- Email: [email protected]
Assessment of canopy stomatal conductance models using flux measurements
Ecological Modelling 220 (2009) 2115–2118
Contents lists available at ScienceDirect
Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel
Short communication
Assessment of canopy stomatal conductance models using flux measurements Shusen Wang ∗ , Yan Yang, Alexander P. Trishchenko Canada Centre for Remote Sensing, Natural Resources Canada, Ottawa, ON, Canada
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 3 December 2008 Received in revised form 16 April 2009 Accepted 27 April 2009 Available online 30 May 2009
Stomatal conductance (g) is a key parameter in controlling energy and water exchanges between canopy and the atmosphere. Stomatal conductance models proposed by Ball, Woodrow and Berry (BWB) and Leuning have been increasingly used in land surface schemes. In a recent study, a new diagnostic index was developed by Wang et al. to examine the response of g to humidity and new models were proposed to resolve problems identified in the BWB and Leuning models. This approach is theoretically sound, but relies on canopy latent heat and CO2 fluxes and environmental variables at the leaf surface which are not available at most eddy correlation (EC) observation sites. In this study, we tested the diagnostic index by empirically correcting EC measurements to canopy-level fluxes and by replacing leaf surface variables by their corresponding ambient air variables, and re-examined the stomatal conductance models of BWB, Leuning, and Wang et al. We found that the impact of the above modifications on the evaluation of g–humidity relationships is very small. This study provides a practical approach to investigate the stomatal response to humidity using routine EC measurements. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.
Keywords: Stomatal conductance Humidity Flux measurement Model
1. Introduction Stomata serve as the channel of water vapour and CO2 exchanges between plant leaves and the ambient air. Most plants open and close their stomata in response to changes in environmental conditions such as humidity, light intensity, temperature, and CO2 concentration. There is a general consensus that stomata have developed sophisticated physiological mechanism that tends to maximize leaf carbon gain while minimizing water loss through transpiration, or the optimization theory first proposed by Cowan (1977) and Cowan and Farquhar (1977). The model that estimates stomatal conductance (g) using leaf photosynthesis (A) was first proposed by Ball–Woodrow–Berry (1987, Eq. (1), hereafter referred to as the BWB model), and later modified by Leuning (1995, Eq. (2)). g = mhs A/Cs + g0
where
f (H) = mhs
g = a1 A/ (Cs − )(1 + Ds /D0 ) + g0 = a1 /(1 + Ds /D0 )
where
(1) f (H) (2)
where m, a1 , and D0 are parameters, Cs is leaf surface CO2 concentration, g0 is the leaf minimum (residual) g as A reaches 0, and is the CO2 compensation point.
∗ Corresponding author at: 588 Booth Street, Ottawa, Ontario K1A 0Y7, Canada. Tel.: +1 613 947 3592; fax: +1 613 947 1385. E-mail address: [email protected] (S. Wang).
The main difference between the two models is the humidity response function f(H). In the BWB model, f(H) is represented as a linear function of relative humidity at leaf surface (hs ), while in the Leuning model, f(H) is modified to a non-linear function of water vapour pressure deficit at leaf surface (Ds ). Independent evaluations on the two models were not in agreement and there has been no compelling evidence in favour of either approach (Cox et al., 1998; Betts et al., 1999; Van Wijk et al., 2000; Mo and Liu, 2001; Gutschick and Simonneau, 2002; Arora, 2003; Wang et al., 2007; Gutschick, 2007). In a recent study, Wang et al. (2009) developed an approach to calculate f(H) through coupling canopy transpiration equation with photosynthesis-based stomatal model, which can be written as f (H) =
(Cs − )Qcan
vıLs (qsat(Tc ) − qs )A
(3)
where v is the volume of gas per mole, ı is a parameter accounting for the difference of stomatal conductance to water vapour and to CO2 , L is the latent heat of vaporization of water, s and qs are the density and specific humidity of the air at leaf surface, qsat(Tc ) is the saturated specific humidity at leaf temperature Tc , and Qcan is canopy latent heat exchange due to transpiration. Note that the second item in the original equation of Wang et al. (2009), which is (Cs − )g0 /A representing the contribution of residue stomatal conductance to f(H), is minor during our analyzing period (daytime when fluxes are reasonably high) and thus excluded in this study. The above approach enables us to evaluate the g–humidity relationships without requiring stomatal measurement which is tedious and costly. It works at the canopy level which is beneficial
0304-3800/$ – see front matter. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2009.04.044
2116
S. Wang et al. / Ecological Modelling 220 (2009) 2115–2118
for most land surface and hydrology schemes as they operate at the canopy level. Moreover, the approach is based on the ratio of canopy latent heat and CO2 fluxes rather than their real quantities such as those used in Stewart (1988), Wu et al. (2000), Blanken and Black (2004), Ewers and Oren (2000), and Oren et al. (2001). This reduces the impacts of measurement accuracies, energy closure problems existed in flux measurements using eddy correlation (EC) method (Barr et al., 2006), and high frequency noise in the high temporal resolution EC flux data, on studying the response of stomatal conductance to humidity. Using Eq. (3) and EC flux measurements at three boreal forest sites in Canada, Wang et al. (2009) critically examined the performance of the BWB and Leuning models. It was found that the BWB model largely underestimated g at high humidity. The Leuning model reduced this bias, but it still could not adequately capture the remarkable increase of g at high humidity. Based on their analysis, Wang et al. (2009) proposed new models that were based on hs (Eq. (4)) and Ds (Eq. (5)), which were found significantly outperformed the BWB and Leuning models. ˇ
g = ˛(1.0 − hs ) A/(Cs − )+g0 g=
ˇ ˛Ds A/(Cs
− ) + g0
where
where f (H) =
f (H) = ˛(1.0 − hs ) ˇ ˛Ds
ˇ
(4) (5)
