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Journal of Environmental Management 113 (2012) 383e389

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Journal of Environmental Management

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

Effects of considering greenhouse gas consequences on fertilizer use in loblollypine plantations

Jianbang Gan a,*, C.T. Smith b, J.W.A. Langeveld c

aDepartment of Ecosystem Science and Management, Texas A&M University, College Station, TX 77843-2138, USAb Faculty of Forestry, University of Toronto, 33 Willcocks Street, Toronto, ON M5S 3B3, CanadacBiomass Research, P.O. Box 247, 6700AE Wageningen, The Netherlands

a r t i c l e i n f o

Article history:Received 20 February 2012Received in revised form10 September 2012Accepted 14 September 2012Available online 22 October 2012

Keywords:Biomass yieldRotation lengthBioenergyLife Cycle AssessmentEconomic optimumSouthern USA

* Corresponding author. Tel.: þ1 979 862 4392; faxE-mail address: j-gan@tamu.edu (J. Gan).

0301-4797/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.jenvman.2012.09.015

a b s t r a c t

Fertilizer use, widely practiced in forest plantation management to stimulate tree growth, contributes togreenhouse gas (GHG) emissions. We explore how accounting for GHG consequences affects optimalfertilizer application rates of commercial forest plantations. A generic model that maximizes theequivalent annual net benefit of timber production and GHG balance is developed and applied to loblollypine (Pinus taeda L.) plantations in the southern United States. We find that fertilizer use still is a viablepractice for managing loblolly pine plantations in the region although fertilizer application rate should bereduced when GHG consequences are valued. A greater reduction in fertilizer application rate is rec-ommended where wood is used for paper production because life cycle GHG emissions of paper productsare much higher than those of solid wood or bioenergy products. A higher fertilizer rate should beapplied when forest residues are used for the production of bioenergy that offsets GHG emissions fromconsuming fossil fuels.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Nutrition management and fertilizer application have beena widely used management practice for forest plantations world-wide because of its positive effects on forest growth and yield(Bowen and Nambiar, 1984; Fox et al., 2007a). Yet fertilizer use hascaused various environmental consequences, among which aregreenhouse gas (GHG) emissions. Although the enhanced growth oftrees by fertilizers accelerates C accumulation in the forests,considerable GHG emissions take place during fertilizer productionand post-application, leading to concerns about environmental andsocial costs of fertilizer use (IPCC,1996, 2006; Sathre et al., 2010; USEnvironmental Protection Agency, 2011). Such concerns are likelyto intensify as forest plantations are playing an increasinglyimportant role in the world’s wood and fibre supply (FAO, 2006).This raises a series of questionsdIs fertilizer use still a viable optionif its GHG consequences are valued; and if yes, to what degreeshould fertilizers be used?

Answers to these questions are empirically valuable as carbonhas emerged as an important aspect of forest management. Yet

: þ1 979 845 6049.

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literature addressing these questions is rare. Previous studiesprimarily focus on the economic benefits of timber yield gains fromfertilizer application and ignore GHG consequences (Bowen andNambiar, 1984; Albaugh et al., 2004; Fox et al., 2007a). Severalstudies also have explored the effect of fertilizer use on forestecosystem carbon. Fertilizer application typically enhances Csequestration in forest ecosystems, with most C gains occurring inaboveground biomass (Shan et al., 2001; Johnson et al., 2003).When trees are harvested, part of the carbon in the biomass will betransferred to wood, paper or energy products, which havedifferent C sequestration/offset implications (Gan, 2007; Skog,2008). The impact of fertilizer application on belowground C iscomplex and varied with biogeographic factors, but generally small(Sartori et al., 2007; Nave et al., 2009). However, these C conse-quences along with GHG emissions from fertilizer production andpost-application have not been incorporated into decisions onfertilizer use. Without inclusion of the GHG impacts of fertilizers,forest management decisions may not truly reflect social, envi-ronmental, or economic optima. This study explores the GHGemissions of fertilizer application in forest plantations and theoptimal fertilizer rate when GHG impacts are taken intoconsideration.

To do this, we employ a dynamic modelling approach that takesinto account fertilizer impacts on wood/biomass yield and GHG

Table 1Descriptions of equation symbols.

