Estimating air emissions from animal production in the United States using statistical models: Ammonia emissions from swine grow-finish barns

Abstract

Animal production has the potential to emit various atmospheric pollutants including ammonia (NH₃), which can impact human health, atmospheric visibility and ecosystem health through gaseous NH₃ and associated ${\text{NH}}_4^{+}$ particulate matter deposition. Emission estimating methodologies were developed using statistical models to estimate daily NH₃ emissions from swine grow-finish barns based on National Air Emissions Monitoring Study (NAEMS) data. Models were developed with variables that represented production, manure management and environmental conditions. Model performance was evaluated for predicting NAEMS and non-NAEMS emissions, consistency of model coefficients and sensitivity to different model input values. Accounting for ease of variable measurement, the best performing models for predicting NAEMS emissions were models 1b and 16a, both of which accounted for the influence of temperature, swine inventory and weight, but used different predictor and response variables. In predicting NAEMS emissions, model 1b had mean error (ME) and mean bias (MB) values of 1.6 kg day⁻¹ (normalized mean error (NME) = 25.9 %) and 0.1 kg day⁻¹ (normalized mean bias (NMB) = 1.2 %), respectively, which were slightly lower than the corresponding values for model 16a (ME/NME = 1.8 kg day⁻¹/25.9 % and MB/NMB = 0.4 kg day⁻¹/5.8 %). Model 1b performed better in predicting non-NAEMS emissions, but model 16a had more reasonable sensitivity when barn live animal weight was >215,000 kg. Models using nitrogen feed intake as a predictor variable also performed well in predicting emissions and although these models have greater uncertainty due to limited NAEMS measurements, they could potentially account for changes in feed practices.

1. Introduction

Animal production emits various pollutants into the atmosphere including ammonia (NH₃). Emissions of NH₃ from animal production are estimated to be responsible for 49 % of anthropogenic NH₃ emissions in the United States (U.S. Environmental Protection Agency (EPA), 2023). Atmospheric NH₃ is the dominant base gas in the atmosphere and reacts with a variety of acidic species (i.e., nitric, sulfuric and hydrochloric acid) to form ammonium $\left({\text{NH}}_4^{+}\right)$ particulate matter (PM) (Seinfeld and Pandis, 2006). As PM, ${\text{NH}}_4^{+}$ impacts atmospheric visibility (Seinfeld and Pandis, 2006) and contributes a significant amount to total PM_2.5 mass (Adams et al., 1999). Human inhalation of PM_2.5 has several adverse health effects including premature mortality (Pope et al., 2002). Gaseous NH₃ and ${\text{NH}}_4^{+}$ PM are removed from the atmosphere through dry and wet deposition to the surface, which can result in the eutrophication of terrestrial and aquatic ecosystems (Galloway et al., 2003).

Estimating NH₃ emissions from animal production accurately is important for assessing potential impacts. Emission factors cannot easily account for the influence of environmental conditions, which have a large impact on emissions, therefore there is a need to develop more sophisticated emission estimating methodologies (EEMs) such as statistical models. Statistical models based on observational data can be developed to determine the influence of environmental conditions, and also production and management conditions on emissions. Thus, statistical models can estimate emissions over a wide range of conditions with reduced uncertainty in comparison to the use of emission factors.

In 2005, the voluntary Air Compliance Agreement (ACA) between the EPA and the animal industries was published. In this agreement, the industry agreed to fund a large-scale emissions monitoring study known as the National Air Emissions Monitoring Study (NAEMS). As part of the ACA, the EPA was to use the NAEMS emissions data and other relevant data sources to develop EEMs, while the animal feeding operation (AFO) industry participants agreed to use these EEMs to estimate their emissions for purposes of complying with applicable EPCRA (Emergency Planning and Community Right-to-Know Act) Clean Air Act (CAA) requirements.

The NAEMS, which can be considered one of the most comprehensive animal production monitoring studies to date, measured emissions of NH₃ and other pollutants (hydrogen sulfide, volatile organic compounds, and PM) from representative swine, dairy, broiler, and layer AFOs in the U.S. over a monitoring period of two years from 2007 to early 2010. While making emission measurements, production, management and environment conditions were also monitored and/or documented. Recently, the U.S. EPA released draft statistical model EEMs for air emissions from AFOs (U.S. EPA, 2024a) based on NAEMS data including for NH₃ emissions from swine grow-finish barns. This manuscript describes in-depth the methodology for the development and evaluation of the aforementioned draft statistical model EEMs using NH₃ emissions from swine grow-finish barns as an example. Furthermore, this manuscript builds upon the draft EEM report for NH₃ emissions from swine grow-finish barns by exploring a greater range of potential statistical models in terms of approach and by also considering additional model variables.

In addition to being used by participants in the ACA to determine whether they meet CAA thresholds, the EEMs may also be useful for other producers that wish to estimate AFO emissions. Furthermore, the emission models developed in this study are useful for improving the estimation of NH₃ emissions for EPA’s National Emission Inventory (NEI) (U.S. EPA, 2023). The NEI is a foundational dataset for many air-quality datasets including EPA’s Community Multiscale Air Quality (CMAQ) modeling system (U.S. EPA, 2024b).

2. Methodology

2.1. Monitoring sites and measurements

In the NAEMS, swine grow-finish (S-GF) operations were monitored at two U.S. sites in the states of Indiana (IN) and North Carolina (NC). For consistency with NAEMS nomenclature, these sites are hereafter referred to as IN3B and NC3B. The monitoring period was an approximate 2-year period at each site with monitoring from 7/14/07 to 7/24/09 at IN3B and 12/4/07 to 1/13/10 at NC3B. The IN3B site had deep-pit barns that stored its manure in pits below the barn for approximately 3–7 months and was considered to be representative of grow-finish operations in Midwestern U.S. The NC3B site has shallow pit barns that were emptied on a weekly basis to an anaerobic lagoon and was considered to be representative of grow-finish operations in Southeastern U.S. Deep pit and shallow pit barns are the main two types of housing in U.S. swine grow-finish operations. Brief descriptions of the S-GF sites are provided in the supplemental, however, for more information the reader is referred to the NAEMS final site reports for IN3B and NC3B (Lim et al., 2010; Bogan et al., 2010).

A brief description of the NH₃ emission measurements and the measurement/monitoring of corresponding production, management and environmental conditions is provided in the supplemental material, however, more information can be found in the final site reports for IN3B and NC3B (Lim et al., 2010; Bogan et al., 2010) and in the QA document associated with the collection of this dataset (Heber et al., 2008).

2.2. NH₃ emissions

As mentioned, monitoring at the IN3B and NC3B sites was conducted over a period of approximately two years, however, the total number of days with valid emission measurements at each barn ranged from 307 to 373 at IN3B (Table 1), which represented 41–50 % of the monitoring time at each barn. On average, these valid daily emission measurements included 50 % of the days when the barn was occupied by swine and 14 % of the days when the barn was unoccupied. Generally, there were more valid daily emission measurements in summer (June–August; 110 days) and spring (March–May; 95 days) than fall (September–November; 71 days) and winter (December–February; 61 days) at IN3B. There were three extended gaps in valid daily NH₃ emissions from January–February 2008, October 2008–January 2009, and March–April 2009 which impacted three of the five monitored rotations. At NC3B, the total number of days with valid daily emissions across the 3 b ranged from 556 to 571 (Table 1), representing 72–74 % of the monitoring time at each barn. On average, these emission measurements included 80 % of the days when the barn was occupied by swine and 13 % of the days when the barn was unoccupied. Similarly to IN3B, there were more valid emission days in summer and spring than fall and winter, but the seasonal differences in number of days were smaller, with the average seasonal number of valid daily emissions across the 4 b of 150 days, 160 days, 142 days and 118 days for summer, spring, fall and winter respectively. There were two extended gaps in valid NH₃ emissions data at NC3B, one associated with the dysentery outbreak from January–March 2008 and the other in December 2008, which impacted two of the six monitored rotations. A description of the observed NH₃ emission trends and corresponding figures are provided in the supplemental material.

Table 1.

Average daily mean (ADM) NH₃ emissions from the IN3B and NC3B sites and barns for the overall monitoring period and also during times when the barn where occupied (O) and unoccupied (U) using different normalizing units.

