Reactive N in the form of NH3 impacts the environment

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1 Journal of Environmental Quality TECHNICAL REPORTS ATMOSPHERIC POLLUTANTS AND TRACE GASES Arrhenius Equation for Modeling Feedyard Ammonia Emissions Using Temperature and Diet Crude Protein Richard W. Todd,* N. Andy Cole, Heidi M. Waldrip, and Robert M. Aiken Temperature controls many processes of volatilization. For example, urea hydrolysis is an enzymatically catalyzed reaction described by the Arrhenius equation. Diet crude protein (CP) controls emission by affecting N excretion. Our objectives were to use the Arrhenius equation to model from beef cattle (Bos taurus) feedyards and test predictions against observed. Per capita emission rate (PCER), air temperature (T), and CP were measured for 2 yr at two Texas Panhandle feedyards. Data were fitted to analogs of the Arrhenius equation: PCER = f(t) and PCER = f(t,cp). The models were applied at a third feedyard to predict and compare predicted to measured. Predicted mean were within 9 and 2% of observed for the f(t) and f(t,cp) models, respectively. Annual emission factors calculated from models underestimated annual emission by 11% [f(t) model] or overestimated emission by 8% [f(t,cp) model]. When T from a regional weather station and three classes of CP drove the models, the f(t) model overpredicted annual emission of the low CP class by 14% and underpredicted of the optimum and high CP classes by 1 and 39%, respectively. The f(t,cp) model underpredicted by 15, 4, and 23% for low, optimum, and high CP classes, respectively. Ammonia emission was successfully modeled using T only, but including CP improved predictions. The empirical f(t) and f(t,cp) models can successfully model in the Texas Panhandle. Researchers are encouraged to test the models in other regions where high-quality data are available. Reactive N in the form of NH3 impacts the environment in many ways. In the atmosphere, combines readily with acidic compounds to form secondary particulates that degrade air quality and can impact the earth s radiation balance (Kelly et al., 2005; Renard et al., 2004). Excessive can overfertilize both terrestrial and aquatic ecosystems, leading to undesirable species changes, noxious or toxic algal blooms, or eutrophication and hypoxia of ecosystems (Krupa, 2003; Todd et al., 2004; Vitousek et al., 1997). Animal waste is a major source of emitted to the atmosphere, accounting for more than half of emitted in the U.S. inventory (Hristov et al., 2011; U.S. Environmental Protection Agency, 2012). Our understanding of from cattle feeding operations has expanded greatly during the last several years (Flesch et al., 2007; Todd et al., 2008, 2011; Rhoades et al., 2010). However, accurately quantifying long-term usually requires expensive instrumentation and a considerable commitment of time and labor. Process-based models are the best approach to estimating across a wide range of production practices and geography (National Research Council, 2003), but their prediction accuracy at the farm scale is not yet proven. Regulatory requirements such as the emission reporting requirements under the U.S. Emergency Planning and Community Right-to-Know Act or the development of national inventories challenge us to provide the best possible estimates of from cattle feedyards. Many processes during volatilization depend on temperature. The chemical pathway leading to volatilization of from animal manure usually begins with urea hydrolysis. Most excreted N, from 50 to 60%, is in cattle urine (Todd et al., 2006). Urea is readily hydrolyzed. For example, urinary N was completely volatilized within 72 h of excretion (Cole and Todd, 2009; Yadav et al., 1987). Hydrolysis of urea in urine to is catalyzed by the extracellular enzyme urease, and the reaction rate constant of urease depends on temperature (Yadav Copyright American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America Guilford Rd., Madison, WI USA. All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. J. Environ. Qual. 42: (2013) doi: /jeq Received 27 Sept *Corresponding author (richard.todd@ars.usda.gov). R.W. Todd, N.A. Cole, and H.M. Waldrip, USDA-ARS, Conservation and Production Research Lab., P.O. Drawer 10, Bushland, TX 79012; and R.M. Aiken, Kansas State Univ., Western Kansas Agricultural Research Centers, th Ave., Hays, KS Mention of trade names or commercial products in this publication is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the USDA. Assigned to Associate Editor Sean McGinn. Abbreviations: CP, crude protein; FYA, Feedyard A; FYC, Feedyard C; FYE, Feedyard E; PCER, per capita emission rate. 666

