lable at ScienceDirect

Atmospheric Environment 44 (2010) 3621e3629

Contents lists avai

Atmospheric Environment

journal homepage: www.elsevier .com/locate/atmosenv

Global sensitivity analysis of a process-based model for ammoniaemissions from manure storage and treatment structures

J. Arogo Ogejo a,*, R.S. Senger a, R.H. Zhang b

aBiological Systems Engineering Dept., Virginia Tech, Blacksburg VA 24061, USAbBiological & Agricultural Engineering Dept., UC Davis, USA

a r t i c l e i n f o

Article history:Received 5 January 2010Received in revised form25 June 2010Accepted 29 June 2010

Keywords:Sensitivity analysisGlobal sensitivity analysisRelative sensitivity analysisAmmonia emissionsLagoon ammoniaEmissions

* Corresponding author at: Biological Systems EngiVirginia Tech, Blacksburg, VA 24061, USA. Tel.: þ1 543199.

E-mail address: arogo@vt.edu (J.A. Ogejo).

1352-2310/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.atmosenv.2010.06.053

a b s t r a c t

The development of process-based models to estimate ammonia emissions from animal feeding oper-ations (AFOSs) is sought to replace costly and time-consuming direct measurements. Critical to process-based model development is conducting sensitivity analysis to determine the input parameters and theirinteractions that contribute most to the variance of the model output. Global and relative sensitivityanalyses were applied to a process-based model for predicting ammonia emissions from the surface ofanaerobic lagoons for treating and storing manure. The objectives were to compare global sensitivityanalysis (GSA) to relative (local) sensitivity analysis (RSA) on a process-based model for ammoniaemissions. Based on the first-order coefficient, both GSA and RSA showed the model input parameters inorder of importance in process model for ammonia emissions from lagoon surfaces were: (i) pH, (ii)lagoon liquid temperature, (iii) wind speed above the lagoon surface, and (iv) the concentration ofammoniacal nitrogen in the lagoon. The GSA revealed that interactions between model parametersaccounted for over two-thirds of the model variance, a result that cannot be achieved using traditionalRSA. Also, the GSA showed that parameter interactions involving liquid pH had more impact on themodel output variance than the single parameters: (i) temperature, (ii) wind speed, or (iii) totalammoniacal nitrogen. This study demonstrates that GSA provides a more complete analysis of modelinput parameters and their interactions on the model output compared to RSA. A comprehensive tutorialregarding the application of GSA to a process model is presented.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Ammonia (NH3) is emitted to the atmosphere from differentsources including synthetic fertilizers, biomass burning, fossil fuelcombustion, and animal manure (Krupa, 2003). Atmospheric NH3plays a role in the acidification and eutrophication of ecosystems(Erisman and Schaap, 2004; Krupa, 2003). Damage to vegetationfoliage has been observed closer to NH3 emission sources, possiblydue to NH3 deposition (Krupa, 2003). While the chemical processesinvolving NH3 in the atmosphere are complex, it is known that itreacts with sulfuric and nitric acids to produce ammonium sulfateand ammonium nitrate, which are considered secondary particu-late matter (Erisman and Schaap, 2004; Seinfeld and Pandis, 1998).Particulate matter can cause health concerns and degradation of

neering Dept., 212 Seitz Hall,0 231 6815; fax: þ1 540 231

All rights reserved.

visibility in the atmosphere (US EPA, 2009). This paper focuses onNH3 emissions from animal feeding operations (AFOs) where themajor sources of NH3 include (i) animal housing, (ii) manurecollection, (iii) treatment and storage structures, and (iv) landapplication of manure (Reidy et al., 2009).

Knowledge of the quantities of gases emitted from AFOs isneeded to make better decisions on the development of optimumand cost-effective best management practices or mitigation strat-egies to control the emissions. In this regard, the National ResearchCouncil (NRC, 2003) recommended that direct measurements ofemissions be combined with the development of process-basedmodels for estimation of emissions from AFOs. Process-basedmodels can be used in lieu of direct measurements to estimategaseous emissions fromAFOs because they are: (i) amenable for usein locations where site characteristics may present physical chal-lenges to performing direct measurements, (ii) cost effective, and(iii) flexible to use (Arogo et al., 2003; NRC, 2003).

Models for estimating NH3 emissions from lagoons and outdoormanure storage facilities have been developed (Aneja et al., 2001;Liang et al., 2002; Pinder et al., 2004; Berthiaume et al., 2005,

J.A. Ogejo et al. / Atmospheric Environment 44 (2010) 3621e36293622

2007; Ro et al., 2008). The generalized equation used in theprocess-based model for surface emission of NH3 is:

MA ¼ A� KLðCL � CaÞ (1)

where, MA is the mass release rate of NH3, kg s�1; A is the surfacearea of exposed to the atmosphere, m2; KL is the mass transfercoefficient of NH3 from liquid to air, m s�1; CL is the concentration ofNH3 in the liquid, kg m�3; and Ca is the concentration of NH3 in theair, kg m�3. The input parameters to this equation are easilymeasured or obtained at the site of the manure storage or treat-ment structure and include: (i) liquid temperature, (ii) airtemperature, (iii) liquid pH, (iv) total ammoniacal nitrogenconcentration of the manure in storage, CTAN, (v) surface area ofmanure stored, and (vi) atmospheric pressure.

