Modelling the limits on the response of net carbon exchange to fertilization in a south-eastern pine forest


Ram Oren.Fax: +1 919 684 8741; e-mail:


Using a combination of model simulations and detailed measurements at a hierarchy of scales conducted at a sandhills forest site, the effect of fertilization on net ecosystem exchange (NEE) and its components in 6-year-old Pinus taeda stands was quantified. The detailed measurements, collected over a 20-d period in September and October, included gas exchange and eddy covariance fluxes, sampled for a 10-d period each at the fertilized stand and at the control stand. Respiration from the forest floor and above-ground biomass was measured using chambers during the experiment. Fertilization doubled leaf area index (LAI) and increased leaf carboxylation capacity by 20%. However, this increase in total LAI translated into an increase of only 25% in modelled sunlit LAI and in canopy photosynthesis. It is shown that the same climatic and environmental conditions that enhance photosynthesis in the September and October periods also cause an increase in respiration The increases in respiration counterbalanced photosynthesis and resulted in negligible NEE differences between fertilized and control stands. The fact that total biomass of the fertilized stand exceeded 2·5 times that of the control, suggests that the counteracting effects cannot persist throughout the year. In fact, modelled annual carbon balance showed that gross primary productivity (GPP) increased by about 50% and that the largest enhancement in NEE occurred in the spring and autumn, during which cooler temperatures reduced respiration more than photosynthesis. The modelled difference in annual NEE between fertilized  and  control  stands  (approximately  200 1;g 2;C 3;m−2 y−1)  suggest that the effect of fertilization was sufficiently large to transform the stand from a net terrestrial carbon source to a net sink.


Over the past decade, several studies suggest that northern temperate forests can act as a large terrestrial sink for carbon (Ciais et al. 1995; Schimel 1995; Tans & White 1998; Houghton, Davidson & Woodwell 1998), and the pine forest of south-east USA is considered among the most productive among North American forests (Johnsen et al. 2001). However, these forests are generally situated at sites with moderate to poor soil fertility, which may limit their potential for carbon sequestration (Vitousek & Howarth 1991; Oren et al. 2001). Southern pine plantations, in particular, are typically nutrient limited (Pritchett & Smith 1975; Schultz 1997) and research has clearly shown productivity can be greatly enhanced by providing nutritional amendments (Albaugh et al. 1998; Samuelson et al. 2001).

When interpreting the effects of forest fertilization on net carbon uptake, it is necessary to evaluate the key processes observed from such experiments at their appropriate scale. At the leaf-scale, fertilization can increase photosynthetic capacity because the carboxylation capacity (Vcmax; please note all abbreviations are defined in Appendix C) increases with nitrogen content (Field & Mooney 1986; Evans 1989). Additionally, long-term fertilization increases the amount of photosynthesizing biomass because of increases in leaf area index (LAI; Brix & Ebell 1969; Vose & Allen 1988).

The commonly observed increase in LAI and total biomass with fertilization can induce several non-linear compensation effects that reduce net ecosystem carbon exchange (NEE) below values expected from leaf-level responses. Specifically, increased LAI will reduce the amount of photosynthetically active radiation (PAR) reaching deep in the canopy thereby reducing assimilation rates in the lower layers. Furthermore, fertilization increases several respiratory components and can significantly increase ecosystem respiration. Thus, fertilization typically enhances LAI and maximum photosynthetic rate, but it is not clear how the interplay between the canopy microclimate and the integrated photosynthetic and respiratory fluxes will affect NEE.

We examine the mechanisms responsible for NEE enhancement by fertilization using models and measurements collected at SETRES2 (South-east Tree Research and Education Site; McKeand et al. 2000). SETRES2 is a large-scale genotype 4;× 5;nutrition interaction experiment designed to quantify the effects of fertilization on the productivity of managed southern pine forests. A multilevel canopy photosynthesis-turbulent transport model, developed by Lai et al. 2000a, b), was used to simulate NEE for the fertilized and control stands for SETRES2. The model was independently tested with fluxes of sensible heat, latent heat, and NEE measured with eddy covariance (EC) over fertilized and unfertilized plots during a 3-week field campaign. The model was then employed to assess NEE and its components on monthly and annual basis.

Materials and methods

To quantify mass and energy exchanges between the vegetation and its microenvironment, a multilevel coupled photosynthesis-turbulent transport model, known as CANVEG after Baldocchi & Meyers (1998; see also Lai et al. 2000a, b), was developed and used. The model combines turbulent transport theory, eco-physiological and biochemical principles, radiation, and energy conservation regimes to predict mean source and flux distribution within the canopy from mean meteorological conditions above the canopy. The model differs from other multilevel photosynthesis models (e.g. Wang & Jarvis 1990; Collatz et al. 1991; Leuning, Denmead & Lang 1995; Williams et al. 1996) in that it resolves the entire canopy microclimate and incorporates feedbacks on biophysical sources associated with vertical variation in microclimate. Because the distribution of mean water vapour and carbon dioxide concentrations, or temperature within canopies are calculated, assumptions regarding the distribution of these state variables are not necessary. In this application, the canopy height (h) was divided into N layers, each of thickness dz (= 6;0·5 7;m), and all the equations and formulations described in the Appendices are solved iteratively at each discrete layer and for each 30 min time step. The model is driven by 30 min averaged air temperature ( inline imagea), water vapour ( inline imagea) and CO2 ( inline imagea) concentration, mean wind speed ( inline image), PAR, leaf area density a(z), soil heat flux (Go) and soil temperature (Tsl) as shown in Fig. 9; 1. Details about the model formulation can be found in Lai et al. (2000a, b). However, for completeness, we review the basic equations and required variables in Appendix A.

Figure 1.

Schematic display of the multilevel CANVEG model. The forcing variables required in CANVEG are also shown.

Study site

The experiment was conducted in a loblolly pine plantation adjacent to the SETRES2 study site in Scotland County of North Carolina, USA (34°48′ 10;N, 79°12′ 11;W). The stand, predominantly Pinus taeda L., was planted in 1993 at 1·5 12;m 13;× 14;2·1 15;m spacing on an infertile, well-drained, sandy, siliceous, thermic Psammentic Hapludult soil (Wakulla series) with a water-holding capacity of 12–14 16;cm in a 2 17;m profile. Mean annual precipitation at this site is 1210 18;mm, evenly distributed throughout the year. Long-term mean air temperatures are 26 19;°C and 9 20;°C in the summer and winter, respectively. Sixteen 45 21;m 22;× 23;75 24;m plots were established at a randomized complete block design. Foliar nutrient ratios (Linder 1995) were used to guide annual fertilizer applications aimed at maintaining a balanced and optimal supply of all nutrients in the fertilized plots, so as to stimulate rapid growth (Allen 1987; Maier, Zarnoch & Dougherty 1998). The nitrogen treatment, approximately 11·2 25;g 26;m−2 27;year−1 as urea, supplemented as necessary with other nutrients was similar to that described in Murthy et al. (1996) and Albaugh et al. (1998).

Fluxes and environmental variables were measured separately for fertilized and unfertilized (control) stands using a mobile tower setup. The experiment was initiated on 23 September and data were collected over the fertilized stand until 3 October 2000. The system was then moved to the control stand and data collection was continued from 3 to 13 October 2000. This experimental period was chosen to coincide with warm soil temperatures and maximum LAI. Thus, if photosynthesis or respiration response to fertilization is large, the effect on NEE would be readily discernible during this period.

