Transpiration and Water Use of an Irrigated Traditional Olive Grove with Sap-Flow Observations and the FAO56 Dual Crop Coefﬁcient Approach

: The SIMDualKc model was applied to evaluate the crop water use and the crop coefﬁcient (K c ) of an irrigated olive grove ( Olea europaea L.) located in Sicily, Italy, using experimental data collected from two crop seasons. The model applies the FAO56 dual K c approach to compute the actual crop evapotranspiration (ET c act ) and its components, i.e., the actual tree transpiration (T c act ), obtained through the basal crop coefﬁcient (K cb ), and soil evaporation according to an evaporation coefﬁcient (K e ). Model calibration was performed by minimizing the difference between the predicted T c act and the observed daily tree transpiration measured with sap ﬂow instrumentation (T SF ﬁeld ) acquired in 2009. The validation was performed using the independent data set of sap ﬂow measurements from 2011. The calibrated K cb was equal to 0.30 for the initial and non-growing season stages, 0.42 for the mid-season, and 0.37 for the end season. For both seasons, the goodness-of-ﬁt indicators relative to comparing T SF ﬁeld with the simulated T c act resulted in root mean square errors (RMSE) lower than 0.27 mm d − 1 and a slope of the linear regression close to 1.0 (0.94 ≤ b 0 ≤ 1.00). The olive grove water balance simulated with SIMDualKc produced a ratio between soil evaporation (E s ) and ET c act that averaged 39%. The ratio between actual (ET c act ) and potential crop evapotranspiration (ET c ) varied from 84% to about 99% in the mid-season, indicating that the values of ET c act are close to ET c , i.e., the adopted deﬁcit irrigation led to limited water stress. The results conﬁrm the suitability of the SIMDualKc model to apply the FAO56 dual K c approach to tree crops, thus assessing the water use of olives and supporting the development of appropriate irrigation management tools that are us-able by farmers. A different way to estimate K cb is based on the approach suggested in 2009 by Allen and Pereira (A&P), which involves the measured fraction of ground covered (shaded) by the crop and the height of the trees. Its application to the studied grove produced the mid-season K cb values ranging from 0.40–0.45 and end-season K cb values ranging from 0.35–0.40. The comparison between the A&P-computed T c act A&P and T SF ﬁeld shows RMSE values ranging from 0.27 to 0.43 mm d − 1 , which demonstrates the adequacy of the latter approach for parameterizing water balance models and for irrigation scheduling decision making.


Introduction
Olives (Olea europaea L.) represent one of the most important perennial crops in the Mediterranean agricultural system, in terms of both the quantities produced and the extent of the cultivated area. Italy ranks second in the world, after Spain, with the main producing areas located in Southern Italy. Olives have been cultivated since ancient times in the Mediterranean basin. Traditional olive groves are frequently grown in terraces, and are rain-fed, with low planting densities and a low degree of mechanization. At present, those olive groves have questionable sustainability [1,2]. Therefore, many olive groves have been transformed into irrigated intensive or super-intensive orchard systems, of which the cropped areas continue to increase [3][4][5]. New olive-production systems consist of very high-density drip-irrigated orchards, with up to 2000 trees/ha, which are well adapted for full mechanization [6,7]. These production systems provide high economic returns but are quite demanding in terms of water, capital and management [8]. Their demand for water faces increased competition with other agricultural and non-agricultural water users, and climate change adds to the uncertainty associated with the quantity and distribution of rainfall throughout the crop season, affecting the sustainability of olive groves [2]. Consequently, the accurate prediction of water use throughout crop seasons, i.e., crop evapotranspiration (ET c ), is essential for accurate irrigation management and for the adoption of water-saving measures [9][10][11].
The potential ET c for olive groves is commonly estimated using the FAO56 K c -ET o approach, which combines the grass reference evapotranspiration value, ET o , defining the atmospheric evaporative demand, and a crop coefficient, K c , reproducing the differences between the bio-physical characteristics of the grass reference crop (canopy properties, ground cover, aerodynamic resistance) and the studied crop [12,13]. The FAO56 K c -ET o approach can be applied with a single or a dual crop coefficient. In the former, soil evaporation and crop transpiration are merged into a single K c value for each crop stage; in the latter, the daily plant transpiration is based on the basal crop coefficient (K cb ), whereas the daily soil evaporation is estimated using an evaporation coefficient (K e ). Thus, ET c is split into crop transpiration (T c = K cb ET o ) and soil evaporation (E s = K e ET o ). The standard tabulated K c and K cb values for trees and vines were recently reviewed and updated [14].