where ˛ and ˇ are parameters (note that they have different values in the two equations). Eq. (3) requires several variables that are not directly measured at most EC sites. First it needs latent heat and CO2 fluxes due to canopy transpiration and photosynthesis while EC system measures them at ecosystem level which also include soil evaporation and ecosystem respiration. Second, it needs variables such as humidity and CO2 concentration at the leaf surface while most EC sites measure the ambient air. One way to solve these problems is to use process-based ecosystem models which can provide outputs required to estimate canopy-level fluxes of latent heat and CO2 from EC measurements as well as the leaf surface variables at the temporal resolution of flux measurements. In Wang et al. (2009), the process-based ecosystem model EALCO was used for the purpose to produce the 30-min flux of soil latent heat flux, ecosystem respiration, and the values of leaf surface variables. To assure the accuracy of model simulations, careful model calibration and validation are required which often need a large number of site parameters. When reliable model simulation is not available, the applications of Eq. (3) could be constrained due to the lack of input variables required. At most EC observation sites, measurement-based empirical estimates of soil latent heat and ecosystem respiration are available. On the other hand, during daytime when ecosystem latent heat and CO2 fluxes are reasonably high, the well coupling of canopy and the atmosphere usually leads to the small differences in variable values between leaf surface and ambient air. In this study, we examined Eq. (3) by using empirically based corrections of ecosystem- to canopy-level fluxes, and by replacing leaf surface variables by their corresponding ambient air variables. We found these modifications only induced very small differences in predicting the response of g to humidity. Our model test results are highly consistent with those in Wang et al. (2009) for all of the four models (Eqs. (1), (2), (4) and (5)) and all study sites. The result indicates that the above modifications which can be readily implemented in most EC observation sites can satisfy the requirement of using Eq. (3) to assess the g–humidity relationships. 2. Method Eq. (3) is rigorous in theory and derived with few assumptions, but its direct applications can be constrained by data availability since leaf surface variables and canopy-level fluxes are usually not directly measured in most EC sites currently in operation. To make
use of field observations, we simplify it to f (Ha ) =
(Ca − )(1 − ε)FLE
vıLa (qsat(Ta ) − qa )(FCO2 + R)
(6)
where a , qa , and Ca are the density, specific humidity, and CO2 concentration of the ambient air, qsat(Ta ) is the saturated specific humidity at air temperature Ta , FLE is the EC measured (ecosystem level) latent heat flux (storage corrected), ε is a correction factor representing the fraction of soil latent heat flux in FLE , FCO2 is the EC measured (ecosystem level) CO2 flux (storage corrected), and R is ecosystem respiration. The difference between Eqs. (3) and (6) is that variables at leaf surface in Eq. (3) were substituted by their corresponding ambient air values (denoted by subscript a) in Eq. (6), and canopy latent heat flux and photosynthesis were obtained by empirically estimating soil latent heat flux using εFLE and R. We assume ε is a constant which means that soil evaporation is proportionally related to total evapotranspiration. The R estimation is based on the Fluxnet Canada Research Network (FCRN) standard methodology which is detailed in Barr et al. (2004). In brief, it first derives simple annual empirical relationships between measured R (night time CO2 flux measurement) and soil temperatures. After that, an additional parameter of soil water content is introduced into the above-obtained equation. The soil water parameter is allowed to vary in time, and it is determined within a moving window using a linear regression of estimates modelled from the annual relationship versus measurements. Eq. (6) is based on input that can be obtained from most EC sites. This study used the same study sites and data as in Wang et al. (2009). It includes three boreal forest sites in Canada known as Southern Old Aspen (SOA, 53.63◦ N, 106.20◦ W), Southern Old Black Spruce (SOBS, 53.99◦ N, 105.12◦ W), and Southern Old Jack Pine (SOJP, 53.92◦ N, 104.69◦ W), and 5 years (2000–2004) observations at each site. Details about the study sites and data can be found in http://www.fluxnet-canada.ca/. Data filtering criteria were also the same as in Wang et al. (2009) which include: (1) full-leaf growing seasons during which the canopy CO2 and latent heat fluxes had the largest contributions in the measured ecosystem CO2 and latent heat fluxes so that the impacts of uncertainties in R and soil evaporation on the canopy flux estimates are minimized; (2) daylight hours when incoming shortwave radiation was above 100 W m−2 , Qcan was above 20 W m−2 , and A was above 2 mol m−2 s−1 . Stomatal behavior has minimal impact on canopy water and CO2 exchanges when radiation and the fluxes are low; (3) time periods when there is no water on the canopy (e.g., intercepted rain or dew) to avoid the complication in canopy transpiration estimate. 3. Results and discussion We first analyzed the impact of the approximations of Eqs. (3)–(6) on f(H) values. We found that the differences between leaf surface and ambient air variable values during the selected time period were very small. Figs. 1 and 2 show the frequency distributions of Ca − Cs and (qsat(Ta ) − qa ) − (qsat(Tc ) − qs ), respectively, at SOA. Note that the leaf surface variables of Cs and qsat(Tc ) − qs were simulated by the EALCO model, and they represented the overall values at canopy level. Their values may have difference from those measured at individual leaves as discussed in Wang (2008). The results show that 90% of Ca − Cs was under 5 mol mol−1 , or less than 1.5% of the average ambient air CO2 concentration (364 mol mol−1 during the study period). During daytime with fairly high solar radiation, canopy temperature Tc was usually higher than Ta which leads to the higher qsat(Tc ) than qsat(Ta ) . On the other hand, qs is usually higher than qa due to the transpiration (water vapour source) of canopy leaves. As the result, the values of (qsat(Ta ) − qa ) were found close to (qsat(Tc ) − qs ). Among our data, 90% of the (qsat(Ta ) − qa ) − (qsat(Tc ) − qs ) values were within
S. Wang et al. / Ecological Modelling 220 (2009) 2115–2118
2117
Fig. 1. Frequency distributions of the differences of CO2 concentrations between ambient air (Ca ) and leaf surface (Cs ) during the selected study period at SOA.
