2.1 The experimental site
The study was carried out in the period 26 June – 30 September 2022, including the most evaporative demanding periods in the site (Katerji et al. 2017). The olive orchard (cv. Arbosana) is located at the University of Bari experimental farm, southern Italy (41° 01’ N; 16° 45’ E; 110 m a.s.l.), on a shallow sandy clay soil (sand 630 g kg− 1; silt 160 g kg− 1; clay 210 g kg− 1) classified as a Typic Haploxeralf (USDA) or Chromi-Cutanic Luvisol (FAO). At 0.5 m of depth is present a parent rock that reduces the capacity of the root systems to expand beyond this layer. The site is characterised by typical Mediterranean climate with a long-term average (1988–2018) annual rainfall of 560 mm, two third concentrated from autumn to winter, and a long-term average annual temperature of 15.6°C. The olive grove has been planted in early summer 2006; the self-rooted trees were trained according to the central leader system and spaced 4.0 m × 1.5 m (1,667 trees ha− 1) with a North–South rows orientation. Trees were 1.75 ± 0.46 m high. Routine nutrition and soil management, pests and diseases control practices were set up as described by Camposeo and Godini (2010). Irrigation was scheduled following the FAO56 guideline (Allen et al. 1998), restoring 100% of crop evapotranspiration. The plots were irrigated by a dripline equipped with 2.5 L h− 1 emitters, 0.6 m apart.
Air temperature (Tair, °C) and vapour pressure deficit (D, kPa) through air relative humidity, global radiation (Rg, W m− 2) and precipitation (P, mm), wind speed (u, ms− 1) were collected at a standard agrometeorological station 120 m far from the experimental field. Net Radiation Rn in Wm− 2, was calculated following Rana and Katerji (2009) as:
$$Rn=\left(1-\alpha \right){R}_{g}-\sigma \left(\frac{{T}_{max}^{4}+{T}_{min}^{4}}{2}\right)\left(0.34-0.15\sqrt{{e}_{a}}\right)\left(1.35\frac{{R}_{g}}{{R}_{g0}}-0.35\right)$$
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where α is the albedo of the crop, directly determined on the orchard as mean of hourly daytime values (0.27) from January to December 2021; Tmax and Tmin (K) are maximal and minimal air temperatures; ea (kPa) is the actual vapour pressure; and Rg0 (MJ m− 2) is the calculated clear-sky radiation (Allen et al. 1998). After a local calibration of twelve months (January-December 2021), soil heat flux G, was considered as a constant at daily scale and equal to 0.09 Rn.
Soil water content in volume (θ, m3 m− 3) was measured by capacitive probes (5TM, Decagon Devices Inc., USA). Three points were monitored following the protocol described in Campi et al. (2020): two points in the rows to intercept the dynamics of θ below the dripping lines, and one point among the rows. At each point, two capacitive probes were installed horizontally into the soil profile and transversely to the row, at -0.12 and − 0.37 m from the soil surface. All sensors were connected to data-loggers (Tecno.el srl, Italy) and acquired at hourly scale; daily soil water content was determined for the soil profile (0.5 m) by integrating the values measured at each depth, since each probe was supposed to detect the water content in a 0.25 m soil layer. θ measurements from the three points were pooled to obtain a single average value for each treatment.
2.2 The TDM method
The transpiration at tree level, as determined by TDM, foresees the measurement of difference in temperature (ΔT, °C) between two probes placed in the conducting xylem of the stem; when the sap flow is low, or close to zero, a maximum difference in temperature (ΔTmax) is recorded and the variable K [unitless] was calculated as:
$$K=\frac{{\varDelta T}_{max}-\varDelta T}{\varDelta T}$$
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ΔT max was determined using night-time measurements, separately for each sensor, according to Lu et al. (2003) and Peters et al. (2010).
