The implications of minimum stomatal conductance on modeling water flux in forest canopies


Corresponding author: D. M. Barnard, Department of Horticulture and Landscape Architecture, Colorado State University, 1173 Campus Delivery, 111 Shepardson Building, Fort Collins, CO 80523, USA. (


[1] Stomatal conductance (gs) models are widely used at a variety of scales to predict fluxes of mass and energy between vegetation and the atmosphere. Several gs models contain a parameter that specifies the minimum gs estimate (g0). Sensitivity analyses with a canopy flux model (MAESTRA) identified g0 to have the greatest influence on transpiration estimates (seasonal mean of 40%). A spatial analysis revealed the influence of g0 to vary (30–80%) with the amount of light absorbed by the foliage and to increase in importance as absorbed light decreased. The parameter g0 is typically estimated by extrapolating the linear regression fit between observed gs and net photosynthesis (An). However, our measurements demonstrate that the gs-An relationship may become nonlinear at low light levels and thus, extrapolating values from data collected over a range of light conditions resulted in an underestimation of g0 in Malus domestica when compared to measured values (20.4 vs 49.7 mmol m−2 s−1 respectively). In addition, extrapolation resulted in negative g0 values for three other woody species. We assert that g0 can be measured directly with diffusion porometers (as gs when An ≤ 0), reducing both the time required to characterize g0 and the potential error from statistical approximation. Incorporating measured g0 into MAESTRA significantly improved transpiration predictions versus extrapolated values (6% overestimation versus 45% underestimation respectively), demonstrating the benefit in gs models. Diffusion porometer measurements offer a viable means to quantify the g0 parameter, circumventing errors associated with linear extrapolation of the gs-An relationship.

1 Introduction

[2] Leaf stomatal conductance (gs) changes in response to physiological signals and environmental conditions to balance carbon assimilation with water loss [e.g., Wong et al., 1979]. Hence, the ability to accurately predict the gs response to changes in environmental conditions is central to estimating carbon and water flux at multiple scales. Damour et al. [2010] recently compared 35 gs models that ranged from phenomenological to semimechanistic. Of the 35 models, the Ball, Woodrow, and Berry [1987] model (BWB), later modified by Leuning [1995] (BBL), has been subjected to decades of testing and validation [e.g., Ball et al., 1987; Leuning, 1990; 1995; Nijs et al., 1997; Medlyn et al., 2001; Katul et al., 2010; Way et al., 2011]. Relative to other gs models, the BWB is easier to apply and requires only four input parameters. The ease of parameterization and predictive accuracy under variable environments make the BWB gs model commonly used at a variety of scales [e.g., Baldocchi and Meyers, 1998; Cox et al., 1998; Battaglia et al., 2004; Hanson et al., 2004; Sato et al., 2007; Friend et al., 2009; Damour et al., 2010; Landsberg and Sands, 2010], including large-scale land surface schemes [e.g., Sellers et al., 1996; Oleson et al., 2010].

[3] The BWB, and more recent BBL model, have semimechanistic predictive capabilities that scale gs linearly with foliage net photosynthesis (An) in lieu of a direct response of the stomata to absorbed solar radiation at the leaf-level (PARL) [Zeiger, 1983; Pieruschka et al., 2010]. For this study, we opted to use the BBL model because it has been shown to be more effective at closing the carbon budget when compared to the BWB [Way et al., 2011]. The Leuning [1995] modification to the BWB model substituted vapor pressure deficit (VPD) for humidity, accounting for air temperature, and added the CO2 compensation point (Γ), to estimate gs as:

display math(1)

where cs and Ds are [CO2] and VPD at the leaf surface respectively, D0 and g1 are empirical coefficients and g0 characterizes the basal gs prediction. It is common to see g0 defined in one of two ways: (1) as a “fit” parameter—an extrapolated intercept from the least squares regression between gs and model parameters [e.g., Ball et al., 1987; Ball, 1988; Collatz et al., 1991; Medlyn et al., 2011; Way et al., 2011] or (2) as the value of gs when An ≤ 0 [e.g., Leuning, 1990; 1995; Dewar, 2002; Lombardozzi et al., 2012]. Although these two definitions are similar, it is the second description that links a physiological significance to g0 and implies that the parameter can be measured directly. Curiously, even the studies that define g0 by the second definition have estimated the parameter value from the relationship between gs and model parameters. Because model parameters vary among formulations [Ball et al., 1987; Leuning, 1995; Medlyn et al., 2011] and become irrelevant when An ≤ 0, we use the term gs-An as a surrogate for the relationship between gs and model parameters. Nevertheless, no study that we are aware of has compared observed and extrapolated values of g0 when parameterizing the BWB or BBL models or the effect of the two different parameterization methods on the accuracy of model estimates.

[4] Several potential sources of error can underlie statistical estimations of g0. First, data for the gs-An regression are often collected mostly under well-lit conditions with a well-stirred cuvette that disrupts boundary layer conditions [Ball, 1988; Leuning, 1990; Collatz et al., 1991; Leuning, 1995; Dewar, 2002; Medlyn et al., 2011; Way et al., 2011]. Second, in the original BWB description, Ball [1988] acknowledged that the gs-An relationship, in low light, may deviate from the linear relationship. Despite this observation, Ball used an extrapolated g0 that was “not statistically different from zero” for parameterizing the C3 species Glycine max, while noting higher observed values. Likewise, Collatz et al. [1992] reported that observed g0 was greater than extrapolated values in the C4 species Zea mays. Third, it is common to see extrapolated values of g0 that are not biophysically possible (i.e. negative values) [Ball and Farquhar, 1984; Schulze et al., 1987; Shimono et al., 2010; Medlyn et al., 2011]. Fourth, when the same data set is used to parameterize different gs models (e.g., the BWB versus the BLB), the resulting extrapolated values of g0 can differ significantly [Way et al., 2011]. Last, least squares estimates can be greatly influenced by the quantity and/or quality of data points used to perform the regression. This can be particularly vexing in studies of the gs-An relationship as data collection can be time consuming due to the stomatal equilibration period (up to 15 min per data point [Franks and Farquhar, 1998; Woods and Turner, 2006]), and the need for multiple data points to extrapolate a single g0 estimate with acceptable error.

