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Chilean journal of agricultural research

On-line version ISSN 0718-5839

Chilean J. Agric. Res. vol.69 no.1 Chillán Mar. 2009 

Chilean Journal of Agricultural Research 69(1):88-96 (January-March 2009)


Model Validation for Estimating the Leaf Stomatal Conductance in cv. Cabernet Sauvignon Grapevines

Validación de un modelo para estimar la conductancia estomática de hojas en vides cv. Cabernet Sauvignon.

Francisco Jara-Rojas1, Samuel Ortega-Farías1*, Héctor Valdés-Gómez1, 2, Carlos Poblete1, and Alejandro del Pozo3

1 Universidad de Talca, Facultad de Ciencias Agrarias, Centro de Investigación y Transferencia en Riego y Agroclimatología (CITRA), Casilla 747, Talca, Chile.
2 Universidad de Talca, Facultad de Ingeniería, Escuela de Bioinformática, Casilla 747, Talca, Chile. Universidad de Talca, Facultad de Ciencias Agrarias, Departamento de Producción Agrícola, Casilla 747, Talca, Chile. *Corresponding Author (
3 Universidad de Talca, Facultad de Ciencias Agrarias, Departamento de Producción Agrícola, Casilla 747, Talca, Chile.


The coupled model of assimilation and stomatal conductance (A-gs) was evaluated to estimate leaf stomatal conductance of a drip-irrigated vineyard (Vitis vinifera L. cv. Cabernet Sauvignon) located in the Pencahue Valley (35º22’ S, 71°47’ W, 150 m.a.s.l.), Maule Region, Chile, during the 2003-2004 and the 2004-2005 growing seasons. Additionally, a calibration of the three parameters mesophyll conductance (gm), maximum specific humidity (Dmax) and coupled factor (f0) was applied on vines growing in 35 L pots. An infrared gas analyzer was used to calibrate and evaluate the A-gs which allowed simultaneous measuring of the leaf net CO2 assimilation (A) and stomatal conductance (gs) in 2 to 3 h intervals of time. The calibration indicated that the gm,, Dmax and f0 values were 1.15 mm s-1, 52.31 g kg-1 and 0.90, respectively. The validation in the drip-irrigated vineyard indicated that the A-gs model was able to estimate the leaf stomatal conductance with a root mean square error (RMSE) of 0.05 mol m-2 s-1, model efficiency of 61% and agreement index of 90%. The sensitivity analysis indicated that the A-gs model is affected considerably by the gm, Dmax and f0 parameterization.

Key words: A-gs model, photosynthesis, mesophyll conductance, stem water potential, sensitivity analysis.


Validación de un modelo para estimar la conductancia estomática de hojas en vides cv. Cabernet Sauvignon.  El modelo acoplado de asimilación neta y conductancia estomática (A-gs) fue evaluado para estimar la conductancia estomática de hojas (gs) de un viñedo regado por goteo (Vitis vinifera L. cv. Cabernet Sauvignon) ubicado en el Valle de Pencahue (35o22’ S; 71o47’ O; 150 m.s.n.m.), Región del Maule, Chile, durante las temporadas 2003-2004 y 2004-2005. Además, se realizó una calibración de la conductancia del mesófilo (gm), valor máximo de humedad específica a saturación (Dmax) y el factor acoplado (f0) en vides creciendo en maceteros de 35 L. Para calibrar y evaluar el modelo A-gs se utilizó un analizador infrarrojo de gases, el cual permitió medir simultáneamente la asimilación neta (A) y la conductancia estomática (gs) en intervalos de tiempo de 2 a 3 h. La calibración indicó que los valores de gm, Dmax y f0 fueron de 1,15 mm s-1; 52,31 g kg-1 y 0,90 respectivamente. La validación en el viñedo regado por goteo mostró que el modelo A-gs fue capaz de estimar la conductancia estomática con una raíz del cuadrado medio del error (RMSE) de 0,05 mol m-2 s-1, una eficiencia del modelo de 61% y un índice de acuerdo de 90%. El análisis de sensibilidad indicó que el modelo es considerablemente afectado por la parametrización de gm, Dmax y f0.

Palabras clave: modelo A-gs, fotosíntesis, conductancia del mesófilo, potencial hídrico del xilema, análisis de sensibilidad.