±0.5 g kg−1 , or 7% of the average specific humidity deficit of the ambient air (7.2 g kg−1 during the study period). We also found that the differences between ambient air and leaf surface variables were slightly larger at SOA than at SOJP, mainly due to the stronger CO2 sink and water vapour source of dense canopies with high leaf area index (LAI) (i.e., SOA) than that of less dense canopies with low LAI (i.e., SOJP). Overall, the differences between Cs and Ca , and between (qsat(Ta ) − qa ) and (qsat(Tc ) − qs ) were small and it indicates the strong coupling between the canopy and the atmosphere due to the much higher aerodynamic conductance than canopy stomatal conductance. As a result, the substitutes of leaf surface variables by ambient air variables, mainly Cs by Ca and (qsat(Tc ) − qs ) by (qsat(Ta ) − qa ), were found to have small effects on f(H). However, in circumstances when coupling between canopy and the atmosphere is weak which results in relatively large differences in leaf surface and ambient air variable values (Leuzinger and Körner, 2007), the magnitudes of Ca − Cs and (qsat(Ta ) − qa ) − (qsat(Tc ) − qs ) and their impact on f(H) need to be further investigated. In general, if (qsat(Ta ) − qa ) − (qsat(Tc ) − qs ) becomes more positive, the weak coupling between canopy and the atmosphere will have less effect. Otherwise, f(H) will be likely overestimated. The impact of uncertainties in soil evaporation and R on f(H) varies among the three study sites. For dense canopies, the contribution of soil evaporation to total evapotranspiration is smaller than those of sparse canopies. The values of ε used in this study were 0.05, 0.12, and 0.25 at SOA, SOBS, and SOJP, respectively, estimated from soil evaporation measurement and modelling results (Blanken et al., 2001; Blanken and Black, 2004; Wang et al., 2009). Similarly, the respirations to photosynthesis ratios (R/A) were smaller at SOA than at SOJP, and their average values during our selected study period were 0.32, 0.51, and 0.53 at SOA, SOBS, and SOJP, respectively. The method for estimating R was tested using night time soil
Fig. 2. Frequency distributions of the differences between specific humidity deficits of ambient air (qsat(Ta ) − qa ) and leaf surface (qsat(Tc ) − qs ) during the selected study period at SOA.
Fig. 3. The response of canopy stomatal conductance to the relative humidity of ambient air at SOBS. The data points represent the 30-min values of f(Ha ) calculated by Eq. (6). The grey line represents the BWB model. The black curve represents Eq. (4).
CO2 efflux measurements in Kljun et al. (2006) which showed reasonably high confidence. The uncertainties in the estimates of soil evaporation and R are difficult to quantify accurately due to data limitation. Given the average quantities of ε and R/A stated above, errors of 10% in soil evaporation and R will result in the estimate error of f(H) less than 4%, 7%, and 9% at SOA, SOBS, and SOJP sites, respectively. We calculated f(H) using Eq. (6) and evaluated the performance of the four stomatal conductance models (BWB, Leuning, Eqs. (4) and (5)). Taken SOBS as an example, Fig. 3 shows the distribution of f(H) with ha together with the BWB model and Eq. (4), and Fig. 4 shows the distribution of f(H) with Da together with the Leuning model and Eq. (5). The results are highly consistent with those in Wang et al. (2009) where leaf surface variables were used in the f(H) calculation and soil evaporation and ecosystem respiration were estimated by the ecosystem model EALCO. The quantitative comparisons of model performance using Eq. (6) and that of Wang et al. (2009) were given in Table 1. In general, the approximation of Eqs. (3)–(6) resulted in higher scattering () and lower correlation coefficient (r) for all of the four models at the three study sites. This is in agreement with the result of Blanken and Black (2004) which showed that relating stomatal conductance to the humidity of ambient air rather than that of leaf surface increased the degree of scattering in g–humidity plots. However, the degradation of model
Fig. 4. The response of canopy stomatal conductance to water vapour pressure deficit of the ambient air at SOBS. The data points represent the 30-min values of the f(Ha ) calculated by Eq. (6). The grey curve represents the Leuning model. The black curve represents Eq. (5).
2118
S. Wang et al. / Ecological Modelling 220 (2009) 2115–2118
Table 1 Model test results. Model
f(Ha ) (this study)
Parameter
f(Hs ) (Wang et al., 2009)
˛
ˇ
n
r
8.5 15.5 1.8 350
– 350 −0.90 −0.65
6941 6956 6687 6923
0.59 0.77 0.82 0.87
(b) Southern Old Black Spruce (SOBS) ˛h (BWB) 8.7 ˛/(1 + D/ˇ) (Leuning) 17.6 1.9 ˛ (1 − h)ˇ (power-h) ˛Dˇ (power-D) 554
− 350 −1.1 −0.7
7219 7219 7091 7165
(c) Southern Old Jack Pine (SOJP) ˛h (BWB) ˛/(1 + D/ˇ) (Leuning) ˛ (1 − h)ˇ (power-h) ˛Dˇ (power-D)
− 350 −1.1 −0.75
6251 6395 6188 6374
(a) Southern Old Aspen (SOA) ˛h (BWB) ˛/(1 + D/ˇ) (Leuning) ˛ (1 − h)ˇ (power-h) ˛Dˇ (power-D)
a b c
7.8 16.3 1.55 800
a
rb
c
3.28 2.69 2.39 2.21
0.61 0.79 0.83 0.88
3.22 2.65 2.36 2.19
0.53 0.75 0.79 0.85
4.91 3.82 3.25 3.05
0.58 0.77 0.82 0.86
4.40 3.55 3.12 3.05
0.52 0.72 0.74 0.80
4.80 3.91 3.59 3.36
0.54 0.75 0.82 0.85
4.72 3.83 3.31 3.15
b
c
n: total number of data used in the analyses. Data with f(H) > 100 were excluded. r: correlation coefficient. : standard deviation.