[5] A growing consensus in the literature acknowledges nighttime gs across species [e.g., Donovan et al., 2003; Barbour and Buckley, 2007; Howard and Donovan, 2007; Seibt et al., 2007; Christman et al., 2008] and plant functional types (PFTs) [reviewed in Caird et al., 2007], whereas a consistent g0 response to water stress has been lacking. The use of observed nighttime gs for g0 parameterization in gs models has not yet been recognized and may represent a significant disconnect between plant physiology studies and ecological modeling efforts. Currently, when not extrapolated from gs-An data, g0 values in gs models are assumed to be constant and/or unrealistically low [e.g., Sellers et al., 1996; Wang and Leuning, 1998; Tuzet et al., 2003; Oleson et al., 2010; Ono et al., 2013]. The relative ease of measuring gs under dark conditions (i.e., when An ≤ 0) with a diffusion porometer may improve on g0 estimates, warranting a reexamination of how g0 is characterized, how g0 may respond to seasonal drought episodes, and the extent to which observations of g0 affect whole canopy transpiration estimates.

[6] In this study, we set out to characterize g0 at the leaf-level, using nighttime in situ observations, in response to season and water stress. We hypothesized that the g0 parameter could be measured and used to improve predictions of canopy transpiration in deciduous species. We scaled up observed g0 values from the leaf to the canopy with MAESTRA, a three-dimensional process-based canopy transpiration model that can successfully predict forest canopy transpiration [Bauerle et al., 2004a; Hanson et al., 2004; Medlyn et al., 2007; Bowden and Bauerle, 2008]. We used MAESTRA, validated on a species-specific basis, as a tool to spatially investigate how g0 influences canopy transpiration estimates and responds to changes in the environment.

2 Materials and Methods

2.1 Site Characteristics and Plant Material

[7] The main design of this study included two separate research sites (Table 1). One, located in Avon, OH, was utilized to parameterize and validate MAESTRA and the other, located in Fort Collins, CO, was constructed to monitor the drought and seasonal response of g0 (growing season was day of year 167-271). A third, supplemental glass house study, took place in Fort Collins, CO (see description below). A full description of the site design for the OH site can be found in Zhu et al. [2005]. Briefly, the OH site was subdivided into six plots, each containing 25 subsurface 57 L socket containers (a pot-in-pot production system). Five sockets comprised each row (five rows per plot), connected in series via PVC to channel container leachate into a tipping bucket (FC525, Texas Electronics Inc., Dallas, TX, USA). Tipping bucket tips were continuously counted and recorded at 1 min intervals (model CR23X, Campbell Scientific, Logan UT, USA). Additionally, one socket per row was equipped with a Theta Probe substrate moisture sensor (model ML2x, Dynamax Inc. Houston, TX, USA) to determine bulk container substrate electric permittivity (ɛa). A two-point calibration, specific to the substrate used in this study, was completed to allow for ±1% volumetric water content (VWC) measurement accuracy. Environmental variables (temperature, wind speed, relative humidity, precipitation, and incident photosynthetically active radiation (PARI)) were measured every minute and averages stored at 5 min intervals (model EM50R, Decagon Devices Inc., Pullman, WA, USA).

Table 1. Locations and Climate Characteristics of the Avon, OH, and Fort Collins, CO Research Sites
 Avon, OHFort Collins, CO
Latitude/Longitude41.433, −82.05240.613, −104.998
Mean annual maximum temperature (°C)27.016.8
Mean annual minimum temperature (°C)−5.71.1
Mean annual precipitation (mm)1056383
Mean annual wind speed (m s−1)1.53.2

[8] In the OH study, we used four tree species with broad ecological and commercial significance (Acer rubrum L. “Red Sunset,” Betula nigra “Cully,” Carpinus betula “Columnaris,” and Cercis canadensis) in 57 L containers. One year old whips were potted into a soil-less organic substrate consisting of a mixture of 64% pine bark, 21% peat moss, 7% Haydite, and 7% sterilized regrind. The remaining 1% was slow release fertilizer 12-0-42 (Agrozz Inc., Wooster, OH, USA). For irrigation, each container had two 180° spray stakes (PC Spray Stake, Netafim Inc., USA, Fresno, CA, USA) operating at a flow rate of 12 L h−1. Substrate moisture status was continually monitored and kept within a VWC range of 35–42% (VWC > 43% was predetermined to exceed the maximum container substrate water holding capacity).

[9] The CO site consisted of eight rows of five replicates each in a pot-in-pot system. The same plant material was studied at the CO and OH site, except Quercus rubra replaced Acer rubrum L. “Red Sunset” at the CO site to broaden the among-species range in growth rates and physiological properties. All else being equal, the CO trees were 1 year older than those in OH and were top-dressed with time release fertilizer (18-5-9, Osmocote Classic; The Scotts Co., Marysville, OH, USA) at the beginning of the season. For the CO water stress study, five replicates each per species were assigned randomly to either well-watered or water-stressed treatments and each treatment was randomly assigned to a uniformly irrigated row. Replicate trees assigned to the well-watered treatment were irrigated to maintain a VWC between the ranges of 35 and 42%—checked weekly with a hand-held Theta Probe. Water deficit irrigation amounts were calculated as a percentage of the well-watered treatment and consisted of the following irrigation amounts held for 10–14 days each: 100%, 80%, 60%, 40%, 20%, and 0%. This irrigation schedule included occasional returns to well-watered status (100%) in an effort to characterize the underlying effect that water deficits may have on g0.

