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Agroclimatology

Net Biome Productivity of Irrigated and Rainfed Maize–Soybean Rotations: Modeling vs. Measurements

^a Dep. of Renewable Resources, Univ. of Alberta, Edmonton, AB, Canada T6G 2E3
^b Dep. of Agronomy and Horticulture, Univ. of Nebraska, Lincoln, NE 68583-0915
^c School of Natural Resources, Univ. of Nebraska, Lincoln, NE 68583-0728

^* Corresponding author (robert.grant{at}afhe.ualberta.ca)

	ABSTRACT

TOP ABSTRACT INTRODUCTION MODEL DEVELOPMENT FIELD EXPERIMENT MODEL EXPERIMENT RESULTS DISCUSSION Appendix A: CO2 Fixation Appendix B: N2 Fixation REFERENCES

 
Estimates of agricultural C sequestration require an understanding of how net ecosystem productivity (NEP) and net biome productivity (NBP) are affected by land use. Such estimates will most likely be made using mathematical models that have undergone well-constrained tests against field measurements of CO₂ exchange as affected by management. We tested a hydraulically driven soil–plant–atmosphere C and water transfer scheme in ecosys against CO₂ and energy exchange measured by eddy covariance (EC) over irrigated and rainfed no-till maize–soybean rotations at Mead, NE. Correlations between modeled and measured fluxes (R² > 0.8) indicated that <20% of variation in EC fluxes could not be explained by the model. Annual aggregations of modeled fluxes indicated that NEP of irrigated and rainfed soybean in 2002 was –30 and –9 g C m^–2 yr^–1 (net C source) while NEP of irrigated and rainfed maize in 2003 was 615 and 397 g C m^–2 yr^–1 (net C sink). These NEPs were within the range of uncertainty in annual NEP estimated from gap-filled EC fluxes. When grain harvests were subtracted from NEP to calculate NBP, both the modeled and measured maize–soybean rotations became net C sources of 40 to 80 g C m^–2 yr^–1 during 2002 and 2003. Long-term model runs (100 yr) under repeated 2001–2004 weather sequences indicated that a rainfed no-till maize–soybean rotation at Mead would lose about 30 g C m^–2 yr^–1. Irrigating this rotation would raise SOC by an average of 6 g C m^–2 yr^–1 over rainfed values. Modeled and measured results indicated only limited opportunity for long-term soil C storage in irrigated or rainfed maize–soybean rotations under the soil, climate, and management typical of intensive crop production in the U.S. Midwest.

Abbreviations: DOC, dissolved organic carbon • EC, eddy covariance • GPP, gross primary productivity • IMZ, intensive measurement zones • LAI, leaf area index • LE, latent heat flux • NBP, net biome productivity • NEP, net ecosystem productivity • NPP, net primary productivity • RMSD, Root mean squares for difference • SOC, soil organic carbon

Net Biome Productivity of Irrigated and Rainfed Maize–Soybean Rotations: Modeling vs. Measurements

^a Dep. of Renewable Resources, Univ. of Alberta, Edmonton, AB, Canada T6G 2E3
^b Dep. of Agronomy and Horticulture, Univ. of Nebraska, Lincoln, NE 68583-0915
^c School of Natural Resources, Univ. of Nebraska, Lincoln, NE 68583-0728

^* Corresponding author (robert.grant{at}afhe.ualberta.ca)

Received for publication November 6, 2006.
Estimates of agricultural C sequestration require an understanding of how net ecosystem productivity (NEP) and net biome productivity (NBP) are affected by land use. Such estimates will most likely be made using mathematical models that have undergone well-constrained tests against field measurements of CO₂ exchange as affected by management. We tested a hydraulically driven soil–plant–atmosphere C and water transfer scheme in ecosys against CO₂ and energy exchange measured by eddy covariance (EC) over irrigated and rainfed no-till maize–soybean rotations at Mead, NE. Correlations between modeled and measured fluxes (R² > 0.8) indicated that <20% of variation in EC fluxes could not be explained by the model. Annual aggregations of modeled fluxes indicated that NEP of irrigated and rainfed soybean in 2002 was –30 and –9 g C m^–2 yr^–1 (net C source) while NEP of irrigated and rainfed maize in 2003 was 615 and 397 g C m^–2 yr^–1 (net C sink). These NEPs were within the range of uncertainty in annual NEP estimated from gap-filled EC fluxes. When grain harvests were subtracted from NEP to calculate NBP, both the modeled and measured maize–soybean rotations became net C sources of 40 to 80 g C m^–2 yr^–1 during 2002 and 2003. Long-term model runs (100 yr) under repeated 2001–2004 weather sequences indicated that a rainfed no-till maize–soybean rotation at Mead would lose about 30 g C m^–2 yr^–1. Irrigating this rotation would raise SOC by an average of 6 g C m^–2 yr^–1 over rainfed values. Modeled and measured results indicated only limited opportunity for long-term soil C storage in irrigated or rainfed maize–soybean rotations under the soil, climate, and management typical of intensive crop production in the U.S. Midwest.

Abbreviations: DOC, dissolved organic carbon • EC, eddy covariance • GPP, gross primary productivity • IMZ, intensive measurement zones • LAI, leaf area index • LE, latent heat flux • NBP, net biome productivity • NEP, net ecosystem productivity • NPP, net primary productivity • RMSD, Root mean squares for difference • SOC, soil organic carbon

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MODEL DEVELOPMENT FIELD EXPERIMENT MODEL EXPERIMENT RESULTS DISCUSSION Appendix A: CO2 Fixation Appendix B: N2 Fixation REFERENCES

 
NATIONAL INVENTORIES of agricultural greenhouse gas emissions and removals require that the net biome productivity (NBP) of key agricultural ecosystems be estimated for representative soils and land use practices. The maize–soybean rotation is one such ecosystem widely found in eastern and central North America that may have potential for large NBP (e.g., Collins et al., 1999; Hollinger et al., 2005). This rotation is characterized by large rates of fertilizer N application in maize and of biological N fixation in soybean that raise net primary productivity (NPP) and hence net ecosystem productivity (NEP). Irrigation can further raise NPP of this rotation in drier areas, but its effect on NEP and NBP is unclear.

The NEP is calculated as gross primary productivity (GPP) minus autotrophic respiration (R_a) minus heterotrophic respiration (R_h); NEP has been estimated in maize and soybean from CO₂ flux measurements using eddy covariance (EC) techniques (Baker and Griffis, 2005; Hollinger et al., 2005; Pattey et al., 2002; Suyker et al., 2005; Verma et al., 2005). These estimates have indicated that NEP of maize can be substantial (530–700 g C m^–2 yr^–1) whereas that of soybean is much smaller (–100 to +200 g C m^–2 yr^–1) (Hollinger et al., 2005; Suyker et al., 2005). The NBP is calculated as NEP minus losses from disturbances such as harvesting. Because grain yields from maize–soybean rotations are large, NBP has been estimated in some cases to be less than zero (net C source) (Baker and Griffis, 2005; Verma et al., 2005), and in other cases slightly greater (net C sink) (Hollinger et al., 2005; 2006—but see Dobermann et al., 2006).

There is some uncertainty in estimates of NEP from EC measurements caused by assumptions required to fill gaps caused by instrument failure or unfavorable weather conditions (Griffis et al., 2003). Such conditions usually occur when low wind speeds cause friction velocity to remain less than threshold values above which turbulence is considered adequate for EC measurements. Furthermore, NEP estimates from EC are expensive and time-consuming to acquire, and cannot be used to project climate change impacts because the validity of these estimates is limited to the conditions under which they were determined. Process-based models of terrestrial ecosystems are generally considered the best method for predicting NEP under known or hypothesized climates and land use practices for which EC measurements are incomplete or not available.

Models used to predict NBP should represent the key biological processes by which GPP, R_a and R_h are determined, and how these processes interact when responding to changes in climate as described above. Tests of these responses in the model are best constrained when conducted at time scales consistent with those at which these responses occur in nature (e.g., hourly or less). The EC measurements provide such well constrained tests when taken under conditions that favor measurement accuracy. If model fluxes can be reconciled with EC measurements taken under favorable conditions, then model fluxes can be used to fill in EC measurements under unfavorable conditions, or to replace them entirely when aggregating fluxes to longer time scales required for impact assessments of climate change and land use practices (Baldocchi and Wilson, 2001).

Ecosys is a detailed process-based model of terrestrial ecosystems that has undergone extensive testing against CO₂ and energy fluxes over coniferous (Grant, 2004; Grant et al., 2001a, 2001b) and temperate (Grant et al., 1999a) forests, irrigated crops (Grant et al., 2004), grasslands (Li et al., 2004), tundra (Grant et al., 2003) and wetlands (Grant and Roulet, 2002). In this article, we extend testing to irrigated and rainfed maize–soybean rotations to estimate how irrigation would affect productivity and C storage of this key agroecosystem. These responses are intended to evaluate possible changes in agricultural C inventories under hypothesized changes in land use practices.

