Spatial Prediction Model of Plant Water Status of an Olive Orchard ( Olea europaea L.) cv. Arbequina Under Semiarid Conditions in the Central Valley of Chile

The Olive ( Olea europaea L.) is a typical fruit tree of Mediterranean areas characterized by high-quality oil production and high tolerance to water deficit. Due to worldwide water scarcity in Mediterranean regions, it becomes indispensable to monitor plant water status, in example, through xylem water potential ( Ψ x ). Unfortunately, measurement is difficult to perform with high spatial resolution at field scale (> 50 measurements per hectare), due to the large amount of manpower required in the prosses which turned this technique into a high-cost solution. This situation drastically hinders its applicability in large production areas. Thus, the objective of this research is implementing a spatial prediction model of plant water status in an olive orchard, using a single Ψ x measurement performed in a reference site over the orchard. The experimental site was established in 2.2 hectares of commercial olive trees in the Pencahue valley located in the Maule region (Chile) during the 2013/14 growing season. Measurements of Ψ x were performed at key phenological stages of olive trees. The proposed methodology allowed to estimate the behavior of Ψ x in unsampled olive trees from reference site measurements, with an average spatial error less than ±0.6 MPa and correlation of 0.8 (R 2 ) ratifying the high spatial dependence between different sites sampled at field scale. Therefore, distribution of spatial variability would be adequate for the application of irrigation in homogeneous management zones, facilitating water management practices in clearly identified zones within the olive orchard under study.


Introduction
The severe lack of precipitation is one of the most critical issues in agriculture these days, especially in Mediterranean climate where significant water deficit areas were emerged worldwide. Chile is no free from this issue where annual mean precipitation has been reduced by 45 to 105 mm in the last 31 years (IPCC, 2021), affecting on water availability for agricultural ecosystems (Del Pozo et al., 2019). Also, high variability in annual climatic conditions, due to the ENSO fluctuations occur lasts years directly affecting on precipitations. ENSO consists of the alternation of two seasonal ocean currents, "Niño" and "Niña" cycles which modifying the climate of a year, especially during the "Niña" significantly reducing the precipitation. Thus, proper water management and implementation of methodologies to optimize irrigation during agricultural growing season is increasingly necessary to consider also on olive trees (Ahumada et al., 2018(Ahumada et al., ). al., 2010. This high tolerance to lack of water of this specie is due to the strong stomatal control in conjunction with osmoregulation mechanisms to regulates transpiration rate (Fernández et al., 1997;Moriana et al., 2003;Tognetti et al., 2006) allowing olive trees to tolerate long periods with strong soil water deficit during season (Dichio et al., 2003;Ahumada et al., 2017Ahumada et al., , 2018. Thus, it has been observed in some investigations, that this species can reach xylem water potential values (Ψ x ) of up to -2.0 MPa while maintaining mild stress, and even reach values of -6.0 MPa, for severe stress values with a significant reduction in photosynthetic capacity (Ahumada et al., 2019).
Knowing the water behavior of olive trees by monitoring Ψ x is fundamental to made decision on irrigation management (Tognetti et al., 2006;Ahumada et al., 2018) (irrigation timing and frequency) to save water, especially considering the current climatic context. However, identifying which sector or plants in the orchard monitor and how many measurements perform in the process is difficult to define, especially in orchards with high soil spatial variability. This variability is present in all agricultural orchards, which is related to some agronomic interest variables (AIV) (López-Granados et al., 2003;Acevedo-Opazo et al., 2010). Thus, the spatialized study of AIV such as Ψ x (among others), would allow as to know and understand how spatial variability of water status is distributed over the field during the season to propose a site-specific irrigation management (López-Granados et al., 2003;Acevedo-Opazo et al., 2008, 2013. Similarly, the water behavior can be predicted from a measurement of water potential at a reference site, thus implementing a spatial prediction model of AIV such as water status (Acevedo-Opazo et al., 2009). This research proposes the implementation of a spatial prediction model of water status in an Olive orchard, to study the spatial variability at field scale and optimize the water resources during the growing season. The model is expected to propose homogeneous management zones for xylem water status management within the orchard, generating significant water savings and facilitating irrigation work.

Study Site
The study was conducted in olive orchard orchard (Olea Europea L., cv. Arbequina) during the 2013/2014 growing season in the "Olivares de Quepu" company, located in Pencahue Valley, Chile (35º23′ LS; 71º44′ LW; 96 m.a.s.l.) in an area of 2.2 hectares (ha). The nine years old orchard has planting by a frame of 5.0 × 1.5 m (1332 pl ha -1 ), with monocone training system, irrigated by two drippers per plant with a discharge of 2.0 L h -1 . Pencahue valley is classified as warm temperate Mediterranean climate, with a prolonged dry season during spring to summer (annual rainfall of 700 mm, concentrated in winter), with average minimum temperatures of 4.4 ºC and average maximum temperature of 30 ºC. Regarding the soils, they correspond to the Pencahue series, which are characterized by being shallow, with slopes that surround 2 to 10%, textures that vary between fine sandy loam and sandy clay loam. Regarding the reference evapotranspiration, this is approximately 6 mm day -1 for the month of January, 4.5 mm day -1 for February and 3 mm day -1 for March.
Due to the conditions of water demand described above and the characteristics of the soil, the irrigations are carried out every 15 to 20 days for the same irrigation sector. However, due to the lack of water as of mid-January, the irrigations are extended every 30 days.