2 et al., 1987). The Arrhenius equation describes this temperature dependence as Ea A p exp = RT [1] where A is the rate constant of the reaction (mol s 1 g 1 urease), p is the pre-exponential factor, E a is the activation energy ( J mol 1 ), R is the gas constant ( J K 1 mol 1 ), and T (K) is the absolute temperature. The Arrhenius equation can be expressed in linear form as Ea ln A= ln p+ [2] RT Once hydrolyzed from urea, total NH x ionizes into NH 4 + and (Ni, 1999), and that process is controlled by an ionization variable that is usually expressed as a semi-empirical function of temperature and ph. In solution, dissociates into aqueous and gaseous forms, and this dissociation is a function of temperature and Henry s coefficient. Clearly, at the process level, temperature is a major driver of volatilization. Another factor that controls is dietary crude protein (CP). Ammonia are sensitive to CP (Cole et al., 2005; Todd et al., 2006, 2011). When cattle are fed enough CP to meet their physiological and growth needs, about 50% of N intake is subsequently lost to the atmosphere as (Hristov et al., 2011; Sakirkin et al., 2011). When CP exceeds cattle needs, however, the excess N is excreted, primarily as urea in the urine. This has the effect of increasing. Near-continuous monitoring of from two commercial Texas Panhandle cattle feedyards for 2 yr (Todd et al., 2011) showed that annual patterns of were closely correlated with temperature (Fig. 1). Summertime were about double those during winter, with during spring and autumn intermediate between summer and winter. We hypothesized that an analog of the Arrhenius equation can empirically describe the annual pattern of mean monthly. Our objectives were to: (i) use the analog Arrhenius equation to model feedyard ; (ii) incorporate dietary CP into the predictive Arrhenius equation; and (iii) test the ability of temperature- and CP-dependent models to predict emission at a third feedyard independent of those used in model development. Materials and Methods Ammonia Emissions We used an equation analogous to the linearized Arrhenius equation (Eq. [2]): 1 ln( PCER) = a + b [3] T where PCER (g animal 1 d 1 ) is the per capita emission rate of, T(K) is air temperature, and a and b are fitted parameters. We used the data set of mean monthly emission and temperature reported in Todd et al. (2011) to parameterize the analog Arrhenius equation. Those data were collected at two Fig. 1. Mean monthly per capita N emission (bars) and air temperature (line and open circles) at Feedyard A, showing correlation of temperature and emission (data are from Todd et al., 2011). active feedyards, designated Feedyard A (FYA) and Feedyard E (FYE) in Deaf Smith County, Texas, during 24 mo from March 2007 through February Ammonia were quantified on a near-continuous basis using open path lasers (Gasfinder 2, Boreal Laser Inc.) to measure the atmospheric concentration, coupled with meteorological measurements, as inputs to an inverse dispersion model (Windtrax , Thunderbeach Scientific). Windtrax has been used successfully to quantify in several studies (e.g., Flesch et al., 2007; McGinn et al., 2007; Harper et al., 2009; Todd et al., 2011). Temperature was measured using a temperature and humidity sensor (HMP45, Vaisala) housed in a gill shield and mounted on a tower at 7-m height near the center of each feedyard. We chose this height because (i) it better represented the regional air temperature, compared with a measurement closer to the feedyard pen surface, and (ii) we also wanted to compare actual with those predicted using temperature from a regional weather station. All data were averaged as monthly means. This model is referred to as the f(t) model. Recognizing the importance of CP in controlling emission through its effect on N excretion, we developed another analog of the linear Arrhenius equation that incorporated CP: 1 ln( PCER) = a + b + c( CP) [4] T where c is a fitted parameter. This model is the f(t,cp) model. Dietary CP was calculated at FYA and FYE by sampling and analyzing feed samples for N content as described below. The model predictions were tested at a third feedyard that was not used to parameterize the models. Feedyard C (FYC) was located in Swisher County, Texas, about 60 km southeast of FYA and FYE. Ammonia were quantified there during seven seasonal field campaigns from July 2002 to June 2005 and were reported in Todd et al. (2008). Ammonia at FYC were quantified using acid gas washing to measure concentration profiles and Windtrax to quantify