2.2 Measurements of g0 and gs

[10] All gs and g0 measurements were collected with hand-held steady-state diffusion porometers (SC-1, Decagon Devices Inc., Pullman, WA, USA) on three randomly selected trees per treatment per species. The parameter g0 in the BBL gs models is defined by Leuning [1995] to be gs as An → 0 as PARL → 0. Using this definition as justification, we sought to investigate the influence of observed g0 (gs measured under dark conditions—1 h after nightfall) on model output as opposed to statistically derived estimates. Midday gs measurements were collected on the same leaves as g0 near solar noon on concurrent cloudless days. Both midday gs and g0 measurements at the CO site were collected 10 times over the course of the season (day of year 167-271) from two leaves per tree and averaged. All leaves sampled were fully expanded and from south facing sun-exposed branches. At the OH site, g0 was measured similar to the trees in CO (three times during the season—day of year 155, 208, and 235).

2.3 Model Parameterization

[11] A full description of MAESTRA is beyond the scope of this paper; however, significant background information, as well as equations, may be found in Bowden and Bauerle [2008] and Bauerle and Bowden [2011], with a full description of the leaf to crown transpiration linkage given in Medlyn et al. [2007]. Briefly, MAESTRA is a hierarchical and iterative computational framework that spatially integrates estimates of leaf energy balance, photosynthesis, and gs by computing grid-point-specific fluxes of mass and energy throughout the entire crown. For gs specifically, photosynthesis estimates (derived from the Farquhar photosynthesis model) are combined with meteorological variables and static leaf-level estimates of g0, g1, Γ, and D0 to calculate a gs prediction via the BBL gs model. The gs prediction is then combined with meteorological variables in an isothermal form of the Penman-Monteith equation to compute latent heat exchange and a transpiration estimate. Because latent heat loss alters the leaf energy balance, initial energy balance estimates are then adjusted and the process is repeated iteratively until estimates reach convergence. This approach has been successfully implemented to predict transpiration fluxes in various models [e.g., Meyers and Paw U, 1987; Collatz et al., 1991; Baldocchi et al., 2002; Medlyn et al., 2007; Staudt et al., 2010].

[12] Leaf-level physiological input parameters were determined primarily by the use of gas exchange analysis with a CIRAS-2 portable photosynthesis system (PP Systems International Inc., Amesbury, MA, USA). Bauerle and Bowden [2011] reported six parameters of high importance (>5% impact) when estimating transpiration. Therefore, a strong emphasis was placed on the careful acquisition of these parameter values (Table 2). Five of the parameters (maximum rate of carboxylation (Vcmax), maximum rate of electron transport (Jmax), dark respiration (Rd), quantum yield (α), and genotype stomatal response coefficient (g1)) are determined through the analysis of photosynthesis versus CO2 and light response curves constructed with the CIRAS-2. A sixth parameter, leaf width (Lw), was measured every other week throughout the growing season. The D0 parameter was assumed to be 1500 Pa [Leuning, 1995; Bauerle and Bowden, 2011]. Canopy and tree physical characteristics (canopy width in the x and y axes, canopy and stem height and stem caliper) were collected at the same time. We measured canopy leaf area (on alternating weeks) throughout the growing season by counting the total number of leaves in individual crowns and multiplying by the average area per leaf—determined by image analysis (Image-J, NIH, Washington, D.C., USA) on 20 randomly selected leaves from three separate randomly selected trees per treatment. We determined genotype specific leaf transmittance, absorptance, and reflectance with a SPAD meter (SPAD-502, Konica Minolta Global, Ramsey, NJ, USA) on the same leaves measured for gas exchange, following the procedure in Bauerle et al. [2004b].

Table 2. Species-Specific Input Parameters Used in MAESTRA. Observed Minimum Stomatal Conductance (g0-obs), Minimum Stomatal Conductance Extrapolated From a Least Squares Fit of the Linear net Photosynthesis and Stomatal Conductance Relationship (g0-ext), Species Stomatal Response Coefficient (g1), maximum rate of carboxylation (Vcmax), Maximum Electron Transport Rate (Jmax), Leaf Dark Respiration (Rd), Quantum Yield of Electron Transport (α), CO2 Compensation Point (Γ), and Leaf Width (Lw)
 UnitsAcer rubrumBetula nigraCarpinus betulaCercis canadensisMalus domestica
g0-obs(mmol m−2 s−1)42.57 ± 22.151.24 ± 14.461.78 ± 32.126.58 ± 12.549.69 ± 3.1
g0-ext(mmol m−2 s−1)15.2 ± 18.2−14.4 ± 40.5−29.6 ± 8.2−29.6 ± 19.320.4 ± 10.2
g1(dimensionless)7.72 ± 3.78.13 ± 3.739.53 ± 2.618.16 ± 3.559.99 ± 0.59
Vcmax(µmol m−2 s−1)45.55 ± 11.756.05 ± 12.943.87 ± 7.243.58 ± 6.922.68 ± 4.1
Jmax(µmol m−2 s−1)131.7 ± 46.6164.3 ± 50.1157.7 ± 65.4120.3 ± 15.981.6 ± 22.8
Rd(µmol m−2 s−1)1.76 ± 0.91.80 ± 0.61.71 ± 0.82.56 ± 1.21.35 ± 0.15
α(mol e mol−1 PAR)0.143 ± 0.060.124 ± 0.020.116 ± 0.030.139 ± 0.040.213 ± 0.07
Γ(ppm)73.3 ± 45.759.8 ± 37.254.1 ± 30.435.9 ± 28.26.78 ± 0.29
Lw(cm)11.4 ± 0.56.4 ± 2.33.8 ± 0.311.3 ± 1.94.7 ± 0.8

2.4 Model Validation

[13] We ran MAESTRA for weather data collected at 1 min intervals and recorded on a 5 min time step from the OH site to compute species-specific water use estimates over the season. To calculate measured water use, we subtracted daily leachate volume from the volume of water applied per treatment (irrigation + precipitation − leachate). We then compared weekly simulated and measured water use averages.