Recent research indicates that it is possible to directly estimate water use or actual evapotranspiration (ET) of crops without using crop coefficients (Olioso et al., 2005; Ortega-Farias et al., 2004; 2007). Soil-vegetation-atmosphere transfer (SVAT) models which require soil and climate information, as well as canopy characterization have been suggested for the ET estimation for diverse vegetal species (Olioso et al., 2005). Recent versions of SVAT models incorporate mathematical formulations of leaf stomatal conductance (gs) which regulate gas exchange (CO2 and water) depending on atmospheric and soil water conditions. Among the many mathematical algorithms to estimate gs we can mention the Jarvis model (1976), which uses climate variables such as incident solar radiation, air temperature, relative humidity and soil water content as its input. Collatz et al. (1991) proposed the use of the CO2 assimilation rate by Farquhar’s model as an input parameter for estimating gs (Farquhar et al., 1980). This model formulation improved the estimation of gs because it included the non-linear interaction between transpiration and net CO2 assimilation. Jacobs (1994) proposed a coupled model of net assimilation (A-gs) to estimate gs in vine leaves. The A-gs model, unlike the one proposed by Jarvis, includes, a description of synergistic interactions among CO2 concentration, atmospheric variables and plant factors. Hence, the A-gs model gives an adequate response to the climatic changes produced by the systematic increase of CO2 in the atmosphere (Jacobs et al., 1996; Calvet et al., 1998b; Calvet, 2000; Calvet et al., 2004).

The A-gs model has been successfully applied to grapevines cv. Airen (Jacobs et al., 1996), discovering that this model was able to predict gs of vine leaves with an experimental error of 16% and a maximum deviation of 4.0 mm s−1 (0.16 mol m-2 s-1). On the other hand, studies by Calvet et al. (1998b) indicate that the A-gs model is sensitive to the parameterization of mesophyll conductance (gm) and internal CO2 concentration. In order to improve the performance of the A-gs model, Calvet et al. (2004) made a non-linear optimization of both gm and of the function that determines the CO2 concentration within the stomatal cavity. In practical terms, the quantification of gs is complex because temporal variability of stomatal conductance is considerable due to changes in environmental, soil and plant conditions (Baldocchi et al., 1991). For well-irrigated grapevines under field conditions, gs values could widely range from 0.6 to 0.1 mol m-2 s-1 (15 mm s-1 to 2.5 mm s-1, respectively) which is mainly affected by the cultivar (Pire and Ojeda, 1999).

Due to the scarcity of information about leaf stomatal conductance formulation, which can be used in SVAT models to directly estimate vine evapotranspiration, the objective of this research was to evaluate the A-gs model in order to estimate the leaf stomatal conductance for a drip-irrigated Cabernet Sauvignon vineyard under semi-arid conditions.

Description of the A-gs model
The estimation of leaf stomatal conductance can be expressed as (Jacobs et al., 1996):

where, gs is the conductance to water vapour flux through the stomata (mol m-2 s-1), 1.6 represents the relationship between the CO2 diffusivity and water vapour in the air, A is the net CO2 assimilation (µmol m-2 s-1), Cs is the CO2 concentration on the surface adjacent to the leaf (μmol mol-1) and Ci is the CO2 concentration in the interior of the stomatal cavity (μmol mol-1). Ci can be calculated using Equations [2] and [3] (Jacobs et al., 1996; Calvet et al., 1998b):

where, f0 is a coupled factor when Ds = 0 g kg-1, Ds is the specific humidity deficit between the sub-stomatal cavity and the atmosphere (g kg−1), Dmax is the maximum specific humidity at saturation (g kg−1), qs is the specific humidity in the atmosphere near the leaf surface (g kg-1), q*(Ts) is the specific humidity in saturation (g kg-1) at the leaf temperature Ts (ºC) and Γ is CO2 compensation point (μmol mol-1). In this case it is assumed that the stomatal cavity, where the gaseous exchange with the atmosphere takes place, is permanently saturated.

Net CO2 assimilation (µmol m-2 s-1) can be estimated according to the saturation equation (Calvet et al., 1998b):

where, Am is net assimilation as a function of CO2 (mg m-2 s-1), Rd is the leaf respiration (mg m-2 s-1), Ia is the photosynthetically active radiation (PAR) that reaches the leaf (µmol m-2 s-1), ε is the initial quantum use efficiency (mg CO2 [J PAR]-1), Fc is the conversion factor between the PAR that reaches the leaf and its associated energy (Fc = 0.22 J PAR µmol-1, in accordance to the relation of 1 mol of photons ≡ 0.22 MJ PAR [Thornley and Johnson, 2000]), and FCO2 is the conversion factor between mass unit and molar unit of CO2 (22.727 µmol CO2 [g CO2]-1).