The standard tabulated values of K c and K cb allow ET c to be evaluated under potential and well-watered conditions [12]. However, under natural field conditions, the crop is often subjected to biotic and abiotic stress due to water deficits caused by insufficient irrigation, inappropriate management practices, soil quality and salinity, or unsuitable crop varieties. Thus, a water stress coefficient, K s , ranging between 0 and 1.0, is introduced as a multiplicative factor to estimate actual values of K c or K cb , i.e., K c act or K cb act . The actual crop evapotranspiration (ET c act ) is generally smaller than the potential value (ET c ) and can be defined as ET c act = (K s K cb + K e ) ET o = K c act ET o (1) Olive crop water requirements, in addition to climate, cultivar and orchard management, depend on crop training, which influences crop height and the fraction of ground cover that results from the tree size and density, as well as on the frequency of irrigation and rain events, which affect the wetted fraction of the soil surface [5,15]. Moreover, woody perennial crops such as olives are characterized by sparse vegetation, with a large fraction of the soil not covered and directly exposed to solar irradiance, and thus subjected to soil evaporation (E s ). The latter, therefore, represents an important fraction of crop ET. For sparse vegetation systems, the dual crop coefficient approach has to be considered more accurate than the single K c because it allows for the separate estimation of T c and E s , thus accounting for the effects of wetting events and soil management practices on the different terms of the water balance [5]. A wide review on crop coefficients for trees and vines [14] has shown that the variability in K c values is large and much greater than the variability in K cb values, particularly by the end season, as well as in the initial and the late seasons, which results from rainfall events occurring during these periods. Aiming at ET partitioning [16], studies have been carried out based on soil evaporation, measured in mi-crolysimeters; actual crop transpiration, determined with sap flow sensors [5,17,18]; and/or actual crop evapotranspiration, obtained using eddy covariance techniques [4,19,20], as reviewed by Pereira et al. [21]. A different approach that is currently used is remote sensing, namely, exploring the relationships between K cb act and a spectral vegetation index [22][23][24][25], which allows its use, together with ground data, in modeling [21]. Properly calibrated models may be used to evaluate crop water requirements, to support proper irrigation management and to evaluate the impact of crops and management, even under the application of water deficit strategies. However, models implement different structures and often do not apply the FAO K c -ET o approach, e.g., in the remote sensing-based two-source energy balance algorithm [19] and the transient model Hydrus-2D [26]. Further examples were recently reviewed [21]. Among the dual K c models, the SIMDualKc model [27,28] is used in the present study since it applies the FAO dual-K c approach, which is suitable for olive orchards [4,5] and other woody perennial crops, such as vineyards [29,30] and peach trees [7].
As an alternative to the use of models, Allen and Pereira [31] proposed the A&P approach for estimating K cb and/or K c , adopting a density coefficient (K d ), which is calculated based on observations of the fraction of the ground covered (shaded) by the plants' canopy (f c ) and the crop height (h). The estimation also takes into consideration two other parameters, the multiplier on f c describing the effect of canopy density (M L ) and the resistance correction factor (F r ). M L represents the canopy's transparency to solar radiation while F r is an empirical downward adjustment when the vegetation exhibits more stomatal adjustment on transpiration. The value of f c may be measured using ground or remotely sensed data [32]. Application examples are provided in other publications [5,25]. A full review of parameter values for M L and F r allowed the calibration of these parameters for numerous annual and perennial crops, including olives [33]. The resulting tabulated F r and M L parameters are therefore available for the application of the A&P approach, but require validation, which is provided in the current study.
The objectives of this article consist of determining and analyzing the seasonal dynamics of the K c and K cb values of the studied traditional olive grove and partitioning ET c act into actual crop transpiration and soil evaporation, thus assessing the terms of the water balance. These objectives are innovative in terms of the calibration and validation of the SIMDualKc model in a traditional olive grove using measured sap-flow and meteorological data, aiming to use the model to support the irrigation water management of olive groves. Our objectives also include the testing of the recently parameterized A&P approach to derive K cb from the observed f c and h values and the tabulated M L and F r [33], which can be considered a useful approach to improving irrigation management in the field practice.

Site Description and Crop Characterization
The field data acquisition was carried out during 2009 and 2011 in the olive field of "Tenute Rocchetta", located in Castelvetrano, Sicily (37 • 64 94 N, 12 • 84 92 E, 123 m a.s.l.). Climatic and irrigation data and crop characteristics were also available for 2010 and could be used for simulations but not for model assessments. The olive grove (Olea europaea L., var. Nocellara del Belice) covers 13 ha, with a plant density of 250 trees/ha spaced 5.0 m along the row, which are roughly oriented from East to West, with 8.0 m between rows [26]. Rallo et al. [18] previously described the studied orchard and reported an average crop height of about 3.5 m and an average effective root depth of 1.0 m. The soil textural class, down to a depth of 1.0 m, is sandy clay loam (clay = 24%, silt = 16%, and sand = 60%). The average soil water content at the field capacity at the same depth is equal to 0.32 cm 3 cm −3 , whereas the soil water content at the wilting point is equal to 0.08 cm 3 cm −3 . At a 1.0 m depth, the total available water (TAW) equals 240 mm. The total (TEW) and readily (REW) evaporable water were initially estimated according to Allen et al. [12,16] and then modified during the model calibration. More details on the physical characterization of the soil profile are provided in [34,35]. The climate is the typical Mediterranean, with annual rainfall ranging between 600 and 800 mm, most of which is concentrated in fall and winter; the average monthly temperatures range from 9 • C to 24 • C respectively in January and July.
The agrometeorological data were available from a weather station with standard equipment installed by the Servizio Informativo Agrometeorologico Siciliano (SIAS), located northwest of the experimental site, at a distance of about 500 m. Moreover, a four-component net radiometer (NR01, Hukseflux, Manorville, New York, NY, USA), installed above the crop canopy at 5.60 m from the ground, allowed the monitoring of the net radiation (R n ) and its components. The weather station provided hourly measurements of standard climate variables (incoming short-wave solar radiation, air temperature and air humidity at 2 m height, wind velocity and direction at 10 m height, and daily precipitation). The monitored climate variables were used to estimate the reference crop evapotranspiration (ET o , mm d −1 ) using the PM-ET o equation [12]. Figure 1 shows the main daily climate variables observed in the period 2009-2011.