2.5 Simulation Experiments

[14] Once validated, we simulated stands that were parameterized with physiology from leaf-level gas exchange (as described above) for Acer rubrum (Table 2). Representative forest stands consisted of 5 m stem spacing, 7.5 m live crown length plus 2.5 m of stem height, and a 5 m crown width shaped as a half-ellipsoid. Simulations aimed to investigate the impact of g0 on transpiration estimates of an individual canopy within a forest. To investigate gradients in the parameter effect of g0 on transpiration along a canopy depth profile, the canopy was separated into a three-dimensional grid of 36 cells with equal volumes, for which point estimates of An, gs, and transpiration were calculated. Whole canopy estimates were calculated as the sum of point estimates from the 36 subvolumes. To determine the g0 parameter effect on transpiration estimates, we held all other input parameters constant and varied the g0 parameter input from the measured mean value (42.57 mmol m−2 s−1) ± one standard deviation (20.47–64.67 mmol m−2 s−1). The parameter effect was then calculated as the absolute value of the difference between transpiration output from MAESTRA parameterized with the upper and lower standard deviations normalized by output from the mean value and then multiplied by 100.

[15] To simplify the BBL model for the purposes of this study and convey the influence of each portion separately, we condensed the dynamic portion of the model (to the right of the addition sign that encompasses the gs-An linkage) with a single term (βgs) expressed as:

display math(2)

[16] This allows the BBL model to be separated into two constituent parts as:

display math(3)

where Σgs represents the total gs prediction. Equation (2) illustrates that the βgs component in the simplified version (equation (3)) of the BBL model is coupled to An—derived from the mechanistic Farquhar photosynthesis model [Farquhar et al., 1980].

2.6 Comparison of Observed and Extrapolated g0 Values

[17] To illustrate the difference in transpiration estimates between observed g0 and those derived by statistical estimation with the least squares fit to the gs-An relationship, we acclimated 1 year old Malus domestica (n = 4) trees planted in 38 L containers with a commercial potting mix in a climate controlled glass house for 7 days. Once acclimated, we collected data to parameterize MAESTRA (see description above). To characterize the gs-An relationship in well-lit conditions, we collected measurements at PARL levels ranging from 200 to 1000 µmol m−2 s−1. Preliminary tests indicated that stomatal equilibration took a maximum of 11 min at each light level; thus, we allowed 12 min for gs acclimation at each step. Stabilized readings were taken at 13, 14, and 15 min and averaged. To illustrate the fine-scale departure from linearity in the gs-An relationship under low-light conditions, we observed gs and An at PARL levels of 0, 25, 50, 75, and 100 following the same stomata acclimation procedure outlined above. Both the high- and low-light measurements were completed in sequence on the same leaf to produce one single gs-An relationship per replicate. The individual replicates were then pooled to derive an estimate of g0. Estimates were determined as the x-y intercept of a linear regression between observed gs and BBL model input parameters calculated as:

display math(4)

[18] Together with gs-An characterization, each container was irrigated daily to container capacity, wrapped in plastic (to eliminate water loss to evaporation) and monitored gravimetrically at minute intervals with a series of scales (Adam CBK, Adam Equipment Inc., Bletchley Milton Keynes, UK). Water use was computed from 30 min averages. Gravimetric water use and glass house environmental conditions were recorded for four continuous days (Decagon EM50R, Decagon Devices Inc., USA). Immediately after 4 days of continuous gravimetric measurements, individual crown physical dimensions were recorded and leaves were removed, bagged, and scanned (Model 3100, Li-Cor Biosciences, Inc., Lincoln, NE, USA). MAESTRA was parameterized on an individual replicate basis and simulations were conducted on a 30 min time step. MAESTRA simulated whole tree transpiration estimates were compared to 30 min averages of gravimetric water use.

3 Results

3.1 Species, Seasonal, and Drought Response of g0 and Midday gs

[19] Seasonal means of g0 differed significantly among species (P = 0.009 one-way ANOVA). Figure 1 shows that observations of g0 did not change significantly over the course of the growing season in Acer rubrum, Carpinus betula, or Cercis canadensis (P > 0.1 for all, repeated measures ANOVA), whereas Betula nigra had a significant seasonal change (P = 0.01). However, when the final measurement time-point is removed from the analysis, the seasonal response of Betula nigra was no longer significant (P = 0.34). Whole-season means between the droughted and well-watered treatments did not differ significantly in any of the species (P > 0.1 for all analyses, two sample t test). However, the drought treatment means were lower for every species except Carpinus betula, which had a higher g0 under drought conditions. There was not a significant interaction between water stress level and season in any species (P > 0.05). When all species were pooled, g0 averaged 38.4 mmol m−2 s−1 and showed no significant response to drought (P = 0.79), but a significant curvilinear response of midday gs to drought was observed (Figure 2, P = 0.0036).

Figure 1.

