Assessing Olive Evapotranspiration Partitioning from Soil Water Balance and Radiometric Soil and Canopy Temperatures

Abstract

Evapotranspiration (ET_c) partitioning and obtaining of FAO56 dual crop coefficient (K_c) for olive was carried out with the SIMDualKc software application for root zone and topsoil soil water balance based on the dual crop coefficients. A simplified two source-energy balance model (STSEB), based on daily remotely sensed soil and canopy thermal infrared data and retrieval of surface fluxes, also provided information on partitioning ET_c for the olive orchard. Both models were calibrated and validated with ground-based, sap flow-derived transpiration rates, and their performance was compared in partitioning ET_c for incomplete cover, intensive olive grown in orchards (≤300 trees ha⁻¹). The SIMDualKc proved adequate in partitioning ET_c. The STSEB model underestimated ET_c mostly by inadequately simulating soil evaporation and its contribution to the total latent heat flux. Such results suggest difficulties in using information from the STSEB algorithm for assessing ET_c and dual K_c crop coefficients of intensive olive orchards with incomplete ground cover.

1. Introduction

A reliable assessment of olive water requirements at different stages in the olive’s development is particularly relevant for the correct estimation of daily water needs and the improvement of irrigation management. For deficit irrigation (DI) scheduling routines applied to olives to reduce production costs, improve fruit quality, and save water [1], such knowledge is particularly relevant to avoid severe water stress on sensitive phases of the growing period [2,3,4,5,6], as the responses to DI regimes are often variable, depending on the timing and severity of water deficits [2,7]. So, the precise monitoring of actual olive water use throughout the irrigation cycle is of utmost importance. The usual approach for the estimation of crop water requirements is the crop coefficient K_c-ET_o approach adopted by FAO56 [8]. Single and dual crop coefficient K_c values are defined and tabulated by FAO56 [8,9] for a wide range of agricultural crops, with K_c expressing differences between reference and target crop in terms of ground cover, canopy properties, and aerodynamic resistance. In the single approach, both crop transpiration (T) and soil evaporation (E_s) components of crop ET_c are timely averaged into a single coefficient (K_c), whereas in the dual approach, the K_c coefficient is the separate sum of a daily basal crop coefficient (K_cb), representing the plant transpiration, and a daily soil evaporation coefficient (K_e). Usage of the dual K_c approach is particularly appealing in two counts; it allows for the partitioning of ET_c and the estimation of potential, non-stressed transpiration, T, which is more suitable for irrigation management purposes, as it closely relates to crop yield [7,10,11,12], and the estimation of soil evaporation, whose accuracy is improved with the procedure [12,13]. For crops with incomplete ground cover, such as olive, Allen and Pereira [9] further refined the concept of dual K_c, and tabulated sets of K_c and K_cb values for orchards and vines by taking into account their planting density, canopy size and height, and active understory growing vegetation. For deficit irrigation strategies that impose some degree of stress to crops, such as in olive irrigation, they adjusted the traditional FAO56 approach to estimate ET_c with the dual crop coefficient method by replacing the potential ET_c with an actual ET_c (ET_{c act}), the result of a K_{c act} coefficient derived from a stress coefficient (K_s), and a soil evaporation coefficient K_e, i.e., K_{c act} = K_sK_cb + K_e. The multiplier K_s is equal to 1.0 for no soil water stress and less than 1.0 with water stress conditions. To estimate K_s and K_e, water balance calculations for the root zone and the topsoil are required on a daily basis, which often entails an appropriate computational model framework [9,14]. The SIMDualKc model [15,16,17] provides such computational structure by incorporating the most recent refinements in the concept of dual crop coefficients and by performing the required soil water balance, to provide information on the stress coefficient K_s, on potential and actual K_cb, on K_e, and finally on potential and actual K_c. The results of using the model compared well with field observations for annual, vine, and woody crops [11,13,17,18,19,20,21,22,23]. The SIMDualKc approach on olives has focused on comparing daily transpiration simulated data with those obtained with sap flow measurements [17,18,19,24], and has been applied exclusively to super high-density olive orchards (≥1500 trees ha⁻¹). The merits of this application to intensive orchards (≤300 trees ha⁻¹) with larger incomplete ground cover such as the one in this study remain uncertain.

