Crop Coefﬁcients and Transpiration of a Super Intensive Arbequina Olive Orchard using the Dual K c Approach and the K cb Computation with the Fraction of Ground Cover and Height

: The SIMDualKc model was used to simulate crop water requirements for a super high density olive orchard in the region of Alentejo, Portugal. This model uses the dual crop coefﬁcient approach to estimate and partitioning the actual crop evapotranspiration (ET c act ) and therefore to perform the soil water balance. The model was calibrated with 2011 tree transpiration using trunk sap ﬂow measurements and was validated using similar data from 2012 and tested with 2013 data. Low root mean square errors (RMSE < 0.53 mm ¨ d ´ 1 ) and acceptable modelling efﬁciency indicators (EF > 0.25) were obtained. Further validation was performed comparing modelled ET c act with eddy covariance measurements. These indicators support the appropriateness of using SIMDualKc to guide irrigation management. The basal crop coefﬁcient (K cb ) curves obtained with SIMDualKc for those 3 years were compared with the K cb values computed with the Allen and Pereira approach (A&P approach) where K cb is estimated from the fraction of ground cover and plant height considering an adjustment factor for crop stomatal control (F r ). F r values were obtained through a trial and error procedure through comparing the K cb estimated with this approach and with SIMDualKc. The K cb curves obtained by both methods resulted highly correlated, which indicates that the A&P approach may be used in the irrigation management practice to estimate crop water requirements. Results of performing the soil water balance with SIMDualKc have shown that soil evaporation is a large fraction of ET c act , varying between 41% and 45% for the 3 years under study. Irrigation, applied with a drip system, represented 39 to 56% of ET c act , which shows the great importance of irrigation to achieve the water requirements of super intensive olive orchards. Nevertheless, the analysis has shown that the irrigation management adopted at the orchard produces a water deﬁcit larger than desirable, with a ratio of ET c act to non-stressed crop evapotranspiration (ET c ) varying from 70% to 94% during the mid-season, when that ratio for a eustress irrigation management could be around 90%. approach for predicting K cb from the fraction of ground cover and crop height; (iv) determining the terms of the actual transpiration and ET c act


Experimental Site
The experimental site (38°24'N, 7°43'W, 143 m a.s.l.) is located in Alentejo, Southern Portugal, in a commercial super-high intensive hedgerow olive orchard farmed by "Olivais do Sul." The orchard has a total area of 78 ha, which land has a smooth undulation. The climate is dry sub-humid of Mediterranean type, with most of the rainfall in autumn and winter; according to the Köppen-Geiger classification [44], the climate is a Csa, characterized by mild rainy winters and dry hot summers. The annual rainfall ranged between 511 and 736 mm in the experimental years, while the average monthly temperature ranged from 9.6 o C in January to 23.3 o C in July and August. Prevailing winds are from the North-West direction. Main daily weather data characterizing the experimental years is presented in Figure 1. The soil is a Cambissol [45] having a sandy loam texture, with moderate to low infiltration. Soil water at field capacity averages 0.24 cm 3 ·cm −3 through the soil profile down to 1.20 m, while the permanent wilting point to the same depth is 0.12 cm 3 ·cm −3 . The total available water to that depth is TAW = 160 mm. Soil water observations were performed weekly with a TDR probe (TRIME, IMKO,   The soil is a Cambissol [45] having a sandy loam texture, with moderate to low infiltration. Soil water at field capacity averages 0.24 cm 3¨c m´3 through the soil profile down to 1.20 m, while the permanent wilting point to the same depth is 0.12 cm 3¨c m´3. The total available water to that depth is TAW = 160 mm. Soil water observations were performed weekly with a TDR probe (TRIME, IMKO, Ettlingen, Germany); data were used to perform the soil water balance considering a soil root zone depth Z r = 1.  Table 1. The fraction of ground cover (f c , dimensionless) was estimated from measurements of the crown diameter along the row direction and perpendicularly to it for 51 trees. In addition, f c values estimated from remote sensing [28] were also considered. f c ranged from 0.17 to 0.38. The tree height (h, m) ranged from 3.0 to 4.0 m. Both f c and h varied through the crop season because trees were pruned during winter, by early January. However, in 2012, after a severe frost that occurred by late February, a heavy pruning was applied after, which caused larger changes in f c and h in that year. Harvesting in the study plots were performed by 16 October in 2011 and 2012 and by 10 October in 2013 ( Table 1). The yield average was 14 ton¨ha´1 in 2011 and 18 ton¨ha´1 in 2013. A low yield of 3 ton¨ha´1 was observed in 2012 due to the referred frost and heavy pruning. Ground cover conditions affecting soil evaporation may be taken into consideration in the water balance simulations by SIMDualKc and were therefore observed. They refer to both crop residues and active ground cover [34,35,46]. In 2011, a reduced active ground cover was present from early January until May, covering 10% of the ground in the row and 5% in the inter-row. In 2012, following the frost by February, a heavy defoliation occurred and leaves formed an organic mulch from late February until early August; its ground cover fraction was estimated as 0.30, corresponding to a reduction of the soil evaporation of 30%. In 2013, an active ground cover of nearly 20% on both the row and the inter-row was observed from January until May, when it dried out and became a residues cover.
Irrigation took place nearly every day during spring and summer and was applied by the evening. A drip system was used, with emitters spaced of 0.75 m along the row. The emitters discharge was of 2.3 L h´1. The wetted fraction (f w = 0.23) was calculated from the area of a wetted ellipse circling each emitter. Irrigations were scheduled by the farmer, who adopted average daily irrigation depths close to 3 mm, however varying from 1 to 8 mm, approximately. Irrigation depths were measured with a tipping-bucket rain gauge (ARG100, Environmental Measurements Ltd., Sunderland, UK).