Measured values of minimum stomatal conductance (g0; gs when An ≤ 0) for the 2011 growing season. Solid circles represent well-watered conditions and open circles represent water stress. The solid horizontal line indicates the whole season g0 mean for the well-watered treatment and the dotted line represents the whole season mean for the drought treatment. Vertical bars represent one standard error (n = 3). Note: differences between seasonal treatment means were not significant for all species (P > 0.1).

Figure 2.

Relationship of midday stomatal conductance (gs) and minimum stomatal conductance (g0) to increasing levels of water stress (reported as percent of well-watered treatment) as an average of four tree species. The gs-irrigation level relationship was significant (P = 0.0036, R2 = 0.97), whereas the g0-irrigation level relationship was not (P = 0.79, R2 = 0.02). Vertical bars represent one standard error (n = 36).

3.2 MAESTRA Validation and g0 Investigations

[20] In comparison to measured weekly transpiration, MAESTRA accurately estimated species-specific whole tree water use (Figure 3). Root mean square error (RMSE) of measured versus predicted transpiration ranged from 0.014 kg m−2 d−1 in Acer rubrum to 0.031 kg m−2 d−1 in Betula nigra. There was a general trend toward a slight overestimation of model estimates, evident by a mean bias error (MBE) ranging from 0.031 kg m−2 d−1 in Cercis canadensis to 0.074 kg m−2 d−1 in Carpinus betula; however, transpiration was slightly biased toward underestimation in Betula nigra (MBE of −0.01 kg m−2 d−1).

Figure 3.

Measured versus predicted values of canopy transpiration per m2 of leaf area for four tree species. Mean bias error (MBE) and root mean square error (RMSE) are reported in kg m−2 d−1. Each point represents the mean value of one week of measured versus predicted transpiration. Bars represent one standard error (n = 7).

[21] A sensitivity analysis demonstrated that g0 was the most significant parameter for estimating seasonal canopy transpiration (Figure 4a). The mean seasonal parameter effect of g0 was 43.4% with a standard deviation of 9.5%. The analysis also showed the g1 parameter to be highly significant with a mean of 25.2% and standard deviation of 4.1%. Alpha, Vcmax, and Jmax had significant impacts (> 5%) on transpiration estimates as well (Figure 4a). Seasonal estimates of transpiration varied significantly when MAESTRA was parameterized with upper or lower bounds (mean ± one standard deviation) of measured g0 values for Acer rubrum (Figure 4b), but the estimates appear to be influenced more by the lower as opposed to upper bound value. Figure 4c illustrates the parameter effect of g0 on daily estimates of water flux changes throughout the season.

Figure 4.

Sensitivity of transpiration estimates to five key input parameters. Figure 4a shows the parameter effect for five physiological parameters averaged across the entire season (minimum stomatal conductance (g0—mmol H2O m−2 s−1), stomatal response coefficient (g1—unit less), quantum yield of electron transport (α—mol e mol PAR−1), maximum rate of carboxylation (Vcmax—µmol CO2 m−2 s−1), and dark respiration (Rd—µmol CO2 m−2 s−1). Figure 4b shows full-season transpiration estimates when MAESTRA was parameterized with the mean measured g0 (g0 = μ—solid black line), the mean plus one standard deviation (g0 = μ + σ—dotted black line), and the mean minus one standard deviation (g0 = μ − σ—dashed grey line). Figure 4c shows the daily change in the g0 parameter effect across the season.

[22] When the canopy was separated into a three-dimensional x, y, and z grid of equal sub volumes, there was strong spatial variation in the within-canopy g0 parameter effect (Figure 5). In simulated canopies with relatively low total leaf area index (LAI) (e.g., LAI = 2 m2 m−2), the effect was less pronounced, but as LAI increased (e.g., LAI = 5 or 10 m2 m−2) there was a large increase in the parameter effect with increasing depth into the canopy (Figure 5). Regression analyses revealed the parameter effect of g0 to be strongly correlated with leaf absorbed PARL (R2 = 0.93) and temperature (R2 = 0.72). However, when the effect of leaf temperature (Tleaf) was tested in the absence of light, there was no change in the g0 parameter effect, indicating that PARL was driving the variation in the parameter effect, not Tleaf.

Figure 5.

The spatially variable minimum stomatal conductance (g0) parameter effect (%) on transpiration estimates in a simulated crown at a leaf area index (LAI) of 2, 5, and 10. The parameter effect was calculated as the difference in transpiration estimates at the upper (64.67 mmol m−2 s−1) and lower (10.47 mmol m−2 s−1) range of measured g0 divided by the mean (42.57 mmol m−2 s−1). Contour lines show changes in the g0 parameter effect (%) at relative canopy height and width.

[23] The influence of g0 is the greatest under low-light conditions, but it can still have a substantial parameter effect (~30%) under sparse foliage conditions (e.g., LAI < 2) and in portions of the canopy that remain well lit (e.g., Figure 5 LAI 5 and 10). Likewise, g0 can have 100% of the control on gs predictions when An ≤ 0, but the g0 parameter effect on Σgs decreases to ~30% at PARL levels above ~400 µmol m−2 s−1 (Figure 6). At lower PARL levels, An is usually below light saturation for C3 foliage and the g0 component becomes larger than βgs, thus contributing to the majority of Σgs. However, as PARL and An increase, the influence of βgs increases and g0 and βgs converge at a species-specific threshold PARL level (~125 µmol m−2 s−1, in the case of red maple). At ~125 µmol m−2 s−1, each contributes exactly 50% to Σgs. As PARL continues to increase above the threshold light level, βgs then has the majority of influence on Σgs.

Figure 6.

A simulated representation of the influence of leaf absorbed photosynthetically active radiation (PARL) on components of the Leuning [Leuning, 1995] stomatal conductance (gs) model—as simplified for this study (refer to equations (1)(3))—where total stomatal conductance (Σgs) is the sum of the minimum stomatal conductance parameter (g0) and the portion of the Leuning model driven primarily by photosynthesis (βgs). The black line represents the percent contribution of g0 and the grey line represents the βgs contribution to Σgs.

