Where M i is the ith measured variable, M ¯ is the average value of all measurements, S i is the ith simulated variable and n is the number of measured values. In addition, the slope, intercept and coefficient of determination ( r 2) obtained by regressing the simulated and measured values were also used. Results Huang, Y., Yu, Y., Zhang, W., Sun, W., Liu, S., Jiang, J., et al. (2009). Agro-C: a biogeophysical model for simulating the carbon budget of agroecosystems. Agric. For. Meteorol. 95, 203–223. doi: 10.1016/j.agrformet.2008.07.013 Want to change it up? Swap out blue cheese for a creamy goat cheese or opt for a milder blue cheese and go with gorgonzola cheese. Our gordal olives have been carefully selected from special harvests and this you will appreciate when tasting their firm and fleshy texture. These gordal olives come in a simple brine with a mild anchovy flavouring, so you can enhance their incredible flavour by creating your own marinade. Try them with fresh red chillies, fresh rosemary and garlic to make these olives become first class. Values of GC, LAD, and R zx required to initialize the model were taken from dedicated measurements. A record of Y dry of the year preceding simulations was also considered. Initial L v values were taken from records measured by Moriana (2001). Statistical Analysis

The goal of this study is to present and test a process-oriented model integrating existing knowledge on the growth and development processes of olive orchards and capable to account for the impacts of water stress, management and climate on their productivity, in the absence of nutrient deficiencies, diseases and pests. The model, hereafter named ‘OliveCan’ -which comes from ‘Olive Canopy-,’ was formulated using the models by Testi et al. (2006); Morales et al. (2016) and García-Tejera et al. (2017a) as starting point. Materials and Methods Model Description Daily effective precipitation ( P eff) is calculated by discounting rainfall interception by the canopy ( P int) from total daily precipitation ( P). P int is calculated using a simplified version of the model of Gómez et al. (2001) and the resulting P eff is distributed proportionally between the two soil zones as a function of the surface fractions that remain rainfed or are wetted by localized irrigation. With regard to P int, the canopy is treated as a capacitor capable of storing rain water up to a certain limit determined by canopy dimensions and leaf area index ( LAI), according to Gómez et al. (2001). The stored water is subsequently lost by direct evaporation, which is simulated based on the Penman–Monteith equation assuming a null canopy resistance. As in Testi et al. (2006), the aerodynamic resistance is deduced from the model proposed by Raupach (1994), parametrized and validated specifically for olive orchards following Verhoef et al. (1997). The direct evaporation from wet foliage prevents tree transpiration ( E p), until the intercepted water is totally lost. Finally, the soil carbon balance and heterotrophic respiration ( RESP H) are computed with an adaptation of the model proposed by Huang et al. (2009) and modified to take into account the effect of soil moisture on the rate of decomposition according to Verstraeten et al. (2006). Then, by considering the different computed fluxes of assimilation and respiration within the orchard, OliveCan provides estimates of the ecosystem respiration ( RESP eco) and net ecosystem exchange ( NEE). Management Component During the development of the model, it became apparent that our current understanding of some of the physiological processes to be simulated was limited. For example, timing of vegetative bud break, dynamics of leaf senescence, fruit photosynthesis and the use of reserves are among the phenomena that have received less attention in the literature. Also, OliveCan is missing a sub-model aimed to properly simulate the dynamics of oil accumulation during the fruit growth period. Further research on these and other topics (e.g., alternate bearing) are clearly needed and might result in model improvements through either a more consistent parametrization or the formulation of better equations for simulating such processes. Alternate year irrigation (AYI), which was rainfed in the year of low crop load (1998) and fully irrigated, as CON, during the heavy crop years (1997 and 1999).Abdel-Razik, M. (1989). A model of the productivity of olive trees under optional water and nutrient supply in desert conditions. Ecol. Modell. 45, 179–204. doi: 10.1016/0304-3800(89)90081-1 When available, the values of the different parameters were taken from the literature. Supplementary Table S2 provides a complete list with the parameter values used for the simulations and the source from which they were taken. In short, the parameters of the SPAC model were taken from García-Tejera et al. (2017a, b), who, in turn, gathered most of the parameter values from different sources. Parameters related to phenology were obtained from reports by De Melo-Abreu et al. (2004) and López-Bernal et al. (2014, 2017). The studies by Mariscal et al. (2000) and Pérez-Priego et al. (2014) were used for setting the maintenance respiration and PV coefficients, respectively. Parameters related to the calculation of fruit number and yield were taken from several sources, including experimental data (see section “Number of Fruits and Alternate Bearing” in Supplementary Material). The coefficient of oil yield to dry fruit matter was taken from experimental data collected in a hedgerow cv. ‘Arbequina’ orchard ( López-Bernal et al., 2015). Partitioning coefficients were based on findings by Mariscal et al. (2000); Villalobos et al. (2006) and Scariano et al. (2008). Reports from Barranco et al. (2005) and Koubouris et al. (2009) were used to parametrize the routines modeling the impacts of frost damage and heat stress, respectively. Coefficients modulating fine root growth distribution were directly taken from Jones and Kiniry (1986). Finally, parameters implied in the soil carbon balance were taken from Verstraeten et al. (2006); Huang et al. (2009) and, to a lesser extent, from other studies. Model Testing Continuous deficit irrigation (CDI), which also applied 75% of the water received by CON (i.e., rainfall plus irrigation), but for the whole irrigation season.