Eddy Covariance Measurements
The eddy covariance (EC) micrometeorological technique was used to measure evapotranspiration during short periods of the irrigation season (July-August in 2011 and June-August in 2012) as a strategy to calibrate the sap flow measurements and obtaining accurate transpiration estimates. This strategy has been successfully used in previous studies [38,47].
The EC system comprised a three-dimensional sonic anemometer and a krypton hygrometer (respectively Models CSAT3 and KH20, Campbell Scientific, Inc., Logan, UT, USA) mounted at a height (Model CR1000, Campbell Scientific, Inc., Logan, UT, USA) and afterwards analysed with the Software package TK3 [48] for correction and calculation of 30 min-averages. Data corrections were performed according to Foken et al. [49]. They included: despiking of the raw data [50]; coordinate rotation using the Double Rotation method [51] to account for the non-flat terrain conditions; corrections for oxygen cross-sensitivity of the krypton hygrometer [52] and spectral loss [53]; conversion of buoyancy flux to sensible heat flux [54]; and the WPL correction for density fluctuations [55]. To evaluate the surface energy balance, soil heat flux (G) and net radiation (R n ) were measured using eight soil heat flux plates (calibrated Peltier modules sealed 20 V, 4.4 A, 40ˆ40ˆ3.9 mm, RS Components, Madrid, Spain) and a net radiometer (Model NR-LITE, Campbell Scientific, Inc., Logan, Utah, USA), respectively. The soil heat flux plates were placed in the tree row and in the inter-rows at a depth of 2 cm. The daily energy balance equation error closure was determined by linear regression forced to origin.
Water 2018, 10, x FOR PEER REVIEW 5 of 24 coordinate rotation using the Double Rotation method [51] to account for the non-flat terrain conditions; corrections for oxygen cross-sensitivity of the krypton hygrometer [52] and spectral loss [53]; conversion of buoyancy flux to sensible heat flux [54]; and the WPL correction for density fluctuations [55]. To evaluate the surface energy balance, soil heat flux (G) and net radiation (Rn) were measured using eight soil heat flux plates (calibrated Peltier modules sealed 20 V, 4.4 A, 40 × 40 × 3.9 mm, RS Components, Madrid, Spain) and a net radiometer (Model NR-LITE, Campbell Scientific, Inc., Logan, Utah, USA), respectively. The soil heat flux plates were placed in the tree row and in the inter-rows at a depth of 2 cm. The daily energy balance equation error closure was determined by linear regression forced to origin. The footprint analysis [56], performed to access the representativeness of the EC measurements, showed that over 90% of the fluxes sensed, determined as cumulative normalized flux (CNF), came from the region of interest, regarding the four main cardinal points. The fetch (distance to the edge of the plot) in the main directions, varying approximately between 350 and 500 m, was then considered adequate ( Figure 3). Measurements were mainly affected by fluxes coming from an upwind area at a distance of 15 m from the tower (maximum of the one-dimensional footprint function, which provides the relative contribution to the vertical flux: Qf = (1/Qo) dQ/dx, for a given height z, being Qo the latent heat flux density measured at point x = (0, z)).  The footprint analysis [56], performed to access the representativeness of the EC measurements, showed that over 90% of the fluxes sensed, determined as cumulative normalized flux (CNF), came from the region of interest, regarding the four main cardinal points. The fetch (distance to the edge of the plot) in the main directions, varying approximately between 350 and 500 m, was then considered adequate ( Figure 3). Measurements were mainly affected by fluxes coming from an upwind area at a distance of 15 m from the tower (maximum of the one-dimensional footprint function, which provides the relative contribution to the vertical flux: Q f = (1/Q o ) dQ/dx, for a given height z, being Q o the latent heat flux density measured at point x = (0, z)).

Direction Fetch (m) CNF
Measurements in days with prevailing winds from the North-East direction were discarded given the vicinity of a building approximately at 200 m in that direction. Prevailing winds, calculated as average frequency for each of the EC measurement periods, were in agreement with historical climatic data, which indicates the North-West direction ( Figure 4). Wind direction frequency was further analysed in detail for individual days and EC data screened accordingly for specific modelling purposes.
The energy balance equation closure error ( Figure 5) was determined with a linear regression analysis forced to the origin using daily values of the measured fluxes (LE, H, R n and G). The error, below 10% (H + LE = 0.91 (R n´G ), R 2 = 0.87), is similar to that found by other authors using this technique in orchards [57][58][59].
showed that over 90% of the fluxes sensed, determined as cumulative normalized flux (CNF), came from the region of interest, regarding the four main cardinal points. The fetch (distance to the edge of the plot) in the main directions, varying approximately between 350 and 500 m, was then considered adequate ( Figure 3). Measurements were mainly affected by fluxes coming from an upwind area at a distance of 15 m from the tower (maximum of the one-dimensional footprint function, which provides the relative contribution to the vertical flux: Qf = (1/Qo) dQ/dx, for a given height z, being Qo the latent heat flux density measured at point x = (0, z)).  showed that over 90% of the fluxes sensed, determined as cumulative normalized flux (CNF), came from the region of interest, regarding the four main cardinal points. The fetch (distance to the edge of the plot) in the main directions, varying approximately between 350 and 500 m, was then considered adequate ( Figure 3). Measurements were mainly affected by fluxes coming from an upwind area at a distance of 15 m from the tower (maximum of the one-dimensional footprint function, which provides the relative contribution to the vertical flux: Qf = (1/Qo) dQ/dx, for a given height z, being Qo the latent heat flux density measured at point x = (0, z)).   Measurements in days with prevailing winds from the North-East direction were discarded given the vicinity of a building approximately at 200 m in that direction. Prevailing winds, calculated as average frequency for each of the EC measurement periods, were in agreement with historical climatic data, which indicates the North-West direction ( Figure 4). Wind direction frequency was further analysed in detail for individual days and EC data screened accordingly for specific modelling purposes.  The energy balance equation closure error ( Figure 5) was determined with a linear regression analysis forced to the origin using daily values of the measured fluxes (LE, H, Rn and G). The error, below 10% (H + LE = 0.91 (Rn-G), R² = 0.87), is similar to that found by other authors using this technique in orchards [57][58][59].   Measurements in days with prevailing winds from the North-East direction were discarded given the vicinity of a building approximately at 200 m in that direction. Prevailing winds, calculated as average frequency for each of the EC measurement periods, were in agreement with historical climatic data, which indicates the North-West direction ( Figure 4). Wind direction frequency was further analysed in detail for individual days and EC data screened accordingly for specific modelling purposes.  The energy balance equation closure error ( Figure 5) was determined with a linear regression analysis forced to the origin using daily values of the measured fluxes (LE, H, Rn and G). The error, below 10% (H + LE = 0.91 (Rn-G), R² = 0.87), is similar to that found by other authors using this technique in orchards [57][58][59].