3.3 Comparison of Observed and Estimated g0 Values

[24] For the trees measured in OH, estimates of g0 from least squares fits were significantly different than observed values (P < 0.005). Three species had negative values of g0 from statistical estimates and the error range of the fourth species included a negative intercept (Table 2). In the fine-scale studies with Malus domestica, observed values of g0 were ~150% larger than those derived from least squares estimates (Figure 7). The inset in Figure 7 shows that the g0 estimates extrapolated from observed versus BBL model parameters (equation (4)) was not different from gs-An g0 estimates (cf. Figure 7 and inset).

Figure 7.

Linear relationship between stomatal conductance (gs) and net photosynthesis (An) for Malus domestica. The g0 parameter can be defined as the extrapolated x-y intercept (An = 0) of a least squares fit to the linear gs-An relationship (g0-ext); however, empirical observations of g0 (An ≤ 0; g0-obs) from the same leaves show it to be higher, suggesting that the linearity between gs and An becomes nonlinear or asymptotic at low light levels. The parameter g0 can also be defined as the x-y intercept of a linear fit of observed gs to model output (inset figure) but it is important to note that the g0 values derived from either fit are not different statistically. See equations (1) and (4) for descriptions of the model and parameter definitions.

3.4 Comparison of Observed and Estimated g0 Canopy Transpiration Estimates

[25] The MAESTRA model was more accurate when parameterized with observed values of g0 as compared to g0 values obtained from a least squares fit to the gs-An relationship (RMSE of 0.0067 and 0.0410 g m−2 s−1 respectively). Over a 4 day period, total observed values of g0 resulted in a slight overestimation (mostly occurring at night, see below) of water flux (6%), whereas the least squares derived g0 value resulted in a ~41% underestimation of transpiration (MBE of 0.0003 and −0.0021 g m−2 s−1 respectively; Figure 8). When error and bias estimate statistics (i.e., RMSE and MBE respectively) are partitioned into daytime and nighttime components, we found predictions from observed values to be overestimated at night (RMSE and MBE of 0.0089 and 0.0015 g m−2 s−1 respectively) versus extrapolated g0 values (RMSE and MBE of 0.0028 and −0.0005 g m−2 s−1 respectively). During the daytime, however, observed g0 input resulted in smaller transpiration estimate error and slight negative bias statistics (RMSE and MBE of 0.0022 and −0.0006 g m−2 s−1 respectively) as compared to extrapolated g0 input values (RMSE and MBE of 0.0382 and −0.011 g m−2 s−1 respectively).

Figure 8.

Comparison of gravimetric and MAESTRA estimated transpiration for containerized Malus domestica. Black circles represent gravimetric measurement values of transpiration, grey circles are transpiration estimates from MAESTRA when parameterized with values of g0 observed at An ≤ 0, and white circles represent transpiration estimates from MAESTRA when parameterized with g0 values derived from a least squares estimate of the linear gs-An regression. Each point represents the mean of four individual trees at a 30 min time step. Root mean square errors of modeled versus measured regressions were 0.0067 and 0.041 g m−2 s−1 for the observed and least squares fit g0 respectively. Mean bias errors were 0.0003 and −0.0021 g m−2 s−1 for the observed and least squares fit g0, respectively.

4 Discussion

[26] Typically, g0 has not been measured directly but has instead been defined as a fit value, extrapolated from a linear regression. Other studies have forgone the data collection required to characterize the gs-An relationship (and thus g0) and have instead assumed constant and often unrealistically low values for g0. In this paper, we challenge these paradigms by showing how the linear fit estimates of g0 can yield erroneous canopy transpiration predictions and small errors in g0 can have a substantial effect on transpiration estimates. We designed this study to have four primary objectives: (1) to characterize observed g0 changes over an entire growing season in droughted and well-watered deciduous trees, (2) to validate a canopy transpiration model parameterized with leaf-level g0 measurements, (3) to use the validated model to investigate the spatial influence of the g0 parameter on water flux estimates in forest canopies, and (4) to test the hypothesis that MAESTRA parameterized with directly observed g0 values would produce more accurate estimates of transpiration than if it were parameterized with g0 values from statistical estimation.

[27] The lack of a consistent g0 response to drought (Figures 1 and 2) conflicts with the findings of several other studies that have shown a decrease in g0 under drought stress [Running, 1976; Cavender-Bares et al., 2007; Zeppel et al., 2011]. We did, however, find a midday gs water stress response (Figure 2), suggesting that the drought response mechanisms that control midday gs versus g0 may not be linked. In several desert species, Ogle et al. [2012] also found that midday gs and g0 decouple, whereas Mott and Peak [2010] reported a coupled response for g0 and gs in the herbaceous species Tradescantia pallida. These two studies highlight the inconsistencies amongst reports attempting to explain the g0 response. Moreover, they emphasize that no one causative environmental factor seems to explain the observed differences. Pressure probe studies have attempted to implicate guard cell mechanics as the source of species difference in g0 [Franks and Farquhar, 1998; 2007], while observed g0 variation within species has often been attributed to environment [Matyssek et al., 1995; Cavender-Bares et al., 2007; Howard and Donovan, 2007; Scholz et al., 2007; Zeppel et al., 2011]. Figure 2 supports the hypothesis that interspecific differences may be governed by guard cell mechanics by showing that drought-induced minimum midday gs (0% applied irrigation) is similar to our observed gs under dark conditions. Another study investigating the response of understory leaves to sun flecks [Allen and Pearcy, 2000] determined that leaves with a higher g0 can reach maximum photosynthesis faster than leaves that began at a lower g0. Unknown, however, is whether g0 is homogenous throughout a forest canopy (especially large and complex canopies), if it varies along a canopy depth profile, or if it differs between sun versus shade leaves. To further understand g0, within canopy variability and driving mechanisms should be investigated.