Regulated deficit irrigation (RDI), which applied 75% of the water received by CON (i.e., rainfall plus irrigation) with a midsummer deficit period (15 July to 15 September) without irrigation. Senescence of leaves and fine roots are simulated using a similar approach to that in the model by Morales et al. (2016). OliveCan takes also into account the conversion of shoots into branches when they exceed 3 years-old. Besides that, the model considers some of the effects of frost events and heat stress. Frost damage is simulated by assuming that a fraction of the standing leaves is defoliated when minimum air temperature falls below a certain temperature threshold. A similar approach is used for simulating the effect of extremely high temperatures during flowering on fruit set: when maximum air temperature exceeds a given threshold, a reduction in the final FN is triggered. Finally, future improvements of OliveCan might include additional sub-models for simulating nutrient uptake and the impact of pests and diseases. Apart from that, the model shows potential for being adapted to other tree species, so its interest may not be only restricted to olive researchers. ConclusionThe measurements (only performed for the central trees of the replicates) used for the model were Y oil and seasonal ET. On the one hand, trees were harvested between December 15th and January 15th for the 3 years. Individual fruit weight of each tree was measured and a subsample of 150 fruits from each tree was used for determining oil content. On the other, cumulative ET was determined by water balance for each season by measuring soil water content with a neutron probe (model 503, Campbell Pacific Nuclear Corp, Pacheco, CA, United States). Eight access tubes were installed between two trees per replicate in the four irrigation treatments and six tubes were placed in the rainfed treatment. Measurements were taken were performed at several depths (from 0.075 to 2.4 m deep). Overall, the results of all the aforementioned comparisons suggest that model performance is fairly satisfactory. However, further testing against experimental data taken from different environmental conditions and orchard characteristics seems highly desirable. This would help to provide additional evidence on the predictive power of OliveCan, or else to identify situations for which model accuracy could be improved through either better calibrations or reformulation of some routines. Apart from that, it should be noted that the reliability of OliveCan for estimating certain output parameters (e.g., NEE, RESP H) has not been tested specifically in the present study, which should also be the focus of future research efforts. Model Applicability

The research leading to these results has received funding from Ministerio de Economía y Competitividad (Grant Nos. AGL-2010-20766 and AGL2015-69822), from Junta de Andalucía (Grant No. P08-AGR-04202), from the European Community’s Seven Framework Programme-FP7 (KBBE.2013.1.4-09) under Grant Agreement No. 613817. 2013–2016 “MODelling vegetation response to EXTREMe Events” (MODEXTREME, modextreme.org) and from ERA-NET FACCE SURPLUS (Grant No. 652615, project OLIVE-MIRACLE), the latter co-funded by INIA (PCIN-2015-259). Besides, ÁL-B was funded by a postdoctoral fellowship (‘Juan de la Cierva-Formación 2015’ Programme, FJCI-2015-24109) from Ministerio de Economía y Competitividad. Conflict of Interest Statement Runoff and infiltration are calculated following a Soil Conservation Service curve number methodology that was specifically calibrated and validated for different typologies of olive orchards ( Romero et al., 2007). The approach requires information on the canopy ground cover ( GC) and the soil hydrological condition ( SHC) -i.e., an indicative of the capacity of infiltration of the soil when it is wet. The water content at field capacity (𝜃 UL), wilting point (𝜃 LL) and saturation (𝜃 sat) are also needed for the computation of infiltration and all the remaining simulated processes. OliveCan is subdivided into three main components (Supplementary Figure S1) that are devoted to the computation of the water and carbon balances of the olive orchard and to simulate the impacts of some management operations. The water and carbon balance components are interdependent (i.e., each one needs data provided by the other) and both of them require information on soil traits and weather data.

Verstraeten, W., Veroustraete, F., and Feyen, J. (2006). On the temperature and water limitation of net ecosystem productivity: implementation in the C-Fix model. Ecol. Modell. 199, 4–22. doi: 10.1016/j.ecolmodel.2006.06.008 The model by García-Tejera et al. (2017a) is used to compute root water uptake ( RWU) from each layer in the two soil zones, canopy transpiration ( E p) and gross assimilation ( A′). By analogy with the Ohm’s law for electric circuits, the model assumes that water transport through the SPAC is driven by differences in water potential and hydraulic resistances. In this regard, three hydraulic resistances are considered: from the soil to the root-soil-interface ( R s), from the soil-root interface to the root xylem ( R r) and from the root xylem to the canopy ( R x). R s depends on soil texture, root length density ( L v), soil water content (𝜃) ( Gardner, 1960). R r is a function of L v and root permeability, the latter being mediated by 𝜃 ( Bristow et al., 1984) and temperature ( García-Tejera et al., 2016). Finally, R x is calculated from xylem anatomical traits and tree height. In the canopy, two leaf populations are considered (i.e., sunlit and shaded). For each one, gross assimilation ( A′), stomatal conductance ( g s), intercellular CO 2 concentration ( C i) and leaf water potential (Ψ l) are calculated iteratively, considering both the models by Farquhar et al. (1980) and Tuzet et al. (2003). In doing so, the environmental CO 2 concentration ( C a) is explicitly taken into account for calculating both A′ and g s on the one hand. On the other, the model requires information on the intercepted photosynthetically active radiation ( IPAR) as well as the sunlit and shaded fractions of the canopy. These inputs are provided by a simple geometric model of radiation interception which assumes a spheroidal shape for the crown and accounts for the shadowing from neighboring trees. Finally, E p is estimated from the imposed evaporation equation assuming that the canopy is coupled to the atmosphere, whereas RWU is deduced in each layer of each soil zone from the corresponding water potential differences and hydraulic resistances. Carbon Balance Component