Transpiration from Sap Flow Measurements with the Granier Method
Plant transpiration was measured with thermal dissipation Granier probes [60] between DOY (day of year) 134 in 2011 and DOY 194 in 2013 (continuous half-hourly records). Six trees, chosen according to trunk diameter class frequency determined in a large sample of the orchard, were equipped with 1 cm length sensors (UP GmbH, Cottbus, Germany). Average data were stored each thirty minutes in a datalogger (Model CR1000, Campbell Scientific, Inc., Logan, UT, USA). Natural temperature gradients in the tree trunk were accounted for using data from non-heated sap flow sensors calculated during long periods. Daily transpiration was calculated from the half-hourly data. For flux calculation, the sapwood area in the cross section of the trunk was evaluated from core samples taken with an increment borer. Observation of the samples allowed considering the whole area conductive except the bark.
Sap flow methods are often referred as underestimating transpiration [19,[61][62][63][64][65]. Although the original calibration of this method, which allows converting temperature differences between the two probes into crop transpiration, was initially considered universal, more recently, evidences show that it is advisable to verify its accuracy. Raw sap flow observations (SF, mm¨d´1) were therefore corrected to obtain calibrated sap-flow transpiration (T SF , mm¨d´1), as referred in previous applications to tree crops [38,47,61]. This was done by mathematically relating sap-flow, SF, with transpiration computed from EC observations (T EC = ET EC -E sim ). T EC represents the difference between ET obtained from EC measurements (ET EC , mm¨d´1) and the soil evaporation (E sim , mm¨d´1) simulated with the two phases Ritchie model [66], the latter computed following Allen et al. [4]. The computation of E sim based upon the water balance of the soil evaporation layer using soil moisture observations. Parameters characterizing that soil layer, with a depth Z e = 0.10 m, consisted of: total and readily evaporable water, respectively TEW = 18 mm and REW = 9 mm. Further information on E sim data was provided by Paço et al. [19]. This procedure allows enlarging the available field information to the entire simulation period [67,68].
The best mathematical relationships between T EC and SF ( Figure 6) were of exponential form: with K SF = 0.34 and α = 1.40 (R 2 = 0.55; n = 13) for 2011 and K SF = 0.34 and α = 1.72 (R 2 = 0.61; n = 28) for 2012, which was extended for 2013. The adjustment of SF was performed with Equation 2 assuming that the transpiration derived from sap-flow measurements (T SF ) equals that estimated from EC observations as referred above (T EC ). The approach used may be affected by uncertainties in computing E sim as well as measurements errors affecting both T EC and SF. Nevertheless, The T SF values resulting from the application of Equation 2, which varied between 0.36 and 3.54 mm¨d´1, are comparable to transpiration values reported for other studies on olive orchards [18,59,69].
Water 2018, 10, x FOR PEER REVIEW 7 of 24 Plant transpiration was measured with thermal dissipation Granier probes [60] between DOY (day of year) 134 in 2011 and DOY 194 in 2013 (continuous half-hourly records). Six trees, chosen according to trunk diameter class frequency determined in a large sample of the orchard, were equipped with 1 cm length sensors (UP GmbH, Cottbus, Germany). Average data were stored each thirty minutes in a datalogger (Model CR1000, Campbell Scientific, Inc., Logan, UT, USA). Natural temperature gradients in the tree trunk were accounted for using data from non-heated sap flow sensors calculated during long periods. Daily transpiration was calculated from the half-hourly data. For flux calculation, the sapwood area in the cross section of the trunk was evaluated from core samples taken with an increment borer. Observation of the samples allowed considering the whole area conductive except the bark.
Sap flow methods are often referred as underestimating transpiration [19,[61][62][63][64][65]. Although the original calibration of this method, which allows converting temperature differences between the two probes into crop transpiration, was initially considered universal, more recently, evidences show that it is advisable to verify its accuracy. Raw sap flow observations (SF, mm·d −1 ) were therefore corrected to obtain calibrated sap-flow transpiration (TSF, mm·d −1 ), as referred in previous applications to tree crops [38,47,61]. This was done by mathematically relating sap-flow, SF, with transpiration computed from EC observations (TEC = ETEC-Esim). TEC represents the difference between ET obtained from EC measurements (ETEC, mm·d −1 ) and the soil evaporation (Esim, mm·d −1 ) simulated with the two phases Ritchie model [66], the latter computed following Allen et al. [4]. The computation of Esim based upon the water balance of the soil evaporation layer using soil moisture observations. Parameters characterizing that soil layer, with a depth Ze = 0.10 m, consisted of: total and readily evaporable water, respectively TEW = 18 mm and REW = 9 mm. Further information on Esim data was provided by Paço et al. [19]. This procedure allows enlarging the available field information to the entire simulation period [67,68].
The best mathematical relationships between TEC and SF ( Figure 6) were of exponential form:   T SF data were screened for outliers taking into consideration: (a) the range of values used to establish the sap flow calibration equation and the respective K cb values (K cb SF = T SF /ET o ), which should be kept within an acceptable range. The common definition of outliers by Tukey [70] was used, thus considering as outliers the K cb SF values higher than 1.5 times the interquartile range, below the first quartile or above the third quartile. The application of these rules led to discarding a total of 177 T SF values, with outliers representing 3.5% and 7% of observations in 2011 and 2012, respectively, contrasting with 56% of values computed for 2013. That high number of discarded values was most likely due to the fact that the SF equation used for 2013 was not purposefully calibrated. It was assumed that discarding the outliers decreased the uncertainties of observations and computations.

Basal Crop Coefficients Derived from Crop Height and Fraction of Ground Cover
To take into account fraction of ground cover by the crop (f c ) and the crop height (h), a density coefficient (K d ) is used with the A&P approach to estimate K cb [43]. K d (dimensionless) is defined as the minimum value among the effective ground cover corrected for the density of shading or corrected for the crop shading depending upon the crop height. Thus, K d is given by: where f c eff is the effective fraction of ground covered or shaded by vegetation near solar noon (dimensionless), M L is a multiplier on f c eff describing the effect of canopy density on shading the ground, thus on maximum relative ET per fraction of ground shaded and h (m) is the mean height of the crop vegetation. K cb is estimated from K d as when the inter-row is bare soil or, when an active ground cover is present, as K cb " K cb cover`Kdˆm ax " K cb full´Kcb cover , K cb full´Kcb cover 2 where K c min is the minimum K c for bare soil (« 0.15 for typical agricultural conditions), K cb cover is the K cb of the ground cover in the absence of tree foliage and reflects the density and vigour of the active ground cover crop and K cb full is the estimated basal K cb during the peak plant growth for conditions having nearly full ground cover. The second term of the max function allows taking into consideration the impacts of shading of the canopy over the ground cover crop. Further information is provided by Allen and Pereira [43]. The K cb full represents a general upper limit on K cb mid for tall vegetation having full ground cover and LAI > 3 under full water supply. K cb full takes into consideration crop stomatal control and is approximated as a function of the mean plant height and adjusted for climate [43], with F r (0-1) is an adjustment factor relative to crop stomatal control, the min function assumes that 1.20 is the upper bound for K cb full prior to adjustment for climate. h (m) is the average maximum crop height, u 2 (m s´1) is the average wind speed at 2 m height, RH min (%) is the average minimum relative humidity during mid-season. The parameter F r applies a downward adjustment when the vegetation exhibits more stomatal control on transpiration than it is typical of most annual agricultural crops. F r < 1.0 for various tree crops and natural vegetation. Standard values for F r for various tree crops are provided by Allen and Pereira [43] but F r values may be adjusted experimentally, namely through comparing K cb obtained with the A&P approach with those derived through a different but accurate procedure, namely through the use of models. F r may also be computed through comparing the leaf resistances for the crop (r l , s m´1) with that of grass (100 s m´1) considering the climate conditions [43], thus: where r l (s¨m´1) is mean leaf resistance for the vegetation in question (s¨m´1) ∆ is the slope of the saturation vapour pressure curve (kPa¨˝C´1), γ is the psychometric constant (kPa¨˝C´1) and u 2 is the average wind speed during the relevant crop stage measured at 2 m height (m¨s´1). r l values for various crops are tabulated by Allen e Pereira [43], who also referred that for most annual agricultural crops r l is often not far from 100 s¨m´1.