Other than using the SIMDualKc soil water balance for partitioning ET_c, the partition is traditionally performed by classic processes grounded on the two-source (soil + vegetation) layer surface energy balance models [25,26,27,28,29,30,31,32]. A simpler version of the two-source configuration (STSEB) has been more recently proposed by [33] and successfully used in assessing the ET_{c act} and the corresponding K_{c act} of cover crops [34,35]. Based on remotely sensed thermal infrared data and retrieval of surface fluxes, the framework computes T and E_s, and hence ET_c, as residuals to the components soil and vegetation energy-balance budgets directly from measured soil (T_s) and canopy (T_c) radiometric temperatures. The success of the developed STSEB relationships in partitioning and establishing accurate ET_c values from the soil and canopy contributions to the total sensible heat flux has been established mainly for herbaceous crops, such as corn [33], sorghum [35], sunflower, and canola [34]. No studies were found evaluating the strength of the STSEB relationships in predicting ET_c for fruit trees, in particular, olives.

In consideration of the above-mentioned methods and techniques and the need to obtain accurate information on actual ET_c partitioning and related dual K_c crop coefficients for better irrigation management of intensive olive orchards grown in southern Portugal, a region of scarce water resources where water plays a decisive role in agricultural development and imposes the optimization of olive-growing irrigation water use, the main objectives of this study were: (1) to test and validate the simplified version of the two-source configuration (STSEB) for olives from thermal infrared radiometry, ancillary meteorological data, and sap flow field measurements; (2) to test and validate the SIMDualKc model with data from sap-flow field measurements; (3) to assess and compare actual olive T, E_s, and ET_c with information derived from the STSEB and SIMDualKc energy- and water-balance models.

2. Material and Methods

2.1. Study Site and Measurements

The experiments were carried out in an intensive commercial olive orchard at the Herdade Álamo de Cima, near Évora (38°29′49.44′’ N, 7°45′8.83′’ W; alt. 75 m) in southern Alentejo, Portugal. The orchard was established with 10-year old trees in grids of 8.0 × 4.2 m (300 trees ha⁻¹) in the E-W direction. Climate in the region is typically Mediterranean, with long-term average annual rainfall of around 650 mm, mostly distributed from September/October to May, with the remaining summer months dry and hot. Half-hour average of the meteorological parameters wind speed, air temperature, solar radiation, precipitation, and relative humidity were evaluated from data recorded in an automatic weather station adjacent to the orchard, equipped with a solar panel and a standard set of sensors recording maximum and minimum air temperature, relative humidity, wind speed and wind direction, barometric pressure, solar radiation, and precipitation. Daily values of ET_o were calculated using the FAO-Penman–Monteith equation and the procedures prescribed in [8]. The average values for the 2-year experimental period (2013 and 2014) of potential evapotranspiration (ET_o) and precipitation (P) were 1161.0 mm and 791.0 mm, respectively. Half-hour average of thirty seconds net radiation above the canopy of trees was obtained throughout the irrigation cycle using one NrLite net radiometer (Kipp & Konen, Delft, The Netherlands) connected to a data logger (Delta-T, DL2e, Delta-T Devices, Cambridge, UK). Collected ground data included fraction of ground shaded by canopy (f_c) and tree height, whose measurements were used to calibrate and validate both models. The f_c was approximately 0.28, and tree height was around 3.5 m. The procedure to obtain f_c was based upon measurements in 35 randomly selected trees of the projection of their crown diameters. Soils are sandy loam Regosoil Haplic of weakly developed and unconsolidated materials [36]. The average apparent bulk soil density was 1.52 Mg m⁻³, and average volumetric soil water content at 0.03 MPa was 0.28 m³ m⁻³, whereas it was 0.16 m³ m⁻³ at 1.5 MPa. The average total available soil water in the root zone (TAW) was 194 mm for a soil depth of 1.2 m. The olive orchard was typically irrigated almost every day, during spring and summer, with a drip system having emitters with 1.0 m spacing along the row and discharging 2.3 L h⁻¹ (0.27 mm h⁻¹). In general, irrigation season started in March/April and ended in September/October. The average daily irrigation amounts were close to 4.2 mm d⁻¹ during the two irrigation seasons. Irrigation dates and depths were provided by the farm manager and were locally measured with a tipping-bucket rain gauge (ARG100, Environmental Measurements Ltd., Sunderland, UK) connected to recording data loggers. Figure 1 shows the study area location in southern Portugal (a) and the intensive commercial orchard where experiments were carried out (b).