Geolocation of the Experimental Site
The develop and implementation of the model, 38 sampling sites were selected within a 2.2 hectares olive orchard ( Figure 1). These sites were distributed in a non-regular grid, according to the nested method (Weitz et al., 1993). This method considers the location of the first points of the grid at smaller distances, to later increase the monitoring distance between them, to minimize the experimental or field error at spatial semi-variance calculating moment. To know the exact localization of each site on grid, a geo-referenced process was made using a DGPS (Trimble, Pathfinder ProXRS, Sunnyvale, California, USA). jas.ccsenet. Within the implementation stages of the plant water status prediction model proposed by Acevedo-Opazo et al. (2008), the reference site (s re ) was determined, which turned out to be S10, with an average correlation of 0.8 with the rest of the sites sampled in the study.

Spatial Distribution Maps
For Ψ x mapping of the olive orchard, sectors with different ranges of plant water status were identified. For this, the range proposed by Ahumada et al. (2019) was used, who determined that for Ψ x from -2.2 MPa a slight stress begins to be observed in the water status of the Olives, and above -3.6 MPa, this stress passes to be moderate. Due to the stress levels reached in this study, the step from zero to slight stress was used to differentiate two different management sectors, considering that the entire orchard was subjected to the same type of irrigation. Thus, thematic cartographies of midday stem water potential were performed using the 3D Field software (Version 2.9.0.0, 2007 Vladimir Galouchko, Rusia).

Model Validation
To statistically corroborate the errors associated with the model, root mean square error (RMSE; Equation 5) and correlation coefficient (R 2 ) was used. With this statistic, cartographies were constructed to observe the spatial distribution of the error of the proposed model.

Semi-variogram Analysis
The semi-variogram models evaluated at different monitoring dates during the season, in most cases, showed a good degree of correlation with the values of Ψ x , being the Exponential model the one that presented the best results. In this sense, the R 2 values ranged between 0.44 and 0.99 (Table 1). The lowest R 2 value was recorded during the first monitoring date (January 1), with a value of 0.44. This result was due to the irrigation criteria used by the grower. An irrigation frequency of around 20 days was considered (at the beginning of the season), which would have generated a condition of null to slight water restriction. The above is shown in Figure 2, where Ψ x showed values below -1.6 MPa. This situation changed from the second monitoring date (January 31), where the irrigation frequency was extended to 30 days, increasing the water potential level above -1.9 MPa (Figure 2). Note. C 0 : Nugget. C 0 + C: Sill. A 0 : Range. SD: Spatial Dependence (%). G: Gaussian, Ex: Exponential.
On the other hand, for different values of A 0 calculated on different sampling dates, an important variability was observed, which ranged between 33 and 280 meters (Table 1), being these values always higher than the sampling distances used in the field (nest method, with actual sampling distances that varied between 1.5 and 23 meters).

Water Status of Olive Tree
For each of the sampling dates (six in total) the mean Ψ x of the 38 sampling sites was calculated (Figure 2). In this regard, it is observed that as the season elapses the Ψ x measurement of the orchard becomes more negative until 59 Julian day with a mean value of -2.4 MPa, date from which the water stress was reduced, reaching values of -1.9 MPa on the last measurement date of the season (73 Julian day). A similar behavior was observed for the standard deviation (SDD), which was higher during the dates with greater water stress (Figure 2). jas.ccsenet.

Model
Within the prediction earlier site measurem its best pre was the lo when the R

Discuss
The , water of the model performance, which show a good degree of spatial coincidence between the proposed zones (spatial motifs) in terms of their spatial distribution and the identification of irrigation management zones, even for the worst performing date (February 7).
When observing the results of the cartographies obtained by the proposed model for the worst estimation date (February 7) ( Figure 5), it is observed that there is an 86% coincidence between the actual values measured in the field compared to the values estimated by the model for the same sampling sites. On the other hand, for the best estimation date (March 14), there is a 95% coincidence between the actual measured values compared to the values estimated by the model for the same sites of the sampling grid. The results obtained are interesting, since when comparing the results obtained in the proposed cartographies, a good degree of coincidence is observed between both plant water status cartographies proposed by the spatial model, allowing to clearly identify two different irrigation management zones within the orchard, facilitating the producer's decision making.
In the Figure 6, the areas of black color represent the sites where the spatial prediction of the model is less reliable. Regarding the spatial distribution of these sectors (black color), they are mainly located in the "eastern" sector of the orchard under study, a sector that coincides with the zone of highest water restriction in the orchard, observed throughout the season. Therefore, as indicated in the research proposed by Acevedo-Opazo et al. (2008) there is an important coincidence between the sectors of highest spatial variability with the zones of highest water restriction and highest spatial error measured within the orchard. This tool represents an important contribution for farmers, since it generates a significant reduction in the labor used for monitoring the water status.
The methodology used in this article was proposed to spatially model the phenology and maturity of the vine with interesting results (Verdugo-Vásquez et al., 2016. This first validation approach in olives orchards opens the opportunity to continue exploring different models of interest in this species, such as phenology, yield, and maturity, among others. There is also space to evaluate its use in other species affected by climate change, such as the cherry tree.

Conclusion
The evaluated orchard presents an important spatial structure, corroborating that most of the semi-variance observed for the plant water status variable, would be explained mainly by the high spatial variability of the field or structural variance "C". Thus, it is possible to propose a site-specific management for the intra-predial irrigation operation. Based on this, it is possible to propose a linear model for spatial prediction of xylem water potential in olive trees with a spatial error of less than 0.4 MPa in more than 80% of the orchard area. This measurement is relevant in conditions of high spatial variability and in a semi-arid climate. Therefore, it is possible to propose two well-defined and structured site-specific management zones within the orchard under study, in which two different irrigation criteria are observed for each of the sectors identified in the study, where the threshold identified between both zones was -2.2 MPa.