The SIMDualKc Model
The SIMDualKc water balance model [34] uses a daily time step to perform the soil water balance at the field scale through computing crop ET with the dual K c approach [4,33,43]. The SIMDualKc model adopts the approach described with Equation 1, thus assuming that ET c act = ET c when the soil water depletion fraction does not exceeds the depletion fraction for no stress, p (dimensionless).
The model computes the soil water depletion at the end of every day: where D r,i and D r,i´1 are the root zone depletion at the end of respectively day i and day i´1 (mm), P e is precipitation (mm), RO is runoff (mm), I is the net irrigation depth that infiltrates the soil (mm), CR is capillary rise from the groundwater table (mm), ET c act is actual crop evapotranspiration (mm) and DP is deep percolation through the bottom of the root zone (mm), all referring to day i. CR and DP are calculated with parametric equations described by Liu et al. [71] and RO is estimated using the curve number approach [72]. Because the groundwater table is quite deep in the region, CR was assumed to be null. The model computes the actual ET (ET c act , mm) as a function of the available soil water in the root zone using a water stress coefficient (K s , 0-1). K s is computed daily as a linear function of the depletion D r in the effective root zone [4,33]: where TAW and RAW are, respectively, the total and readily available soil water (mm) relative to the root zone depth Z r and p is the soil water depletion fraction for no stress, therefore with RAW = p TAW. Thus, ET c act = ET c when K s = 1.0; otherwise, when water and/or salinity stress occurs, ET c act < ET c and K s < 1.0. Then, because K cb act = K s K cb , it results K cb act < K cb . Similarly, it results that actual transpiration will be smaller than its potential value, thus T c act < ET c when K s < 1.0. The evaporation from the soil surface (E s , mm¨d´1) is limited by the amount of energy available at that surface in conjunction with the energy consumed as crop transpiration [4,72]. The model computes the evaporation coefficient (K e ) performing a daily water balance of the evaporation soil layer, which is characterized by its depth (Z e , m), the total evaporable water (TEW, mm) and the readily evaporable water (REW, mm). TEW is the maximum depth of water that can be evaporated from the evaporation soil layer when that layer has been fully wetted and REW is the depth of water that can be evaporated without water availability restrictions. E s is maximum when the topsoil is fully wetted by rain or irrigation and the soil surface shadowed by the crop is minimum. Differently, E s is minimum when the crop fully shadows the soil and energy available for evaporation is minimum [4,34,72].
The maximum value of K e is attained when the soil is wet. That value is limited by the energy available at the soil surface, which corresponds to the difference between K c max , representing maximum ET when the crop would fully cover the soil and K cb , representing the effective transpiration of the crop. As the topsoil dries, less water is available for evaporation and E s is reduced. This reduction in E s is proportional to the amount of water remaining in the surface soil layer. K e is then computed considering an evaporation reduction coefficient (K r ď 1.0) as K e " K r pK cmax´Kcb q Ñ with K e ď f ew Kc max (50) where K c max is the maximum value of K c (i.e., K cb + K e ) following a wetting event by rain or irrigation, generally 1.20 and f ew is the fraction of the soil that is both exposed to radiation and wetted by rain or irrigation, that is, the fraction of soil surface from which most evaporation occurs. Thus, f ew depends upon the fraction of ground covered by the crop (f c ) and of the fraction of soil wetted by irrigation (f w ), thus f ew = min(1´f c , f w ). K r is calculated using the 2-stage drying cycle approach [4,66], where the first stage is the energy limiting stage and the second is the water limited stage or falling rate stage, where evaporation decreases as evaporable water decreases in the evaporation soil layer beyond the readily evaporable water (REW): Further descriptions of the model and auxiliary equations are given by Rosa et al. [34]. The input data required by the model include: i Daily climatic data: reference evapotranspiration (ET o , mm), precipitation (P, mm), minimum relative humidity (RH min , %) and wind speed at 2 m height (u 2 , m¨s´1). ii Soil data for a multi-layered soil: number of layers and related depths d (m); the respective soil water content at field capacity and at the wilting point (θ FC and θ WP , m 3¨m´3 ) or the total available water (TAW, mm); the characteristics of the soil evaporation layer (Z e , REW and TEW); and the soil water content at planting in both the root zone and the evaporation layer expressed as a % of depletion of TAW and TEW, respectively. iii Crop data: dates of the crop growth stages (non-growing, initial, crop development, mid-season and end season); the basal crop coefficients for the non-growing, initial, mid-season and end season (K cb non-growing , K cb ini , K cb mid and K cb end ); the soil water depletion fractions for no stress at the same stages (p non-growing , p ini , p mid and p end ); root depths (Z r , m), plant height (h, m) and the fraction of ground cover by the crop (f c , %) throughout the crop season. iv Irrigation scheduling data: dates and depths of observed irrigation events. In addition, the model requires data relative to the fraction of soil wetted by irrigation (f w ). In this application, f w = 0.23 because the soil was wetted by micro-irrigation. v Parameters required to compute capillary rise and deep percolation when using the parametric equations proposed by Liu et al [71]; in the present application only the parameters a D and b D characterizing DP were used. vi Base data to compute surface runoff using the Curve Number method [72]. vii Information characterizing the active ground cover, soil residues and mulches and related effects on E s [34]. viii soil and water salinity information, however not used in the present application.