The net assimilation as a function of CO2 (mg m-2 s-1) can be expressed through the following equation (Calvet et al., 2004):

where, Am,max is the maximum net CO2 assimilation (mg m-2 s-1), gm is mesophyll conductance (mm s-1) and ΦCO2 is a conversion factor  (ΦCO2 = 1.799 mg CO2 m-3 at 25 ºC and 1 atm).

The leaf respiration, Rd (mg m-2 s-1), is calculated as (Calvet et al., 2004):

The initial quantum use efficiency (mg CO2 [J PAR]-1) is defined as (Jacobs et al., 1996; Calvet et al., 1998b; 2004):

where, ε0 is the maximum quantum use efficiency (mg CO2 [J PAR]-1).

The values of Γ, Am,max and gm are adjusted according to the leaf temperature (Ts) by the functions Q10 as shown in Equations [8] and [9] (Jacobs et al., 1996; Calvet et al., 1998b):

where, X(@25) is the value of the parameters at 25 ºC (Table 1), Q10 is a relationship for the effect of temperature on a process such that the process rate increases by the same multiple for every 10ºC rise in temperature. Ts is the leaf temperature (ºC), T1 is the inferior reference temperature (ºC) and T2 is the superior reference temperature (ºC). The temperature adjustment for Γ was performed using Equation [8], and for Am,max and gm was performed using Equation [9]. The summary of the input parameters is shown in Table 1.

Table 1. Input parameters used in the coupled assimilation-stomatal conductance (A-gs) model for vines.


With the purpose of evaluating the estimations of gs using the A-gs model, an experiment was carried out during the 2003-2004 and 2004-2005 growing seasons. Data were registered between January and March in a drip-irrigated commercial vineyard with 11-year-old Cabernet Sauvignon vines without grafting. The vineyard is located in the Pencahue Valley (35º22’ S; 71º47’ W; 150 m.a.s.l.), Maule Region, Chile. The vine spacing was 3.0 m between rows x 1.2 m within rows, with plants trained on a vertical shoot-positioned system and bilateral-cordon pruned (20 buds m−1) with vine rows oriented 18º W in relation to the N-S axis.

The climate of the area is semi-arid Mediterranean with maximum and minimum average daily temperature of 32.6 and 5.5 ºC, respectively. The annual average precipitation reaches 709 mm, and the water deficit reaches 863 mm, with a dry period of 7 months. The details of the climatic conditions during the measurement period are summarized in Figure 1. The soil in the vineyard is classified as Cunculén Series (Aquic Palexeralfs) with a sandy loam texture and an effective root depth of 60 cm. At this point, the bulk density, field capacity, wilting point and available water are at 1.48 g cm-3, 30% (180 mm), 11% (66 mm) and 19% (114 mm), respectively. The irrigation schedule was determined according to the daily ET values of the vineyard (Acevedo et al., 2005) and the water supply was made using 3.5 L h-1 drippers spaced at 1.2 m.

Figure 1 . Micrometeorological characterization of experimental area in Pencahue Valley during the 2003-2004 (left) and 2004-2005 (right) growing seasons. A and B: solar radiation (Rg, W m-2); C and D: temperature (T, ºC); E and F: vapour pressure deficit (DPV, kPa); G and H: wind speed (u, km h-1). Each point represents an average of at least 5 days of measurements. Vertical bars represent mean standard error. CLT: Chilean local standard time.

An automatic meteorological station (Adcon Telemetry, model A730, Klosterneuburg, Austria) was installed in the vineyard to measure air temperature, relative humidity, solar radiation, precipitation, wind velocity and direction at 30 min intervals. The sensors were located at 2.5 m above the ground, with the exception of the temperature and relative humidity sensors that were located within the canopy at 1.5 m above ground, and the pluviometer was located at 3 m above ground.