Critical to process-based model development is conductingsensitivity analysis (SA) to determine the parameters that contributemost to the variance of the model output. Sensitivity analysis helpsidentify significant model parameters and their interactions and/orinsignificant ones that could be removed and not affectmodel output(Saltelli et al., 2000). Thus,whenused correctly, SA canhelpminimizethe number of measurements needed at an AFO to effectively predictNH3 emissions. Two types of SA can be performed: (i) local sensitivityanalysis (LSA) and (ii) global sensitivity analysis (GSA) (Saltelli et al.,1999; Campolongo and Saltelli, 1997). Local sensitivity analysis canbe further divided into absolute and relative sensitivity analysis(RSA). Currently, RSA is the more popular SA method used for NH3emission models from manure treatment and storage structures(Aneja et al., 2001; Liang et al., 2002; Misselbrook et al., 2004; Bajwaet al., 2006; Berthiaume et al., 2007). In RSA, the response of themodel output is obtained by varying one input parameter at a timeover a defined range, while holding the others fixed at their meanvalues as described by Eq. (2):

Sr ¼ DY=YDXi=X

(2)

where, Sr is the relative sensitivity index; DY is the change in themodel output; Y is the mean of the model output; DXi is the changein input parameter over the range being considered; and X is themean value of the input parameter being varied (Liang et al., 2002;Arogo et al., 1999; Zerihun et al., 1996).

The quantity of NH3 volatilized from liquid manure depends on(i) animal diets, (ii) liquid pH and temperature, and (iii) environ-mental factors such as air temperature and relative humidity(Ndegwa et al., 2008). Using the RSA approach, Aneja et al. (2001)considered pH, surface liquid temperature, wind speed, andlagoon CTAN concentration in their model and concluded that NH3emissions from lagoons was most sensitive to liquid temperature.The authors noted that pH and wind speed were more sensitive insome cases. Liang et al. (2002) applied RSA to their model andshowed model output was sensitive to (in order of importance) pH,liquid temperature, and wind speed. Bajwa et al. (2006) reportedthat lagoon temperature, pH, CTAN, and wind speed had significanteffects on NH3 flux but quantitative measures were not given.Berthiaume et al. (2007) used RSA to show that nitrogen fluxesfrom outdoor manure storage were sensitive to amount of proteinsin feed, pH of the manure in storage, and air velocity above themanure surface. The use of RSA to identify pertinent modelparameters in the approaches above has excluded potential inter-actions of model parameters, which are known to exist. The RSAapproach also does not explore the entire input space of parametervalues. The RSA method, although widely used, is (i) limited toa given point in space, (ii) cannot consider the entire ranges of inputparameter values, and (iii) does not explore interactions betweenparameters.

The GSA method uses Monte Carlo simulations to calculatemodel outputs based on inputs generated over the entire range ofpossible parameter values. The sensitivity of a model input is thenevaluated using a variance-based analysis method described bySaltelli et al. (2000). In the variance-based method, the sensitivityanalysis is estimated using the contribution of each input variable,Xi, to the total variance, V(Y) of the output Y. To calculate thesensitivity indices for each input variable, Xi, the decompositionproperty of the total variance is utilized as shown in Eq. (3). Thedecomposition consists of all first-, second-, and higher-ordervariances for each variable. The main advantage of GSA over thepartial derivative-based RSA is that it allows the influence andinteraction of model input parameters over their entire input rangeon the model output (Saltelli et al., 2008).

VðYÞ ¼Xi

Vi þXi<j

Vi;j þX

i<j<m

Vi;j;m þ. (3)

The objectives of this study were to (i) conduct a GSA ona process-based model for NH3 emissions from liquid manurestorage and treatment surfaces and (ii) compare the use of GSA andRSA on predicting importantmodel input parameters. Significant tothis work is that the GSA will provide a measure of the impact ofmodel parameter interactions (e.g., temperature and pH) on thevariance of the model output. Despite the fact that a considerableamount of literature has been published in recent years on themethods of GSA, the implementation of GSA can be difficult. So,a simplified tutorial for effective implementation of GSA has beenincluded in this study. Although the tutorial is based on the NH3emissions model, it provides a step-by-step guide for analyzing anymodel using GSA.

2. Procedure

2.1. Model equations for NH3 emissions

The process of NH3 volatilization from liquid manure surfaces isgenerally described by Eq. (1) based on the two-film theoryproposed by Whitman (1923). The two-film theory assumes thata stagnant fluid layer comprised of two films is formed at theinterface of the two fluids in contact. The two stagnant filmsprovide resistance to the transfer of matter between the two fluids.The pertinent equations used in the model for NH3 volatilization inthis study are presented in Table 1 were developed by Zhang et al.(2005) and briefly described below.