Model Calibration and Validation and Goodness of Fit Indicators
So far, the calibration and validation of the SIMDualKc model have been performed either through comparing computed actual transpiration with sap-flow measurements [38,39], simulated ET c act with EC observed evapotranspiration [73,74] or, more commonly, simulated with observed soil water content [35,37,41,75,76]. In this study, model calibration was considered as the process of adjusting influential model parameters and inputs within their reasonable ranges so that the simulated T c act values were in agreement with sap flow derived data (T SF ).
The calibration procedure consisted of adjusting the crop parameters-K cb and p values relative to the non-growing, initial-, mid-and end-season growth stages-, the soil evaporation parameters-TEW, REW and Z e -, the deep percolation parameters a D and b D and the CN of the runoff curve number algorithm, by minimizing the differences between T SF and simulated T c act . Daily data of 2011 was used. An initial set of parameters was selected: crop parameters (K cb and p) from Allen et al. [4] and Paço et al [19]; soil evaporation parameters from Paço et al. [19], CN from Allen et al. [72] and DP parameters from Paço et al. [19]. The initial soil water conditions in 2011 were observed in the field and consisted of the initial depletion of the evaporation layer, that was 40% of TEW and the initial depletion in the entire root zone, that was 40% of TAW. A trial and error procedure was then developed for selecting first the K cb values. In the following, the trial and error procedure was applied to the p values, then to the referred soil evaporation, deep percolation and, lastly, to the CN parameters.
The validation of SIMDualKc consisted of using the previously calibrated parameters (K cb non-growing , K cb ini , K cb mid , K cb end , p non-growing , p ini, p mid , p end , TEW, REW, Z e , a D , b D and CN) with daily data of 2012. T SF data relative to 2013 was used for model testing with the same calibrated parameters. The process of calibration and validation was considered satisfactory when the goodness-of-fit indicators relative to the validation were within 20% of variation relative to the calibration.
A set of goodness-of-fit indicators were used to assess the model accuracy, as in prior studies with SIMDualKc. These indicators are fully described by Pereira et al. [37]. They included a linear regression coefficient (b 0 ) of the regression forced through the origin between observed T SF and predicted T c act and the determination coefficient R 2 of the ordinary least squares regression. A regression coefficient b 0 close to 1.0 indicates that the predicted values are statistically close to the observed ones and a determination coefficient R 2 near 1.0 indicates that most of the variance of the observed values is explained by the model estimates. Errors of estimation were assessed using the root mean square error (RMSE) and the average absolute error (AAE) as indicators. Targeted values for error indicators are 0.0 which corresponds to a perfect match between simulated and observed values. In addition, to assess any bias tendency of the estimations, the percent bias (PBIAS, %) was used. The PBIAS measures the average tendency of predictions to be larger or smaller than the corresponding observations, with positive values indicating an over-estimation bias and negative values indicating an under-estimation bias. To assess the modelling quality, the Nash and Sutcliff [77] modelling efficiency (EF, dimensionless) was used. The EF is a normalized statistic that determines the relative magnitude of the residual variance compared to the measured data variance or how well observations versus simulations fit the 1:1 line [78]. EF values close to 1.0 indicate that the variance of residuals is much smaller than the variance of observations, thus that model performance is excellent. Contrarily, when EF is negative this means that there is no gain in using the model, thus that the mean of observations is as good predictor as the model.