Water 2021, 13, x FOR PEER REVIEW 4 of 21 readily (REW) evaporable water were initially estimated according to Allen et al. [12,16] and then modified during the model calibration. More details on the physical characterization of the soil profile are provided in [34,35]. The climate is the typical Mediterranean, with annual rainfall ranging between 600 and 800 mm, most of which is concentrated in fall and winter; the average monthly temperatures range from 9 °C to 24 °C respectively in January and July. The agrometeorological data were available from a weather station with standard equipment installed by the Servizio Informativo Agrometeorologico Siciliano (SIAS), located northwest of the experimental site, at a distance of about 500 m. Moreover, a fourcomponent net radiometer (NR01, Hukseflux, Manorville, New York, NY, USA), installed above the crop canopy at 5.60 m from the ground, allowed the monitoring of the net radiation (Rn) and its components. The weather station provided hourly measurements of standard climate variables (incoming short-wave solar radiation, air temperature and air humidity at 2 m height, wind velocity and direction at 10 m height, and daily precipitation). The monitored climate variables were used to estimate the reference crop evapotranspiration (ETo, mm d −1 ) using the PM-ETo equation [12]. Figure 1 shows the main daily climate variables observed in the period 2009-2011.     The dates defining the beginning and the end of crop phenological stages are indicated in Table 1 for the three years of study. They follow the FAO56 guidelines [12] adapted to evergreen trees, thus including a non-growing stage, which corresponds to the period of dormancy of the crop. The initial stage starts when the dormancy ends at budburst after chilling requirements are completed and the cumulative degree-days satisfy the heat requirements. The dates from the beginning of the initiation until the late season (Table 1) are analogous to those considered by other authors [36][37][38][39]. The initiation stage is rather short, and the crop development stage runs until the initiation of flowering. The mid-season is the longest stage and ends at the beginning of fruit maturity. Irrigation water was applied using a drip irrigation system with drip-lines placed along the crop rows with four 1.0 m-spaced on-line auto-compensating emitters per tree, having a nominal discharge of 8 L h −1 . After irrigation, the soil wetted fraction f w was observed to average 0.11 [18]. Observations of f w [12] were determined by simply measuring the ground surface wetted by a few emitters. The fraction of ground covered (shaded) by vegetation (f c ) was visually estimated using photographs of the ground shadow taken 2 m above the tree canopy near solar noon and was estimated to be approximately 0.35 during the mid-season and the end season [18,40]. Seasonal irrigation depths, supplied according to the farmer's decision, were 81, 33, and 150 mm respectively for 2009, 2010, and 2011. Table 2 summarizes the amounts of precipitation and irrigation applied to the field at each crop stage during those three years.

Sap Flow and Transpiration Data
The hourly transpiration of three olive trees having trunk diameter dimensions representative of the whole field was estimated based on sap-flow measurements and the heat dissipation technique (HDT) [41], from day of the year (DOY) 160 to 276 in 2009, and 130 to 306 in 2011 [18]. HDT involves direct measurements in the trunk section. It consists of two short needles inserted radially into the trunk at a distance of about 10 cm and equipped with two thermocouples, allowing one to measure the difference in temperature (∆T) between them. Therefore, HDT measures the heat dissipated in the sapwood, which rises with increasing sap flow. The lower the sap-flow velocity, the higher the temperature difference between the two needles due to the reduced dissipation of heat from the heated upper needle. Hence, on a daily time step, the maximum difference in temperature between the probes (∆T max ) indicates minimum or null flux in the sapwood [41][42][43].
The sap flow density ν (m 3 m −2 s −1 ), is calculated with a species-independent relationship, calibrated empirically [44]: where ∆T is the difference in temperature and ∆T max is the maximum value of ∆T. The knowledge of the conductive xylem area, A (m 2 ), allows the calculation of the sap flux F (m 3 s −1 ) as: This method has been used in several studies, including with olive trees [4,23,43]. In each monitored olive tree, two thermal dissipation probes (TDPs) (SFS2 TypM-M, UP GmbH Firmensitz, Ibbenbüren, Germany) were installed in the concave and convex part of the trunk exposed to the north side, at about 40 cm from the ground, and insulated to avoid direct sun exposure. All the probes were connected to a CR1000 datalogger (Campbell Scientific Inc., Logan, Utah) and acquired at an hourly time step.
The sapwood area was determined at the end of the experiment by measuring the sapwood depths of six cores extracted with a Pressler gimlet [18].
For each tree, the daily integral of hourly sap fluxes, F, computed with Equation (3) was assumed as corresponding to tree transpiration, after neglecting the effects of tree capacitance [45], at a daily time step. The daily transpiration depth (T SF plant , mm d −1 ) was determined as the ratio between the daily flux (l d −1 ) and the area dominated by a single tree, A plant = 40 m 2 . Then, to upscale T SF plant to the whole field (T SF field ) , the average leaf area index measured in the field (LAI field , m 2 m −2 ) was normalized according to the corresponding LAI obtained for the same tree where sap flow sensors were installed (LAI plant , m 2 m −2 ); thus, it was assumed as the proximal variable: The values of LAI field and LAI plant were measured with the LAI-2000 (Li-Cor Inc., Lincoln, NE, USA) as proposed by Villalobos et al. [46] and explained in detail by Cammalleri et al. [23]. The average LAI field and LAI plant were 0.89 and 1.27, respectively [18,23].

The SIMDualKc Model and Simulation of Transpiration Fluxes
The SIMDualKc soil water balance model [27,28] adopts the dual crop coefficient approach proposed in FAO56 [12,16] to compute both components of ET c act with a daily time step. The resulting model outputs of actual transpiration (T c act , mm) and soil evaporation (E s , mm) fluxes are suitable to assess the fate of the water used by the crop (precipitation and irrigation), which is of particular interest for partial-cover woody perennial crops, as demonstrated in previous model applications [4,5,7,29].