2.1.1. Overall mass transfer coefficient (kL)The over all mass transfer coefficient (kL) was calculated using

the resistance to the transfer of NH3 by the stagnant gas and liquidlayers, kG and kL, respectively, and Henry’s constant,H. The stagnantgas layer resistance (kG) is a function of the: (i) wind velocity 8 mabove the liquid surface (U8), (ii) diffusivity of NH3 in air ðDair;NH3

Þ,and (iii) diffusivity of water vapor in air ðDair;H2OÞ. The stagnantliquid layer resistance (kL) is a function of the: (i) U8, (ii) diffusivityof NH3 in water DH2O;NH3

, (iii) and diffusivity of oxygen in water(DH2O;O2

). Henry’s constant (H) is expressed as a function of theliquid temperature (TLiquid).

2.1.2. Concentration of NH3 in the liquid (CL) and NH3 in air (CA)The concentration of NH3 in the liquid (CL) is expressed as

a fraction, F , of total ammonium nitrogen (CTAN) in solution. Thefraction, F, is a function of the liquid pH. The concentration of NH3 inthe air (CA) is the measured ambient NH3 concentration. Thebackground ambient ammonia concentration in the SoutheasternUnites States where data used in this study were derived have been

Table 1Pertinent equations used in the storage emissions model.

Parameter Symbol Units Equation

Ammonia emission rate MA kg s�1 MA ¼ A � KL(CL�Ca)

Overall mass transfer coefficient KL m s�1 1KL

¼ 1kL

þ 1HkG

Henry’s constant H e2:395� 105

Tliquid þ 273:15e

��4151

Tliquidþ273:15

�

Mass transfer coefficient in the gas phase kG m s�1 ð5:167� 10�5 þ 1:955� 10�3U8ÞhDair;NH3Dair;H2O

i0:67

Mass transfer coefficient in the liquid phase kL m s�1 ð1:676� 10�6e0:236U8ÞhDH2O;NH3DH2O;O2

i0:57

Dissociation constant for ammonia Kd e 10��0:0897þ 2729

Tliquidþ273:15

�

Fraction of free ammonia F e KdKdþ10�pH

Diffusivity of ammonia in air Dair;NH3m2 s�1 3:056�10�8T1:75

air26:829�P

Diffusivity of NH3 in water DH2O;NH3m2 s�1 7:282�10�15Tliquid

e

�1622

Tliquid�12:406

�

Diffusivity of water vapor in air Dair;H2O m2 s�1 3:003�10�8T1:75air

25:523�P

Diffusivity of oxygen in water DH2O;O2m2 s�1 6:145�10�15Tliquid

e

�1622

Tliquid�12:406

�

Temperature of the air Tair �C Tliquidþ2:90:86

CTAN(aq) e Total ammonium (NH3 þ NH4þ) nitrogen in the manure storage, CNH3ðairÞe Concentration of NH3 in the atmosphere or air above the liquid in storage.

Table 2Input parameters.

Parameter Range

Liquid temperature (Tliquid), �C 5e35TAN (CTAN), kg m�3 0e0.6Ambient ammonia concentration (CA), kg m�3 0e2.0 � 10�5

Lagoon pH 6.5e8.5Wind speed (U8), m s�1 0e15Atmospheric pressure (P), atm 0.876e1.025Bottom width (BW), m 15e120Bottom length (BL), m 15e120Side slope (Z) 1.5e3Depth above minimum treatment volume (d), m 0e5.8

J.A. Ogejo et al. / Atmospheric Environment 44 (2010) 3621e3629 3623

reported to range from 0 to 20 mg m�3 (Harper et al., 2004a,b).Given the presence of mass transfer boundary layers, the value of CAwas varied, and the GSA was repeated. No differences in the finalresults were observed (data not shown), so, CA was assumed to bezero in this study.

2.1.3. Surface area (A)The surface area (A) of the liquid containment depends on the

geometry of the structure. For lagoons, it is a function of the bottomlength (BL) and bottomwidth (BW), the side slope (Z), the depth ofliquid above minimum treatment volume (d) and the volume ofaccumulated sludge (MWPS, 1993). Thus, the surface area of thelagoon was calculated by the following relationship.

A ¼ ðBL þ 2ZdÞ � ðBWþ 2ZdÞ (4)

2.2. Input parameters

The input parameters to the model were: (i) ambient airtemperature (Tair), (ii) lagoon TAN concentration (CTAN), (iii) lagoonliquid pH (pH), (iv) wind velocity 8m above the lagoon surface (U8),(v) atmospheric pressure (P), (vi) lagoon bottom width (BW), (vii)lagoon bottom length (BL), (viii) lagoon side slope (Z), and (ix) thedepth of liquid above the minimum treatment volume and sludgevolume (d). The hourly average weather data for the years2001e2008 were obtained from State Climate Office of North Car-olina (personal communication, state weather office, Raleigh NorthCarolina) and were used to determine the range of air temperature,wind speeds, and atmospheric pressure to use in the model. Theranges of values of the input parameters are in Table 2.

2.3. Global sensitivity analysis

Global sensitivity analysis was performed according to pub-lished methods and protocols (Saltelli et al., 2008, 2004) to assessthe importance and investigate interactions of model inputparameters. Briefly, the sensitivity coefficient, Sx, of a parameter x inGSA is calculated as follows:

Sx ¼ vðEðyjxÞÞVy

(5)

where Vy is the variance of the model output, y, over NMonte Carlosimulations. The numerator is the variance of the expected value ofy given a constant x. For the analysis to be independent of the valueof x, the above relationship was taken over all values of x andaveraged. Similarly, the second-order sensitivity index whichdescribes interaction of two model parameters on the modeloutput was calculated using Eq (6).

