Contribution of competition for light to within-species variability in stomatal conductance

Authors


Abstract

[1] Sap flux (JS) measurements were collected across two stands dominated by either trembling aspen or sugar maple in northern Wisconsin. Observed canopy transpiration (EC-obs) values derived from JS were used to parameterize the Terrestrial Regional Ecosystem Exchange Simulator ecosystem model. Modeled values of stomatal conductance (GS) were used to determine reference stomatal conductance (GSref), a proxy for GS that removes the effects of temporal responses to vapor pressure deficit (D) on spatial patterns of GS. Values of GSref were compared to observations of soil moisture, several physiological variables, and a competition index (CI) derived from a stand inventory, to determine the underlying cause of observed variability. Considerable variability in GSref between individual trees was found, with values ranging from 20 to 200 mmol m−2 s−1 and 20 to 100 mmol m−2 s−1 at the aspen and maple stands, respectively. Model-derived values of GSref and a sensitivity to D parameter (m) showed good agreement with a known empirical relationship for both stands. At both sites, GSref did not vary with topographic position, as indicated by surface soil moisture. No relationships were observed between GSref and tree height (HT), and a weak correlation with sapwood area (AS) was only significant for aspen. Significant nonlinear inverse relationships between GSref and CI were observed at both stands. Simulations with uniform reductions in incident photosynthetically active radiation (Q0) resulted in better agreement between observed and simulated EC. Our results suggest a link between photosynthesis and plant hydraulics whereby individual trees subject to photosynthetic limitation as a result of competitive shading exhibit a dynamic stomatal response resulting in a more conservative strategy for managing hydrologic resources.

1. Introduction

[2] Stomata function to regulate plant hydraulics and concurrently control carbon dioxide exchange between the biosphere and atmosphere. Accurate estimates of stomatal conductance are essential to model water and carbon cycles from local to global scales [Bonan, 1991; Denning et al., 2003; Famiglietti and Wood, 1994; Foley et al., 1996; Kuchment et al., 2006; Landsberg and Waring, 1997; Running and Coughlan, 1988]. Estimates of stomatal conductance for species or plant functional types are typically obtained at the leaf or whole plant level using gas exchange and sap flux measurements, respectively, and scaled as required for specific model applications. Homogeneity within species or functional groups is implicit in current scaling methods, which until recently have been relatively limited by data acquisition [Mackay et al., 2002; Williams et al., 2004; Wullschleger et al., 2001]. A number of recent studies have demonstrated varying degrees of heterogeneity in forest transpiration at the stand or hillslope scale [Adelman et al., 2008; Kumagai, 2008; Loranty et al., 2008; Traver et al., 2010; Tromp-van Meerveld and McDonnell, 2006]. Understanding the drivers and mechanistic underpinnings of spatial and temporal variation in stomatal control of transpiration is crucial to improve scaling and predictive understanding of water and carbon fluxes.

[3] Stomata close to prevent hydraulic failure at high atmospheric vapor pressure deficit (D) in response to increased leaf water potential that is caused by high transpiration rates [Mott and Parkhurst, 1991]. This response occurs because high transpiration rates as a result of high D are responsible for hydraulic stress that can be lethal if unrestricted [Sperry et al., 1998; Tyree and Sperry, 1989]. When D and light are low, stomata exhibit a linear response to photosynthetic photon flux density (Q0) to maximize carbon uptake for productivity. Stomatal conductance (GS) has been described as a response to key environmental drivers [Jarvis, 1976] that can be expressed as a function of plant hydraulics [Oren et al., 1999b], and alternatively as a function of photosynthetic carbon uptake [Ball et al., 1987]. Subsequently several models varying in complexity have been developed that define stomatal conductance in terms plant hydraulics. The following model defines GS using Darcy's law [Whitehead and Jarvis, 1981; Whitehead et al., 1984]:

equation image

where GS is canopy average stomatal conductance (mmol m−2 s−1), KS is whole tree hydraulic conductance (mmol m−2 s−1 MPa−1), AS is sapwood area (m2), AL is leaf area (m2), D is vapor pressure deficit, ψS is soil water potential (MPa), ψL is leaf water potential (MPa), wg is the gravitational pull (g) on the water column of height (h) and density (ρw). Recently GS (mmol m−2 s−1) has been described solely by its saturating response to D in terms of reference stomatal conductance (GSref) (mmol m−2 s−1), which is GS at D = 1 kPa [Katul et al., 2009; Oren et al., 1999b]:

equation image

where m = −∂GS/∂lnD is interpreted as stomatal sensitivity to D. In mesic environments a proportional relationship between GS and sensitivity to D, where m = 0.6 GSref has been observed within and between species [Addington et al., 2004; Ewers et al., 2001; Oren et al., 1999a, 1999b; Wullschleger et al., 2002]. Species that exhibit this relationship regulate transpiration in order to maintain critical minimum leaf water potential and prevent run away cavitation, and are referred to as isohydric [Franks et al., 2007; Tardieu and Simonneau, 1998].

[4] Recent studies at a variety of sites [Adelman et al., 2008], including the ones used in the present study [Loranty et al., 2008; Traver et al., 2010], have shown that spatial variability in transpiration changes temporally in response to D. Briefly, at low D under minimal hydraulic stress GS and thus canopy transpiration (EC) are relatively homogeneous. However, individual trees exhibit differing responses to increasing D, and so greater variability in EC is observed during midday periods of high D. Thus, for isohydric plants it is ideal to use GSref as a proxy for direct comparison of stomatal function between individuals because the effects of D are removed. This allows the effects of other variables, such as soil moisture, edaphic factors, or incident radiation (i.e., equations (1) and (2)), on variability in GS to be examined more explicitly, without the confounding effects of temporal changes in D on spatial patterns of GS.

[5] Decreases in sap flow velocity per unit xylem area (JS) as a result of declines in soil moisture, indicating a stomatal response to hydraulic stress, have been reported in the literature for a variety of species [Gazal et al., 2006; Lagergren and Lindroth, 2002; Oren and Pataki, 2001; Pataki et al., 2000]. Topography, soil composition, and soil depth can contribute to soil moisture heterogeneity and have been linked to spatial variation in EC during transitions between wet and dry periods [Granier et al., 2000; Tromp-van Meerveld and McDonnell, 2006]. However, recent work at the sites used for this study suggest that variability in soil properties or soil moisture do not contribute to variability in EC [Traver et al., 2010].