The model algorithms are detailed by Rosa et al. [27] and were recently described by Pereira et al. [21]. The model presents several options: (a) the computation of crop irrigation water requirements; (b) the calibration and validation of the model for crops cultivated in well-defined environmental and cropping conditions, e.g., with and without ground cover; (c) the development of irrigation scheduling alternatives for field applications; (d) the assessment of a given irrigation schedule; and (e) the computation of water balance terms.
The soil water balance is solved with a daily time step by considering the depletion, D r , in the root zone at days i and i − 1 as: where D r,i and D r,i−1 (mm) refer to the end of days i and i − 1, respectively; (P − RO) i is the infiltrated precipitation, obtained as the difference between gross precipitation P i and runoff RO; I i , CR i , ET c act,i , and DP i , are respectively the net irrigation, the capillary rise, the actual crop evapotranspiration and the deep percolation, with all terms expressed in mm and referring to the day i. The runoff term is computed according to the curve number method [47], whereas capillary rise and deep percolation are computed according to the method of Liu et al. [48]. Considering Equation (1), the actual daily crop transpiration and soil evaporation are given as: For each day, the stress factor K s is estimated as a linear function of the root zone depletion D r (mm): where TAW is the total available soil water (mm) and RAW is the readily available soil water (mm), with RAW = p TAW, and p is the soil water depletion fraction for no-stress [12]. K s < 1.0 when the root zone depletion exceeds RAW, i.e., the water depleted fraction is larger than p.
The soil evaporation coefficient, K e , is maximum immediately after the occurrence of wetting events (rainfall or irrigation) and when the canopy partially covers the wetted soil surface. That maximum depends upon the maximum K c value (K c max ), which represents the upper limit of evaporation and transpiration from any cropped surface and reflecting the natural constraints placed on available energy upon the transpiration coefficient K cb in the same day, thus upon K c max − K cb [12,31,49] . However, it varies daily with the amount of water available for evaporation in the topsoil; K e is estimated through a dimensionless reduction factor, K r , as: (9) where f ew represents the fraction of soil wetted and exposed to direct solar radiation, which may be estimated as f ew = min(1 − f c , f w ) based on the fractions of ground covered (shaded) by the vegetation canopy (f c ) and wetted by irrigation (f w ). The value of K r depends upon the cumulative depth of water depleted from the topsoil and is calculated through the daily soil water balance of the soil evaporation layer of thickness Z e (m). Computations assume that the drying cycle occurs in two stages, the first limited by the available energy at the soil surface and the second by the water available in the topsoil [12,16], thus with K r decreasing when the evaporated depleted water exceeds the readily evaporable water (REW). Thus, K r is computed as: where D e,i−1 is the amount of water evaporated from the evaporable soil layer at the end of day i − 1.
The model input requirements in the current study consider the following data: (a) Soil data: soil depth (m); the soil water content at field capacity (θ FC , m 3 m −3 ) and at the permanent wilting point (θ WP , m 3 m −3 ), the values of which were measured; the depth of the soil evaporation layer (Z e , m) and the total and readily evaporable water (TEW and REW, mm), which were estimated based on [12]; and the measured values of the initial soil water available in the root zone and the Z e soil layer, expressed as a percentage of TAW and TEW, respectively. (b) Climatic forcing at the daily time-step: rainfall (P, mm), reference crop evapotranspiration (ET o , mm d −1 ), minimum and maximum air temperature (T min and T max , • C), minimum relative air humidity (RH min , %), and wind speed measured at a 2 m height (u 2 , m s −1 ). (c) Crop data: dates for the start of the crop stages (non-growing, initial, crop development, mid-season, late-season and end-season); initial values of K cb for the considered crop stages; the soil water depletion fraction p for no stress for the same stages; root depth (Z r , m); tree height (h, m); the fraction of ground covered by vegetation (f c ) at the same stages; and the row orientation and spacing. (d) Irrigation data: fraction of soil wetted (f w ); applied depths (I i , mm) and the respective dates. (e) Other data: the initial default values a D and b D for the deep percolation parametric function proposed by Liu et al. [48]; the initial value for the curve number (CN) used to estimate runoff following Allen et al. [47]. Capillary data were not observed because a groundwater table was not present.
Output results refer to the daily variation of soil water availability in the root zone, the actual crop evapotranspiration and transpiration, and of the other terms of the soil water balance related to water use. Intermediate results of computations may also form part of the output data.

Estimation of K cb Values from Observations of the Fraction of Ground Cover and Crop Height: The A&P Approach
The practical application of the dual K c approach for supporting field irrigation management may be easier when adopting the A&P approach [31], as recently reviewed in [32,33]. In the A&P approach, K cb A&P is expressed as a function of a density coefficient (K d ). For bare soil in the inter-row, it is estimated as: where K cb full is the estimated K cb during peak plant growth for conditions having nearly full ground cover (or LAI > 3), and K c min is the minimum basal K c for bare soil (0.15 under typical agricultural conditions). The density coefficient K d is estimated from observations of the fraction of the ground covered by vegetation (f c ) and of plant height (h) and describes the increase in K c with increases in the amount of vegetation. Following [31], K d is estimated as: (12) where f c eff is the effective fraction of the ground covered or shaded by vegetation (0.01-1) near solar noon, M L is a multiplier on f c eff describing the effect of canopy density on shading and maximum relative ET per fraction of shaded ground (1.0-2.0), and h is the mean vegetation height (m), as recently reviewed [33].
