sensor changes characteristics) and bias and drift in sensors grouped by N₂O and other sensors. Furthermore, the table also presents how many variables are affected by missing data and negative data, including the mean, minimum, and maximum percentage across all variables in every plant.

The number of variables in each dataset varies between 7 (Fredericia) and 22 (Avedøre) variables. In spite of this, the number of sensors that have changing characteristics throughout the dataset is consistent over the datasets. The results suggest that this kind of quality issue does not depend on the size of the dataset. It was observed that the NO₃ sensor ranges often are changed to cover a larger span of concentrations as shown in Figure S5. Similarly, the N₂O sensor ranges have been observed to be adjusted after a period. This adjustment of both N₂O and NO₃ sensors suggests that the operators are not prepared for the high concentrations of nitrogenous substances.

The drift/bias investigation targeted nitrous oxide and dissolved oxygen sensors, revealing that 15 out of the 18 assessed variables exhibited signs of drift or bias. The findings suggest a correlation between operator attentiveness and sensor calibration frequency. Table 3 provides the minimum and maximum drift values for each sensor, expressed in mg/L. The outcomes underscore the presence of drift and/or bias in WWTP data, with a notable impact on 8 out of 15 affected sensors being N₂O sensors. This drift may arise from inadequate maintenance, marked by the non-replacement of sensor heads, or significant changes in wastewater temperature exceeding 3C since the last calibration. In Skanderborg, the N₂O sensor exhibits a substantial negative drift with a magnitude of 0.33 mg/L, likely attributed to a lack of calibration or sensor head replacement. In other plants, the observed drift/bias is comparatively more modest, reaching a maximum magnitude of 0.05 mg/L. While still significant, these deviations necessitate vigilant monitoring and potential corrective action.

Table 3

Quantification of bias/drift across case plants

Plant .	Sensor .	Minimum (mg/L) .	Maximum (mg/L) .
Avedøre line 1	N2O tank 1	0.035	0.032
	N2O tank 2	0.035	0.013
	DO tank 1	0.033	0.384
	DO tank 2	0.031	0.03
Avedøre line 3	N2O tank 1	0.024	0.034
	N2O tank 2	0.024	0.054
	DO tank 1	0.038	0.304
	DO tank 2	0.039	0.319
Fredericia	N2O	0	0.013
	DO	0	0.01
Køge	N2O tank 1	0	0
	N2O tank 2	0	0.01
	DO tank 1	0	0.066
	DO tank 2	0	0.069
Skanderborg	N2O tank 1	0.333	0.004
	N2O tank 2	0.066	0.038
	DO tank 1	0	0
	DO tank 2	0	0

Plant .	Sensor .	Minimum (mg/L) .	Maximum (mg/L) .
Avedøre line 1	N2O tank 1	0.035	0.032
	N2O tank 2	0.035	0.013
	DO tank 1	0.033	0.384
	DO tank 2	0.031	0.03
Avedøre line 3	N2O tank 1	0.024	0.034
	N2O tank 2	0.024	0.054
	DO tank 1	0.038	0.304
	DO tank 2	0.039	0.319
Fredericia	N2O	0	0.013
	DO	0	0.01
Køge	N2O tank 1	0	0
	N2O tank 2	0	0.01
	DO tank 1	0	0.066
	DO tank 2	0	0.069
Skanderborg	N2O tank 1	0.333	0.004
	N2O tank 2	0.066	0.038
	DO tank 1	0	0
	DO tank 2	0	0

Notes: Minimum and maximum values are given in mg/L. A visual representation of the analysis is provided in Figure S2(b).

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All variables were investigated for missing data and incorrect negative values. For each dataset, the results in Table 2 show the number of variables affected along with the mean and min/max of percent-wise missing or negative values. Figure 3 illustrates the variation in data accuracy across plants, and the results support the finding that the general quality of data varies across plants. Note that for every case plant, all the signals/variables exhibit missing values, as the missing values (#) is the same as the total number of variables investigated.

Regarding accuracy, the mean percentage of missing data in all variables varies from 1.91 % for Køge to an alarming 15.24% for Skanderborg. In the datasets from Avedøre, Fredericia, and Skanderborg, we see high variations with differences between minimum and maximum above 20%. The missing data grouped by sensor type were likewise investigated, and the results are presented in Table S1. The highest percentage of missing values was for each of the plants – Avedøre, Fredericia, Køge, and Skanderborg – found in the variables N₂O, NH₄, and temperature.