	MODEL DEVELOPMENT

TOP ABSTRACT INTRODUCTION MODEL DEVELOPMENT FIELD EXPERIMENT MODEL EXPERIMENT RESULTS DISCUSSION Appendix A: CO2 Fixation Appendix B: N2 Fixation REFERENCES

 
Most of the key algorithms used to model C and nutrient transformations in ecosys have been described in earlier papers cited below, and so are described only in general terms here. Algorithms in ecosys for C₄ photosynthesis and symbiotic N₂ fixation, two key processes that determine NEP in maize–soybean rotations, have not yet been documented, and so are described in greater detail below, with reference to equations in Appendix A (C₄ photosynthesis) and Appendix B (N₂ fixation).

Energy Exchange
Energy exchanges between the atmosphere and terrestrial surfaces are resolved in ecosys into those between the atmosphere and the leaf and stem surfaces of each population (e.g., species or cohort) within the plant community, and that between the atmosphere and each of the surfaces (soil, plant residue, snow) of the ground beneath (Grant et al., 1999b). Total energy exchange between the atmosphere and terrestrial surfaces is calculated as the sum of exchanges with all plant and ground surfaces. Surface energy exchange is coupled with soil heat and water transfers, including runoff (Manning), infiltration (Green-Ampt), macropore flow (Poiseuille), and micropore flow (Richards).

Canopy energy exchange in ecosys is calculated from an hourly two-stage convergence solution for the transfer of water and heat through a multi-layered multi-population soil–root–canopy system. The first stage of this solution requires convergence to a value of canopy temperature T_c for each plant population at which the first-order closure of the canopy energy balance (net radiation, sensible heat flux, latent heat flux, and change in heat storage) is achieved (Eq. [1–15] in Grant et al., 1999b). These fluxes are controlled by aerodynamic (r_a) and canopy stomatal (r_c) resistances. Two controlling mechanisms are postulated for r_c:

1. At the leaf level, leaf resistance r_lf controls gaseous CO₂ diffusion through each leaf surface when calculating CO₂ fixation {Eq. [A1] (C₄) or [A27] (C₃)} from concurrent solutions for diffusion {Eq. [A2] (C₄) or [A28] (C₃)} and carboxylation {Eq. [A3] (C₄) or [A29] (C₃)}. The value of r_lf {Eq. [A4] (C₄) or [A30] (C₃)} is calculated from a minimum leaf resistance r_lfmin for each leaf surface that allows an initial C_i/C_a ratio of 0.45 (C₄) or 0.67 (C₃) to be maintained at carboxylation rates calculated under ambient irradiance, temperature, C_a, and zero canopy water potential (_c) {Eq. [A5] (C₄) or [A31] (C₃)}. This ratio will be allowed to vary diurnally as described in Gross Primary Productivity below when _c is solved in the second stage of the convergence solution, described under "Water Relations" below. Values of r_lf are aggregated by leaf surface area to a canopy value r_c for use in the energy balance convergence scheme (Grant et al., 1999b).
   
2. At the canopy level, r_c rises from that at zero _c through an exponential function of canopy turgor potential _t {as for r_lf in Eq. [A4] (C₄) or [A30] (C₃)} calculated from _c and osmotic water potential during convergence for transpiration vs. water uptake. The exponential function of _t used here is based on that proposed by Zur and Jones (1981) to account for the effects of osmotic adjustment on stomatal resistance. There is no direct response of r_c to vapor pressure deficit (D) in ecosys, although such a response is included in most other models of r_c. However, larger D raises transpiration, forcing lower _c and _t to be calculated in ecosys during convergence for transpiration vs. water uptake. The exponential function used to calculate r_c from _t causes r_c to become more sensitive to _t as _c and _t decline. Thus, in wet soil with high _s and low hydraulic resistance, _c and _t may remain high enough that r_c is not very sensitive to D, as has been found experimentally by Garcia et al. (1998). However, r_c becomes more sensitive to D as soil water deficits become more severe.
   

Water Relations
After convergence for T_c is achieved, the difference between canopy transpiration E_c from the energy balance and total water uptake U_c from all rooted layers in the soil is tested against the difference between canopy water content from the previous hour and that from the current hour (Eq. [A38]) (Grant et al., 1999b). This difference is minimized by adjusting _c, which determines each term from which this difference is calculated. The value of _c determines that of _t, and hence of r_c, through its effect on (Eq. [A39–A40]) (Grant et al., 1999b). The difference between _c and soil water potential _s determines U by establishing potential differences across soil–root and root–canopy hydraulic resistances _s and _r in each rooted soil layer (Eq. [A38]; Eq. [32–37] in Grant et al., 1999b). Hydraulic resistances are calculated from Poiseuille's law using root radial and axial resistivities derived by Doussan et al. (1998) with root lengths and surface areas from a root system submodel (Grant, 1998). Changes in _c determine those in canopy water content (Eq. [A38]) according to plant water potential–water content relationships (e.g., Saliendra and Meinzer, 1991). Because r_c and T_c both drive E_c, the canopy energy balance described under "Energy Exchange" above is recalculated for each adjusted value of _c during convergence.

Gross Primary Productivity
C₄ Mesophyll
In C₄ plants, the mesophyll carboxylation rate is the lesser of CO₂–limited and light-limited reaction rates (Eq. [A3]) (Berry and Farquhar, 1978). The CO₂–limited rate is a Michaelis-Menten function of PEP carboxylase (PEPc) activity and aqueous CO₂ concentration in the mesophyll (Eq. [A6]) parameterized from Berry and Farquhar (1978) and from Edwards and Walker (1983). The light-limited rate (Eq. [A7]) is a hyperbolic function of absorbed irradiance and mesophyll chlorophyll activity (Eq. [A8]) with a quantum requirement based on 2 ATP from Berry and Farquhar (1978). The PEPc (Eq. [A9]) and chlorophyll (Eq. [A10]) activities are calculated from specific activities multiplied by set fractions of leaf surface N density, and from functions of C₄ product inhibition (Jiao and Chollet, 1988; Lawlor, 1993) (Eq. [A11]), _c (Eq. [A12] as described in Grant and Flanagan, 2007), and T_c (Eq. [A13]). Leaf surface N density is controlled by leaf structural N/C and P/C ratios calculated during leaf growth from leaf nonstructural N/C and P/C ratios arising from root N and P uptake (Grant, 1998) vs. CO₂ fixation.

C₄ Mesophyll-Bundle Sheath Exchange
Differences in the mesophyll and bundle sheath concentrations of the C₄ carboxylation product drive mesophyll-bundle sheath transfer (Leegood, 2000) (Eq. [A14]). The bundle sheath concentration of the C₄ product drives a product-inhibited decarboxylation reaction (Laisk and Edwards, 2000) (Eq. [A15]), the CO₂ product of which generates a concentration gradient that drives leakage of CO₂ from the bundle sheath to the mesophyll (Eq. [A16]). The CO₂ in the bundle sheath is maintained in 1:50 equilibrium with HCO₃^– (Laisk and Edwards, 2000). At this stage of model development, the return of a C₃ decarboxylation product from the bundle sheath to the mesophyll is not simulated. Parameters used in Eq. [A14–A16] allowed mesophyll and bundle sheath concentrations of C₄ carboxylation products (from Eq. [A17–A18]) to be maintained at values consistent with those in Leegood (2000), bundle sheath concentrations of CO₂ (from Eq. [A19]) to be maintained at values similar to those reported by Furbank and Hatch (1987), and bundle sheath CO₂ leakiness (Eq. [A16]), expressed as a fraction of PEP carboxylation, to be maintained at values similar to those in Williams et al. (2001), in sorghum [Sorghum bicolor (L.) Moench] as described in Grant et al. (2004).

C₄ Bundle Sheath
A C₃ model in which carboxylation is the lesser of CO₂–limited and light-limited reaction rates (Farquhar et al., 1980) has been parameterized for the bundle sheath of C₄ plants (Eq. [A20]) from Seeman et al. (1984). The CO₂–limited rate (Eq. [A21]) is a Michaelis-Menten function of RuBP carboxylase (RuBPc) activity and bundle sheath CO₂ concentration (Eq. [A19]). The light-limited rate (Eq. [A22]) is a hyperbolic function of absorbed irradiance and activity of chlorophyll associated with the bundle sheath with a quantum yield based on 3 ATP (Eq. [A23]). The provision of reductant from the mesophyll to the bundle sheath in NADP-ME species is not explicitly simulated. The RuBPc (Eq. [A24]) and chlorophyll (Eq. [A25]) activities are the products of specific activities and concentrations multiplied by set fractions of leaf surface N density, and from functions of C₃ product inhibition (Bowes, 1991; Stitt, 1991) (Eq. [A26]), _c (Eq. [A12] from Grant and Flanagan, 2007), and T_c (Eq. [A13]).

Rates of C₃ product removal are controlled by phytomass biosynthesis rates driven by concentrations of nonstructural products from leaf CO₂ fixation and from root N and P uptake. If biosynthesis rates are limited by nutrient uptake, consequent depletion of nonstructural N or P and accumulation of nonstructural C will constrain specific activities of RuBP and chlorophyll (Eq. [A24–A26]), and thereby slow C₃ carboxylation (Eq. [A20]), raise bundle sheath CO₂ concentration (Eq. [A19]), accelerate CO₂ leakage (Eq. [A16]), slow C₄ decarboxylation (Eq. [A15]), raise C₄ product concentration in the bundle sheath (Eq. [A18]), slow C₄ product transfer from the mesophyll (Eq. [A14]), raise C₄ product concentration in the mesophyll (Eq. [A17]), and slow mesophyll CO₂ fixation (Eq. [A9–A12]). This reaction sequence simulates the progressive inhibition of C₃ and C₄ carboxylation hypothesized by Sawada et al. (2002) following partial removal of C sinks in C₄ plants.