[6] Plant hydraulics and photosynthetic capacity have recently been linked empirically [Brodribb and Feild, 2000; Maherali et al., 2008] and theoretically [Katul et al., 2003] in studies that seek to explain different strategies of hydraulic regulation and elucidate further the mechanisms responsible for stomatal regulation. Fractions of absorbed incident and diffuse radiation vary according to branching patterns, leaf distribution, leaf angle and orientation, and crown morphology [Campbell and Norman, 1998; Cescatti, 1998; Ewers et al., 2007b]. Developmental light environment has been shown to impact leaf photosynthetic capacity [Niinemets et al., 2004], and so competitive shading between crowns can be considered as a source of variability photosynthetic capacity among individuals. Potential sources of variability in factors contributing to light limited of photosynthesis can thus be considered in the context of plant hydraulics and the implications for GS. Particularly decreased light availability through shading, as this has been shown to affect GS [Ewers et al., 2007b]. Additionally, competitive shading may be explored as a mechanistic explanation for the connection between spatial and temporal patters of transpiration mentioned above [Loranty et al., 2008; Traver et al., 2010].

[7] The following study has been conducted to test three hypotheses: (1) Within species, GSref exhibits spatial variation across stands, (2) GSref remains isohydric within species despite spatial variability, and (3) competition for light contributes to variability in GSref. We accomplish this using sap flux data, leaf gas exchange, and a model with coupled hydraulic and photosynthetic constraints on GS. The goal is to elucidate the mechanisms responsible for variable stomatal control of biosphere-atmosphere gas exchange.

2. Methods

2.1. Site Description

[8] The study was conducted at two forest stands near the town of Park Falls in northern Wisconsin (45.95°N, 90.27°W) (Figure 1). Both stands are located within the Chequamegon-Nicolet National Forest less than 2 km from the WLEF Ameriflux tower, and associated with the Chequamegon Ecosystem Atmosphere Study (ChEAS) [Bakwin et al., 1998; Davis et al., 2003]. Topography in the area is gently rolling and the dominant geomorphic features in the area are outwash, pitted outwash, and moraines. The climate of the region is characterized by a long winter and a short growing season with mean January and July temperatures of −12°C and 19°C, respectively [Fassnacht and Gower, 1997].

Figure 1.

Map of (a) aspen and (b) maple sites. Large gray circles indicate 5 m and 10 m radius competition plots centered on the sap flux trees used for analysis in this study for aspen and maple, respectively. On both maps, crosses denote trees from the species used for analysis in this study instrumented for sap flux, and open circles represent trees sampled for sap flux only. The cyclic sampling design is reflected in the clustered location of (and subsequent gaps between) sap flux trees.

[9] The first site chosen for this study, hereafter referred to as aspen, captures a forested wetland-to-upland transition dominated by speckled alder (Alnus incana (DuRoi) Spreng) and white cedar (Thuja occidentalis L.) in the wetland, and quaking aspen (Populus tremuloides Michx) in the upland. The aspen stand was a regenerating clear-cut area approximately 20 years old. The aspen study site measures 120 m × 120 m with an elevation gradient of ∼3 m across the site. The second stand, referred to as maple, was dominated by mature sugar maple (Acer saccharum Marsh.) surrounding a large patch of plantation red pine (Pinus resinosa Ait.) with trees ranging in age from approximately 55–75 years. The portion of the site dominated by red pine comprised roughly 25% of the total area of the site in the form of an elongated area oriented in the northwest direction. The maple site was slightly larger measuring 132 m × 140 m and had approximately 15 m of variation in elevation across the site.

2.2. Data Collection

[10] A series of sample plots, measuring 5 m and 6.5 m in diameter at the aspen and maple sites, respectively, were established using a cyclic sampling design [Burrows et al., 2002; Clinger and Vanness, 1976]. Initial site surveys revealed that tree size, indicated by diameter at breast height (DBH) varied across the site. Subsequently selecting the largest tree in each plot from the dominant species for sap flux instrumentation yielded a representative sample [Adelman et al., 2008; Loranty et al., 2008]. For the aspen site the dominant species were aspen, alder, and cedar. At the maple site maple and red pine were the dominant species. In plots containing members of more than one of the dominant species one member of each species was selected for sampling, where resources allowed. Cyclic sampling is an efficient sampling method for geostatistical analysis, and a full description of the sampling and analyses at the aspen and maple sites is given by Loranty et al. [2008] and Traver et al. [2010], respectively.

[11] During the summer of 2005 approximately 300 trees were instrumented for sap flux measurements using the heat dissipation method [Granier, 1987]. Measurements at the aspen site began 27 May and ended 8 July. During the period from 15–20 June the site was shut down in order to recharge the power supply. Continuous measurements were made at the maple site from 19 July through 19 August. Sap flux data was processed using dynamic baselines to account for changes in sapwood moisture content and nighttime transpiration [Oishi et al., 2008]. Point measurement of sap flux in the outer 20 mm of sapwood were scaled to the whole tree based on species specific radial trend measurements in sap flux and allometric relationships between sapwood depth and diameter measured ∼10 km away in similar stands [Ewers et al., 2002]. Estimates of observed EC (mm s−1, converted from g s−1) were calculated from JS measurements using the following equation:

equation image

where JS is sap flux per unit xylem area (g m−2 s−1) including species specific radial trend variation, AS is sapwood area (m2), AG and is ground area (m2). DBH was measured using a dendrometer band for each tree selected for sap flux instrumentation. Values of AS were calculated from DBH using species specific allometric relationships established at nearby sites [Ewers et al., 2002]. AG was assumed to be the projected cross-sectional crown area for each individual. At the aspen site this was calculated from DBH using an allometric relationship developed with a subset cross-sectional crown area measurements made in conjunction with measurements taken to describe the competitive light environment within the canopy (described below). At the maple site the same approach was used, however the species specific allometric relationships used were taken from the literature [Frelich and Lorimer, 1985].

[12] Measurements of temperature and relative humidity (Vaisala HMP 45C, Vaisala Oyj, Helsinki, Finland) were made at two-thirds canopy height at both sites. Sap flux, temperature, and relative humidity measurements were recorded every 30 s (CR10X, Campbell Scientific, Logan, UT, USA) and aggregated to 30 min values. We measured volumetric surface (0–6 cm) soil moisture (Theta Probe, Delta-T, Cambridge, UK) in each plot on 30 May, 9, 13, 17, 22, and 25 June, and 12 and 14 July at the aspen site, and on 21 July at the Maple site. Values for each plot were determined by calculating the mean of three measurements taken at random locations within the plot. The soil moisture measurements were intended to represent the relative wetness of the plots rather than to serve as an indication absolute of root zone available moisture. Drought occurrence in these stands is rare [Ewers et al., 2007a; Mackay et al., 2002, 2007; Samanta et al., 2008], and a piezometer installed at the aspen site supported this, as the water table remained <1 m from the surface near the edge of the wetland. Additionally obtaining root zone measurements for all 288 plots was not feasible.

