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Published in Agron. J. 96:1693-1705 (2004).
© American Society of Agronomy
677 S. Segoe Rd., Madison, WI 53711 USA

Agronomic Modeling

Modeling Elevated Carbon Dioxide Effects on Water Relations, Water Use, and Growth of Irrigated Sorghum

R. F. Granta,*, B. A. Kimballb, G. W. Wallb, J. M. Triggse, T. J. Brooksf, P. J. Pinter, Jr.b, M. M. Conleyb, M. J. Ottmanc, R. L. Lamorteb, S. W. Leavittc, T. L. Thompsond and A. D. Matthiasd

a Dep. of Renewable Resour., Univ. of Alberta, Edmonton, AB, Canada T6G 2H1
b USDA-ARS, U.S. Water Conserv. Lab., 4331 E. Broadway, Phoenix, AZ 85040
c Lab. of Tree-Ring Res., Tucson, AZ 85721
d Dep. of Soil, Water, and Environ. Sci., Univ. of Arizona, Tucson, AZ 85721
e Maricopa Agric. Cent., Univ. of Arizona, Maricopa, AZ 85239
f Dep. of Geogr., Arizona State Univ., Tempe, AZ 85287

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

Received for publication November 28, 2004.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENT
 SIMULATION EXPERIMENT
 RESULTS
 DISCUSSION
 REFERENCES
 
Elevated concentrations of atmospheric CO2 (Ca) are believed to raise sorghum [Sorghum bicolor (L.) Moench] productivity by improving water relations. In ecosys, water relations are simulated by solving for the canopy water potential ({psi}C) at which water uptake from a model of soil–root–canopy water transfer equilibrates with transpiration from the canopy energy balance. Simulated water relations were tested with {psi}C, water uptake, and energy exchange measured under ambient (363 µmol mol–1) and elevated (566 µmol mol–1) Ca and high vs. low irrigation in a free air CO2 enrichment experiment during 1998 and 1999. Model results, corroborated by field measurements, showed that elevated Ca raised {psi}C and lowered latent heat fluxes under high irrigation and delayed water stress under low irrigation. Changes in {psi}C modeled under ambient vs. elevated Ca varied diurnally, with lower {psi}C causing earlier midafternoon stomatal closure under ambient Ca. Modeled changes in sorghum water status caused elevated Ca to raise seasonal water efficiency under high and low irrigation by 20 and 26% (vs. 20 and 13% measured) in 1998 and by 9 and 27% (vs. 6 and 26% measured) in 1999. Ecosys was used to generate an irrigation response function for sorghum yield, which indicated that yields would rise by {approx}13% for a range of irrigation rates if air temperatures were to rise by 3°C and Ca by 50%. Current high sorghum yields could be achieved with {approx}120 mm or {approx}20% less irrigation water if these rises in temperature and Ca were to occur.

Abbreviations: Ca, atmospheric CO2 • Ci, intercellular CO2 concentration • DOY, day of year • FACE, free air CO2 enrichment (experiment) • gC, stomatal conductance • GCM, general circulation model • gL, leaf conductance • H, sensible heat • IRTs, infrared thermometers • LE, latent heat • Rn, net radiation • TC, canopy temperature • VPD, vapor pressure deficit • WUE, water use efficiency • {psi}C, canopy water potential • {psi}S, soil water potential • {psi}T, canopy turgor potential • {psi}{pi}, osmotic potential • {Omega}R, root–canopy hydraulic resistances • {Omega}S, soil–root hydraulic resistances


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MODEL DEVELOPMENT
 FIELD EXPERIMENT
 SIMULATION EXPERIMENT
 RESULTS
 DISCUSSION
 REFERENCES
 
RISING CONCENTRATIONS of Ca and other greenhouse gases are believed to be causing changes in climate that may have important impacts on water use in food production. These impacts will result from several contrasting effects of climate change on terrestrial water use. The most direct impact is the reduction in transpiration caused by lower stomatal conductance (gC) commonly found under elevated Ca. In several FACE experiments with ample water and N, Kimball et al. (2002) reported that a 190 µmol mol–1 rise in Ca reduced gC's measured in sorghum, wheat (Triticum aestivum L.), and cotton (Gossypium hirsutum L.) by {approx}37, 34, and 15%, respectively. These reductions may be larger under N limitation (Wall et al., 2001a).

However, the effect of lower gC on transpiration under elevated Ca may be partially offset by a rise in canopy temperature (TC) and hence canopy vapor pressure (Kimball et al., 1999). This effect may also be offset by an increase in leaf area and hence radiative loading (Kimball et al., 2002). In FACE experiments with ample water and N, Kimball et al. (2002) reported that a 190 µmol mol–1 rise in Ca raised temperatures and leaf area index of C3 grasses by 0.6°C and 11%, respectively.

Another direct impact of climate change on water use is the increase in transpiration caused by larger canopy–atmosphere vapor pressure gradients that develop under rising air temperatures. The increase in these gradients is believed to be only partially offset by rising atmospheric humidity caused by more rapid evapotranspiration. Thus, regional soil drying is a projected consequence of some climate change scenarios unless accompanied by substantial increases in precipitation. On the other hand, rising air temperatures also hasten crop development and hence shorten growing seasons, reducing water use. There is much uncertainty about the net effects of elevated Ca and temperature on crop water requirements.