performance was found fairly small. It indicates that ambient air variables and the empirical methods used in this study for correcting EC measurement to canopy level can be used in Eq. (6) to assess the response of canopy stomatal conductance to humidity with acceptable accuracy. Over the past two decades, large volume of EC flux measurements has been accumulated over most of the major biomes around the world. This study provides a useful approach to study the stomatal conductance–humidity relationships by using these large data resources. Acknowledgments Flux data used in this study were collected in Fluxnet Canada Research Network (FCRN) program. We thank Dr. A. Barr, Dr. T.A. Black, and Dr. H. McCaughey for their contributions in this study. This study was conducted in the ecosystem and water modelling activities in the “Enhancing Resilience in a Changing Climate Program” and the “Groundwater Mapping Program” of Earth Sciences Sector, Natural Resources Canada. References Arora, V.K., 2003. Simulating energy and carbon fluxes over winter wheat using coupled land surface and terrestrial ecosystem models. Agric. For. Meteorol. 118, 21–47. Ball, J.T., Woodrow, I.E., Berry, J.A., 1987. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. In: Biggens, J. (Ed.), Prog. Photosynth. Res., 4. Martinus-Nijhoff Publishers, Dordrecht, Netherlands, pp. 221–224. Barr, A.G., Black, T.A., Hogg, E.H., Kljun, N., Morgenstern, K., Nesic, Z., 2004. Interannual variability in the leaf area index of a boreal aspen-hazelnut forest in relation to net ecosystem production. Agric. For. Meteorol. 126, 237–255. Barr, A.G., Morgenstern, K., Black, T.A., McCaughey, J.H., Nesic, Z., 2006. Surface energy balance closure by the eddy-covariance method above three boreal forest stands and implications for the measurement of the CO2 flux. Agric. For. Meteorol. 140, 322–337. Betts, A.K., Goulden, M.L., Wofsy, S.C., 1999. Controls on evaporation in a boreal spruce forest. J. Climate 12, 1601–1618. Blanken, P.D., Black, T.A., Neumann, H.H., den Hartog, G., Yang, P.C., Nesic, Z., Lee, X., 2001. The seasonal water and energy exchange above and within a boreal aspen forest. J. Hydrol. 245, 118–136.
Blanken, P.D., Black, T.A., 2004. The canopy conductance of a boreal aspen forest, Prince Albert National Park, Canada. Hydrol. Process. 18, 1561–1578. Cowan, I.R., 1977. Stomatal behaviour and environment. Adv. Bot. Res. 4, 117–228. Cowan, I.R., Farquhar, G.D., 1977. Stomatal function in relation to leaf metabolism and environment. Symp. Soc. Exp. Biol. 31, 471–505. Cox, P., Huntingford, C., Harding, R., 1998. A canopy conductance and photosynthesis model for use in a GCM land surface model. J. Hydrol. 212–213, 79–94. Ewers, B.E., Oren, R., 2000. Analyses of assumptions and errors in the calculation of stomatal conductance from sap flux measurements. Tree Physiol. 20, 579–589. Gutschick, V.P., 2007. Plant acclimation to elevated CO2 – from simple regularities to biogeographic chaos. Ecol. Model. 200, 433–451. Gutschick, V.P., Simonneau, T., 2002. Modelling stomatal conductance of field-grown sunflower under varying soil water status and leaf environment: comparison of three models of response to leaf environment and coupling with an ABA-based model of response to soil drying. Plant Cell Environ. 25, 1423–1434. Kljun, N., Black, T.A., Griffis, T.J., Barr, A.G., Gaumont-Guay, D., Morgenstern, K., McCaughey, J.H., Nesic, Z., 2006. Response of net ecosystem productivity of three boreal forests stands to drought. Ecosystems 9, 1128–1144, doi:10.1007/s10021005-0082-x. Leuning, R., 1995. A critical-appraisal of a combined stomatal-photosynthesis model for C-3 plants. Plant Cell Environ. 18, 339–355. Leuzinger, S., Körner, C., 2007. Tree species diversity affects canopy leaf temperatures in a mature temperate forest. Agric. For. Meteorol. 146, 29–37. Mo, X., Liu, S., 2001. Simulating evapotranspiration and photosynthesis of winter wheat over the growing season. Agric. For. Meteorol. 109, 203–222. Oren, R., Sperry, J.S., Ewers, B.E., Pataki, D.E., Phillips, N., Megonigal, J.P., 2001. Sensitivity of mean canopy stomatal conductance to vapor pressure deficit in a flooded Taxodium distichum L. forest: hydraulic and non-hydraulic effects. Oecologia 126, 21–29, doi:10.1007/s004420000497. Stewart, J.B., 1988. Modelling surface conductance of a pine forest. Agric. For. Meteorol. 43, 19–35. Van Wijk, M.T., Dekker, S.C., Bouten, W., Bosveld, F.C., Kohsiek, W., Kramer, K., Mohren, G.M.J., 2000. Modeling daily gas exchange of a Douglas-fir forest: comparison of three stomatal conductance models with and without a soil water stress function. Tree Physiol. 20, 115–122. Wang, J., Miller, D.R., Sammis, T.W., Gutschick, V.P., Simmons, L.J., Andales, A.A., 2007. Energy balance measurements and a simple model for estimating pecan water use efficiency. Agric. Water Manage. 91, 92–101. Wang, S., 2008. Simulation of evapotranspiration and its response to plant water and CO2 transfer dynamics. J. Hydrometeorol. 9, 426–443, doi:10.1175/2007JHM918.1. Wang, S., Yang, Y., Trishchenko, A.P., Barr, A.G., Black, T.A., McCaughey, H., 2009. Modelling the response of canopy stomatal conductance to humidity. J. Hydrometeorol. 10, 521–532. Wu, A., Black, T.A., Verseghy, D.L., Blanken, P.D., Novak, M.D., Chen, W., Yang, P.C., 2000. A comparison of parameterizations of canopy conductance of aspen and Douglas-fir forests for CLASS. Atmos.-Ocean 38, 81–112.