[13] Several environmental variables required as model inputs including wind speed, Q0, and precipitation (P) were acquired from the nearby WLEF (∼2 km) [Davis et al., 2003] and Lost Creek (∼10 km) [Cook et al., 2004] eddy covariance towers, respectively, depending on data availability and temporal resolution. Ewers et al. [2007a, 2008] have shown no difference between D measured at the WLEF tower and 2/3 canopy height from six stands in the region, indicating high canopy coupling. Leaf gas exchange measurements were made during the study period for a subset of trees at the aspen site. Scaffolding was erected over a period of several days and measurements of photosynthesis for sunlit and shaded leaves were obtained for approximately 6 aspen individuals in the upland portion of the site, and 6 individuals in the wetland portion of the site. Standard photosynthetic light response curves [Long and Bernacchi, 2003] were generated using observations made with an LI 6400 (Li-COR Biosciences, Lincoln, NE).

[14] In order to consider the potential effects of competitive shading we selected cloudless and cloudy days for data analysis because they are dominated by direct and diffuse radiation, respectively, and represent end-members of radiation conditions. Cloudless days were defined as days on which midday Q0 was greater than 1800 μmol m−2 s−1 and diel plots of Q0 exhibited minimal high-frequency variation indicative of partial cloud cover (Figures 2b and 2f). Cloudy days were defined as having relatively low Q0, where ideally, midday values were in the range of 1000–1300 mmol m−2 s−1 and if possible no spikes exceeded 1500 mmol m−2 s−1 (Figures 2d and 2h). This measure was taken to ensure that individual values of GSref could be considered in the context of a tree's competitive light environment within the canopy, without the confounding effects of variation in Q0 as a result of passing cloud cover, and then compared with values on cloudy days. Despite continuous monitoring, the extensive nature of the sites and the magnitude of upkeep required for sap flux sampling meant that days with site-wide data sets suitable for analysis were uncommon. Coincidentally large portions of both sites experienced power failures during the limited cloudless periods, and therefore a subset of approximately 20 trees from each site (Table 1) was selected for analysis based randomly on data availability related to the absence of power outages.

Figure 2.

Diurnal trends of EC-obs from half-hourly sap flux data from three trees, and D and Q0 for (a and b) cloudy and (c and d) cloudless at the aspen site, and (e and f) cloudy and (g and h) cloudless at the maple site.

Figure 2.

(continued)

Table 1. Mean Values of Biometric Measurements for Individuals Sampled for Analyses, and Stand Inventories for Each Sitea
SpeciesNbDBH (cm)HT (m)CILAIc (m2 m−2)Gsrefd (mmol m−2 s−1)m (mmol m−2 s−1)
  • a

    Mean GSref and m values are listed as well. Values in parentheses represent standard errors.

  • b

    Not all individuals selected were included for analyses based on model results.

  • c

    Only individuals with acceptable model results are included in parameter means.

  • d

    Site-wide mean LAI is not available because allometry for all species is not available.

Aspen188.1 (0.70)10.0 (0.68)1.43 (0.80)4.06 (0.28)73.0 (10.5)42.7 (8.3)
 6569.0 (0.13)11.0 (0.11)
Maple2023.5 (1.5)17.6 (0.52)1.13 (0.75)7.15 (0.53)49.3 (3.8)24.7 (4.2)
 45422.1 (0.38)16.4 (0.15)

2.3. Stand Measurements

[15] Estimates of leaf area index (LAI) were required for the modeling portion of our study (described below). In order to ensure that modeled results were not artifacts of inaccurate canopy representation we calculated unique estimates of LAI for each individual tree used for analysis. An allometric equation relating LAI to DBH was developed via destructive harvest of 12 representative individuals across the stand. Such an approach was not feasible at the maple stand, and so we relied on regional allometric relationships taken from the literature [Frelich and Lorimer, 1985; Perala and Alban, 1994].

[16] Distance-dependent measures of competitive crowding are commonly employed in ecological studies [Bella, 1971; Berger and Hildenbrandt, 2000; Canham et al., 2004; Lorimer, 1983] including sap flux studies [Lagergren and Lindroth, 2004; Phillips and Oren, 1998]. To this end a series of measurements intended to describe the competitive light environment within the canopy were collected during August 2006 for the aspen site and August 2007 for the maple site. For each aspen and maple individual instrumented for sap flux an inventory was recorded of all neighbors within 5 m and 10 m, respectively. Distance and direction of each neighbor from the sap flux tree was recorded. Trees lying to the north of the sap flux tree between 345° and 45° were excluded on the grounds their competitive effects with respect to light within the canopy would be negligible. In addition tree heights for all trees were measured at the aspen site with triangulation methods using a laser rangefinder and clinometer. A combination of factors including a higher and denser canopy, a thick understory, and increased microtopography made height observation at the maple site impossible. As such tree heights at the maple stand were calculated using species-specific allometric equations developed for stands with similar structure and age within the region [Frelich and Lorimer, 1985; Perala and Alban, 1994]. At the maple site differences in relative tree height were determined using a LiDAR derived digital elevation model with 1 m resolution.

[17] Distance, direction, and height measurements for all competitors of an individual sap flux tree were used to calculate a competition index (CI), which was defined as:

equation image

where for each competitor i, a is the degree of southness to the sap flux tree when a ≤ 180° and 1/2 azimuth direction where a > 180° (°), di is the distance between the sap flux tree and the competitor (m), hs is the height of the sap flux tree, and hi is the height of the competitor (m).

2.4. Model Description

[18] A brief overview of the Terrestrial Regional Ecosystem Exchange Simulator (TREES) [Ewers et al., 2008; Mackay et al., 2003; Samanta et al., 2007, 2008] is provided in the following section, and more detail can be found in Appendix A. TREES is a canopy model that uses a modified big-leaf approach to simulate transpiration with a hybrid hydraulic and biochemical model of stomatal conductance [Katul et al., 2000]. Light attenuation through the canopy for a given solar zenith angle, assuming a spherical leaf angle distribution and using a species-specific clumping parameter (Ω), is used to partition a given value of LAI into sunlit and shaded canopy elements. The model uses an initial hydraulic limited value of canopy stomatal conductance (GSref0), sampled at random from an uninformed distribution, which is constrained further using a photosynthesis model. This process is carried out in parallel for horizontal sunlit and shaded canopy layers. Final values of canopy stomatal conductance to water vapor are used to calculate transpiration for sunlit and shaded canopy elements individually, and then summed to yield simulated whole canopy transpiration (EC-sim).

