1 Introduction

Olive orchards are one of the most important crops in the semiarid Mediterranean region. Olives covered about 4.3 million of ha in Europe in 2007, of which 50 % were located in Spain (Eurostat 2011). Traditional olive orchards in Spain are rainfed, with around 100 trees per ha and ground cover rarely exceeding 25 % and generally located on hillsides.

Crop-water requirements for olive vary during the growing period and among orchards, mainly due to variation in crop canopy and density and in climatic conditions. Scientific efforts in measuring evapotranspiration of olive orchards are all relatively recent (Testi et al. 2004). A common method for assessing olive ET is the direct measurement of the total water vapour flux density from the orchard using the eddy covariance technique (Villalobos et al. 2000; Testi et al. 2004; Martínez-Cob and Faci 2010). However, these methods generally sample ET from single orchards or parts of orchards, only. Whole orchard ET has been measured in olive using the water balance method (Michelakis et al. 1996; Palomo et al. 2000) and estimated using daily soil water balance – atmospheric process models such as the relatively simple FAO 56 model which is based on the concepts of reference evapotranspiration ETo, crop coefficient Kc and root zone water balance (Allen et al. 1998). The Kc ETo approach has been commonly used for the estimation of olive water requirements in commercial orchards, and also to understand the relations between water use and yield (Martín-Vertedor et al. 2011). Er-Raki et al. (2010) have evaluated the ability of the FAO 56 dual crop coefficient model to reproduce the temporal evolution of ET and its components in olive. However, there is no simple way to calculate crop coefficients for olives, as they must integrate several factors depending on agricultural practices and orchard architecture (Er-Raki et al. 2008; Allen and Pereira 2009; Minacapilli et al. 2009; Cammalleri et al. 2010a; b). Allen and Pereira (2009) provided an updated formulation for estimating potential Kc for orchards as a function of fraction of ground shaded by the canopy and climate.

Remote sensing techniques represent a promising tool to overcome problems related to uncertainties in crop coefficient calculation in olive and other crops having sparse woody canopies, as suggested by studies carried out by Er-Raki et al. (2008) for an olive orchard in Central Morocco and by Hoedjes et al. (2008) who used an eddy covariance system to compare against daily ET values derived using ASTER satellite-based instantaneous estimates of ET from an olive orchard. Compared with traditional Kc-based ET estimations in olive orchards, remote sensing methods have a strong advantage in spatial accuracy because of the estimation ET by energy balance for each pixel of a satellite image using observed reflected radiation and temperature. Therefore, characterization of individual fields, including impacts of canopy density and tree spacing as well as relative water supply, are better addressed.

Surface energy balance (SEB) approaches for direct estimation of actual evapotranspiration have been developed over the past 20 years (Norman et al. 1995; Roerink et al. 1997; Bastiaanssen et al. 1998; Kustas and Norman 1999; Allen et al. 2007a; Gontia and Tiwari 2010; Awan et al. 2011; Elhag et al. 2011). These approaches have recently been applied to estimate ET from a variety of sparse woody canopies, for example, by Samani et al. (2009) to estimate the daily ET for pecan orchards in the lower Rio Grande Valley, New Mexico. The SEBAL model has been tested over grapes, peaches and almonds in Spain, Turkey and California (Bastiaanssen et al. 2008). Minacapilli et al. (2009) compared two SEB approaches, the SEBAL model and the TSEB (Two-Source Energy Balance model; Norman et al. 1995) to estimate the actual ET from typical spatially sparse Mediterranean vegetation (with olive, citrus and vineyards). However, this analysis did not determine which SEB model produced better performance. Cammalleri et al. (2010a) applied a coupled hydrological/SEB model to estimate actual evapotranspiration in an irrigated olive grove from a semi-arid region located in Sicily. The model was compared with energy fluxes measurements from a dual-beam small aperture scintillometer system.