Sx;y ¼ VðEðyjx; zÞÞVy

� VðEðyjxÞÞVy

� VðEðyjzÞÞVy

(6)

Finally, the total effect index of a model parameter is described asthe summation of all sensitivity indices containing the modelparameter of interest. This includes the first-order sensitivitycoefficient and all multi-dimensional sensitivity indices (e.g.,second-, third-, fourth-order terms, etc.) containing the parameter.Obtaining an accurate representation of the VðEðyjxÞÞ term over allvalues of x is not trivial.

The “sample” and “re-sample” matrices approach to GSA wasused to calculate the first- and second-order sensitivity coefficientsfor the model parameters: (i) Tliquid, (ii) CTAN, (iii) pH, (iv) U8, and (v)P. These were also calculated for the lagoon geometry-relatedparameters: (vi) BW, (vii) BL, (viii) Z, and (ix) d. The model

J.A. Ogejo et al. / Atmospheric Environment 44 (2010) 3621e36293624

parameters examined are not all independent. For example: pH isa function of Tliquid, P is a function of Tair; and the available fractionof CTAN that can be volatilized is a function of pH. In GSA, for non-independent input parameters (e.g., pH), the first-order sensitivitycoefficient represents the amount of (output) variance caused bypH changes only. The variance from the temperature dependence ofpH shows up in the second-order coefficient that contains both pHand Tliquid. This is the significant strength of GSA over RSA (Saltelliet al., 2008, 2004). Relative sensitivity analysis can only assess thefirst-order impact of inputs on the model output variance.

The GSA was performed for the three cases involving thecalculation of: (i) total NH3 emission rates (MA) with the lagoonsurface area calculated by Eq. (4), (ii) the NH3 emissions flux (JA),and (iii) MA with a specified surface area. In case (i), sensitivitycoefficients were calculated for all lagoon geometry-relatedparameters; however, in case (iii), these were all lumped togetheras a single total surface area (Atotal) parameter. This method allowedfor the direct calculation of first- and second-order sensitivityindices for each of the model input parameters listed in Table 2.Sample calculations are presented in Figs. 1e4 to serve as a tutorialfor applying GSA using the “sample” and “re-sample” matricesapproach. We found this method the most effective for performinga GSA on the NH3 emissions model of this research; however, thismethod will apply for any model.

The first step of the GSA procedure is shown in Fig. 1. Twomatrices, M1 (the “sample” matrix) and M2 (the “re-sample”matrix), are created. Each column of these matrices is dedicatedto a model parameter. The number of rows of these matricescorresponds to the number of simulations performed (N). For theNH3 emissions simulations N was set to 100,000. The elements ofeach column in M1 and M2 are filled in with uniformly distributedvalues generated randomly within the upper- and lower-limits(Table 2) of that parameter. We also tested normally distributedrandom values and found no change in the results (data not

Fig. 1. Creation of the “sample” and “re-sample” matrices for global sensitivity analysis bunconditional means and variances are calculated from these data as shown.

shown). Each row of both matrices is used to simulate the model.The resulting NH3 emission rates (MA) were stored in the outputvectors Y1 and Y2. The estimated unconditional meansðbEY1

and bEY2Þ of MA values from Y1 and Y1 were calculated and

used in the calculation of the estimated unconditional variancesðbVY1

and bVY2Þ shown in Fig. 1.

An example for the use of these unconditional means andvariances of the “sample” and “re-sample” matrices to calculatea first-order sensitivity coefficient is shown in Fig. 2 for the modelparameter, Tliquid. First, a new matrix (P) was created from M1 andM1. The P matrix contains the values from the “sample” matrix forthe model parameter for which the first-order SA is being per-formed. All other columns in P were taken from the “re-sample”matrix. The rows of this new matrix P were then used as modelinputs, the model was simulated N times, and the results werestored in a new vector, Yp. The vectors Y1 and Yp were then used tocalculate the variable Up, shown in Fig. 2. Then, Up, bEY1

, bEY2, and bVY2

were used to calculate the first-order sensitivity coefficient, shownin Fig. 2 for Tliquid ðSTL Þ.

An example for the calculation of the second-order (i.e., inter-action) sensitivity coefficient between Tliquid and pH for the NH3

emissions model is given in Fig. 3. Here, another new matrix Q wascreated and contains parameter values from the “sample” matrix(M1) for model parameters being used to calculate a second-ordersensitivity coefficient. All other columns of Q contain values fromthe “re-sample”matrix (M2). Rows of this newmatrix (Q) were usedto run model simulations and outputs were stored in the YQ vector.The Y1 and YQ vectors were used to calculate UQ (see Fig. 2). Finally,the second-order sensitivity coefficient was calculated from UQ, bEY1

,bEY2, and bVY1

, and the first-order sensitivity coefficients of theparameters being considered for the second-order calculation.Calculation of the second-order sensitivity coefficient for Tliquid andpH ðSTL ;pHÞ from the “sample” and “re-sample” matrices is shownin Fig. 3.

ased on limits of input parameters and calculation of model outputs. The estimated

Fig. 2. Creation of the P matrix from M1 and M2 and calculation of the first-order sensitivity coefficient. This example is based on the Tliquid.