An infrared gas analyzer (ADC BioScientific Ltd., model LCi, Hoddesdon, UK) was used to measure the daytime variation of photosynthetically active radiation (PAR), stomatal conductance (gs), transpiration (E) and net CO2 assimilation (A) from 30 healthy leaves as well as other variables related to gas exchange (Ci, Cs, Ts and Ds). The measurements of gas exchange were made between 08:00 and 20:00 h at regular intervals (every 2 or 3 h) during the both growing seasons. At the same time, the midday stem water potential (Ψx) was measured using a pressure chamber (PMS Instrument Co., model 600, Corvallis, Oregon, USA) (Choné et al., 2001). In this case, six full expanded leaves were encased in plastic bags and then wrapped in aluminium foil at least 2 h before taking the measurements, these were taken between 13:00 and 14:00 h (Ortega-Farías et al., 2004). For measurements of each gas exchange and plant water status leaves were chosen from the middle zone of the canopy and had east and west sunlight exposure, respectively (Jacobs et al., 1996; Moutinho-Pereira et al., 2004).

The database of gas exchange was submitted to an exploratory data analysis to determine the existence of measurement errors. Data were removed from the dataset when: (i) temperature within the infrared gas analyzer chamber was over 42 ºC (Jacobs, 1994) and (ii) when they exceed a reference value of mean ± 2 standard deviations.

Prior to the evaluation of the model, values of gm, Dmax and f0 were calibrated with 6-year-old vines growing in 35 L pots. In order to achieve this objective, an experiment was conducted at the ‘Panguilemo’ Experimental Station (36º26' S, 71º41' W; 110 m.a.s.l.) belonging to Universidad de Talca, Maule Region, during the 2004-2005 growing season. Sixteen own-rooted vines (Vitis vinifera L., cv. Cabernet Sauvignon) were used in the experiment and four vines were randomly selected for measuring gas exchange. A commercial organic soil was used as pot substrate. The bulk density, field capacity and wilting point of the substrate were 0.6 g cm-3, 37% (167 mm) and 12% (54 mm), respectively. The sixteen pots were distributed outdoors in rows with N-S orientation and spaced at 3 x 1 m. Each pot was covered with white plastic to minimize soil evaporation and to lessen heating from solar exposure. The vines were trained on a vertical shoot-positioned system and were pruned in bilateral cordons. The evaluations were carried out post-setting from the end of November to February. Due to the crop load variability among the vines observed in previous seasons, all the clusters were reaped before berry set. The irrigation scheduling was determined using the same criteria used at the field experiment (Acevedo et al., 2005). Data of the gas exchange, stem water potential and climatic variables were measured using the same equipment and frequency as described in the field experiment.

The calibration of gm, Dmax and f0 was performed using a non-linear optimization method that consisted of minimizing the root mean square error (RMSE) between the observed and the estimated values of net CO2 assimilation (Calvet et al., 1998a; 1998b; 2004; Calvet, 2000). Using the calibrated values of gm, Dmax and f0, and the constant parameters from literature (Table 1), the performance of A-gs model was evaluated with data measured from the drip-irrigated Cabernet Sauvignon vineyard located in the Pencahue Valley. The evaluation of the model was done using the RMSE, agreement index (AI) and model efficiency (EF) (Willmott, 1982; Mayer and Butler, 1993) between the observed and the estimated values of A and gs. Finally, a sensitivity analysis of the A-gs model was carried out varying the values of ε0, f0, Γ, gm, Am,max and Dmax by ± 30% to detect the critical parameters of the model.


Environmental conditions and vine water status
The maximum and minimum air temperatures were 37.6 and 9 °C, respectively, in the 2003-2004 growing season, and 38.0 and 5.9 °C, in the 2004-2005 growing season. For both of these, the minimum temperature occurred between 07:00 and 08:00 h and the maximum temperature was reached between 16:00 and 17:00 h (Figure 1C and 1D). The maximum vapour pressure deficit ranged around 4.5 kPa in both seasons and was registered in the same hours the maximum temperatures were observed. Cloud cover during the days in which measurements were taken was less than 10%, which provided an adequate sunlight exposure to the plants (Figure 1A and 1B). Total rainfall from budbreak to harvest was 120 and 131 mm for the 2003-2004 and 2004-2005 growing seasons, respectively, where over 80% of the total rainfall was concentrated in spring.

The measured values of midday stem water potential in both study seasons ranged between -0.5 and -1.0 MPa with the lowest values of Ψx being observed between veraison and harvest in the 2004-2005 growing season (Figure 2). These Ψx values indicate that vines were not subject to significant water stress during both study periods (Ortega-Farias et al., 2007).