2.2. Field Data

Data obtained from ground-based measurements were used to validate information obtained with the SIMDualKc and STSEB simulation models. Olive daily sap flow-based transpiration rates (T_sf) on a ground area basis (mm d⁻¹) were assessed for the 2-year experimental seasons using sap flow measurements by the Compensation Heat Pulse method [37,38]. A set of six heat-pulse probes (Tranzflo, Palmerston, New Zealand) was distributed by seriated trees, according to trunk diameter class frequency, established in a larger sample of the plot [17] and continuously monitored from the period 113 to 304 DOY (day of year) in 2013, and 126 to 278 DOY in 2014. Thirty-minute data were stored in a datalogger (Model CR1000, Campbell Scientific, Inc., Logan, UT, USA). Heat-pulse (ideal) velocity was corrected for probe-induced wounding effects in the trunk near the probes using coefficients after [39]. To calibrate and validate the SIMDualKc and STSEB models, and support the derivation of olive crop coefficients, which is analyzed in Section 3, daily sap flow-based transpiration data were used, thus comparing transpiration rates simulated by SIMDualKc (T_SDual) and STSEB (T_STSEB) with derived T_sf (n = 146 in 2013 for calibration and n = 146 in 2014 for validation). Radiometric soil (T_s) and canopy (T_c) surface temperatures were measured according to procedures in [34]. Apogee S-111 thermal infrared radiometers (IRT) were used. One was placed at a height of 2.0 m above the canopy level, looking at the surface with nadir view, and a second radiometer was placed between rows, directly pointing to the soil at 0.40 m height and 1.2 m distance from the tree row, respectively. A third IRT was placed at 2.0 m above canopy height at an angle of 53° to measure sky brightness temperature. Data were used for atmospheric correction of the surface temperature (Apogee Instruments, Logan, UT, USA, 2016), as the STSEB model requires calibrated thermal-infrared observations adjusted for atmospheric effects and corrected for surface emissivity in the thermal infrared band to produce accurate results. All thirty-minute data were stored in dataloggers (Model CR1000, Campbell Scientific, Inc., Logan, UT, USA). IRT measurements were limited to year 2014 and were collected for the period 163 to 304 DOY. An independent energy balance between the atmosphere and each component of the surface was established, leading to daily values of soil evaporation (E_sSTSEB) and olive transpiration (T_STSEB), as discussed below.

Incident daily photosynthetically active radiation (PAR) and the fraction of PAR intercepted by the canopy were obtained from logged (CR10X, Campbell Scientific, Inc., Logan, UT, USA) measurements (umol m⁻² s⁻¹) of a set of six Quantum sensors (QPAR-02, 400–700 nm, Tranzflo, Palmerston, NZ, USA) placed in a fixed transect of three sensors on each side (East and West) of the tree line (N-S) at 0.2, 1.0, and 1.88 m, respectively, with one placed on top of the canopy (5.0 m). On clear sky days, leaf area index (LAI) measurements were taken periodically with a ceptometer (Accupar-LP80, Decagon Devices Inc., Pullman, WA, USA) that takes into account the canopy’s leaf distribution to make the calculation of LAI an instant measurement from the radiation measurements. We followed the measurement strategy proposed in [40] for olive orchards. Half-hour average of thirty seconds net radiation above the canopy of trees was obtained throughout the irrigation cycle using one NrLite net radiometer (Kipp & Konen, Delft, The Netherlands) connected to a data logger (Delta-T, DL2e, Delta-T Devices, Cambridge, UK). Mean weather variables for both study seasons are shown in

Table 1. Summary of the monthly values of maximum and minimum temperatures (°C), rainfall (mm month⁻¹), and reference evapotranspiration (mm month⁻¹) for the two study years.

	Mean Maximum Temperature (°C)		Mean Mimimum Temperature (°C)		Rainfall (mm Month−1)		ETo (mm Month−1)
Month	2013	2014	2013	2014	2013	2014	2013	2014
January	15.2	14.9	6.3	6.8	89.9	102.2	28.4	31.9
February	14.8	14.5	3.8	5.6	48.9	148.0	42.5	35.0
March	16.2	18.5	7.9	5.9	240	40.1	51.5	80.9
April	20.8	21.3	7.7	9.7	26.2	119.1	99.9	82.3
May	24.6	25.7	8.2	9.9	15.2	16.7	134.6	144.1
June	29.8	28.5	12.3	13.1	13.0	9.4	167.6	150.7
July	33.1	31.5	15.3	14.3	0.1	5.5	175.3	173.8
August	35.0	31.7	15.0	14.6	0.1	0.0	176.0	175.2
September	31.0	27.7	14.4	15.6	55.9	124.1	125.4	97.8
October	24.3	24.8	12.8	13.9	159.9	106.3	83.5	80.1
November	16.9	16.8	5.9	7.7	8.2	172.8	52.8	53.5
December	15.6	14.3	4.4	3.7	79.7	9.0	43.0	35.0

. The olive trees are of cultivar Cobrançosa.