Symbol Description

i Index (1, 2, ., n) for type of wood materials (i.e. biomass, sawtimber,chip and saw, and pulpwood), assuming that biomass feedstockfor energy production is indexed by 1 for notation simplicity

F Amount of the fertilizer usedT Rotation length of the plantationpi Stumpage price of wood material type iyi Yield of wood material type i at the end of rotationy Total yield at the end of rotation, i.e. y ¼ P

yimi Utilization rate of wood material type i in making final productsd Discount ratesi Carbon decay rate in wood material type ic Unit cost of purchasing and applying fertilizerI Total fertilizer-independent costs incurred during the rotations Number of years between the beginning of the rotation and

fertilizer applicationr Price of GHGs (CO2 equivalent)a Carbon content of wood materials (assuming it is fixed for all types

of wood materials from the plantation)b Efficiency of converting biomass to bioenergy (e.g. bioenergy yield

converted from one unit of biomass)q Amount of GHG emissions displaced by one unit of bioenergyl GHG emissions from fertilizer production, application, and

post-application3i GHG emissions from converting one unit of wood material type i

to final products (solid wood products, paper products,or bioenergy/electricity)

4 Collectable rate of biomass (harvest residues)

J. Gan et al. / Journal of Environmental Management 113 (2012) 383e389384

emissions. Our model maximizes the annual equivalent netrevenue from a forest plantation including life cycle GHG conse-quences. Using the theoretical model we illustrate an approach todetermining the optimal fertilizer application rate, and deriveanalytical results on optimal rotation length and fertilizer rate. Wethen apply our model to loblolly pine (Pinus taeda L.) plantations inthe southern United States, an important and productive forestregion in the US and the world. Our simulation results elucidate theimpact of valuing GHG consequences on the optimal fertilizerapplication rate, the optimal forest rotation length, as well as themarginal benefit and marginal cost of fertilizer use.

2. Materials and methods

2.1. Theoretical framework

We focus on mid-rotation fertilizer use as it is the most widelyused nutrition management practice in the US (Albaugh et al.,2007; Fox et al., 2007a). Fertilizer application enhances treegrowth; hence trees can be harvested earlier than those withoutfertilizer (Fig.1) (Fox et al., 2007b). This also implies the existence ofinteractions between fertilizer rate and rotation length of a plan-tation, an important aspect that needs to be considered in deter-mining the optimal fertilizer rate.

Let us consider a forest plantation established on bare land.Wood (timber and biomass) sales at the end of the rotation willgenerate an income valued as stumpage. Growing trees will incurcosts, which are classified into two categories: fertilizer-independent and fertilizer-dependent costs. The latter include thecosts of purchasing and applying fertilizers. The former includecosts of plantation establishment, silvicultural practices (exceptnutrient additions), land rent, overhead, and others. The carbonimpacts of fertilizer use involve several components: GHGsreleased from fertilizer production and post-application, andchanges in the carbon pools of the forest and the products of solidwood, paper, and bioenergy. Our model, maximizing the equivalentannual net benefit (EANB), can be written as follows:

Max EANB ¼ Aðd; TÞ"Xni¼1

piyiðT; FÞe�dT � cFe�ds � I � uðT ; FÞ#:

(1)

The symbols used in this and other equations are defined inTable 1. In Eq. (1), A(d, T) is the annuity factor for converting the netpresent value to an equivalent annual value (a function of discountrate and rotation length). The first term inside the square bracketsof Eq. (1) is the present value of wood/biomass sales; the secondterm is the present value of fertilizer costs; the third term is thepresent value of all other costs (independent of fertilizer use); andthe last term is the present value of GHG emissions from the

Fig. 1. Idealized fertilizer impact on forest stand yield and rotation length.

production, application, and post-application of fertilizers and fromthe manufacture of wood, paper, and bioenergy products lessadditional carbon sequestrated in (or offset by) the forest, woodand paper products, and bioenergy products resulting from fertil-izer use.We assume that unutilized portions of merchantable woodas well as harvest and mill residues (y1) are all used for bioenergyproduction. Only a fraction of harvest residues is collectable due toterrain, machine, and sustainability constraints (Gan and Smith,2010). All GHGs associated with the fertilizer (excluding carbon inwood and paper products) will be released to the atmosphere at thetime when the fertilizer is applied1; and the GHGs contained inunutilized merchantable wood and biomass feedstock will beemitted when they are converted to bioenergy, which will displacefossil fuels, leading to GHG emission offsets. We also assume thatfertilizer use does not change other plantation management prac-tices, so GHG consequences of these other practices remain thesame with or without fertilizer.