Ecosystem models have frequently been used to account for these contrasting impacts of climate change on terrestrial water use. Hatch et al. (1999) used the CROPGRO (e.g., Jones et al., 1988) and CERES (Jones and Kiniry, 1986) models to predict reductions of up to 50% in the irrigation requirements of field crops after 100 yr of climate change simulated by the U.K. Meteorological Office (UKMO) general circulation model (GCM) in the southeast USA. These reductions were attributed to higher Ca and precipitation and to shortened growing seasons caused by more rapid phenological advance under higher temperatures. Strzepek et al. (1999) used the same crop models to predict reductions of up to 20% in the irrigation requirements of maize (Zea mays L.) after 50 yr of Goddard Institute of Space Studies (GISS) and Geophysical Fluid Dynamics Laboratory (GFDL) GCM climate change in the midwestern USA. These reductions were also attributed to shortened growing seasons caused by higher temperatures. In the same study, Strzepek et al. (1999) predicted increases of up to 75% in the irrigation requirements of soybean [Glycine max (L.) Merr.]. These increases were attributed to longer growing seasons caused by the photoperiod response of soybean to earlier planting. Tubiello et al. (2000) used CropSyst (Stockle et al., 1994) to predict that shortened growing seasons would reduce irrigation requirements by 60% for maize, 50% for soybean, and 10% for sorghum in Italy after 100 yr of GISS and GFDL GCM climate change. However, they found that increases in irrigation of 60 to 90% for maize and soybean and of 15% for sorghum would be required to maintain current yields under these climate change scenarios.

The effects of elevated Ca on crop water requirements have been modeled on a daily time step by altering the Priestley–Taylor (Strzepek et al., 1999) or Penman–Monteith (Tubiello et al., 2000) equations to account for decreased gC under elevated Ca. Crop water use in these models may be constrained by soil water uptake calculated daily from soil–canopy water potential gradients and empirically estimated root distributions (Jara and Stockle, 1999). However, these modeling techniques require the temporal averaging of diurnally varying phenomena such as {psi}C and gC, which respond very nonlinearly to diurnal changes in weather. Important effects of elevated Ca on transpiration caused by higher TC's (Kimball et al., 1999) and water potentials (Wall et al., 2001b) cannot be simulated with these techniques. These modeling techniques can only be tested with temporally aggregated field data (e.g., seasonal phytomass or evapotranspiration) that cannot distinguish among alternative process-level hypotheses. The effects of elevated Ca on transpiration would in theory be better modeled at time scales more consistent with that at which these effects occur (e.g., hourly).

It is important that model results be subjected to well-constrained tests before models are used in predictive studies of climate change effects. Generally speaking, model tests become better constrained as their spatial and temporal resolutions increase. The use of energy fluxes in model testing is well constrained in that test data are highly resolved temporally and flux theory is comparatively well defined. Atmospheric CO2 effects on crop water requirements are therefore best modeled by explicitly simulating the diurnal changes in ecosystem–atmosphere energy exchange by which evapotranspiration is driven. This modeling requires the coupling of closure schemes for canopy and soil surface energy balances with transfer schemes for soil water movement and root water uptake. This coupling must occur at a time scale that allows the large diurnal variation in these energy balances to be represented. In earlier work, we tested algorithms for coupling energy balances with water uptake in ecosys (http://www.rr2.ualberta.ca/Research/ecosys/; verified 26 Aug. 2004) (Grant, 2001) with findings from a FACE experiment on wheat (Grant et al., 1995a, 1995b, 1999). We now extend this testing to sorghum to determine whether these same algorithms can simulate Ca effects on water use by a C4 crop grown under much higher temperatures. We then use these algorithms to estimate climate change effects on irrigation requirements of sorghum.


   MODEL DEVELOPMENT
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
FIELD EXPERIMENT
 SIMULATION EXPERIMENT
 RESULTS
 DISCUSSION
 REFERENCES
 
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 those between the atmosphere and each of the surfaces (soil, plant residue, and snow) of the ground beneath (Grant et al., 1999). 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 multilayered multipopulation soil–root–canopy system. The first stage of this solution requires convergence to a value of TC 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., 1999). These fluxes are controlled by aerodynamic conductance (gA) and gC. Two controlling mechanisms are postulated for gC:

  1. At the leaf level, a maximum leaf conductance (gL) is calculated for each leaf surface that allows an initial intercellular CO2 concentration (Ci)/Ca ratio for sorghum of 0.45 (Williams et al., 2001) to be maintained at carboxylation rates calculated under ambient irradiance, temperature, Ca, and full turgor. This ratio will be allowed to vary diurnally when hourly canopy water status is solved at a later stage in the calculations as described in the Carbon Dioxide Fixation section below. The modeling of carboxylation rates has been elaborated from earlier work to include C4 processes. In C4 plants, the mesophyll carboxylation rate is the lesser of CO2– and light-limited reaction rates (Berry and Farquhar, 1977). The CO2–limited rate is a Michaelis–Menten function of PEP carboxylase activity and aqueous CO2 concentration in the mesophyll parameterized from Berry and Farquhar (1977) and from Edwards and Walker (1983). The light-limited rate is a hyperbolic function of absorbed irradiance and mesophyll chlorophyll activity with a quantum requirement from Berry and Farquhar (1977). The mesophyll concentration of the C4 carboxylation product drives a mesophyll-bundle sheath transfer algorithm that maintains a set bundle sheath/mesophyll C4 concentration ratio. The bundle sheath concentration drives a decarboxylation reaction, the CO2 product of which drives a C3 carboxylation model (Farquhar et al., 1980) in the bundle sheath parameterized for C4 plants from Seeman et al. (1984) and a leakiness algorithm that returns CO2 from the bundle sheath to the mesophyll. Carboxylase and chlorophyll activities in both the mesophyll and bundle sheath are the products of specific activities and concentrations. Specific activities are constrained by C4 and C3 (Bowes, 1991; Stitt, 1991) product inhibition so that both mesophyll and bundle sheath carboxylation rates are fully coupled to rates of product removal. Product removal rates are determined by phytomass biosynthesis rates that are controlled by plant water and nutrient status. Carboxylase and chlorophyll concentrations in both the mesophyll and bundle sheath are set from leaf structural N concentrations. These concentrations are determined by leaf nonstructural N/C ratios controlled by plant nutrient status. This C4 carboxylation model gives bundle sheath CO2 concentrations similar to those reported by Furbank and Hatch (1987) and bundle sheath CO2 leakiness, expressed as a fraction of PEP carboxylation, similar to that measured by Williams et al. (2001). Leaf carboxylation rates from this model are then used with the initial Ci/Ca to calculate maximum gL, which is then aggregated by leaf surface area to maximum gC for use in the energy balance convergence scheme (Grant et al., 1999).
  2. At the canopy level, gC is then reduced from that at full turgor through an exponential function of canopy turgor potential ({psi}T) determined from total {psi}C and osmotic potential ({psi}{pi}) generated during convergence for transpiration vs. water uptake. The calculation of {psi}C is described in the Water Relations section below. The exponential function of {psi}T used here is based on that proposed by Zur and Jones (1981) to account for the effects of osmotic adjustment on gC. There is no direct response of gC to vapor pressure deficit (VPD) in ecosys although such a response is included in most other models of gC. However, larger VPD raises transpiration, forcing lower {psi}C and {psi}T to be calculated in ecosys during convergence for transpiration vs. water uptake. The exponential function used to calculate gC from {psi}T causes gC to become more sensitive to {psi}T as {psi}C and {psi}T decline. In wet soil, {psi}C and {psi}T may be high enough that gC is not very sensitive to VPD, as has been found experimentally by Garcia et al. (1998). However, gC becomes more sensitive to VPD as soil or atmospheric water deficits become more severe.