2.3. The STSEB Simplified Energy Balance Model

The simplified version (STSEB) of the two-source modeling configuration for computing surface fluxes using soil and canopy temperature observations introduced by [34] was used in this study. According to the approach described in [34], the latent heat flux, λET_c, represents the energy required for ET_cSTSEB and is computed as the residual of the following surface energy balance simplified form,

$$R_n=H+E{T}_{cSTSEB}+G$$

(1)

in which R_n is the net radiation flux (W m⁻²), H is the sensible heat flux (W m⁻²), and G is the soil heat flux (W m⁻²). Soil and canopy sensible fluxes, H_s (W m⁻²) and H_c (W m⁻²), weighed by their partial cover areas, add to total sensible flux, H, as:

$$H=f_c{H}_c+\left(1-f_c\right)H_s$$

(2)

A complete and independent energy balance between the atmosphere and each component of the surface is then established by the following relationships:

$$\lambda E{T}_{cSTSEB}=f_c\lambda T_{STSEB}+\left(1-f_c\right)\lambda E_{sSTSEB}$$

(3)

$$\lambda T_{STSEB}=R_{nc}-H_c$$

(4)

$$\lambda E_{sSTSEB}=R_{ns}-H_s-\frac{G}{\left(1-f_c\right)}$$

(5)

in which λE_sSTSEB and λT_STSEB are the energy required for soil evaporation, E_sSTSEB, and canopy transpiration, T_STSEB, respectively. Calculated λE_sSTSEB, and λT_STSEB, and λET_cSTSEB are converted to soil evaporation (E_sSTSEB), plant transpiration (T_STSEB), and evapotranspiration (ET_cSTSEB), respectively, by means of the latent heat of vaporization, λ, (MJ kg⁻¹). The energy connected to soil warming, G, is estimated as a fraction (C_G) of the soil contribution to the net radiation as follows, in which C_G can vary in a range of 0.2–0.5 depending on the soil type and moisture.

$$\mathrm{G}=C_G\left(1-f_c\right)R_{ns}$$

(6)

Net radiation is computed from a balance between the incoming and outgoing short-wave and long-wave radiances, in which R_nc and R_ns are the contributions of the canopy and soil, respectively, to the total net radiation flux.

$$R_n=f_c{R}_{nc}+\left(1-f_c\right)R_{ns}$$

(7)

$$R_{nc}=\left(1-{\alpha }_c\right)S+{\epsilon }_c{L}_{sky}-{\epsilon }_c\sigma T_c^4$$

(8)

$$R_{ns}=\left(1-{\alpha }_s\right)S+{\epsilon }_s{L}_{sky}-{\epsilon }_s\sigma T_s^4$$

(9)

in which α and ε are the surface parameters albedo and emissivity, respectively, σ is the Stefan-Boltzman constant, S is the solar radiation (W m⁻²), and L_sky (W m⁻²) is the incident long-wave radiation, T_c and T_s, and the canopy and soil surface temperatures (K). The soil and canopy contributions to the total sensible heat flux, H_s and H_c, respectively, are expressed as:

$$H_c=\mathsf{\rho }{C}_p\frac{T_c-T_a}{r_a^h}$$

(10)

$$H_s=\mathsf{\rho }{C}_p\frac{T_s-T_a}{r_a^{\alpha }+r_a^s}$$

(11)

in which ρC_p is the volumetric heat capacity of air (J K⁻¹ m⁻³), T_a is the air temperature at a reference height (K), $r_a^h$is the aerodynamic resistance to heat transfer between the canopy and the reference height at which the atmospheric data are measured (s m⁻¹), $r_a^{\alpha }$is the aerodynamic resistance to heat transfer between the point z_OM + d (z_OM: canopy roughness length for momentum, and d: displacement height) and the reference height (s m⁻¹), and $r_a^s$ is the aerodynamic resistance to heat flow in the boundary layer immediately above the soil surface (s m⁻¹). We used expressions to estimate the resistances reported in [33]. Using daily radiometric temperatures data collected in 2014, together with the meteorological variables wind speed, solar and long-wave radiation, and biophysical information on canopy height and fractional vegetation cover as inputs in the above equations, we obtained results of the different terms of the energy balance equation for every 30 min. Modeled daily values of transpiration (T_STSEB) were then tested by comparison with field observed sap flow daily transpiration rates (T_sf). To further test the performance of the STSEB model, these findings, as well as soil evaporation (E_sSTSEB) and evapotranspiration (ET_cSTSEB) results, were compared with related 2014 SIMDualKc results, and their recognized robustness in modeling soil evaporation and crop evapotranspiration was considered [20,21].