Thus, u(T, F) can be written as

uðT ; FÞ ¼ r

8<:lFe�ds þ

ZNT

Xni¼2

hsimiyiðT ; FÞe�siðt�TÞe�dt

þ 3imiyiðT ; FÞe�dTidt

�"Xni¼2

ð1� miÞyiðT ; FÞ þ fy1ðT ; FÞ#

� ðbq� a� 31Þe�dT �ZT0

dyðT ; FÞdt

ae�dtdt

9=;: ð2Þ

1 Fertilizer production releases GHGs prior to its application. Yet it takes sometime for the nutrients leached from the applied fertilizer to transfer to and releasefrom water bodies. The time span of this process is difficult to estimate. Forsimplicity, we assume that all GHGs released from this entire process occurimmediately after fertilizer application.

J. Gan et al. / Journal of Environmental Management 113 (2012) 383e389 385

The first term inside the curly brackets of Eq. (2) is GHGemissions from fertilizer; the second term represents emissionsfrom decay and manufacture of wood and paper products; thethird term is the net GHG offset of bioenergy (including offset ofthe emissions from fossil fuels displaced by bioenergy, release ofthe carbon in biomass feedstock when bioenergy is produced andconsumed, and emissions from converting biomass to bioenergy);the last term measures carbon sequestered in the forest. Fertilizerimpacts on the carbon pools of belowground biomass and deadorganic matter are neglected because they are small relative tothose on aboveground biomass and because data on such impactsare scant (Castro et al., 1994; Sartori et al., 2007; Nave et al., 2009;Vogel et al., 2011). As u(T, F) is a present discounted value, the GHGfigures represented by these terms also can be considered asdiscounted values.

GHG emissions or sequestration reflect carbon fluxes betweenforest ecosystems or product pools and the atmosphere. All GHGsare converted to CO2 equivalent (CO2_e) using global warmingpotentials (at 100 years) (IPCC, 1996). Fertilizer use, on the onehand, releases GHGs as a result of both direct and indirect emis-sions as well as GHG emissions generated from fertilizer produc-tion. For nitrogenous fertilizers, direct emissions are due tonitrification and denitrification processes of both on-site and off-site (leached and deposited) N (Bouwman, 1996). Indirect emis-sions result from interactions between fertilizers and soil, leadingto change in soil carbon, which is complex and varied thoughrelatively small as mentioned earlier.

Another impact of fertilizer application is enhancement ofcarbon stored in wood and paper products and GHG emissionoffsets by bioenergy. Fertilizer makes trees grow faster, leading toa higher annual increment in yield and a shorter rotation length. Asharvest or harvesting frequency increases, more carbon will bestored in wood and paper products, and more GHG emissions areoffset by bioenergy.

The first-order necessary conditions for an interior optimalsolution of Eq. (1) are

Xni¼1

pivyiðT ; FÞ

vFe�dT ¼ ce�ds þ vuðT; FÞ

vF(3)

Aðd; TÞ" Pni¼1

pi

�vyiðT ; FÞ

vT� dyiðT; FÞ

�e�dT � vuðT; FÞ

vT

#

¼ vAðd; TÞvT

"Xni¼1

piyiðT ; FÞe�dT � cFe�ds � I � uðT; FÞ#:

(4)

Eqs. (3) and (4) comprise a partial differential equation systemthat can be solved for the optimal rotation length and optimalfertilizer rate simultaneously. Obviously it is not easy to solve thisanalytically. Instead, its solution can be approximated usinga numerical solution approach (to be explained in the case studybelow).