[19] In the model, photosynthesis (An) was calculated as described by Farquhar et al. [1980], and several parameters are required. Light acclimated quantum yield of photosynthesis (ϕJ) expressed as mole electrons per mole of photons, is particularly important because it characterizes the response of An to Q0 under low-light (light-limiting) conditions. This variable can be specified separately for sunlit and shaded canopy elements. At the aspen site in situ gas exchange measurements were collected and light response curves were constructed to determine ϕJ. For the maple site gas exchange measurements from a nearby site were used. For both species no differences between sunlit and shaded leaves, or differences across edaphic conditions were observed. Values of 0.32 and 0.2 were used for aspen (this study) and maple (E. Kruger, unpublished data, 2010), respectively. Because EC-sim and GSref are modeled at the canopy scale accurate estimates of leaf area are essential for accurate estimates of fluxes and conductances. To achieve this we used unique estimates of LAI for each tree based on allometry described in section 2.3.

[20] For this study the model was run inversely using a Monte Carlo technique whereby multiple simulations are generated through repeated parameter sampling to yield a series of estimates of transpiration, which are subsequently evaluated against EC-obs. Transpiration models calibrated using stand average EC-obs likely benefit from a reduction in signal noise resultant from data aggregation. Model calibration with data from individual trees should then be approached with this in mind. Here the parameters GSref0 and m were allowed to vary to highlight differences in strategy for hydraulic regulation between individuals. An initial set of simulations were evaluated against an empirical estimate of stomatal conductance using only daytime observations and a fuzzy uncertainty approach [Samanta and Mackay, 2003] was used to constrain the range over which GSref0 and m varied for each tree. A final set of simulations was generated using the constrained parameter ranges and then assessed by comparing EC-sim and EC-obs. We found index of agreement (IOA):

equation image

[Willmott, 1982] to be more robust than other fit statistics and so simulations were sorted by IOA in order identify the best model. Values of GSref0 are initial estimates that may be further constrained by photosynthesis. Therefore we plotted simulated values of stomatal conductance (GS) against D and fit a boundary line to the upper envelope of the curve by using the parameter m from the best model with equation (2), and adjusting GSref until the line passed through the upper envelope of the cloud of points (Figure 3).

Figure 3.

Boundary line fit to the upper envelope of GS versus D used to determine GSref. The dashed curve represents the relationship GS = GSrefmln(D). The parameter value of m from the best model is used, and GSref is adjusted until the line to passes through the upper boundary of the point cloud. This allows GSref to be reduced relative to GSref0 in the case that GS has been reduced to account for light limitation. This process is repeated for each tree at both sites, under both light conditions.

2.5. Statistical Analysis

[21] A preliminary analysis revealed that where the highest IOA < 0.80 for a tree, there was typically a high degree of mismatch between simulated and observed data and a lack of convergence among parameter values (GSref0 and m). Subsequently boundary lines formed using equation (2) did not pass through the upper envelope of the point cloud as expected (i.e., Figure 3), indicating that the parameters did not represent the data. Gaps in the data (i.e., partially missing days), erroneous data values, or a combination of both appeared to be the culprit. It is denoted in the results where IOA < 0.80 for an individual, and if this impacted the results parallel analysis with and without the data were conducted. Linear and nonlinear regression analyses were used to test for significant relationships (p < 0.05) between variables. All regression analyses were conducted with Sigmaplot (version 11.0 Systat Software, California, USA). Monte Carlo analyses and accompanying statistical evaluation of EC-sim and EC-obs were conducted using TREES, as described above.

3. Results

[22] Analysis of a preliminary set of simulations that were performed without the constrained parameterization technique described above yielded nearly identical results in terms of parameter values and goodness of fit (data not shown). The primary difference was a broader range of parameter values for the top models, some of which made little physiological sense (i.e., very low values of GSref0 and high values of m) and made any analysis using only the top model questionable. Once the constrained parameterization was applied the model converged on a narrow range yielding a much more robust set of parameter values for each tree that are essentially identical for the best fitting models (Table 2).

Table 2. Summary of Model Parameterization Results for All Trees on Cloudless and Cloudy Daysa
 TreeCloudlessCloudy
IOAbGSref (mmol m−2 s−1)m (mmol m−2 s−1)IOAbGSref (mmol m−2 s−1)m (mmol m−2 s−1)
BestMeanBestMeanBestMeanBestMeanBestMeanBestMean
  • a

    Values of IOA, GSref, and m for the best fit model are compared with mean values from the top 100 models to illustrate model convergence. The range of mean IOA values is indicated in parentheses, and standard error of the mean is in parentheses for mean G and m.

  • b

    Values in parentheses indicate the range of IOA values for the top 100 models.