Contents lists available at ScienceDirect
Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel
Short communication
Assessment of canopy stomatal conductance models using flux measurements Shusen Wang ∗ , Yan Yang, Alexander P. Trishchenko Canada Centre for Remote Sensing, Natural Resources Canada, Ottawa, ON, Canada
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 3 December 2008 Received in revised form 16 April 2009 Accepted 27 April 2009 Available online 30 May 2009
Stomatal conductance (g) is a key parameter in controlling energy and water exchanges between canopy and the atmosphere. Stomatal conductance models proposed by Ball, Woodrow and Berry (BWB) and Leuning have been increasingly used in land surface schemes. In a recent study, a new diagnostic index was developed by Wang et al. to examine the response of g to humidity and new models were proposed to resolve problems identified in the BWB and Leuning models. This approach is theoretically sound, but relies on canopy latent heat and CO2 fluxes and environmental variables at the leaf surface which are not available at most eddy correlation (EC) observation sites. In this study, we tested the diagnostic index by empirically correcting EC measurements to canopy-level fluxes and by replacing leaf surface variables by their corresponding ambient air variables, and re-examined the stomatal conductance models of BWB, Leuning, and Wang et al. We found that the impact of the above modifications on the evaluation of g–humidity relationships is very small. This study provides a practical approach to investigate the stomatal response to humidity using routine EC measurements. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.
Keywords: Stomatal conductance Humidity Flux measurement Model
1. Introduction Stomata serve as the channel of water vapour and CO2 exchanges between plant leaves and the ambient air. Most plants open and close their stomata in response to changes in environmental conditions such as humidity, light intensity, temperature, and CO2 concentration. There is a general consensus that stomata have developed sophisticated physiological mechanism that tends to maximize leaf carbon gain while minimizing water loss through transpiration, or the optimization theory first proposed by Cowan (1977) and Cowan and Farquhar (1977). The model that estimates stomatal conductance (g) using leaf photosynthesis (A) was first proposed by Ball–Woodrow–Berry (1987, Eq. (1), hereafter referred to as the BWB model), and later modified by Leuning (1995, Eq. (2)). g = mhs A/Cs + g0
where
f (H) = mhs
g = a1 A/ (Cs − )(1 + Ds /D0 ) + g0 = a1 /(1 + Ds /D0 )
where
(1) f (H) (2)
where m, a1 , and D0 are parameters, Cs is leaf surface CO2 concentration, g0 is the leaf minimum (residual) g as A reaches 0, and is the CO2 compensation point.
∗ Corresponding author at: 588 Booth Street, Ottawa, Ontario K1A 0Y7, Canada. Tel.: +1 613 947 3592; fax: +1 613 947 1385. E-mail address: [email protected] (S. Wang).
The main difference between the two models is the humidity response function f(H). In the BWB model, f(H) is represented as a linear function of relative humidity at leaf surface (hs ), while in the Leuning model, f(H) is modified to a non-linear function of water vapour pressure deficit at leaf surface (Ds ). Independent evaluations on the two models were not in agreement and there has been no compelling evidence in favour of either approach (Cox et al., 1998; Betts et al., 1999; Van Wijk et al., 2000; Mo and Liu, 2001; Gutschick and Simonneau, 2002; Arora, 2003; Wang et al., 2007; Gutschick, 2007). In a recent study, Wang et al. (2009) developed an approach to calculate f(H) through coupling canopy transpiration equation with photosynthesis-based stomatal model, which can be written as f (H) =
(Cs − )Qcan
vıLs (qsat(Tc ) − qs )A
(3)
where v is the volume of gas per mole, ı is a parameter accounting for the difference of stomatal conductance to water vapour and to CO2 , L is the latent heat of vaporization of water, s and qs are the density and specific humidity of the air at leaf surface, qsat(Tc ) is the saturated specific humidity at leaf temperature Tc , and Qcan is canopy latent heat exchange due to transpiration. Note that the second item in the original equation of Wang et al. (2009), which is (Cs − )g0 /A representing the contribution of residue stomatal conductance to f(H), is minor during our analyzing period (daytime when fluxes are reasonably high) and thus excluded in this study. The above approach enables us to evaluate the g–humidity relationships without requiring stomatal measurement which is tedious and costly. It works at the canopy level which is beneficial
0304-3800/$ – see front matter. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2009.04.044
2116
S. Wang et al. / Ecological Modelling 220 (2009) 2115–2118
for most land surface and hydrology schemes as they operate at the canopy level. Moreover, the approach is based on the ratio of canopy latent heat and CO2 fluxes rather than their real quantities such as those used in Stewart (1988), Wu et al. (2000), Blanken and Black (2004), Ewers and Oren (2000), and Oren et al. (2001). This reduces the impacts of measurement accuracies, energy closure problems existed in flux measurements using eddy correlation (EC) method (Barr et al., 2006), and high frequency noise in the high temporal resolution EC flux data, on studying the response of stomatal conductance to humidity. Using Eq. (3) and EC flux measurements at three boreal forest sites in Canada, Wang et al. (2009) critically examined the performance of the BWB and Leuning models. It was found that the BWB model largely underestimated g at high humidity. The Leuning model reduced this bias, but it still could not adequately capture the remarkable increase of g at high humidity. Based on their analysis, Wang et al. (2009) proposed new models that were based on hs (Eq. (4)) and Ds (Eq. (5)), which were found significantly outperformed the BWB and Leuning models. ˇ
g = ˛(1.0 − hs ) A/(Cs − )+g0 g=
ˇ ˛Ds A/(Cs
− ) + g0
where
where f (H) =
f (H) = ˛(1.0 − hs ) ˇ ˛Ds
ˇ
(4) (5)