2.4. The SIMDualKc Water Balance Model

The SIMDualKc is a soil water balance model that applies the dual crop coefficient approach to simulate ET_c, the basal (K_cb) and soil evaporation (K_e) coefficients that relate to crop transpiration (T_c), and soil evaporation (E_s), respectively, as:

$$E{T}_{cSDual}=\left(K_{cbSDual}+K_{eSDual}\right)E{T}_o$$

(12)

in which ET_cSDual is crop evapotranspiration for no stress conditions. When water stress occurs, ET_cSDual is adjusted as a function of the available soil water in the root zone by considering a stress coefficient (K_sSDual), thus providing ET_cSDual act (mm d⁻¹), which is the actual evapotranspiration.

$$E{T}_{cSDual}\mathrm{act}=T_{SDual }+E_{sSDual}=\left(K_{sSDual}{K}_{cbSDual}+K_{eSDual}\right)E{T}_o$$

(13)

in which K_sSDual, the water stress coefficient, is an indicator of the relative intensity of the stress effect on a specific growth process and growth stage. The coefficient K_sSDual is in essence a modifier of the parameter K_cbSDual and ranges in value from one (no stress) to zero (full stress). The coefficient is often used to adjust ET_cSDual to reflect the soil water conditions [9,16]; it is computed by SIMDualKc through a daily soil water balance algorithm for the entire root zone, and as a function of root zone water depletion. Concerning adjustments of FAO crop coefficients [12], the model takes into account plant density and height [9], through a density coefficient K_d, to better adjust the final computations of K_cSDual or K_cbSDual.

$$K_{cbSDual}=K_{cbSDual min} +K_d\left(K_{cbSDual full} - K_{cSDual min}\right)$$

(14)

in which K_cSDualfull is the estimated basal K_cbSDual during the peak plant growth for conditions of full ground cover, and K_cSDualmin is the minimum K_cSDual for bare soil [16,17]. K_d is estimated from the effective fraction of ground cover as:

$$K_d=\min (1,M_L{f}_{c eff},f_{c eff}^{(1/1+h)})$$

(15)

in which f_{c eff} is the effective fraction of ground covered or shaded by vegetation near solar noon, M_L is a multiplier on f_{c eff} describing the effect of canopy density on shading and on maximum relative ET_c per fraction of ground shaded, and h (m) is the mean height of the vegetation.

As previously mentioned, measured sap flow data (T_sf) from 2013 was used to calibrate the SIMDualKc model, and validation was performed with 2014 collected T_sf data.

Table 2. Standard and calibrated parameters used in SIMDualKc model (p—depletion fraction, 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 end-season stage, 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).

Parameters	Initial	Calibrated
KcbSDual ini	0.5	0.4
KcbSDual mid	0.55	0.3
KcbSDual end	0.5	0.5
pini, pmid, pend	0.5	0.4; 0.4; 0.5
Soil evaporation parameters
REW (mm)	9.0	8.0
TEW (mm)	22.0	22.0
Ze (mm)	0.10	0.10
Runoff and deep percolation parameters
CN	68	68
aD	235	235
bD	0.02	0.02

shows the standard and calibrated parameters used in SIMDualKc model. In the calibration and validation processes, we used the methodologies and procedure described in [15,16,17].

2.5. Statistical Analysis

Agreement between observed and measured values, as well as the goodness of fit, was assessed in terms of the Willmot [41] index of agreement (W_IA, dimensionless), the root mean squared error (RMSE), mean absolute error (MAE), average absolute error (AAE), and mean bias error (MBE). The software StatPlus, AnalystSoft Inc. version 6 was used.

3. Results and Discussion

3.1. Validation of the SIMDualKc Model

As stated previously, the SIMDualKc model was calibrated with data of 2013 and validated with data of the year 2014. The values of all initial and calibrated parameters are presented in Table 2. Model results are analyzed in detail in Section 3.3.