J.A. Ogejo et al. / Atmospheric Environment 44 (2010) 3621e3629 3625

The final calculation of the GSA is that of the total effect index.Conceptually, the total effect index can be thought of as the sum ofthe first-order and all second- and higher-order sensitivity coeffi-cients containing a parameter of interest. An example computed forTliquid in the NH3 emissionsmodel is presented in Fig. 4. Here, a finalnew matrix R is created. This matrix contains values from the “re-sample” matrix (M2) for the parameter of interest. All otherparameters contain values from the “sample” matrix (M1). Modelsimulations with the rows of R produce outputs that are stored inthe YR vector. Again, the UR variable is calculated from Y1 and YR,and the total effect index is calculated from UR, bEY1

, and bVY1. The

total effect index for Tliquid ðSTðTLÞÞ is calculated from the “sample”and “re-sample” matrices in Fig. 4.

For the calculations in this study, a total of 100,000 simulations(N ¼ 100,000) were used. The first-order sensitivity coefficientswere calculated for all model parameters. Then, second-ordersensitivity coefficients were calculated for all combinations of

Fig. 3. Creation of the Qmatrix fromM1 andM2, using the Tliquid as an example. This enablesThese calculations are repeated for all possible variable interactions. This method is also us

model parameters. Finally, the total effect index was calculated forevery model parameter using these methods. The completeanalysis was repeated 20 times, and results were averaged. Thestandard deviations of SA results were calculated. All GSA arereported as the average of these 20 replicates (�1 standarddeviation).

As shown in Eq. (1), the model implies a direct correlationbetween the rate of NH3 emission and the surface area of thelagoon. We have interests in determining (i) whether the geometryof the lagoon is important in determining NH3 emission rates and(ii) which lagoon liquid and environmental parameters areimportant in determining NH3 emissions per unit surface area. Toassess these, we performed the GSA twice. In the first set ofsimulations, the model output was set to be the total NH3 massrelease rate, MA. This allowed investigation of lagoon geometry. Inthe second set of simulations, the model output was set to be theNH3 emissions flux, _MA.

calculation of the second-order interaction coefficient between Tliquid and pH as shown.ed to calculate higher-order interactions between three or more variables.

Fig. 4. Creation of the R matrix from M1 and M2, using the Tliquid as an example. This matrix is used to produce model outputs used to calculate the total effect index for eachparameter.

Table 3First- and second-order sensitivity coefficients of model parameters calculated usinga global sensitivity analysis.

Parameter Case I: SensitivityCoefficient (Si or Sij)for MA

Case II: SensitivityCoefficient (Si or Sij)for JA

Case III: SensitivityCoefficient (Si or Sij)for MA (Total Area)

First-Order CoefficientspH 0.147 0.206 0.154Tliquid 0.0693 0.0940 0.0719U8 0.0590 0.0876 0.0634CTAN 0.0418 0.0563 0.0440BL 0.0162 0 0BW 0.0160 0 0d 0.00510 0 0P 0 0 0Z 0 0 0ATotal e e 0.0385Total 0.355 0.447 0.367

Second-Order Coefficientsa

Tliquid$pH 0.0778 0.114 0.0861pH$U8 0.0689 0.103 0.0790CTAN$pH 0.0492 0.0630 0.0557Tliquid$U8 0.0373 0.0532 0.0396CTAN$U8 0.0246 0.0282 0.0227pH$BL 0.0219 0 e

pH$BW 0.0210 0 e

Tliquid$CTAN 0.0196 0.0309 0.0233Tliquid$BL 0.0106 0 e

Tliquid$BW 0.0103 0 e

Tliquid$ATotal e e 0.0214CTAN$ATotal e e 0.0161pH$ATotal e e 0.0488U8$ATotal e e 0.0243Total 0.378 0.377 0.454

Higher-Order CoefficientsTotal 0.267 0.176 0.179

This analysis assumed total ammoniacal nitrogen content of the air (Cair) of 0mg L�1.a A total of 45 s-order coefficients were calculated for each column. Only those

coefficients with a value greater than 0.01 in any simulation are reported here. Allother second-order coefficients are close to zero.

J.A. Ogejo et al. / Atmospheric Environment 44 (2010) 3621e36293626

2.4. Relative sensitivity analysis

The RSA was performed using the following parameters: (i)liquid temperature (Tliquid), (ii) TAN concentration (CTAN), (iii) pH ofthe lagoon, and (iv) The wind speed 8 m above the surface (U8). Therelative sensitivity values were calculated using Eq. (7) described byZerihun et al. (1996).

Sr ¼ DJA=JADX=X

(7)

where, Sr is the relative sensitivity coefficient; JA is the NH3 emis-sions flux; DJA is the change in NH3 emissions flux; X is the meanvalue of the input parameter; and DX is the change in the inputparameter over the range being considered.