2.2. Application to loblolly pine plantations in the US South

We applied the above theoretical model to loblolly pine plan-tations in the southern United States. This region is an importantand productive forestry region in the US and the world. It provides16% of the world’s supply of industrial roundwood with 7% of theworld’s timberland, accounting for 60% of US timber harvest (Wearand Greis, 2002; Wear et al., 2007). Pine (predominantly loblollypine) plantations have played a significant role in the region’ssawtimber and pulpwood supply. Since 1999, between 486,000 and648,000 ha has been planted each year (Fox et al., 2006). These

plantations are among the most intensively managed forests in theworld; tree improvement, site preparation, weed control, andfertilizers are widely used (Fox et al., 2007b). About 85% of theplantations are fertilized using mainly N (168e224 kg ha�1) withsupplementary P typically at mid-rotation (Fox et al., 2006;Albaugh et al., 2007; Fox et al., 2007b). Fertilizer has enhanced thegrowth of pine plantations in the region by approximately 25%(Jokela and Stearns-Smith, 1993; Amateis et al., 2000; Fox et al.,2007a).

Because the optimal rotation length and optimal fertilizer rateare interrelated, we adopted an interactive solution approach.This approach consists of three major steps. First, we employedthe PTAEDA4.0 model (Burkhart et al., 2008) to simulate theimpacts of fertilizer application on timber and biomass yields.PTAEDA4.0, a regional loblolly pine growth and yield model, hasbeen widely tested and used to predict the yields of sawtimber,chip and saw, and pulpwood at different stand ages with differentfertilizer rates. The yield simulation was based on a loblolly pineplantation established at a 2.44 m � 2.74 m spacing with a siteindex of 22.86 m (base age 25) in the Coastal Plains region. Nothinning was implemented as it was not a common practice formost forestland owners in the region. N (urea) and P (dia-mmonium phosphate) were assumed to be applied at a ratio of 8:1at age 5 (Albaugh et al., 2007; Fox et al., 2007a). Based on the yieldpredictions, the values of timber and biomass, as well as carbonsequestrated in wood and paper products and GHG emissionsoffset by bioenergy, were computed using stumpage and carbonprices along with Life Cycle Assessment (LCA) results on carbonbalance in wood, paper, and bioenergy products. All costs andrevenues were discounted to the present time using a 5% realdiscount rate. This simulation identified the optimal rotationlengths at different fertilizer rates including zero fertilizerapplication.

Second, we derived the optimal fertilizer rates at differentrotation length values. Simulations using PTAEDA4.0 also revealedthe marginal benefit of fertilizer (in terms of the values of timber,pulpwood, and biomass), the left-hand-side of Eq. (3). To determinethe optimal fertilizer ratewe also needed to know themarginal costof fertilizer application, the right-hand-side of Eq. (3). Fertilizercosts were drawn from Fox et al. (2007a) and USDA EconomicResearch Service (2011). The average fertilizer prices over thepast five years (2006e2011) were used; application costs wereestimated to be US$0.15 kg�1 fertilizer (personal communicationwith Thomas Fox).

Carbon consequences of fertilizer use depend upon the balanceof GHG emissions from fertilizer and carbon sequestered or offsetby wood, paper, and bioenergy products produced from increasedwood/biomass yields as a result of fertilizer application. GHGemissions from fertilizer manufacture, cultivation (plantation)sites, and leached N were estimated based on Wood and Cowie(2004) and Delucchi (2003). We assumed that 4% of N in fertil-izers was emitted on-site after application, that 30% of N applied onforestlands leached out of the land into aquatic systems (IPCC,1996; 2006), and that part (0.4e5.5%) of the N deposited in waterbodies released into the atmosphere in the form of N2O (Delucchi,2003).

We performed life cycle carbon budgeting for wood and paperproducts using the approaches proposed by Skog (2008). Theconversion rates of lumber and pulp were estimated to be 0.63(Spelter et al., 2007) and 0.50 (White et al., 2009), respectively.Producing 1 m3 of solid wood products would generate 0.254 dryMg of chips and 0.085 dry Mg of sawdust and shavings; 96% of thechips and 59% of sawdust and shavings were used for pulping, 12%of sawdust and shavings were used for bedding (Spelter et al.,2007), and the rest was available for electricity production. The

Fig. 2. Discounted total and marginal values of fertilizer (N/P ¼ 8) application toloblolly pine plantations (discount rate ¼ 5%). (a) Total present value of fertilizerapplication. (b) Marginal present value of fertilizer application.