METRIC (Mapping EvapoTranspiration with high Resolution and Internalized Calibration) is a blended-source energy balance-based ET estimation model developed by the University of Idaho, USA (Allen et al. 2007a) and originated from the SEBAL model of Bastiaanssen et al. (1998). METRIC has been applied in the Western United States (Allen et al. 2005, 2007b) and in Southern Spain (Santos et al. 2008, 2010), to produce high resolution ET maps from the Landsat satellite. Estimates of ET by METRIC have compared favourably with a series of lysimeter ET measurements at two locations in the Northwest US (Tasumi et al. 2005) and with measured fluxes via eddy covariance in central Iowa (Choi et al. 2009). However, there has not been extensive testing nor focused application on non homogeneous or sparse woody canopies, such as olives, where biases in model estimates may be caused by the soil and shadow effects on pixel temperature estimation and uncertainties regarding roughness and aerodynamic profiles, mixture and shading effects on surface temperature (Ts) and the near surface air temperature gradient (dT) function in the sensible heat flux calculation (Allen et al. 2007a).

The procedure used in METRIC, where a single dT function and aerodynamic resistance (rah) term are used to estimate H, is referred to as a blended model (Allen et al. 2011), where the lower endpoint of dT and rah are placed in the equilibrium boundary layer at some z1 distance above the zero plane displacement height. The intention is to estimate the near surface temperature gradient and aerodynamic conductance in the mixed, somewhat chaotic layer of air where dT and rah combine effects of both vegetation and soil surface. This approach seems justified, especially under conditions of greater than calm wind speed, where horizontal flow of air from vegetation to soil and from soil to vegetation is poorly structured and includes the combination with more vertical aerodynamic structures created by buoyancy for differentially heated surfaces (sunlit soil vs. shaded soil and sunlit, dry canopy vs. shaded canopy). The large spatial size of thermal pixels in Landsat images (60–120 m) produces blended, bulk values for Ts that tend to correlate with the blended dT, producing ET as a residual of the energy balance for sparse olive orchards that are in line with independent estimates, as shown for this study. The use of the blended layer model reduces speculation or potential component malformation in TSEB models associated with the largely unknown and canopy architecture-specific microscale air circulations and feedbacks between soil and canopy that are, in turn, associated with differential heating, air bouyancies, and mechanical forcings. Although the TSEB model might be more suitable for sparse canopies, uncertainties in parameterizing the intercanopy processes noted above were judged to create too much uncertainty in model behavior and too much 'freedom' in model parameterization. The application and calibration of a TSEB model in this study would have been complicated for the relatively large number of fields and canopy architectures in the study. The calibration of the blended layer METRIC model uses upper and lower ranges of radiometric temperature and fractional vegetation cover within a scene to internally calibrate its variables and to remove many systematic biases in satellite retrievals and assumptions regarding energy balance components (Allen et al. 2011). TSEB generally uses the remotely sensed data as direct inputs to the computation of the soil, canopy aerodynamic surface temperatures and heat flux components. As result, TSEB has greater sensitivity to uncertainty in radiometric temperature values caused by error in atmospheric and emissivity corrections and to error or uncertainties in defining the spatially distributed air temperature that can vary widely with partitioning of available energy. Air temperature is implicitly tied to dT in the blended METRIC approach.

The objective of this work was to contrast METRIC results for olives made for year 2005 against water balance-based ET estimations from non-irrigated olive fields where ET was constrained by rainfall data and stored soil moisture. Similarity in estimates by the methods reveals strengths of each method regarding accuracy of simulation and parameterizations and sensitivity to how components are estimated. Differences in estimates indicate where behaviour of SEB or soil water balance models is not well understood or where models are inadequately defined and where more work is needed.