The RSA result represents the percent change in NH3 flux perunit percent change in the input parameter over the range beingconsidered. For each input parameter, the relative sensitivity wascalculated for specified ranges while keeping all other parametersconstant at their mean values. The range of input parameter valuesare presented in Table 2 and the mean values of the input factorsused were: Tliquid ¼ 20 �C, (ii) CTAN ¼ 0.456 kg m�3, (iii) pH ¼ 7.8,and (iv) U8 ¼ 3.6 m s�1. The RSA considers only the first-ordercomponents of model input parameters.

3. Results

3.1. Global sensitivity analysis

The GSA results are listed in Table 3. The summation of all first-and higher-order sensitivity coefficients is equal to 1 by definition(Saltelli et al., 2008, 2004). For case (I), only the atmosphericpressure (P) and the side slope (Z) returned first-order sensitivitycoefficients of zero. These two parameters have first-order coeffi-cients of zero for all three cases. As expected, the lagoon geometryfirst-order coefficients were zero for cases (II) and (III). Thesummation of the first-order coefficients related to lagoon geom-etry is 0.0373 in case (I). When all lagoon geometry parameterswere lumped into the Atotal parameter (case (III)), the first-ordercoefficient was 0.0385. The pH returned the highest first-ordersensitivity coefficient, followed by (in order) Tliquid, U8, and CTAN, for

all three cases. The summation of the first-order coefficients were0.355, 0.447, and 0.367 for cases (I), (II), and (III), respectively. Thismeans that 35.5%, 44.7%, and 36.7% of the variance of the modeloutput can be explained by individual model parameters for these

Table 4Total effect indices of model parameters.

Parameter Case I: Total EffectIndex ðSTJ Þ for MA

Case II: Total EffectIndex ðSTJ Þ for JA

Case III: Total EffectIndex ðSTJ Þfor MA

(Total Area)

pH 0.593 0.627 0.598Tliquid 0.405 0.424 0.379U8 0.376 0.402 0.365CTAN 0.277 0.286 0.267BW 0.140 0 e

BL 0.131 0 e

d 0.040 0 e

P 0 0 0Z 0 0 e

ATotal e e 0.260

J.A. Ogejo et al. / Atmospheric Environment 44 (2010) 3621e3629 3627

cases. The remaining variance must be explained by parameterinteractions.

The first-order influence of each model parameter is illustratedin Fig. 5. Here, the results of stochastic model simulations(N ¼ 100,000) were plotted against the input values of each modelparameter, individually. Parameters with a higher first-ordersensitivity coefficient have higher-ordered data sets, with largervalues of the model output corresponding with higher values of themodel parameter itself. This is a simple method to visualize theimpact of the calculated first-order sensitivity coefficients. Second-order coefficients are presented in Table 3. Only those with a valuegreater than 0.01 (in at least one case) are listed in Table 3. Theinteraction of Tliquid with pH produced the highest second-ordersensitivity coefficient in all three cases. This reveals a possiblysignificant interaction between these two model parameters. Themodel parameter pH also showed an elevated interactionwithU8 inall three cases. Over 37% of model output variance could beexplained by second-order model parameter interactions for allthree cases (with >45% for case (III)). This leaves 18% (over 26% forcase (I)) attributed to higher-order interactions of model parame-ters. These are interactions of three or more parameters.

The total effect index defined as the summation of all first- andhigher-order sensitivity measures that contain a particular modelparameter are presented in Table 4. Because higher-order sensi-tivity measures count for multiple model parameters when calcu-lating the total effect index, the summation of all total effect indicesis greater than one, when higher-order indices are non-zero. Asshown in Table 4, pH is the most sensitive model parameter fol-lowed by Tliquid and U8. The total effect indices for these parametersare greater than that of Atotal. This suggests that liquid and envi-ronmental parameters have more influence in determining totalNH3 emissions from a lagoon than the surface area of the lagoon. Of

Fig. 5. Plots of MA as a function of all parameter values for case (I). Significant order is ob

course, this is only true for the range of area values considered bythis study.

3.2. Relative sensitivity analysis

The RSA results are presented in Fig. 6. In general, the sensitivityofthe model output increased with increasing absolute values of therelative sensitivity index. The relative sensitivities ranged from 15.3to 17.9, 0.3 to 2.7, and 0.75 to 1.54 for pH, Tliquid, and U8, respectively(Fig. 6a,b,c). The relative sensitivity for CTANwas constant at a value of1.0 (Fig. 6d). The constant sensitivity index for CTAN implies that NH3emission is directly proportional to the CTAN concentration (constantslope). The order of importance of model parameters as predicted byRSA are: (i) pH, (ii) Tliquid, (iii) U8 and (iv) CTAN$RSA showed that CTANmay be an important parameter compared to Tliquid and U8 attemperatures below 10 �C and wind velocity below 3 m s�1.

served for all parameters with a first-order sensitivity coefficient greater than zero.

Fig. 6. Relative sensitivity analysis for the effect of pH, Tliquid, wind speed (U8), and total ammonia concentration (CTAN) on the ammonia emissions from a lagoon estimated by themodel.