J. Gan et al. / Journal of Environmental Management 113 (2012) 383e389386

unused portions of logs also were assumed to be used for elec-tricity generation. The use of residues and unutilized woodmaterials for electricity production, a common practice in theregion, has greater potential to offset GHG emissions from fossilfuels than liquid biofuels. The carbon offsets by bio-electricitywere calculated based on the average emissions per unit of elec-tricity generated from fossil fuels in the US (Energy InformationAdministration, 2011). Carbon decay in wood and paper prod-ucts was computed based on Skog (2008). Black liquor resultingfrom pulping was assumed to be converted into electricity andheat using the process (Tomline power/recovery system)described by Larson et al. (2006).

GHG emissions of making wood and paper products from oneunit of roundwood were derived based on the total GHG emis-sions from each industrial sector (National Center forManufacturing Sciences, 2003) and total roundwood used byeach sector (Howard, 2007) in the same year (2002). GHG emis-sions from bioenergy productionwere estimated according to Ganand Smith (2006) and Larson et al. (2006) and from timber har-vesting and transport using the approaches outlined byAthanassiadis (2000).

Finally, combining the results from the first and second steps,the optimal rotation length and optimal fertilizer rate were deter-mined simultaneously for the plantation. Four scenarios wereconsidered in calculating the marginal cost of fertilizer use. Thebase scenario, scenario I, included only fertilizer costs, i.e. with u(T,F) ¼ 0. Scenario II included the costs of fertilizers and resultantGHGs released from fertilizer manufacture and utilization. ScenarioIII covered the costs under scenario II plus the values/credits ofGHGs sequestered in wood and paper products. The last scenario(scenario IV) incorporated all costs in scenario III and the values ofGHGs offset by bioenergy produced from harvest and mill residues,representing the broadest accounting of GHG consequences offertilizer use.

3. Results and discussion

3.1. Analytical results

Several guiding principles can be drawn from the optimalityconditions, Eqs. (3) and (4), of the theoretical model. First, at theoptimal fertilizer rate the present value of marginal benefits offertilizer (gains in stumpage value) should equate the present valueof marginal costs of fertilizer use (costs of fertilizers and GHGemissions).

Second, fertilizer use can not only increase forest growth andyield but also reduce plantation rotation length (Fox et al., 2007b).Both increases in yield and reductions in rotation length affectcarbon sequestration in the forest ecosystem and wood products.

Third, the sign of the impacts of fertilizer use on GHG emissionsis ambiguous, depending on the magnitude of GHG emissions fromfertilizers, carbon stored in wood and paper products, and GHGemissions offset by bioenergy. Hence, the type of final productsproduced from wood materials has an effect on the optimal fertil-izer rate. It is apparent that increased use of fertilizer can bejustified when woody biomass (not large diameter logs) is used toproduce bioenergy that can significantly offset GHG emissions fromfossil fuel combustion.

Fourth, increases in the stumpage prices of wood materialswould stimulate fertilizer use as the marginal benefit of fertilizerapplication rises. However, the impact of GHG prices on fertilizerrate is uncertain given the ambiguity of fertilizer effects on theoverall GHG balance. If fertilizer use causes net emissions (asshown in the case study below), fertilizer rate should be reduced asGHG prices go up.

3.2. Empirical results

3.2.1. Impact of fertilizer use on the value of timber/biomass yieldsFig. 2 shows the discounted total and marginal values of fertil-

izer use in terms of wood/biomass yield gains for the simulatedloblolly pine plantation. Using the simulation results (the dots inFig. 2(a)) from PTAEDA4.0, we estimated the relationship betweenthe present value of wood/biomass yield gains and the N applica-tion rate via nonlinear regression. The model shows a statisticallygood fit (R2 ¼ 0.98). Taking the derivative of the total value functionwith respect to fertilizer rate yields the following marginal benefitfunction of fertilizer use (MBF).

MBF ¼ 1:6243þ 0:1272N� 0:0009N2 (5)

where MBF is measured in US dollars; N is the amount (kg) of Napplied. Obviously, MBF is a nonlinear function (Fig. 2(b)), sug-gesting that the marginal benefit of fertilizer increases initially andthen decreases as more fertilizer is applied. This echoes the findingson the tree growth response to fertilizer application (Fox et al.,2007a).