During simulations of C₄ plant species without major nutrient or water limitations (e.g., Grant et al., 2004), this parameterization of C₄ CO₂ fixation generated bundle sheath CO₂ concentrations (C_c(b4) in Eq. [A19]) of about 1 mM, consistent with those measured in maize under high irradiance by Furbank and Hatch (1987). These concentrations drove modeled bundle sheath–mesophyll leakage (V_(b4) in Eq. [A16]) that was about 0.1 of daily integrated V_c(m4) (Eq. [A3]), as found experimentally by Hatch et al. (1995).

C₃ Mesophyll
Carboxylation reactions in C₃ plants (Eq. [A29], [A32–A37]) are the same as those in C₄ bundle sheaths (Eq. [A20–A26]), but are coupled directly to gaseous CO₂ diffusion (Eq. [A27–A28]) through r_lf (Eq. [A30–A31]), as are the carboxylation reactions in C₄ mesophyll (Eq. [A1–A2], [A4–A5]).

Coupling Carbon Dioxide Fixation with Water Uptake
After successful convergence for T_c and _c (described in "Water Relations" above), leaf carboxylation rates are adjusted from those calculated at _c = 0 to those under ambient _c. This adjustment is required by stomatal effects on gaseous CO₂ diffusion caused by the increase in r_c from its minimum value {Eq. [A5] (C₄) or [A31] (C₃)} to that at ambient _t {Eq. [A4] (C₄) or [A30] (C₃)}, and by nonstomatal effects of ambient _t on carboxylation (Eq. [A12]), parameterized from Medrano et al. (2002) and tested in Grant and Flanagan (2007). The adjustment is achieved through a convergence solution for C_i at which the diffusion rate of gaseous CO₂ between boundary layer CO₂ concentration (C_b) and C_i through r_lf {Eq. [A2] (C₄) or [A28] (C₃)} equals the carboxylation rate at the temperature-dependent aqueous counterpart of C_i {Eq. [A3] (C₄) or [A29] (C₃)}. As r_lf rises, this convergence arrives at a lower C_i than that at full _t so that C_i/C_b declines under water stress as found in C₄ plants by Williams et al. (2001). The CO₂ fixation rate of each leaf surface at convergence is then added to arrive at a value for gross canopy CO₂ fixation (gross primary productivity GPP) by each tiller (or branch) of each plant population (i.e., species or cohort) in the model {Eq. [A1] (C₄) or [A27] (C₃)}.

Autotrophic Respiration
The C₃ fixation products are added to a nonstructural C pool _c3, which is the first-order substrate for autotrophic respiration, R_a (Eq. [26–31] in Grant et al., 1999b). Autotrophic respiration is first used to meet requirements for maintenance respiration R_m, then any excess is expended as growth respiration R_g to drive biosynthesis according to organ-specific growth yields. If R_a is less than R_m, the shortfall is made up through respiration of remobilizable protein C withdrawn from leaf and sheath or petiole C, driving the loss of associated structural C as litterfall. Environmental constraints such as nutrient, heat, or water stress that deplete _c3 and hence reduce R_a with respect to R_m, therefore, hasten litterfall. Net primary productivity (NPP) is calculated as the difference between GPP and R_a.

Heterotrophic Respiration
Dissolved organic C (DOC) drives heterotrophic respiration, R_h, by obligately aerobic, facultatively anaerobic, obligately anaerobic, and diazotrophic decomposers associated with each substrate, including plant litter (from litterfall in "Autotrophic Respiration"), animal manure, particulate organic matter and humus (Eq. [A11–A13] in Grant et al., 2006). Heterotrophic respiration by each population is constrained by rates of electron acceptor (O₂, NO₃^–, NO₂^–, N₂O, organic C) uptake (Eq. [A14–A16] in Grant et al., 2006). All microbial populations undergo maintenance respiration, R_m, and decomposition. Heterotrophic respiration in excess of R_m is used as growth respiration R_g, which drives microbial growth according to specified growth yields (Eq. [A17–A24] in Grant et al., 2006). Active microbial biomass resulting from microbial growth drives decomposition of each litter and SOC pool, depending on volume of microbial habitat determined from soil water content (Eq. [A1–A4] in Grant et al., 2006). These pools are partitioned into components of differing vulnerability to hydrolysis according to results of proximate analysis. Decomposition produces DOC, which then drives R_h. Autotrophic and heterotrophic respiration are described in greater detail in Grant (2004).

Symbiotic Nitrogen Fixation
Microbial Growth
Modeling the activity of symbiotic N₂ fixing bacteria in roots follows a protocol similar to that of nonsymbiotic N₂ fixing bacteria in soil. Respiration demand is driven by specific activity, microbial biomass, M_n, and nonstructural C concentration, [_n], in root nodules (Eq. [B1]), and is constrained by temperature (Eq. [B2]) and microbial N or P status (Eq. [B3]). Nodule respiration, R, is constrained by the extent to which O₂ uptake meets O₂ demand (Eq. [B4]) imposed by respiration demand (Eq. B5). The O₂ uptake is in turn constrained by rhizosphere [O_2r] (Eq. [B6a]), which is controlled by radial diffusion of O₂ through soil water to roots and nodules (Eq. [B6b]). Soil water [O₂] is maintained by dissolution of O₂ from soil air, which is in turn maintained by soil–atmosphere gas exchange and vertical diffusion (Grant, 2004). Heterotrophic respiration is first allocated to maintenance respiration, R_m (Eq. [B7–B8]), and the remainder if any is allocated to growth respiration, R_g (Eq. [B9]). If R_m exceeds R_h, the shortfall is made up from respiration of microbial protein C, forcing senescence and litterfall of associated nonprotein C (Eq. [B10–B11]).

Nitrogen Fixation
Nitrogen fixation V_N2 is driven by R_g (Eq. [B12]), but is constrained by accumulation of nonstructural N, _n, with respect to nonstructural C and P also required for microbial growth in the nodule (Eq. [B13]). Nonstructural N, _n, is the product of V_N2, so that Eq. [B12] simulates the inhibition of N₂ fixation by its product (Postgate, 1998). The value of V_N2 is also limited by the additional N needed to maintain bacterial N content, [N_n'], of M_n (Eq. [B12]), so that N₂ fixation is constrained by the need of nodule bacteria for N not met from other sources (Postgate, 1998). Respiration required for N₂ fixation, R_N2, (Eq. [B14]) is subtracted from R_g (Eq. [B15]) when calculating microbial growth (Eq. [B16–B18]).

Nodule–Root Exchange
Exchange of nonstructural C, N, and P between roots and nodules is driven by concentration gradients (Eq. [B21–B23]) created by generation, transfer, and consumption of nonstructural C, N, and P in shoots, roots, mycorrhizae, and nodules. Nonstructural C is generated in shoots and transferred along concentration gradients to roots and thence to nodules (Eq. [B21]). Nonstructural P is generated in roots and transferred along concentration gradients to shoots and nodules (Eq. [B23]). Nonstructural N is generated in roots through mineral uptake and in nodules through gaseous fixation. Nonstructural C, N, and P in nodules is determined by root–nodule exchange, by nodule respiration and fixation, and by remobilization from nodule litterfall (Eq. [B24–B26]).

Root nonstructural N (_r) may rise if high mineral N concentrations in soil sustain rapid N uptake by roots. Large _r suppresses or even reverses the transfer of _n from nodule to root (Eq. [B22]), raising _n (Eq. [B25]), and hence suppressing V_N2 (Eq. [B12] and Eq. [B13]). Large _r also accelerates the consumption of _r, slowing its transfer to nodules (Eq. [B21]), reducing _n (Eq. [B24]), and hence slowing nodule growth (Eq. [B1]). Conversely, slow root N uptake caused by low soil mineral N concentrations would lower _r and raise _r, hastening the transfer of _n from nodule to root and of _rt from root to nodule, lowering _n, raising _n, and accelerating V_N2. This control of V_N2 by _r simulates the observation by Parsons and Sunley (2001) that phloem concentrations of N-rich amino acids likely control root nodule activity, likely through their effects on photoassimilate transfer to nodules (Fujikake et al., 2003). However, Eq. [B13] also allows V_N2 to be constrained by nonstructural C and P concentrations arising from CO₂ fixation and root P uptake.

	FIELD EXPERIMENT

TOP ABSTRACT INTRODUCTION MODEL DEVELOPMENT FIELD EXPERIMENT MODEL EXPERIMENT RESULTS DISCUSSION Appendix A: CO2 Fixation Appendix B: N2 Fixation REFERENCES

 
Site Management
A 52.4-ha field (41°9'53.5356'' N, 96°28'12.36'' W, 362 amsl, irrigated with a center pivot system), and a 65.4-ha field (41°10'46.8012'' N, 96°26'22.7256'' W, 362 amsl, rainfed) of deep silty clay loams, (Mollic Hapludalfs, Pachic Argialbolls, and Vertic Argialbolls) were maintained from 1991 to 2001 under a no-till maize–soybean rotation (irrigated) and a tilled wheat, soybean, oat, and maize rotation (rainfed) at the University of Nebraska Agricultural Research and Development Center near Mead, NE. Both fields were tilled in fall of 2000 to homogenize the topsoil (disking to a depth of about 10 cm) and incorporate P fertilizer. Since 2001, both fields have been maintained under no-till maize–soybean rotations according to best management practices for production-scale maize systems. Results from the 2002 (soybean)–2003 (maize) rotation were used for model comparisons in this study. Site conditions and crop management were described in greater detail by Verma et al. (2005).