Calibration and Validation of SIMDualKc with Sap Flow Data
The initial and calibrated values of the parameters relative to the SIMDualKc model are presented in Table 2 and they refer to the conditions observed in field. The calibrated K cb parameters are smaller than the initial ones, mainly those relative to the non-growing season and the initial periods (K cb non-growing and K cb ini ). Differences for K cb mid resulted relatively small. However, K cb mid adjusted to the climate are slightly smaller than reported in Table 2 (0.44 to 0.47) because local climate is dry and RH min is small, while K cb end are slightly increased (0.44 to 0.48) since RH min is also increased by the end-season. The calibrated p parameters closely follow those proposed by FAO56 [4]. Runoff CN changed little and deep percolation parameters did not change because these parameters were adjusted in a previous study [19]. Deep percolation a D 246 246 b D´0 .02´0.02 K cb non-growing -basal crop coefficient for the non-growing stage; K cb ini -basal crop coefficient for the initial crop development stage, K cb mid -basal crop coefficient for the mid stage, K cb end -basal crop coefficient for the late-season stage, p-depletion fraction, M L parameter, TEW-total evaporable water, REW-readily evaporable water, Z e -thickness of the evaporation layer, CN-curve number, a D and b D -deep percolation parameters.
Most studies in literature report on actual K cb values, that is, when the crop was affected by water stress since deficit irrigation is mostly used in olive orchards. In addition, most studies focus on the irrigation season only and data relative to other crop growth stages are quite scarce, namely for the non-growing period and initial crop stage. Moreover, K cb values reported in literature are not adjusted to the climate. Therefore, it results difficult to compare our results with those relative to other studies. K cb mid values of this study are similar to those reported by Santos et al. [26] when using remote sensing observations of an olive orchard under water stress conditions. Slightly lower K cb mid values were reported by Conceição et al. [59]. Differently, López-Olivari et al [69] reported much lower K cb mid values, averaging 0.28, which is likely due to water stress as commonly imposed by farmers. Higher K cb mid values (0.58˘0.14) were reported by Cammalleri et al. [18] for an intensive olive orchard with f c = 0.35. Er-Raki et al. [20] also reported a higher K cb mid of 0.54. Much higher K cb values were proposed by Allen and Pereira [43]. The p values are similar to those reported by Er-Raki et al. [20] and by Rallo et al. [79].
Results in Figure 7, comparing model simulated T c act with transpiration derived from sap-flow measurements (T SF ), show a good agreement between T c act and T SF along the three years of study. The dynamics of both T c act and T SF are coherently described for all three years but fitting is less good for 2012 due to the heavy frost and subsequent pruning that occurred by that winter. Apparently, the trees responded well to pruning and that exceptional condition could have justified using specific K cb and p values but that option was not adopted because validating the model requires using the calibrated parameters. However, despite the peculiar condition occurring in 2012, as well as the uncertainties associated with deriving T SF , model predicted T c act described reasonably well the dynamics of transpiration of the olive orchard throughout the three experimental seasons.  The dynamics of the actual crop evapotranspiration (ETc act) simulated along 2011 and 2012, which was computed with the calibrated model parameters of Table 2, is presented in Figure 8. ETc act are compared with evapotranspiration values observed with the eddy covariance system (ETEC). Despite ETEC observations were in reduced number, they could be used for further validate the model since results show that the model was able to adequately estimate the dynamics of ETc act during the mid-season stage when ETEC was measured. The average ETEC value during this stage was 2.5 mm·d −1 (±0.41, n = 28). Goodness-of-fit indicators for 2012 show a tendency for the SIMDualKc model to under-estimate ETEC (b0 = 0.94 and PBIAS = −6.0%), thus contrary to the tendency observed when Tc act was compared with TSF. However, given the reduced number of EC observations, it is not possible to draw a conclusion about model trending. An acceptably high R 2 = 0.64 was obtained, which indicates that a large fraction of the variance of ETEC observations is explained by the model. In addition, acceptable estimation errors of ETc act were obtained with RMSE = 0.42 mm·d −1 , AAE = 0.35 mm·d −1 and, consequently, a reasonably good EF value of 0.45 was obtained. Higher estimation errors for ETc act, ranging from 0.54 to 0.71 mm·d −1 , were reported by Er-Raki et al. [20]. The goodness-of-fit indicators (Table 3) show a slight tendency for the model to over-estimate T SF , with b 0 = 1.04 and PBIAS = 3.9% in the calibration year; the same trend for over-estimation was observed in 2012 and 2013, with b 0 of 1.03 and 1.17 and PBIAS of 5.2% and 13.3%. The determination coefficients are high for the first and third years, with respectively R 2 = 0.75 and 0.78; due to the problems identified to 2012, it resulted R 2 = 0.60, however reasonably high. These R 2 values indicate, therefore, that a large fraction of the variance of T SF is explained by the model. Estimation errors are reasonably low, with RMSE ranging from 0.37 to 0.53 mm¨d´1 and AAE ranging from 0.25 to 0.42 mm¨d´1. The modelling efficiency is reasonably high for the calibration year, with EF = 0.57 and acceptable for the validation and testing years. Overall, results for the goodness-of-fit indicators show that the predicted T c act values were statistically close to the sap-flow observed ones and that most of the variation of the observed values is explained by the model. Higher errors of estimation were reported by Rallo et al. [79] when using a modification of the FAO56 approach for an intensive olive orchard, with RMSE ranging from 0.30 to 0.78 mm¨d´1. Er-Raki et al. [20], also reported higher T c act estimation errors, with RMSE = 0.59 mm¨d´1. Table 3. Goodness-of-fit indicators relative to the SIMDualKc simulated transpiration (T c act ) when compared with transpiration obtained from sap flow (T SF ). The dynamics of the actual crop evapotranspiration (ET c act ) simulated along 2011 and 2012, which was computed with the calibrated model parameters of Table 2, is presented in Figure 8. ET c act are compared with evapotranspiration values observed with the eddy covariance system (ET EC ). Despite ET EC observations were in reduced number, they could be used for further validate the model since results show that the model was able to adequately estimate the dynamics of ET c act during the mid-season stage when ET EC was measured. The average ET EC value during this stage was 2.5 mm¨d´1 (˘0.41, n = 28). Goodness-of-fit indicators for 2012 show a tendency for the SIMDualKc model to under-estimate ET EC (b 0 = 0.94 and PBIAS =´6.0%), thus contrary to the tendency observed when T c act was compared with T SF . However, given the reduced number of EC observations, it is not possible to draw a conclusion about model trending. An acceptably high R 2 = 0.64 was obtained, which indicates that a large fraction of the variance of ET EC observations is explained by the model. In addition, acceptable estimation errors of ET c act were obtained with RMSE = 0.42 mm¨d´1, AAE = 0.35 mm¨d´1 and, consequently, a reasonably good EF value of 0.45 was obtained. Higher estimation errors for ET c act , ranging from 0.54 to 0.71 mm¨d´1, were reported by Er-Raki et al. [20].

Dual and Single Crop Coefficients
The standard and actual Kcb curves, the Ke curves and the standard and actual single Kc curves derived for the 3-year observed hedgerow olive orchard are shown in Figure 9. Precipitation and irrigation events are also depicted to easily interpreting the behaviour of the Ke, Kcb and Kc curves. The represented Kcb values were adjusted for climate as a function of wind speed, RHmin and crop height as proposed in FAO56 [4], so resulting slightly different from those given in Table 2 as referred before. The time-averaged standard Kc relative to the various crop stages was computed by summing the standard Kcb of the same crop stages with the daily Ke values computed for the same periods, that is, Kc = Kcb + Ke. Differently, Kc act = Kcb act + Ke, thus varying daily.
The Kcb and Kcb act curves ( Figure 9) are coincident during winter and most of autumn and spring periods when rainfall was enough to avoid water stress, that is, when Kcb act = Kcb as discussed about Equation 1. Differently, high water stress occurred during most of the mid-season stage, particularly during 2012 and 2013, when those curves indicated Kcb act < Kcb. This water stress occurred because the orchard was under-irrigated following the common practice of deficit irrigation in olive orchards, in particular because irrigations were started too late in those years. To achieve a eustress irrigation management it would be desirable that irrigation would start earlier in both 2012 and 2013, eventually adopting larger irrigation depths applied every two or three days instead of 3 mm depths every day. However, further studies are required to better defining the best eustress management with consideration of impacts of transpiration deficits on yields.
Soil evaporation Ke curves show to react daily to the soil wetting events, mainly with various peaks occurring in response to rainfall events (Figure 9). During the rainfall season, from early autumn to early spring, Ke is often high because the inter-row is wide and solar energy is then available at the soil surface. During mid-season soil evaporation decreases and Ke drops because soil dries and residues of the ground cover vegetation act as an organic mulch to limit evaporation. Ke peaks are much small during most of the mid-season stage because irrigation was applied along the row of trees, so under crop shadow, thus resulting in limited energy available for evaporating the