Eddy covariance flux measurements

The turbulent fluxes of sensible heat (FT), latent heat (Fq) and CO2 (Fc) above the canopy were measured with a conventional eddy covariance system consisting of an open path CO2/H2O gas analyser (LI-7500; LI-COR Inc., Lincoln, NE, USA) and a triaxial sonic anemometer (CSAT3; Campbell Scientific Inc., Logan, UT, USA). The sonic anemometer also provided the mean wind speed ( inline image) and other flow statistics for the scalar transport calculations. The system was mounted on a customized telescoping mast, which is an integral part of a mobile laboratory (Wolf Coach Inc., Auburn, MA, USA). The mobile laboratory is hydraulically levelled and guide wires were used to minimize mast ­vibration.

The open path gas analyser used is a non-dispersive infrared analyser measuring simultaneously CO2 (Ca) and water vapour (qa) concentration. The internal high-speed scan rate (150 28;Hz) was digitally filtered to permit a true high frequency response (up to 20 29;Hz bandwidth). The analyser was pre-calibrated in the laboratory prior to the experiment. The heads of both sensors were at the same height and approximately 10 30;cm from each other to minimize instrument separation corrections. The sampling rate was at 10 31;Hz, and all the data were transmitted by sequential digital measurement connection (Campbell Scientific Inc.) to avoid any lag or time delay. All signals were processed by a datalogger (CR23X; Campbell Scientific Inc.). The averaging interval for computing all turbulent fluxes was 30 32;min. The measured Fq and Fc were adjusted for density variations due to sensible heat using the standard Webb–Leuning correction (Webb, Pearman & Leuning 1980; Leuning et al. 1982).

Meteorological measurements

In addition to the EC flux measurements above the canopy, a Ta/RH probe (HMP45C; Campbell Scientific Inc.) was installed at z 33;= 34;15·6 35;m to measure mean air temperature and relative homidity, where z is the height above the forest floor. The vapour pressure deficit (Dv) was computed from the latter measurements. A Fritchen-type net radiometer and a quantum sensor (Q7 and LI-190SA; LI-COR Inc.) were positioned to measure net radiation (Rn) and PAR above the canopy. Five soil heat flux plates (HFT3; Campbell Scientific Inc.) were installed in a grid within the footprint of the net radiometer to measure soil heat flux and assess energy closures. All the meteorological measurements were sampled at 1 36;s and averaged over a 30 37;min period.

Footprint analysis

Due to the limited size of the experimental plots, an extensive footprint analysis on the EC measurements was necessary. Figure 2 shows the location of the EC system and the dominant wind direction over the sampling period. To ensure that the measurements were conducted in the atmospheric surface layer (ASL), the measurement height of the EC system was set at z 38;= 39;15·6 40;m (≥ 41;2 42;h). The fact that EC measurements were conducted in the ASL greatly simplifies the estimation of the footprint or source weight function. The latter analysis was conducted using the model of Hsieh, Katul & Chi (2000), in which the peak location of the footprint (xc) for different stability conditions was computed. Based on this analysis, we found that 63% of the runs collected at the fertilized stand were of flux originating within the stand (> 43;90% of source identified); about 51% of runs at the control stand were of local flux.

Figure 2.

Placement of the mobile tower and the dominant wind direction measured at (a) the fertilized (F) and (b) the control (C) stands during the experiment. The centre of the polar coordinate plot is the location of the tower. Also shown is the wind direction histogram (blocks) relative to the North (0°) and the number of runs from each wind direction (shown as radii).

A more direct evaluation of potential influence on flux measurements over one treatment by flux originating from the other treatment is to quantify biases in the relationship between measured water vapour fluxes (Fq) against net radiation measurements. Here, the expected differences in Fq between the treatments should be large due to the large difference in LAI, which would infuse bias into the RnFq relationship for runs with an uncertain source footprint. The EC runs for which 90% of the computed source area is within the representative plot were related to their respective Rn measurements. We found that < 5% of the EC measurements deviated significantly from the expected RnFq slope in each treatment. Furthermore, the difference in slopes between the two treatments was significantly larger than the difference in slopes between measurements whose source contribution was uncertain, collected over the same stand (P 44;< 45;0·05).

As a final test of how well the EC measurements taken at each measurement period represent mostly one treatment, we calculated the one-dimensional energy balance closure for fertilized and control stands and found that they were within 16% (R2 46;= 47;0·91) and 3% (R2 48;= 49;0·93), respectively. Combining this diagnosis with the footprint analysis, we conclude that 95% of the EC measurements in each period represent the intended treatment. These flux measurements were used to validate CANVEG model calculations for both stands.

Plant area density measurements

The mean canopy heights for fertilized and unfertilized plots were 6·8 50;± 51;0·5 and 4·1 52;± 53;0·5 54;m, respectively, at the time of the experiment. The vertical profile of plant area index (PAI, the leaf area plus branches) was measured at 1 55;m intervals from the top of the canopy to 1 56;m above the ground by gap fraction techniques following the theory described in Norman & Welles (1983). A pair of optical sensors with hemispherical lenses (LAI-2000; Li-Cor) was used in each of the two stands in Fig. 2 for canopy light transmittance measurements, from which gap fraction and plant area densities were calculated.

Leaf gas exchange measurements

Leaf level physiological parameters were determined from porometric measurements using a portable infrared gas analyser for CO2 and H2O (Li-6400 portable photosynthesis system; Li-Cor) and an integrated gas CO2 supply system. The data were collected for upper canopy foliage at z 57;= 58;0·95 59;h under sunny conditions, at a constant leaf temperature (28 60;°C). The ACi curves were measured and used to determine Vcmax and Jmax using a least-square regression procedure described in Wullschleger (1993), where A is photosynthesis and Ci is the leaf-level intercellular CO2. Needles were collected following gas exchange measurements and analysed for total nitrogen content after combustion based on the Dumas technique (NA-1500; Carlo-Erba Strumentiazone, Milan, Italy). The measured leaf nitrogen content (Na) near the canopy top was 2·35 and 3·02 61;g 62;m−2 projected leaf at the control and fertilized plots, respectively. The dependency of Vcmax on nitrogen content was then determined using the measurements conducted on the same foliage. Figure 3 shows that the data from the two treatments fell along the same positive linear relationship between leaf Vcmax and Na established for this species at Duke Forest (Ellsworth, unpublished results). This relationship was therefore used in this study for modelling Vcmax and Jmax to drive the CANVEG calculation of CO2 flux. The physiological parameters of the stomatal conductance model of Collatz et al. (1991) were also determined from these gas exchange data (see Lai et al. 2000b). All measured gas exchange rates are reported on a unit projected leaf area basis.

Figure 3.

Relationship between maximum leaf carboxylation capacity (Vcmax) and leaf nitrogen content measured at z/h 242;= 243;0·95.

To estimate Vcmax at different canopy levels, we assumed that maximum Na was at the canopy top, and attenuate the measured Na value down the LAI profile following the approach described in Hirose & Werger (1987). According to Hirose & Werger (1987), the distribution of foliar nitrogen concentration within the canopy volume is given by:


where ξ is defined using relative cumulative leaf area index, and Ko is the nitrogen attenuation coefficient equivalent to the light attenuation coefficient (≈ 63;0·52 in this study) estimated from our light attenuation calculation (Campbell & Norman 1998). Sampson & Allen (1998) showed that in loblolly pine plantations, a Ko 64;= 65;0·5 is reasonable. Such distribution of Na(z) is now widely used in different types of canopies, and agrees well with measurements from other experiments (Field 1991; Leuning et al. 1995). Figure 4 shows the modelled PAR attenuation and the vertical distribution of Na(z) within the canopy; the latter was strictly used to estimate the vertical distribution of Vcmax(z) based on the relationship in Fig. 3. We emphasize that the differences between measured and modelled Na(z) would lead to minor differences in Vcmax(z), at least when compared to the scatter shown in Fig. 66;3.