The K cb full value in Equation (11) represents an upper limit on K cb mid for vegetation under an adequate water supply having a full ground cover and a LAI value higher than 3. Following [12], the K cb full value can be approximated as a function of mean h and adjusted for climate conditions as: where u 2 is the average daily wind speed (m s −1 ) at a height of 2 m above ground level during the growth period, RH min (%) is the average daily minimum relative humidity during the growth period, and h is the mean plant height (m) during the mid-season. Before climatic adjustment, an upper limit for K cb full is 1.20 (Equation (13)). The effect of the crop height is considered through the sum (1 + k h h), with k h = 0.1 for tree and vine crops [32,33].
Higher K cb full (Equation (13)) values are expected for taller crops and in cases in which the local climate is drier or windier than the standard climate conditions (RH min = 45% and u 2 = 2 m s −1 ). The parameter F r applies an empirical adjustment (F r ≤ 1.0) when the vegetation shows more stomatal adjustment upon transpiration, which is typical of most annual crops. For trees and vines, F r is high when crops exhibit great vegetative vigor and decreases due to the effect of pruning and training, as well as under a limited water supply. Adopting the definition proposed by Allen et al. [12] for F r , it is assumed that: r l r typ (14) where r l and r typ are, respectively, the mean leaf resistance and the typical leaf resistance (s m −1 ) for the vegetation in question, ∆ is the slope of the saturation vapor pressure vs. air temperature curve, kPa • C −1 , and γ is the psychrometric constant, kPa • C −1 , both relative to the period when K cb full is computed. The original version of that equation was established with a fixed r typ = 100 s m −1 , a common value for annual crops, but default F r values were recently reviewed for trees and vines and several annual crops [33].
Examples of the application of the K cb A&P approach to several annual and perennial crops are given by Pereira et al. [32], including for active soil cover in the inter-row. The application of this approach does not require any process of calibration/validation when using the tabulated parameters [33]. However, because data were available, a validation was performed by comparing K cb A&P and K cb computed with the model SIMDualKc.

SIMDualKc Model Calibration and Validation; Goodness-of-Fit Indicators
The model calibration procedure consisted of progressively adjusting the values of the non-measured parameters, aiming at minimizing the differences between the modelsimulated and sap-flow-observed values of daily transpiration, i.e., T c act and T SF field data, acquired in 2009. The set of adjusted parameters included the K cb and p values relative to each crop growth stage, as well as the parameters used to estimate soil evaporation, deep percolation, and runoff. The initial crop and evaporation parameters were selected from FAO56 and Rallo et al. [18], whereas those relative to DP and RO were obtained from the parameter values proposed by Liu et al. [48] and Allen et al. [47], respectively.
Calibration was performed using a trial-and-error iterative procedure to minimize the T c act estimation errors [50]. The trial-and-error procedure consisted, first, of the iterative searching of K cb and p values for the various crop growth stages until the differences in T c act − T SF field become small and their variations from one iteration to the next were found to be lower than 0.01. After obtaining the best set of K cb and p values, the trial-anderror procedure was applied to CN, and the deep percolation parameters a D and b D [48], again aiming at lowering the estimation errors with negligible differences in consecutive iterations. Finally, the procedure was applied again to the crop parameters K cb and p to further reduce the differences in T c act − T SF field .
To evaluate the goodness-of-fit associated with the model simulations during the calibration process, different methodologies were applied. The first referred to the qualitative graphical analysis of the temporal dynamics of simulated and observed T c act and T SF field values. This analysis allowed us to discern trends or biases in the modeling and therefore to make decisions regarding parameter changes in each iteration. The second step referred to the quantitative evaluation of estimation errors using several goodness-of-fit indicators as in previous studies using SIMDualKc [28,50,51].
Using the calibrated parameters, the model was validated using T SF field data acquired in the 2011 season, so the model accuracy was verified by comparing the simulated T c act with the observed T SF field values in that season. The model accuracy relative to the validation was evaluated with the same goodness-of-fit indicators used at calibration and described below. The calibration/validation process was considered acceptable when the goodness-of-fit indicators associated with the validation were found to be comparable to those obtained for the calibration [50,52,53].
The goodness-of-fit indicators used to assess the matching of the differences in T c act − T SF field were as follows:  Table 3 summarizes the initial and final values of the parameters considered for the model calibration: K cb , p, TEW, REW, Z e , CN, a D , and b D . The calibrated K cb parameters relative to all crop growth stages were found to be slightly larger than the initial ones and those obtained previously using different modeling approaches [18,23]. The K cb non-growing and K cb ini values obtained in this study are comparable to those obtained by [5] in a super-intensive hedgerow olive orchard. Moreover, the calibrated K cb values are in the range of those reviewed by [14] and confirm the values proposed by [33]. The values of the depletion fraction p are equal to those proposed by [12] and similar to those previously adopted in other studies [5,17,18,23]. A value of p = 0.65 reflects the tolerance of the olives crop to water stress.