2 Materials and Methods

2.1 Selection of Fields for ET Evaluation

Sixty-seven non-irrigated olive fields in the eastern portion of Córdoba province were investigated during the evaluation of METRIC. The ET from these olive fields was estimated using the FAO 56 Kc ETo/soil water balance-based method (Allen et al. 1998) and using the METRIC model. For both methodologies, weather data including rainfall, air temperature, relative humidity, wind speed and solar radiation from five weather stations within or near the study area were obtained from the Agroclimatic Information Network of Andalusia (Gavilán et al. 2006). METRIC was applied to Landsat 5 satellite images for the period between 22 April and 13 September, 2005. In sampling METRIC-based ET, 30 sample pixels were identified and selected per field where all sampled pixels resided at least 120 m inside field boundaries to avoid the contamination of thermal pixels of the Landsat 5 satellite by areas lying outside the fields. Small fields that did not meet these requirements were eliminated from the selection, so that finally 22 non-irrigated olive fields with an averaged size of 72 ha qualified for the study (Fig. 1). Average tree density on these fields ranged from 70 to 200 trees per ha, and ages of trees ranged from approximately 20 to 50 years. Tree heights ranged from 1.7 to 6 m across the fields.

Fig. 1
figure 1

Selected non-irrigated olive fields located east/south of Córdoba, Spain, aerial photograph and detail of one of these fields, overlaid on a Landsat 5 image

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2.2 Water Balance-Based Estimates

ET from the non-irrigated olive fields was estimated using the FAO 56 dual Kc based daily soil water balance method (Allen et al. 1998):

$$ E{T_{{c(adj)}}} = \left( {{K_s}{K_{{cb}}} + {K_e}} \right)E{T_o} $$
(1)

where Ks is a water stress coefficient, Kcb is the basal crop coefficient, Ke is the soil evaporation coefficient, and ETo is grass reference evapotranspiration. The water stress coefficient is obtained following Allen et al. (1998) as:

$$ {K_s} = \frac{{TAW - {D_r}}}{{\left( {1 - p} \right) \cdot TAW}} $$
(2)

where TAW is the total available soil water in the root zone (mm), Dr is the root zone depletion (mm) and p is the fraction of TAW that a crop can extract from the root zone without suffering water stress. The primary soil type in the study area was silt loam, estimated to hold 150 mm/m of available water. The root zone of the rainfed olives was set at 1.5 m depth based on typical rooting by olives (Allen et al. 1998), and p was set at 0.65 for the olive crop, following Allen et al. (1998). The root zones were assumed to be dry at the beginning of the simulation period (September 1, 2004), which followed a very dry summer.

Estimates for Kcb were based on average groundcover and tree height of the sampled fields, and adjusted for climate and reduction for effective stomatal control on transpiration following Allen et al. (1998) and Allen and Pereira (2009). First we obtained a Kcb mid from an effective ground cover of 0.25 and height of 4 m where a reduction factor for stomatal control was set to 0.67 (Allen et al. 1998, p 192), and adjustment was made for impacts of the dry, windy climate of the study area where wind speed at 2 m averages 2.2 m/s and average daily minimum RH averages 19 % during the summer. The resulting value obtained for Kcb mid adj was 0.5, based on a value for the ML coefficient of Allen and Pereira (2009) of 1.8, and the values of Kcb ini adj and K cb end adj were set to 0.42, to maintain proportions to baseline K cb values from Allen and Pereira (2009) of 0.3, 0.35 and 0.3 for the same effective fraction of ground cover and a standard climate.

Er-Raki et al. (2010) obtained an average seasonal value of basal crop coefficient of 0.54 in a Moroccan olive orchard having similar semi-arid conditions using sap flow measurements. That value is similar to our Kcb values. The Ke coefficient was estimated using potential values for Kc, a soil evaporation reduction coefficient Kr, and the exposed and wetted soil fraction (0.75).