Figure 4.

Modelled PAR attenuation, modelled Na(z) and computed Vcmax (z) within canopy for control and fertilized stands. The symbols are measured leaf nitrogen at the control (open circles) and fertilized (closed circles) stands.

Respiration measurements

Soil respiration Rsl was measured with a custom-designed, chamber-based system – Automated CO2 Efflux System (ACES). ACES is a multiport, dynamic gas sampling system that utilizes an open flow-through design to measure carbon dioxide fluxes sequentially from up to 15 chambers using a single infrared gas analyser (EGM-3; PP Systems Inc., Hertfordshire, UK) integrated into the system. Each chamber is equipped with a pressure equilibration port, ensuring that the chamber pressure was held near ambient (Fang & Moncrieff 1996; Maier & Kress 2000). Each chamber is sampled for 10 67;min to ensure steady-state conditions, and a value of Rsl was recorded on the tenth minute of the cycle. Nine complete runs (135 values) are recorded every day. When not being actively sampled, all chambers are continuously supplied with ambient air to prevent CO2 build-up. Four plots (two fertilized and two control) were sampled concurrently using four ACES units, beginning two days before the eddy covariance monitoring commenced and ending 2 68;days after the monitoring was completed. In each plot, soil CO2 efflux was measured with 13 chambers, and woody respiration was measured with two chambers, resulting in 26 chambers per treatment measuring soil CO2 efflux, and four chambers per treatment measuring woody respiration. Detailed specification of the characteristics and operation of the two chamber types are provided below.

Soil component

Soil chambers (25 69;cm in diameter, i.e. 490 70;cm2, 10 71;cm height) were placed on the forest floor with litter left intact. To ensure the measured Rsl is not biased by root density distribution, chambers of each ACES system were placed in the following manner: trees within the sampling area of the respiration units were randomly selected to receive a chamber, chambers were then randomly placed into one of the four position zones as shown in Fig. 5. The azimuth bearing from the tree was also randomly selected. We regressed measured Rsl with simultaneously measured Tsl to obtain a RslTsl response curve for each chamber, then averaged the coefficients of RslTsl curves situated at the same zone (see Fig. 5). Finally, a representative RslTsl curve for the block was generated by weight-averaging the coefficients of RslTsl curve from each zone based on the ground area covered by that zone. The resulting RslTsl function is shown in Table 1 for both fertilized and unfertilized stands.

Figure 5.

Schematic display of the placement of chambers connected to the Automatic Carbon Efflux System (ACES). The percentage of ground area covered by each zone and an example of chamber arrangement are shown.

Table 1.  Eco-physiological and canopy attributes used in the CANVEG model for the period in September–October 2000. The forest floor respiration-to-temperature (RslTsl) response function from chamber measurements is:Rsl 260;= 261;κ1 exp(κ2Tsl), where Rsl is in µmol 262;m−2 263;s−1, and Tsl is soil temperature (°C). The above-ground woody respiration (Rw, µmol CO2 264;m−3 s−1) was estimated from Rw 265;= 266;ω1 267;+ 268;ω2 269;× 270;(Vw)exp (ω3Tw), where Vw is woody volume (m3), and Tw is bole temperature (°C)
LAI (m2 271;m−2) 1·65 3·51
Characteristic leaf length 0·001
Leaf absorptivity for PAR, α  0·83
Clumping factor, Ω  0·8
Foliar N @z/h 272;= 273;0·95 (g 274;m−2 275;leaf) 2·35 3·02
Vcmax@z/h 276;= 277;0·95 (µmol 278;m−2 279;leaf 280;s−1)85·4100·2
Stomatal slope parameter, m  7·5
Stomatal intercept parameter, b  0·015
Coefficients of RslTsl curve
κ1 0·728 0·322
κ2 0·069 0·121
Estimated woody biomass Vw (m3 281;ha−1)38·3 88·4
Coefficients of Rw equation
ω1    −0·0146
ω2  70·1049
ω3  0·041

Above-ground component

We estimated stem respiration by measuring CO2 efflux from stem segments into respiration chambers. Chambers were constructed of Teflon film attached to the stem using closed-cell foam collars positioned below the first live branch (approximately 0·5 72;m). Aluminium foil covered the Teflon film to exclude light and to prevent chamber warming. All chambers were 23·5 73;cm in length. Air volume within the chambers ranged from 825 to 1733 74;cm−3 depending on stem diameter (9·5–17·0 75;cm). Air entered and exited the bottom and top of the chamber, respectively, via Teflon diffuser rings. Chamber air and cambium temperatures were measured simultaneously using thermocouples constructed from 24-gauge copper–constantan wire. Airflow rates were sufficiently high to ensure well-mixed conditions within the chamber. Stem respiration measurement was included as part of the ACES sampling cycle of soil respiration.

At the conclusion of the study, we measured stem diameter within each of the chambers. Above-ground woody respiration (Rw) was modelled as a function of cambium temperature (Tw) and the enclosed stem volume including bark (Vw). The equation used to estimate Rw was summarized in Table 76;1. The coefficients were calibrated specifically for this study via a multiple regression analysis (Maier et al. 1998).

To estimate Vw for the stand, tree height must be known. Height was measured on all trees annually and, beginning in year three, breast height diameter was also measured. Using locally developed allometric equations (McKeand et al. 2000), individual tree volume (stem and branches) was calculated, summed for the plot, and converted to per volume unit ground area. Canopy woody biomass data was not available for the exact time of the measurement campaign. To estimate the woody biomass for the end of year 2000 growing season, we used the measurements collected over the pervious three years (1997–99) and generated a linear relationship (least-square regression approach) of total above-ground woody biomass versus stand age for each treatment (R2 77;= 78;0·99 for both control and fertilized plots). Using these relationships, we estimated mean woody biomass as 38·3 and 88·4 79;m3 80;ha−1 for the control and fertilized plots, respectively, for the experimental blocks in which measurements were made. We then estimated the vertical woody biomass distribution by scaling the total woody volume according to the woody biomass profile reported for Pinus taeda by Pataki, Oren & Phillips (1998).

Soil moisture measurements

Volumetric soil moisture content (θ) was measured by transects of automated time domain reflectometry (TDR) probes (Theta Probe; Delta-T Devices, Cambridge, UK) placed at two depths for each treatment plot. Two sets of five TDR probes were installed horizontally at 10 and 30 81;cm below ground surface. The variability in the depth-averaged θ computed from this  soil  moisture  measurement  array  was small, with measured mean = 0·052 and 0·045 82;m3 83;m−3 at z 84;= 85;−10 and −30 86;cm for the fertilized plot, and 0·047 and 0·048 87;m3 88;m−3 at the two corresponding depths for the control plot.


To quantify the effects of fertilization on NEE, it is convenient to decompose NEE into its two primary components,


where RE is ecosystem respiration, and Sc are sources or sinks of CO2 from a canopy layer of thickness dz at elevation z from the forest floor (see Fig. 89;1). In this study, the sign convention is negative for canopy carbon uptake by the forest.

The CANVEG model, which computes NEE from these two components, was first tested using NEE measurements conducted sequentially at the fertilized and the unfertilized stands. After diagnosing the model's ability to reproduce NEE and other biosphere-atmosphere exchange processes for this short experiment, we used the model to guide our understanding of the interplay between canopy carbon uptake and respiration from seasonal to annual time scales. These analyses permit direct contrasts of fluxes between fertilized and control stands using identical environmental conditions but different canopy physiological and structural properties.