Water Relations
After convergence for TC is achieved, the difference between canopy transpiration E from the energy balance and total water uptake U 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 (Grant et al., 1999). This difference is minimized by adjusting {psi}C, which determines each term from which this difference is calculated. The value of {psi}C determines that of {psi}T, and hence of gC, through its effect on {psi}{pi} (Girma and Krieg, 1991; Grant, 1995; Eq. 24–25 in Grant et al., 1999). The difference between {psi}C and soil water potential ({psi}S) determines U by establishing potential differences across soil–root ({Omega}S) and root–canopy ({Omega}R) hydraulic resistances and in each rooted soil layer (Eq. 32–37 in Grant et al., 1999). 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 {psi}C determine those in canopy water content according to plant water potential–water content relationships (e.g., Acevedo et al., 1979; Saliendra and Meizner, 1991). Because gC and TC both drive E, the canopy energy balance described under the Energy Exchange section above is recalculated for each adjusted value of {psi}C during convergence.

Carbon Dioxide Fixation
After successful convergence for TC and {psi}C, leaf carboxylation rates are adjusted from those calculated under full {psi}T to those under ambient {psi}T. This adjustment is required by the decrease in gC from its maximum value (calculated in the Energy Exchange section above) to that at ambient {psi}T (calculated in the Water Relations section above). The adjustment is achieved through a convergence solution for Ci at which the diffusion rate of gaseous CO2 between Ca and Ci through gL (Eq. 48–53 in Grant et al., 1999) equals the carboxylation rate of aqueous CO2 at the aqueous equivalent of Ci (described in the Energy Exchange section above). This convergence arrives at a lower Ci than that at full {psi}T so that Ci/Ca declines under water stress as found by Williams et al. (2001). The CO2 fixation rate of each leaf surface at convergence is added to arrive at a value for gross canopy CO2 fixation by each tiller (or branch) of each plant population (i.e., species or cohort) in the model.

Carbon Respiration
The product of CO2 fixation is added to a nonstructural C pool from which C is oxidized (Eq. 26–31 in Grant et al., 1999). Oxidized C is first used to meet requirements for maintenance respiration, and then any excess is used to drive biosynthesis according to organ-specific growth yields. Low nonstructural C may cause C oxidation to be less than maintenance requirements, in which case the shortfall is made up through respiration of remobilizable protein C withdrawn from lamina and sheath C. Upon exhaustion of the remobilizable protein C in each lamina or sheath, the remaining structural C is dropped from the tiller and added to the soil surface as litter. Environmental constraints such as nutrient, heat, or water stress that reduce nonstructural C formation and hence oxidation with respect to maintenance requirements will therefore hasten the loss of lamina and sheath C from the plant. Net canopy CO2 fixation is calculated as the difference between aggregated leaf carboxylation rates and C oxidation rates.


   FIELD EXPERIMENT
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENT
SIMULATION EXPERIMENT
 RESULTS
 DISCUSSION
 REFERENCES
 
Crop Management
A 12-ha laser-leveled field of Trix clay loam [fine-loamy mixed (calcareous) hyperthermic Typic Torrifluvent] at the University of Arizona's Maricopa Agricultural Research Center (MAC) 30 km south of Phoenix, AZ, was fertilized and cultivated on 10 June 1998 and 1 June 1999 (Table 1). Sorghum (DeKalb hybrid ‘DK54’) was planted on 15–16 July 1998 and 15–16 June 1999 in 0.76-m rows to give populations of 22 plants m–2 (1998) and 26 plants m–2 (1999). Research plots in the "wet" treatment were flood-irrigated from adjacent canals to replace evapotranspirational demand whenever {approx}30% of plant available water in the rooted soil zone was depleted (Table 1). Plots in the "dry" treatment received fewer irrigations. Additional fertilizer was added in irrigation water (Table 1). The field was located within an irrigated area that extended for more than 1 km in all directions so that most of the area surrounding the site was irrigated during the entire experiment. Some damage to the sorghum was caused by frosts after 10 Nov. 1998 and by hail on 16 Sept. 1999. Plots were harvested on 21 Dec. 1998 and 26 Oct. 1999. Further details about crop management are given in Ottman et al. (2001).


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  		Table 1. Dates and amounts of irrigation and fertilization in the wet and dry treatments during 1998–1999.