Field Measurements
Within each field, six 20 by 20 m intensive measurement zones (IMZ) were established at different landscape positions. Soil water contents (0.10, 0.25, 0.5, and 1.0 m; Delta-T Devices, Cambridge, UK) were recorded daily in four of the IMZs. Soil temperature (0.06, 0.1, 0.2 m; platinum RTD, Omega Engineering, Stamford, CT), air temperature and humidity (3.0 and 6.0 m; Humitter50Y, Vaisala, Helsinki, Finland), photosynthetically active radiation (LI 190SA Quantum sensor, Li-Cor) and net radiation (5.5 m; Q* 7.1, Radiation and Energy Balance Systems, Seattle,WA) at 6 m, and soil heat flux (0.06 m; Radiation & Energy Balance Systems) were recorded at a flux tower site within each field.

Shoot biomass and green leaf area were determined in each IMZ from destructive samples at 10- to 14-d intervals until physiological maturity and again just before harvest. Root biomass was measured at tasselling (VT) and physiological maturity (R6) (maize) and at R3 and physiological maturity (soybean) in 18 transects per field (three per IMZ), each transect consisting of four cores taken to a depth of 0.6 m (2001) and 1.2 m (2002 and 2003). Harvesting was conducted at 24 locations in each field, including the six IMZs. Net export of C from each field was computed by multiplying the average grain C concentration by the amount of grain removed. Soil CO₂ effluxes were measured biweekly in each IMZ using an infrared gas analyzer (model LI-6200, Li-Cor, Lincoln, NE) with chambers of 8 x 10^–4 m³ and 9.3 x 10^–2 m³ volume, average values from which are used here.

Eddy Covariance Measurements
Carbon dioxide, water vapor, sensible heat, and momentum fluxes were measured using eddy covariance (EC) (Suyker et al., 2005) with an omnidirectional 3D sonic anemometer (Model R3: Gill Instruments Ltd., Lymington, UK), a closed-path infrared CO₂/H₂O gas analyzing system (Model LI6262: Li-Cor, Lincoln, NE), and a krypton hygrometer (Model KH20: Campbell Scientific, Logan, UT). To have sufficient fetch in all directions representative of the cropping systems being studied, the eddy covariance sensors were mounted 3.0 m above the ground when the canopy was shorter than 1 m, and later moved to a height of 6.0 m until harvest (maize only). Methods for gap-filling were described in Verma et al. (2005).

	MODEL EXPERIMENT

TOP ABSTRACT INTRODUCTION MODEL DEVELOPMENT FIELD EXPERIMENT MODEL EXPERIMENT RESULTS DISCUSSION Appendix A: CO2 Fixation Appendix B: N2 Fixation REFERENCES

 
Ecosys was initialized with the physical properties of a representative Tomek soil series (Pachic Argialbolls) at the Mead site (Table 1 ) and the biological properties of maize and soybean (input values in appendices A and B). The model was then run through 11, 2-yr cycles of a fertilized, no-till maize–soybean rotation under repeated sequences of hourly weather (solar radiation, air temperature, humidity, wind speed, and precipitation) recorded at Mead during 2002 and 2003. Model results attained repeating values after three 2-yr cycles of hourly weather and maintained them thereafter, indicating that soil microbial activity (Eq. [A1] to [A26] in Grant et al., 2006) had equilibrated under conditions similar to those that existed at the experimental site before 2001. The model run was then continued under hourly weather recorded during 2001 to 2004 (the full range of hourly weather available at the time of writing) with simulated tillage, fertilizer, planting, irrigation, and harvesting practices corresponding to those conducted at the field site (Table 1 in Verma et al., 2005). During the model run, all biological (Eq. [A1–A26] in Grant et al., 2006; Eq. [A1] to [A36] and [B1] to [B26] below) and physical (Eq. [A27]–A36] in Grant et al., 2006) processes were solved on time steps of 1 h and 3 min, respectively, with surface boundary conditions assumed constant during each hour. Model algorithms for coupling gaseous CO₂ diffusion (Eq. [A28]) and carboxylation (Eq. [A29]) with plant water status (Eq. [A30]) as determined by transpiration and root water uptake were tested by comparing modeled energy and CO₂ exchange with EC and chamber measurements over soybean (2002) and maize (2003) under contrasting soil and atmospheric water deficits. The model runs were extended through 24 more cycles of 2001–2004 weather data to observe long-term (100 yr) changes in SOC modeled under irrigated and dryland rotations.

	RESULTS

TOP ABSTRACT INTRODUCTION MODEL DEVELOPMENT FIELD EXPERIMENT MODEL EXPERIMENT RESULTS DISCUSSION Appendix A: CO2 Fixation Appendix B: N2 Fixation REFERENCES

View larger version (22K): [in this window] [in a new window]   Fig. 1. (a) Recorded solar radiation and air temperature (Ta); (b) recorded precipitation, irrigation, and vapor pressure deficit (D); and (c) measured (symbols) vs. modeled (lines) water content of the Tomek soil at 0.10 m () (Table 1) during DOY 218–227 (6–15 August) 2002 at Mead, NE.

View larger version (26K): [in this window] [in a new window]   Fig. 2. (a) Canopy stomatal conductance (gc), (b) latent heat fluxes (LE), and (c) CO2 fluxes measured (squares) or gap-filled (diamonds) and modeled (lines) over irrigated and rainfed soybean during DOY 218–227 (6–15 August) 2002 at Mead, NE. Positive and negative values denote downward and upward fluxes, respectively.

Midday CO₂ influxes (NEP = GPP – R_a – R_h) modeled and measured under irrigation remained near 30 µmol m^–2 s^–1 during DOY 218 to 227 (Fig. 2c). In the rainfed treatment, strongly nonlinear rises in r_lf (Eq. [A30]) with declining _t forced lower V_g (Eq. [A28]), while corresponding declines in f (Eq. [A12]) forced lower V_c (Eq. [A29] from Eq. [A35] and [A36]). Lower V_g and V_c caused lower GPP (Eq. [A27]), apparent in the declining CO₂ influxes modeled and measured in the rainfed vs. irrigated treatments with time after rainfall events on DOY 217 and 224 (Fig. 2c). Rainfed CO₂ influxes were close to irrigated values whereas g_c was high after rainfall on DOY 217 (Fig. 2a), but declined during soil drying, especially during afternoons with high D (e.g., DOY 223). Rainfed influxes recovered briefly after rainfall on DOY 224, but remained lower than those under irrigation, especially under high D on DOY 226.

Carbon dioxide effluxes measured and modeled under irrigation reached 10 µmol m^–2 s^–1 during most nights (Fig. 2c), but declined to 8 µmol m^–2 s^–1 in the rainfed treatment. This decline was attributed in the model to:

1. A decline in heterotrophic respiration R_h caused by lower specific microbial activity from reduced substrate–microbe contact with lower (Eq. [A1–A4] in Grant et al., 2006).
   
2. A decline in autotrophic respiration R_a from nodules (Eq. [B4]) modeled from lower GPP that slowed assimilation of root nonstructural N _r and hence slowed translocation of nodule nonstructural N _n to roots (Eq. [B22]). This raised nodule structural N N_n (Eq. [B17]), reducing nodule N requirements and hence nodule N₂ fixation V_N2 (Eq. [B12] from [B13]) and associated respiration R_N2 (Eq. [B14]). This slowed consumption of nodule nonstructural C _n (Eq. [B24]), and hence translocation of root nonstructural C _r (Eq. [B21]) that drove R (Eq. [B1]).
   

These smaller CO₂ effluxes modeled in the rainfed treatment were consistent with those measured by EC during the nights of DOY 218, 223, and 226 when higher wind speeds met criteria for EC measurement accuracy.

Maize 2003
Weather recorded during DOY 221 to 230 (9–18 August) 2003 presented an opportunity to test the response of modeled LE and CO₂ fluxes to rising T_a (Fig. 3a ) and D (Fig. 3b) over drier soil in the rainfed rotation (Fig. 3c). Irrigated maize maintained maximum daily g_c in the model of 17 to 20 mm s^–1 under irrigation with little effect of rising D (Fig. 4a ) because high caused low _s and _a (Fig. 3c) while high irradiance and T_a (Fig. 3a) caused rapid GPP (Eq. [A1] from Eq. [A2] and [A3]), and therefore low r_lf (Eq. [A4] from Eq. [A5]) and r_c (Eq. [A41]). The limited effect of D on g_c in irrigated maize was apparent from rising LE modeled and measured under rising D during DOY 224 to 230 (Fig. 4b).

View larger version (21K): [in this window] [in a new window]   Fig. 3. (a) Recorded solar radiation and air temperature (Ta); (b) recorded precipitation, irrigation, and vapor pressure deficit (D); and (c) measured (symbols) vs. modeled (lines) water content of the Tomek soil at 0.10 m () (Table 1) during DOY 221–230 (9–18 August) 2003 at Mead, NE.