Model Calibration and Validation Using Transpiration Measurements
The initial values concerning Z e , REW, and TEW were estimated according to the soil particle size distribution analysis and the water holding capacity of the evaporation soil layer [12]. Thus, the calibrated soil evaporation parameters are similar to those given in FAO56 for silty-clay-loam soil texture. The calibrated runoff parameter CN slightly changed in respect to the initial value proposed by Allen et al. [47]. The parameters associated with deep percolation consisted of a D , estimated from the available soil water at saturation and field capacity, and b D , estimated from the drainage characteristics of the soil [48]. Therefore, their calibrated values are in line with those indicated by these authors for medium-textured soils ( Table 3).   Estimation errors are small, as indicated by RMSE ≤ 0.27 mm d −1 and AAE ≤ 0.22 mm d −1 . The EF was high (0.71 and 0.81), implying that the mean square error is much smaller than the measured data variance. Generally, the goodness-of-fit indicators suggest that the model was properly calibrated and performed as a good predictor of transpiration dynamics, and the calibrated parameters, particularly the basal Kcb, may be used with confidence in the field practice.     Table 4. Goodness-of-fit indicators relative to the comparison between simulated transpiration (T c act ) and the corresponding values obtained from sap-flow measurements (T SF field ). Estimation errors are small, as indicated by RMSE ≤ 0.27 mm d −1 and AAE ≤ 0.22 mm d −1 . The EF was high (0.71 and 0.81), implying that the mean square error is much smaller than the measured data variance. Generally, the goodness-of-fit indicators suggest that the model was properly calibrated and performed as a good predictor of transpiration dynamics, and the calibrated parameters, particularly the basal K cb , may be used with confidence in the field practice.
The goodness-of-fit indicators were of the same magnitude as those estimated in another application comparing the SIMDualKc simulated T c act with sap-flow T SF measurements obtained in a super-intensive olive orchard [5]. The T c act estimation errors obtained in this study were smaller than those reported by other authors [17,18]. Moreover, it is important to note that the daily variability of transpiration during the study periods was enormous (Figure 3). Similar findings were reported by Villalobos et al. [55].
The goodness-of-fit indicators were of the same magnitude as those estimated in another application comparing the SIMDualKc simulated Tc act with sap-flow TSF measurements obtained in a super-intensive olive orchard [5]. The Tc act estimation errors obtained in this study were smaller than those reported by other authors [17,18]. Moreover, it is important to note that the daily variability of transpiration during the study periods was enormous (Figure 3). Similar findings were reported by Villalobos et al. [55]. Table 4. Goodness-of-fit indicators relative to the comparison between simulated transpiration (Tc act) and the corresponding values obtained from sap-flow measurements (TSF field).

Dynamics of the Single and Basal Crop Coefficients throughout the Season
The Kcb and Kcb act curves, the daily Ke, and the time-averaged single Kc curves estimated using the SIMDualKc model are presented in Figure 3 for the three experimental years. For 2009 and 2011, these curves included sap-flow data, which were not available for 2010. The standard Kc was time-averaged in the different crop stages and calculated as the sum of the daily standard Kcb and the corresponding Ke.
The Kcb and Kcb act curves in Figure 3 are coincident (Kcb act = Kcb) when rainfall events are sufficient to avoid water stress, i.e., during winter, autumn, and spring. On the contrary, water stress (Kcb act < Kcb) occurred for several days during the mid-season of 2009

Dynamics of the Single and Basal Crop Coefficients throughout the Season
The K cb and K cb act curves, the daily K e , and the time-averaged single K c curves estimated using the SIMDualKc model are presented in Figure 3 for the three experimental years. For 2009 and 2011, these curves included sap-flow data, which were not available for 2010. The standard K c was time-averaged in the different crop stages and calculated as the sum of the daily standard K cb and the corresponding K e .
The K cb and K cb act curves in Figure 3 are coincident (K cb act = K cb ) when rainfall events are sufficient to avoid water stress, i.e., during winter, autumn, and spring. On the contrary, water stress (K cb act < K cb ) occurred for several days during the mid-season of 2009 and 2010 because deficit irrigation was practised, with few irrigation events-three in 2009 and one in 2010 using uncommonly large irrigation depths. By contrast, water stress was not observed in 2011, when six irrigation events were practised. The presented K c curves reveal a behaviour contrary to the common K c curves in FAO56, similar to that reported in [5], because soil evaporation was small in summer, when the water use mainly consisted of transpiration.
The soil evaporation curves in Figure 3 show numerous K e peaks that represent the responses to rainfall and irrigation events during the different stages of crop growth, with peaks in the mid-season mostly corresponding to irrigation events. K e peaks are larger when responding to rainfall because the ground is entirely wetted (f w = 1). During the mid-season, K e peaks are small and of short duration; because the wetted and exposed fraction f ew is small, the soil dries out quickly and the ground is shaded by the canopies. Thus, during the mid-season, the reduced soil evaporation is due to the limited energy reaching the soil and the location of the wet areas, which are mostly placed under the shadow of the tree canopy.
The K c and K cb curves show contradictory dynamics (Figure 3) because K c values are highly influenced by soil evaporation, whereas K cb values are not. Thus, the time-averaged K c curve for the mid-season, when E s is small, is lower than the K c segments relative to the late and the non-growing seasons, where rainfall occurs, and soil evaporation increases. On the contrary, the standard K cb mid values are higher during the mid-season because crop transpiration is high at that time, and K cb is lower outside of this period since transpiration is reduced. Table 5 presents the time-averaged K c values for each crop growth stage for the three seasons. The K c ini values range from 0.81 to 1.00, following the variability of rainfall in the same period. This range of variation is comparable to that reported in [5] for the K c ini values of a super-intensive olive orchard (0.70-0.96). In contrast, other authors obtained smaller K c ini values in a hedge-pruned intensive olive orchard, which likely reflects differences in climate [56]. The time-averaged K c mid values varied little, from 0.54 to 0.56, for the three study years, resulting in similar values to those reported in [23]. The K c mid values are higher than the standard values proposed in [14], which may result from the high number of wetting events in the current study. The K c mid values are also larger than those proposed in [33] after using the A&P approach. The K c end values are high, ranging from 0.86 to 1.03, due to the occurrence of rainfall events during the late season. These values are in line with those proposed by other authors [5,23,56,57] but are higher than the standard value of K c end = 0.65 and 0.70, as indicated in [33] and [14], respectively, likely due to the presence of grass on the soil surface and/or the tree age.