[28] Over the course of an entire growing season, g0 was by far the most influential parameter on water flux estimates in simulated tree canopies (Figure 4a). Our three-dimensional analysis revealed (1) an increase in the parameter effect of g0 with increasing canopy LAI and (2) an increasing parameter effect toward the center of individual crowns and forest canopies (e.g., Figure 5). The spatially variable transpiration response to g0 may be explained by a gradient in environmental variables. Even though MAESTRA is a three-dimensional canopy model, it is unable to resolve within-canopy CO2 concentration gradients and wind speed attenuation is calculated at each vertical-layer (i.e., in two dimensions). However, Tleaf and PARL are both resolved three dimensionally. Regression analyses revealed that these two factors are correlated with the g0 parameter effect on transpiration estimates. To isolate the influence of Tleaf and PARL from one another, we held one constant and varied the other over a realistic range, finding that both were correlated with the g0 parameter effect. We then analyzed the canopy transpiration response in the absence of within canopy light variation and found that the parameter effect of g0 was not influenced by changes in Tleaf. Instead, the parameter effect remained steady at approximately 80% across a range of Tleaf. The lack of a Tleaf effect can be attributed to the difference in transpiration estimates when βgs is zero (PARL = 0), thus leaving Σgs entirely dependent upon g0 over the tested range of Tleaf (Figure 6). The lack of a g0 response to Tleaf may appear counter-intuitive, but it is important to note that the magnitude of the g0 parameter effect is inversely proportional to the contribution of βgs to Σgs. As the contribution of βgs is driven by the magnitude of An (thus PARL), lower PARL levels create an environment where g0 has the maximum influence on transpiration estimates.

[29] Typically, g0 has been parameterized by a linear least squares fit to the gs-An relationship or to a linear fit between model parameters (equation (4)) and observed gs (both of which produced similar intercepts in our fine-scale study in Malus domestica (Figure 7)). Unfortunately, this statistical method is prone to errors (e.g., linear fits that result in negative values) [Ball and Farquhar, 1984; Schulze et al., 1987; Medlyn et al., 2011]. Medlyn et al. [2011] provide a prime example of the error influence in a recent effort to reconcile empirical and optimal gs theories into a simple theoretical framework when they attempt to drop g0 from a form of the BBL model. The de-emphasis on g0 was based in part on the conventional optimal gs theory that gs = 0 when An = 0 [Cowan and Farquhar, 1977]. While g0 was ultimately retained, this example illustrates, yet again, that using linear extrapolation to derive g0 neglects to recognize the potential for the gs-An relationship to depart from linearity at lower light levels [Ball, 1988; Collatz et al., 1991]. Our measurements in Malus domestica show a large departure from linearity at lower light levels (Figure 7), with a lower asymptote to gs measurements being achieved well above the light compensation point (LCP; horizontal dashed line in Figure 7). We note that the measured LCP for Malus domestica was low (~10 µmol m−2 s−1; data not shown); thus, our measurements were unable to provide a high degree of gs resolution near the LCP. However, this point may be moot because gs appeared to reach an asymptote well above the LCP (Figure 7). The same departure from linearity was evident in the trees measured in OH, for which statistical estimates of g0 in three out of four species were negative and substantially disagreed with observed values.

[30] Small errors in g0 parameterization can act multiplicatively on transpiration estimates and can compound errors over longer time periods (e.g., Figure 3). To illustrate this, we parameterized two versions of MAESTRA for Malus domestica, one with observed g0 (49.7 mmol m−2 s−1) and one with statistically estimated g0 (20.4 mmol m−2 s−1, Table 2). When parameterized with observed g0, the model performed with a slight overestimation (~6%) over a 4 day period with the majority of overestimation occurring at nighttime. However, when parameterized with g0 values from statistical estimates, the model did not perform as well, underestimating water use by >40% (Figure 8). We were unable to test the influence of the extrapolated g0 values from the trees measured in OH because negative g0 inputs cause a fatal error within the MAESTRA programming. While the influence of g0 on transpiration estimates is greater under lower light conditions (Figure 5), it is important to note that the mathematical formulation of the BBL equation (e.g., equation (1)) specifies that g0 will be applied across the entire range of gs predictions. Hence, in the Ball-Berry family of equations, the g0 parameter independently influences daytime as well as nighttime transpiration estimates.

[31] Our finer-scale tests that use observed versus extrapolated g0 for Malus domestica transpiration estimates point to g0 having a substantial influence on transpiration estimates at night. Published reports show significant levels of nighttime transpiration (up to 25% of daytime) [e.g., Daley and Phillips, 2006; Dawson et al., 2007]. In extreme cases, such as well-watered fast-growing Eucalyptus species, weekly measurements of nighttime transpiration can approach 80% of daytime [Benyon, 1999]. Thus, nighttime estimates of transpiration should be given greater importance in future research. Our data show similar trends in containerized Malus domestica grown under glass house conditions, with nighttime transpiration ranging from 10 to 25% of average daytime water use (Figure 8). We found that observed g0 improved the predictive accuracy of canopy transpiration estimates versus extrapolated g0 and the improved accuracy was more pronounced during the daytime periods. However, the slightly lower accuracy of MAESTRA during nighttime periods could be due to our low resolution wind data at nighttime, where intermittent venting in the glass house produces low and variable wind speeds that could influence nighttime transpiration.