Dual and Single Crop Coefficients
The standard and actual K cb curves, the K e curves and the standard and actual single K c curves derived for the 3-year observed hedgerow olive orchard are shown in Figure 9. Precipitation and irrigation events are also depicted to easily interpreting the behaviour of the K e , K cb and K c curves. The represented K cb values were adjusted for climate as a function of wind speed, RH min and crop height as proposed in FAO56 [4], so resulting slightly different from those given in Table 2 as referred before. The time-averaged standard K c relative to the various crop stages was computed by summing the standard K cb of the same crop stages with the daily K e values computed for the same periods, that is, K c = K cb + K e . Differently, K c act = K cb act + K e , thus varying daily.
The K cb and K cb act curves ( Figure 9) are coincident during winter and most of autumn and spring periods when rainfall was enough to avoid water stress, that is, when K cb act = K cb as discussed about Equation 1. Differently, high water stress occurred during most of the mid-season stage, particularly during 2012 and 2013, when those curves indicated K cb act < K cb . This water stress occurred because the orchard was under-irrigated following the common practice of deficit irrigation in olive orchards, in particular because irrigations were started too late in those years. To achieve a eustress irrigation management it would be desirable that irrigation would start earlier in both 2012 and 2013, eventually adopting larger irrigation depths applied every two or three days instead of 3 mm depths every day. However, further studies are required to better defining the best eustress management with consideration of impacts of transpiration deficits on yields.  Soil evaporation K e curves show to react daily to the soil wetting events, mainly with various peaks occurring in response to rainfall events (Figure 9). During the rainfall season, from early autumn to early spring, K e is often high because the inter-row is wide and solar energy is then available at the soil surface. During mid-season soil evaporation decreases and K e drops because soil dries and residues of the ground cover vegetation act as an organic mulch to limit evaporation. K e peaks are much small during most of the mid-season stage because irrigation was applied along the row of trees, so under crop shadow, thus resulting in limited energy available for evaporating the irrigation water.
Differently of the time-averaged standard K c curves, the K c act curves show numerous peaks in response to the rainfall events ( Figure 9) since these curves represent K c act = K cb act + K e as referred above. The K c and K c act curves are coincident in the periods without water stress, thus during the rainy season, roughly from October to May. The standard and actual K c values during the non-growing periods and the initial stage are highly dependent upon the precipitation amounts. Differently, the K c act curves lay bellow the K c curve under water stress conditions during mid-season. Figure 9 clearly shows the contrasting behaviour of standard K c and K cb . The above described dynamics of K c curves, particularly the dependence of K c values from soil evaporation, mainly due to soil wettings by precipitation, explains why the time-averaged standard K c mid is smaller than K c non-growing and K c ini , that refer to the rainy season, while the higher standard K cb values are for the mid-season, K cb mid , thus when transpiration is higher under irrigation.
The time averaged K c are presented in Table 4 for all crop stages of 2011, 2012 and 2013. K c ini values, ranging 0.70 to 0.96, are in the range of values reported for intensive olive orchards [43,80,81]. The K c mid values ranged 0.70 to 0.78, which are comparable with values reported by various authors [18,43,81,82]. K c values for the late season (0.79 to 0.90) increased relative to the mid-season due to the occurrence of various precipitation events. High K c end values found in the present study are comparable with those reported by Testi et al. [80].

K cb Predicted with the A&P Approach vs. K cb Obtained with SIMDualKc
The A&P approach (Section 2.4, Allen & Pereira [43]) was applied with f c and h data observed along the three seasons. The dynamics of f c and h are presented in Figure 10a in conjunction with the corresponding computed values for K cb (K cb A&P ), which are compared with the standard K cb obtained with SIMDualKc for the same days (K cb SIMDualKc ), resulting a close match (Figure 10b) except for the cases that follow the heavy frost with great defoliation and severe pruning in the winter of 2012.
When computing the density coefficient K d (Equation (3)) the value M L = 1.5 proposed by Allen and Pereira [43] was used. Nevertheless, because insufficient information on shadowing was available, it was assumed f c = f c eff¨Kcb full (Equation (5)) was computed with observed weather data for the various crop stages and considering the observed crop height. The F r values were obtained after applying a simple trial and error procedure against the values obtained by the model. That trial and error procedure was initiated with the value F r = 0.48 proposed by Allen and Pereira [43] for the entire season and olive orchards without ground cover but just with residues of old leaves. The resulting value for the non-growing and the initial stages was F r = 0.49, thus about the same as the proposed one, while values for both the mid-and late-season were respectively 0.55 and 0.53. These slightly higher values of F r were likely due to the fact that less stomatal control was required by Arbequina olives under irrigation. Nevertheless, the estimated F r = 0.48 proposed by Allen and Pereira [43] would also provide for quite good K cb estimations. The regression coefficient relating both Kcb sets ( Figure 11) results close to the unit (b0 = 0.97), thus indicating a good overall match, while the determination coefficient is high (R 2 = 0.77). The estimation of Kcb A&P approach has a small RMSE of 0.05 relative to the modelled Kcb SIMDualKc values. Comparing the mean square error of Kcb A&P with the variance of the Kcb SIMDualKc values it resulted a high EF of 0.76. In conclusion, results of comparing both sets of Kcb values indicate that the A&P approach is adequate for estimating Kcb values to be used when assessing crop water requirements for olives and to support irrigation management decision making.   For the period from November to April, K cb were computed from K d with Equation 4b relative to the case when active ground cover exists. A variable K cb cover , from 0.004 to 0.01, was used. For May to October, the Equation 4a was used with K c min = 0. 15 Results in Figure 10b show that K cb computed with the A&P approach match quite well the K cb SIMDualKc except for the cases that follow the heavy frost that occurred in the winter of 2012, which produced a great defoliation and required a severe pruning. Consequently, K cb A&P were then smaller than the K cb non-growing obtained with SIMDualKc. For all other cases, K cb A&P values were close to the K cb SIMDualKc estimates.
The regression coefficient relating both K cb sets ( Figure 11) results close to the unit (b 0 = 0.97), thus indicating a good overall match, while the determination coefficient is high (R 2 = 0.77). The estimation of K cb A&P approach has a small RMSE of 0.05 relative to the modelled K cb SIMDualKc values. Comparing the mean square error of K cb A&P with the variance of the K cb SIMDualKc values it resulted a high EF of 0.76. In conclusion, results of comparing both sets of K cb values indicate that the A&P approach is adequate for estimating K cb values to be used when assessing crop water requirements for olives and to support irrigation management decision making.
The regression coefficient relating both Kcb sets ( Figure 11) results close to the unit (b0 = 0.97), thus indicating a good overall match, while the determination coefficient is high (R 2 = 0.77). The estimation of Kcb A&P approach has a small RMSE of 0.05 relative to the modelled Kcb SIMDualKc values. Comparing the mean square error of Kcb A&P with the variance of the Kcb SIMDualKc values it resulted a high EF of 0.76. In conclusion, results of comparing both sets of Kcb values indicate that the A&P approach is adequate for estimating Kcb values to be used when assessing crop water requirements for olives and to support irrigation management decision making.