A11Aspen0.840.83 (0.83–0.84)87.090.0 (0.93)60.061.0 (0.07)0.720.72 (0.71–0.72)92.074.4 (0.75)60.262.2 (0.15)
C11Aspen0.920.91 (0.91–0.92)105.0111.6 (1.14)86.989.4 (0.39)0.830.83 (0.83–0.83)150.0156.2 (1.58)118.0119.2 (0.32)
D7Aspen0.920.92 (0.92–0.92)155.2154.3 (1.59)105.3107.0 (0.41)0.930.93 (0.93–0.93)175.0213.8 (2.16)116.3115.9 (0.32)
D9Aspen0.840.83 (0.83–0.84)46.046.8 (0.50)26.027.8 (0.11)0.760.76 (0.75–0.76)42.042.7 (0.43)28.030.0 (0.27)
D11Aspen0.830.83 (0.83–0.83)33.734.4 (0.38)20.121.2 (0.08)0.720.70 (0.70–0.72)27.027.8 (0.28)20.422.4 (0.17)
D12Aspen0.880.87 (0.86–0.88)37.047.5 (0.73)10.247.5 (0.73)0.850.83 (0.81–0.85)31.536.9 (0.67)10.236.9 (0.67)
E7Aspen0.920.92 (0.92–0.92)162.0161.0 (1.65)116.8117.2 (0.36)0.920.92 (0.92–0.92)152.0174.6 (1.76)121.3122.6 (0.24)
E10Aspen0.890.89 (0.89–0.89)45.947.2 (0.50)22.123.5 (0.11)0.700.69 (0.68–0.70)28.534.4 (0.36)22.323.8 (0.11)
E11Aspen0.860.86 (0.86–0.86)41.042.3 (0.45)20.121.0 (0.08)0.810.81 (0.81–0.81)36.537.3 (0.38)21.423.3 (0.22)
E12Aspen0.830.83 (0.83–0.83)52.353.7 (0.58)24.025.3 (0.09)0.720.72 (0.72–0.72)42.542.7 (0.47)24.025.3 (0.08)
F11Aspen0.890.89 (0.89–0.89)50.150.1 (0.52)19.220.1 (0.08)0.750.75 (0.75–0.75)40.041.5 (0.42)19.221.6 (0.18)
G3Aspen0.670.67 (0.66–0.67)22.022.6 (0.22)11.011.2 (0.02)0.800.80 (0.80–0.80)23.022.6 (0.22)11.011.3 (0.02)
G5Aspen0.900.90 (0.90–0.90)105.0107.1 (1.09)42.744.4 (0.25)0.800.79 (0.79–0.80)57.560.5 (0.63)41.043.5 (0.18)
G6Aspen0.870.87 (0.86–0.87)33.035.1 (0.37)11.011.5 (0.03)0.700.69 (0.69–0.70)24.525.6 (0.26)11.112.0 (0.08)
H2Aspen0.790.78 (0.78–0.79)30.034.4 (0.45)10.011.6 (0.10)0.680.66 (0.65–0.68)30.017.5 (0.33)10.111.2 (0.09)
H6Aspen0.810.80 (0.80–0.81)27.628.3 (0.41)15.015.9 (0.05)0.670.66 (0.65–0.67)30.027.3 (0.39)15.016.3 (0.10)
H6-3Aspen0.940.94 (0.94–0.94)73.081.5 (0.84)43.145.5 (0.18)0.810.80 (0.80–0.81)71.073.3 (0.74)44.048.4 (0.36)
I6Aspen0.910.91 (0.91–0.91)95.0108.0 (1.13)70.070.4 (0.43)0.840.83 (0.83–0.84)130.094.4 (0.95)68.774.4 (0.73)
A03Maple0.950.95 (0.95–0.95)42.056.0 (0.65)20.827.4 (0.53)0.890.89 (0.89–0.89)58.088.4 (0.90)29.829.9 (0.31)
A05Maple0.960.96 (0.96–0.96)61.071.0 (0.77)28.630.0 (0.70)0.870.87 (0.86–0.87)80.0105.4 (1.09)18.221.7 (0.25)
A08Maple0.950.96 (0.91–0.96)40.541.4 (0.61)28.629.4 (1.14)0.920.92 (0.92–0.92)30.534.6 (0.36)11.913.4 (0.17)
A12Maple0.980.98 (0.98–0.98)49.555.4 (0.57)18.319.2 (0.31)0.910.91 (0.91–0.91)54.563.1 (0.64)41.741.2 (0.29)
C03Maple0.930.93 (0.92–0.93)19.219.5 (0.24)10.111.5 (0.09)0.910.90 (0.89–0.91)14.315.3 (0.22)10.111.2 (0.08)
C05Maple0.890.94 (0.94–0.94)52.750.4 (0.51)76.527.1 (0.64)0.950.95 (0.95–0.95)46.547.2 (0.49)31.047.2 (0.49)
C11Maple0.970.97 (0.97–0.97)37.543.4 (0.44)20.120.8 (0.19)0.930.93 (0.93–0.93)37.045.6 (0.46)18.117.8 (0.15)
E01Maple0.980.98 (0.98–0.98)40.042.7 (0.43)21.921.6 (0.11)0.930.93 (0.93–0.93)38.045.3 (0.45)15.315.7 (0.26)
E02Maple0.970.97 (0.97–0.97)38.039.4 (0.40)10.413.2 (0.20)0.890.88 (0.88–0.89)37.539.3 (0.40)10.213.5 (0.24)
E06Maple0.950.95 (0.94–0.95)68.571.1 (0.72)14.318.3 (0.30)0.920.92 (0.92–0.92)65.071.7 (0.72)55.953.8 (0.63)
E07Maple0.950.95 (0.95–0.95)25.528.7 (0.31)10.211.9 (0.11)0.940.94 (0.94–0.94)24.527.9 (0.30)10.111.7 (0.12)
G09Maple0.950.95 (0.95–0.95)50.054.2 (0.56)26.327.3 (0.30)0.930.93 (0.93–0.93)54.563.2 (0.64)47.147.9 (0.34)
I08Maple0.940.94 (0.94–0.94)35.046.3 (0.50)14.317.3 (0.34)0.890.89 (0.89–0.89)49.561.0 (0.63)52.752.9 (0.40)
J07Maple0.920.92 (0.92–0.92)52.752.2 (0.54)40.941.4 (0.27)0.900.90 (0.90–0.90)53.064.7 (0.65)46.947.8 (0.41)
J08Maple0.920.92 (0.92–0.92)79.091.5 (0.95)74.076.1 (0.47)0.920.91 (0.91–0.92)65.0126.8 (1.80)122.3125.9 (1.56)
J11Maple0.950.95 (0.95–0.95)33.035.9 (0.39)19.919.6 (0.29)0.800.80 (0.80–0.80)15.515.4 (0.17)28.228.8 (0.26)
J12Maple0.950.95 (0.95–0.95)35.539.8 (0.41)17.117.5 (0.23)0.850.85 (0.84–0.85)50.057.5 (0.58)10.214.1 (0.28)
K10Maple0.950.95 (0.95–0.95)32.537.2 (0.42)14.015.3 (0.36)0.930.93 (0.92–0.93)75.041.3 (0.48)10.012.4 (0.16)
L09Maple0.960.96 (0.96–0.96)29.536.2 (0.38)16.017.4 (0.08)0.950.95 (0.95–0.95)25.041.4 (0.44)16.116.9 (0.06)
L12Maple0.960.96 (0.96–0.96)60.074.2 (0.77)11.116.3 (0.34)0.930.93 (0.93–0.93)67.580.9 (0.83)53.054.0 (0.45)

[23] Simulations with TREES achieved varied results across the range of conditions and species (Table 2). In general the model performed better on cloudless days when EC-obs was high and limiting drivers exhibited consistent diurnal trends (Figure 2). Simulated transpiration showed highest agreement with observations from the maple site taken on sunny days, with IOA values between 0.92 and 0.98. At the aspen site values of IOA ranged from 0.58 to 0.92 for simulations parameterized against the cloudless data subset. On cloudy days when D and Q0 were low and exhibited more variability, there was less agreement between EC-sim and EC-obs. Values of IOA ranged from 0.80 to 0.95, and 0.67 to 0.93 for simulations parameterized against data from the cloudy subset for maple and aspen, respectively.

[24] Values of GSref derived from boundary line analyses were compared to the parameter m generated using TREES (Figure 4). Models showed good agreement with the expected 0.6 proportionality between m and GSref, with individuals at the maple site showing slightly more deviation during both cloudless and cloudy days. Comparison of GSref within species for cloudless and cloudy days revealed little variation (Figure 5). In light of this relative invariance in GSref between light conditions (cloudy or cloudless), subsequent analyses utilizing GSref were conducted utilizing both separately and with a combined cloudless and cloudy data set, and the combined analyses is presented in cases where cloudless and cloudy results are consistent.

Figure 4.

GSref plotted against m for aspen on (a) cloudless and (b) cloudy days, and maple on (c) cloudless and (d) cloudy days. Open circles represent acceptable models, and solid circles represent models with IOA < 0.80. The dashed line represents m = 0.6GSref after equation (2), and solid lines are linear regressions.