NH3 Emissions	IN3B-R5	IN3B-R6	IN3B-R7	IN3B-R8	IN3B (All)	NC3B-B1	NC3B-B2	NC3B-B3	NC3B (All)
Overall (kg day−1)	7.50a (2.68)b N = 373c	7.87 (2.78) N = 336	6.74 (3.31) N = 331	6.93 (3.16) N = 307	7.28 (3.01) N = 1347	5.20 (2.53) N = 571	4.97 (1.94) N = 561	5.00 (2.16) N = 556	5.05 (2.23) N = 1688
Overall (g m−2 day−1)	10.25 (3.66) N = 373	10.76 (3.79) N = 336	9.21 (4.53) N = 331	9.47 (4.31) N = 307	9.94 (4.11) N = 1347	8.66 (4.22) N = 571	8.28 (3.23) N = 561	8.33 (3.60) N = 556	8.42 (3.71) N = 1688
Overall (kg-N yr−1)	2738	2874	2461	2530	2657	1897	1813	1824	1845
Occupied (kg day−1)	7.53 (2.66) N = 371	7.90 (2.75) N = 335	7.27 (3.03) N = 299	7.18 (3.05) N = 290	7.49 (2.87) N = 1295	5.27 (2.51) N = 557	4.98 (1.93) N = 557	5.08 (2.11) N = 544	5.11 (2.20) N = 1658
Occupied (g hd−1 day−1)	8.77 (7.65) N = 371	8.37 (4.76) N = 335	7.75 (5.79) N = 299	8.73 (6.37) N = 290	8.42 (6.29) N = 1295	7.59 (5.76) N = 557	7.51 (3.70) N = 557	7.31 (3.52) N = 544	7.47 (4.45) N = 1658
Occupied (g AU−1 day−1)	78.09 (42.04) N = 371	75.51 (37.54) N = 335	59.04 (30.75) N = 299	61.15 (31.71) N = 290	69.23 (37.19) N = 1295	54.95 (24.60) N = 554	55.62 (24.95) N = 556	57.59 (25.32) N = 544	56.04 (24.96) N = 1654
Unoccupied kg day−1	2.69 (1.02) N = 2	0.01 (N/A) N = 1	1.82 (1.03) N = 32	2.63 (1.34) N = 17	2.08 (1.21) N = 52	2.20 (1.52) N = 14	2.66 (1.23) N = 4	1.34 (0.40) N = 12	1.92 (1.23) N = 30

^aMean average daily mean (ADM).

^b±1 Standard Deviation of ADMs.

^cN represents the number ADMs. AU = animal unit, which is 500 kg of live animal weight.

Average daily mean (ADM) emissions (Table 1) across all rooms at IN3B was 7.28 kg day⁻¹ with room specific emissions for R5 (7.50 kg day⁻¹) and R6 (7.87 kg day⁻¹) slightly higher than R7 (6.74 kg day⁻¹) and R8 (6.93 kg day⁻¹), which is likely related to those rooms being occupied for longer periods. At NC3B, emissions were less variable across different units than IN3B and ranged from 4.97 to 5.20 kg day⁻¹ with an ADM emission across all barns of 5.05 kg day⁻¹, which is approximately 30 % less than the corresponding value for IN3B (7.28 kg day⁻¹). If emissions are normalized for barn surface area (732 m² for IN3B barns and 600 m² for NC3B barns), NC3B emissions are only 15 % less than IN3B emissions. As expected, days when the barns were occupied had slightly higher emissions (7.49 kg day⁻¹ for IN3B and 5.11 kg day⁻¹ for NC3B) than overall emissions (7.28 kg day⁻¹ for IN3B and 5.05 kg day⁻¹ for NC3B). Unoccupied ADM emissions, which are generated by the manure that is stored in the pit of the barn, were similar between IN3B and NC3B, with average overall site values of 2.08 kg day⁻¹ and 1.92 kg day⁻¹, respectively. As expected, unoccupied emissions are less than when the barns are occupied by swine. Individual barn unoccupied emissions were highly variable, which is partly related to the limited valid emission measurements during unoccupied periods, with three of the seven monitored barns unoccupied emission values (IN3B-R5, IN3B-R6 and NC3B-B2) being based on less than five days of valid measurements. Occupied emissions were normalized per head (g hd⁻¹ day⁻¹) and per 500 kg of live animal weight (LAW) (equals 1 animal unit (AU); g AU⁻¹ day⁻¹) and are presented in Table 1. The difference in emissions between sites was less when emissions were normalized by head or LAW in comparison to when units of kg day⁻¹ are used, with the overall average barn emission at IN3B, 13 % (8.42 g hd⁻¹ day⁻¹) and 24 % (69.23 g AU⁻¹ day⁻¹) higher than the corresponding emissions at NC3B (7.47 g hd⁻¹ day⁻¹ and 56.04 g AU⁻¹ day⁻¹). Further discussion of production (i.e., inventory and LAW) trends are included in the supplemental material. The occupied emissions are also expressed in units of kg-N yr⁻¹ which involves a 14/17 NH₃ to nitrogen (N) conversion and the sum of the measured emissions expressed on an annual scale.

Emissions of NH₃-N were compared to estimates of NH₃-N excretion, which was determined by applying a N mass-balance approach (see supplemental material for N mass-balance methodology and calculations). The percentage loss of NH₃-N from N-excreted ranged from 34 to 37 % for IN3B and 29–30 % for NC3B, which is within the range of 5–40 % reported by Koelsch and Stowell (2009) for typical losses from swine barns.

2.3. Development of statistical models

2.3.1. Statistical modeling approach

To estimate daily NH₃ emissions, linear mixed models (SAS version 9.4, Proc Mixed, SAS^®) were developed to account for correlation errors among successive measurements. This type of general linear model characteristic is needed as the dataset consists of successive daily averaged measurements that are not necessarily independent of each other. For the linear mixed effects model, NH₃ emission is the dependent variable and the variables or parameters that influence emissions are the independent variables. To help produce a normal distribution for the dependent variable, NH₃ emission values were natural log-transformed. Accordingly, the format of the linear mixed models was the following:

$$\text{ln}\left(Y\right)={\beta }_0+{\beta }_1{X}_1+\dots +{\beta }_k{X}_k$$ (1)

where Y is the dependent variable (NH₃ emissions), ${\beta }_0$ is a constant and ${\beta }_1$ and ${\beta }_k$ are the coefficients for parameters (variables) $X_1$ and $X_k$, respectively. The linear mixed effects model determined the effects of predictor variables on emissions by accounting for correlation among successive measurements using a repeated statement with spatial power covariance structure, which was selected as it can account for uneven temporal gaps in the data set (i.e., missing data). Back-transforming eq. (1) and applying logarithmic rules yields the following equation for back transformed predicted emissions (Y_bp):

$$Y_{\mathit{\text{bp}}}=A{e}^{\left({\beta }_1{X}_1+\dots +{\beta }_k{X}_k\right)}\text{where}\text{A}=e^{\left({\beta }_0\right)*}{E}_i$$ (2)

where A is a constant and is the product of back-transformed ${\beta }_0$ (y-intercept) and E_i, which is the adjustment for bias associated with log back-transformation and is determined by calculating the average residual between model predicted and observed emissions on the natural log scale (Newman, 1993). As can be observed in eq. (2), the log-transformation and subsequent back-transformation results in the independent variables having a non-linear influence on emissions, which is desirable as many factors (e.g., temperature) have been found to have a non-linear influence on emissions. Accordingly, the effect of parameters on NH₃ emissions in eq. (2) can be considered multiplicative, for example a one unit increase in X₁ results in Y_bp increasing by a factor of $e^{\left({\beta }_1\right)}$.

As previously mentioned, NH₃ emissions were log-transformed. The dataset contained some small negative NH₃ emissions that could not be log-transformed. Accordingly, a constant C had to added to all emissions, so that all emissions could be log-transformed. Thus, this constant had to subtracted from the Y_bp, as follows to yield the predicted emissions (Y_p):

$$Y_p=Y_{\mathit{\text{bp}}}-C$$ (3)

2.3.2. Candidate parameters for model development

Parameters were considered candidate parameters for model development based on whether theoretical considerations or literature identified an established influence on NH₃ emissions and the amount of NAEMS data available for the parameters. Based on theoretical considerations, one of the main fundamental factors that influences the magnitude of NH₃ emissions from manure in barns is the amount of nitrogen in the barn manure, which is influenced by production and management conditions. Additional fundamental factors include the manure characteristics and the surrounding environmental conditions (e.g., temperature, air flow) that influence the biological, physical and chemical processes that result in the generation and release of pollutants. Candidate parameters for model development are described in the following sub-sections and can be categorized into three groups, production parameters (sub-section 2.3.2.1), manure characteristic parameters (sub-section 2.3.2.2) and environmental parameters (su-bsection 2.3.2.3). Exploratory data analysis (i.e., summary statistics, time series trend and simple linear regression) of the candidate parameters that examines their potential influence on emissions is provided in the supplemental material.

2.3.2.1. Production parameters.

Since, the amount of nitrogen in the barn manure cannot be directly measured, surrogate production parameters can be measured or recorded that either estimate the amount of manure or the nitrogen content of manure, which can be used in combination to estimate the amount of nitrogen content in the barn manure. Surrogate potential parameters that estimate the amount of manure include inventory, LAW, average pig weight, and number of days of manure storage accumulation. In this study, all these parameters are potential candidates for model development except for the number of days of manure storage accumulation, which was not recorded in NAEMS and therefore could not be directly investigated. However, general information for manure removal frequency was known, with NC3B shallow pit site removing manure typically on a weekly basis and the IN3B shallow pit site removing manure approximately every 3–7 months (exact dates not recorded during NAEMS).

2.3.2.2. Manure characteristic parameters.

The nitrogen content of the manure is important as it controls the amount of nitrogen available for emissions. The nitrogen concentration in relation to NH₃ emissions is commonly measured as total kjeldahl nitrogen (TKN) or total ammoniacal nitrogen (TAN). An additional manure characteristic that influences NH₃ emissions is the manure pH, which determines the chemical equilibrium between NH₃ and ${\text{NH}}_4^{+}$ (Ni et al., 2009; Aneja et al., 2001; Montes et al., 2009). Manure TKN, manure TAN and manure pH are considered candidates for model development, however there were limited measurements of manure characteristics at the sites.