The comparison of transpiration data simulated by SIMDualKc (T_SDUal) with observed data (T_sf), for the two years is shown in Figure 2, which includes ET_o, rainfall, and irrigation data.

The data plots visually indicate that the model produces transpiration estimates close to observed data for the calibration year 2013, with no conspicuous patterns of deviations for the validation year 2014. Related goodness of fit and error indicators presented in

Table 3. Goodness of fit indicators relative to SIMDualKc predicted transpiration values when compared with observed transpiration data derived from sap-flow measurements.

TSDual vs. Tsf	n	b	R2	RMSE (mm d−1)	Emax (mm d−1)	AAE (mm d−1)	ARE (%)	EF	WIA
Calibration, 2013	146	1.02	0.72	0.20	0.52	0.215	20.3	0.67	0.92
Validation, 2014	146	0.97	0.81	0.20	0.55	0.201	16.0	0.62	0.92

n = number of observations; b = regression coefficient; R² = determination coefficient; RMSE = root mean square error; E_max = maximum absolute error; AAE = average absolute error; ARE = average relative error; EF = modeling efficiency; W_IA = index of agreement; T_SDual and T_sf are for transpiration simulated with SIMDualKc and observed with sapflow, respectively.

allow one to assume that SIMDualKc model performed well in capturing the characteristics of our intensive olive orchard of incomplete cover (≤300 trees ha⁻¹), as it did for a super-intensive orchard (≥1500 trees ha⁻¹) in the region, reported in [17,18]. 2014 observed (T_sf) and estimated transpiration data (T_SDual) were compared (Figure 2) to validate the model.

Data show good correlation, with a higher determination coefficient (R² = 0.81) and a regression coefficient b = 0.97, which is smaller than that for the calibration year (Table 3). Results indicate a slight underestimation but a strong explanation of data variance with overall goodness of fit data showing a good performance of the model during validation, with good agreement between T_SDual and T_sf.

Table 4. Mean, maximum, and minimum values of predicted (T_SDual) and observed (T_sf) olive orchard transpiration rates for calibration (2013) and validation years (2014).

DOY 130 to 276	TSDual (mm d−1)	Tsf (mm d−1)
Calibration year (2013)
Mean	1.25	1.21
Maximum	1.79	1.94
Minimum	1.29	1.31
Validation year (2014)
Mean	1.31	1.35
Maximum	1.89	1.92
Minimum	0.58	0.49

shows the mean modeled and observed transpiration values for the calibration and validation years (DOY 130 to 276, the period with available sap flow data).

Mean values were very similar in 2013 (1.25 and 1.21 mm d⁻¹, respectively) and in 2014 (1.31 and 1.35 mm d⁻¹). Minimum and maximum transpiration values in Table 4 were also quite close for both the calibration and validation years.

3.2. Validation T_STSEB with Field Sap Flow Transpiration Rates

Almost 960 half-hour canopy and soil surface temperature observations were obtained from DOY 166 to 273 and were used to run and evaluate the STSEB model output. For estimation of the contribution of canopy and soil, respectively, to the total net radiation flux, Equations (8) and (9) were applied using values of α_s = 0.12, α_c = 0.20, ε_s = 0.96, and εc_s = 0.985, which were characteristics of the olive canopy [28,42,43]. The soil and canopy contributions to the total sensible heat flux, H_s and H_c, respectively, were evaluated with Equations (10) and (11). Related expressions, parameters, and constants to estimate the aerodynamic resistances were obtained from literature (Appendix A in [26,29,33,44] and ancillary meteorological and biophysical measurements of key variables to the STSEB model (vd. Section 2.1, and Section 2.2). The energy required for canopy transpiration and soil evaporation was evaluated with Equations (4) and (5), and the total energy balance was estimated with Equation (3). A constant value of C_G = 0.35 was used in Equation (6), corresponding to the midpoint between its likely units [33,45]. Modeled daily values of transpiration (T_STSEB) were then tested by comparison with field observed sap flow daily transpiration rates (T_sf). The comparison is shown in Figure 3, with related goodness of fit indicators presented in

Table 5. Goodness of fit indicators relative to STSEB predicted transpiration values when compared with observed transpiration data derived from sap-flow measurements.

TSTSEB vs. Tsf	n	b	R2	RMSE (mm d−1)	Emax (mm d−1)	AAE (mm d−1)	ARE (%)	EF	WIA
2014	107	0.99	0.86	0.20	0.68	0.169	12.4	0.70	0.87

n = number of observations; b = regression coefficient; R² = determination coefficient; RMSE = root mean square error; E_max = maximum absolute error; AAE = average absolute error; ARE = average relative error; EF = modeling efficiency; W_IA = Wilmott index of agreement. T_STSEB and T_sf are for transpiration simulated with STSEB and observed with sapflow, respectively.