3.2.2. Greenhouse gas consequences of fertilizer useEstimated emissions from fertilizer production and utilization

were 45.9 kg of CO2_e (Table 2). The carbon of the increased wood/biomass yields resulting from fertilizer application is initially storedin the forest and then transferred to wood and paper products afterharvest. Additionally, bioenergy produced from residues andunutilized wood materials offsets GHG emissions from fossil fuels(Gan, 2007). Emissions from wood and paper products take placefrom the time of timber harvest to the infinite future as the carbonof these products decays (Skog, 2008). On average, the discounted,accumulative carbon sequestered in the forest and then wood,paper, and bioenergy products amounts to 73 kg of CO2_e for 1 kg of

Table 2Greenhouse gas consequences of applying 1 kg of N to loblolly pine plantations inthe southern United States.

GHG consequence Amounta

(kg CO2_e)Time of occurrence

Emissions from fertilizer production 1.5 Year of fertilizer applicationb

Emissions from fertilizer utilization(post-application)

44.3 Year of fertilizer applicationb

Emissions from wood harvestingand transportation

9.1 Year of timber harvest

Emissions from making wood andpaper products

233.7 Year of timber harvest

Sequestration in forest and wood,paper, and bioenergy products

73.0c During tree growth andproduct life cycle

a The figures represent the average amount of emissions or sequestration fromapplying 1 kg of N.

b The year is approximated.c It measures the discounted, accumulative balance of carbon stored in the

plantation initially and then transferred to products including net GHG offsets ofbioenergy.

Fig. 4. Marginal cost of fertilizer use at different CO2 prices for different modelledscenarios. ‘No GHGs’: GHGs excluded, ‘Fertilizer GHGs’: GHGs from fertilizer included,‘Fertilizer þ products GHGs’: GHGs from fertilizer, wood and paper products included,and ‘Fertilizer þ products þ bioenergy GHGs’: GHGs from fertilizer, wood and paperproducts, and bioenergy included.

J. Gan et al. / Journal of Environmental Management 113 (2012) 383e389 387

N applied. Production of these products as well as wood harvestingand transportation releases 233.7 kg of CO2_e. Overall, applying Nto the loblolly pine plantation leads to positive net emissions.

The positive net emissions are partly because a significantportion (28% in weight) of the yield gain is pulpwood, traditionallyused for paper making in the region. Paper products overallgenerate life cycle net GHG emissions whereas wood products ingeneral lead to a net GHG sequestration and bioenergy productsdisplace GHG emissions from consuming fossil fuels. Thus, from theperspective of GHG benefits, growing timber or biomass for energyproduction (especially power and heat generation) is better off thangrowing pulpwood.

3.2.3. Optimal rotation lengthWithout fertilizer, the optimal rotation length for the loblolly

pine plantation is 31 years (Fig. 3), similar to that reported byHuang and Kronrad (2002). Fertilizer reduces the optimal rotationlength by 5 years. There was only a minor impact of valuing GHGemissions/sequestration on the rotation length. This attributes to (i)the low value of GHGs relative to the value of wood and (ii) thetradeoff between GHG emissions from fertilizer production andpost-application and GHG sequestration/offsets by wood and bio-energy products.

3.2.4. Optimal fertilizer intensityThe marginal cost of fertilizer use varies across GHG

accounting scenarios and GHG prices (Fig. 4). The economically

Fig. 3. Optimal rotation lengths of loblolly pine plantations under different fertilizerand GHG scenarios. ‘Fertilizer without GHGs’ refers to plantations where fertilizer wasapplied but GHGs were not valued, and ‘Fertilizer with GHGs’ refers to plantationswhere fertilizer was applied and GHGs were valued at US$25 Mg�1 CO2.

optimal N application rate can be determined at the point wherethe MBF curve (Fig. 2(b)) intersects the marginal cost curve fromabove. The optimal fertilizer intensity under four GHG scenarios(Fig. 5) is measured against a benchmark, which is normalized toone and represents the N application rate without consideringGHGs. The benchmark rate is about 150 kg ha�1, close to thelower end of the current N application range (Fox et al., 2007a,2007b). The fertilizer intensity decreases as GHGs are includedand valued at a higher price. Considering GHG emissions fromfertilizer increases the marginal cost of fertilizer use (Fig. 4), thusdecreasing the optimal fertilizer intensity (Fig. 5). At a CO2 priceof US$25 Mg�1 and with the inclusion of all GHGs, the optimalfertilizer rate decreases by some 6% relative to the benchmark.Reductions in the optimal fertilizer rate drastically increase asthe price of CO2 rises above US$70 Mg�1. Because of GHG offsetsby bioenergy and higher GHG emissions from paper productsthan from wood products, a higher fertilizer rate should beapplied to timber or energy feedstock plantations than to pulp-wood stands.