Model validation

Figure 6 shows the comparisons between modelled and measured NEE, water vapour flux, and sensible heat flux for the fertilized and unfertilized plots. The sensible heat flux comparisons assess the model's ability to quantify the integrated leaf-energy balance and the modelled flow-field inside the canopy. The latent heat flux comparisons assess the ability of the model to quantify integrated stomatal conductance, and the NEE comparisons assess the ability of the model to reproduce net carbon exchange as the difference between photosynthesis and respiratory components. There was good agreement between model calculations and measurements for both stands (Fig. 6, Table 2). Furthermore, the radiative transfer scheme and the associated energy balance were reproduced well by the model as is apparent from the good agreement between modelled and measured sensible heat flux and Rn (Figs 6 & 7; Table 2).

Figure 6.

Comparison of CO2 flux (Fc or NEE) water vapour flux (Fq) and sensible heat flux (FT) values measured with eddy-covariance(EC) versus values modelled with CANVEG (CV) at control (left column) and fertilized (right column) stands. The 1 244;: 245;1 line is also shown.

Table 2.  Regression statistics for comparisons between modelled and measured fluxes of CO2 (Fc), latent heat (Fq), and sensible heat (FT), and mean canopy stomatal conductance (Gc) in control and fertilized stands. The linear regression model is y 282;= 283;Ax 284;+ 285;B, where y and x are modelled and measured variables, and the coefficients A and B represent the regression slope and intercept, respectively. Also provided are coefficient of determination (R2), root-mean square error (RMSE), and number of points in the regression analysis (Nr)
Fc (mg 286;C 287;m−2 288;s−1)3620·96− 0·020·80 0·14
Fq (W 289;m−2)3620·85  290;1·740·8826·36
FT (W 291;m−2)3620·81 292;12·980·9239·47
Rn (W 293;m−2)4781·00− 1·040·9921·45
Gc(mmol 294;m−2 295;leaf 296;s−1) 490·53 297;54·50·7319·77
Fc (mg 298;C 299;m−2 300;s−1)3910·98  0·030·83 0·17
Fq (W 301;m−2)3910·97− 1·240·8929·47
FT (W 302;m−2)3910·95  7·510·8924·54
Rn (W 303;m−2)4601·02− 9·820·9828·40
Gc(mmol 304;m−2 305;leaf 306;s−1) 440·49 28·490·77 6·54
Figure 7.

Comparison between modelled and measured net radiation (Rn) for control (top panel) and fertilized (bottom panel) stands.

Using a parallel resistor network, an effective canopy conductance (Gc, per unit leaf area) can be computed from the CANVEG modelled leaf conductance gs(z) (Lai et al. 2000b). The response of modelled Gc to Dv was similar to that for mean canopy stomatal conductance (= 90;gc/LAI) obtained with scaled sap-flux measurements conducted at a nearby site on an older stand (Ewers, Oren & Sperry 2000), showing a linear decrease with increasing ln 91;Dv. Using this approach, the intercept of the relationship (i.e. Gc at Dv 92;= 93;1 94;kPa) can serve as a reference conductance (Oren et al. 1999). The reference conductance can be evaluated in relations to hydraulic constraints imposed by, for example, tree height and leaf-to-sapwood area ratio (Schäfer, Oren & Tenhunen 2000), both of which affect leaf specific hydraulic conductivity. In addition to stand age, height was also affected by fertilization, and fertilization affected leaf-to-sapwood area ratio as well. Using a simple hydraulic model (Schäfer et al. 2000), we estimated the theoretical rate of decrease in Gc and plotted it as a line in relation to tree height (Fig. 8a). The actual data fell quite close to the theoretical line, with the two older, taller stands showing lower Gc than the younger, shorter stands, and the fertilized, taller stand showing lower Gc than the unfertilized, shorter stand within the same age group. Moreover, lower leaf-to-sapwood area ratio with fertilization was sufficient to partially reverse the expected exponential decay in Gc with tree height, resulting in a nearly linear decline in both the theoretical calculations and the empirical data.

Figure 8.

(a) The decrease in canopy conductance per unit leaf area (Gc) at vapour pressure deficit (Dv) of 1 246;kPa, as a reference conductance, with mean stand height in control and fertilized stands as compared with a trend predicted by hydraulic model that accounts for differences in canopy height and leaf area to sapwood area (see Schäfer et al. 2000). Model (CANVEG) combined with eddy-covariance measurements were used to estimate Gc at a 6-year-old-plantation in 2000, whereas sap-flux based estimates were obtained at a nearby stand in 1996–98 (Ewers et al. 2000). In (b) Gc sensitivity to Dv is assessed in relation to the reference conductance shown in (a). The expected slope of the response is ∼ 0·6 (Oren et al. 1999).

Furthermore, based on Oren et al. (1999), the sensitivity of Gc to Dv (i.e. dGc/d 95;lnDv) is directly related to Gc at Dv 96;= 97;1 98;kPa, with a theoretical slope of ∼ 0·6, as has been found in the nearby older stand (Ewers et al. 2000, 2001). Again, presenting the data from all four stands show that the response of Gc to Dv was indeed proportional to Gc at Dv 99;= 100;1 101;kPa, with a slope not very different from the theoretical (Fig. 102;8b). We note that the data used in both analyses in Fig. 103;8 were obtained from long-term measurements in the two older stands and from the CANVEG model calculations for the two younger stands. Nevertheless, these data, which also represent different collection periods, and stands of different ages receiving different treatments and displaying a wide range in structural characteristics, seamlessly combined to show that the four stands behaved very similar to theoretical expectations. We consider this a demonstration that the model is capable to faithfully reproduce long-term stomatal behaviour.

Having demonstrated that the model is capable of reproducing all three scalar fluxes, radiative forcing above the canopy, and expected behaviour of stomata when scaled to canopy conductance, we proceeded to examine the effects of fertilization on the individual components of NEE.

The effects of fertilization on biosphere–atmosphere exchange

To assess the effects of fertilization, we used the measured, RH, PAR, Ta, ¯U and CO2 concentration for the entire 20-day period and computed the components of NEE in addition to the three scalar fluxes. The comparisons between fertilized and control plots are shown in Fig. 9, which shows ensemble averaged fluxes by time of day. In this period, one of the largest effects of fertilization was to double LAI (Table 104;1). For this 3-week period, the model results in Fig. 105;9 suggest that:

Figure 9.

The effect of fertilization on modelled Fc (or NEE), net radiation (Rn), water vapour flux (Fq) and sensible heat flux (FT) during the measurement period in September–October, 2000. The control (dashed) and fertilized (solid) ensemble-averages with time of day for the entire two 10-day periods are contrasted. Net canopy photosynthesis (Ac), soil respiration (Rsl), above-ground woody respiration (Rw) and foliar respiration (Rfl) differences between the two treatments is also shown as ensemble averages with time of day.

  • 1Despite the two-fold increase in LAI with fertilization, net canopy photosynthesis was enhanced by only 25%.
  • 2All respiratory components, including forest floor, wood, and leaf, were substantially increased by fertilization. Thus, the total ecosystem respiration, defined as the sum of these components, increased by more than 50%.
  • 3As a result, increased night-time respiration by all these components counterbalanced all daytime gain in photosynthesis. For this reason, differences in daily NEE between treatments were minor.
  • 4The 24 106;h latent heat flux was enhanced by more than 16% due to fertilization; this enhancement is only slightly lower than the value reported for the summer months in the nearby older stand (Ewers et al. 1999; data not shown).

A response curve of EC-derived ecosystem daytime NEE, normalized by LAI, versus light in September–October, reveals the reason for the little enhancement in net canopy photosynthesis (Fig. 10). The daytime NEE–light response curve was fitted to (Landsberg 1986; Ruimy et al. 1995)

Figure 10.

