Controls on carbon and energy exchange by a black spruce–moss ecosystem: Testing the mathematical model Ecosys with data from the BOREAS Experiment

Stomatal limitations to mass and energy exchange over boreal black spruce forests may be caused by low needle N concentrations that limit CO2 fixation rates. These low concentrations may be caused by low N uptake rates from cold boreal soils with high soil C:N ratios and by low N deposition rates from boreal atmospheres. A mathematical model of terrestrial ecosystems ecosys was used to examine the likelihood that slow N cycling could account for the low rates of mass and energy exchange measured over a 115‐year old boreal spruce/moss forest as part of the Boreal Ecosystem‐Atmosphere Study (BOREAS). In the model, net N mineralization was slowed by the high C:N ratios measured in the forest floor and by high lignin contents in spruce litterfall. Slow mineralization caused low N uptake rates and hence high C:N ratios in spruce and moss leaves that reduced specific activities and areal densities of rubisco and chlorophyll. Consequent low CO2 fixation rates caused low stomatal conductances and transpiration rates which in turn caused high soil water contents. Wet soils, in conjunction with large accumulations of surface detritus generated by slow litter mineralization, caused low soil temperatures that further slowed mineralization rates. Model outputs for ecosystem N status were corroborated by low needle N concentrations (< 10 mg g−1), stomatal conductances (< 0.05 mol m−2 s−1) and CO2 fixation rates (< 6 μmol m−2 s−1), and by high canopy Bowen ratios (1.5–2.0) and low canopy net CO2 exchange rates (< 10 μmol m−2 s−1) measured over the black spruce/moss forest at the BOREAS site. Modeled C accumulation rates of 60 (wood) + 10 (soil) = 70 g C m−2 yr−1 were consistent with estimates from aggregated CO2 fluxes measured over the spruce canopy and from allometric equations developed for black spruce in Canadian boreal forests. Model projections under IS92a climate change indicate that rates of wood C accumulation would rise and those of soil C accumulation would decline from those under current climate. Because these rates are N‐limited, they would be raised by increases in atmospheric N deposition.

old aspen site [Grant et al., 1999a]. This model simulates transformations and transfers of C, N and P in soils mid plmits as affected by soil temperature [Grant, 1993a;1994b;Grant et al., 1993a, b;Grant and Rochette, 1994;Grant et al., 1995a], water content [Grant et al., 1993a, b;Grant and Rochette, 1994] and aeration [Grant, 1993b;Grant et al., 1993c, d;Grant and Pattey, 1999]. In the model• low net mineralization rates may constrain N uptake rates through plant roots which may cause low concentrations of N and P in plant leaves. These low concentrations may limit specific activities mid densities of leaf rubisco and chlorophyll, thereby constraining leaf CO2 fixation and stomatal conductance, and hence canopy mass and energy exchmige. •l•nis model is thus well suited to test the hypothesis that low rates of N mineralization in soils under boreal coniferous forests cause N limitations on leaf carboxylation activity that result in the low rates of cmiopy CO2 fixation and trmispiration measured at boreal coniferous sites. This hypothesis was tested by comparing results for mass and energy exchange from the model with those reported by Jarvis et al. [1997] froln the old black spruce site in the southern study area of BOREAS. The model was then used to siinulate changes in long-term C accumulation at the old black spruce site under changes in Co, precipitation and temperature hypothesized for the IS92a emissions scenario.