2.3.2.3. Environmental parameters.

Temperature plays an important role in the physical, chemical and biological processes involved in the generation and release of NH₃ from manure. These processes include microbial degradation (Zhang and Day, 1996), equilibrium between the manure and air surface (Montes et al., 2009), chemical equilibrium (Montes et al., 2009) and mass transfer (Ni et al., 2009). Air flow rate is an additional environmental variable that influences emissions as it impacts the transfer of NH₃ across the manure surface (Arogo et al., 1999). Accordingly, ambient temperature, barn exhaust temperature and ventilation rate, which were continuously measured during the NAEMS, are candidate parameters for model development.

2.3.3. Developing candidate models

To represent the fundamental factors that influence NH₃ emissions, it is preferable to have a model that contains variables that represent the production, manure and environmental conditions. While there are multiple potential options for variables that represent the production and environmental conditions, the limited manure characteristic data means that these parameters are not good candidates for inclusion as variables representing manure conditions. However, as discussed in the exploratory data analysis summary (see supplemental material), the different manure management systems may influence TAN/TKN concentrations and potentially other manure characteristics. Accordingly, the effects of the different manure management systems on manure conditions were investigated by determining combined (Combined Pit (CP)) and individual y-intercepts for the shallow pit (SP) and deep pit (DP) manure management systems. Table 2 shows the candidate models with these different y-intercepts used in combination with different production variables, environmental variables and emission response variables. For each different model, the type of y-intercept used is denoted by ‘a’ or ‘b’ after the model number, with ‘a’ representing a CP y-intercept and ‘b’ representing individual DP and SP y-intercepts. The candidate models account for the influence of production variables using different approaches. In one approach, the production variables (i. e., LAW (models 1–3), inventory (models 4–6), and inventory and average weight (models 7–9)) are used as predictor variables with the emission response variable in units of kg day⁻¹. Collectively, these models (1–9) are hereafter referred to as ‘non-normalization models’, indicating that the emission response variable has not been normalized for production units before developing the model. The other approach involves normalizing emissions by a production unit to serve as the response variable. Collectively, these models (10–18) are hereafter referred to as “normalization models” with emissions normalized by LAW and inventory for models 10–12 and 13–18, respectively. Both non-normalization and normalization models account for the barn inventory and/or the pig growth cycle by using six different combinations of production variables and/or emission normalization (i.e., models 1–3, 4–6,7–9, 10–12, 13–15, 16–18). Each of the six different combinations of production variables is combined with the three different variables representing environmental conditions (i.e., ambient temperature, barn exhaust temperature and airflow), resulting in 18 different models. Combining these 18 models with the two different intercept approaches yields 36 candidate models in total.

Table 2.

Response and predictor variables for candidate models to predict NH₃ emissions.

	Response Variable	Constant	Predictor Variables
Model #	Units of NH3 Emission	Y-intercept (s)	Production Var.1 (input unit)a	Production Var.2 (input unit)	Environmental Var.1 (input unit)
1a	kg day−1	CP	LAW/Mg	–	Amb Temp (°C)
1b	kg day−1	DP, SP	LAW/Mg	–	Amb Temp (°C)
2a	kg day−1	CP	LAW/Mg	–	Exh Temp (°C)
2b	kg day−1	DP, SP	LAW/Mg	–	Exh Temp (°C)
3a	kg day−1	CP	LAW/Mg	–	Airflow (dsm3 s−1)
3b	kg day−1	DP, SP	LAW/Mg	–	Airflow (dsm3 s−1)
4a	kg day−1	CP	Inventory/k	–	Amb Temp (°C)
4b	kg day−1	DP, SP	Inventory/k	–	Amb Temp (°C)
5a	kg day−1	CP	Inventory/k	–	Exh Temp (°C)
5b	kg day−1	DP, SP	Inventory/k	–	Exh Temp (°C)
6a	kg day−1	CP	Inventory/k	–	Airflow (dsm3 s−1)
6b	kg day−1	DP, SP	Inventory/k	–	Airflow (dsm3 s−1)
7a	kg day−1	CP	Inventory/k	Ave. Weight (kg)	Amb Temp (°C)
7b	kg day−1	DP, SP	Inventory/k	Ave. Weight (kg)	Amb Temp (°C)
8a	kg day−1	CP	Inventory/k	Ave. Weight (kg)	Exh Temp (°C)
8b	kg day−1	DP, SP	Inventory/k	Ave. Weight (kg)	Exh Temp (°C)
9a	kg day−1	CP	Inventory/k	Ave. Weight (kg)	Airflow (dsm3 s−1)
9b	kg day−1	DP, SP	Inventory/k	Ave. Weight (kg)	Airflow (dsm3 s−1)
10a	g day−1 AU−1	CP	–	–	Amb Temp (°C)
10b	g day−1 AU−1	DP, SP	–	–	Amb Temp (°C)
11a	g day−1 AU−1	CP	–	–	Exh Temp (°C)
11b	g day−1 AU−1	DP, SP	–	–	Exh Temp (°C)
12a	g day−1 AU−1	CP	–	–	Airflow (dsm3 s−1)
12b	g day−1 AU−1	DP, SP	–	–	Airflow (dsm3 s−1)
13a	g day−1 hd−1	CP	–	–	Amb Temp (°C)
13b	g day−1 hd−1	DP, SP	–	–	Amb Temp (°C)
14a	g day−1 hd−1	CP	–	–	Exh Temp (°C)
14b	g day−1 hd−1	DP, SP	–	–	Exh Temp (°C)
15a	g day−1 hd−1	CP	–	–	Airflow (dsm3 s−1)
15b	g day−1 hd−1	DP, SP	–	–	Airflow (dsm3 s−1)
16a	g day−1 hd−1	CP	Ave. Weight (kg)	–	Amb Temp (°C)
16b	g day−1 hd−1	DP, SP	Ave. Weight (kg)	–	Amb Temp (°C)
17a	g day−1 hd−1	CP	Ave. Weight (kg)	–	Exh Temp (°C)
17b	g day−1 hd−1	DP, SP	Ave. Weight (kg)	–	Exh Temp (°C)
18a	g day−1 hd−1	CP	Ave. Weight (kg)	–	Airflow (dsm3 s−1)
18b	g day−1 hd−1	DP, SP	Ave. Weight (kg)	–	Airflow (dsm3 s−1)

^aFor the LAW and inventory variables in models 1–6, the input units were changes to Mg and thousands (k), respectively. This was done to avoid model non-convergence, which can occur when there are several orders of magnitude difference between predictor variable values.

It should be noted that the emissions normalization approach (models 10–18) has a limitation in that you cannot normalize emissions when the barn is unoccupied (i.e., LAW or inventory = 0) and thus the developed model will not be able to predict emissions when the barn is unoccupied. As previously mentioned, barns are a source of NH₃ when the barn is unoccupied due to the manure storage in the barn pit, which represents 11 % and 12 % of monitored days and 3 % and 5 % of total emissions at IN3B and NC3B, respectively. However, the non-normalization approach, which uses LAW and inventory as predictor variables in candidate models, allows the model to predict when the barn is unoccupied. In addition, using inventory and LAW as predictor variables potentially allows factors that correlate with the predictor variables to influence the predictor variable coefficients. This could be potentially advantageous in circumstances where there are no direct measurements of a particular variable. For example, in NAEMS, nitrogen feed consumption is not directly measured, however, it can be assumed that nitrogen feed consumption trend will correlate to some degree with LAW as pigs will generally consume greater quantities of feed as their LAW increases, therefore the influence of nitrogen feed consumption trends on emissions could be partially reflected in the production predictor variable coefficient.

2.4. Model evaluation

2.4.1. Candidate models

As outlined in Table 2, different combinations of predictor variables are being used to develop models. The significance of an individual predictor parameter within the model in influencing emissions will be determined by the probability (p) of t-statistics of the data to be more or less than that of the threshold of 0.05 with a parameters p-value ≤0.05 indicting significant influence on emissions and a p-value ≥0.05 indicating that the parameter does not have a significant influence on emissions.

Agreement between observed (Y_o) and model predicted (Y_p) emissions was assessed using a variety of different methodologies that have been used in the evaluation of atmospheric models (Huang et al., 2021; Simon et al., 2012), including mean error (ME), normalized mean error (NME), mean bias (MB), normalized mean bias (NMB) and correlation coefficient (r).

$$\mathit{\text{ME}}=\frac{\sum \left|Y_p-Y_o\right|}{n}$$ (4)

$$\mathit{\text{NME}}=\frac{\sum \left|Y_p-Y_o\right|}{\sum Y_o}\times 100\%$$ (5)

$$\mathit{\text{MB}}=\frac{\sum \left(Y_p-Y_o\right)}{n}$$ (6)

$$\mathit{\text{NMB}}=\frac{\sum \left(Y_p-Y_o\right)}{\sum Y_o}\times 100\%$$ (7)

$$r=\left(\frac{\sum \left(\left(Y_p-\overline{Y_p}\right)\times \left(Y_o-\overline{Y_o}\right)\right)}{\sqrt{\sum {\left(Y_p-\overline{Y_p}\right)}^2\times \sum {\left(Y_o-\overline{Y_o}\right)}^2}}\right)$$ (8)

For the evaluation methods, Y_p was converted, if needed, into units of kg day⁻¹. The closer the values of ME, NME, MB, and NMB are to zero the better the performance of the model, while for the r value, the closer that value is to 1 the better the performance of the model. The performance of the models was also evaluated by examining the relationship between observed and predicted emissions using scatterplots with a 1:1 reference line.