Variation of measured daytime Net Ecosystem Exchange (NEE) per unit leaf area index (LAI) with photosynthetically active radiation (PAR) for control and fertilized stands during the measurement period in September–October 2000. 


where NEEd is the daytime NEE. Figure 107;10 shows the twoNEEdPAR curves generated for control and fertilized plots (R2 108;= 109;0·49 and 0·70, respectively). The estimated mean apparent quantum yield (αp), net CO2 flux at light saturation (Fsat), and the mean net CO2 flux at PAR= 0 (R0) for both control and fertilized plots are presented in Table 3. The large increase in LAI with fertilization reduced NEE per unit leaf area, especially in high PAR, a reduction that nearly eliminated the advantage gained in fertilized stands by having a higher LAI. Next we evaluate how the increase in LAI caused redistribution of PAR and scalar sources and sinks along the canopy depth such that the effect on canopy net photosynthesis was small relative to the increase in LAI.

Table 3.  Parameters of the response of net ecosystem exchange (NEE) estimated from eddy-covariance measurements to photosynthetically active radiation (PAR) obtained over the control and fertilized stands in September–October 2000. The parameters are: mean apparent quantum yield (αp), net CO2 flux at light saturation (Fsat), and the mean net CO2 flux at PAR= 0 (R0). For reference, we include estimates from a 17-year-old Loblolly Pine (Pinus taeda L.) forest in North Carolina (Lai et al. 2002) and a 24-year-old Slash Pine (Pinus elliotii var. elliotii) forest in Florida (Clark et al. 1999)
Pine, NC
Pine, FL
αp 0·021 0·034 0·029 0·044
Fsat (µmol 308;m−2 309;s−1)23·231·531·226·5
R0mol 310;m−2 311;s−1) 3·25 3·28 3·90 4·62

The effects of fertilization on the vertical distribution of scalar sources and sinks

To investigate the effects of increased LAI on light transmission, photosynthesis distribution within the canopy, and in turn NEE, we modelled sunlit leaf area density and inline imagei/inline imageawith height (Fig. 11). Leaf area doubled with fertilization, yet mid-day (i.e. maximum) sunlit LAI was estimated to increase by 45%, and integrated daytime sunlit LAI by only 25% (not shown in Fig. 11). The ratio of sunlit (photosynthetically effective) LAI to the total LAI was reduced from 0·63 to 0·43 due to fertilization. The modelled increase in inline imagei/inline imagea at deeper canopy layers was a result of reduced leaf photosynthesis. When integrated with respect to height, the net canopy carbon uptake increased only slightly in the fertilized stand, which is consistent with the leaf-level findings in a Pinus elliottii forest (Teskey, Gholz & Cropper 1994).

Figure 11.

Comparison of midday (or maximum) sunlit leaf area density (asl) between fertilized (solid) and control (dashed) stands (top panel). Temporal variation in modelled intercellular to ambient CO2 concentrations (Ci/Ca) at three levels within the canopy for control (middle panel) and fertilized (bottom panel) stands.

Although inline imagei/inline imagea differences between fertilized and control stands suggest changes in photosynthetic forcing variables at different levels, the vertical distribution of scalar sources is more important. These source/sink profiles, shown in Fig. 12, are calculated by accounting for differences in leaf area density (see Appendix A). Fertilization stimulated CO2 uptake in the middle third canopy layer, just above the height of maximum a(z), but reduced uptake from the lower third canopy layer, where shading has increased. The CO2 uptake from the top third layers was barely affected by fertilization. Similar patterns of source response are evident for water vapour. For heat, the upper 40% of the canopy realized a significant reduction in heat sources within the fertilized plots. This reduction in heat sources is due to the combined effect of lower mean wind speed and lower surface temperatures at these canopy levels. We note that maximum-modelled difference between air and surface temperatures does not exceed 0·5 110;°C, yet this gradient is sufficient to maintain an appreciable sensible heat flux. This small difference between leaf and air temperature is similar to that measured in the nearby older stand (Ewers & Oren 2000).

Figure 12.

Fertilization-caused enhancement in the time-averaged source and sink profiles of CO2 (Sc), water vapour (Sq), and heat (ST) for control (dashed line) and fertilized (solid line) stands. All the source/sink profiles are normalized by their vertically integrated value at the control plots to illustrate the relative effect of fertilization. The leaf area density distribution a(z) is shown for reference.

The effects of fertilization on respiration

The other significant response to fertilization evident from Fig. 9 is an increase in RE. Figure 13 shows the temporal progression of RE in fertilized versus control stands, ensemble averaged by time of day. We find that the more than 50% enhancement with fertilization in night-time respiration can offset all of the daytime gains in photosynthesis, resulting in no appreciable enhancement in NEE over the 3 111;week measurement period.

Figure 13.

Enhancement of ecosystem respiration (RE) due to fertilization for the entire two 10-day experimental periods. The ensemble-averaged air and soil temperatures are shown for reference.

We expect these counteracting responses of increased canopy photosynthesis and respiration with fertilization, shown in Fig. 112;9, to be large at the end of the growing season, when LAI is near maximum and soil temperature through much of the root zone is high. However, fertilized stands at the site grow much more than unfertilized stands. We used the now tested CANVEG model to identify the time in the year in which the enhancement of photosynthesis with fertilization is not balanced by RE, thus supporting greater growth.

The effects of fertilization on the annual carbon cycle

We forced the CANVEG model with meteorological values typical to central North Carolina, collected at Duke Forest (36°2′ 113;N, 79°8′ 114;W) in North Carolina (see Lai et al. 2000a, b). The soil temperature measurements were corrected to account for observed differences between fertilized and control stands. These soil temperature adjustments were based on Maier & Kress (2000) who showed that monthly mean soil temperature of the control plots is usually 3–4 115;°C higher than that of the fertilized plots. For each month, at least 16 116;d (768 30 117;min runs) were used in the simulations to obtain a monthly mean flux. Electric power failure, lightning strikes, precipitation, and calibration runs prevented continuous measurements over the entire year.

The monthly LAI was used along with environmental drivers in the CANVEG model calculations. The monthly LAI was derived by scaling the LAI measurements in October with the monthly LAI variation measurements conducted in 1996 on a nearby stand with the same fertilization treatment. The LAI varied between 1·9 and 3·6 118;m2 119;m−2, and between 1·0 and 1·7 120;m2 121;m−2 for fertilized and control plots, respectively. Additionally, the physiological parameters in Table 122;1 were assumed static throughout the year. Table 4 summarizes the carbon balance for both fertilized and control stands. As a check, we compare these estimates of NEEd to others derived by utilizing the relationships shown in Fig. 10 based on measured 30 123;min averaged PAR, monthly LAI throughout the year, and the parameters in Table 124;3. These two approaches represent two end members of model complexity: detailed multilevel approaches (Wang & Jarvis 1990; Williams et al. 1997; Baldocchi & Meyers 1998) and a semi-empirical relationship (Running & Coughlan 1988; Landsberg & Waring 1997; Coops, Waring & Landsberg 1998; Cropper 2000).

Table 4.  Annual carbon balance for control and fertilized stands using typical meteorological conditions in central North Carolina and eco-physiological properties in Table 312;1. All units are in g 313;C 314;m−2 315;year−1unless stated otherwise. The sign convention for canopy carbon uptake is negative. For differences, positive implies gain in carbon due to fertilization
VariableControlFertilizedDifferencesModelled/estimated by
  1. a Night-time RE was estimated from the modelled monthly mean respiration components by CANVEG multiplied by the length of night-time hours for each month, and then summed for the entire year.