CO• Fixation. CO• fixation is calculated in ecosys froln coupled algorithms for carboxylation and diffusion.
Carboxylation rates are calculated for each leaf surface, defined by height, azimuth and inclination, of inultispecific plant canopies as the lesser of dark and light reaction rates [Grant et al., 1999b] according to Farquhar et al. [1980]. These rates are driven by irradiance, temperature and CO: concentration. Maximum dark or light reaction rates used in these functions are determined by specific activities and surficial concentrations of rubisco or chlorophyll respectively. These activities and concentrations are determined by environmental conditions during leaf growth (CO• fixation, water, N and P uptake) as described in section 2.1.4. Diffusion rates are calculated for each leaf surface froln the CO• concentration difference between the cmiopy atmosphere and the mesophyll multiplied by leaf stmnatal conductance [Grant et al., 1999b] required to maintain a set C,: C• ratio at the leaf carboxylation rate. Stomatal conductance is also an exponential function of canopy turgot [Grant et al., 1999b] generated from a convergence solution tbr cmiopy water potential at which the difference between transpiration and root water uptake [Grant et al., 1999b] equals the difference between canopy water contents at previous and current water potentials. Canopy transpiration is solved froln a first order solution to the canopy energy balance of each plant species [Grant et al., 199961. 2.1.2. Autotrophic Respiration and Senescence. The product of CO2 fixation is added to a C storage pool for each branch of each plant species ffmn which C is oxidized to meet maintenance respiration requirements using a first order function of storage C [Grant et al., 1999b]. If the C storage pool is depleted, the C oxidation rate may be less than the maintenance respiration requirement, in which case the difference is made up through respiration of remobilizable C in leaves and twigs. Upon exhaustion of the remobilizable C in each leaf and twig, the remaining C is dropped from the branch as litterfall and added to residue at the soil surface where it undergoes decomposition as described in section 2.2.1. Environmental constraints such as nutrient, heat or water stress that reduce net C fixation mid hence C storage will theretbre accelerate litterfall. When storage C oxidation exceeds maintenance respiration, the excess is used for growth respiration to drive the formation of new biomass [Grant et al., 1999b] as described in section 2.1.4. 2.1.3. Nutrient Uptake. Nutrient (N and P) uptake is calculated lBr each +plant species by solving for aqueous concentrations of NI-I4 , NO.•' and H2PO4-at root mid mycorrhizal surfaces in each soil layer at which radial transport by mass flow and diffusion from the soil solution to the surfaces equals active uptake by the surfaces [Grant and Robertson, 1997;Grmit, 1998b]. This solution dynmnically links rates of soil nutrient transformations with those of root and mycorrhizal nutrient uptake. Nutrient transformations control the aqueous storage C, N and P between nodule and root that drives nutrient exchange.