 
Hourly averages of solar radiation, air temperature, wind speed and humidity, and hourly totals of precipitation were recorded at a height of 2 m over the field site and at the Arizona Meteorological Network (AZMET) station on the Maricopa Research Center about 1 km away. Soil water contents were measured before and after each irrigation in all plots using a neutron probe (Hydroprobe Model 503 CR, Campbell Pacific Co., Martinez, CA) at 0.3-m increments from 0.46 to 1.8 m (1998) or from 0.23 to 3.0 m (1999). Evapotranspiration was calculated for each plot as irrigation + rainfall – change in soil water content within the estimated rooting zone during both growing seasons (Conley et al., 2001). A pressure chamber (Model 3000, Soil Moisture Equipment Corp., Santa Barbara, CA) was used to measure midday water potentials in the midribs of blades excised from uppermost fully expanded leaves (Wall et al., 2001b). Dry masses of different plant components (leaves, crowns, stems, chaff, and grain) were measured weekly from eight plants in each replicate of each treatment (Ottman et al., 2001). Leaf area was measured weekly on the sampled plants using a leaf area machine (LI-3100, LI-COR, Lincoln, NE).

Carbon Dioxide Treatments
Four replicates of control and FACE treatments (Hendrey, 1993), consisting of toroidal plenum rings constructed from 30-cm-diam. pipe with 2.5-m vertical pipes located every 2.4 m around the periphery, were established in 25-m-diam. circular plots shortly after seeding. These rings were mounted on 15-cm blocks to avoid interfering with the flood irrigation and located such that one-half of each ring was in each of the wet and dry irrigation treatments. From 31 July to 8 December 1998 and from 2 July to 19 October 1999 (50% emergence to maturity), a computer control system used wind speed, wind direction, and CO2 concentration measured at the center of each control vs. FACE ring to regulate CO2 emission from vertical pipes upwind of the plots. During emission, ambient air (control) or CO2–enriched air (FACE) was released upwind of the plots through holes in the vertical pipes at elevations from 0.5 to 2.0 m, depending on crop height. Average daytime CO2 concentration maintained over the FACE plots was 556 µmol mol–1 in 1998 and 566 µmol mol–1 in 1999 while those over the control plots were 363 µmol mol–1 in 1998 and 373 µmol mol–1 in 1999. One-minute-averaged CO2 concentrations measured in the plots were within 10% of these values 87% of the time. Further details about CO2 treatments are given in Ottman et al. (2001).

Energy Exchange Measurements
The plots were semicircular with a useable radius of only about 10 m, providing limited fetch for calculating CO2 x irrigation effects on evapotranspiration from profiles of wind speed, temperature, and water vapor measured above the crop. Therefore, a residual energy balance method was used to calculate latent heat fluxes from the individual plots (e.g., Huband and Monteith, 1986). This technique was reasoned to be less sensitive to fetch constraints because:

  1. All plots were in a field of sorghum in which all structural elements were close to the same size and geometry. Therefore, aerodynamic resistance would not be expected to vary much among plots.
  2. Turbulent transfer processes are a logarithmic function of height above the crop surface so that gradients close to the crop are largest and most important in determining rates of heat transfer. Crop surface temperatures were measured with infrared thermometers (IRTs) that were not affected by wind speed, thereby minimizing fetch requirements. The parameters for canopy emittance and reflected sky radiation used in the calculation of surface temperatures for this study were found by Huband and Monteith (1986) to give unbiased differences between radiative and aerodynamic temperatures of not >1.5 K and usually <1 K. Under the conditions of the FACE experiment, a difference of 1 K between radiative and aerodynamic temperatures would cause a difference of as much as 60 W m–2 in the calculation of sensible heat flux. However, this difference would not be systematic.

During most of the experiment, net radiation (Rn) was measured every 15 min using net radiometers (Model Q6, Radiation and Energy Balance Syst. Inc., Seattle, WA) calibrated before and after the experiment against a standard net radiometer (Model LXV 055, DR Lange, Germany). The net radiometers were mounted 1.0 m above the crop in two replicates of each Ca and irrigation treatment where they were raised, cleaned, and leveled weekly. Soil heat flux was measured from four soil heat flux plates (Model HFT-3, Radiation Energy Balance Syst., Seattle, WA) placed at a depth of 10 mm between sorghum rows in two replicates of each Ca x irrigation treatment. A thermocouple was placed at a depth of 5 mm above each heat flux plate to measure changes in soil heat storage. Sensible heat flux was calculated from TC's measured with stationary IRTs (Model 4000a, 15° field of view, Everest Interscience, Tustin, CA) calibrated against an extended-area black-body source (Model EABB-250, Advanced Kinetics, Huntington Beach, CA) and from dry and wet bulb temperatures measured with a pair of aspirated psychrometers. The IRTs were positioned 1 m above the sorghum in two replicates of each Ca x irrigation treatment to view the crop canopy northward at a zenith angle of 45°. Infrared thermometer temperatures were corrected for canopy emittance and reflected sky radiation to account for differences between radiative and aerodynamic surface temperatures (Huband and Monteith, 1986). The aspirated psychrometers were mounted at a height of 2 m in the same plots as the net radiometers. Aerodynamic resistances used in sensible heat flux calculations were computed from wind speed measured at 2 m above the ground with a three-cup anemometer and photochopper (Model 12102D, R.M. Young Co., Traverse City, MI) and from zero plane displacement and roughness length calculated from canopy height (Azevedo and Verma, 1986), using a nonisothermal stability correction (Mahrt and Ek, 1984). Further details about the energy exchange measurements are given in Triggs et al. (2004).