J.A. Ogejo et al. / Atmospheric Environment 44 (2010) 3621e36293628

4. Discussion

A comparison of results for GSA (Tables 3 and 4) and RSA (Fig. 6)reveal the same order of importance of the parameters used in themodel as: (i) pH, (ii) Tliquid, (iii) U8, and (iv) CTAN in the lagoon.Additionally, GSA shows that the second-order coefficients can bemore important than some first-order coefficients, an aspect notcaptured by RSA. In our case, GSA shows the interaction betweenpH and Tliquid was more important than Tliquid alone (Table 3). Thisalso confirms the dependence of pH onTliquid. The GSA also suggeststhat attention should be paid to the interaction between pH and U8,rather than U8 alone. Previous studies using RSA have reportedmixed results on what was the most sensitive model inputparameter for ammonia emissions from lagoons. It is suspected thatparameter interactions may account for the significant modeloutput variance that has led to conflicting results obtained from theprevious studies that used RSA only.

The GSA approach shows that about two-thirds of the modeloutput variance is determined by second- and higher-order modelparameter interactions. This effect would be missed by thecommonly used RSA methods. Thus, first-order sensitivity coef-ficients, like those returned from local sensitivity analyses, inad-equately represents model output variation with changes ininputs. The first- and second-order measures of sensitivity ofmodel parameters P and Z were zero. This provides considerableevidence that the atmospheric pressure (P) and the lagoon sideslope (Z) parameters are insignificant compared to other modelparameters. From the total effect indices using GSA, it is apparentthat the model is not dominated by a single parameter as sug-gested by RSA, where the sensitivity index for pH was an order ofmagnitude higher than other parameters. For both GSA and RSA,the pH of the system was found to be the most influential modelparameter on the prediction of NH3 volatilization. Secondly, GSAshows that the factors that impact the interaction between thelagoon liquid pH and temperature are of importance compared to

liquid temperature alone. Methods that could possibly controla temperature and wind velocity interaction should then beconsidered.

The CTAN was the least sensitive model parameter compared toTliquid, pH, and U8. The total effect index of CTAN was approximately46% of the value for pH. Global sensitivity analysis results suggestthat even for high values of CTAN, theMA or JA is controllable throughthe manipulation of other system parameters, particularly pH.However, it is most likely a combination of system parameters (e.g.,Tliquid and pH) that may be used to manipulate the system orexplain system variance, as the summation of the higher-ordersensitivity measures is greater than that for the first-order coeffi-cients. Although RSA predicted similar ranking of input parametersbased on the first-order sensitivity coefficients, the fatal limitationof RSA (and all derivative-based sensitivity analysis methods) is incases where the input parameters are uncertain and have unknownlinearity (Saltelli et al., 2008). In this study, the wind velocity andtemperature are examples of parameters which may not be certain.The derivative-basedmethods provide information valid only at thebase point for which they are computed and are only good for linearsystems where extrapolation from the points of computation ispossible (Saltelli et al., 2008).

Ammonia emissions can be mitigated by (i) the changing thenitrogen content in animal diets, (ii) implementation of processesthat use biological principles to convert ammonia to other nitrogenforms that are non-volatile, (iii) chemical processes that react withammonia to produce non-volatile forms, and (iv) physical methodsthat bind ammonia (Ndegwa et al., 2008). Thus, if one was tochoose from the several strategies to control ammonia emissions,sensitivity analysis results could be used to target technologies thatmanage input parameters the model output is most sensitive. Ourresults suggest that the management of the liquid pH is of theutmost importance compared to CTAN. Also, significant reductionsin ammonia emissions will be observed with implementation oftechnologies that can control both pH and Tliquid.

J.A. Ogejo et al. / Atmospheric Environment 44 (2010) 3621e3629 3629

5. Conclusions

SA allows identification of significant model parameters andelimination of model parameters that have little impact on modeloutput variance. Further, calculation of higher-order coefficientsidentifies critical model parameter interactions. When applied tothe estimation of ammonia emissions from lagoons, sensitivityanalysis can minimize the number of measurements needed toestimate ammonia emissions/inventory from animal feedingoperations. Currently, RSA is the most commonly used method forprocess-based models. We have demonstrated that:

(i) GSA provides a complete understanding of model inputparameters and their interactions on the model output vari-ance compared to RSA,

(ii) some higher-order coefficients (parameter interactions)calculated using GSA, may contribute more to model outputvariance than some individual parameters, and

(iii) although GSA and RSA ranked model parameters with thesame order of importance for the case presented here, onlyGSA accounted for 100% of the model output variance.

Thus, GSA is much more ideal for the development of process-based models and design of emissions control and mitigationstrategies.

Acknowledgements

This study was part of a project supported by National ResearchInitiative Competitive Grant no. 2006-35112-16677 from the USDACooperative State Research, Education, and Extension Service AirQuality.

References

Aneja, V.P., Malik, B.P., Tong, Q., Kang, D., Overton, J.H., 2001. Measurement andmodeling of ammonia emission at waste treatment lagoon-atmospheric inter-face. Water, Air, and Soil Pollution 1, 177e188.

Arogo, J., Zhang, R.H., Riskowski, G.L., Christianson, L.L., Day, D.L., 1999. Masstransfer coefficient of ammonia in liquid swine manure and aqueous solutions.Journal of Agricultural Engineering Research 73 (1), 77e86.

Arogo, J., Westerman, P.W., Heber, A.J., 2003. A review of ammonia emissions fromconfined swine feeding operations. Transactions of the ASAE 46 (3), 805e817.