View larger version (25K): [in this window] [in a new window]   Fig. 4. (a) Canopy stomatal conductance (gc), (b) latent heat fluxes (LE), and (c) CO2 fluxes measured (squares) or gap-filled (diamonds) and modeled (lines) over irrigated and rainfed maize during DOY 221–230 (9–18 August) 2003 at Mead, NE. Positive and negative values denote downward and upward fluxes, respectively.

Midday CO₂ influxes modeled and measured over irrigated maize were maintained at about 50 µmol m^–2 s^–1 (Fig. 4c), indicating that stomatal and nonstomatal effects of rising T_a and D did not much affect V_g (Eq. [A2]), V_c(m4) (Eq. [A3]), or V_c(b4) (Eq. [A20]). In the rainfed treatment, strongly nonlinear rises in r_lf (Eq. [A4]) with declining _c and _t forced lower V_g (Eq. [A2]), while corresponding declines in f (Eq. [A12]) forced lower V_c(m4) (Eq. [A3] from Eq. [A6] and [A10]) and V_c(b4) (Eq. [A20] from Eq. [A21–A25]). Lower V_g and V_c(m4) caused lower GPP (Eq. [A1]), apparent in the declining midafternoon CO₂ influxes modeled and measured under rising D during DOY 225–230 (Fig. 4c).

Declines in nighttime CO₂ effluxes from about 8 µmol m^–2 s^–1 in irrigated maize to about 6 µmol m^–2 s^–1 in rainfed maize (Fig. 4c) were attributed in the model to declines in R_h as described for soybean above. Inadequate turbulence forced replacement of measured effluxes with gap-filled values, limiting opportunity to corroborate this attribution from EC data. However, infrequent measurements of CO₂ effluxes under adequate turbulence at other times in 2003 indicated similar declines in rainfed vs. irrigated maize to those modeled here (data not shown).

Comparison of Modeled and Measured Fluxes
Modeled LE and CO₂ fluxes were significantly correlated with hourly averaged EC fluxes measured during 2002 and 2003 (Table 2 ). Regressions of modeled on measured LE fluxes (a and b in Table 2) gave intercepts near zero and slopes near one, indicating little apparent bias in the model except for rainfed maize where modeled LE was underestimated (e.g., Fig. 4b). However, modeled LE of rainfed maize in 2003 made full use of available soil water, which was constrained at the seasonal time scale by recorded precipitation. Regressions of modeled on measured CO₂ fluxes over soybean in 2002 gave intercepts near zero but slopes of 1.2. These parameter values arose from a greater response of modeled vs. measured CO₂ influxes to radiation (Fig. 5b vs. 5a) driven by values of and in Eq. [A34], both of which were derived independently of the model. This greater response was sometimes apparent as earlier rises in modeled vs. measured CO₂ influxes during mornings, although declines in modeled CO₂ influxes during afternoons more closely tracked measured values (Fig. 2c). A greater response of modeled vs. measured CO₂ influxes to radiation was also apparent in maize during 2003 (Fig. 5d vs. 5c) driven by and in Eq. [A8] and [A23]. However, earlier morning rises in modeled vs. measured CO₂ influxes over maize were not as apparent as those over soybean (Fig. 4c), and the slope of modeled on measured CO₂ fluxes in irrigated maize was close to one (Table 2). This slope in rainfed maize was slightly lower, consistent with the corresponding slope for LE. Carbon dioxide fluxes modeled and measured in the rainfed treatment diverged more strongly from those in the irrigated treatment under higher vs. lower radiation, and in 2003 vs. 2002 (Fig. 5).

View larger version (33K): [in this window] [in a new window]   Fig. 5. Response of CO2 fluxes to solar radiation (a, c) measured and (b, d) modeled over irrigated and rainfed (a, b) soybean during DOY 200–250, 2002 and (c, d) maize during DOY 195–255, 2003, when LAI > 2.5.

Between 44 and 67% of EC measurements in 2002 and 2003 were replaced by values derived from gap-filling algorithms (Verma et al., 2005), mostly during nights with low wind speeds. Consequently, gap-filled fluxes tended to be smaller in magnitude than measured fluxes, so that correlation coefficients and RMSDs from regressions of gap-filled fluxes on modeled fluxes were smaller than those of measured fluxes (Table 2). Intercepts from regressions of modeled fluxes on gap-filled fluxes were near zero, but slopes from these regressions were about 0.1 larger than those from regressions of modeled fluxes on measured fluxes (Table 2). These larger slopes indicated that CO₂ fluxes calculated from gap-filling algorithms (mostly CO₂ effluxes as in Fig. 2c and 4c) were smaller relative to modeled values than were the EC CO₂ fluxes from the algorithms were derived. These smaller values may indicate a bias in the techniques used to fit EC CO₂ fluxes to environmental drivers such as soil temperature when deriving gap-filling algorithms.

Seasonal Carbon Dioxide and Energy Exchange
Net Ecosystem Productivity
Daily aggregates of gap-filled net CO₂ exchange (daily NEP) over soybean in 2002 rose rapidly with early growth from-2 g C m^–2 d^–1 (net C emission) between spring thaw and planting in mid-May, through 0 g C m^–2 d^–1 (C neutral) by late June, to 4 to 6 g C m^–2 d^–1 (net C uptake) during late July and early August (Fig. 6a ). Daily NEP then declined through 0 g C m^–2 d^–1 by mid-September to –3 g C m^–2 d^–1 during late September, and then rose to –1 g C m^–2 d^–1 for the rest of the year. Modeled NEP exceeded values calculated from gap-filled EC measurements during peak periods of C uptake in June and emission in September. Both positive and negative values of rainfed NEP were smaller than those of irrigated NEP, although differences remained less than 1 g C m^–2 d^–1 during most of the year. Modeled NEP explained about 80% of variation in gap-filled NEP with no bias (a near zero in Table 3 ), although the range in modeled values exceeded that in gap-filled EC measurements (b > 1 in Table 3 as in Table 2).

View larger version (21K): [in this window] [in a new window]   Fig. 6. Daily net ecosystem productivity (NEP) of irrigated and rainfed (a) soybean in 2002 and (b) maize in 2003 calculated from gap-filled eddy covariance fluxes (symbols) and modeled (lines) at Mead, NE. Vertical lines indicate periods shown in Fig. 1–4.

Variation in daily NEP modeled during both years was attributed to effects of radiation, T_a, D, and on CO₂ fluxes (e.g., Fig. 2, 4) at an hourly time scale, and to changing LAI at a seasonal time scale. A similar seasonal course of daily NEP, but with smaller values, was derived by Baker and Griffis (2005) from gap-filled EC measurements over rainfed maize and soybean under a cooler climate in Minnesota.

Soil Respiration
Smaller NEP of soybean vs. maize (Fig. 6) was partly attributed to smaller CO₂ influxes (Fig. 2c vs. 4c) driven by smaller GPP (Eq. [A27] vs. Eq. [A1]), and partly to larger soil CO₂ effluxes driven by larger R_h + belowground R_a. Much of this larger R_a in the model was generated by symbiotic N₂ fixation R_N2 in soybean (= _t,l R_N2i,l in Eq. [B14] from V_N2i,l in Eq. [B12]), and by R_m + R_g of the nodules in which N₂ fixation took place (Eq. [B7] and [B9]). These larger effluxes were apparent in soil respiration measured and modeled during 2002 vs. 2003 (Fig. 7a vs. 7b). Gaseous transport algorithms in ecosys caused soil CO₂ effluxes to be suppressed briefly by soil wetting during irrigation and heavy precipitation, and to rise briefly with soil drying immediately afterward, causing short-term variability in soil CO₂ effluxes. Soil CO₂ effluxes modeled during May and June each year were smaller than those measured by surface chamber, although ecosystem CO₂ effluxes modeled during the same period were close to EC measurements.

View larger version (23K): [in this window] [in a new window]   Fig. 7. Soil CO2 effluxes measured (symbols) and modeled (lines) in irrigated and rainfed (a) soybean in 2002 and (b) maize in 2003. Negative values denote upward fluxes.

Crop Growth
The more rapid rise of NEP to larger values in maize during 2003 than in soybean during 2002 (Fig. 6) was apparent in the more rapid rise of aboveground and reproductive phytomass to larger values (Fig. 8b vs. 8a). Early maize growth in the model lagged that measured by about 1 wk (Fig. 8b) as did NEP (Fig. 6b), but later growth enabled modeled phytomass to reach measured values later in the season. Rainfed phytomass diverged below irrigated phytomass more during 2003 than 2002 in both the model and the field, as did rainfed NEP (Fig. 6b vs. 6a) and CO₂ fluxes (Fig. 4c vs. 2c; Fig. 5c,d vs. 5a,b).

View larger version (14K): [in this window] [in a new window]   Fig. 8. Aboveground total and reproductive phytomass measured (symbols) and modeled (lines) in irrigated and rainfed (a) soybean in 2002 and (b) maize in 2003 at Mead, NE.