   SIMULATION EXPERIMENT
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENT
 SIMULATION EXPERIMENT
RESULTS
 DISCUSSION
 REFERENCES
 
The simulation model ecosys was initialized with the physical and chemical properties of Trix clay loam (Table 1 in Grant et al., 1999) and the biological properties of sorghum derived from literature sources [including kinetic constants and concentrations of carboxylases and chlorophyll for C3 and C4 reactions (Berry and Farquhar, 1977; Ku et al., 1979; Seeman et al., 1984), Ci/Ca ratio (Williams et al., 2001), leaf optical properties, canopy and root architecture parameters (Aguirrezabal et al., 1993; Klepper, 1990), kinetic constants for root nutrient uptake (Barber and Cushman, 1981), and parameters for root (Reid and Huck, 1990; Doussan et al., 1998) and stomatal (Girma and Krieg, 1992) conductances]. The model was run from 1 May 1998 to 31 Oct. 1999 at Ca = 363 or 556 µmol mol–1 (1998) and at Ca = 373 or 566 µmol mol–1 (1999) under the irrigation and fertilization schedules for the wet and dry treatments (Table 1) using management practices and hourly meteorological data reported from the field site. Because some of the flood irrigation was observed to flow through soil cracks, soil macroporosity was set in the model to approximate the loss of irrigation water inferred from neutron probe readings taken immediately before and after each irrigation. Initial soil water, NH+4, and NO–3 contents were selected to give those measured on 23 July 1998 in each soil horizon of each treatment. All site-specific inputs required by ecosys were confined to site, soil, and plant properties that could be measured independently of the model. All model parameters for CO2 fixation (except PEP carboxylation), respiration, and partitioning by plant and microbial populations were the same as those used in earlier studies of C and energy exchange over agricultural crops (Grant and Baldocchi, 1992; Grant et al., 1993, 1995a, 1995b, 1999).

Hourly totals of canopy + ground Rn (Eq. [2] and [17] in Grant et al., 1999), latent heat (LE) (Eq. [3] and [18] in Grant et al., 1999), and sensible heat (H) (Eq. [5] and [19] in Grant et al., 1999) simulated in ecosys were compared with hourly averaged Rn, LE, and H measured under 363 vs. 556 µmol mol–1 Ca (1998) or 373 vs. 566 µmol mol–1 Ca (1999) in the wet and dry treatments. Accumulated evapotranspiration simulated by ecosys from LE in each Ca x irrigation treatment was compared with that estimated from neutron probe measurements during both growing seasons. Phytomass simulated for each Ca x irrigation treatment was compared with weekly measurements.

A relationship between irrigation amount and sorghum yield was then derived by running ecosys from 1 May to 31 Oct. 1999 using 1999 meteorological data and crop management with a range of irrigation rates applied in a biweekly schedule. Initial conditions for these runs were those simulated on 30 Apr. 1999 by the 1998–1999 ecosys model run under ambient Ca and high irrigation (Table 1). The relationship was then derived under hypothesized rises of 3.0°C in 1999 air temperatures and of 50% in ambient Ca to establish its sensitivity to likely changes in future climate.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENT
 SIMULATION EXPERIMENT
 RESULTS
DISCUSSION
 REFERENCES
 
Diurnal Energy Exchange under Ambient vs. Elevated Atmospheric Carbon Dioxide
In the model, elevated Ca caused only small increases in leaf carboxylation rates because aqueous CO2 concentrations maintained in the bundle sheath (1–2 mM depending on rates of C4 production in the mesophyll) were much larger than the Michaelis–Menten constant (Km) for C3 carboxylation (30 µM at 25°C). However, elevated Ca caused an increase in the Ca–Ci gradient that was proportional to that in Ca because Ci/Ca ratios in the model were conserved although not constant. Dividing the carboxylation rate by the Ca–Ci gradient therefore gave smaller values when calculating maximum gL under elevated vs. ambient Ca. When scaled to the canopy level, smaller gC reduced LE simulated under elevated Ca from that under ambient Ca. This effect of gC on LE was partially offset by that of a rise in vapor pressure gradient caused by a rise in TC modeled from the first-order closure of the canopy energy balance under elevated vs. ambient Ca.

The net effects of gC and TC on LE under elevated vs. ambient Ca are shown from day of year (DOY) 247 to 251 (4 to 9 September) 1999, immediately after irrigation on DOY 246 (Table 1), during the second year of the model run (Fig. 1). In the wet treatment, high {psi}S and low {Omega}S and {Omega}R allowed {psi}C and {psi}T in the model to be maintained at values high enough that gC did not decline, even under high VPD. High gC allowed rapid effluxes of LE (up to 700 W m–2 in Fig. 1a), even though midafternoon VPD reached 5 kPa, indicating that gC was correctly modeled not to be sensitive to VPD when {psi}S was high. Elevated Ca reduced both simulated and measured LE and increased simulated and measured H by 0 to 50 W m–2 (Fig. 1b vs. 1a). In the dry treatment, lower {psi}S and higher {Omega}S and {Omega}R forced {psi}C and {psi}T in the model to decline under higher VPD to values that caused gC to decline, reducing LE (midday values declined from 250 W m–2 to 150 W m–2 during this period with soil drying in Fig. 1c). Thus, gC was correctly modeled to be more sensitive to VPD when {psi}S was low. Elevated Ca caused lower LE to be simulated earlier in the season, slowing soil water depletion and delaying the onset of water stress. During DOY 247 to 251, higher {psi}S simulated under elevated Ca allowed sorghum to maintain higher {psi}C and {psi}T, and hence higher gC, so that simulated and measured LE were raised and H lowered by 50 to 100 W m–2 from those under ambient Ca (Fig. 1d vs. 1c). Higher {psi}T and gC under elevated Ca in the dry treatment caused midday Bowen ratios in both the model and the field to be reduced from >1 under ambient Ca to <1 under elevated Ca during early September 1999.



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  		Fig. 1. Net radiation, latent heat (LE), and sensible heat (H) fluxes simulated (lines) and measured (symbols) over sorghum during day of year 247 to 251 (4–8 September) 1999 in the (a) control wet, (b) free air CO2 enrichment (FACE) wet, (c) control dry, and (d) FACE dry treatments. Downward fluxes (influxes) are positive, and upward fluxes (effluxes) are negative. For irrigation schedules, see Table 1.