Soil Water Balance and Water Use
The different values of the soil water balance, computed with SIMDualKc for the three years, are summarized in Figure 4. The observed differences among years are due to the inter-annual variability of precipitation, and its distribution during the various crop growth stages. The wettest year was 2011, with higher runoff and deep percolation (RO and DP, mm) than in the other two years. In 2011, RO and DP represented 33% of precipitation, which can be contrasted with the low values observed in 2009, when they corresponded to only 5% of precipitation. In 2010, RO and DP corresponded to about 31% of the precipitation. In the wet year of 2011, runoff represented the smallest fraction of precipitation (14%), less than DP (19%). These percentages indicate that in 2011 the rainfall was mostly used as crop evapotranspiration. The largest amounts of RO and DP mainly occurred during the rainy season, corresponding to the non-growing crop stage, in a period with the smallest crop ET (Table 6). RO and DP did not originate from excess irrigation, which would occur during the mid-season when both the variables were nearly null.
Irrigation events occurred only during the mid-season and corresponded to 22%, 11% and 39% of ETc act in 2009, 2010, and 2011, respectively (Table 2). Irrigation events were more frequent in 2011, resulting in smaller variations in the stored soil water and fewer days with crop water stress compared to the other years. Consequently, in 2011, with higher precipitation and more adequate irrigation, both Tc act and ETc act were larger ( Table  6). Because of irrigation events, the contribution of soil water storage to ETc act is larger during the mid-season, thus indicating that infiltrated and stored soil water played a major role in actual crop evapotranspiration.
The ETc act partition reported in Table 6 shows that soil evaporation, Es, was the dominant component of the evapotranspiration process during the non-growing and initial stages. Es values ranged from 63% to 72% of ETc act because rainfall is then larger and more frequent, thus keeping the soil wet most of the time. On the contrary, Es were much smaller during the mid-season (from 16% to 24%) because a few precipitation events occurred, and drip irrigation was applied mostly under the canopies and at nighttime. It was found that Es values during the entire crop season represented 39% to 40% of ETc act, with the latter value referring to the wettest year, when the number of precipitation events was higher. Naturally, transpiration represented the largest fraction of the total ETc act, which indicates that water use was quite efficient.  The wettest year was 2011, with higher runoff and deep percolation (RO and DP, mm) than in the other two years. In 2011, RO and DP represented 33% of precipitation, which can be contrasted with the low values observed in 2009, when they corresponded to only 5% of precipitation. In 2010, RO and DP corresponded to about 31% of the precipitation. In the wet year of 2011, runoff represented the smallest fraction of precipitation (14%), less than DP (19%). These percentages indicate that in 2011 the rainfall was mostly used as crop evapotranspiration. The largest amounts of RO and DP mainly occurred during the rainy season, corresponding to the non-growing crop stage, in a period with the smallest crop ET (Table 6). RO and DP did not originate from excess irrigation, which would occur during the mid-season when both the variables were nearly null.
Irrigation events occurred only during the mid-season and corresponded to 22%, 11% and 39% of ET c act in 2009, 2010, and 2011, respectively (Table 2). Irrigation events were more frequent in 2011, resulting in smaller variations in the stored soil water and fewer days with crop water stress compared to the other years. Consequently, in 2011, with higher precipitation and more adequate irrigation, both T c act and ET c act were larger ( Table 6). Because of irrigation events, the contribution of soil water storage to ET c act is larger during the mid-season, thus indicating that infiltrated and stored soil water played a major role in actual crop evapotranspiration.
The ET c act partition reported in Table 6 shows that soil evaporation, E s , was the dominant component of the evapotranspiration process during the non-growing and initial stages. E s values ranged from 63% to 72% of ET c act because rainfall is then larger and more frequent, thus keeping the soil wet most of the time. On the contrary, E s were much smaller during the mid-season (from 16% to 24%) because a few precipitation events occurred, and drip irrigation was applied mostly under the canopies and at nighttime. It was found that E s values during the entire crop season represented 39% to 40% of ET c act , with the latter value referring to the wettest year, when the number of precipitation events was higher. Naturally, transpiration represented the largest fraction of the total ET c act , which indicates that water use was quite efficient. Table 6. Olives' actual evapotranspiration (ET c act ) and its partitioning into soil evaporation (E s ) and actual transpiration (T c act ), and ratios between soil evaporation and actual evapotranspiration (E s /ET c act , %) between actual crop transpiration and actual evapotranspiration (T c act /ET c act , %) and between actual evapotranspiration and potential evapotranspiration (ET c act /ET c, %) throughout the diverse crop stages and years.