When the price of CO2 reaches a certain threshold, fertilizer useis no longer economically efficient. For example, when all GHGconsequences are considered, no N fertilizer should be applied to

Fig. 5. Optimal fertilizer application intensity at different CO2 prices for differentmodelled scenarios. ‘No GHGs’: GHGs excluded, ‘Fertilizer GHGs’: GHGs from fertilizerincluded, ‘Fertilizer þ products GHGs’: GHGs from fertilizer, wood and paper productsincluded, and ‘Fertilizer þ products þ bioenergy GHGs’: GHGs from fertilizer, woodand paper products, and bioenergy included.

J. Gan et al. / Journal of Environmental Management 113 (2012) 383e389388

the plantation at a CO2 price of US$140 Mg�1 or higher. This pricelevel is certainly beyond the reach of current and foreseeable GHGmarkets or compensationmechanisms. Hence, fertilizer applicationremains economically viable for loblolly pine plantations in the USSouth though fertilizer intensity should be reduced given theestimated GHG emissions.

4. Conclusion

Although fertilizer use in forest plantations should be reducedwhen its GHG emissions are taken into account, it remainseconomically viable as long as the price of CO2 is below a certainthreshold. For the loblolly pine plantation in the US South, sucha threshold is US$140 Mg�1 of CO2 if residues are used for elec-tricity production and US$75 Mg�1 of CO2 if the plantation ispurely for timber and pulpwood production, either of which ismuch higher than current and projected CO2 prices. Contrary tocommon wisdom and current practices, less fertilizer should beapplied to pulpwood plantations than to sawtimber stands orenergy plantations because paper products have higher net GHGemissions thanwood or bioenergy products. When forest residuesare used to produce bioenergy that offsets GHG emissions fromfossil fuels, a higher fertilizer rate can be applied. Our genericmodel can be applied to other forest plantations in differentregions. Because of data limitation, we did not include the impactof fertilizer use on the carbon pools of belowground biomass anddead organic matter. Although it is expected to be small, futurestudies can explore this impact and incorporate it into thedetermination of fertilizer rate.

Acknowledgements

The study leading this paper was supported in part by TexasA&M AgriLife Research and the US Department of Agriculture.

Appendix

Taking partial derivative of Eq. (1) with respect to F and T andsetting them to equate zero yields

vEANBvF

¼ Aðd; TÞ"Xni¼1

pivyiðT; FÞ

vFe�dT � ce�ds � vuðT ; FÞ

vF

#h0;

(A.1)

vEANBvT

¼ Aðd;TÞ"Xni¼1

pi

�vyiðT;FÞ

vTe�dT �dyiðT;FÞe�dT

��vuðT ;FÞ

vT

#

�vAðd;TÞvT

"Xni¼1

piyiðT ;FÞe�dT �cFe�ds� I�uðT ;FÞ#h0:

(A.2)

Eq. (A.1) implies

Xni¼1

pivyiðT ; FÞ

vFe�dT ¼ ce�ds þ vuðT ; FÞ

vF: (A.3)

That is, the optimal fertilizer rate is achieved when the presentvalue of marginal benefits from wood sales equates the presentvalue of marginal costs of the fertilizer and resultant net GHGemissions.

Simplifying Equation (A.2) gives rise to

Aðd; TÞ" Pni¼1

pi

�vyiðT ; FÞ

vTe�dT � dyiðT ; FÞe�dT

�� vuðT ; FÞ

vT

#

¼ vAðd; TÞvT

"Xni¼1

piyiðT ; FÞe�dT � cFe�ds � I � uðT ; FÞ#:

(A.4)

A change in rotation length will, on the one hand, affectstumpage values and consequently carbon sequestered in woodand bioenergy products, and on the other hand, will change theannuity factor that affects the equivalent annual value of theprevious net benefit. For an optimal solution, the magnitude ofthese two impacts must be the same.

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