Results of the FAO 56 soil water balance-based (SWB) calculations are summarized in Fig. 2 and Table 1. The 2005 season was extremely dry, and the FAO 56 model and water balance estimated large amounts of water stress for the non-irrigated olive trees, so that the Ks function tended to dominate over the Kcb and Ke estimates. The model suggested that essentially all rainfall during the 12 month period was evaporated or transpired, with no gain in soil water storage nor any deep percolation flux to ground-water over the 12 month period. The time series of ET shown in Fig. 2 was created using rainfall, ETo, soil type and tree architecture data averaged over the 22 fields. The spikes in ET during May and September were caused by evaporation stemming from rain events. Extremely low ETc values were detected during July and August due to extremely dry conditions (see Table 1). As a confirmation of the extreme dryness, trees were observed to lose leaves during this period. The similarity of results from all five weather stations permitted the comparisons with METRIC and statistical analyses to be based on averages over the stations.

Fig. 2
figure 2

a) Water stress coefficient (Ks) and precipitation for each of five weather stations used in the study; b) SWB-derived potential and adjusted evapotranspiration for the five weather stations used in the study data

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Table 1 Annual rainfall amounts and ETo (mm) for the September 2004 to September 2005 period and associated estimated ET from non-irrigated water-stressed olives by the FAO 56-based dual Kc and soil water balance method for the five weather stations used in the study
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2.3 Improving METRIC ET Application for Olives

2.3.1 Standard METRIC zom Estimate

The METRIC energy balance procedure (including the Mountain model) of Allen et al. (2007a) was applied to seven Landsat 5 images spread across the 2005 growing season. METRIC-based ET was produced as a residual of the surface energy balance, where energy consumed by the ET process was calculated as a residual of the surface energy equation:

$$ LE = {R_n} - G - H $$
(3)

where LE is the latent energy consumed by ET, Rn is net radiation, G is sensible heat flux conducted into the ground, and H is sensible heat flux to the air.

Net radiation was computed by subtracting all outgoing radiant fluxes from all incoming radiant fluxes and included solar and thermal radiation, considering the slope effects on the solar components of the energy balance. Soil heat flux was estimated as a function of net radiation, vegetation indexes and surface temperature (Ts), where surface temperature is computed using the Landsat satellite thermal sensor. Sensible heat flux was estimated by deriving a near surface air-temperature gradient (dT) and aerodynamic resistance between two near surface heights (0.1 and 2 m above the zero plane displacement), and assuming dT in the blended layer to be linear in proportion to radiometric Ts. This approach constitutes one of the pioneering components of the SEBAL model developed by Bastiaanssen (1995), who provided empirical evidence for using the linear relation between dT and Ts. Calibration of the dT function was accomplished by selecting two extreme “calibration pixels” representing very dry and very wet agricultural surfaces, as described in Allen et al. (2007a). Daily ET, ET24 was estimated by assuming that the instantaneous ETrF (ratio between current and reference ET) computed at image time was the same as the average ETrF over the 24 h average. This assumption has been validated through lysimeter measurements as shown in Allen et al. (2007a, b).

METRIC-estimated ET was used to describe the degree of water stress over time by computing a METRIC water stress coefficient (\( {K_{{s\,METRIC}}} \)), that is similar to, and was compared against, the FAO 56 water stress coefficient:

$$ {K_s}_{{METRIC}} = \frac{{E{T_{{METRIC}}}}}{{{K_{{cb}}} \cdot E{T_o}}} - \frac{{{K_e}}}{{{K_{{cb}}}}} $$
(4)

where Kcb and Ke were averaged values of the basal and evaporation coefficient from the FAO-56 SWB model, with Kcb representing potential (non-stressed) conditions. The inclusion of Ke in Eq. 4 is necessary because the ETMETRIC estimate contains a soil water evaporation component.

The initial applications of METRIC used a general equation for momentum roughness length (zom) that is designed for annual agricultural crops and conditions (Allen et al. 2007a):

$$ {{\text{z}}_{\text{om}}} = 0.{12} h $$
(5)

where zom is in meters, h is crop height (m). Roughness length is used to estimate momentum transport, which is a measure of the form drag, air turbulence and skin friction for the layer of air that interacts with the surface. This is used in METRIC in the aerodynamic resistance-based estimation of sensible heat flux (Allen et al. 2007a). In general, the smaller the value specified for zom in METRIC, the smaller the estimate for sensible heat flux, and thus the larger the estimate for ET calculated as a residual of the energy balance.