Gross primary productivity (GPP1)−1220−1795 316;575CANVEG
Respiration components   CANVEG
(i) Forest floor (Rsl)  1107  1140  33 
(ii) Above-ground woody (Rw)   156 395 239 
(iii) Foliar (Rfl)  63 133  70 
Total ecosystem respiration (RE)  1326  1668 342RE 317;= 318;Rsl 319;+ 320;Rw 321;+ 322;Rfl
Net ecosystem exchange (NEE1)   106 −127 233NEE1 323;= 324;GPP1 325;− RE
Net primary production (NPP) 781  1185 602NPP (control) 326;= 327;0·64 328;GPP1
NPP (fert.) 329;= 330;0·66 331;GPP1
Daytime NEE (NEEd) −525 −993 466NEEdPAR curve
Night-time REa 695 901 206CANVEG
NEE2 170 −92 262NEE2 332;= 333;NEEd 334;− Night-time RE
GPP2−1156−1760 604GPP2 335;= 336;–NEE2 337;+ 338;RE
Woody increment  121 403 282Woody biomass increment measurements
Litterfall  117 250 133LAI measurements
Above-ground NPP (NPPa)  238 653 415NPPa 339;= 340;Woody increment 341;+ 342;Litterfall
Below-ground NPP (NPPb)  543 532−11NPPb=NPPNPPa
NPPb/NPP (%) 70   45−25 
Autotrophic respiration (Ra)  440 610 170Ra 343;= 344;GPP1 345;− NPP
Heterotrophic respiration (Rb)  886  1058 172Rh 346;= 347;RE 348;− Ra


The gross primary productivity (GPP 125;≈ 126;photosynthesis in the absence of photorespiration, as discussed in Schulze, Wirth & Heimann 2000) estimated by CANVEG is about 1200 and 1800 127;g 128;C 129;m−2 130;y−1 for the control and fertilized stands, respectively. GPP estimated by the semi-empirical method agree with the CANVEG estimate to within 2% (see Table 131;4). The GPP of the control stand is similar to the GPP  estimated  by Law,  Ryan  &  Anthoni  (1999)  for  a  45-year-old Pinus  ponderosa  pine  forest  on  a  sandy  site in Oregon with a similar LAI (= 132;1·5). The GPP of the fertilized   stand  is  similar  to  a  recently  reported GPP  for a  19-year-old  loblolly  pine  forest  in  North  Carolina with a similar LAI (= 133;3·5; Lai et al. 2001). Figure 14 shows that the estimated monthly GPP for the fertilized stand is always larger than that of the control stand. When averaged over the entire year, we find that doubling LAI by fertilization increased GPP only 50%, consistent with other studies (Miller 1984; Linder et al. 1987; Gholz et al. 1991).

Figure 14.

Variation of modelled monthly gross primary productivity (GPP), ecosystem respiration (RE) and net ecosystem exchange (NEE) for control and fertilized stands. The monthly NEE (bottom panel) is computed as NEE 247;= 248;GPP 249;− 250;RE.

The effects of fertilization on annual ecosystem respiration, modelled by the CANVEG (Table 134;4), are also shown on a monthly basis in Fig. 135;14. The enhancement due to fertilization for Rw and foliar respiration Rfl are 150 and 110%, respectively. The Rsl estimates are approximately 1100 136;g 137;C 138;m−2 139;year−1 for both control and fertilized plots. The effect of fertilization on Rsl is not significant, consistent with previous studies in pine plantations (Cropper & Gholz 1991; Castro et al. 1994; Maier & Kress 2000). Of the respiratory components here, Rsl is the dominant contributor (> 140;65%) to ecosystem respiration in both stands.

From estimates of GPP and RE in a sparse Pinus ponderosa stand we calculated NEE near zero (Law et al. 1999). The results from our study (Table 141;4; Fig. 142;14) show that 6 years after planting the control stand with LAI similar to that in the Pinus ponderosa stand is still a week source of carbon (106 143;g 144;C 145;m−2 146;year−1); however, the fertilized stand already turned into a carbon sink (−127 147;g 148;C 149;m−2 150;year−1). The modelling results suggest that fertilization in poor nutrition sites shortens the time since regeneration required for pine forests to switch from an atmospheric carbon source to a sink, as proposed by Maier & Kress (2000).

On seasonal time scales, higher temperatures and increased self-shading in the summer may cause RE to become somewhat greater than GPP (see Fig. 151;14). The consequence is a positive NEE (source) for both fertilized and control stands for three of the summer months. More importantly, RE in the fertilized stand is greater than in the control stand because fertilization increased the above-ground respiratory biomass. During the non-growing season, RE decreases more than GPP, but the cause of the decrease is different for each flux: lower temperature decreases RE, whereas reduced light intensity and sunlight hours decrease GPP. The consequence of these reductions is a negative NEE (sink) in both stands, but the sink is much smaller in the control stand in spring and late autumn. Thus, based on the model results, the counteracting effects of fertilization on NEE measured with EC in September–October are not sustained over the entire year, and fertilization can lead to increases in NEE, although not in summer and early autumn months. The difference in NEE between fertilized and control stands during non-growing-season months more than compensates for the opposite difference in NEE during the rest of the year, supporting the annual responses discussed earlier.

The modelled value of annual NEE for both plots is much lower than the measured above-ground net primary productivity (NPP). Because the stands accumulate biomass, this suggest that much of the NPP is supported by internal recycling of C respired in the decomposition of tissues originating in the previous stand. We investigated this possibility further by analysing the components of GPP further and assessing whether modelled annual NEE values are qualitatively reasonable.

Recent studies suggest that the ratio of net primary productivity (NPP) to GPP is approximately constant for several terrestrial ecosystems (Ryan 1991; Ryan et al. 1996; Williams et al. 1997; Waring, Landsberg & Williams 1998). Waring et al. (1998) found that NPP/GPP 152;= 153;0·47 is nearly constant for 12 widely differing forested ecosystems although their assumptions leading to a constant ratio has been questioned (Medlyn & Dewar 1999). The ratio 0·47 has been adopted in simple models that estimate forest productivity from GPP (Landsberg & Waring 1997; Coops et al. 1998). Other studies found that NPP/GPP varies significantly with age or above-ground biomass (Mäkelä & Valentine 2001), as can be seen from a relationship of NPP/GPP versus above-ground biomass (mag; Fig. 15) based on data for pine stands reported in Ryan et al. (1994) and Mäkelä & Valentine (2001).

Figure 15.

Variation in the ratio of net primary productivity (NPP) to gross primary productivity (GPP) in relations to above-ground biomass (mag, g 251;C 252;m−2) for young pine stands (age 253;< 254;40 255;years). The closed circles are measurements reported in Ryan et al. (1994), and the open circle is from a fertilized-irrigated Pinus sylvestris stand. For small above-ground biomass, we used the suggested value (diamond) in Mäkelä & Valentine (2001) derived for P. sylvestris. For reference, the NPP/GPP 256;= 257;0·47 of Waring et al. (1998) is shown. The solid line represents the regression fit through the unfertilized stands (R2 258;= 259;0·69).

Using  the  biomass  estimates  for  control  (684 154;g 155;C 156;m−2) and fertilized (1579 157;g 158;C 159;m−2) stands and based on the relationship  in Fig. 160;15, the NPP/GPP for the respective stands are 0·64 and 0·59. Fertilization tends to increase NPP/GPP over the range of low above-ground biomass (< 161;4000 162;g 163;C 164;m−2) above its expected value (∼ 165;1·3; Ryan et al. 1994; Fig. 166;15). Such proportional enhancement in NPP/GPP would have produced an NPP/GPP 167;= 168;1·3 0·59 169;= 170;0·77, which  is  unrealistically  high,  above  all  reported  values  for pines. Given that the maximum NPP/GPP for mag 171;< 172;4000 173;g 174;C 175;m−2 is 0·66, we adopted this value to reflect the effect of fertilization enhancement rather than the lower 0·59 that reflects the ratio of unfertilized stands. Thus, for estimating NPP from GPP, we used the following:


which are higher than the mean value of 0·47 calculated by Waring et al. (1998).