Plant Growth. Growth respiration from section 2.1.2 drives expansive growth of vegetative and reproductive organs through mobilization of storage C, N and P in each branch of each plant species according to phcnology-dependent partitioning coefficients and biochemically-based growth yields.
This growth is used to simulate the lengths, areas and volumes of individual internodes, twigs and leaves [Grant, 1994b;Grant and Hesketh, 1992] from which heights and areas of leaf and stem surfaces are calculated Ibr irradim•ce interception and aerodynamic conductance algorithms used in energy balance calculations. Growth respiration also drives extension of primary and secondary root axes and of mycorrhizal axes of each plant species in each soil layer through Inobilization of storage C, N and P in each root zone of each plant species [Grant, 1993a, b;Grant, 1998b]. This growth is used to calculate lengths and areas of root and mycorrhizal axes from which root uptake of water [Grant et al., 1999b] and nutrients [Grant, 1991;Grant and Robertson, 1997] is calculated.
The growth of different branch organs and root axes in the model depends upon transfi2rs of storage C, N and P among branches, roots and mycorrhizae. These transfers are driven from concentration gradients within the plant that develop from different rates of C, N or P acquisition and consmnption by its branches, roots or mycorrhizae [Grant, 1998b]. When root N or P uptake rates described in section 2.1.3 are low, storage N or P concentrations in roots and branches become low with respect to those of storage C. Such low ratios in branches reduce the specific activities and surficial concentrations of leaf rubisco and chlorophyll which in turn reduce leaf COs fixation rates. These low ratios also cause smaller root-to-shoot transfers of N and P and larger shoot-to-root transfers of C [Grant, 1998b], thereby allowing more plant resources to be directed towards root growth. The consequent increase in root:shoot ratios and thus in N and P uptake, coupled with the decrease in C fixation rate, redresses to some extent the storage C:N:P imbalance when N or P uptake is limiting. The model thus implements the functional equilibrium between roots and shoots proposed by Thorriley [1995].
For perelmial nonconiferous plant species, soluble C, N and P are withdrawn from storage pools in branches into a long-term storage pool in the crown during autumn, causing leaf senescence. Soluble C, N and P are remobilized from this pool to drive leaf and petiole or sheath growth the following spring. The timing of withdrawal and remobilization is determined by duration of exposure to low temperatures (between 3øC and 8øC) under shortening and lengthening photoperiods respectively. Litterfall froIn section 2.1.2 is added to the plant residue complex and partitioned into carbohydrate, protein, cellulose and lignin structural colnponents according to Trofyrnow et al. [1995]. Rates of colnponent hydrolysis are the product of the active biomass and specific activity of each microbial l•nctional type within each complex Grant and Rochette, 1994]. Specific activity is constrained by substratemicrobe density relationships Grant and Rochette, 1994], and by the temperatures and water contents of surface residue and a spatially resolved soil profile [Grant, 1997;Grant and Rochette, 1994;Grant et al., 1998]. A fraction of the hydrolysis t)roducts of lignin are coupled with those of protein and carbohydrate according to the stoichiometry proposed by Shulten and Schnitzer[19971 and the resulting compound is transferred to the solid substrate of the particulate organic matter complex. Rates of particulate organic matter formation are thus determined by substrate lignin content and heterotrophic microbial activity.

Microbial
Growth. The concentration of the soluble hydrolysis products in section 2.2.1 determines rates of C oxidation by each hcterotrophic population, the total of which drives CO2 elnission from the soil surlhce. This oxidation is coupled to the reduction of 02 by all aerobic populations [Grant et al., 1993a, b;Grant and Roebette, 1994], to the sequential reduction of NO3-, NO2-and N20 by heterotrophic denitrifiers [Grant et al., 1993c, d;Grant and Pattey, 1999] and to the reduction of organic C by t•nnenters and of acetate by heterotrophic •nethanogens [Grant, 1998a]. The energetics of these oxidation-reduction reactions determine growth yields and hence the active biomass of each hcterotrophic functional type I¾om which its decomposer activity is calculated as described in section 2.2.1. In addition, autotrophic nitriflers conduct NH4 + and NO2-oxidation [Grant, 1994a] and N20 evolution [Grant, 1995], and autotrophic methanotrophs conduct CH4 oxidation [Grant, 1999]

Model Initialization and Run
The ecosystem model ecosys was initialized with data tbr the physical properties of the Cunfic Hmnic Regosol at the southern black spruce site of BOREAS [Table 1], and with values tbr the biological properties of black spruce and moss (Table 2) (1) The shape parameter relating leaf turgor to stomatal resistance used for vascular plants [Grant et al., 1999b, equation (13)] was set to zero for moss, thereby replacing the dynamic stomatal response to turgor with a constant diffusive resistance taken froln Proctor [1982]. This constant resistance forced lnoss water potential to equilibrate with atanospheric relative humidity during the convergence solution for energy exchange. (2) The effect of plant water status on CO2 fixation in moss was calculated froin moss relative humidity according to data given by Proctor [1982] and by Clymo and tta,vward [1982], rather than lYmn stmnatal resistance and water potential as in vascular plants.
The biochemical composition of moss litter is currently asstuned to be the same as that of deciduous vegetation, although some cronpounds produced by moss may slow decmnposition. All other model parameters lbr C fixation, respiration and partitioning by plant and lnicrobial pcopulations were the stone as those used in earlier studies of C and energy exchmige over agricultural crops [Grant and Baldocchi, 1992;Grant et al., 1993e;1995b;1999b], forests [Grant et al., 1999a] and soils [Grant, 1994a;Grant and Rochette, 1994;Grant et al., 1993a, b, c, d;1995a;1998]. The values of all lnodel parameters were derived independently of data recorded at the field site.
The lower boundary of the modeled soil profile was set to prevent subsurlhce drainage or capillary rise. The upper boundary of the •nodeled soil profile was set to allow fairly rapid surface runoff so that any water accumulating beyond the surface storage capacity of the soil was rmnoved within a few hours. These settings were intended to si•nulate the hydrology of the field site which had poor subsurface drainage but fairly good surface drainage. The •nodel was then run for 150 years under randran yearly sequences of hourly-averaged •neteorological data recorded in the coniferous zone of the BOREAS southern study area during 1994, 1995 and 1996 by the Saskatchewan Research Council and cronpiled for modeling purposes by BOREAS staff.