Figure 2. Evolution of midday stem water potential (Ψx) during the experiment (Cabernet Sauvignon vines, 2003-2004 and 2004-2005 growing seasons, Pencahue, Maule Region, Chile)

Model evaluation and sensitivity analysis
The non-linear optimization made with the data obtained from the potted vines indicated that the values of gm, Dmax and f0 were 1.15 mm s-1, 52.31 g kg-1 and 0.90, respectively. These were in the range of values reported by Calvet et al. (2004) for fruit trees, where gm varied between 0.21 and 8.5 mm s-1, Dmax between 20 and 300 g kg-1 and f0 between 0.434 and 0.90. These results differed from those found by Jacobs (1994) and Jacobs et al. (1996) who indicated values for gm, Dmax and f0 in Airen vines equivalent to 2.0 mm s-1, 58.2 g kg-1 and 0.92, respectively. Likewise, gm is different from the value of 2.5 mm s-1 obtained by Düring (2003) for Riesling vines. This difference in the values of gm could be associated with specific characteristics of each cultivar as it was pointed out by Patakas et al. (2003). These researchers studied the photosynthetic rates of three vine cultivars (Syrah, Athiri, and Asyrtiko) during different phenological stages and observed that the differences among them could be explained by, among other factors: i) their inherent anatomical differences (thickness of the spongy and palisade parenchyma, fraction of inter-cellular space), ii) the age of the leaf, and iii) the differences in the resistance of the liquid-CO2 phase of the leaves. From this same study, it can be inferred that the value of the mesophyll conductance, corresponding to the stem water potential measured in our study was near 0.9 mm s-1, which is close to the optimized value for cv. Cabernet Sauvignon. The prior information indicates that the cultivar, plant water status and leaf age are factors to consider when studying gas exchange over time. In a global study of 32 databases of agricultural, forestry and ornamental plants, Calvet et al. (2004) proposed that there is a relationship between gm and f0, that would be stable among species under study. This relation provides a value of gm = 1.0 mm s-1 for f0 values close to 0.9, like those obtained in the present study.

The field comparison indicated that A and gs models presented RMSE values of 2.28 μmol m-2 s-1 and 0.05 mol m-2 s-1 for net CO2 assimilation and gs, respectively (Table 2). These values are similar to those observed in pine trees by Calvet et al. (2004), who indicated that the models were capable of predicting net CO2 assimilation and gs with RMSE values of 2.95 μmol m-2 s-1 and 0.03 mol m-2 s-1, respectively. In this study, the model efficiency values were greater than 60% and the agreement index exceeded 90%, which indicates a good performance of the A-gs model (Garnier et al., 2001). Figure 3 shows that estimations of net CO2 assimilation showed more variability around the 1:1 line than those of gs, and the values of gs were underestimated for observed values of gs greater than 0.3 mol m-2 s-1.

Table 2. Statistical analysis for the leaf net assimilation and stomatal conductance models (cv. Cabernet Sauvignon).

Figure 3. Comparison between observed and estimated values of net assimilation (A) and stomatal conductance (gs) (Cabernet Sauvignon grapevines, 2003-2004 and 2004-2005 growing seasons. Pencahue, Maule Region, Chile).

The sensitivity analysis suggested that A-gs model is highly sensitive to errors in the parameterization of gm Dmax and  f0 (Table 3). In this case, an error of ± 30% in the values of gm Dmaxy and f0 would respectively produce variations in the simulation of gs between 17.9 and -21.5%, 33.3 and -40.1% and -241 and -51%, respectively. On the other hand, the model presented a low sensitivity to the parameterization of Am,max, Γ and ε0. These results positively confirm the choice made of calibrating gm, Dmax and f0, which had been suggested by Calvet et al. (2004) to achieve a better performance of the A-gs model to simulate the leaf stomatal conductance.

Table 3. Sensitivity analysis for net assimilation and stomatal conductance models of vine leaves (cv Cabernet Sauvignon).


