1. Introduction
The water availability for irrigation has been reduced in the recent years due to frequent drought and competition between agriculture, industrial, and urban areas (Molden et al. 2010; Calzadilla et al. 2010; Hoekstra et al. 2012). The Mediterranean oliviculture areas, such as Chile, have been significantly affected by the changes in precipitation at local scale (Meza et al. 2012). Water scarcity has become into the main limitation to maintain the olive oil production. Thus, the estimation of water requirements plays an important role in establishing irrigation managements of olive orchards under water scarcity scenarios. The water consumption is estimated through the computation of the actual evapotranspiration (ETa), which is a function of the reference evapotranspiration (ETo) and crop coefficients Kc (Allen et al. 1998). The main limitation of this approach is the selection of the right value of Kc, which may be markedly influenced by tree vigor, the training system (expressed in LAI and fractional vegetation cover fc values) and nonlinear interactions of the soil, the cultivar and the climate conditions (López-Olivari et al. 2016; Martínez-Cob and Faci 2010). Additionally, Kc values can be affected by the partitioning of net radiation Rn into latent (LE), sensible H, and soil G heat fluxes. For a drip-irrigated olive orchard, Testi et al. (2004) showed that there was more energy distributed to evapotranspiration (LE) than to heating air (H) as the leaf area increased from 0.01 to 1.0 m2 m−2. Additionally, Ortega-Farias et al. (2016) indicated that in a drip-irrigated olive orchard (fc = 0.31 and LAI = 1.32 m2 m−2), the H produced at the soil surface between rows was the main component of the orchard energy balance that affected the partitioning of ETa into transpiration T and soil evaporation E. Thus, the direct estimation of ETa over heterogeneous (or discontinuous) canopies of such orchards is very complex because water requirements are significantly affected by the partitioning of energy balance over the soil surface and the tree canopy.
For discontinuous canopies, incomplete soil cover leads to a differentiation of LE from soil in two sources: 1) soil under the canopy and 2) the bare soil between rows. Source 1 generates high LE and low H because there is high water content in the soil surface from the wetted area below the drippers, while source 2 yields low LE and high H because the water content in the soil surface is low, even close to the wilting point. Under these conditions, several researchers have suggested using clumped models to directly estimate ETa over discontinuous canopies such as fruit orchards and vineyards (Poblete-Echeverría and Ortega-Farias 2009; Were et al. 2008; Zhou et al. 2006). The effectiveness of estimating ETa from discontinuous clumped canopies has been reported in the literature (Domingo et al. 1999; Poblete-Echeverría and Ortega-Farias 2009; Were et al. 2008) considering the modifications proposed by Brenner and Incoll (1997) to the sparse-crop model of Shuttleworth and Wallace (1985). These modifications generated the clumped model, an approach that uses a mixture between the Shuttleworth–Wallace model and the energy distribution proposed by Dolman (1993), who suggested weighing the partitioning by the fractional cover from the plant and bare soil. The clumped model considers three sources from where LE is transferred to the atmosphere: the canopy, the soil under canopy, and the soil between rows. Then, ETa is obtained by the sum of Penman–Monteith equations that estimate LE from each source, weighed by their fractional covers and a set of coefficients that represent the combination of aerodynamic resistances (Poblete-Echeverría and Ortega-Farias 2009). Unlike the Shuttleworth–Wallace model, which assumes that vegetation is uniformly distributed over a surface, the clumped model takes into account the clumping of the vegetation. This consideration would explain the changes in the energy absorbed by the plant canopy and the substrate below it (Brenner and Incoll 1997). In summary, this model differentiates LE sources into vegetative and nonvegetative components.
The clumped model has been applied in several heterogeneous canopies with an RMSE for ETa ranging from 0.13 to 1.85 mm day−1. For discontinuous canopy (fc = 34%, LAI is between 1.71 and 3.4 m2 m−2), Brenner and Incoll (1997) indicated that the clumped model underestimated T with an error of 5%. For bush vegetation in Spain (fc = 17%, LAI = 0.81 m2 m−2), Were et al. (2008) found that the clumped model estimated ETa with an RMSE of 0.13 mm day−1. For a discontinuous vegetated stand (Anthyllis cytisoides L.) (fc = 40%, LAI between 0.66 and 1.44 m2 m−2), Villagarcía et al. (2010) reported RMSE values ranging from 0.21 to 1.85 mm day−1. For a furrow-irrigated vineyard (fc = 35% and LAI = 0.2 m2 m−2) in the arid desert region of northwest China, Zhang et al. (2008) observed that the clumped model underestimated LE by approximately 1% with a MAE of 32 W m−2. Finally, for a drip-irrigated Merlot vineyard (fc = 30% and LAI between 0.6 and 1.25 m2 m−2), Poblete-Echeverría and Ortega-Farias (2009) estimated the LE and ETa with RMSE values of 33 W m−2 and 0.32 mm day−1, respectively.