Sensor maintenance and calibration are typical reasons for the incompleteness of data. Those two causes are often related to long-term monitoring where short monitoring campaigns of a few months do not have these issues to the same extent. Datasets based on monitoring campaigns only containing a few months of data may, hence, surpass the full-scale permanently monitored data on the dimension of completeness. Specifically for the N₂O sensor, there are several possible reasons for missing data, including (i) broken sensor membrane, (ii) water intrusion, and (iii) electrical fault (e.g., loose wiring) (Unisense Environment A/S 2022).

The four datasets include a total of 51 variables, for which 11 variables exhibited negative values, corresponding to 22%. The results presented in Table 2 show a variation across variables within the same plant, ranging from 0.01 to 32.3% for the Avedøre variables and from 33.2 to 47.2% for Skanderborg. Table S2 shows the distribution of erroneous negative values across different sensors. In the Skanderborg dataset, the percent-wise erroneous negative data are over a third of the entire dataset. This is alarming, especially because the two variables affected are N₂O measurements. Of the 11 variables experiencing incorrect negative values, the most common faulty variable was N₂O, representing 6 of those 11 affected variables.

These results shed light on an issue of high importance when data-driven modeling is applied to wastewater processes: that is, to which extend the operational data can be trusted, and thus following the accuracy of the model, when trained on similar operational data. Evidently, the findings presented here demonstrate that each case is unique, and model development must be adapted to the specific plant and appertaining dataset. Future research should consider adapting models so that more influence is linked to reliable measurements, rather than just assuming that all variables are of equal quality.

Five issues were identified with respect to data quality; however, there are more data quality issues that should be clarified to get the full extent and thorough quantification of data quality. The problem is that the datasets obtained from municipal WWTPs lack metadata. In the datasets presented in this study, none of the plants register or store metadata such as time of calibration, maintenance of sensors, and replacement of sensors. It has been noted through interviews with plant operators that some of the case plants involved in this study have had interruptions in the daily operation for various reasons. This is to be expected when operational data covering several years are collected, but the problem is the lack of metadata. To increase the accuracy and completeness of the stored data, it is thus suggested that future initiatives are taken toward the collection and storing of metadata in WWTPs.

From Figure 4, it is evident that the N₂O is a heteroscedastic variable in all the plants. For the Fredericia case presented in Figure 4(a), the process characteristics differ from year to year, and there is a pattern showing that N₂O production is highest in winter and spring around January to April. Fredericia and Skanderborg have similar plant designs with single circular tanks where nitrification and denitrification happen alternately. Nevertheless, when comparing the profiles of Skanderborg (Figure 4(b)) to Fredericia (Figure 4(a)), we see different characteristics. The N₂O production in Skanderborg WWTP peaks in November and December as opposed to the Fredericia case. Through personal communication, the authors were informed that the Skanderborg plant underwent some challenging periods with limited resources for daily operation, resulting in decreased maintenance of sensors. This may be one explanation for missing data and drift in the N₂O sensor, but it may also explain why Skanderborg measures the highest concentrations of N₂O in the winter. The N₂O measurements at Skanderborg are only monitored for a year, but the data still provide valuable information as a frame of reference.

In Figure 4(c) and 4(d), the N₂O measurements from Avedøre biological treatment line 1 and 3 are presented. Similar to the data from Fredericia, the N₂O has seasonal patterns that repeat over the years. The N₂O measurements at Avedøre are highest in late spring and summer, peaking around April to June.

The N₂O profile of Køge WWTP is presented in Figure 4(e), where we see very different profiles for the two interconnected reactors. In tank 2, the N₂O concentration rarely exceeds 0.1 mg/L, whereas tank 1 generally has higher concentrations. Køge WWTP and Avedøre WWTP both utilize the Biodenitro design. Similar to the Skanderborg–Fredericia comparison, the two Biodenitro plants do not exhibit similar N₂O profiles. The N₂O at Avedøre seems to correlate across all lines and tanks, which is not the case at Køge WWTP. Furthermore, the concentrations at Køge WWTP peak around September to October, which does not match the profile of Avedøre WWTP.