where ˛ and ˇ are parameters (note that they have different values in the two equations). Eq. (3) requires several variables that are not directly measured at most EC sites. First it needs latent heat and CO2 fluxes due to canopy transpiration and photosynthesis while EC system measures them at ecosystem level which also include soil evaporation and ecosystem respiration. Second, it needs variables such as humidity and CO2 concentration at the leaf surface while most EC sites measure the ambient air. One way to solve these problems is to use process-based ecosystem models which can provide outputs required to estimate canopy-level fluxes of latent heat and CO2 from EC measurements as well as the leaf surface variables at the temporal resolution of flux measurements. In Wang et al. (2009), the process-based ecosystem model EALCO was used for the purpose to produce the 30-min flux of soil latent heat flux, ecosystem respiration, and the values of leaf surface variables. To assure the accuracy of model simulations, careful model calibration and validation are required which often need a large number of site parameters. When reliable model simulation is not available, the applications of Eq. (3) could be constrained due to the lack of input variables required. At most EC observation sites, measurement-based empirical estimates of soil latent heat and ecosystem respiration are available. On the other hand, during daytime when ecosystem latent heat and CO2 fluxes are reasonably high, the well coupling of canopy and the atmosphere usually leads to the small differences in variable values between leaf surface and ambient air. In this study, we examined Eq. (3) by using empirically based corrections of ecosystem- to canopy-level fluxes, and by replacing leaf surface variables by their corresponding ambient air variables. We found these modifications only induced very small differences in predicting the response of g to humidity. Our model test results are highly consistent with those in Wang et al. (2009) for all of the four models (Eqs. (1), (2), (4) and (5)) and all study sites. The result indicates that the above modifications which can be readily implemented in most EC observation sites can satisfy the requirement of using Eq. (3) to assess the g–humidity relationships. 2. Method Eq. (3) is rigorous in theory and derived with few assumptions, but its direct applications can be constrained by data availability since leaf surface variables and canopy-level fluxes are usually not directly measured in most EC sites currently in operation. To make
use of field observations, we simplify it to f (Ha ) =
(Ca − )(1 − ε)FLE
vıLa (qsat(Ta ) − qa )(FCO2 + R)
(6)
where a , qa , and Ca are the density, specific humidity, and CO2 concentration of the ambient air, qsat(Ta ) is the saturated specific humidity at air temperature Ta , FLE is the EC measured (ecosystem level) latent heat flux (storage corrected), ε is a correction factor representing the fraction of soil latent heat flux in FLE , FCO2 is the EC measured (ecosystem level) CO2 flux (storage corrected), and R is ecosystem respiration. The difference between Eqs. (3) and (6) is that variables at leaf surface in Eq. (3) were substituted by their corresponding ambient air values (denoted by subscript a) in Eq. (6), and canopy latent heat flux and photosynthesis were obtained by empirically estimating soil latent heat flux using εFLE and R. We assume ε is a constant which means that soil evaporation is proportionally related to total evapotranspiration. The R estimation is based on the Fluxnet Canada Research Network (FCRN) standard methodology which is detailed in Barr et al. (2004). In brief, it first derives simple annual empirical relationships between measured R (night time CO2 flux measurement) and soil temperatures. After that, an additional parameter of soil water content is introduced into the above-obtained equation. The soil water parameter is allowed to vary in time, and it is determined within a moving window using a linear regression of estimates modelled from the annual relationship versus measurements. Eq. (6) is based on input that can be obtained from most EC sites. This study used the same study sites and data as in Wang et al. (2009). It includes three boreal forest sites in Canada known as Southern Old Aspen (SOA, 53.63◦ N, 106.20◦ W), Southern Old Black Spruce (SOBS, 53.99◦ N, 105.12◦ W), and Southern Old Jack Pine (SOJP, 53.92◦ N, 104.69◦ W), and 5 years (2000–2004) observations at each site. Details about the study sites and data can be found in http://www.fluxnet-canada.ca/. Data filtering criteria were also the same as in Wang et al. (2009) which include: (1) full-leaf growing seasons during which the canopy CO2 and latent heat fluxes had the largest contributions in the measured ecosystem CO2 and latent heat fluxes so that the impacts of uncertainties in R and soil evaporation on the canopy flux estimates are minimized; (2) daylight hours when incoming shortwave radiation was above 100 W m−2 , Qcan was above 20 W m−2 , and A was above 2 mol m−2 s−1 . Stomatal behavior has minimal impact on canopy water and CO2 exchanges when radiation and the fluxes are low; (3) time periods when there is no water on the canopy (e.g., intercepted rain or dew) to avoid the complication in canopy transpiration estimate. 3. Results and discussion We first analyzed the impact of the approximations of Eqs. (3)–(6) on f(H) values. We found that the differences between leaf surface and ambient air variable values during the selected time period were very small. Figs. 1 and 2 show the frequency distributions of Ca − Cs and (qsat(Ta ) − qa ) − (qsat(Tc ) − qs ), respectively, at SOA. Note that the leaf surface variables of Cs and qsat(Tc ) − qs were simulated by the EALCO model, and they represented the overall values at canopy level. Their values may have difference from those measured at individual leaves as discussed in Wang (2008). The results show that 90% of Ca − Cs was under 5 mol mol−1 , or less than 1.5% of the average ambient air CO2 concentration (364 mol mol−1 during the study period). During daytime with fairly high solar radiation, canopy temperature Tc was usually higher than Ta which leads to the higher qsat(Tc ) than qsat(Ta ) . On the other hand, qs is usually higher than qa due to the transpiration (water vapour source) of canopy leaves. As the result, the values of (qsat(Ta ) − qa ) were found close to (qsat(Tc ) − qs ). Among our data, 90% of the (qsat(Ta ) − qa ) − (qsat(Tc ) − qs ) values were within
S. Wang et al. / Ecological Modelling 220 (2009) 2115–2118
2117
Fig. 1. Frequency distributions of the differences of CO2 concentrations between ambient air (Ca ) and leaf surface (Cs ) during the selected study period at SOA.