To our knowledge, there is little information about the evaluation of LE and ETa over hedge-pruned olive orchards trained on a superintensive system. Thus, the objective of this research was to parameterize the clumped model for estimating LE and ETa over a commercial superintensive drip-irrigated olive orchard (Olea europaea L. cv. Arbequina) under non-water-stress conditions. Additionally, this study includes a parameterization of submodels for estimating Rn, G, and 
2. Materials and method
a. Study site
A superintensive drip-irrigated olive orchard (cv. Arbequina) located in the Pencahue Valley, Maule Region, Chile (35°23′S, 71°44′W; 96 m above sea level) was used to evaluate the clumped model during the 2009/10 and 2010/11 growing seasons. The experimental unit presented a clay loam texture soil texture and was classified as the Quepo series (Vertisol; fine, Thermic Xeric Apiaquerts). The trees were trained on a hedgerow system with a row spacing of 5.0 m × 1.5 m and irrigated using two drippers per tree at a 2.0 L h−1 flow rate.
b. Field measurements
1) Plant and soil monitoring
For irrigation management, the midday stem water potential 
2) Surface energy balance data
List of sensors used for micrometeorological and meteorological measurements.
c. Model description
d. Parameterization
1) Available energy using meteorological data
2) Aerodynamic resistances
3) Canopy resistance
List of constants used in the clumped model.
e. Model performance
3. Results and discussion
The climatic conditions over the olive orchard were hot and dry during the two growing seasons. Table 3 indicates that mean values of Ta were between 17.7° and 21.1°C while those of D ranged between 1.0 and 4.0 kPa. Furthermore, the daily maximum Rn ranged between 667 and 764 W m−2 for both seasons. In the case of u, the average was approximately 1.5 m s−1, with a maximum value of 4.7 m s−1.
Maximum, minimum, and mean values of air temperature Ta, soil temperature Tsoil, vapor pressure deficit D at zr, net radiation Rn, and wind speed u recorded in days during the model evaluation period.
For the 2009/10 growing season, the average θ at 20- and 60-cm depth under the canopy were 0.09 and 0.23 m3 m−3, while those for the 2010/11 growing season were 0.11 and 0.18 m3 m−3, respectively. Meanwhile, the θ at 20-cm depth between rows for both growing seasons ranged 0.14–0.11 m3 m−3, respectively. Under these soil moisture conditions, 
The obtained ratio of turbulent fluxes (Hec + LEec) to available energy (Rn − G) was different from one (EBR = 0.87) indicating that the EC measurements presented a lack of energy closure equal to 13% (Fig. 1). For a young drip-irrigated orchard (fc = between 1% and 25% and LAI = between 0.1 and 1.0 m2 m−2), Testi et al. (2004) reported an energy closure ranging between 85% and 95%, while for a flood-irrigated olive orchard, Williams et al. (2004) found a lack of energy closure of 26%. Ezzahar et al. (2007) reached an energy closure of 95% over a flood-irrigated olive orchard (fc = 55%). Er-Raki et al. (2008) showed a lack of energy balance closure between 8% and 10% over a flood-irrigated olive orchard (fc = between 15% and 20% and LAI = 3.0 m2 m−2). Cammalleri et al. (2013) obtained an energy closure between 90% and 92% in a drip-irrigated olive orchard (fc = 35% and LAI between 1.1 and 2.4 m2 m−2). Finally, Martínez-Cob and Faci (2010) obtained a lack of energy closure equal to 26% in a drip-irrigated hedge-pruned olive orchard (fc = 34%). Therefore, the literature shows a general lack of energy balance closure between 5% and 20% even under ideal fetch conditions (Twine et al. 2000; Wilson et al. 2002). Based on this problem, many sources of the lack of energy balance closure have been proposed, such as 1) errors in measurements, 2) incorrect accounting for the storage of energy in the soil and canopy, or 3) advective flux due to heterogeneities in vegetation cover, among others (Leuning et al. 2012).
Regression analysis between turbulent fluxes (H + LE) from the eddy covariance and the available energy of the system (Rn − G). The solid line represents the 1:1 relationship.