Smaller NPP and greater R_h caused NEP of irrigated and rainfed soybean to be slightly less than zero (net C emissions) during 2002 (–30 and –9 g C m^–2 yr^–1 modeled vs. –48 and –18 g C m^–2 yr^–1 EC), whereas greater NPP and smaller R_h caused NEP of maize to be much greater than zero (net C uptake) during 2003 (615 and 397 g C m^–2 yr^–1 modeled vs. 572 and 397 g C m^–2 yr^–1 EC). Uncertainty in the annual EC values has been estimated to be ±45 g C m^–2 (Verma et al., 2005). Grain removal lowered NBP of irrigated and rainfed soybean (–221 and –163 g C m^–2 yr^–1 modeled vs. –218 and –171 g C m^–2 yr^–1 EC) and of irrigated and rainfed maize (69 and 27 g C m^–2 yr^–1 modeled vs. 57 and 100 g C m^–2 yr^–1 EC). The larger EC value for NBP of rainfed maize was due to a smaller measured vs. modeled grain yield, possibly caused by adverse effects of water stress on seed set. These effects were apparent in the lower ratio of measured dryland vs. irrigated yield (0.55) compared with that of gap-filled GPP (0.75). This lower ratio of yield vs. GPP in the dryland vs. irrigated treatments was not fully modeled (0.68 vs. 0.76), indicating the importance of modeling midseason water stress and its effects on seed set. Consequently, SOC declined under soybean but rose under maize, as found experimentally from measurements of surface litter mass (Table 4).

Irrigated vs. Rainfed Productivity
The GPP of rainfed soybean was reduced from irrigated values by 9% (modeled) and 13% (EC) in 2002, and GPP of rainfed maize by 24% (modeled) and 25% (EC) in 2003 (Table 4). These reductions were also apparent in lower rainfed vs. irrigated hourly CO₂ influxes (Fig. 2c vs. 4c) and in daily NEP (Fig. 6). Commensurate reductions from irrigated values were also modeled in rainfed R_a and hence NPP. However, rainfed litterfall was reduced comparatively less from irrigated values (1% modeled in 2002 and 16% modeled in 2003) than was NPP, while rainfed grain removal was reduced comparatively more (19% modeled vs. 16% measured in 2002, and 32% modeled vs. 45% measured in 2003) (Table 4). Smaller reductions in litterfall vs. grain were caused by a larger allocation of NPP to roots and a smaller allocation of NPP to grain in the rainfed vs. irrigated crops. This reallocation reduced the loss of C from harvesting, so that rainfed soybean was a smaller C source than was irrigated soybean (–163 vs. –221 g C m^–2), and rainfed maize was a C sink only slightly smaller than irrigated maize (27 vs. 69 g C m^–2).

Centennial Ecosystem Productivity
The NBP of the irrigated maize–soybean rotation from the model vs. gap-filled EC fluxes was –76 vs. –81 g C m^–2 yr^–1 during 2002–2003, while NBP of the rainfed rotation was –68 vs. –36 g C m^–2 yr^–1 (Table 4). The lower rainfed NBP in the model vs. EC was attributed to the larger grain removal modeled from rainfed maize. The negative NBP of the rotations caused declines in SOC (including litter) of the entire soil profile (0–2 m in Table 1) toward lower equilibrium values during a 100-yr model run under repeating sequences of 2001–2004 weather (Fig. 9 ). During the first 4 yr of the model run (April 2001–April 2005), SOC to 2 m in the irrigated and rainfed rotations declined by 344 and 238 g C m^–2, respectively. During this same period, SOC measured from more than 100 samples (400 kg dry soil m^–2 corresponding to a depth of ca. 0.3 m) in each of the irrigated and rainfed rotations declined by 244 ± 61 g C m^–2 (P = 0.059) and 144 ± 43 g C m^–2 (P = 0.500), respectively. Consequently, total SOC (including litter) declined more rapidly in the irrigated rotation during the first 20 yr of the model run (Fig. 9).

View larger version (9K): [in this window] [in a new window]   Fig. 9. Soil + litter C of irrigated and rainfed maize–soybean rotations modeled to depths of 0.2 and 2 m under repeating 4-yr weather sequences (2001–2004) recorded at Mead, NE.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MODEL DEVELOPMENT FIELD EXPERIMENT MODEL EXPERIMENT RESULTS DISCUSSION Appendix A: CO2 Fixation Appendix B: N2 Fixation REFERENCES

 
In earlier EC studies of maize–soybean rotations, annual NEP of maize and soybean have been calculated to be 576 and 33 g C m^–2, respectively, over three rotation cycles at a rainfed no-till site in Illinois (Hollinger et al., 2005), 300 and 50 g C m^–2, respectively, at a no-till rainfed site in Minnesota (Baker and Griffis, 2005), and 572 vs. 397 g C m^–2 and –48 vs. –18 g C m^–2, respectively, at no-till irrigated vs. rainfed sites in Nebraska (Verma et al., 2005) (Table 4). The NEP of 615 g C m^–2 modeled for irrigated maize in this study (Table 4) was within the range of those calculated from gap-filled EC in Illinois and similar to that at the irrigated site in Nebraska. The NEP of 397 g C m^–2 modeled for rainfed maize in this study was similar to that calculated at the rainfed sites in Minnesota and Nebraska. The NEP of near zero g C m^–2 modeled for irrigated and rainfed soybean in this study (Table 4) was in the midrange of those calculated from gap-filled EC fluxes at these other sites. The lower NEP of soybean was attributed to the less productive C₃ pathway for CO₂ fixation, and the large respiratory cost of symbiotic N₂ fixation (Table 4). However, this respiratory cost avoids C emissions from manufacturing N fertilizer, the use of which would reduce NBP of maize by 11 and 20 g C m^–2 yr^–1 for applications of 9 and 17 g N m^–2 yr^–1 in the rainfed and irrigated fields during 2003, based on the total C costs of fertilizer manufacture, transport, and application calculated by Schlesinger (2000).

The total C removed as soybean and maize grain from the modeled irrigated and rainfed rotations was greater than their NEP during 2002–2003, so rotation NBP was negative (net C source) if grain C was assumed to return to the atmosphere (Table 4). These negative values for NBP were consistent with those calculated from most EC studies of maize–soybean rotations (Baker and Griffis, 2005; Verma et al., 2005), although not all (Hollinger et al., 2005—but see Dobermann et al., 2006). In both the modeled and EC studies, negative rotation NBP was caused by the failure of positive maize NBP to offset negative soybean NBP.

Because annual plants do not maintain C stocks at a yearly time scale, long-term NBP of maize–soybean rotations can also be estimated from changes in soil + litter C. These changes arise from differences between R_h and litter inputs from unharvested shoots, roots, nodules, and mycorrhizae (e.g., Table 4). Long-term field studies of rainfed maize–soybean rotations in the U.S. midwest have indicated only small changes in SOC over time (e.g., –21 ± 13 g C m^–2 yr^–1 after 20 yr and +30 ± 24 g C m^–2 yr^–1 after 45 yr at two tilled sites in Iowa from Russell et al., 2005). More generally, long-term field studies have found that maize–soybean rotations can gain 90 ± 59 g C m^–2 yr^–1 under no-till vs. conventional till (West and Post, 2002), suggesting that no-till rotations are capable of rapid gains in SOC. However, changes of SOC reported in these studies are usually measured to depths of only 0.15 to 0.30 m, and so do not consider changes in deeper SOC that also contribute to CO₂ exchange in EC studies. Our model results indicate small gains in near-surface SOC + litter of 13 (rainfed) and 20 (irrigated) g C m^–2 yr^–1 (Fig. 9), such as are frequently found in no-till cropping systems. However, these model results also indicate that these gains are offset by losses of deeper SOC, resulting in net losses over the entire soil profile, consistent with the negative rotation NBP modeled and calculated from EC fluxes (Table 4). Including the C costs of fertilizer and other inputs would lower this NBP still further.

Long-term field studies of SOC in irrigated rotations are scarce, limiting our ability to corroborate the average long-term gain of 6 g C m^–2 yr^–1 in soil + litter C modeled in the irrigated vs. rainfed rotation (Fig. 9). Lal et al. (1998) estimated that irrigation raised soil C sequestration by 5 to 15 g C m^–2 yr^–1. Certainly gains in SOC under irrigated maize–soybean rotations, if any, would be unlikely to offset CO₂–C emissions from pumping irrigation water, estimated to be about 20 g C m^–2 yr^–1 (range 8.5–33 g C m^–2 yr^–1) depending on the source of energy (Follett, 2001). Therefore, irrigation would not likely contribute to net C sequestration by maize–soybean rotations.