The initial estimate for h was based on a standard METRIC algorithm by Tasumi (2003) for annual, irrigated crops characteristic of the temperate climate of Kimberly, Idaho, USA, and is based on estimated LAI (Leaf Area Index):

$$ h = 0.{\text{15 LAI}} $$
(6)

In the case of olives, h is substantially underestimated by Eq. (6), and therefore, zom is underestimated, so that ET is overestimated. Application of Eqs. 5 and 6, developed for dense, annual crops, is inappropriate for sparse olive orchards, but was included to demonstrate sensitivity of METRIC ET estimation to error in zom for a stressed, rainfed system.

2.3.2 Estimating zom Using Olive Height and Tree Density

Orgaz et al. (2005) defined a Shape Index to describe the canopy architecture of olive trees as the ratio between the olive crown diameter and height. The ratio tends to vary with density of olive plants for old Spanish orchards (Table 2) and was used here to estimate zom, where crown diameters were estimated using 0.5 m ortho-rectified aerial imagery collected over the entire area of the study (Junta de Andalucía 2002). Olive tree density was estimated by counting and identifying the center point of each tree, resulting in an image with 1x1m pixels assigned a digital number of “1” if an olive tree and “0” otherwise. That image was aggregated to produce a coarsened density map having 30 m resolution by multiplying all pixels by 900 and then, using a degradation tool, calculating the average value. The resulting map expressed the number of trees per 30x30m pixel. Olive tree height was estimated using the crown density and Shape Indices previously determined (Table 2). The estimates of tree height averaged 4.4 m, which is much more realistic than the value of 0.03 m that resulted from Eq. 6, due to the low LAI of olive trees. Finally values for z om were estimated from h using Eq. 5.

Table 2 Values of the Shape Index (SI = D/H) for old olive orchards in Spain having different plant densities (following Orgaz et al. 2005) where D is crown diameter and H is tree height, both in meters
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2.3.3 The Perrier Function for zom

Perrier (1982) developed a zom function based on LAI and tree canopy architecture for sparse trees:

$$ {z_{{om}}} = \left( {\left( {1 - \exp \left( {\frac{{ - aLAI}}{2}} \right)} \right)\exp \left( {\frac{{ - aLAI}}{2}} \right)} \right)h $$
(7)

where a is an adjustment factor for the LAI distribution within the canopy with a = (2f) for f ≥ 0.5 and a = \( {\left( {2 \cdot \left( {1 - f} \right)} \right)^{{ - 1}}} \) for f < 0.5. The factor f is the proportion of LAI lying above h/2. In the case of the olives of the study, they are mostly old trees, where nearly 40 % of branches lay above the half-way point (f = 0.4), so an appropiate value for a is 0.83. Various other models such as those by Raupach (1992, 1994, 1995) have been proposed to describe zom for sparse canopies, but those models contain a number of coefficients whose values must be determined empirically. The Perrier function performs similarly to the Raupach density-based functions.

LAI values were computed in the METRIC procedure using the soil adjusted vegetation index (SAVI; Allen et al. 2007a) as:

$$ LAI = - \frac{{\ln \left[ {\left( {0.69 - SAVI} \right)/0.59} \right]}}{{0.91}} $$
(8)

where, for application with Landsat images, SAVI is based on top of atmosphere reflectance of bands 3 and 4 and the SAVI parameter “L” was set to 0.1.