Figure 5.

GSref from cloudy days plotted against GSref from cloudless days for (a) aspen and (b) maple. Open circles represent acceptable models. Solid circles represent models with IOA < 0.80 for aspen (Figure 5a), and trees with less than 2 full days worth of data for maple (Figure 5b). Dashed lines denote a 1:1 relationship, and solid lines are linear regressions.

[25] Topoedaphic position, as indicated by surface soil moisture, appears to exert little or no influence on GSref for either site. At the maple site there was minimal variability in soil moisture and subsequently no relationship between GSref and soil moisture (r2 = 0.0, p > 0.05) (Figure 6). Despite a pronounced soil moisture gradient at the aspen site no relationship was observed between GSref and soil moisture (r2 = 0.0, p > 0.05) (Figure 6).

Figure 6.

GSref plotted against surface soil moisture for (a) aspen and (b) maple sites. Volumetric soil moisture measurements for each site were obtained for the top 6 cm of soil and are intended to be a proxy for topoedaphic positions rather than an indication of absolute available root zone soil moisture. Linear regressions are shown as solid lines.

[26] In order to test the hypothesis that competition for light contributes to variability in GSref we simulated the effects of reduced light using the model (Figure 7), and compared GSref to CI and its component variables. Inverse relationships were observed between GSref and CI for both aspen and maple under both light conditions. At the maple site a linear regression revealed a significant relationship between GSref and CI (r2 = 0.32, p < 0.001). At the aspen site a significant nonlinear relationship was found between GSref and CI (r2 = 0.36, p < 0.01) (Figure 8). Excluding cloudy data from this analysis improved the relationship with the same nonlinear model (r2 = 0.50, p < 0.01). To test the idea that the relationship between GSref and CI was indicative of competitive shading we selected two individuals from the aspen site with poor IOA values on cloudy days (A11, H6). A simple uniform reduction in radiation was achieved by reducing observed Q0 by 50%. We then used otherwise identical methodology to generate a new set of 10,000 simulations for each tree. In both cases IOA for the best model increased substantially, yielding fits acceptable for analysis (IOA > 0.80) (Figure 7).

Figure 7.

Plots of EC for aspen trees (a) H6 and (b) A11. Simulations generated using full Q0 and Q0 reduced by 50% are compared to observations. These trees were selected for reanalysis based on their originally low values of IOA, in order to test the hypothesis that competition for light affects GSref and that not accounting for competitive shading may be a cause for poor model performance.

Figure 8.

GSref plotted against (a and b) AS, (c and d) HT, and (e and f) CI for aspen and maple, respectively. Lines represent regressions, and r2 values are shown. Significant relationships were observed between GSref and AS (r2 = 0.58, p < 0.01) for aspen, and GSref and CI for both aspen and maple (r2 = 0.36, p < 0.1, and r2 = 0.31, p < 0.01), respectively.

[27] A weak positive correlation was observed between GSref and AS at both sites for cloudless and cloudy days combined, this correlation was statistically significant at the aspen site (r2 = 0.58, p < 0.001) but not at the maple site (r2 = 0.06, p > 0.05) (Figure 8). Similarly, weak nonsignificant (r2 = 0.12, r2 = 0.0, p > 0.05) correlations between GSref and HT were observed for both aspen and maple sites, respectively. Additional analyses were conducted with each individual distance, direction, and height component of CI (p > 0.05). Excluding each component of CI for maple similarly degraded the relationship between it and GSref, suggesting an equal contribution to CI. For aspen the direction of competitors appeared to have little or no influence on GSref, and excluding it from CI had negligible impacts on the relationship between GSref and CI. A stepwise regression was conducted between GSref and CI, AS, HT, and soil moisture, and no significant correlation between variables was revealed (p > 0.05).

4. Discussion

[28] Our results show within species variability in GSref for aspen and maple, and this finding supports the first hypothesis that GSref is heterogeneous at the stand scale. For both species we observed a linear relationship between GSref and m, a finding that supports our second hypothesis. This result is not particularly unexpected, but there have been few studies with adequate data to address questions regarding intraspecies variability in GSref and so it has not been explicitly tested. The relationship between GSref and CI supports our third hypothesis that competition for light contributes to variability in GSref.

4.1. Model Evaluation

[29] Simulated transpiration showed good overall agreement with our observations, and there are several points to be considered when evaluating model performance and results. Ecosystem models such as TREES are typically parameterized and evaluated with stand-scale flux observations utilizing either aggregated sap flux or tower based eddy covariance data [Kuchment and Demidov, 2006; Raulier et al., 2002; Stoy et al., 2006; Wang et al., 2007]. In this context, aggregated flux estimates benefit from data smoothing, and subsequently a relatively high degree of agreement between simulations and observations can often be achieved. On the other hand, the relatively low signal-to-noise ratio of sap flux observations [Oren et al., 1998] for individual stems can make parameterization more difficult.

[30] Diurnal plots of sap flux data for individual aspen stems generally exhibit a relatively high degree of microscale temporal variability (i.e., lack of smoothing), particularly in comparison to maple (i.e., Figures 2a and 2c versus Figures 2d and 2f). So, while simulated transpiration values for both species may accurately capture the diel response of whole plant water use to D, variability at small timescales for aspen, typically during midday, result in lower IOA between simulated and observed values (Table 2). A likely explanation is that aspen sap flux exhibits a much more dynamic response to environmental drivers because of its relatively small size and high water use [Ewers et al., 2002, 2005, 2007a]. Ewers and Oren [2000] report increased variability between consecutive measurements with a decrease in storage capacity. More recently, Burgess and Dawson [2008] have cautioned against using continuous heat sensors for inferring capacitance because of lags associated with heat buildup in the xylem tissue surrounding the sensors. In contrast Ewers et al. [2007b] observed no lags between water fluxes measured in stems using continuous heat sensors (Granier) and branch fluxes measured using compensating heat sensors (Kucera), and similar results are described in a recent review by Phillips et al. [2009]. Both of these studies report higher fluxes in illuminated branches than shaded ones. Thus it is reasonable to expect more variability at half-hourly time steps for aspen because they have smaller stems.

4.2. Non-Light-Limiting Effects

[31] No significant relationship between GSref and soil moisture was observed at either site, and this is consistent with findings from other studies in the region [Ewers et al., 2002, 2007a, 2008; Samanta et al., 2008]. At a variety of scales an inverse relationship has been observed between soil water potential and GS (and subsequently JS, and EC-obs) [Aranda et al., 2005; Cochard et al., 2002], and so an increase in GSref with soil moisture could be expected. At the aspen site water table height, observed using a pair of soil water wells in the wetland portion of the site, was never further than 1 m from the soil surface (data not shown). This suggests an absence of drought stress [Mackay et al., 2003], less heterogeneity in soil moisture with depth, and unlikely occurrence of upland drought stress. Alternatively, near saturated soils in the wetland portion of the site may have been detrimental to aspen, an assertion supported by their relative lack of abundance and small size there [Traver et al., 2010]. A concurrent study by Traver et al. [2010] found no significant correlations between soil texture, moisture, bulk density, nitrogen content, or C:N and within species JS, EC-obs, or EL at either site.