.

Overall, simulated (T_STSEB) overestimate transpiration rates for values in-between 1.75 and 2.0 mm d⁻¹ and underestimate them for lower values, indicated in the b = 0.99 coefficient of regression. Mean observed (T_sf) and simulated (T_STSEB) transpirations of 1.77 and 1.81 mm d⁻¹, respectively, show the STSEB overestimation, also indicated in the percent value of the bias indicator PBIAS (−1.9%), with the negative sign referring to the occurrence of overestimation bias [14]. Generally, the statistical indicators show an acceptable performance of the model in simulating olive transpiration from July to mid-September, the region-relevant period for olive irrigation. To further test the performance of the STSEB model, soil evaporation (E_sSTSEB) and evapotranspiration (ET_cSTSEB) results are compared below with related 2014 results obtained with the validated SIMDualKc model. Additionally, simulated T, E_s, and ET_c with the two models are compared.

3.3. Assessing ET_c with the SIMDualKc and STSEB Models

Series of ET_c act (ET_cSDual act) with the same length as simulated T_SDual were obtained with SIMDualKc for 2014, with Figure 4 showing the time evolution of E_sSDual, T_SDual, and ET_c act (ET_cSDual act).

A mean E_sSDual value of 0.56 mm d⁻¹ is predicted for a maximum of 2.4 mm d⁻¹ in DOY 177, a minimum of 0.02 mm d⁻¹ in DOY 156, and a total of 202.2 mm for the year. Mean ET_cSDual act of 1.4 mm d⁻¹ (0.82 mm d⁻¹ for T_cSDual) is predicted for a maximum of 3.8 mm d⁻¹ (1.89 mm d⁻¹ for T_SDual), a minimum of 0.31 mm d⁻¹ (0.14 mm d⁻¹ for T_SDual), and a total of 500.8 mm for the year (298.6 mm for T_SDual). The SIMDualKc approach to dual K_c for olives with incomplete ground cover takes into account the fraction of soil surface wetted by irrigation and exposed to radiation [46,12,19], hence reflected in the values of E_sSDual [17,18].

Similarly, series of ET_cSTSEB were obtained with STSEB model for 2014; the time evolution of E_sSTSEB, T_STSEB, and ET_cSTSEB for the period in-between June 15th and September 30th is presented in Figure 5.

A mean E_sSTSEB value of 1.12 mm d⁻¹ is predicted for a maximum of 1.36 mm d⁻¹ in DOY 192, a minimum of 0.81 mm d⁻¹ in DOY 265, and a total of 121.4 mm for the period. Mean ET_cSTSEB of 1.33 mm d⁻¹ (1.80 mm d⁻¹ for T_cSTSEB) is predicted for a maximum of 1.61 mm d⁻¹ (2.21 mm d⁻¹ for T_STSEB), a minimum of 0.95 mm d⁻¹ (1.27 mm d⁻¹ for T_STSEB), and a total of 143.4 mm for the period (194.8 mm for T_STSEB).

To further test the STSEB model, the ET_cSTSEB simulated values with Equation (3) were compared to ET_cSDual values. Figure 6 presents such values, as well as the T_SDual, E_sSDual, E_sSTSEB, and T_STSEB plots.

The deviation of E_sSTSEB from the values obtained with the SIMDualKc model is apparent. The mean E_sSDual value of 0.89 mm d⁻¹ (for a maximum of 2.36 mm d⁻¹ and a minimum of 0.02 mm d⁻¹) contrasts with the 1.12 mm d⁻¹ value simulated with STSEB model (for a maximum of 1.36 and a minimum of 0.81 mm d⁻¹), showing that simulated STSEB soil evaporation values stayed relatively high throughout the period, with a 0.55 mm d⁻¹ difference between the maximum and minimum values, for a corresponding 2.24 mm d⁻¹ difference with the SIMDualKc simulation. Moreover, ET_cSTSEB values also considerably depart from simulated ET_cSDual values. They stay always below T_STSEB values and very close to E_sSTSEB values, which is an incongruity. The ratio of mean ET_cSTSEB/ET_cSDual = 0.56 and corresponding maximum and minimum ratios of 0.42 and 0.79, respectively, emphasize the inconsistency.