2.4.2. Selected models

Additional model evaluation techniques were performed for selected models of interest. These include determining confidence limits, evaluating the model coefficient consistency, performing a sensitivity analysis on predicted emissions, and evaluating the performance of models in predicting emissions for barns from different studies (hereafter referred to as secondary barn data sets).

The 95 % upper and lower confidence limits were reported for daily model predicted emissions via the SAS PROC Mixed function and were transformed using the same methodology that was used for model predicted emissions (i.e., eq. (2) and eq. (3)).

The model coefficient consistency was evaluated using the jackknife cross validation method (Christensen et al., 2013; Van Der Leeden et al., 2007). The jackknife method used only the sample data and examines the effect of removing independent sample units from the data set on model coefficient values. The independent sample units for this study are the individual barns and thus models were developed with different sample units removed each time. The model coefficients and model evaluation metrics (i.e., ME, NME, MB, NMB) for each jackknife model were then compared to the model developed on the full data set.

To provide a guide to the generalizability of the model parameters and to evaluate the influence of parameters on predicted emissions, a sensitivity analysis for individual models was performed by holding all but one of the model variables constant. The parameter of interest was then varied across the range of data that the model could reasonably expect to be used in different regions and for different AFO inventories, which was beyond the range of the NAEMS data.

The representativeness and applicability of the models to other regions and different management practices was explored by evaluating the performance of the models in predicting emissions for secondary datasets. Data sets selected for secondary data analysis were those obtained through the 2011 EPA Call for information. Subsequently, the data sets were evaluated based on compatibility with the NAEMS data and whether they contained appropriate information to assess model performance. Compatibility requirements included that the monitoring data be conducted at animal confinement structures at commercial sites and that the methods used to determine emissions were consistent with NAEMS procedures. For the data set to be appropriate to assess model performance, the requirements were for the data set to contain daily emissions and the necessary corresponding production and environmental parameters to be input into the models to predict emissions. For swine grow-finish barns, appropriate data sets were obtained for 4 b from two AFOs in different states (Iowa, (IA) and Texas (TX)) that were part of the Heber et al. (2006) study. The TX barns stored their manure in shallow pits with the barns emptying and recharging approximately every 7 days. The IA barn used a deep pit for manure storage with manure being removed once a year. More information about the study and the characteristics of the AFO sites and barns can be found in Heber et al. (2006). Parameter values from the data associated with Heber et al. (2006) study were input into the selected models to predict emissions and then compared to the observed emissions from the data associated with the Heber et al. (2006) study using the model evaluation methodologies outlined in section 2.4.1.

3. Results and discussion

3.1. Performance of models in predicting NAEMS emissions

The y-intercept constants and model coefficients for the candidate models are presented in Table 3. In all models, the y-intercept values for deep pit were higher than the shallow pit values with the combined pit y-intercept values between the model corresponding deep pit and the shallow pit values. As expected, all production variable coefficients were positive and have a significant influence on emissions (p < 0.01). In addition, all environmental variables (ambient temperature, exhaust temperature and airflow) were positive and significant. The positive influence of these environmental variables on emissions is supported by theoretical considerations and literature (e.g., Montes et al., 2009; Ni et al., 2009; Arogo et al., 1999; Zhang and Day, 1996). The E_i and C values associated with the model predicted emissions (see eq. (2) and eq. (3) in section 2.3.1) are provided in the supplemental material (Table S6).

Table 3.

Constant and predictor variable coefficient values for candidate models to predict NH₃emissions.

	Response Variable	Constant	Predictor Variables
Model #	Units of NH3 Emission	Y-intercept(s)	Production Variable (s)	Environmental Variable
1a	kg day−1	CP: 1.2014	LAW: 0.0095	Amb T: 0.0090
1b	kg day−1	DP: 1.3086, SP: 1.1174	LAW: 0.0090	Amb T: 0.0091
2a	kg day−1	CP: 0.8887	LAW: 0.0088	Exh T: 0.0212
2b	kg day−1	DP:0.9849, SP: 0.7928	LAW: 0.0084	Exh T: 0.0218
3a	kg day−1	CP: 1.3752	LAW: 0.0079	AF: 0.0069
3b	kg day−1	DP:1.4945 SP: 1.2876	LAW: 0.0073	AF: 0.0065
4a	kg day−1	CP: 1.4924	Inv: 0.2358	Amb T: 0.0096
4b	kg day−1	DP: 1.6444, SP: 1.3989	Inv: 0.208959	Amb T: 0.0097
5a	kg day−1	CP: 1.1712	Inv: 0.1542	Exh T: 0.0235
5b	kg day−1	DP: 1.3278, SP: 1.0620	Inv: 0.122264	Exh T: 0.0239
6a	kg day−1	CP: 1.6103	Inv: 0.1956	AF: 0.0083
6b	kg day−1	DP: 1.7546, SP: 1.5177	Inv: 0.149503	AF: 0.008161
7a	kg day−1	CP:1.0945	Inv: 0.2296, AW: 0.0065	Amb T:0.0090
7b	kg day−1	DP: 1.2105, SP:0.9435	Inv: 0.1971, AW: 0.0067	AmbT: 0.0091
8a	kg day−1	CP:0.8643	Inv: 0.1661, AW: 0.0060	ExhT: 0.0201
8b	kg day−1	DP:0.9678, SP: 0.6891	Inv: 0.1300, AW: 0.0062	Exh T: 0.0208
9a	kg day−1	CP: 1.2144	Inv: 0.2366, AW: 0.0057	AF: 0.0074
9b	kg day−1	DP: 1.3208, SP: 1.0867	Inv: 0.2017, AW: 0.0058	AF: 0.0069
10a	g day−1 AU−1	CP: 3.8341	–	Amb T: 0.0119
10b	g day−1 AU−1	DP:3.9182, SP: 3.7568	–	Amb T: 0.0120
11a	g day−1 AU−1	CP: 3.4914	–	Exh T: 0.0227
11b	g day−1 AU−1	DP:3.5667, SP: 3.4248	–	Exh T: 0.0228
12a	g day−1 AU−1	CP: 3.9249	–	AF: 0.0071
12b	g day−1 AU−1	DP:3.9777, SP: 3.8858	–	AF: 0.0069
13a	g day−1 hd−1	CP: 1.9158	–	Amb T: 0.0105
13b	g day−1 hd−1	DP: 1.9905, SP: 1.9006	–	Amb T: 0.0095
14a	g day−1 hd−1	CP: 1.6126	–	Exh T: 0.0201
14b	g day−1 hd−1	DP: 1.6682, SP: 1.5954	–	Exh T: 0.0198
15a	g day−1 hd−1	CP: 1.9798	–	AF: 0.0083
15b	g day−1 hd−1	DP: 1.9812, SP: 1.9659	–	AF: 0.0082
16a	g day−1 hd−1	CP: 1.0790	AW: 0.0119	Amb T: 0.0097
16b	g day−1 hd−1	DP: 1.1350, SP: 1.0232	AW: 0.0118	Amb T: 0.0099
17a	g day−1 hd−1	CP: 0.7964	AW: 0.0118	Exh T: 0.0185
17b	g day−1 hd−1	DP: 0.8420, SP: 0.7535	AW: 0.0118	Exh T: 0.0186
18a	g day−1 hd−1	CP: 1.2117	AW: 0.0110	AF: 0.0061
18b	g day−1 hd−1	DP: 1.2393, SP: 1.1833	AW: 0.0110	AF: 0.0060

Table 4 shows the performance evaluation metrics for the different models. Scatterplots of predicted and observed emissions (Figs. S24–S41) show the performance of the models in predicting observed emissions, which is largely driven by the different approaches used to account for production conditions. Non-normalized emission models with LAW as a predictor variable (models 1–3) have the lowest NME (25–27 %) in comparison to the other models. Models 1–3 also have near zero (<±1 %) NMB and high r values (0.66–0.72). Non-normalized emission models with inventory as a predictor variable (models 4–6) have higher NME (31–36 %) and similar NMB (<±1 %) compared to the non-normalized emission models that have LAW as a predictor variable (models 1–3). The higher NME is partly due to the pig growth cycle not being accounted for in models 4–6, which is visually highlighted by the predicted emission versus observed emission scatterplots (Figs. S27–S29), where predicted emissions remain relatively constant while the observed emissions increase, resulting in low r values (0.14–0.50). Non-normalized emission models with inventory and average weight as predictor variables (models 7–9) also have low NME (26–30 %), low NMB (<±1 %) and high r values (0.57–0.70), reflecting the model’s ability to account for the growth cycle. Models 10–12, which are normalized by LAW emission models and do not include another production variable, have high NME (37–39 %) and r values (0.66–0.7) in addition to high positive NMB values (16–18 %), which is also apparent in the scatterplots (Figs. S33–S35). Models 13–15, for which emissions are normalized by inventory and contain no other production variable, have both the highest NME (40–43 %) of the candidate models and the lowest r values (0.14–0.29), as these models do not account for swine weight during the growth cycle. Models with emissions normalized by inventory with average weight as a predictor variable (models 16–18) have low NME values (28–29 %) and high r values (0.66–0.69). And while these models do have some negative bias, the absolute magnitude of the bias (6–7 %) is approximately 10 % lower than the models where emissions were normalized by LAW (model 10–12). In summary, the models with the best performance contain a pig weight predictor variable (LAW or average weight) or are normalized by pig weight, which includes models 1–3, 7–9, 10–12 and 16–18. This supports theoretical considerations and reflects the importance of pig weight during the growth cycle in influencing the amount of nitrogen available to be emitted.