[32] Numerous studies have explored relationships between stomatal conductance and biometric variables related to tree size and age such as AS [Moore et al., 2004], HT [Franks, 2004; Novick et al., 2009; Schafer et al., 2000; Woodruff et al., 2007], and AS:AL [McDowell et al., 2002]. Increases in AS and height with age are typically accompanied by an increase in AS:AL and subsequently whole canopy stomatal conductance. This can be attributed to increases in resistance along the hydraulic pathway from the soil to the atmosphere. This type of hydraulic limitation typically occurs in trees much taller than the ones at our sites. An inverse relationship between HT and GSref has been observed [Novick et al., 2009; Schafer et al., 2000]; however, the range of HT in our study was small relative to the range of GSref values. Additionally, HT was used as a proxy for emergence. Absence of a strong relationship between GSref, and AS, or HT suggests additional information regarding ecosystem structure is necessary to elucidate apparent differences in GSref between individuals for the species in question, although the use of allometry to obtain HT for maple may introduce variability (i.e., Figures 8d and 8f).

[33] Correlation between GSref and CI (Figure 8) implicates stand structure as a factor that contributes to variation in hydraulic regulation between individuals. One possibility is that stem density serves as a proxy for water and nutrient demand in the soil. Increased root density could place greater demand on the supply of available water and nutrients. Lower ψS as a consequence of increased demand would lower stomatal conductance (equation (1)). Reduced N availability may potentially lower photosynthetic capacity and GS in turn. However, no relationship was found between GSref and stem density alone (data not shown).

4.3. Light-Limiting Effects

[34] We suggest competition for light between canopies as an explanation for variable GSref. A known relationship exists between solar irradiance and photosynthetic rates [Walcroft et al., 2002], and increased transpiration has also been observed in illuminated branches [Burgess and Dawson, 2008; Ewers et al., 2007b]. Functional differences between sunlit and shaded leaves, typically found in the upper and lower portion of canopies, respectively, have also been observed [Naidu and Delucia, 1997]. The light environment in which leaf development occurs has been shown to affect leaf photosynthetic capacity, i.e., individuals that develop in shade have lower capacity for photosynthesis [Lei and Lechowicz, 1997; Niinemets et al., 2004]. Although observation have been observed in seedlings and saplings, similar affects manifested in biomass allocation (leaf mass per unit area) have been observed in mature trees [Jones and Thomas, 2007]. As such a reasonable hypothesis is that trees at a competitive disadvantage to their neighbors with respect to canopy light environment may have a higher proportion of shaded leaves and subsequently light-limited photosynthesis that would in turn limit stomatal conductance. For these trees it would not be beneficial to have high GS during periods of low D and Q0 (i.e., high GSref) because water loss would be disproportionately large in comparison to carbon gain due to light limitation. Conversely for emergent trees with little competition and relatively little light limitation a more economical approach would be to maximize productivity with readily available light before hydraulic limitation forces stomatal closure.

[35] Our finding that a simple light reduction improves IOA for two aspen individuals (Figure 7) supports the assertion that competition for light may explain variability in GSref. This light reduction was intended to represent a shift of the crown from an emergent position in the canopy to a “submergent” one. As such a decrease in incident radiation without concurrent changes in other microclimate variables can be assumed. It has been shown that changes in soil temperature and moisture across understory light gradients are negligible [Porté et al., 2004] and even in canopy gaps understory vegetation has been shown to exert more control on such variables than overstory absence [Clinton, 2003]. Additionally previous studies in this region have shown D to be well mixed throughout canopies over a range of conditions [Ewers et al., 2007a, 2008]. This information in combination with prior findings that exhibit the lack of a clear relationship between GSref and other edaphic variables that related to competition in general indicate that CI is a suitable proxy for competition for light despite a lack of explicit light measurements.

[36] Simulations for certain individuals at the aspen site may be interpreted in the context of light limited stomatal conductance. The model was achieved good agreement with data from aspen trees E7 and D7, two individuals with very low values of CI values of 0.41 and 0.21, respectively. Effectively these trees were in the open, as they grew on the north edge of a large gap, created by a series of blow-downs preceding the study period. Subsequently these trees also have among the highest GSref values at the site (Figure 8). One possible explanation is that individuals such as these with minimal light limitation exhibit higher GSref in order to maximize carbon gain before the onset of hydraulic limitation by D, whereas trees subject to competitive shading would be light limited and therefore not benefit from high GSref. For reference tree E7 is located at (41°E, 50°N) in Figure 1a, and transpiration data are shown in Figures 2a and 2c.

[37] TREES accounts for self-shading within a bulk canopy and so it is likely that inaccuracies exist in estimates the proportions of absorbed direct and diffuse radiation that are manifested in GSref estimates. For bulk canopies this may be appropriate, but when applied to a single crown this means that sunlit and shaded canopy elements are derived as a function of light attenuation through the crown itself with no consideration for the effects of horizontal or vertical heterogeneity (i.e., neighboring trees). As a result it is probable that the model does not capture spatial variability in light limited photosynthesis as a consequence of canopy structural heterogeneity. In cases where photosynthesis is light-limited and stomatal conductance is affected overall model performance would be improved, as evidenced in Figure 7. Our results suggest most trees receive sufficient radiation for maximum photosynthesis on cloudless days, and that only trees with high CI are light limited on cloudy days (as evidenced, for example, by decreased IOA on cloudy days at the aspen site). This indicates that trees overestimates incident radiation for cloudy days. Incorporating spatial variability in incident radiation into TREES through three-dimensional radiative transfer modeling may offer a clearer mechanistic explanation [Chen et al., 2008; Courbaud, 2003; Lappi and Stenberg, 1998; Larocque, 2002].

5. Conclusions

[38] We have employed a simple ecosystem model that utilizes hydraulic and photosynthetic constraints to illustrate that stomatal conductance exhibits within species variability across two forested stands in northern Wisconsin. Individuals for both species remained isohydric, exhibiting a linear relationship between reference stomatal conductance and sensitivity to atmospheric vapor pressure deficit, and these results were consistent with cloudless and cloudy days for both sites. Analysis of a series of environmental and biological factors indicates that a competition index, designed to characterize competition for light as a results of canopy structural heterogeneity, is most strongly related to spatial variability in stomatal conductance for both sites. On cloudy days at the aspen site the model generally over predicted transpiration resulting in poor agreement between simulated and observed data. Two trees with relatively low CI values are of notable exception. It is suggested that variability in photosynthetic light limitation as a result of competitive shading offers a mechanistic explanation for this finding. Furthermore absence of clear physiological differences between sunlit and shaded leaves within species indicates a dynamic stomatal response to light environment rather than long-term physiological acclimation.