Bajwa, K.S., Aneja, V.P., Arya, S.P., 2006. Measurement and estimation of ammoniaemissions from lagooneatmosphere interface using a coupled mass transferand chemical reactions model, and equilibrium model. Atmospheric Environ-ment 40, S275eS286.

Berthiaume, P., Bigras-Poulin, M., Rousseau, A.N., 2005. Dynamic simulation ofnitrogen fluxes in pig housing and outdoor storage facilities. Biosystems Engi-neering 92 (4), 453e467.

Berthiaume, P., Bigras-Poulin, M., Rousseau, A.N., 2007. Sensitivity analysis andapplication of a dynamic simulation of nitrogen fluxes in pig housing andoutdoor storage facilities. Biosystems Engineering 96 (4), 455e470.

Campolongo, F., Saltelli, A., 1997. Sensitivity analysis of an environmental model, anapplication of different analysis methods. Reliability Engineering and SystemSafety 57, 49e69.

Erisman, J.W., Schaap, M., 2004. The need for ammonia abatement with respect tosecondary PM reductions in Europe. Environmental Pollution 129 (1),159e163.

Harper, L.A., Sharpe, R.R., Simmons, J.D., 2004a. Ammonia emissions from swinehouses in the Southeastern United Stae. Journal of Environmental Quality 33,449e457.

Harper, L.A., Sharpe, R.R., Parkin, T.B., De Visscher, A., van Cleemput, O., Byers, F.M.,2004b. Nitrogen cycling through swine production systems: ammonia, dini-trogen, and nitrous oxide emissions. Journal of Environmental Quality 33,1189e1201.

Krupa, S.V., 2003. Effects of atmospheric ammonia (NH3) on terrestrial vegetation:a review. Environmental Pollution 124 (2), 179e221.

Liang, Z.S., Westerman, P.W., Arogo, J., 2002. Modeling ammonia emission fromswine anaerobic lagoons. Transactions of the ASAE 45 (3), 787e798.

Misselbrook, T.H., Sutton, M.A., Scholefield, D., 2004. A simple process-based modelfor estimating ammonia emissions from agricultural land after fertilizerapplications. Soil Use and Management 20, 365e372.

MWPS, 1993. Livestock Waste Management, third ed. Midwest Plan Service, AmesIowa.

Ndegwa, P.M., Hristov, A.N., Arogo, J., Sheffield, R.E., 2008. A review of ammoniamitigation techniques for concentrated animal feeding operations. BiosystemsEngineering 100, 453e469.

NRC, 2003. Air Emissions from Animal Feeding Operations: Current Knowledge,Future Needs. The National Academies Press, Washington, D.C.

Pinder, R.W., Pekney, N.J., Davidson, C.I., Adams, P.J., 2004. A process-based modelfor ammonia emissions from dairy cows: improved temporal and spatialresolution. Atmospheric Environment 38, 1357e1365.

Reidy, B., Webb, J., Misselbrook, T.H., Menzi, H., Luesink, H.H., Hutchings, N.J.,Eurich-Menden, B., Dohler, H., Dammgen, U., 2009. Comparison of models usedfor national agricultural ammonia emission inventories in Europe: litter-basedmanure systems. Atmospheric Environment 43, 1632e1640.

Ro, K.S., Szogi, A.A., Vanotti, M.B., Stone, K.C., 2008. Process based model forammonia volatilization from anaerobic swine lagoons incorporating varyingwind speeds and gas bubbling. Transactions of the ASABE 51 (1), 259e270.

Saltelli, A., Tarantola, S., Chan, K., 1999. A quantitative model-independentmethod for global sensitivity analysis of model output. Technometrics 41(1), 39e56.

Saltelli, A., Chan, K., Scott, M., 2000. Sensitivity Analysis. Wiley, Sussex.Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M., 2004. Sensitivity Analysis in

Practice: a Guide to Assessing Scientific Models. Wiley, Hoboken.Saltelli, A., Ratto, M., Andres, T., Camplongo, F., Cariboni, J., Gatelli, D., Saisana, M.,

Tarantola, S., 2008. Global Sensitivity Analysis: The Primer. Wiley, Hoboken.Seinfeld, J.H., Pandis, S.N., 1998. Atmospheric Chemistry and Physics. Wiley & Sons,

New York.US EPA. http://www.epa.gov/airscience/quick-finder/particulate-matter.htm

(accessed December 09).Whitman, W.G., 1923. The two-film theory of gas absorption. Chemical and

Metallurgical Engineering 29 (4), 146e149.Zerihun, D., Feyen, J., Reddy, J.M., 1996. Sensitivity analysis of furrow irrigation

performance parameters. Journal of Irrigation Drainage Engineering 122 (1),49e57.

Zhang, R.H., Rumsey, T.R., Fadel, J.R., Arogo, J., Wang, Z., Xin, H., Mansell, G.E., 2005.Development of an Improved Process Based Ammonia Emission Model forAgricultural Sources, Final Science Document submitted to Lake Michigan AirDirectors Consortium, Des Plaines, IL. 134 p. http://www.conceptmodel.org/nh3/sciencedoc.htm (accessed 01.11.09).