Table 4.

Performance evaluation metrics for models.

Model #	n	ME (kg day−1)	NME (%)	MB (kg day−1)	NMB (%)	r
1a	2932	1.67	27.4	0.06	0.9	0.66
1b	2932	1.58	25.9	0.07	1.2	0.70
2a	3015	1.63	27.0	0.01	0.2	0.69
2b	3015	1.54	25.4	0.04	0.6	0.72
3a	2921	1.61	26.7	0.00	0.0	0.69
3b	2921	1.55	25.7	0.05	0.8	0.71
4a	2936	2.24	36.7	0.05	0.7	0.14
4b	2936	2.08	34.1	0.04	0.7	0.34
5a	3019	2.20	36.3	0.00	0.0	0.25
5b	3019	2.00	33.1	−0.01	−0.1	0.43
6a	2925	2.01	33.4	−0.05	−0.9	0.46
6b	2925	1.91	31.7	0.00	−0.1	0.50
7a	2932	1.84	30.2	−0.03	−0.4	0.57
7b	2932	1.61	26.4	−0.01	−0.2	0.67
8a	3015	1.82	30.1	−0.06	−0.9	0.60
8b	3015	1.56	25.8	−0.04	−0.7	0.70
9a	2921	1.71	28.3	−0.06	−1.0	0.65
9b	2921	1.56	26.0	−0.01	−0.1	0.70
10a	2850	2.32	37.2	1.02	16.4	0.66
10b	2850	2.36	37.9	1.06	17.1	0.69
11a	2933	2.26	36.7	0.97	15.7	0.68
11b	2933	2.29	37.2	1.01	16.4	0.70
12a	2857	2.36	38.5	1.07	17.5	0.69
12b	2857	2.40	39.2	1.11	18.1	0.70
13a	2854	2.62	42.1	0.79	12.7	0.14
13b	2854	2.65	42.6	0.84	13.4	0.18
14a	2937	2.59	42.1	0.78	12.7	0.17
14b	2937	2.62	42.5	0.83	13.4	0.20
15a	2861	2.43	39.8	0.69	11.3	0.28
15b	2861	2.44	39.9	0.71	11.5	0.29
16a	2850	1.80	29.0	0.36	5.8	0.66
16b	2850	1.80	28.9	0.42	6.7	0.67
17a	2933	1.76	28.6	0.35	5.6	0.68
17b	2933	1.76	28.6	0.40	6.4	0.69
18a	2857	1.76	28.8	0.37	6.1	0.69
18b	2857	1.78	29.0	0.41	6.7	0.69

The approach used for the y-intercept had different impacts on model performance depending on the model type. For the non-normalization models (1–9), the NME is 1–4 % lower for the deep/shallow pit models (1b–9b) than the combined pit models (1a-9a) while the correlation coefficient is also higher by 0.02–0.20 for the combined pit models. Bias values, however, were similar (<± 0.9 %) for non-normalization models with different pit management y-intercept approaches. For the normalization models (models 10–18), the combined pit models had similar or slightly lower NME and NMB values versus the non-normalization models (absolute difference of 0.1 to 0.9 % for both NME and NMB). The effect of the pit management y-intercept also had a smaller effect on r values for the non-normalization models with r values 0.01–0.04 higher for the deep/shallow pit models.

Including the different pit management y-intercepts, there are 12 different combinations of emission response variable and production variables that were developed in combination with each of the three different environmental variables (ambient temperature, exhaust temperature and air flow). For each of these twelve combinations, the environmental variables had a similar influence on the performance of models in predicting emissions, with NME and NMB values varying by less than 2.7 % and 1.9 %, respectively. The effect of the environmental variables on the correlation coefficient was also small (<0.08) for models that accounted for the growth cycle (models 1–3, 7–12 and 16–18). While the models containing the barn exhaust temperature and airflow variables have the lowest error and bias and highest correlation coefficient, the similar performance of the models for the different environmental variables means that the ease in which the parameter can be measured could be an important factor in model preference. Of the three environmental parameters, ambient temperature is considered the easiest to obtain, as this parameter does not have to be directly measured and can be obtained from nearby meteorological stations. Taking the aforementioned ease of variable measurement into account, models 1b and 10a and 16a were selected for further investigation and evaluation, as they are the best performing (in terms of error and bias) non-normalized, normalized by inventory, and normalized by LAW emission models. The scatterplots for these selected models are shown in Fig. 1 with the equations for the predicted emissions summarized below.

Fig. 1.

Predicted emissions vs. observed emissions for model 1b (top left), model 10a (top right) and model 16a (bottom).

Model 1b-DP:

$$N{H}_3\mathit{\text{Emission}}\left(\mathit{\text{kg}}\mathit{\text{da}}{y}^{-1}\right)=\left(\left(e^{1.3086}*1.062\right)*\left(e^{\left(0.0090*\mathit{\text{LAW}}+0.0091*\mathit{\text{Amb}}T\right)}\right)\right)-1$$ (9)

Model 1b-SP:

$$N{H}_3\mathit{\text{Emission}}\left(\mathit{\text{kg}}\mathit{\text{da}}{y}^{-1}\right)=\left(\left(e^{1.1174}*1.062\right)*\left(e^{\left(0.0090*\mathit{\text{LAW}}+0.0091*\mathit{\text{Amb}}T\right)}\right)\right)-1$$ (10)

Model 10a:

$$N{H}_3\mathit{\text{Emission}}\left(g\mathit{\text{da}}{y}^{-1}A{U}^{-1}\right)=\left(\left(e^{3.8341}*1.115\right)*\left(e^{\left(0.0119*\mathit{\text{Amb}}T\right)}\right)\right)$$ (11)

Model 16a:

$$N{H}_3\mathit{\text{Emission}}\left(g\mathit{\text{da}}{y}^{-1}h{d}^{-1}\right)=\left(\left(e^{1.0790}*1.041\right)*\left(e^{\left(0.0119*\mathit{\text{AW}}+0.0097*\mathit{\text{Amb}}T\right)}\right)\right)-1$$ (12)

The units of input variables for eqs. (9)–(12) are Mg for LAW, °C for ambient air temperature (Amb T) and kg for average weight (AW).

3.2. Further investigation and evaluation of selected models

Models 1b, 10a and 16a were further investigated by conducting a closer examination of predicted emission trends and through the additional model evaluation techniques outlined in section 2.4.2.

3.2.1. Emission trends

The model predicted emissions for models 1b, 10a and 16a for each barn over the measurement period are provided in Figs. 2, 3, 4, 5. Generally, the models do well capturing the emission trend across the rotation, however, for rotations where there is an atypical emissions trend, such as the rotations from Feb–July 2009 at IN3B-R5 or May–Oct 2009 at NC3B-B1, the models do not perform as well, with large overpredictions. This suggests that during these rotations, there are factors influencing emissions that are not included in the model. When comparing model predicted trends between models for the early weeks of the rotations, model 1b almost always predicts the highest emissions of the three models, followed by model 10a. In comparison to measured emissions for the early weeks of the rotation, the three models have mixed success in predicting emission magnitude, but generally overpredict emissions. In the middle portion of the rotation, the models predict similarly, with model 10a generally having the highest emissions. In the latter portion of the rotation, model 1b performs best in reproducing the plateauing in the observed emissions trend, whereas the other two models (and particularly model 10a) have increasing emissions and thus higher predicted emissions during this period. The poorer performance of model 10a for the latter portion of the rotation is likely the result of the way the different models reflect the influence of the growth cycle on emissions (further discussion provided below).

Fig. 2.

Observed and model predicted NH₃ emissions for R5 (top) and R6 (bottom) at IN3B. Vertical lines indicate where a room is transitioning from occupied to unoccupied or unoccupied to occupied with the O and U letters indicating approximate periods where the rooms were occupied and unoccupied, respectively.

Fig. 3.

Observed and model predicted NH₃ emissions for R7 (top) and R8 (bottom) at IN3B. Vertical lines indicate where a room is transitioning from occupied to unoccupied or unoccupied to occupied with the O and U letters indicating approximate periods where the rooms were occupied and unoccupied, respectively.

Fig. 4.

Observed and model predicted NH₃ emissions for B1 (top) and B2 (bottom) at NC3B. Vertical lines indicate where a barn is transitioning from occupied to unoccupied or unoccupied to occupied with the O and U letters indicating approximate periods where the barns were occupied and unoccupied, respectively.