Daytime variation of stomatal conductance and net CO2 assimilation
For the two study periods, the Figures 4 and 5 indicate that estimated and observed values of A and gs were close from 8:00 h to 18:00 h. The measured values of gs and net CO2 assimilation of leaves are in the ranges reported by literature for a great number of vine cultivars (Jacobs et al., 1996; Pire and Ojeda, 1999; Patakas et al., 2003; Düring, 2003; Singsaas et al., 2003). However, not many studies indicate the effect of leaf position or leaf orientation inside the canopy on the magnitude of the measurements. Related to this, Jacobs et al. (1996) reported for grapevines (cv. Airen), maximum values of gs equal to 0.29 mol m-2 s-1 for the shaded side of the canopy and 0.33 mol m-2 s-1 for the sunlit side.  Maximum assimilation values were 5.7 μmol m-2 s-1 for the shaded side of the canopy and 15.6 μmol m-2 s-1 for the sunlit side. These values are very close to those measured in our research for cv. Cabernet Sauvignon.

Figure 4. Daytime variation of net assimilation (A) of sunlit and shaded leaves for one day each season: 6 February, 2004 (A and C) and  8 February, 2005 (B and D). Each point represents average of three replicates. Cabernet Sauvignon grapevines, Pencahue, Maule Region, Chile. Vertical bars represent mean standard error. CLT: Chilean local standard time.

Figure 5. Daytime variation of stomatal conductance (gs) of sunlit and shaded leaves for one day each season: 6 February, 2004 (A and C) and 8February, 2005 (B and D). Each point represents average of three replicates. Cabernet Sauvignon grapevines, Pencahue, Maule Region, Chile. Vertical bars represent mean standard error. CLT: Chilean local standard time.

Good daytime performance to estimate leaf stomatal conductance to water vapour suggests that A-gs model could be used in the mathematical algorithm of SVAT models to directly estimate grapevine water use. This allows for studying the mid and long-term impact of global climatic change in the vine water requirement, which is very important to optimize the water application at farm and regional level.


The results of this study indicate that the A-gs model was able to estimate stomatal conductance of vine leaves (cv. Cabernet Sauvignon) with a root mean square error (RMSE) of 0.05 mol m-2 s-1, model efficiency of 61% and an agreement index of 90%. The model reproduces, in general terms, the daytime variation of stomatal conductance in both sides of the vineyard canopy (sunlit and shaded side). The calibration indicated that values of gm, Dmax and f0 were 1.15 mm s-1, 52.31 g kg-1 and 0.90, respectively. Also, the sensitivity analysis suggested that the A-gs model is considerably affected by the errors in the parameterization of gm, Dmax and f0.


The research study leading to this report was supported by the Chilean projects FONDECYT Nº 1030314 and Bicentenario PSD-86/2006.


Acevedo, C., S. Ortega-Farías, C. Hidalgo, Y. Moreno, y F. Córdova. 2005. Efecto de diferentes niveles de agua aplicada en poscuaja y pospinta sobre la calidad del vino cv. Cabernet Sauvignon. Agric. Téc. (Chile) 6:397-410.         [ Links ]

Baldocchi, D.D., R.J. Luxmoore, and J.L. Hatfield. 1991. Discerning the forest from the trees: an essay on scaling canopy stomatal conductance. Agric. For. Meteorol. 54:197-226.         [ Links ]

Calvet, J.-C. 2000. Investigating soil and atmospheric plant water stress using physiological and micrometeorological data. Agric. For. Meteorol. 103:229-247.         [ Links ]

Calvet, J.-C., J. Noilhan, and P. Bessemoulin. 1998a. Retrieving the root-zone soil moisture from surface soil moisture or temperature estimates: a feasibility study based on field measurements. J. Appl. Meteorol. 37:371-386.         [ Links ]

Calvet, J.-C., J. Noilhan, J.-L. Roujean, P. Bessemoulin, M. Cabelguenne, A. Olioso, and J.-P. Wigneron. 1998b. An interactive vegetation SVAT model tested against data from six contrasting sites. Agric. For. Meteorol. 92:73-95.         [ Links ]

Calvet, J.-C., V. Rivalland, C. Picon-Cochard, and J.-M. Guehl. 2004. Modeling forest transpiration and CO2 fluxes-response to soil moisture stress. Agric. For. Meteorol. 124:143-156.         [ Links ]

Choné, X., C. Van Leeuwen, D. Dubourdieu, and J.P. Gaudillère. 2001. Stem water potential is a sensitive indicator of grapevine water status. Ann. Bot. (London) 87:477-483.         [ Links ]