Water Balance and Respective Components
The terms of the soil water balance computed with the SIMDualKc model are presented in Table 5. There are appreciable differences among years which mainly steam from the differences in precipitation (P, mm). This is particularly the case of deep percolation and runoff (DP and RO, mm), which are much higher in the wet year of 2013, representing 47% of precipitation, which contrast with smaller DP and RO values in 2011 that represent 34% of the precipitation total. Those percent values indicate that most of precipitation, 53 to 66%, was used by the crop. As it could be expected, the larger amount of DP and RO occurred during the non-growing, initial, crop development and late season crop stages, that is, during the rainy season, which coincides with the period when crop water demand, evapotranspiration, is smaller as analysed relative to Figures 7 and 9. However, the distribution of DP and RO throughout the year varied enormously as a consequence of the inter-and intra-annual variability of the precipitation, as it may be noticed in Figure 1. DP and RO were very small during the mid-season and their occurrence refers only to a few rainfall events. The use of small drip irrigation applied depths makes that DP and RO are not originated by irrigation; moreover, the deficit irrigation management adopted also, likely, did not influence DP or RO occurrences.
The soil water storage (∆SW, mm) at end of each crop stage and of the year greatly varied inter and intra-annually, mostly due to the referred variability of precipitation and likely less influenced by irrigation management as indicated by similar ∆SW values at end of the late season. This fact agrees with the conclusion that the adopted deficit irrigation management did not contribute to operational water losses.
Because rainfall was very small during the periods of large crop water demand, irrigation represented 39%, 56% and 50% of ET c act respectively in 2011, 2012 and 2013. Overall, irrigation occurred during the mid-and late season, mainly the former. These results show the great contribution of irrigation to achieve successful olives growth and yields, particularly in case of super-intensive olives orchards. Naturally, most of evapotranspiration occurred during the mid-season and, however less important, during the late-season. Soil evaporation exceeded transpiration during the non-growing and initial crop stages because E s mostly originated from the inter-row when wetted by rainfall.
The large values of E s estimated for the mid-season were mostly due to rainfall events that occurred early in that season; similarly, most of E s estimated for the late season also were due to rainfall events wetting the exposed inter-row. E s originated from irrigation was reduced because energy available under the canopy shadow was little. Table 5. Simulated soil water balance components (all variables in mm).

Crop Growth Stages
Year P  I  ∆SW  RO  DP  E s  T c act  ET c act   Non-growing   2011  189  0´20  11  54  70  34  104  2012  76  0  35  0  30  37  45  82  2013  224  0´20  12  85  63  43  106   Initial   2011  37  0´16  0  3  11  7  18  2012  36  5  8  0  0  20  30  50  2013  106  0´15  5  54  23  10  The consumptive use of water is analysed in Table 6. The ratios of E s /ET c act show that E s represents 45 to 67% of ET c act during the non-growing stage and 40 to 70% during the initial crop stage. These periods are those when more precipitation occurs, so where the soil is frequently wetted by rain and soil cover is less, particularly in the inter-row. Thus, soil evaporation is the main consumptive water use during those stages. During the crop development, mid-season and late season stages, transpiration becomes the most important, corresponding to 52 to 67% of ET c act . The variability of the ratio E s /ET c act is then quite small, depending upon the occurrence of precipitation, which is the main source of soil wetting in the inter-row and of the subsequent evaporation. E s could likely be reduce if less frequent but larger irrigation amounts would be used instead of daily irrigation events averaging 3 mm per event. E s /ET c act ratios smaller than those computed in this study were reported by various researchers but referring to the irrigation season only [18,20,69]. Less frequent irrigations are also referred in these studies. Table 6. Ratios of soil evaporation to actual evapotranspiration (E s /ET c act, %) and of actual to potential evapotranspiration (ET c act /ET c %).

Years
Non Results relative to the ratio ET c act /ET c ( Table 6) show that ET c act was smaller by 3%, 18% and 14% relative to the potential ET c in 2011, 2012 and 2013, respectively. During the mid-season, that ratio ET c act /ET c was small for the years of 2012 and 2013, when ET c act was smaller by respectively 30% and 22% comparatively to the potential ET c . Those decreases are likely excessive as analysed before ( Figure 9) and may have affected yields, namely that of 2012. Adopting eustress irrigation, the ratio ET c act /ET c should likely not decrease below 90%. However, this threshold needs to be better assessed in terms of yield and economic impacts.

Conclusions
The calibration, validation and testing of the SIMDualKc model for a super high density Arbequina olive orchard was successfully performed using measurements of sap flow plant transpiration and eddy covariance evapotranspiration. Three years of field studies, from 2011 to 2013, were used, which made it possible to partitioning olive orchard ET into actual transpiration and soil evaporation. The results showed a good accuracy of the model to simulate transpiration during both the growing and non-growing seasons. Goodness of fit indicators were less good for 2012 when the orchard suffered an intense defoliation following a great frost and, later, a heavy pruning. However, the model could well represent the dynamics of evapotranspiration, transpiration and soil evaporation throughout the three years.
The calibration of the model and its validation and testing provided for updated basal and single crop coefficient curves for potential and actual crop water use, as well as soil evaporation coefficients. The standard K cb were close to 0.30 during the non-growing and initial crop stages and 0.48 during the mid-season. Differently, the standard K c varied from 0.70 to 0.96 during the non-growing and initial crop stages and decreased to 0.66 to 0.78 during the mid-season. The variability of standard K c values results from the fact that, contrarily to K cb , the K c values depend upon soil evaporation, consequently also upon precipitation. It may be concluded that for perennial crops, as olive orchards and other woody crops, it is important to focus on using the dual instead of single K c , thus in using basal K cb .
The A&P approach for estimating K cb values from the fraction of ground cover and crop height was tested against the K cb values obtained with the model SIMDualKc after calibration. The K cb obtained with A&P matched well the K cb values obtained from SIMDualKc. Thus, results allow assuming that the A&P approach is useful to accurately estimating the K cb values required to assess crop water requirements and deciding irrigation management practices of olives orchards. Likely, that conclusion may be extended to other crops under condition of properly parameterizing K cb full used for computing K cb from f c and h.
For the three years, deep percolation and runoff totalized 34% to 47% of the precipitation, thus with most of precipitation being used as crop evapotranspiration. Those percent values highly depend upon the annual distribution of precipitation and were not depending upon irrigation because frequent and small application depths were used. Soil water storage also revealed to vary along the year with precipitation. Soil evaporation ranged from 42% to 45% of annual olives ET, with E s > T c act during the rainy season, the contrary occurring during the irrigation period. This fact also relates with the above referred irrigation management practiced. Irrigation amounts for 39% to 56% of the actual crop ET, which confirms the great importance of irrigation for super intensive olive orchards. However, those amounts correspond to deficit irrigation, with ET c act smaller than potential ET c by 30% and 22% in 2012 and 2013, respectively. Those deficits are apparently excessive relative to a desirable eustress management that could lead to high yields and save water. Further research is required along these lines.