Fig. 5.

Observed and model predicted NH₃ emissions for B3 at NC3B. Vertical lines indicate where a barn is transitioning from occupied to unoccupied or unoccupied to occupied with the O and U letters indicating approximate periods where the barn was occupied and unoccupied, respectively.

While the performance of the models varies for each individual rotation, some general trends were identified by examining the performance metrics (Table S7) and the predicted emission vs. observed emission scatterplots for individual sites (Figs. S42–S44). Overall, the NME for predicted emissions for all three selected models was 4.4–6.8 % lower for IN3B versus NC3B. For model 1b, NMB values were similar and near zero (<2.3 %) between the two sites. However, for models 10a and 16a, there was a larger bias for NC3B than IN3B, with NMB values of 24.3 % (model 10a) and 10.3 % (model 16a) for the NC3B site and 9.8 % (model 10a) and 2.1 % (model 16a) for the IN3B site. The r value was also higher for IN3B versus NC3B (difference of 0.10–0.13) for the selected models. It is hypothesized that the difference in model performance between the two sites is partly due to the flat emission trend in observed NH₃ emissions for the last rotation at the NC3B barns (Figs. 4 and 5).

In summary, models 1b and 16a perform better than 10a as they have predictor variables that can reflect the non-linear influence of swine weight trends on NH₃ emissions during the growth cycle. This supports theoretical considerations as in a typical rotation, swine weight and feed intake will increase rapidly during the first half of the rotation and then start to plateau as the rate of increase of swine weight and feed intake decreases (DeRouchey et al., 2010; Van Heugten, 2010), while swine crude protein/nitrogen requirements (U.S. Department of Agriculture-Natural Resources Conservation Service (USDA-NRCS, 2003) and thus also likely nitrogen feed content decrease during the swine growth cycle with the rate of decrease slowing. In combination, this means that the amount of nitrogen excreted and available for emission will have a non-linear relationship with increasing swine weight during the growth cycle. As model 1b and 16a contain swine weight predictor variables (LAW and average weight), the nature of the models means they these variables will have a non-linear influence on the emissions response variable (see section 2.3.1 for further details). Accordingly, models 1b and 16a will reflect the non-linear influence of swine weight during the growth cycle and will perform better in predicting emissions than model 10a, which models the effect of swine weight linearly due to using LAW as a normalizing variable for the emission response variable.

In comparison, models 1b and 16a perform fairly similarly in terms of predicting NAEMS emissions, however, an advantage of model 1b is that it can produce an emission estimate when the barn is unoccupied. One possible approach that could be used along with model 16a to better predict emissions when barns are unoccupied is to assume that the emissions are zero, which in the case of NAEMS data would result in a 3 % and 5 % underestimation of total emissions for IN3B and NC3B, respectively.

3.2.2. Confidence limits

The average 95 % confidence limits for predicted emissions were similar for models 1b, 10a and 16a, with lower and upper error values ranging from 0.41 kg day⁻¹ to 0.49 kg day⁻¹. For all models, the upper error is slightly higher than the lower error due to the log transformation. When expressing the errors as a percentage of predicted emissions, the average lower and upper error were 7.6 % and 8.2 %, 6.0 % and 6.3 %, and 6.5 % and 6.9 % for models 1b, 10a and 16a, respectively. A table summarizing the 95 % confidence limits results is available in the supplemental material (Table S8).

3.2.3. Model coefficient consistency

The jackknife method was applied to models 1b, 10a and 16a to evaluate model coefficient consistency. When removing a barn from the dataset and redeveloping the models, the ambient temperature, LAW and average weight coefficients (Tables S9–S11) were all significant (p < 0.0001), although there is some variation in the coefficient values (Figs. S45–S49). For models 1b and 16a, the LAW and average weight coefficients are consistent, with variations across barn removal less than 5 % and 8 % for LAW and average weight, respectively. However, the ambient temperature variable is less consistent across all three models, particularly when barn IN3B-R5 is removed, which results in a coefficient increase of 24 % (model 1b), 25 % (model 10a), and 22 % (model 16a). This may be related to the unusual emission trend observed for the last rotation at IN3B-R5 (Fig. 2), when emissions are constant or slightly decreasing during the February–July 2009 rotation, a period when an increasing trend in emissions due to increasing ambient temperatures and pig growth would be expected. A similar phenomenon may also explain why IN3B-R8 has the next highest variation in ambient temperature coefficient with values being higher by 12 %, 10 % and 11 % for models 1b, 10a and 16a, respectively. Another trend in model coefficient consistency for the ambient temperature coefficient is that for both models removing an IN3B barn has either a very small or positive effect on the coefficient, whereas removing an NC3B barn from the models decreases the model coefficient by 1–17 % depending on the model and the barn removed. This suggests that the relationship between ambient temperature and emissions may be different at the sites, which could be related to the closer relationship between ambient temperature and barn exhaust temperature at NC3B than IN3B (see summary of exploratory data analysis for candidate parameters section in supplemental material)

3.2.4. Sensitivity analysis

To evaluate the influence of parameters on predicted emissions, a sensitivity analysis was performed for models 1b, 10a and 16a. The sensitivity analysis data range, the NAEMS data range, and the constant values used (based on the average value for all data) are provided in the supplemental material (Table S12), while the results of the sensitivity analysis are shown in Figs. S50 and S51. The sensitivity analysis shows that as ambient temperature increases the predicted emissions increase for all three models (Fig. S50). The daily emission increases at a near linear rate, with a slight increase in emission trend rate as temperatures increase. Across the entire NAEMS temperature range, the predicted emissions increase by 74 % (deep pit) and 78 % (shallow pit) for model 1b, and 86 % and 80 % for models 10a and 16a, respectively. For ambient temperature, the models were additionally tested for a range from −40 to 50 °C, the results of which showed that the models perform reasonably for these set of conditions also. For model 1b, the sensitivity analysis for the LAW parameter (Fig. S50) shows that the rate of increase for emissions slightly increases with increasing LAW, with an increase in predicted emissions across the entire NAEMS LAW range by approximately a factor of 4. For reference, the linear influence (due to the normalization of emissions by LAW for this model) of LAW on predicted emissions for model 10a is also displayed in Fig. S50. For the set of conditions used in this sensitivity analysis, model 10a predicted emissions increase by 0.61 kg day⁻¹ per 5000 kg increase in LAW. Beyond the upper limit of the NAEMS LAW data (130,000 kg), model 1b and model 10a predict similar emissions up to a LAW of around 215,000 kg, which is over one and a half times the upper limit of the NAEMS LAW data. For LAW above 215,000 kg, a rapid increase in predicted emissions can be observed. This rapid increase occurs because LAW as a predictor variable has a non-linear effect on emissions due to the nature of the model. For model 16a, the sensitivity analysis shows predicted emissions increase by a factor of approximately six, as average weight is varied across the NAEMS data range of 0–130 kg (Fig. S51). The influence of the parameter on model 16a emissions was also tested beyond the NAEMS upper limit to an average weight of 150 kg and performed reasonably. The influence of inventory is linear for model 16a (Fig. S51) since the emissions are normalized by inventory. For the set of values used in this sensitivity analysis, emissions increased by 0.71 kg day⁻¹ for every additional 100 pigs.

3.2.5. Secondary data

The summary statistics for the model input production and environmental conditions and observed NH₃ emissions associated with the secondary barn data sets are provided in the supplemental material (Table S13). Generally, the barns had similar production parameters to the NAEMS barn data, with all model input data within the range of the NAEMS data. Ambient air temperature was on average colder at the IA barn than the NAEMS data, but the data were within the range of the NAEMS data. Average observed NH₃ emissions from the barns ranged from 5.24 to 7.82 kg day⁻¹, which was within the average barn NH₃ emissions for the NAEMS data (4.97–7.87 kg day⁻¹) (Table 1). Model evaluation metrics for the performance of models 1b, 10a, and 16a in predicting the observed emissions for different barns are provided in Table 5. As with predicting NAEMS data, models 1b and 16a performed well predicting emissions and generally outperformed model 10a. For all 4 b, model 1b had the lowest NME (ME) values, with an average NME (ME) across all 4 b of 24.0 % (1.01 kg day⁻¹). Model 16a had the next lowest NME (ME) value for all barns, with an average NME (ME) across all barns of 36.0 % (1.57 kg day⁻¹). model 10a had the highest NME (ME) value of the three models, with an average NME (ME) across all models of 44.2 % (1.92 kg day⁻¹). In terms of bias, model 1b had the smallest NMB (MB) for three of the 4 b, the exception being IA-NB, where model 10a had the smallest NMB (MB) value. Across all barns, the average absolute NMB (MB) was lowest for model 1b (14.4 % (0.13 kg day⁻¹)), followed by Model 16a (27.2 % (0.56 kg day⁻¹)) and then model 10a (33.6 % (1.20 kg day⁻¹)). Similar to model predictions for NAEMS data, model 10a generally overpredicted, with a positive bias for three of the 4 b. The greatest difference in model performance occurred for the TX barns (TX-BB and TX-BC). Although all three models overpredicted for TX-BB and TX-BC, the NME/ME and NMB/MB were considerably lower for model 1b than models 10a and 16a. The r values for predicted vs. observed emissions are also provided in Table 5 (corresponding scatterplot figures are provided in the supplemental material (S52-S55)). All three models had lower ME/NME and absolute MB/NMB for barn IA-SB than IA-NB, with the poorer model performance for IA-NB in comparison to IA-SB likely due to the larger frequency of anomalous observed emission peaks for IA-NB (Fig. 6) which the models do not capture. This suggests that there are additional factors that have a large influence on emissions in this barn. Overall, all three models capture the observed emission trend quite well, which is reflected in the r values being >0.49 for all models at both IA barns. For barn TX-BC, all three models do well predicting emissions for most of the monitoring period, the exceptions being the last two months of the monitoring period when there is a declining observed emission trend (Fig. 7). The reason for the declining emission trend as LAW increases throughout the rotation is unknown. Emissions also decline in the last couple of months of monitoring for TX-BB, however predicted model emissions are not as large as those for TX-BC. At barn TX-BB, models 10a and 16a also overpredict in the second half of the rotation during the period from July–October 2003 (Fig. 7), which explains the larger error and bias values for emission prediction in comparison to TX-BC. It is worth noting that the observed emissions are lower at barn TX-BB despite barn TX-BB and TX-CC having similar production and environmental conditions (See Table S13 in supplemental material), which contributes to the difference in model performance between the 2 b.