Year
Non

Assessing the Applicability of the A&P Approach
The parameterization of the A&P approach was performed using the available average values of f c observed for the mid-and end seasons (0.35) and the average h = 3.5 m. The selected value for the parameter M L was 1.5, as proposed by Pereira et al. [33] for a traditional olive orchard with medium tree density. As discussed in that study, due to some uncertainty in the targeted K cb values, two values for F r mid and F r end were used, one relative to a K cb central value (K cb A&P central ) and the other to an upper value (K cb A&P upper ). Thus, F r mid central = 0.60, F r end central = 0.52, F r mid upper = 0.68, and F r end upper = 0.60 were used with Equation (14). These F r values show the ability of olive trees to perform differentiated stomatal control throughout the season, with slightly higher stomatal control at the end season when compared with the mid-season. Applying Equations (12)-(14), the following K cb A&P values were computed: K cb A&P mid central = 0.40 and K cb A&P end central = 0.35, and for the upper values K cb A&P mid upper = 0.45 and K cb A&P end upper = 0.40. In the following, these K cb A&P values were used to compute T c act A&P and these estimations were compared with T SF field . The goodness-of-fit indicators relative to this comparison are presented in Table 7. Table 7. Goodness-of-fit indicators relative to the comparison between transpiration obtained from sap-flow measurements (T SF field ) with the transpiration estimated with the A&P approach (T c act A&P ). The results show that using the K cb A&P central values, the RMSE values are nearly similar to those obtained when using the SIMDualKc model (Table 4). However, the A&P approach led to a lower performance due to the insufficient number of f c and h observations, since it was intended to adjust K cb A&P along the season. The RMSE values were higher for the drier season of 2009 and when the K cb A&P upper values were used. These differences were expectable because by 2009 there was higher water stress during the mid-season stage (as depicted in Figure 3), which was not perceived when using the A&P approach due to the lack of adequate f c surveillance which would allow the adjustment of the K c A&P upper value. Table 8 shows the estimated time-averaged K cb act values for the mid-and end-season stages obtained using the A&P approach, as well as the SIMDualKc model for the experimental years 2009 and 2011. Overall, results show that during the mid-season the K cb A&P central value and during the end-season the K cb A&P upper value are adequate for the prevailing conditions of the studied olive grove, which is in line with the K cb values derived when calibrating the SIMDualKc model.

Conclusions
The SIMDualKc model was successfully calibrated and validated for an irrigated olive orchard in Sicily using transpiration data acquired with sap-flow sensors. Estimation errors associated with actual crop transpiration were fairly small, with an average RMSE of 0.26 mm d −1 . The performance of the model confirmed the appropriateness of the SIMDualKc model for estimating the T c act of olive orchards and supports the quality of the water balance results obtained.
The calibration and validation of SIMDualKc allowed us to derive updated single and basal crop coefficient curves for the investigated olive orchard. Since olives are perennials, in addition to the common crop stages proposed by FAO56, K c and K cb values were considered for the non-growing period. Greatly contrasting K c and K cb curves were obtained, analogous to those previously obtained for a super-intensive olive orchard. Although K cb values do not include the effects of soil evaporation, the latter may be the largest fraction in K c . Thus, while K cb is larger when T c act is high during the mid-season, K c is larger when the sum of K cb + K e is greater, which happens when E s is large. In contrast, K c is smaller under limited rainfall and soil evaporation conditions. Contrastingly, K cb is smaller when actual crop transpiration is limited by the available soil water and/or solar radiation. This means that K cb is larger during the mid-season, when K c is smaller and, on the contrary, K cb is smaller during the non-growing period when K c is high. These results were only evident when the study focused on the full year and not only on the growing season.
Using the SIMDualKc model, it was possible to define the standard K cb values for the initial, mid-season, end-season, and non-growing periods, which were 0.30, 0.42, 0.37, and 0.30 respectively. On the other hand, the dependency of K c on soil evaporation and on rainfall events makes it difficult to define a standard K c value for periods exhibiting a large inter-annual variability of rainfall. Therefore, the results for the initial, end, and non-growing seasons showed a large inter-annual variability in K c values: K c mid = 0.55 (average between 0.54 and 0.56), K c ini = 0.92, and K c end = 0.95 and K c non-growing = 0.93. This behavior is common to other woody perennial crops. The use of the dual crop coefficient approach is likely to be more appropriate when assessing crop water use during the crop season and when precision irrigation is desired, whereas the single crop coefficient is likely to be more appropriate when performing less accurate soil water balance measurements for irrigation. The use of the dual K c approach makes it easier to assess both soil evaporation and crop transpiration, thus providing a better understanding of the dynamics of ET c act under conditions of incomplete ground cover, as for orchards.
Results of the partitioning of ET c act with SIMDualKc show that the E s /ET c act ratio was higher during the non-growing and initial periods when E s was mainly influenced by the frequent rainfall events. Contrarily, that ratio was smaller during the mid-season, when the transpiration ratio T c act /ET c act was greater.
The results confirm the suitability of the SIMDualKc model to simulate the terms of the soil water balance of the olive orchards and to derive the respective single and basal crop coefficients for irrigation scheduling purposes. Nevertheless, further studies are required to improve the model outputs, aimed at providing advice to farmers, specifically for designing appropriate irrigation scheduling strategies to save water and enhance yields and oil quality, as well as combining higher water productivity with reducing the water footprint of olives.
The assessment of the usability of the A&P approach with the observed f c and h values, along with the calibrated/tabulated M L and F r values, showed appropriate results for the estimation of T c act when the central K cb A&P is targeted. The results were constrained by the lack of measured f c and h values required to identify the crop coefficient during the entire crop season. Further applications may support the extensive use of the A&P approach, which may aid in parameterizing soil water balance models that are used to support the enhancement of yields, water productivity, and to provide water savings.
Author Contributions: Implementation and planning of the field experimental protocol, M.M., G.P. and G.R.; model simulation and analysis, manuscript redaction, and data interpretation, L.S.P., T.A.P., P.P., À.P.-S. and G.R.; review and editing, P.P., L.S.P., G.P., À.P.-S. and G.R. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author upon request.