3 Cattle Dietary Crude Protein Cattle ration samples were collected monthly from five randomly selected feed bunks at each feedyard (five grab samples per bunk combined into each analyzed sample). The samples were dried, milled, and passed through a 0.4-mm mesh sieve. Subsamples of 0.25 g were acid digested with H 2 SO 4 and H 2 O 2 using the regular Kjeldahl method (Bremner, 1970) and then colorimetrically analyzed for N using a flow injection analyzer (QuikChem Method E, Lachat Instruments). Crude protein (% w/w) was calculated as CP = 6.25N feed, where N feed is the mineral N fraction of the sample (g g 1 ). We also relied on monthly animal counts, dry matter intake data, and ration composition provided by the feedyard management. Data Analysis Data were analyzed in SAS 9.2 (SAS Institute). The Proc Reg procedure was used for individual feedyard year linear regressions. The Proc Mixed procedure with repeated monthly measurements was used to fit the combined data set from both feedyards to the analog Arrhenius equations, with ln(pcer) as the dependent variable. Two linear models were fitted that used as independent variables (i) inverse T (the f(t) model, Eq. [3]) or (ii) inverse T and CP in the cattle diet (f(t,cp) model, Eq. [4]). The fit statistics Akaike s information criterion (AIC) and Schwarz s Baysian criterion (BIC) were used to compare the two models. Observed and predicted PCER from the two models were evaluated using a selection of univariate, regression, and comparison statistics (Willmott, 1982, 1984). Results and Discussion Ammonia Emissions and the Arrhenius Equation For the purpose of discussion, 2007 refers to the 12 mo from March 2007 to February 2008, and similarly for We first looked at each feedyard year combination using the linear model of the analog Arrhenius equation (Eq. [3]) that used only temperature as the independent variable. The Arrhenius equation modeled reasonably well in three of four feedyard-years, with temperature accounting for 66 to 84% of the variability in PCER (Fig. 2; Table 1). Feedyard E in 2007 was exceptional, with an adjusted r 2 of regression of only Data collected during this feedyard-year were limited because of sparse data early in the year, with only 7 mo from August through February accepted for analysis. Given that, we would still expect to see a greater range in PCER than was observed. Winter were elevated, averaging 89 g animal 1 d 1, and were the same as those of the following spring, which averaged 88 g animal 1 d 1. In spite of these anomalous results, nothing in the data justified deleting these higher than expected winter Fig. 2. Mean monthly per capita emission (PCER) as a function of temperature (T) modeled using the analog Arrhenius equation for Feedyard A (FYA) and Feedyard E (FYE) in 2007 and emission rates, so we chose to retain the FYE 2007 data and use the full combined data set for further analysis. There was no difference (P = 0.92) in PCER between FYA and FYE in 2007, but PCER was greater at FYA than FYE in 2008 (P < 0.001). Per capita at FYA were significantly greater (P < 0.01) in 2008 than in In March of 2008, FYA began to substitute wet distillers grains (WDG) for corn (Zea mays L.) in cattle diets, increasing the CP content of the rations fed to the cattle. The optimum CP for finishing cattle diets ranges from 12.5 to 13.5%. Crude protein peaked in August, September, and October of 2008 at more than 18%, when WDG comprised about 40% of the rations, and emission similarly peaked during those months, averaging 213 g animal 1 d 1. Recognizing the effect of CP on PCER, we added it as an independent variable in the Arrhenius analysis. All feedyard-years were combined and linear models fitted that modeled ln(pcer) as a function of either T [the f(t) model] or as a function of T and CP [the f(t,cp) model]. Slightly higher fit criteria (AIC and BIC) suggested that adding CP to the Arrhenius analog model did not improve the model (Table 2). Because the CP effect was real, however, we desired to further test the effectiveness of the two models to predict using data from a feedyard independent from the two used to develop the models. Ammonia Emission Predictions at an Independent Feedyard The f(t) and f(t,cp) equations from Table 2, developed using data from FYA and FYE, were used to predict at the third feedyard, FYC. Dietary CP was 14.0% during the first two campaigns (Table 3). Then, in the spring of 2003, corn gluten feed, a wet milling byproduct, replaced some corn in the rations. This increased the CP to as high as 17.5% by winter 2004 Table 1. Linear regression coefficients, coefficients of determination, and standard errors of regression for the analog Arrhenius equation model: ln(pcer) = a + b(1/t). Variables are monthly mean per capita emission rate (PCER, g animal 1 d 1 ) and air temperature (T, K). Feedyard Year n a b adjusted r 2 RMSE A E Journal of Environmental Quality

4 Table 2. Regression coefficients and model fit criteria for the models ln(pcer) = a + b(1/t) and ln(pcer) = a + b(1/t) + c(cp). Variables are monthly mean per capita emission rate (PCER, g animal 1 d 1 ), air temperature (T, K) and diet crude protein (CP, % dry matter basis). Model a b c AIC BIC ln(pcer) = a + b(1/t) ln(pcer) = a + b(1/t) + c(cp) Akaike s information criterion. Schwarz s Baysian criterion. Table 3. Dry matter intake, feed N intake, and crude protein at Feedyard C from 2002 to 2005 (data are from Todd et al. [2008] and previously unpublished data). Campaign month and year Dry matter intake Feed N intake Crude protein g animal 1 d 1 % Aug Jan July Feb July Apr June and provided us with a range of CP to test the predictive power