Collatz, G.J., J.T. Ball, C. Grivet, and J.A. Berry. 1991. Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: a model that includes a laminar boundary layer. Agric. For. Meteorol. 54:107-136.         [ Links ]

Düring, H. 2003. Stomatal and mesophyll conductances control CO2 transfer to chloroplasts in leaves of grapevine (Vitis vinifera L.). Vitis 42:65-68.         [ Links ]

Farquhar, G.D., S. von Caemmerer, and J.A. Berry.1980. A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149:78-90.         [ Links ]

Garnier, P., C. Néel, B. Mary, and F. Lafolie. 2001. Evaluation of a nitrogen transport and transformation model in bare soil. Eur. J. Soil Sci. 52:253-268.         [ Links ]

Jacobs, C.M.J. 1994. Direct impact of atmospheric CO2 enrichment on regional transpiration. 179 p. Ph.D. Thesis. Agricultural University, Wageningen, The Netherlands.         [ Links ]

Jacobs, C.M.J., B.J.J.M. van den Hurk, and H.A.R. de Bruin. 1996. Stomatal behaviour and photosynthetic rate of unstressed grapevines in semi-arid conditions. Agric. For. Meteorol. 80:111-134.         [ Links ]

Jarvis, P.G. 1976. The interpretation of the variations in leaf water potential and stomatal conductance found in canopy in the field. Phil. Trans. Roy. Soc. Lond. B. 273:593-610.         [ Links ]

Mayer, D.G., and D.G. Butler. 1993. Statistical validation. Ecol. Model. 68:21-32.         [ Links ]

Moutinho-Pereira, J.M., C.M. Correia, B.M. Gonçalves, E.A. Bacelar, and J.M. Torres-Pereira. 2004. Leaf gas exchange and water relations of grapevines grown in three different conditions. Photosynthetica 42:81-86.         [ Links ]

Olioso, A., S. Ortega-Farías, H. Valdés, y R. Antonioletti. 2005. Estimación de la evapotranspiración en tomate usando el modelo de interacción suelo-vegetación-atmósfera (ISBA). Agric. Téc. (Chile) 65:284-294.         [ Links ]

Ortega-Farias, S., M. Carrasco, A. Olioso, C. Acevedo, and C. Poblete. 2007. Latent heat flux over a Cabernet Sauvignon vineyard using the Shuttleworth and Wallace model. Irrig. Sci. 25:161-170.         [ Links ]

Ortega-Farías, S., A. Olioso, R. Antonioletti, and N. Brisson. 2004. Evaluation of the Penman-Monteith model for estimating soybean evapotranspiration. Irrig. Sci. 23:1-9.         [ Links ]

Patakas, A., G. Kofidis, and A.M. Bosabalidis. 2003. The relationships between CO2 transfer mesophyll resistance and photosynthetic efficiency in grapevine cultivars. Sci. Hortic. (Canterbury, Engl.) 97:255-263.         [ Links ]

Pire, R., and M. Ojeda. 1999. Effects of the irrigation regime on water relations of a table grape and two wine grape cultivars in a semiarid region of Venezuela. Acta Hort. (ISHS) 493:97-102.         [ Links ]

Sibille, I., H. Ojeda, J. Prieto, S. Maldonado, J.N. Lacapere, and A. Carbonneau. 2007. Relation between the values of three pressure chamber modalities (midday leaf, midday stem and predawn water potential) of 4 grapevine cultivars in drought situation of the southern of France. Applications for the irrigation control. p. 685-695. In Proceeding of the XVth Conference of Groupe d’Etude des Systèmes de Conduite de la Vigne (GESCO), Porec, Croacie. 20-23 June 2007.         [ Links ]

Singsaas, E.L., D.R. Ort, and E.H. DeLucia. 2003. Elevated CO2 effects on mesophyll conductance and its consequences for interpreting photosynthetic physiology. Plant Cell Environ. 27:41-50.         [ Links ]

Thornley, J.H.M., and I.R. Johnson. 2000. Plant and crop modelling: A mathematical approach to plant and crop physiology. 669 p. The Blackburn Press, Caldwell, New Jersey, USA.         [ Links ]

Willmott, C.J. 1982. Some comments on the evaluation of model performance. Bull. Am. Meteorol. Soc. 63:1309-1313.         [ Links ]


Received:  30 November 2007                                            Accepted: 21 April 2008

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