Canopy Mass and Energy Exchange
During the same year of the model run as that used in the leaf CO2 fixation study described above, hourly mass and energy

Long-Term C Exchange
Model results for mmual net primary productivity (NPP), net ecosystmn productivity (NEP) and above-ground phytomass growth of a 115-year old spruceqnoss forest under 1994 cli•nate were then compared with esti•nates of NPP, NEP and growth derived from aggregated flux data, tree ring analyses and other measurements taken at the field site during 1994. Long-term model results for C accumulation in spruce wood and soil were compared with results from measure•nents of spruce growth and forest floor development in the same ecological zone as that of the field site. The response of CO2 fixation to rising te•nperature in the model arose from cmnplex interactions among several processes. These included changing aqueous CO2 versus O2 concentrations caused by declining gaseous solubilities, changing carboxylation, oxygenation mid electron transport rates caused by more rapid reaction kinetics, and declining turgor potentials, and hence stmnatal conductances, caused by increasing vapor pressure differences and hence transpiration rates. These interactions caused simulated leaf CO2 fixation and stomatal conductance to increase with te•nperature below 23øC, and to decrease with temperature above 23øC for the conditions of irradiance, C• and vapor pressure under which the field chainber lneasureinents were taken (Figure l c and d). Increases at lower temperatures were attributed in the model to more rapid reaction kinetics arising froin the Arrhenius fi•nction for carboxylation, while declines at higher telnperatures were attributed to lower CO2:O2 ratios, lower turgor potentials and higher inaintenance respiration. These lower potentials were calculated from the convergence solution described above for equilibrating soil-rootcanopy water uptake with canopy-atmosphere vapor diffusion under canopy-atmosphere vapor pressure gradients that rose with temperature. Leaf CO2 fixation rates lneasured in this study changed little with temperature, although fixation rates measured in other studies of spruce [e.g. Man and LiefJkrs, 1997] have shown a temperature sensitivity si•nilar to that in the inodel. (Table 2)  Downward fluxes remained below 10 gmol m '2 s '• during the days while upward fluxes rose from 6 to 9 pmol m '2 s '• under rising temperatures during the nights, due mostly to larger soil effiux both in the model and at the field site. These upward fluxes were larger than those during late May because both measured and •nodeled temperatures in the organic soil zone had reached 15øC-20øC (Figure 4c), and the mineral soil below had completely thawed by late July.