	Appendix A: CO2 Fixation

TOP ABSTRACT INTRODUCTION MODEL DEVELOPMENT FIELD EXPERIMENT MODEL EXPERIMENT RESULTS DISCUSSION Appendix A: CO2 Fixation Appendix B: N2 Fixation REFERENCES

 

C4 CO2 Fixation C4 Mesophyll [1] A1 [2] A2 [3] A3 [4] A4 [5] A5 [6] A6 [7] A7 [8] A8 [9] A9 [10] A10 [11] A11 [12] A12 [13] A13 [14] A14 [15] A15 [16] A16 [17] A17 [18] A18 [19] A19 C4 Bundle Sheath [20] A20 [21] A21 [22] A22 [23] A23 [24] A24 [25] A25 [26] A26 C3 CO2 Fixation C3 Mesophyll [27] A27 [28] A28 [29] A29 [30] A30 [31] A31 [32] A32 [33] A33 [34] A34 [35] A35 [36] A36 [37] A37 [71] as in A12 [72] as in A13 C4 and C3 Water Relations [38] A38 [39] A39 [40] A40 [41] A41

Definition of Variables in Appendix A

Variable Definition Units Equations Input values Alfi,j,k leaf area m–2 leaf m–2 ground A9, A10, A24, A25, A35, A36 shape parameter for response of Ji,j,k,l,m,n,o to Ii,l,m,n,o – A8, A23, A34 0.75 B parameter such that ft = 1.0 at Tc = 298.15 K A13 17.533 ß shape parameter for stomatal effects on CO2 diffusion and non-stomatal effects on carboxylation MPa–1 A4, A12, A30 –5.0 Cb [CO2] in canopy air µmol mol–1 A2, A5, A28, A31 Cc(b4)i,j,k [CO2] in C4 bundle sheath µM A15, A16, A19, A21 Cc(m3)i,j,k,l,m,n,o [CO2] in C3 mesophyll in equilibrium with Cii,j,k,l,m,n,o µM A32 Cc(m4)i,j,k,l,m,n,o [CO2] in C4 mesophyll in equilibrium with Cii,j,k,l,m,n,o µM A6, A16 Ci(m3)i,j,k,l,m,n,o [CO2] in C3 mesophyll air µmol mol–1 A28 Ci(m3)'i [CO2] in C3 mesophyll air when ci = 0 µmol mol–1 A31 0.67 x Cb Ci(m4)i,j,k,l,m,n,o [CO2] in C4 mesophyll air µmol mol–1 A2 Ci(m4)'i [CO2] in C4 mesophyll air when ci = 0 µmol mol–1 A5 0.45 x Cb [c3(b4)i,j] concentration of non-structural C3 fixation product in C4 bundle sheath kg kg–1 A26, A39 [c3(m3)i,j] concentration of non-structural C3 fixation product in C3 mesophyll kg kg–1 A37, A39 C4(b4)i,j,k non-structural C4 fixation product in C4 bundle sheath g C m–2 A14, A15, A18 C4(m4)i,j,k non-structural C4 fixation product in C4 mesophyll g C m–2 A14, A17 [C4(m4)i,j,k] concentration of non-structural C4 fixation product in C4 mesophyll µM A11 ea atmospheric vapor density at Ta and ambient humidity g m–3 A38 eci canopy vapor density at Tc and c g m–3 A38 quantum yield µmol e– µmol quanta–1 A8, A23, A34 0.45 (Farquhar et al., 1980) fC(c3)i,j,k C3 product inhibition of RuBP carboxylation activity in C4 bundle sheath or C3 mesophyll – A24, A25, A26, A35, A36, A37 fC(m4)i,j,k C4 product inhibition of PEP carboxylation activity in C4 mesophyll – A9, A10, A11 ftvi temperature effect on carboxylation – A9, A10, A13, A24, A25, A35, A36 fi nonstomatal water effect on carboxylation – A9, A10, A12, A24, A25, A35, A36 (b4)i,j,k CO2 compensation point in C4 bundle sheath µM A21 (m3)i,j,k CO2 compensation point in C3 mesophyll µM A32 (m4)i,j,k CO2 compensation point in C4 mesophyll µM A6 Ha energy of activation J mol–1 A13 57.5 x 103 Hdh energy of high temperature deactivation J mol–1 A13 220 x 103 Hdl energy of low temperature deactivation J mol–1 A13 190 x 103 Ii,l,m,n,o irradiance µmol m–2 s–1 A8, A23, A34 Jmax' specific electron transport rate at nonlimiting I and 25°C when ci = 0 and nutrients are nonlimiting µmol g–1 s–1 A10, A25, A36 400 J(b4)i,j,k,l,m,n,o electron transport rate in C4 bundle sheath µmol m–2 s–1 A22, A23 J(m3)i,j,k,l,m,n,o electron transport rate in C3 mesophyll µmol m–2 s–1 A33, A34 J(m4)i,j,k,l,m,n,o electron transport rate in C4 mesophyll µmol m–2 s–1 A7, A8 Jmax(b4)i,j,k electron transport rate in C4 bundle sheath at nonlimiting I µmol m–2 s–1 A23, A25 Jmax(m3)i,j,k electron transport rate in C3 mesophyll at nonlimiting I µmol m–2 s–1 A34, A36 Jmax(m4)i,j,k electron transport rate in C4 mesophyll at nonlimiting I µmol m–2 s–1 A8, A10 Kc(b4)i Michaelis-Menten constant for carboxylation in C4 bundle sheath µM A21 30.0 at 25°C and zero O2 (Lawlor, 1993) Kc(m3)i Michaelis-Menten constant for carboxylation in C3 mesophyll µM A32 12.5 at 25°C and zero O2 (Lawlor, 1993) Kc(m4)I Michaelis-Menten constant for carboxylation in C4 mesophyll µM A6 3.0 at 25°C (Lawlor, 1993) KIC4(b4) constant for CO2 product inhibition of C4 decarboxylation in C4 bundle sheath µM A15 1000.0 KIC4(m4) constant for C4 product inhibition of PEP carboxylation activity in C4 mesophyll µM A11 5 x 106 KIlf constant for C3 product inhibition of RuBP carboxylation activity in C4 bundle sheath or C3 mesophyll caused by [lfi,j] g C g N–1 A26, A37 100 KIlf constant for C3 product inhibition of RuBP carboxylation activity in C4 bundle sheath or C3 mesophyll caused by [lfi,j] g C g P–1 A26, A37 1000 Cc(b4) conductance to CO2 leakage from C4 bundle sheath h–1 A16 20 C4(m4) rate constant for transfer of C4 fixation product from mesophyll to bundle sheath h–1 A14 0.5 C4(b4) rate constant for decarboxylation of C4 fixation product in C4 bundle sheath h–1 A15 0.5 Mc phytomass C g C m–2 A38 M average molecular mass of c3i g mol–1 A39 Nlfi,j,k total leaf N g N m–2 leaf A9, A10, A24, A25, A35, A36 [Nchl(b4)i,j,k]' ratio of chlorophyll N in C4 bundle sheath to total leaf N g N g N–1 A25 0.05 [Nchl(m3)i,j,k]' ratio of chlorophyll N in C3 mesophyll to total leaf N g N g N–1 A36 0.04 [Nchl(m4)i,j,k]' ratio of chlorophyll N in C4 mesophyll to total leaf N g N g N–1 A10 0.05 [Nrub(b4)i,j,k]' ratio of RuBP carboxylase N in C4 bundle sheath to total leaf N g N g N–1 A24 0.025 [Nrub(m3)i,j,k]' ratio of RuBP carboxylase N in C3 mesophyll to total leaf N g N g N–1 A35 0.20 [Npep(m4)i,j,k]' ratio of PEP carboxylase N in C4 mesophyll to total leaf N g N g N–1 A9 0.025 ai,l,z,x axial resistance to water transport along axes of primary (x = 1) or secondary (x = 2) roots or mycorrhizae MPa h m–1 A38 ri,l,z radial resistance to water transport from surface to axis of roots or mycorrhizae MPa h m–1 A38 si,l,z radial resistance to water transport from soil to surface of roots or mycorrhizae MPa h m–1 A38 [lfi,j] concentration of nonstructural root N uptake product in leaf g N g C–1 A26, A37 [lfi,j] concentration of nonstructural root P uptake product in leaf g P g C–1 A26, A37 c canopy water content m3 g C–1 A38, A39 ci' canopy water content when ci = 0 MPa m3 g C–1 A39 R gas constant J mol–1 K–1 A13, A39 8.3143 rai canopy aerodynamic resistance s m–1 A38 rci canopy stomatal resistance s m–1 A38, A41 rlfi,j,k,l,m,n,o leaf stomatal resistance s m–1 A2, A4, A12, A28, A30, A41 rlfmaxi leaf cuticular resistance s m–1 A4, A30 rlfmini,j,k,l,m,n,o leaf stomatal resistance when ci = 0 s m–1 A4, A5, A12, A30, A31 S change in entropy J mol–1 K–1 A13 710 Tci canopy temperature °C A13, A39 Vb(b4)i,j,k CO2–limited carboxylation rate in C4 bundle sheath µmol m–2 s–1 A20, A21 Vb(m3)i,j,k,l,m,n,o CO2–limited carboxylation rate in C3 mesophyll µmol m–2 s–1 A29, A32 Vb(m4)i,j,k,l,m,n,o CO2–limited carboxylation rate in C4 mesophyll µmol m–2 s–1 A3 Vbmax(b4)' RuBP carboxylase specific activity in C4 bundle sheath at 25°C when ci = 0 and nutrients are nonlimiting µmol g–1 s–1 A24 80 Vbmax(m3)' RuBP carboxylase specific activity in C3 mesophyll at 25°C when ci = 0 and nutrients are nonlimiting µmol g–1 s–1 A35 40 Vbmax(m4)' PEP carboxylase specific activity in C4 mesophyll at 25°C when ci = 0 and nutrients are nonlimiting µmol g–1 s–1 A9 160 Vbmax(b4)i,j,k CO2–nonlimited carboxylation rate in C4 bundle sheath µmol m–2 s-1 A21, A24 Vbmax(m3)i,j,k CO2–nonlimited carboxylation rate in C3 mesophyll µmol m–2 s–1 A32 Vbmax(m4)i,j,k CO2–nonlimited carboxylation rate in C4 mesophyll µmol m–2 s–1 A6, A9 Vc(b4)i,j,k,l,m,n,o CO2 fixation rate in C4 bundle sheath µmol m–2 s–1 A20 Vc(m3)i,j,k,l,m,n,o CO2 fixation rate in C3 mesophyll µmol m–2 s–1 A27, A29 Vc0(m3)i,j,k,l,m,n,o CO2 fixation rate in C3 mesophyll when ci = 0 MPa µmol m–2 s–1 A31 Vc(m4)i,j,k,l,m,n,o CO2 fixation rate in C4 mesophyll µmol m–2 s–1 A1, A3, A17, A18 Vc0(m4)i,j,k,l,m,n,o CO2 fixation rate in C4 mesophyll when ci = 0 MPa µmol m–2 s–1 A5 VC4(b4)i,j,k decarboxylation of C4 fixation product in C4 bundle sheath g C m–2 h–1 A15, A18, A19 VC4(m4)i,j,k transfer of C4 fixation product between C4 mesophyll and bundle sheath g C m–2 h–1 A14 Vg(m3)i,j,k,l,m,n,o CO2 diffusion rate into C3 mesophyll µmol m–2 s–1 A27, A28 Vg(m4)i,j,k,l,m,n,o CO2 diffusion rate into C4 mesophyll µmol m–2 s–1 A1, A2 Vj(b4)i,j,k,l,m,n,o irradiance-limited carboxylation rate in C4 bundle sheath µmol m–2 s–1 A20, A22 Vj(m3)i,j,k,l,m,n,o irradiance-limited carboxylation rate in C3 mesophyll µmol m–2 s–1 A29, A33 Vj(m4)i,j,k,l,m,n,o irradiance-limited carboxylation rate in C4 mesophyll µmol m–2 s–1 A3, A7 V(b4)i,j,k CO2 leakage from C4 bundle sheath to C4 mesophyll g C m–2 h–1 A16, A19 Wlf(b4)i,j,k C4 bundle sheath water content g m–2 A14, A16 Wlf(m4)i,j,k C4 mesophyll water content g m–2 A14 Y(b4)i,j,k carboxylation yield from electron transport in C4 bundle sheath µmol CO2 µmol e–1 A22 Y(m3)i,j,k,l,m,n,o carboxylation yield from electron transport in C3 mesophyll µmol CO2 µmol e–1 A33 Y(m4)i,j,k,l,m,n,o carboxylation yield from electron transport in C4 mesophyll µmol CO2 µmol e–1 A7 ci canopy water potential MPa A38, A40 i canopy osmotic potential MPa A38, A40 'i canopy osmotic potential at ci = 0 MPa MPa A39 sl soil water potential MPa A39 ti canopy turgor potential MPa A4, A30, A40