Table 5.

Evaluation metrics for the selected models in predicting emissions for secondary data sets.

Site-Barn ID	Model #	n	ME (kg day−1)	NME (%)	MB (kg day−1)	NMB (%)	r
IA-NB	1b	324	1.44	27.6	−0.78	−15.0	0.49
	10a	324	1.61	30.9	−0.41	−7.9	0.53
	16a	324	1.57	30.0	−0.88	−16.9	0.51
IA-SB	1b	323	0.85	18.8	−0.13	−2.6	0.57
	10a	323	1.14	25.1	0.33	7.2	0.58
	16a	323	1.00	22.1	−0.30	−6.5	0.57
TX-BB	1b	231	0.87	24.7	0.71	20.0	0.83
	10a	229	2.39	67.6	2.39	67.6	0.84
	16a	229	1.77	50.3	1.74	49.5	0.80
TX-BC	1b	274	0.87	24.7	0.71	20.0	0.83
	10a	262	2.56	53.3	2.48	51.8	0.61
	16a	262	1.96	41.3	1.69	35.7	0.53

Fig. 6.

Observed and model predicted emissions for the North (N; top) and South (S; bottom) barns in IA.

Fig. 7.

Observed and model predicted emissions for the barns BB (top) and BC (bottom) in TX.

In summary, the selected models performed well in estimating emissions at other S-GF operations in different regions, however it would be beneficial to further evaluate the models with data that represents different environmental, production and management conditions.

3.3. Nitrogen intake models

3.3.1. Developing N-intake models

A limitation of the previously described models 1–18 is that they cannot reflect changes in pig feed, which may have varying nitrogen content and thus different potential for emissions. Although there is limited NAEMS data in comparison to other variables, the potential influence of N-intake was explored by estimating daily N-intake values using a combination of the available N feed content measurements and assumptions (see nitrogen balance methodology in supplemental for more information). Some of these assumptions result in potentially greater model uncertainty than models containing more frequently measured parameters, however exploring the development of models that can account for changes in N-feed content is still useful as they can account for changes in feed practices by industry, including dietary strategies that could be implemented as best management practices.

For the exploration of models that reflect daily N-intake, nine models were developed using two different variables related to N-intake, which were the daily N-intake for the barn (N_in-b) and daily nitrogen intake per pig (N_in-p). The Nin-b values were obtained directly from the nitrogen mass balance calculations (see supplemental material) and Nin-p values were determined by multiplying the calculated feed intake per pig values (FI_p; see supplemental material) by the %N content of the feed. Summary statistics for N_in-b and N_in-p are provided in the supplemental material (Table S14). In comparison, the overall N_in-b value at IN3B (49.70 kg-N) was 16 % higher value than the value for NC (39.77 kg-N), whereas N_in-p values at NC3B were 20 % higher at NC3B than IN3B.

Similarly to previously developed models, the nine models were developed with deep/shallow pit and combined pit intercepts and the ambient temperature, barn exhaust temperature and airflow variables (Table 6). These developed models (models 19–27) can be considered to be similar to the previous developed models 1–3, 7–9 and 16–18, but with the N_in-b and N_in-p variables replacing equivalent weight related production variables (i.e., N_in-b is equivalent to LAW, and N_in-p is equivalent to average weight).

Table 6.

Constant and predictor variable coefficient values for N-intake models to predict NH₃emissions.

	Response Variable	Constant	Predictor Variables
Model #	Units of Emission	Y-intercept (s)	Production Var.1 (input unit)1	Production Var.2 (input unit)	Environmental Var.1 (input unit)
19a	kg day−1	CP	Nin-b (kg-N)	–	Amb Temp (°C)
19b	kg day−1	DP, SP	Nin-b (kg-N)	–	Amb Temp (°C)
20a	kg day−1	CP	Nin-b (kg-N)	–	Exh Temp (°C)
20b	kg day−1	DP, SP	Nin-b (kg-N)	–	Exh Temp (°C)
21a	kg day−1	CP	Nin-b (kg-N)	–	Airflow (dsm3 s−1)
21b	kg day−1	DP, SP	Nin-b (kg-N)	–	Airflow (dsm3 s−1)
22a	kg day−1	CP	Inventory/k	Nin-p (kg-N)	Amb Temp (°C)
22b	kg day−1	DP, SP	Inventory/k	Nin-p (kg-N)	Amb Temp (°C)
23a	kg day−1	CP	Inventory/k	Nin-p (kg-N)	Exh Temp (°C)
23b	kg day−1	DP, SP	Inventory/k	Nin-p (kg-N)	Exh Temp (°C)
24a	kg day−1	CP	Inventory/k	Nin-p (kg-N)	Airflow (dsm3 s−1)
24b	kg day−1	DP, SP	Inventory/k	Nin-p (kg-N)	Airflow (dsm3 s−1)
25a	g day−1 hd−1	CP	Nin-p (kg-N)	–	Amb Temp (°C)
25b	g day−1 hd−1	DP, SP	Nin-p (kg-N)	–	Amb Temp (°C)
26a	g day−1 hd−1	CP	Nin-p (kg-N)	–	Exh Temp (°C)
26b	g day−1 hd−1	DP, SP	Nin-p (kg-N)	–	Exh Temp (°C)
27a	g day−1 hd−1	CP	Nin-p (kg-N)	–	Airflow (dsm3 s−1)
27b	g day−1 hd−1	DP, SP	Nin-p (kg-N)	–	Airflow (dsm3 s−1)

3.3.2. Performance of N-intake models in predicting NAEMS emissions

Table 7 presents the constants and predictor variable coefficients for the N-intake models. The predictor variables coefficients for the models were all positive and significant (p < 0.01). The E_i and C values associated with the N-intake model predicted emissions are provided in the supplemental material (Table S15). The model performance metrics for the N-intake models (models 19–27) are shown in Table 8, while scatterplots of model predicted emissions vs. observed emissions are provided in the supplemental material (Figs. S56–S64). The N-intake models perform similarly to the equivalent average weight/LAW models (models 1–3, 7–9, 16–18) in terms of error and bias, with the average weight/LAW models having (on average) NME and absolute NMB values 0.5 % and 0.4 % less, respectively, than the equivalent N-intake models. The N-intake models generally do not do as well predicting emission trends, with r values that are 0.08 higher (on average) for the average weight/LAW models than the N-intake models. For a more in-depth comparison of N-intake models to their equivalent average weight/LAW models, the N-intake models equivalent to models 1b and 16a were selected (specifically models 19b and model 25a) as models 1b and 16a were the best performing of the average weight/LAW models.

Table 7.

Constant and predictor variable coefficient values for N-intake models.

	Response Variable	Constant	Predictor Variables
Model #	Units of Emission	Y-intercept(s)	Production Variable (s)	Environmental Variable
19a	kg day−1	CP: 1.2846	Nin-b 0.0117	Amb T: 0.0057
19b	kg day−1	DP: 1.3855, SP: 1.1646	Nin-b: 0.0113	Amb T: 0.0060
20a	kg day−1	CP: 1.022177	Nin-b 0.0107	Exh T: 0.0170
20b	kg day−1	DP: 1.1173, SP: 0.8975	Nin-b: 0.0103	Exh T: 0.0176
21a	kg day−1	CP: 1.3831	Nin-b: 0.0108	AF: 0.0061
21b	kg day−1	DP: 1.4635, SP: 1.2439	Nin-b: 0.0103	AF: 0.0061
22a	kg day−1	CP: 1.2298	Inv: 0.1506, Nin-p: 9.0019	Amb T: 0.0056
22b	kg day−1	DP: 1.3254, SP: 0.9755	Inv: 0.0986, Nin-p: 10.3168	Amb T:0.0059
23a	kg day−1	CP: 1.0231	Inv: 0.1099, Nin-p: 8.2141	ExhT: 0.0159
23b	kg day−1	DP: 1.1094, SP: 0.7566	Inv: 0.0538, Nin-p: 9.6358	Exh T: 0.0166
24a	kg day−1	CP: 1.3363	Inv: 0.1321, Nin-p: 8.7033	AF: 0.0059
24b	kg day−1	DP: 1.3933, SP: 1.0610	Inv: 0.0974, Nin-p: 9.5136	AF: 0.0057
25a	g day−1 hd−1	CP: 1.0875	Nin-p: 16.4464	Amb T: 0.0064
25b	g day−1 hd−1	DP: 1.1418, SP: 0.9499	Nin-p: 17.5132	Amb T: 0.0066
26a	g day−1 hd−1	CP: 0.8590	Nin-p: 16.4249	Exh T: 0.0142
26b	g day−1 hd−1	DP: 0.9126, SP: 0.7368	Nin-p: 17.3829	Exh T: 0.0143
27a	g day−1 hd−1	CP: 1.1051	Nin-p: 16.9936	AF: 0.0053
27b	g day−1 hd−1	DP: 1.1495, SP: 1.0015	Nin-p: 17.7036	AF: 0.0051

Table 8.

