Measurements of leaf gas exchange and water relations were performed in 1998 within an irrigation experiment conducted in an 18-year-old olive (*Olea europaea* L., cv Picual) orchard located at the CIFA Experimental Station, Cordoba, Spain (38°N, 4·8°W, 110 m altitude). Tree arrangement was 6 m × 6 m and the four differential irrigation treatments, which started in 1997, were:

#### Gas exchange measurements

Net photosynthesis (*A*) and leaf conductance (*g*_{l}) were measured using a portable open infrared gas analyser (CIRAS-1; PP System, Hitchin, Herts, UK) and fitted to a Parkinson leaf chamber operated at 250 mL min^{−1}. The leaf chamber was specially designed for measurements in olive leaves and covered an exposed area of 1·75 cm^{2}. Readings were taken after steady-state conditions in gas exchange were achieved (around 1 min). The CO_{2} concentration inside the chamber was automatically controlled by the CIRAS-1 porometer at 350 *µ*mol mol^{−1}, whereas the radiation, temperature and evaporative demand were those of ambient conditions. Carbon dioxide and water vapour concentration differences between the inlet and outlet gas circulating through the leaf chamber, as well as leaf temperatures obtained from energy balance equations, were used to calculate leaf area based rates of CO_{2} assimilation (*A*), transpiration (*T*) and stomatal conductance (*g*_{l}) using von Caemmerer & Farquhar’s equation (von Caemmerer & Farquhar 1981), taking into account that olive is a hypostomatous species. Transpiration efficiency (TE) was calculated as the ratio of leaf photosynthesis to transpiration as measured instantaneously with the CIRAS-1 porometer. The VPD values used in modelling *g*_{l}, were calculated using the air humidity and temperature measured with the CIRAS-1. Such VPD values exceeded those measured in a weather station nearby (300 m away from the experimental orchard) by about 0·8 kPa.

For gas exchange, three fully expanded, sunlit leaves in four trees per treatment were randomly selected and measurements of *A* and *g*_{l} started in mid-June, 1998. Diurnal cycles were performed with the porometer on 25 June, 7 July, 29 July, 20 August, 14 September, 21 September, 2 October and 14 October 1998. In addition, gas exchange measurements were routinely performed in the morning (0700–0800 h GMT) and at midday (1300–1600 h GMT), at least once a week, from June until mid-October.

#### Leaf conductance models

Two models were evaluated to compute leaf conductance in olive trees; the model proposed by Jarvis (1976) hereafter termed the J model, and the model of Leuning (1995) hereafter named the L model.

The J model is defined in general form as:

- (1)

where *g*_{l} is the leaf conductance and *g*_{max}, is the maximum leaf conductance under optimal conditions of temperature and ambient humidity and also, under maximum *A*.

Jarvis (1976) defined *f*(*i*) as empirical functions to characterize the influence of various environmental factors on *g*_{l}. Each function provides a value between 0 and 1.

In our J model, the effects of specific humidity deficit (*H*_{S}) are defined as:

- (2)

- (3)

where *K*_{D} and *D*_{C} are constants that are optimized using the experimental data.

The effect of radiation are computed as:

- (4)

where *K*_{R} is a constant and *I* is the photosynthetically active radiation (PAR; W m^{−2})

The temperature function is:

- (5)

- (6)

where *K*_{T} is a constant that the model optimizes; *T* is the leaf temperature; *T*_{H} is an upper temperature limit (50 °C) and *T*_{L} is a lower temperature limit (0 °C)

The effect of water deficits are defined as:

- (7)

where *K*_{p} is a constant; *Ψ* is the midday stem water potential and *Ψ*_{max} is the maximum value of *Ψ*, assumed to be −0·5 MPa based on our observations.

- (8)

where, *a*, *g*_{0} and *D*_{0} are constants, *D* is the VPD (kPa); *c*_{s} is the CO_{2} concentration at the leaf surface (p.p.m) and *Γ* is the CO_{2} compensation point. The first two variables (*D* and *c*_{s}) were measured with the CIRAS-1 porometer at the same time as *g*_{l} and *A*. The value of *Γ* was taken as 46 *µ*mol mol^{−1}, obtained by Bongi & Palliotti (1994) in potted olive trees. We observed that the *D*_{0} values varied with the optimization interval used. Leuning, Dunin & Wang (1998) and Van Wijk *et al*. (2000) reported that the L model had low sensitivity to variations in *D*_{0}. Therefore, we used a constant value of 3·5 kPa for *D*_{0} (Leuning *et al.* 1995) and then obtained the values for the other constants.

To include the effects of water deficits in the L model, we tested another model (hereafter model L*Ψ*) by incorporating Eqn 7 into Eqn 8 as:

- (9)

The *A* and *g*_{l} data described above were used in the calibration and verifications of the models. Experimental *A* and *g*_{l} values for T1 and T2 were used for model calibrations. *A* and *g*_{l} data from T3 and T4 were used for model verification under conditions of moderate (T3) and severe (T4) water stress. Data from the diurnal cycles were also used to verify the model under a different set of environmental conditions.