of the f(t,cp) model at FYC. The f(t) model tended to underpredict, showing a negative bias and a slope close to unity, while the f(t,cp) model had a smaller positive bias and tended to approach the 1:1 line of complete agreement more closely (Fig. 3). The mean average error, root mean square difference, and index of agreement were similar for both models (Table 4). The f(t,cp) model preserved the observed mean (126 g animal 1 d 1 ) better than the f(t) model; the f(t,cp) prediction averaged 129 g animal 1 d 1 and the f(t) prediction averaged 115 g animal 1 d 1. The means of both models were within ±9% of the observed mean. Predicted monthly using the f(t) model ranged from 35 to 4% of observed, while the f(t,cp) predictions ranged from 7.1 to 15.6% of the observed monthly. The f(t,cp) model overpredicted emission the most during July 2003 and February These two campaigns followed the inclusion of corn gluten feed and the subsequent increase in ration CP and had the greatest CP concentrations, 16.7 and 17.5%, respectively. It s possible that CP was overestimated during these two campaigns because the CP concentration stabilized at 14.5 to 15.5% in the following campaigns, nearer to the concentration we expected with the feeding of corn gluten feed. Fig. 3. Comparisons of observed mean monthly per capita emission (PCER) at Feedyard C, with PCER predicted using either the f(t) model (solid circle and line) using only temperature (T) or the f(t,cp) model (open circle and dashed line) with crude protein (CP) added. The 1:1 line indicates agreement between observed and predicted values. An advantage of the f(t) model is that air temperature is easy to measure and has low uncertainty. Crude protein, on the other hand, is subject to sampling errors; for example, are samples collected for N analysis representative of feedyard rations? In spite of this, Fig. 3 and 4 strongly suggest that including CP in the model improved emission predictions even though objective criteria suggested that the models were similar in their effectiveness of prediction. We wanted to explore a practical application of the two empirical models: how well will they predict annual required for an annual emission inventory? We calculated the mean annual at FYC for 2 yr (2003 and 2004) using four methods: the annual production-based emission factor (EF) developed at FYC and reported in Todd et al. (2008), one-time capacity emission factors based on the f(t) and f(t,cp) models, and the emission factor recommended by Faulkner and Shaw (2008) based on a literature review of beef cattle emission factors. The mean annual emission calculated from measurements (average of two summer and two winter campaigns) during the 2-yr period was 1999 Mg yr 1. Ammonia emission predicted by the production-based EF (1967 Mg yr 1 ) closely matched the observed emission, as expected, because it was derived from much of the same measured data (Table 5). The f(t) model EF underestimated the mean annual emission by 11% and the f(t,cp) model overestimated by 8%. The EF that Faulkner and Shaw (2008) recommended greatly underestimated the Table 4. Regression, univariate, and comparison statistics for the comparison of observed and predicted mean monthly per capita (PCER) at Feedyard C for 7 mo for the predictive models f(t), which uses only temperature (T) and f(t,cp), which also uses crude protein (CP). The mean observed per capita emission rate was 126 g animal 1 d 1 (comparison statistics are from Willmott, 1982, 1984). Predictive model n Intercept Slope r 2 Mean SD MBE MAE RMSD IA PCER = f(t) PCER = f(t,cp) Mean bias error. Mean average error. Root mean square difference. Index of agreement

5 mean annual emission by 70%. For southern High Plains feedyards, the experimentally determined EFs are far more accurate and applicable than the literature-derived EF reported by Faulkner and Shaw (2008). Predicting Ammonia Emissions Using General Inputs We were also interested in testing the performance of the f(t) and f(t,cp) models using more general input data. For example, what if temperature at a feedyard wasn t measured and the actual concentration of CP wasn t known? We acquired long-term mean monthly air temperature data ( ) from the airport at Hereford, TX, the county seat of Deaf Smith County. We defined three classes of dietary CP: low with a nominal CP of 11%, optimum with a CP of 13.5%, and high with a CP of 16%. The observed for the low CP class were taken from FYE in 2008, the observed for the optimum CP class were from FYA and FYE in 2007, and the observed for the high CP class was from FYA in The f(t) model predicted a mean annual emission (average of predicted monthly ) of 37.6 kg animal 1 yr 1 (Table 6). This prediction overestimated the low CP case by 14% and underestimated the optimum and high CP cases by 1.3 and 39%, respectively. In contrast, the f(t,cp) model underpredicted by 15, 4, and 23% for the low, optimum, and high CP classes, respectively. This