 
Regressions of modeled on measured LE during 1998 and 1999 indicated that differences between modeled and measured fluxes were comparable to replicate differences in the measured fluxes for all four Ca x irrigation treatments (Table 2). Regression parameters indicated close agreement between modeled and measured LE in the wet treatments of both years (b > 0.9, R2 > 0.8) and in the dry treatment of 1998 but lower modeled vs. measured LE in the dry treatment of 1999 (b < 0.8, R2 < 0.8).


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  		Table 2. Statistics from regressions of simulated on measured hourly latent heat fluxes over sorghum under ambient vs. elevated concentrations of atmospheric CO2 (Ca) in the wet vs. dry treatments during 1998 until frost on 10 November (n = 1512 hourly data pairs) and in 1999 until hail on 16 September (n = 936 hourly data pairs). Numbers in parentheses indicate Ca and total irrigation during each year.

 
Water Relations under Ambient vs. Elevated Atmospheric Carbon Dioxide
Lower gC and hence lower LE allowed higher {psi}S and smaller soil–root–canopy {psi} gradients to be simulated during convergence for canopy transpiration vs. root water uptake under elevated vs. ambient Ca. These changes allowed higher {psi}C to be maintained in the model under elevated vs. ambient Ca as was found in the field plots (Fig. 2). During the measurement periods in 1998 and 1999, the average simulated (vs. measured) rises in midday {psi}C were 0.17 MPa (vs. 0.04 ± 0.06 MPa) in the wet treatment and 0.21 MPa (vs. 0.16 ± 0.06 MPa) in the dry treatment (measured values from Wall et al., 2001b). Simulated and measured {psi}C were usually within 0.5 MPa, except after late September 1998 when simulated values rose above –1 MPa while measured values declined below –1 MPa. During this period, rising {psi}C was modeled in response to declining LE that was simulated under declining radiation and temperature. Both modeled and measured midday LE effluxes declined from >500 W m–2 in late September 1998 to <400 W m–2 in mid-October 1998 and <300 W m–2 in late October 1998, allowing modeled {psi}C to rise.



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  		Fig. 2. Midday canopy water potential ({psi}C) simulated (lines) and measured (symbols) in sorghum during the growing seasons of (a) 1998 and (b) 1999 under control wet, free air CO2 enrichment (FACE) wet, control dry, and FACE dry treatments. Arrows indicate dates of irrigation in wet and dry treatments. For irrigation schedules, see Table 1. Measured data from Wall et al. (2001b).

 
Elevated Ca raised modeled CO2 fixation rates directly by raising aqueous CO2 concentrations in the mesophyll and hence the bundle sheath (although this effect was small as described earlier). Elevated Ca raised modeled CO2 fixation rates indirectly by lowering gC and hence transpiration (Fig. 1), thereby raising {psi}C (Fig. 2). This indirect effect became more apparent during soil drying, as illustrated in Fig. 3 during a hot, dry period starting 9 d after irrigation on DOY 218 (6 August) in 1999. Midafternoon air temperatures rose from 37°C on DOY 227 and 228 (15 and 16 August) to >40°C on DOY 229 to 231 (17 to 19 August) while midafternoon relative humidities declined from 30 to 25% (Fig. 3a). These changes caused simulated and measured midafternoon effluxes of LE to rise from –600 W m–2 to –650 W m–2, forcing lower {psi}C in the model to increase root water uptake rates. Midafternoon {psi}C modeled under ambient Ca declined below –1.5 MPa during this 5-d period (Fig. 3b), at which point midafternoon gC declined markedly (Fig. 3c). Lower LE modeled under elevated Ca allowed midafternoon {psi}C to remain above –1.5 MPa (Fig. 3b) so that midafternoon gC did not show marked midafternoon declines (Fig. 3c). While {psi}C remained above –1.5 MPa during DOY 227 and 228, LE modeled under ambient Ca exceeded that under elevated Ca, indicated by positive differences in Fig. 3d. When {psi}C declined below –1.5 MPa during DOY 229 to 231, lower midafternoon gC modeled under ambient vs. elevated Ca (Fig. 3c) reduced midday LE below that under elevated Ca, indicated by negative differences in Fig. 3d. Early morning and late afternoon gC modeled during this period remained higher under ambient vs. elevated Ca (Fig. 3c) so that LE modeled under ambient Ca remained higher than that under elevated Ca. Similar diurnal differences were detected in measured LE (Fig. 3d), indicating a greater stomatal limitation to energy exchange under ambient vs. elevated Ca as atmospheric and soil water deficits increased. These differences in LE modeled and measured under ambient vs. elevated Ca were more apparent in the dry vs. wet treatment (Fig. 1c and 1d vs. Figure 1a and 1b). Lower midday {psi}C and gC also reduced midafternoon net CO2 exchange modeled under ambient vs. elevated Ca during DOY 229 to 231 (Fig. 3e). Thus, gains in CO2 fixation modeled under elevated vs. ambient Ca depend on both atmospheric and soil water status.




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  		Fig. 3. (a) Air temperature and relative humidity (RH), (b) canopy water potential ({psi}C), (c) canopy conductance (gC), (d) difference in latent heat (LE) between free air CO2 enrichment (FACE) and control treatments, and (e) net ecosystem CO2 flux simulated (lines) and measured (symbols in Fig. 3d) during day of year 227 to 231 (15–19 August) 1999 under control wet and FACE wet treatments. For irrigation schedules, see Table 1.