Table 6. Total, mean, maximum, and minimum actual evapotranspiration (ET_c), transpiration (T), and soil evaporation (E_s) simulated with the SIMDualKc and STSEB models in the year 2014 during the period DOY 166 to 273.

DOY 166 to 273 (2014)	SIMDualKc	Total (mm)	STSEB	Total (mm)
Mean (mm d−1)
ETc	2.37	245.1	1.33	143.4
T	1.48	147.2	1.80	194.8
Es	0.89	98.0	1.12	121.4
Maximum (mm d−1)
ETc	3.81		1.61
T	1.89		2.21
Es	2.36		1.36
Minimum (mm d−1)
ETc	1.20		0.95
T	0.58		1.27
Es	0.02		0.81

summarizes the results of actual ET_c, T, and E_s simulated with both models, in which the overestimation of T_STSEB for the entire period (T_cSTEB of 194.8 mm vs. T_cSDaul of 147.2 mm) and the high discrepancy between the total ET_c (ET_cSTEB of 143.4 mm vs. ET_cSDaul of 245.1 mm) and E_s values (ET_sSTEB of 121.4 mm vs. ET_sSDaul of 98 mm), are apparent.

In the latter above two cases, the source and main reason for the described inconsistencies appear to result from the built-in expectation in the STSEB model that the canopy geometry and evolution of fractional vegetation cover (f_c) would rapidly progress as a function of the leaf area index (LAI) to a value close to 1, as it does for row crops [34,35]. Consequently, the estimated values of the fraction 1-f_c, and E_sSTSEB in Equation (3), would evolve to approach zero at the stage of complete ground cover by canopy, with T_STSEB weighted by its respective partial shaded area approaching 1.0, thus becoming the major contributor to ET_c. In the case of our intensive olive orchard, with nearly constant f_c (0.28 in our study) throughout the growing period, such assumption does not apply, leading to a clear underestimation of ET_cSTSEB values (Figure 6, Table 6). Moreover, with practically constant values of E_sSTEB estimated for the summer dry months (low or no rainfall, and efficient drip irrigation), the available energy for soil evaporation accounted for by Equation (5) does not in fact translate into a real soil evaporation, resulting in misleadingly high modeled soil evaporation results. As seen, the nearly constant ET_sSTSEB values (mean of 1.12 mm d⁻¹) are higher than the ones simulated with the SIMDualKc model (mean of 0.89 mm d⁻¹), with the latter showing through the model soil surface water balance the existence of peaks and valleys from the occasional rainfall and the recurrent dry summer spells (Figure 4). Contrarily, the STSEB model, which tends to simulate nearly constant E_sSTSEB values, shows E_sSTSEB no reaction to the cycle of wet and dry spring and summer events. Moreover, weighing E_sSTSEB by its constant partial cover area in Equation (3) also lowers ET_cSTSEB simulated values, leading to its unrealistically low actual values for olive (Figure 6) and, moreover, it does not add up to the sum of T_STSEB and E_sSTSEB (Table 6). In partitioning ET_c for sunflower and canola_, Sánchez [34] also obtained higher values of K_eSTSEB than the ones proposed by FAO56, which reproduces lower values for soil E_s. The study also refers to significant deviations in ET_c between the lower STSEB simulated values and the ones proposed by FAO56 [34].

4. Conclusions

The main objective of the present study was the partitioning and computation of olive ET_c with energy and water balance models. Simple soil and canopy radiometric measurements, as well as sap flow-derived transpiration measurements, provided the main required information for the SIMDualKc and STSEB ET_c modeling. Good results obtained in the validation year between SIMDualKc and observed transpiration data encourage its use to validate the partitioning of intensive olive orchard ET_c (≤300 trees ha⁻¹) in both T and E_s components. The simplified two-source energy balance (STSEB) model was also able to partition ET_c into E_s and T, with reasonable agreement between predicted T_STSEB and sapflow measured T values. The E_sSTSEB clearly overestimated E_s when compared to the E_sSDual benchmark values, mainly due to the inability of the model in responding to the dynamics of E_s throughout the irrigation period, with its higher and lower values generated from soil wetting and drying episodes. The obtained results show that E_s and T, and consequently ET_c, for intensive olive orchards are affected by several factors including the canopy architecture, the fraction of ground shaded by canopy, and the crop management practices, which are well captured into the SIMDualKc water balance modeling. The heterogeneous and incomplete ground cover associated with this type of perennial crop increases the relative importance of adequately modeling the soil evaporation component of ET_c.