±0.5 g kg−1 , or 7% of the average specific humidity deficit of the ambient air (7.2 g kg−1 during the study period). We also found that the differences between ambient air and leaf surface variables were slightly larger at SOA than at SOJP, mainly due to the stronger CO2 sink and water vapour source of dense canopies with high leaf area index (LAI) (i.e., SOA) than that of less dense canopies with low LAI (i.e., SOJP). Overall, the differences between Cs and Ca , and between (qsat(Ta ) − qa ) and (qsat(Tc ) − qs ) were small and it indicates the strong coupling between the canopy and the atmosphere due to the much higher aerodynamic conductance than canopy stomatal conductance. As a result, the substitutes of leaf surface variables by ambient air variables, mainly Cs by Ca and (qsat(Tc ) − qs ) by (qsat(Ta ) − qa ), were found to have small effects on f(H). However, in circumstances when coupling between canopy and the atmosphere is weak which results in relatively large differences in leaf surface and ambient air variable values (Leuzinger and Körner, 2007), the magnitudes of Ca − Cs and (qsat(Ta ) − qa ) − (qsat(Tc ) − qs ) and their impact on f(H) need to be further investigated. In general, if (qsat(Ta ) − qa ) − (qsat(Tc ) − qs ) becomes more positive, the weak coupling between canopy and the atmosphere will have less effect. Otherwise, f(H) will be likely overestimated. The impact of uncertainties in soil evaporation and R on f(H) varies among the three study sites. For dense canopies, the contribution of soil evaporation to total evapotranspiration is smaller than those of sparse canopies. The values of ε used in this study were 0.05, 0.12, and 0.25 at SOA, SOBS, and SOJP, respectively, estimated from soil evaporation measurement and modelling results (Blanken et al., 2001; Blanken and Black, 2004; Wang et al., 2009). Similarly, the respirations to photosynthesis ratios (R/A) were smaller at SOA than at SOJP, and their average values during our selected study period were 0.32, 0.51, and 0.53 at SOA, SOBS, and SOJP, respectively. The method for estimating R was tested using night time soil
Fig. 2. Frequency distributions of the differences between specific humidity deficits of ambient air (qsat(Ta ) − qa ) and leaf surface (qsat(Tc ) − qs ) during the selected study period at SOA.
Fig. 3. The response of canopy stomatal conductance to the relative humidity of ambient air at SOBS. The data points represent the 30-min values of f(Ha ) calculated by Eq. (6). The grey line represents the BWB model. The black curve represents Eq. (4).
CO2 efflux measurements in Kljun et al. (2006) which showed reasonably high confidence. The uncertainties in the estimates of soil evaporation and R are difficult to quantify accurately due to data limitation. Given the average quantities of ε and R/A stated above, errors of 10% in soil evaporation and R will result in the estimate error of f(H) less than 4%, 7%, and 9% at SOA, SOBS, and SOJP sites, respectively. We calculated f(H) using Eq. (6) and evaluated the performance of the four stomatal conductance models (BWB, Leuning, Eqs. (4) and (5)). Taken SOBS as an example, Fig. 3 shows the distribution of f(H) with ha together with the BWB model and Eq. (4), and Fig. 4 shows the distribution of f(H) with Da together with the Leuning model and Eq. (5). The results are highly consistent with those in Wang et al. (2009) where leaf surface variables were used in the f(H) calculation and soil evaporation and ecosystem respiration were estimated by the ecosystem model EALCO. The quantitative comparisons of model performance using Eq. (6) and that of Wang et al. (2009) were given in Table 1. In general, the approximation of Eqs. (3)–(6) resulted in higher scattering () and lower correlation coefficient (r) for all of the four models at the three study sites. This is in agreement with the result of Blanken and Black (2004) which showed that relating stomatal conductance to the humidity of ambient air rather than that of leaf surface increased the degree of scattering in g–humidity plots. However, the degradation of model
Fig. 4. The response of canopy stomatal conductance to water vapour pressure deficit of the ambient air at SOBS. The data points represent the 30-min values of the f(Ha ) calculated by Eq. (6). The grey curve represents the Leuning model. The black curve represents Eq. (5).
2118
S. Wang et al. / Ecological Modelling 220 (2009) 2115–2118
Table 1 Model test results. Model
f(Ha ) (this study)
Parameter
f(Hs ) (Wang et al., 2009)
˛
ˇ
n
r
8.5 15.5 1.8 350
– 350 −0.90 −0.65
6941 6956 6687 6923
0.59 0.77 0.82 0.87
(b) Southern Old Black Spruce (SOBS) ˛h (BWB) 8.7 ˛/(1 + D/ˇ) (Leuning) 17.6 1.9 ˛ (1 − h)ˇ (power-h) ˛Dˇ (power-D) 554
− 350 −1.1 −0.7
7219 7219 7091 7165
(c) Southern Old Jack Pine (SOJP) ˛h (BWB) ˛/(1 + D/ˇ) (Leuning) ˛ (1 − h)ˇ (power-h) ˛Dˇ (power-D)
− 350 −1.1 −0.75
6251 6395 6188 6374
(a) Southern Old Aspen (SOA) ˛h (BWB) ˛/(1 + D/ˇ) (Leuning) ˛ (1 − h)ˇ (power-h) ˛Dˇ (power-D)
a b c
7.8 16.3 1.55 800
a
rb
c
3.28 2.69 2.39 2.21
0.61 0.79 0.83 0.88
3.22 2.65 2.36 2.19
0.53 0.75 0.79 0.85
4.91 3.82 3.25 3.05
0.58 0.77 0.82 0.86
4.40 3.55 3.12 3.05
0.52 0.72 0.74 0.80
4.80 3.91 3.59 3.36
0.54 0.75 0.82 0.85
4.72 3.83 3.31 3.15
b
c
n: total number of data used in the analyses. Data with f(H) > 100 were excluded. r: correlation coefficient. : standard deviation.