Performance evaluation metrics for the N-intake models.

Model ID	n	ME (kg day−1)	NME (%)	MB (kg day−1)	NMB (%)	r
19a	2669	1.71	27.5	−0.04	−0.6	0.59
19b	2669	1.65	26.5	0.00	0.1	0.63
20a	2728	1.71	27.7	−0.05	−0.8	0.60
20b	2728	1.64	26.4	−0.01	−0.2	0.64
21a	2637	1.64	26.6	−0.06	−0.9	0.64
21b	2637	1.63	26.3	0.02	0.3	0.66
22a	2669	1.88	30.2	−0.06	−0.9	0.50
22b	2669	1.57	25.3	−0.06	−1.0	0.67
23a	2728	1.89	30.6	−0.06	−1.0	0.51
23b	2728	1.56	25.2	−0.07	−1.2	0.68
24a	2637	1.77	28.7	−0.08	−1.4	0.59
24b	2637	1.55	25.1	−0.03	−0.6	0.68
25a	2587	1.90	29.9	0.40	6.3	0.52
25b	2587	1.95	30.7	0.49	7.7	0.57
26a	2646	1.89	29.9	0.41	6.4	0.54
26b	2646	1.94	30.7	0.49	7.7	0.58
27a	2573	1.85	29.5	0.40	6.3	0.58
27b	2573	1.92	30.6	0.48	7.7	0.60

For individual sites, the performance of models 19b and 25a is similar to the equivalent models 1b and 16a, with differences of less than 4 % between corresponding NME and absolute NMB values (Table S16). Figs. S65–S68 in the supplemental material show the trend in emission prediction for models 19b and 25a along with models 1b and 16a. The general trend is for models 19b and 25a to have higher predicted emissions than model 1b and 16a for the first half of the rotation when N_in-b and N_in-p values are high and lower emissions for the second half of the rotation when N_in-b and N_in-p values are lower. This change in model predicted emissions improves model performance during some rotations. For example, during the second half of the March–August 2008 rotations at IN3B-R7 and IN3B-R8, the decrease in predicted emissions matches the observed emissions trend well, whereas model 1b and 16a overpredict during this same period. There are, however, periods when models 19b and 25a do not perform as well, such as the first half of the rotations in January–May 2009 and May–October 2009 at the NC3B barns, when emissions are overpredicted. It is hypothesized that the poorer performance of the N-intake models is somewhat related to the limited NAEMS data these variables were developed from, and that with more frequently measured data these N-intake models would potentially perform better in predicting emissions than the models that contain the LAW and average weight variables.

3.3.3. Further evaluation of selected N-intake models

Similar to the previously selected models, the 95 % confidence limits for predicted emissions were determined for models 19b and 25a. The average lower and upper errors were slightly higher than the equivalent models (1b and 16a), with lower/upper error values of 0.55/0.60 kg day⁻¹ and 0.59/0.64 kg day⁻¹ for models 19b and 25a, respectively. The % lower errors and % upper errors were also higher for the selected N-intake models with equivalent values ranging from 1 to 3 % higher. A summary of the confidence limit results for selected N-intake models is provided in the supplemental material (Table S17).

The same jackknife method as applied to previous selected models (see section 2.4.2) was also applied to models 19b and 25a. When removing a barn from the dataset, the ambient temperature, N_in-b and Nin-p coefficients were all significant (Tables S18 and S19), although there is some variation in the coefficient values (Figs. S69–S72). The model coefficient consistency results for models 19b and 25a were similar to the equivalent models 1b and 16a, with N_in-b and N_in-p values being relatively consistent and variations for barn removal less than 6 % for Nin-b and less than 9 % for N_in-p. Similar to models 1b and 16a, ambient temperature coefficient values were less consistent, particularly when IN3B-R5 is removed. For models 19b and 25a, the removal of the IN3B-R5 data results in coefficient increases of 32 % and 28 %, respectively. An explanation for this trend is provided in the previous section 3.2.3.

Sensitivity analysis was also performed for the parameters in model 19b and 25a (ambient air temperature, N_in-b and N_in-p) using the same approach as the previous models. Sensitivity analysis figures are provided in the supplemental material (Figs. S73 and S74). Ambient air temperature was also varied using the same values as the previous models (see section 3.2.4) and for models 19b and 25a. Ambient temperature varied slightly less than the previous models across the NAEMS temperature range, with predicted emissions increasing by 44 % (deep pit) and 46 % (shallow pit) for model 19b and 46 % for model 25a. For N_in-b, the rate of increase is non-linear, with a slight increase in this rate as N_in-b increases. Across the NAEMS N_in-b range (0–86 kg-N), the predicted emissions increase by approximately a factor of three for model 19b. The influence of N_in-b on predicted emissions was also tested beyond the NAEMS upper limit to a N_in-b value of 130 kg-N (50 % beyond the NAEMS upper limit) and performed reasonably. For N_in-p, the rate of increase is also non-linear, with a slight increase in rate of increase as N_in-p increases. Across the NAEMS N_in-p range (0–0.073 kg-N), the predicted emissions increase by over a factor of four for model 25a. The influence of N_in-p on predicted emissions was also tested to a value 50 % beyond the NAEMS upper limit (0.11 kg-N) and performed reasonably. Further evaluation of these models using other datasets would be useful, however, there are currently no secondary data sets available with appropriate N-intake information to complete such analysis.

4. Summary and conclusions

The U.S. EPA is developing EEMs for use by participants in the ACA to determine whether their emissions meet certain CAA thresholds. In addition, the EEMs may be useful for other producers that wish to estimate AFO emissions. To estimate NH₃ emissions from barns at swine grow-finish operations, 18 statistical models were developed that contained variables that represented varying production and environmental conditions as well as differences in manure management systems. Of these models, the models that had the best performance in predicting emissions where those that had LAW (model 1–3) or average weight (model 7–9, 16–18) predictor variables that accounted for pig growth during the rotation. Three different environmental predictor variables (ambient temperature, barn exhaust temperature and airflow) were included in the statistical models and influenced model performance similarly, suggesting that any of these variables could be potentially used to estimate emissions. However, ambient temperature is considered the easiest obtain for estimating emissions as it does not have to be directly measured and can be obtained from nearby meteorological stations. Based on model performance evaluation metrics and ease of variable measurement, models 1b, 10a and 16a were considered to be the best performing non-normalization, normalization by LAW, and normalization by inventory models, respectively, for predicting NAEMS NH₃ emissions from swine grow-finish barns. Further investigation of emission trends indicated that models 1b and 16a had better performance than model 10a, which tended to overpredict emissions due to the lack of a pig weight-related predictor variable in the model. When evaluating the performance of the selected models to predict secondary data emissions, model 1b performed the best, followed by model 16a. Sensitivity analysis was also conducted for selected models, which showed that there would be potential concerns with applying model 1b for barns with a LAW of approximately 215,000 kg and higher due to the non-linear effect of the variable resulting in a rapid increase in predicted NH₃ emissions. Using the barn inventory statistics provided by swine grow-finish operations as part of the ACA and assuming a maximum average pig weight of 130 kg, less than approximately 15 % of swine-grow finish barns will have an LAW greater than 215,000 kg (determined using an inventory of 1654 at a maximum weight of 130 kg) for any given day. These results suggest that model 1b be used to predict emissions for barns when the LAW is 215,000 kg or less and that model 16a be used to predict emissions for barns with a LAW of 215,000 kg or greater. Alternatively, model 16a could potentially be used to predict emissions for all ranges of inventory and LAW, but will have greater error than model 1b and will not be able to predict emissions when the barn is unoccupied.

Nine statistical models were also developed to predict emissions that could account for changes in feed and thus N-feed content by estimating N-intake. A selection of these models also performed well in predicting emissions, although further testing using other data sets is needed, particularly since these models were developed on limited N-feed data. In addition, while the N-intake models can account for changes in pig diet, the N-content of feed is a more difficult and expensive measurement for AFOs to obtain. Appropriate N-intake models could be potentially useful though, as they would have the ability to evaluate the effectiveness of diet change related best management practices.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.aeaoa.2025.100404.

Data availability

Data available at https://catalog.data.gov/dataset/epa-sciencehub