 
Seasonal Evapotranspiration and Growth under Ambient vs. Elevated Atmospheric Carbon Dioxide
In the wet treatment, lower gC and hence LE simulated under elevated vs. ambient Ca (Fig. 1b vs. 1a; Fig. 3d) reduced cumulative simulated (vs. measured) evapotranspiration by 8% (vs. 11%) in 1998 and 5% (vs. 9%) in 1999 (Fig. 4; Table 3). In the dry treatment, higher LE simulated during the onset of water stress under elevated vs. ambient Ca (Fig. 1d vs. 1c) offset lower LE simulated earlier in the growing season so that cumulative evapotranspiration simulated (vs. measured) under elevated vs. ambient Ca was unchanged (vs. unchanged) in 1998 and reduced by only 3% (vs. 6%) in 1999 (Fig. 4; Table 3). Cumulative evapotranspiration in the model was within 10% of that measured by neutron probe in the 1998 and 1999 wet treatments but was about 20% higher and 20% lower in the 1998 and 1999 dry treatments, respectively. During 1998, the shallowest neutron probe measurements were taken at 0.46 m, requiring estimates of soil water contents to be made between this depth and the surface (Conley et al., 2001). Agreement between modeled and measured evapotranspiration in the wet treatments during 1998 and 1999 (Fig. 4) was corroborated by agreement between modeled and measured LE (b > 0.9, R2 > 0.8 in Table 2). The larger modeled vs. measured evapotranspiration in the 1998 dry treatments (Fig. 4a) was not apparent in the modeled vs. measured LE fluxes (b < 1, R2 > 0.8 in Table 2). The smaller modeled vs. measured evapotranspiration in the 1999 dry treatments (Fig. 4b) was consistent with the smaller modeled vs. measured LE (b < 0.8). In both years, evapotranspiration (Fig. 4) was much less than irrigation (Table 1) even though soil water contents declined during sorghum growth, indicating substantial drainage. In the model, much of this drainage was simulated as rapid, gravity-driven flow through macropores. This drainage was not included in the cumulative ET estimated from the neutron probe measurements and did not contribute to ET in the model.



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  		Fig. 4. Cumulative evapotranspiration simulated (lines) and measured (symbols) in sorghum during the growing seasons of (a) 1998 and (b) 1999 under control wet, free air CO2 enrichment (FACE) wet, control dry, and FACE dry treatments. For irrigation schedules, see Table 1. Measured data from Conley et al. (2001).

 

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  		Table 3. Aboveground phytomass, total evapotranspiration (ET), and seasonal water use efficiency (WUE) of sorghum simulated (S) and measured (M) under ambient vs. elevated concentrations of atmospheric CO2 (Ca) in the wet vs. dry treatments during 1998 and 1999. Numbers in parentheses indicate Ca and total irrigation during each year.

 
The direct and indirect effects of elevated Ca on CO2 fixation rates (Fig. 3e) combined to raise simulated (vs. measured) aboveground phytomass in 1998 by 10% (vs. 7%) in the wet treatment and by 26% (vs. 13%) in the dry treatment (Fig. 5a; Table 3). The effects of elevated Ca on CO2 fixation rates combined with those on gC to raise simulated (vs. measured) water use efficiency (WUE) in the wet and dry treatments by 20% (vs. 20%) and 26% (vs. 13%), respectively. The dry treatment reduced simulated (vs. measured) aboveground phytomasses in 1998 to 72% (vs. 76%) and 82% (vs. 80%) of those in the wet treatment under ambient and elevated Ca, respectively (Table 3). These reductions in phytomass were relatively smaller than those in evapotranspiration so that both modeled and measured WUE were larger in the dry vs. wet treatment.



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  		Fig. 5. Aboveground phytomass simulated (lines) and measured (symbols) in sorghum during the growing seasons of (a) 1998 and (b) 1999 under control wet, free air CO2 enrichment (FACE) wet, control dry, and FACE dry treatments. For irrigation schedules, see Table 1. Measured data from Ottman et al. (2001).

 
Low harvest indices reported in 1999 (Ottman et al., 2001) indicated that late-season growth was impaired by the hailstorm on 16 September so that late-season phytomass in the model was slightly larger than that in the field (Fig. 5b). Elevated Ca raised modeled (vs. measured) aboveground phytomass in 1999 by 4% (vs. –1%) in the wet treatment and by 23% (vs. 18%) in the dry treatment (Fig. 5b; Table 3). Elevated Ca raised modeled (vs. measured) WUE in 1999 by 9% (vs. 8%) and 27% (vs. 26%) in the wet and dry treatments, respectively. Modeled and measured WUE was lower in 1999 than in 1998 because earlier planting caused growth to occur under higher temperatures and VPD. Modeled WUE was larger in the dry vs. wet treatments in 1998 and 1999 because reductions in phytomass were relatively smaller than those in evapotranspiration. However, measured WUE was smaller in the dry vs. wet treatments in 1999 because phytomass was reduced more than was evapotranspiration. This reduction could have occurred if the hailstorm had damaged the dry treatment more than the wet.

Irrigation vs. Yield under Current and Changed Climate
Because only 152 mm of precipitation was received in 1999, modeled shoot mass rose sharply with irrigation up to 600 mm but rose little thereafter (Fig. 6). Modeled grain mass rose comparatively more with irrigation than did shoot mass so that harvest index rose from 0.25 with no irrigation to 0.40 with full irrigation. In ecosys, grain set is determined by postanthesis water and C status, both of which were adversely affected by low irrigation. Modeled root mass rose comparatively less with irrigation than did shoot mass so that shoot/root ratios rose from 3:1 under no irrigation to 8:1 under full irrigation. In ecosys, improved shoot water status allows more rapid oxidation of nonstructural C in the shoot and hence comparatively less translocation of nonstructural C to the roots.



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  		Fig. 6. Response of phytomass to seasonal irrigation amounts (sum of biweekly applications) simulated under current (1999) climate (closed symbols) and under changed (1999 + 3°C, Ca x 1.5) climate (open symbols).