performance was found fairly small. It indicates that ambient air variables and the empirical methods used in this study for correcting EC measurement to canopy level can be used in Eq. (6) to assess the response of canopy stomatal conductance to humidity with acceptable accuracy. Over the past two decades, large volume of EC flux measurements has been accumulated over most of the major biomes around the world. This study provides a useful approach to study the stomatal conductance–humidity relationships by using these large data resources. Acknowledgments Flux data used in this study were collected in Fluxnet Canada Research Network (FCRN) program. We thank Dr. A. Barr, Dr. T.A. Black, and Dr. H. McCaughey for their contributions in this study. This study was conducted in the ecosystem and water modelling activities in the “Enhancing Resilience in a Changing Climate Program” and the “Groundwater Mapping Program” of Earth Sciences Sector, Natural Resources Canada. References Arora, V.K., 2003. Simulating energy and carbon fluxes over winter wheat using coupled land surface and terrestrial ecosystem models. Agric. For. Meteorol. 118, 21–47. Ball, J.T., Woodrow, I.E., Berry, J.A., 1987. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. In: Biggens, J. (Ed.), Prog. Photosynth. Res., 4. Martinus-Nijhoff Publishers, Dordrecht, Netherlands, pp. 221–224. Barr, A.G., Black, T.A., Hogg, E.H., Kljun, N., Morgenstern, K., Nesic, Z., 2004. Interannual variability in the leaf area index of a boreal aspen-hazelnut forest in relation to net ecosystem production. Agric. For. Meteorol. 126, 237–255. Barr, A.G., Morgenstern, K., Black, T.A., McCaughey, J.H., Nesic, Z., 2006. Surface energy balance closure by the eddy-covariance method above three boreal forest stands and implications for the measurement of the CO2 flux. Agric. For. Meteorol. 140, 322–337. Betts, A.K., Goulden, M.L., Wofsy, S.C., 1999. Controls on evaporation in a boreal spruce forest. J. Climate 12, 1601–1618. Blanken, P.D., Black, T.A., Neumann, H.H., den Hartog, G., Yang, P.C., Nesic, Z., Lee, X., 2001. The seasonal water and energy exchange above and within a boreal aspen forest. J. Hydrol. 245, 118–136.
Blanken, P.D., Black, T.A., 2004. The canopy conductance of a boreal aspen forest, Prince Albert National Park, Canada. Hydrol. Process. 18, 1561–1578. Cowan, I.R., 1977. Stomatal behaviour and environment. Adv. Bot. Res. 4, 117–228. Cowan, I.R., Farquhar, G.D., 1977. Stomatal function in relation to leaf metabolism and environment. Symp. Soc. Exp. Biol. 31, 471–505. Cox, P., Huntingford, C., Harding, R., 1998. A canopy conductance and photosynthesis model for use in a GCM land surface model. J. Hydrol. 212–213, 79–94. Ewers, B.E., Oren, R., 2000. Analyses of assumptions and errors in the calculation of stomatal conductance from sap flux measurements. Tree Physiol. 20, 579–589. Gutschick, V.P., 2007. Plant acclimation to elevated CO2 – from simple regularities to biogeographic chaos. Ecol. Model. 200, 433–451. Gutschick, V.P., Simonneau, T., 2002. Modelling stomatal conductance of field-grown sunflower under varying soil water status and leaf environment: comparison of three models of response to leaf environment and coupling with an ABA-based model of response to soil drying. Plant Cell Environ. 25, 1423–1434. Kljun, N., Black, T.A., Griffis, T.J., Barr, A.G., Gaumont-Guay, D., Morgenstern, K., McCaughey, J.H., Nesic, Z., 2006. Response of net ecosystem productivity of three boreal forests stands to drought. Ecosystems 9, 1128–1144, doi:10.1007/s10021005-0082-x. Leuning, R., 1995. A critical-appraisal of a combined stomatal-photosynthesis model for C-3 plants. Plant Cell Environ. 18, 339–355. Leuzinger, S., Körner, C., 2007. Tree species diversity affects canopy leaf temperatures in a mature temperate forest. Agric. For. Meteorol. 146, 29–37. Mo, X., Liu, S., 2001. Simulating evapotranspiration and photosynthesis of winter wheat over the growing season. Agric. For. Meteorol. 109, 203–222. Oren, R., Sperry, J.S., Ewers, B.E., Pataki, D.E., Phillips, N., Megonigal, J.P., 2001. Sensitivity of mean canopy stomatal conductance to vapor pressure deficit in a flooded Taxodium distichum L. forest: hydraulic and non-hydraulic effects. Oecologia 126, 21–29, doi:10.1007/s004420000497. Stewart, J.B., 1988. Modelling surface conductance of a pine forest. Agric. For. Meteorol. 43, 19–35. Van Wijk, M.T., Dekker, S.C., Bouten, W., Bosveld, F.C., Kohsiek, W., Kramer, K., Mohren, G.M.J., 2000. Modeling daily gas exchange of a Douglas-fir forest: comparison of three stomatal conductance models with and without a soil water stress function. Tree Physiol. 20, 115–122. Wang, J., Miller, D.R., Sammis, T.W., Gutschick, V.P., Simmons, L.J., Andales, A.A., 2007. Energy balance measurements and a simple model for estimating pecan water use efficiency. Agric. Water Manage. 91, 92–101. Wang, S., 2008. Simulation of evapotranspiration and its response to plant water and CO2 transfer dynamics. J. Hydrometeorol. 9, 426–443, doi:10.1175/2007JHM918.1. Wang, S., Yang, Y., Trishchenko, A.P., Barr, A.G., Black, T.A., McCaughey, H., 2009. Modelling the response of canopy stomatal conductance to humidity. J. Hydrometeorol. 10, 521–532. Wu, A., Black, T.A., Verseghy, D.L., Blanken, P.D., Novak, M.D., Chen, W., Yang, P.C., 2000. A comparison of parameterizations of canopy conductance of aspen and Douglas-fir forests for CLASS. Atmos.-Ocean 38, 81–112.