The response of CO: fixation to rising C• in the model was determined by the relationship between aqueous CO2 concentration and the Km for carboxylation
The contribution of moss to mass and energy exchange in the spruce-moss stand is indicated by the fluxes simulated over the moss layer (Figure 6). Daytime net radiation modeled over this layer was --0.15 of that over the black spruce during the last week of July (Figure 6a). h• the model daytime moss temperatures were higher than those of the air while soil surface temperatures were lower, so that upward sensible heat fluxes t¾om the moss to the air were otl•et by downward fluxes t¾om the air to the soil. Both the moss and the soil surface contributed upward latent heat fluxes to the atmosphere.
Modeled daytime CO: fixation by the moss offset autotrophic plus heterotrophic respiration fi-om the soil and moss so that downward CO:fluxes of 1-2 pmol in '2 s 'l were si•nulated above the moss during most days (Figure 6b). However these fluxes were smaller than those of respiration at 'light so that the modeled soil-moss system was a net mnitter of rdO2. A similar relationship between CO2 fixation and respiration over a moss layer in a black spruce-moss forest wa:, •neasured by Goulden and Crill [1997]. The average modeled r•te. of daytime CO2 fixation by moss during this period was • 3 pmol m '2 s '• from a phytomass of 40 g C m '2. This rate is equivalent to 3 mg C g C -• h -• which is close to average values of 2 mg C g C '• h 4 reported from controlled enviromnent chambers by Busby and Whitfield [1977] and others [e.g. Proctor, 1982].
Radiation fluxes reported ti'mn the field site during the second week of Septe•nber were lower than those during May and July (Figure 7a) gmol m '2 s '• as weather cooled during the week. These rates were less than those during late July because both measured and modeled temperatures in the orgmiic soil zone had declined to 10øC -15øC by early September (Figure 7c).

Annual C Exchange
By sintuning CO2 fluxes recorded continuously between May 23 and September 21, 1994 (e.g. Figures 3b, 5b and 8b), Jarvis et al. [1997] estimated that the forest ecosystexn at the southern old black spruce site was a net si•tk of 95 g C m '2 during these four months. hi the •nodel the sum of net CO2 fluxes by spruce (199 g C •n'2), •noss (75 g C m '2) and soil/detritus (-218 g C •n '2) was 56 g C m '2 during this stone period. Similarly Jarvis et al.
[1997] estimated total evapotranspiration between May 23 mid September 21, 1994 to be 237 nun by sununing continuous measurements of latent heat flux (e.g. Figures 3a, 5a and 8a). In the model the stun of evapotranspiration by spruce, •noss and the soil/detritus surfaces was 252 nun during this same period.
The 2) was slightly less than that measured by Gower et al. [1997] (4300, 500 and 60 g C m'2), but rising Under IS92a climate change (Table 3) (Table 2), and from the slow mineralization of soil organic matter caused by its high soil C:N ratios ( and hence P uptake, growth and activity by both microbial and plant populations (notably inoss, the rooting depth of which was confined to the low pit zone). Low CO2 fixation rates caused by low N:C ratios forced low stomatal conductances in the inodel (Figure 1)  The low soil nutrient content at the old black spruce site thus caused a series of self-reinforcing processes in ecosys (low nutrient and high lignin content in detritus --} slow detritus decomposition --} slow nutrient mineralization • surface detritus accumulation--} cold soil --} slow nutrient uptake --} low CO2 fixation --} low transpiration • wet soil • slow detritus decomposition • slow nutrient mineralization ...) that caused NPP and NEP to stabilize at low values (Table 4; Figure 9). Evidence from the model supports the hypothesis that soil N availability is an important constraint to mass and energy exchange over black spruce.
Rates of mass mid energy exchm•ge simulated by ecosys at the southern old black spruce site (Figures 3, 5 8; Table 4) were lower than those at the southern old aspen site [Grant et al., 1999a , Figures 4, 5, 7, 8, 10, 11 and Table 4] where simulated microbial activity was more rapid. Nonetheless the modeled spruce/moss forest remained a stable net sink for atmospheric C of about 60 (wood) + 10 (soil) = 70 g C in '2 yr '• (Figure 9), largely because soil C oxidation was constrained in the model by the chemical composition of the detritus, and by the low nutrient, heat and periodically the low 02 contents of the soil. Nakane et al. [1997] used measurements and models of litterfall and soil respiration to estimate net eains in soil C at this site