The seasonal analysis of N₂O underlines the critical need for high-quality data. In line with the combined work of others (Kosonen et al. 2016; Vasilaki et al. 2018; Chen et al. 2019), the results identify substantial variations over time and over different plants, emphasizing that inaccurate data significantly influence the interpretation of observed plants. Considering the reported 5% uncertainty in the N₂O sensor and the substantial contribution of drift and missing data to the measurement characteristics, addressing these issues is imperative. This is crucial as it can impact the relationships identified between various process measurements. These results point to the need for more data, as seasonal variations are, evidently, not represented in datasets shorter than 1 year.

Another point that can be drawn from these results is that different plants require different models. This direct comparison, of periods longer than 8 months, emphasizes the need for case-specific models, developed solely to predict and estimate the processes that are represented in the dataset the model was trained on.

Examining data from Fredericia in Figure 5 shows that the similarity between N₂O, NH₄, and DO varies throughout the dataset. The similarity between N₂O and NO₃ shows analogous behavior to that of N₂O and NH₄. Comparing Figure 5 to the seasonal variations shown in Figure 4(a), the mean and standard deviation of N₂O and correlation nitrogenous variables is simultaneously low. That is, in the periods from March to May 2020, May to November 2021, and May to September 2022, the N₂O mean and standard deviation are below 0.06 mg/L while the correlation to nitrogenous substances in the same periods is below 0.5. The correlation between N₂O and DO is, similarly, not constant over time.

In addition to the observed seasonal variations of N₂O in all the case plants, the relationship between N₂O and NH₄, NO₃ varies as well. Vasilaki et al. (2018) concluded that there was no significant correlation between N₂O and operational variables in a plug-flow carousel reactor; and Kosonen et al. (2016) also identified different relationships over two periods of monitoring N₂O. Our results are in line with those findings, as the sliding window rank correlation shows period-wise high correlation but also periods with no significant relationship between N₂O and nitrogenous variables. The results show clear variations within the case plants, where there were no recognizable patterns. A likely cause of this may be threefold. First, the plants differ in size and capacity. Second, some of the plants have different process designs and primary treatment facilities. In this study, we only address the secondary treatment, and specifically the biological nutrient removal, but future research may include analyses involving data from the primary treatment. Third, for seemingly similar process designs, the processes are monitored differently with different sensors, sensor locations, sensor ranges, etc. This fact alone highly supports and suggests that mechanistic modeling/first principal modeling will be difficult to implement, and also a challenge to achieve great results due to the inherent differences between all plants and the characteristics of the influent wastewater.

Taken together, these findings provide support for the belief that, to model N₂O dynamics across different WWTPs, there is a need for several years of high-quality operational data and an application of data-driven modeling.

The quality of WWTP operational data varies across plants. Within the plants, the quality also varies across sensor types. The findings demonstrate that each case is unique, and model development must be adapted to the specific plant and appertaining dataset. It is, furthermore, suggested that future research should consider adapting models so that more influence is linked to reliable measurements identified by evaluation of data quality. This discovery underscores the complexity of legislating and regulating N₂O emissions. Crafting effective legislation on the subject extends beyond merely setting limits; it necessitates inclusion of requirements for data quality and measurement frequency. Regarding N₂O modeling, these findings emphasize the importance of metadata. Ensuring accurate models requires meticulous attention to metadata to prevent development and fitting to incorrect data. This study suggests that taking tangible action to curb GHG emissions demands substantial resource investment (time, sensors, maintenance) and commitment from plants and operators. Analyzing, quantifying, and acting upon actual GHG emissions require significant effort.

A recurrent seasonal N₂O concentration pattern was found for Avedøre and Fredericia WWTPs. For the remaining plants, the datasets were not long enough to confirm a recurrent pattern. The N₂O concentration is a heteroscedastic variable across all four case plants, hence confirming that the full N₂O dynamics are not represented in datasets shorter than 1 year.

The investigation of time-varying interrelation between N₂O and nitrogenous variables showed no clear pattern within or across different case plants. The findings establish that there is a need for several years of high-quality operational data and an application of data-driven modeling. To increase the accuracy and completeness of the stored data, it is also suggested that future initiatives are taken toward the collection and storing of metadata in WWTPs.

The authors thank Krüger-Veolia Colleagues for their technical and supervisory support. This project was supported by the Danish Innovation Foundation (grant number: 1044-00031B).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.