Commercial 20 mm sap flow probes (SFS2 Type M, UP, Steinfurt, Germany) were installed at 0.30–0.40 m height above the ground. Probes were installed in each sampled tree in the north side to avoid direct solar heating; to prevent thermal interference, the heated probe was inserted 0.10 m above the unheated one; the probes in each sampled tree were covered by a reflecting radiation screen which also protected them from rain. ΔT was continuously monitored by a data loggers (CR10X, Campbell Scientific, Utah, USA) every 10 s, and the average values recorded every 10 min, to be further averaged at hourly scale.
The sap flow density (Js0, gm− 2s− 1) was determined by the relation (Granier 1985; Lu et al. 2003):
with a and b determined by specific calibration as detailed in the following. Measurements were carried out in three replicate trees chosen to be representative of the olive orchard, considering the similar vigour, according to frequency distribution of trunk diameters and tree size of whole plot.
2.3 The TDM species-specific local calibration
According to Alarcón et al. (2005), McCulloh et al. (2007) and Zhou et al. (2017), the calibration to find the specific coefficients a and b in the Eq. (3) was carried out on three 5-year-old trees of the investigated variety (Arbosana) cultivated in pots placed in plastic cylindric pots (diameter 0.45 m, height 0.66 m) filled by the same soil of the experimental field and mulched by a plastic film to avoid soil evaporation. Sap flow density Js0 was computed as
$${J}_{s0}=\frac{{Tr}_{m}}{SWA}$$
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where Trm is the measured transpiration (gs− 1) determined by recording the weight loss in the pots at 150 minutes intervals, for one week (15–21 July 2022) during daytime, with an electronic balance (Radwag, Poland, model C315.150.C5.K). Every 150 minutes, the pot weights were obtained by averaging measurements carried out every one minute for 10 minutes; the pots were placed in open air, close to the experimental field to avoid differences in the mean meteorological conditions. SWA is the sapwood area determined by measuring sapwood depth on a core collected, at the end of the experiment, with a 5-mm-diameter increment borer at the middle between the two probes in the north side of monitored trees (Rana et al., 2019). At the same time, ΔT was continuously monitored by the same type of TDM sap flow probes used in the field, following the same protocol, recording data every 10 s (data logger CR10X, Campbell Scientific, Utah, USA), with the average values recorded every 10 min. In post processing, the 10-minute values were averaged to meet the interval times of the pot weight determination. By using these measurements of temperature, K values were determined. The calibration curve is obtained plotting the Js0 of Eq. (4) vs the K values.
2.4 The TDM corrections
To assure the correctness of the TDM in the sap flow density measurement at tree level, Js0 was corrected for: (i) the damages caused by the trunk wounds by the probes set up, (ii) the azimuth variations (iii), the radial gradient of sap velocity in trunks.
2.4.1 The wound effect
A coefficient Cw was determined to correct the sap flow density for the wound effects (Wiedemann et al. 2016). For this aim, a couple of TDM probes (20 mm) were installed in parallel to the already measuring probes (installed in the first part of January 2021) in two trees, at the same height and 20 mm from the already installed ones, in the period 23 June – 23 August 2022. Hence, since the wound effect is due to the probe insertion in the trunk and then, affects the measured ΔT, correction is limited to the K parameter (see Eq. 2) and the sap flux density becomes:
$${J}_{s0}=a{\left({C}_{w}K\right)}^{b}$$
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2.4.2 The azimuth effect
The azimuthal variations of sap flux density were analysed in two sampled trees, by adding two couples of TDM probes (20 mm) at 120° and 240°, in the period 23 June – 23 August 2022. For taking into account this azimuth effect, a correction coefficient due to azimuthal variations, Ca, was introduced following Shinohara et al. (2013), to extrapolate sap flux density in the north direction, using the north sensor as a reference to the three integrated directions (averaged over the three directions). Hence, Ca is calculated as the ratio of the mean sap flux density in the three directions to sap flux density in the north direction; therefore, the sap flow density is now:
$${J}_{s0}={C}_{a}a{\left({C}_{w}K\right)}^{b}$$
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2.4.3 The radial gradient effect
Finally, to account for radial gradient in sap flux density, the sapwood depth of each sampled tree was divided in a set of 20 mm increments and a Gaussian function was applied to estimate the sap flux density in each increment as suggested by Pataki et al. (2011) for angiosperms:
$${J}_{si}=1.033{J}_{s0}exp\left[-0.5{\left(\frac{x-0.09963}{0.4263}\right)}^{2}\right]$$
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where Jsi is the sap flux density in each increment i, x is the normalized depth of each sapwood increment (0 ≤ x < 1) and Js0 is calculated using Eq. (6).