Citation: Journal of Hydrometeorology 20, 5; 10.1175/JHM-D-18-0135.1
In this study, the average value of 
Statistical analysis of the clumped model to estimate directly latent heat flux (LEc) and evapotranspiration (ETa) of a commercial superintensive drip-irrigated olive orchard. Also, evaluation of submodels to compute the net radiation Rn, soil heat flux G, and canopy resistance 
The validation indicated that the submodel estimated the Rn with values of RMSE = 65 W m−2, MBE = −7.7 W m−2, and dr = 0.99. For the simulation period, the roe value was significantly different from 1.0, suggesting an overestimation of 6%. These results are in accordance to those reported by López-Olivari et al. (2015), who observed that three semiempirical models of Rn presented RMSE values ranging between 26 and 101 W m−2. Major disagreements in the estimation of Rn are usually associated to the effects of cloudy days on the parameterization of 
Using 30-min time intervals, Table 4 shows that the clumped model estimated the LE with RMSE, MBE, and dr values of 35 W m−2, −1.0 W m−2, and 0.96, respectively. In addition, the roe value was 0.89 and significantly different from the unity, indicating that the clumped model underestimated the LE measured using the EC system by 11%. In the interval 0 < LE < 250 W m−2, the points were close to the 1:1 line (Fig. 2), meanwhile LE values outside this interval exhibited higher scatter. The overall daily comparison between estimated and observed ETa (Table 4) indicated that the clumped model was able to predict the daily water consumption with RMSE, MBE, and dr values of 0.48 mm day−1, 0.04 mm day−1, and 0.64, respectively. Moreover, the roe value was significantly different from 1.0 indicating that ETa was underestimated by 3.0%. Also, Fig. 3 shows that the points were close to 1:1 line for ETa ranging between 1.15 and 4.10 mm day−1. Also, 73% of the absolute differences |LEBR − LEc| were lower than 30 W m−2 (Fig. 4).
Comparison between latent heat fluxes measured by the eddy covariance system (LEec) and computed by clumped model (LEc) over 30-min intervals. The solid line represents a 1:1 relationship.
Citation: Journal of Hydrometeorology 20, 5; 10.1175/JHM-D-18-0135.1
Comparison between actual evapotranspiration (ETec) obtained from the eddy covariance system and that computed by the clumped model (ETc). The solid line represents a 1:1 relationship.
Citation: Journal of Hydrometeorology 20, 5; 10.1175/JHM-D-18-0135.1
Distribution of the absolute difference between the observed and estimated values of latent heat flux (LEec and LEc, respectively).
Citation: Journal of Hydrometeorology 20, 5; 10.1175/JHM-D-18-0135.1
The sensitivity analysis of uncertainties in the input parameters is shown in Table 5. For the clumped model, the sensitivity of ETa to uncertainties in C, zo, 
Sensitivity analysis to actual evapotranspiration (ETa) estimated by the clumped model. Values represent the percentage of deviation of the output ETa for a ±30% change of the parameters.
The proper performance of the clumped model could rely on the fact that LAI and water status were almost constant during both seasons as result of the agricultural management. Thus, this research could only be extended to orchards with the same training system, row orientation and irrigation system (drip irrigation) under semiarid climate conditions. First, because the ETa depends on the intercepted solar radiation by the canopy and soil, it may significantly change with variations of interrow width and the hedgerow orientation (Connor et al. 2014; Trentacoste et al. 2015). Second, the estimation of 
4. Conclusions
The clumped model was tested using an EC system installed above a commercial superintensive drip-irrigated olive orchard with a constant value of fc (30%) and LAI (1.32 m2 m−2) during two consecutive growing seasons. The estimation of ETa and LE by the clumped model agreed well with the measurements of the EC system on daily and 30-min periods, respectively. For the two seasons, the clumped model underestimated LE and ETa with errors of 11.0% and 3.0%, respectively. In addition, submodels of Rn, G, and 
These results suggest that it is possible to directly estimate ETa using the clumped model, which was very sensitive to errors in the values of stomatal resistance and leaf area index. Future research will be concentrate on the effect of water stress on the parameterization of Rn, G, and 
This study was supported by the Chilean government through the projects CONICYT PFCHA/Doctorado Nacional 21141010, CONICYT PAI/Sector Productivo T7816120002, FONDEF (D10I1157), FONDECYT (1100714), and by the University of Talca through the research program “Adaptation of Agriculture to Climate Change (A2C2).” The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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