	Appendix B: N2 Fixation

TOP ABSTRACT INTRODUCTION MODEL DEVELOPMENT FIELD EXPERIMENT MODEL EXPERIMENT RESULTS DISCUSSION Appendix A: CO2 Fixation Appendix B: N2 Fixation REFERENCES

 

Microbial Growth [42] B1 [43] B2 [44] B3 [45] B4 [46] B5 [47] B6a [48] B6b [49] B7 [50] B8 [51] B9 [52] B10 [53] B11 N2 Fixation [54] B12 [55] B13 [56] B14 [57] B15 [58] B16 [59] [73] B17a [60] [74] B17b [61] [75] B18a [62] [76] B18b [63] [77] B19 [64] [78] B20 Nodule–Root Exchange [65] B21 [66] B22 [67] B23 [68] B24 [69] B25 [70] B26

Definition of Variables in Appendix B

Variable Definition Units Equations Input values B parameter such that ft = 1.0 at Tl = 298.15 K B2 17.533 ni,l nodule nonstructural C g m–2 B17a, B18a, B21, B22, B23, B24 [ni,l] nodule nonstructural C concentration g g–1 B1, B13 ri,l root nonstructural C g m–2 B21, B22, B23 DsO2 diffusivity of aqueous O2 m2 h–1 B6b EN2' direct energy cost of N2 fixation g N g C–1 B12, B14 0.25 (Gutschick, 1981, Voisin et al., 2003) FLCl fraction of nodule C litterfall remobilized as nonstructural C – B24 FLNl fraction of nodule N litterfall remobilized as nonstructural N – B25 FLPl fraction of nodule P litterfall remobilized as nonstructural P – B26 fCP effect of nodule nonstructural C or P content on N2 fixation – B12, B13 fNP effect of nodule N or P content on respiration – B1, B3 ft temperature function for nodule respiration – B1, B2 ftm temperature function for nodule maintenance respiration – B7, B8 Ha energy of activation J mol–1 B2 57.5 x 103 Hdh energy of high temperature deactivation J mol–1 B2 220 x 103 Hdl energy of low temperature deactivation J mol–1 B2 190 x 103 Kn Michaelis-Menten constant for nodule respiration of ndi,l kg kg–1 B1 0.01 KIn inhibition constant for nonstructural N:C on N2 fixation kg kg–1 B13 10 KIn inhibition constant for nonstructural N:P on N2 fixation kg kg–1 B13 1000 KN2r Michaelis-Menten constant for nodule N2 uptake g N m–3 B12 0.14 KO2r Michaelis-Menten constant for nodule O2 uptake g O m–3 B6a rate constant for nonstructural C,N,P exchange between root and nodule h–1 B21, B22, B23 Lri,l root length m m–2 B6b LCi,l nodule C litterfall g C m–2 h–1 B11, B16, B24 LNi,l nodule N litterfall g N m–2 h–1 B19, B25 LPi,l nodule P litterfall g P m–2 h–1 B20, B26 Mni,l nodule structural C g C m–2 B1, B11, B12, B16, B17, B18, B21 Mri,l root structural C g C m–2 B21 [Nn'] maximum nodule structural N concentration g N g C–1 B3, B12 0.1 Nni,l nodule structural N g N m–2 B7, B11, B12, B17, B19, B25 [Nni,l] nodule structural N concentration g N g C–1 B3, B17a [N2ri,l] rhizosphere aqueous N2 concentration g N m–3 B12 ni,l nodule nonstructural N g N m–2 B17a, B22, B25 ri,l root nonstructural N g N m–2 B22 [ni,l] nodule concentration of nonstructural N g g–1 B13, B17a [O2ri,l] rhizosphere aqueous O2 concentration g O m–3 B6a, B6b [O2l] soil aqueous O2 concentration g O m–3 B6b [Pn'] maximum nodule structural P concentration g P g C–1 B3, B18a 0.01 Pni,l nodule structural P g P m–2 B18a, B20, B26 [Pni,l] nodule structural P concentration g P g C–1 B3, B11 ni,l nodule nonstructural P g P m–2 B18a, B23, B26 ri,l root nonstructural P g P m–2 B23 [ni,l] nodule concentration of nonstructural P kg kg–1 B13 R gas constant J mol–1 K–1 B2 8.3143 Rgi,l nodule growth respiration g C m–2 h–1 B9, B12, B15 R' specific nodule respiration at 25°C, and nonlimiting O2, ndi,l, ndi,l, and ndi,l h–1 B1 0.125 Ri,l nodule respiration under ambient O2 g C m–2 h–1 B4, B9, B10, B24 Rm specific nodule maintenance respiration at 25°C g C g C–1 h–1 B7 Rmaxi,l nodule respiration under nonlimiting O2 g C m–2 h–1 B1, B4, B5 Rmi,l nodule maintenance respiration g C m–2 h–1 B7, B9, B10, B24 RN2i,l nodule respiration for N2 fixation g C m–2 h–1 B14, B15, B24 Rsi,l nodule senescence respiration g C m–2 h–1 B9, B11 rri,l root radius m B6b rwl radius of soil water films m B6b S change in entropy J mol–1 K–1 B2 710 Tl soil temperature K B2, B8 Ui,l uptake of nodule nonstructural C for growth g C m–2 h–1 B15, B16, B24 Vi,l nonstructural C transfer between root and nodule g C m–2 h–1 B21, B24 Vi,l nonstructural N transfer between root and nodule g N m–2 h–1 B22, B25 VN2i,l N2 fixation g N m–2 h–1 B12, B14, B25 VO2maxi,l O2 uptake by nodules under nonlimiting O2 g O m–2 h–1 B4, B5, B6a VO2i,l O2 uptake by nodules under ambient O2 g O m–2 h–1 B4, B6 Vi,l nonstructural P transfer between root and nodule g P m–2 h–1 B23, B26 Yn' nodule growth yield g C g C–1 B15, B16 0.67 y shape parameter for ftm – B8 0.081

Subscript Definition Value used in this study i population (e.g., species or cohort) 1 j branch or tiller up to 5 k node up to 25 l layer (canopy or soil) up to 10 (canopy), 12 (soil) m azimuth 4 n inclination 4 o exposure (sunlit or shaded) 2

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TOP ABSTRACT INTRODUCTION MODEL DEVELOPMENT FIELD EXPERIMENT MODEL EXPERIMENT RESULTS DISCUSSION Appendix A: CO2 Fixation Appendix B: N2 Fixation REFERENCES

 

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