[39] Our results suggest that forest stand structure should be considered when generating estimates of stomatal conductance for use in hydrologic models, particularly where structural heterogeneity is high. With regards to stand and regional scale estimates of water fluxes these results are in line with results of previous studies from these sites in that they highlight the need for thoughtful plot location of point measurements, but do not negate the current point-to-area scaling method. Additionally the apparent link between stomatal conductance and ecosystem structure suggests that high-resolution remote sensing can be utilized to identify areas with high variability in ecosystem fluxes where representative sampling is imperative for accurate upscaling. Future research should seek to further elucidate the effects of variable incident radiation on stomatal control of transpiration in order to better understand temporal changes in spatial variability that occur on diurnal timescales.

Appendix A

A1. Model Description

[40] TREES was initialized with an approximation of stomatal conductance (GS0) (mmol m−2 s−1) limited by hydraulics using equation (2) where parameter values of reference stomatal conductance (GSref0) and m were sampled at random. For each canopy element (k) leaf specific CO2 conductances (gc0,k) were calculated using the following equation:

equation image

where Lk is element leaf area index (m2 m−2), gva is aerodynamic conductance which is a function of turbulent and laminar heat and vapor conductance (mmol m−2 s−1), and 1.6 is the proportionality between molar H2O and molar CO2. These values of hydraulically constrained stomatal conductance to CO2 were subsequently used to calculate photosynthesis using a hybridization of models described by Katul et al. [2000, 2003], and de Pury and Farquhar [1997], that allows for electron transport (light) limited and Rubisco (nitrogen) limited photosynthesis. The results of this model were used to calculate stomatal conductance to H2O for each canopy element (gv,k):

equation image

where An is net photosynthesis (μmol m−2 s−1), ca is atmospheric CO2 concentration (Pa), and ci is intercellular CO2 concentration (Pa). This relationship assumes atmospheric CO2 and leaf surface CO2 concentrations to be equivalent. At this point canopy element transpiration was calculated using the Penman-Monteith Combination Equation [Monteith, 1965]:

equation image

where λ is the latent heat of vaporization (J kg−1), s is the slope of the saturation vapor pressure temperature curve (mbar °C−1), Rn is net radiation (W m−2), γ* is the modified apparent psychrometric constant (mbar °C−1), and pa is the density of air (kg m−3). Values of transpiration for each canopy element are then summed to yield total canopy transpiration.

[41] As previously mentioned the above calculations are conducted in parallel for sunlit and shaded canopy elements. Sunlit leaf area of the canopy (L*), as described by Campbell and Norman [1998], is defined as:

equation image

where L is leaf area index (m2 m−2), and Kbe(Ψ) is the extinction coefficient for light in the canopy at zenith angle Ψ, based upon an ellipsoidal leaf angle distribution. The shaded portion of the canopy is then calculated by subtracting L* from L. Kbe(Ψ) is calculated as follows:

equation image

where x is the leaf angle distribution, and Ω(ψ) is a canopy clumping parameter ranging from 0 to 1 that varies with zenith angle according to the following equation:

equation image

where Ω is the clumping parameter when the canopy is viewed from nadir, and p is a variable related to the ratio of crown height to crown diameter. Typically x, Ω, and p are species-specific model input parameters derived from literature values [Campbell and Norman, 1998]. Incident radiation is partitioned into direct and diffuse components according to Spitters et al. [1986].

A2. Model Parameterization

[42] To assure adequate parameterization with respect to GSref0, we ran a preliminary set of 10,000 simulations for each tree under cloudless conditions. Parameter values for GSref0 and m were allowed to vary over a range that was based on previous measurements of these species near the current stands [Ewers et al., 2007a]. The preliminary analysis evaluated simulated GS against empirically derived values of GS during hours of peak EC (approximately 1000–1600 local standard time), when stomatal limitation was apparent. We calculated GS using the following empirical equation derived by inverting the Penman-Monteith equation [Monteith and Unsworth, 1990] and assuming high canopy coupling:

equation image

where KG [Phillips and Oren, 1998] is the conductance coefficient (115.8 + 0.4236T) that accounts for the latent heat of vaporization, temperature effects on the psychrometric constant, the density of air, and the specific heat of air at constant pressure (kPa m3 kg−1), and EL is transpiration per unit leaf area (m s−1). Following the method of Samanta and Mackay [2003] each of the 10,000 models from a set of simulations was assigned a membership grade based on a series of goodness-of-fit measures, and a subset of acceptable models was treated as a fuzzy set with inherent uncertainty [Ewers et al., 2008; Mackay et al., 2003]. An alpha cut is assigned and used to determine the cardinality of the subset of acceptable models and this in turn is used to determine the cardinality for a crisp set. From this crisp set the range of parameter values for the GSref0 and m was then used to constrain the range of parameters for the second set of simulations. Using the constrained ranges of possible parameter values a further 10,000 simulations were generated for each tree, under both cloudless and cloudy conditions. For this second set of simulations the models were evaluated against values of EC-obs over entire days.

[43] As described above, parameter values for GSref0 are initial estimates that may be further constrained by photosynthesis. Therefore we plotted simulated values of stomatal conductance (GS) against D and fit a boundary line to the upper envelope of the curve by using the parameter m from the best model with equation (2), and adjusting GSref until the line passed through the upper envelope of the cloud of points (Figure 3). GS was calculated as:

equation image

where gvsun and gvshd are stomatal conductance for sunlit and shaded canopy elements, respectively (equation (A2)) (mmol m−2 s−1), gva is bulk aerodynamic conductance (mmol m−2 s−1), and L is leaf area index. Lsun and Lshd are sunlit and shaded leaf area index (m2 m−2). This process was performed for the top simulation for each tree under both cloudless and cloudy conditions, and the resulting values of GSref and m were used for analysis. Using simulated values of GS to calculate GSref is beneficial because it removes the effects of gva, which is not the case for empirical approaches.

Acknowledgments

[44] Funding for this study was from the National Science Foundation, Hydrologic Sciences Program (EAR-0405306 to D.S.M., EAR-0405381 to B.E.E., and EAR-0405318 to E.L.K.). In addition, M.M.L. was supported by the NSF IGERT program. The statements made in this manuscript reflect the views of the authors and do not necessary reflect the views of NSF. We are also grateful to personnel at Kemp Natural Resources Station, and to Dave Roberts for their assistance with field work. We wish to thank three anonymous reviewers whose comments helped improve earlier drafts of the manuscript.