Here, to test the used function (Eq. 7) over the active sapwood (Rana et al., 2019), two new set of TDM probe were installed in parallel to the already measuring probes in two sampled trees, at the same height and 20 mm from the other ones, in the period 23 June – 23 August 2022. In this case, beyond the 20 mm probes, commercial sap flow probes of 10 mm length (SFS2 Type M, UP, Steinfurt, Germany) were installed. From the sap flow density measured from the couple of probes the Js0 values in the layer 10–20 mm of the sapwood depth was derived according to Iida and Tanaka (2010) as follows:
$${J}_{s 10-20}=\frac{{J}_{s 0-20}-\alpha {J}_{s 0-10}}{\beta }$$
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where α and β are the proportions of the sapwood area from depths of 0–10 mm to that of 0–20 mm, and from depths of 10–20 mm to that of 0–20 mm, respectively.
2.5 The transpiration at field scale
Finally, the whole tree transpiration of each sampled tree (Trtree, gs− 1) was determined as:
$${Tr}_{tree}=\sum _{i=0}^{m}{J}_{si}{SWA}_{i}$$
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where m is the number of 20-mm increments in sapwood depth, Jsi is the sap flux density determined by Eq. (7) and SWAi is the sapwood area at each depth increase i. SWA was determined as above described in pot experiment.
Since Trtree measurements were referred to the projected canopy area, transpiration by TDM at field scale was calculated as
$${Tr}_{TDM}={A}_{p}\stackrel{-}{{Tr}_{tree}}$$
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where TrTDM is expressed per unit of projected canopy area, i.e., kg m− 2 or mm, with \(\stackrel{-}{{Tr}_{tree}}\) the mean of the monitored trees and Ap the area occupied by the mean vertical projection of each tree, (Lu et al. 2003).
A p was calculated using a digital surface model (DSM) obtained from an automatic flight of an Unmanned Aerial Vehicle (UAV); a Phantom 4 multispectral with RTK system was used. The flight was planned at 40 m altitude with 85% overlap in vertical and horizontal. The acquired images were processed with Pix4d software to obtain the orthomosaic and DSM. The DSM was then used in QGIS environment to extract the canopy surface in accordance with Albuquerque et al. (2022) and Torres-Sanchez et al. (2017) (Fig. 1). A value of Ap equal to 0.25 was used in Eq. (1).
Transpiration on daily time scale was calculated by integrating transpiration at daytime (i.e., when Rg > 10 W m− 2).
2.6 Soil water balance
According to Fujime et al. (2021) the test and performance evaluation of the transpiration determined by the applied TDM has been carried out by comparing the transpiration TrTDM (mm) calculated by the Eq. (10) and the transpiration calculated from soil water balance TrWB (mm). In this Mediterranean site, characterised by shallow soil irrigated by localized drip irrigators, the soil water balance can be written:
$${ET}_{WB}={P}_{eff}+Ir\pm SWC$$
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with ETWB evapotranspiration (mm), Peff effective rain (mm), Ir irrigation (mm); the deep percolation, runoff and capillary rising terms were considered neglectable (Rana and Katerji 2000). Due to the relatively high soil infiltration rate and the flat field, all rainfall over 0.2 mm was considered as effective precipitation (Villalobos and Fereres 2017).
Tr WB comes from subtracting soil evaporation (ES) from ETWB as
$${Tr}_{WB}={ET}_{WB}-{E}_{s}$$
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According to López-López et al. (2018), ES was calculated following Bonachela et al. (2001), who modelled this term specifically for drip irrigated olive orchards.