Using these ratios, we estimated total NPP from GPP modelled with CANVEG (Table 176;4) as 780 and 1185 177;g 178;C 179;m−2 for the control and fertilized stands, respectively. The below-ground portion of NPP (NPPb) was then estimated by subtracting the measured above-ground NPP (NPPa) from the total NPP. The values of estimated NPPb were similar in both treatments (Table 180;4). We emphasize that the uncertainty in NPPb is mainly due to the choice of NPP/GPP, and that small bias in the ratio can alter the estimate of NPPb in these stands by> 50 181;g 182;C 183;m−2. Nevertheless, this analysis is carried out in order to assess whether the change in carbon allocation above- and below-ground corresponds to established patterns. Although NPPa increased by more than 170% with fertilization, modelled NPPb/NPP (70 versus 45% for control and fertilized stands, see Table 184;4) suggests that a smaller fraction of carbon was allocated below ground in the fertilized plot. Studies on carbon allocation in trees have shown an inverse relationship between relative carbon allocation below ground and soil fertility (Santantonio 1989; Burke, Raynal & Mitchell 1992; Haynes & Gower 1995; Beets & Whitehead 1996; Van der Werf & Nagel 1996; Reynolds & D'Antonio 1996; Albaugh et al. 1998), and this response has been incorporated into certain growth models (Landsberg & Waring 1997). That the annual budget (Table 185;4) is consistent with such inverse relationship lends qualitative supports to the annual GPP and NEE modelled with CANVEG.

The measured NPP can be used in another independent assessment of the capability of the model to capture the effects of fertilization on annual NEE. Because NPP response to fertilization was large, yet NEE response was small, a pre-treatment soil organic carbon pool must have supplied through the forest floor efflux a large amount of CO2 for assimilation. After the harvest of the previous forest in 1994, soil C content (2300 186;g 187;C 188;m−2, Maier & Kress 2000) and the root biomass (416 189;g 190;C 191;m−2, unpublished results from Maier) provide a rough estimate of 2700 192;g 193;C m−2 soil organic C content prior to planting. Based on 6% annual decomposition rate (Waring & Schlesinger 1985), we estimated 130 194;g 195;C 196;m−2 of C was added to the forest floor efflux in the year 2000 from decomposition of soil organic matter carried over from the previous forest. Assuming for first-order estimate of NEE that root and litter turnover rates balance their production, the atmospheric contribution to NEE necessary to meet the demand for above-ground woody increments (121 and 403 197;g 198;C 199;m−2 for control and fertilized stands, see Table 200;4) are 9 and −273 201;g 202;C 203;m−2. The annual NEE modelled with CANVEG is 106 and −127 204;g 205;C 206;m−2 (Table 207;4), in the correct sign but approximately 100–150 208;g 209;C 210;m−2 less negative than required in both stands. Despite the simplification and inherent errors, both NEE estimates suggest that the control stand is a weak source of CO2 to the atmosphere whereas the fertilized stand is a sink.

In conclusion, fertilization increases LAI and Vcmax, yet the increases do not result in comparable increase in modelled photosynthesis or NEE. The results from the model show that climatic and environmental conditions in combination with greater biomass due to fertilization can increase respiration more than photosynthesis, thus diminishing fertilization-caused enhancement of NEE. Nevertheless, with enhanced nutrition, stands on relatively infertile soils are likely to switch earlier in the stand development from a source of, to a sink for atmospheric CO2.


The authors thank Karen Wesson, Ben Poulter, Hyun-Seok Kim and Heather McCarthy for helping to set up the experiment and Peter Anderson for his help to maintain instruments and to download data. This project was funded, in parts, by the Biological and Environmental Research (BER) Program, US Department of Energy (DOE) through the FACE-FACTS project under contract DE-FG05-95ER62083, the Terrestrial Carbon Processes (TCP) project, and through the National Institute for Global Environmental Change (NIGEC), South-east Regional Center at the University of Alabama, Tuscaloosa (DOE cooperative agreement DE-FC030-90ER61010). Additional support is provided by the National Science Foundation (NSF-BIR 95-12333 and EAR-9805395).

Received 21 December 2001; received in revised form 12 March 2002; accepted for publication 26 March 2002

Appendix a. the canveg model formulation

The basic conservation equations and parameterization schemes used in CANVEG are reviewed below.

A.1Scalar mass balance

For a horizontally uniform and rigid canopy, the time and horizontally averaged one-dimensional scalar mass conservation equations for carbon dioxide (CO2), water vapour, and heat, can be written as:


where, inline imagea, inline imagea and inline imagea , are the mean air CO2, water vapour concentration and temperature, respectively, Fc, Fq, FT are the mean vertical fluxes of CO2, water vapour and heat, and Sc, Sq, and ST are vegetation source strength of CO2, water vapour, and heat, respectively, t is time, and z is height above the forest floor. Mean quantities are subject to both time and horizontal averaging as discussed in Raupach & Shaw (1982). Equation A1 represents three equations with nine unknowns necessitating additional formulations to solve for, Fc, Fq, FT, Sc, Sq and ST.

A.2Turbulent transport

The required additional formulations can be derived from the relationship between source strength and mean concentration via Lagrangian fluid mechanics principles. A set of prognostic equations describing the relationship between concentration and source (or sink) for CO2, water vapour and temperature is:

image((A2) )

where ρ is the mean air density, and P(z,t; z0,t0) is the transition probability density function determined from measured or modelled turbulent flow statistics within the canopy volume as described in Raupach (1988). For practical estimation of P(z,t; z0,t0), Lagrangian analytical models were developed and tested for a wide range of vegetation types (Raupach 1989a, b; Warland & Thurtell 2000). In particular, the localized near field theory (LNF) proposed by Raupach (1989a, b) proved to be a parsimonious model for such applications (Katul et al. 1997; Gu et al. 1999; Denmead, Harper & Sharpe 2000; Leuning 2000; Siqueira, Lai & Katul 2000).

In this study, we used LNF theory to characterize canopy turbulent scalar dispersion or P(z,t; z0,t0) modified to include atmospheric stability effects using the approach in Leuning (2000). The within-canopy flow statistics required for the LNF calculations were modelled using second-order closure principles (Wilson & Shaw 1977; Katul & Albertson 1998; Katul & Chang 1999). These second-order closure schemes solve the conservation of mean momentum and Reynolds stress equations within the canopy, and provide the flow statistics relevant for scalar transport from measured leaf area density and estimated foliage drag coefficients. Upon combining Eqns A1 and A2, the problem of estimating, Fc, Fq, FT, Sc, Sq and ST is now reduced to six equations with nine unknowns and remains unsolvable. To mathematically close this problem, three additional equations describing mass transfer from leaves to the atmosphere are needed.

A.3Scalar transfer from leaves

The scalar source strength S can be related to the atmospheric concentration by a Fickian diffusion formulation through the stomatal cavity and the leaf boundary layer. These formulations lead to the following expressions:

image((A3a) )
image((A3b) )
image((A3c) )

where subscripts a and i represent the ‘free’ atmosphere and subcavity space concentration values, λl is the latent heat of vapourization, Cp is the specific heat of dry air under constant pressure, a(z) is the plant area density, rb(z) is the mean boundary layer resistance, and rs(z) is the mean stomatal resistance at a given z. For simplicity, all the symbols representing mean resistances (or conductance) are shown without overbar throughout this study. Combining Eqns A1–A3, then inline imagea, inline imagea, inline image1;a, Fc, Fq, FT, Sc, Sq, and ST can be solved if rb(z), rs(z), inline imagei, inline imagei and inline imagei are modelled or parameterized. The modelling of rb(z), rs(z), inline imagei, inline imagei and inline imagei is discussed next.