 
Initial model runs under climate change gave lower shoot and grain yields at high irrigation than did those under current climate because sorghum phenology was accelerated by higher temperatures. To avoid confounding phenology with growth, 2.5 phytomers (following the phenology model in Grant, 1989) were added to the juvenile growth stage of modeled sorghum under changed climate to synchronize growth stages with those under current climate. Climate change raised shoot and grain yields by 6 to 10% across a wide range of irrigation rates (Fig. 6). As under current climate, shoot and grain yields under climate change rose little with irrigation > 600 mm. Model results indicated that high sorghum grain yields (e.g., 325 g C m–2 = {approx}8 Mg ha–1 at 12% moisture content) could be achieved with {approx}150 mm or {approx}25% less irrigation water if air temperatures were to rise by 3°C and Ca by 50%. This water saving was simulated because the effects of higher Ca on transpiration (Table 3) offset the effects of higher temperature on evapotranspiration.


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENT
 SIMULATION EXPERIMENT
 RESULTS
 DISCUSSION
REFERENCES
 
Modeled energy balances and water relations, corroborated by measurements of energy flux (Fig. 1) and water potential (Fig. 2), indicated that elevated Ca reduced transpiration and hence improved water status of sorghum. These changes lowered the vulnerability of sorghum CO2 fixation to soil or atmospheric water deficits, even when irrigation was high (Fig. 3e). These observations are consistent with those of Williams et al. (2001), who found that elevated Ca reduced the effects of water deficits on bundle sheath leakiness and C isotope discrimination by reducing transpiration, prolonging soil water availability, and enhancing plant water status. They concluded that direct effects of elevated Ca on CO2 fixation in sorghum were likely minimal and that indirect effects depended on soil water supply. These model and experimental results support the suggestion by Rogers et al. (1983) that improved WUE (e.g., Table 3) is the most likely cause of the increased sorghum growth frequently reported under elevated Ca (e.g., Amthor et al., 1994). Increases in growth under elevated Ca would therefore be greatest when soil and atmospheric water deficits are most frequent, as indicated by the larger gain in phytomass in the dry vs. wet treatment (Table 3). These gains would likely be smaller in cooler, more humid climates than that at the FACE site in Arizona.

Rising air temperatures hypothesized in projections of future climate will cause greater atmospheric water deficits if assumptions that atmospheric relative humidity remains largely unchanged are correct. Rising Ca should reduce the impact of these deficits on sorghum CO2 fixation and thereby improve sorghum growth more under future climates than inferred from experiments conducted under current climate. Model projections of sorghum growth and irrigation requirements under hypothesized climate changes should therefore be based on a robust and accurate simulation of sorghum water relations as affected by Ca. These effects are strongly influenced by diurnal changes in atmospheric conditions (Fig. 3) and so need to be modeled at time steps appropriate to those changes (e.g., hourly). Experiments that monitor diurnal changes in water relations (energy fluxes, water potentials, and gC's) provide the best-constrained tests for such models.

The reduction in irrigation requirements of {approx}25% modeled under higher Ca and temperature (Fig. 6) is consistent with that in Hatch et al. (1999), Strzepek et al. (1999), and Tubiello et al. (2000). The magnitude of the reduction modeled here depended on some critical assumptions: (1) relative humidity and wind speed did not change, (2) precipitation did not change, and (3) the duration of the crop life cycle did not change. Assumption 1 is commonly made due to the large uncertainty in estimating changes in humidity and wind speed. The low precipitation at the FACE site limits the effect of Assumption 2 on irrigation requirements. However most 2 x Ca climate scenarios predict rises in precipitation of {approx}10% that contribute to modeled reductions in irrigation requirements (e.g., Hatch et al., 1999). Assumption 3 required the addition of 2.5 phytomers to the sorghum life cycle to remove the effects of temperature on the dates of crop growth stages. Climate change is frequently predicted to reduce crop growth and irrigation requirements by hastening crop maturation (Hatch et al., 1999, Strzepek et al., 1999; Tubiello et al., 2000). Lengthening the crop growth cycle by earlier planting under climate change has been predicted to increase the irrigation needed to maintain current sorghum yields (Tubiello et al., 2000). However, such an increase was not modeled under the conditions of this study.

The simulated response of sorghum growth to irrigation, and the impact of climate change on this response (Fig. 6), should be seen as specific to the site conditions (e.g., weather, antecedent soil water content, soil hydraulic properties, irrigation technique, and fertilization rate) of this experiment. Models such as ecosys provide a means to simulate these responses under more diverse site conditions and management practices as needed for regional estimates of water requirements. However detailed, well-constrained tests of these models under well documented site conditions are a vital prerequisite for these simulations.


   ACKNOWLEDGMENTS
 
The research was supported by Interagency Agreement no. DE-AI03-97ER62461 between the Department of Energy, Office of Biological and Environmental Research, Environmental Sciences Division and the USDA-ARS (Bruce A. Kimball, PI) by Grant no. 97-35109-5065 from the USDA, Competitive Grants Program to the University of Arizona (Steven W. Leavitt, PI) and by the USDA-ARS. It is part of the DOE/NSF/NASA/USDA/EPA Joint Program on Terrestrial Ecology and Global Change (TECO III). This work contributes to the Global Change Terrestrial Ecosystem (GCTE) Core Research Programme, which is part of the International Geosphere-Biosphere Programme (IGBP). We also acknowledge the helpful cooperation of Dr. Robert Roth and his staff at the Maricopa Agricultural Center. Portions of the FACE apparatus were furnished by Brookhaven National Laboratory, and we are grateful to Mr. Keith Lewin, Dr. John Nagy, and Dr. George Hendrey for assisting in its installation and consulting about its use. Ecosys was run on a DEC cluster made available through the Multimedia Advanced Computational Infrastructure (MACI) project at the University of Alberta.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 FIELD EXPERIMENT
 SIMULATION EXPERIMENT
 RESULTS
 DISCUSSION
 REFERENCES