[32] If typical methods of obtaining g0 through statistical estimation are faulty, yet the BWB and BBL models provide accurate predictions of leaf-level gs, then other parameters in the gs or An models may be in error. From the standpoint of modeling gs specifically, this error must be due to the parameterization of one of the other three parameters (Γ, g1, or D0). Our full season sensitivity analysis of the coupled gs-An scheme revealed g1 to be the parameter with the second largest influence on transpiration (~25%) with Γ and D0 both having <1% influence (data not shown). Like g0, g1 has received little attention in the literature. The parameter g1 is often described, similar to g0, as a parameter fit to observed data (i.e., the slope of equation (4) when plotted against observed gs), even though a physiological significance for g1 has been described [Xu and Baldocchi, 2003; Medlyn et al., 2011]. Currently, it is not agreed upon whether g1 changes or not in response to environmental factors [Baldocchi, 1997; Xu and Baldocchi, 2003]. While there are several methods for calculating g1 as an index of An, CO2, and VPD [equation (4), see also: Ball, 1988; Medlyn et al., 2011], these methods rely on statistical extrapolations from a linear regression fit that, like g0, may not be representative of observed values.

[33] The values for nighttime gs in the literature come from a broad range of species, ecotypes and PFTs, ranging from 1 to 400 mmol m−2 s−1 (with a mean of 75.4 mmol m−2 s−1), and include only a few instances of a value ≤ 10 mmol m−2 s−1 (Table 3). The reported nighttime gs values could be useful for parameterizing g0, directly connecting plant physiology studies with ecological modeling efforts. In light of our analyses and the data in the literature, we strongly encourage modeling efforts at all scales to pay more attention to this parameter. For example, the values used in Sellers et al. [1996] (10 mmol m−2 s−1) and Oleson et al. [2010] (2 mmol m−2 s−1), two prominent large-scale land surface schemes, are unrealistically low and also use the same value for all PFTs. While our study does not represent a comprehensive survey, our computed average for four broadleaf deciduous tree species was closer to 40 mmol m−2 s−1. An even greater range of values are reported in Table 3 that might help provide general PFT g0 parameterization guidance. We acknowledge the difficulty in species or PFT specific parameterization. However, we find it important to reiterate that species-specific g0 parameterization in our study greatly improved full season model estimates.

Table 3. Measurements of Nighttime Stomatal Conductance (gs) (Surrogate for Minimum Stomatal Conductance (g0)). Values are Reported in mmol m−2 s−1
 Species/Functional Typeg0 Ming0 Maxg0 MeanReference
Functional typeSeep ecotype20120 [Snyder et al., 2003]
 Warm desert15100  
 Conifer trees2060 [Caird et al., 2007]
 Broadleaf evergreen20180  
 Broadleaf deciduous20260  
 Herbaceous dicots20220  
 Perennial grasses20140  
SpeciesPinus ponderosa10120 [Misson et al., 2004]
 Pinus ponderosa123 [Grulke et al., 2004]
 Styrax ferrugineus50145 [Bucci et al., 2004]
 Roupala Montana45125  
 Ouratea hexasperma3575  
 Quercus rubra240 [Barbour et al., 2005]
 Ouratea hexasperma3060 [Scholz et al., 2007]
 Blepharocalyx salicifolius7781  
 Qualea grandiflora102158  
 Betula papifera  200[Daley and Phillips, 2006]
 Quercus rubra  20 
 Acer rubrum  20 
 Helianthus annuus40400 [Howard and Donovan, 2007]
 Quercus virginiana  50[Cavender-Bares et al., 2007]
 Ricinus communis50200 [Barbour and Buckley, 2007]
 Picea sitchensis5100 [Seibt et al., 2007]
 Fagus sylvatica525  
 Prunus x yedoensis231288 [Bowden and Bauerle, 2008]
 Acer rubrum159249  
 Acer buergeranum82211  
 Prunus serrulata213233  
 Platanus x acerifolia131210  
 Acer rubrum3548 [Bauerle and Bowden, 2011]
 Eucalyptus sideroxylon1580 [Zeppel et al., 2011]
 Eucalyptus delegatensis5436 [Medlyn et al., 2007]

5 Conclusions

[34] The g0 parameter in the BBL gs model has a substantial influence on transpiration estimates at the whole crown level. Historically, little attention has been paid to g0 and it has typically been parameterized as an empirical fitting coefficient. In this paper, we assert that g0 is a parameter with physiological significance and it can be measured. Knowing this, an additional “mechanistic” attribute may be associated with the BWB family of models. By shifting the current paradigm from g0 as a linear extrapolation “fitting coefficient” to a basal gs rate, additional focus can move toward refining measurements of the remaining model parameters. Although we did not find g0 to change in response to season or drought, understanding the underlying mechanisms that cause interspecific and intraspecific g0 differences are still warranted, especially given the disagreements found in the literature. Currently, empirical g0 measurements are easy to obtain with simple hand-held porometers, providing a supplement to data collected with photosynthesis gas-exchange equipment. Finally, models should consider species-specific characterization of g0 when predicting water flux rather than assume a single value among species or PFTs.


[35] We thank Tom Demaline for donating plant material and research space for this study, Willoway Nursery staff for site maintenance, Dan Banks and Becky Barnard for assistance in data collection, David Kohanbash and George Kantor for development of the wireless node data collection network, the USDA Application Technology Research Unit for access and use of the leachate monitoring pot-in-pot research site, two anonymous reviewers for excellent critical reviews, the USDA-National Institute of Food and Agriculture, Specialty Crops Research Initiative (Award No. 2009-51181-05768), and USDA Cooperative Agreement (Award No. 58-6618-2-0209). Decagon Devices Inc. subsidized equipment costs in Award No. 2009-51181-05768.