A.4Resistance parameterizations: rb(z) and rs(z)

The estimation of rb is based on flat plate theory (Schuepp 1993; Baldocchi & Meyers 1998), but computed using the mean wind speed within the canopy, which in turn is modelled from second-order closure principles. Collatz et al. (1991) developed a physiological model to relate stomatal conductance gs to leaf photosynthesis, given by


where m and b are species-specific parameters, determined by gas-exchange measurements, An is the net leaf assimilation rate, and inline images and rh are the mean CO2 concentration and mean relative humidity at the leaf surface, respectively.

A.5Photosynthesis and inline imagei parameterization

In order to calculate An and inline imagei, Farquhar's biochemical model (Farquhar, Von Caemmerer & Berry 1980) is used in conjunction with the Collatz model. According to Farquhar et al. (1980), An is given by


where min {} denotes the minimal value among variables considered, JE and Jc are the leaf assimilation rates constrained by electron transport capacity (Jmax) and maximum carboxylation rate (Vcmax), respectively, and Rd is the respiration rate during daytime without photorespiration. The functional relationship between An and inline imagei (i.e. the ACi curve) generated by gas-exchange measurements can be used to determine Jmax and Vcmax, also summarized in Table 211;1 for the model calculation. Details of the Farquhar formulation and parameterization of JE, Jc and Rd are given in Appendix B.

A.6Radiative transfer

Radiation attenuation inside the canopy is critical to both the Farquhar photosynthesis model and the leaf energy budget. In our CANVEG model, the light transmission model of Campbell & Norman (1998) was adopted and is briefly described below.

The solar (short-wave) radiation was decomposed into direct beam, diffuse and reflective radiation as described in Campbell & Norman (1998). For thermal or long-wave radiation, the atmosphere was assumed to function as a grey body (Campbell & Norman 1998). This permits the use of an averaged sky emissivity for calculating atmospheric thermal emittance. For simplicity, we used a constant emissivity of 0·97 for the entire period.

Light transmission through the canopy is computed for sunlit and shaded portions separately to estimate PAR and near-infrared (NIR) irradiance absorbed at each canopy level. This waveband decomposition is necessary because leaf absorptivity is different for these two spectral bands (Monteith & Unsworth 1990; Campbell & Norman 1998).

The fraction τb(ψ) of incident beam radiation from a zenith angle ψ penetrating through the canopy is given by


where α is the leaf absorptivity for PAR, Kbe(ψ) is the extinction coefficient for an ellipsoidal leaf distribution (see Campbell & Norman 1998), al () is the cumulative leaf area density integrated from the canopy top, and Ω is the clumping factor of leaf distribution (Ω 212;= 213;1 when leaves are randomly distributed in space). The model in Eqn A6 is sufficiently accurate if a(z) 214;< 215;0·5 at a given layer (Norman & Welles 1983) as is the case for our study.  All the radiative parameters (e.g. α and Ω) measured or assumed for this study are listed in Table 216;1.

A.7Parameterization of inline imagei, and inline imagei: the leaf energy budget

The energy budget at the leaf surface is used to solve for surface variables (i.e. inline imagei, and inline imagei) and absorbed radiation for estimating gs. Due to the strong non-linearity in the leaf energy budget, a Taylor series expansion along with a Penman approximation were used to derive an explicit algebraic equation for mean leaf surface temperature ( inline images), given by


where Qab is the absorbed energy at each canopy layer, gv is the water vapour conductance (derived from gs and gb for water vapour), Dv is the vapour pressure deficit, pa is the atmospheric pressure, ɛ is the leaf emissivity, σ is the Stefan–Boltzmann constant, hc is a convection coefficient, and Δ is the slope of the saturation vapour pressure–temperature function. The linearization in Eqn A7 is reasonable for ?inline images 217;− 218; inline imagea? 219;< 220;2 221;°C (Tracy et al. 1984), and is the case for more than 95% of the runs in this study, as was demonstrated in a similar setup by Ewers & Oren (2000).

A.8Boundary conditions

The solution of Eqns A1–A3 requires boundary conditions at the canopy-top and at the forest floor. The upper boundary conditions are directly specified every 30 222;min from measured inline imagea, inline imagea, inline imagea, PAR and inline image. The lower boundary conditions required are Fc, Fq and FT at z= 0. The latter are parameterized from a combination of measurements and simplifying assumptions. We estimated soil respiration (Rsl) from measured soil temperature (Tsl) every 30 223;min and a stand-specific respiration–temperature response curve. For water vapour, we assume that the forest-floor flux is about 50% of equilibrium evaporation and is estimated by


with αeq set to 0·5 to ensure that the soil evaporation rate does not exceed the ability of sandy soils to transmit water (estimated from the soil diffusivity for sand), γ is the psychrometric constant, Go is the measured soil heat flux, and FT(0,t) 224;= 225;Rn(0,t) 226;− 227;Go(t) 228;− 229;Fq(0,t).


Much of the following material is presented in Lai et al. (2000b), and thus we repeat only the key equations. According to Farquhar et al. (1980), the net photosynthetic rate at the leaf scale depends on light, CO2 and leaf temperature and can be described as:


where JE and Jc are the assimilation rate restricted by light and ribulose bisphosphate (RuBP) carboxylase (or Rubisco), respectively, and Rd is the respiration rate during daytime without photorespiration. In Eqn B1, JE describes the light restriction on photosynthesis, given by:


where α is the leaf absorptivity for PAR, em is the maximum quantum efficiency for CO2 uptake, Qp is the PAR irradiance on the leaf, inline imagei represents mean intercellular CO2 concentration. The CO2 compensation point, Γ*, is the CO2 concentration at which An 230;= 231;0 in the absence of photorespiration, and is given by:

image((B3) )

where [O2] is the oxygen concentration in air (≈ 232;210 233;mmol 234;mol−1), and ω is a ratio of kinetic parameters describing the partitioning of RuBP to the carboxylase or oxygenase reactions of Rubisco.

Jc is the Rubisco-limited rate and is estimated from:

image((B4) )

where Vcmax is the maximum catalytic capacity of Rubisco per unit leaf area (µmol 235;m−2 236;s−1), Kc and Ko2 are the Michaelis constants for CO2 fixation and O2 inhibition with respect to CO2, respectively. Equation B4 shows that Jc increases linearly with increasing inline imagei, , but approaches a maximum Vcmax under high CO2 concentration state which is rarely encountered under natural conditions.

Following Collatz et al. (1991), the respiration rate Rd can be estimated by:


Temperature dependence of kinetic variables is computed following the equations in Campbell & Norman (1998). Five kinetic parameters are needed to adjust for temperature: Kc, Ko, ω, Vcmax and Rd. For the first three parameters, a modified Q10 temperature function is employed:


where k is defined at leaf surface temperature Ts, k25 is the value of the parameter at 25 237;°C, and y is the temperature coefficient for that parameter from Campbell & Norman (1998). In addition, Vcmax andRd are adjusted by a more complex function incorporating deactivation effects at extremely high temperatures, such as:

image((B7) )


image((B8) )

where Vcmax,25 and Rd,25 are the values of Vcmax and Rd at 25 238;°C, respectively.

Finally, inline images, inline imagei, and inline imagea, are related by:

image((B9) )


image((B10) )

where gs (= 239;rs-1) is the stomatal conductance and gb(=rb-1 240;) is the leaf boundary layer conductance.