was not a completely independent test because some of the data in the observed had been used to develop the empirical equations, but it suggests a robustness in predictions when regional temperature and a qualitative estimate of dietary CP can yield reasonable estimates of a feedyard s emission. Although can be modeled using T only, in the case where cattle are fed diets with optimum CP, including CP in the Arrhenius model improved predictions. The ability of the temperature crude protein model to predict is encouraging, considering that even careful measurements of at the whole-farm scale probably have a measurement uncertainty of 10 to 20%. We reiterate that the equations and coefficients in Table 2 are empirical. We are confident that they can be used to reasonably model, for example for regulatory reporting requirements or for emission inventories, in the Texas Panhandle of the southern High Plains. We caution against extending the coefficients to other regions with different temperature regimes or feeding practices. For example, losses as a fraction of N intake are similar when Texas and Nebraska studies are compared (Sakirkin et al., 2011; Todd et al., 2008), but the annual temperature pattern in Nebraska is different from Fig. 4. Mean monthly per capita emission rate observed at Feedyard C and predicted using either the f(t) model using only temperature (T) or the f(t,cp) model with crude protein (CP) added. Note that July has one set of bars from 2003 (Jul1) and one set of bars from 2004 (Jul2) and that the months are not chronological. Texas. Using mean monthly temperature data from North Platte, NE, and Amarillo, TX, and the f(t,cp) equation, we found that predicted annual emission was 9% less at North Platte than Amarillo. Unanswered is the effect that other factors could have on. For example, colder northern winters could reduce or even suppress emission, and the buildup of NH 4 + in frozen feedyards could be suddenly released with spring thaw, a situation not normally experienced on the southern High Plains. Warmer summers and greater evaporative demand on the southern High Plains generally result in drier feedyard conditions compared with northern feedyards, and this dryness could impact the warm-season pattern of loss. Rations on the Texas High Plains are generally based on steam-flaked corn, while those in Nebraska tend to feature dry-rolled corn. This difference impacts the digestibility of the feed, which can affect N excretion and subsequent volatilization, especially with high CP diets that include distillers grains. Considering these points, we strongly recommend that Eq. [3] and [4] be fitted in diverse regions and production practices to determine regionspecific coefficients and to test their applicability. The best approach to predicting from beef cattle feedyards will be the application of process models. These models should be widely applicable because they are based on mathematical descriptions of the chemical and physical processes that actually control volatilization. We encourage their further development and testing with reliable data sets of experimentally determined. Until Table 5. Annual emission predictions at Feedyard C using an annual production-based emission factor (Todd et al., 2008) and one-time capacity emission factors based on either a temperature model [f(t)], a temperature crude protein model [f(t,cp)], or an emission factor derived from a literature review (Faulkner and Shaw, 2008). Annual calculated from measurements during the 2-yr period (2003 and 2004) averaged 1999 Mg yr 1. Method Model Animal population Emission factor Predicted emission no. kg head 1 yr 1 Mg yr 1 Annual production Todd et al. (2008) 100, One-time capacity f(t) 45, One-time capacity f(t,cp) 45, One-time capacity Faulkner and Shaw (2008) 45, Assumes a mean population of 45,648 animals, 165 d on feed, and 2.21 population turnovers per year. Table Journal of Environmental Quality

6 Table 6. Observed mean annual per capita emission rates (PCER) and PCER predicted using Hereford, TX, 1971 to 2000 mean monthly temperature (T) and crude protein (CP) classes as inputs into f(t) or f(t,cp) equations. Case Observed Predicted f(t) f(t,cp) kg animals 1 yr 1 Low CP (11%) Optimum CP (13.5%) High CP (16%) Feedyard E, Feedyards A and E, Feedyard A, process models are readily available, temperature and the Arrhenius equation can be used to predict monthly and annual for feedyards on the southern High Plains of Texas when cattle are fed optimum CP diets. Predictions are improved by including dietary CP in the Arrhenius equation, however, especially for cases where less than optimum or excessive CP is fed. We are confident that the Arrhenius approach used here can be successfully applied in other regions where high quality data are available, which will provide a simple predictive tool for feedyard managers, inventory compilers, and regulators. 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