Low LAI values are common to traditional rainfed orchards, where representative LAI for 30 % ground cover is about 0.33 (Gómez et al. 2001). Our values were even lower in some cases, as our ground cover was also lower, with maximum LAI for olive orchards in the study of around 0.4 and decreasing from April to July due to intense pruning and due to a decrease in green vegetation beneath trees that dried up during summer. In addition there was some reduction in numbers of leaves of olives resulting from stress during the summer period. The average Perrier multiplier from Eq. 7, averaged over the 22 fields and seven Landsat images, produced an average zom/h relationship:

$$ {{\text{z}}_{\text{om}}} = 0.0{68} h $$
(9)

3 Results

3.1 Application of the Standard METRIC zom Estimate

Crop coefficients Kco derived for the 22 non-irrigated sample fields from METRIC are plotted in association with the continuously modelled averaged Kco from the SWB model in Figs. 3a. These plots suggest some over-estimation of ET by the initial application of METRIC using the standard h vs. LAI relationship of METRIC for the non-irrigated olive orchards (RMSE of Kco = 0.188 and of ET = 1.12 mm/day). However, the midsummer depression of ET from the rainfed olive fields was in relatively good agreement with the ET as modelled by the SWB due to the large magnitude of stress reduction to Kc during this period as determined by low available soil water, which is in turn, governed by precipitation, which is considered to be known with relatively good accuracy. The variation in METRIC-derived Kco among the 22 fields was caused by variation in size of tree canopy, tree age, style of tree pruning, soil type and depth, and also to some degree, random error in the Kco estimated by METRIC stemming from minor variation in surface temperature for the same energy balance condition.

Fig. 3
figure 3

a) Kco derived from METRIC formulation using h from equation 6 and from Table 2 vs. results from the SWB model; b) METRIC water stress coefficients (Ks) and SWB-based estimates of ET for actual conditions

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Fig. 4
figure 4

a) Kco derived from default METRIC formulation and using zom = 0.068 h (where h is obtained from Table 2), vs. results from the SWB model; b) METRIC water stress coefficients (Ks) and SWB-based estimates of ET for actual conditions

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Figure 3a shows METRIC results for Kco using zom based on Eq. 5 combined with an improved estimate for h from the D/H ratios of Orgaz et al. (2005). This method for zom caused, on average, some underestimation of ET in comparison to the SWB estimates for 3–4 images during mid-spring and summer although comparisons were good for other dates (RMSE of Kco = 0.058 and of ET = 0.34 mm/day). Figure 3b compares the SWB-estimated water stress coefficient (Ks) and a METRIC-derived Ks from Eq. 4 for the zom/h = 0.12 estimation. Because the zom/h relationship of Eq. 5 is based on a dense vegetation cover, this relationship does not apply well to olive trees having only partial ground cover.

3.2 zom Derived from the Perrier Function

The zom function developed by Perrier (1982) for tall and potentially sparse vegetation such as forests, riparian areas or orchards was applied in METRIC calculations, where zom was calculated from zom/h = 0.068. That approach produced estimates for Kco that were closest to the SWB-based estimates (RMSE of Kco = 0.045 and of ET = 0.25 mm/day; Fig. 4a). Figure 4b shows METRIC-derived water stress coefficients using the Perrier function compared with SWB-based estimates. The similarity and consistency of estimates by the METRIC energy balance and by the FAO 56 dual Kc and water balance model is quite good. There was some disagreement for the last METRIC image (13/09/05), where SWB-based estimates, averaged over the five weather stations, did not incorporate effects of spatial variability in precipitation (see Fig. 2).

The similarity of estimates between models does not validate either model, since validation via measurement of ET from the 22 rainfed fields examined in this study was logistically not possible. However, the FAO based estimates for ET were constrained by reported rainfall data, so that, integrated over time, the estimates are considered to be accurate and largely independent of METRIC.

3.3 Sensitivity Analyses on Soil Parameters and Kc

Sensitivity analyses were made to the SWB model to determine to extent to which ET and actual Kco derived from that model (via Eq. 1) vary with changes in values for soil parameters. Results are summarized on Table 3.

Table 3 Sensitivity analysis on the FAO 56 soil water balance model showing RMSE of Kco using tree height as determined from Table 2 (last 2 columns)
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First we evaluated the influence of soil water storage at the beginning of the simulation period where we initially assumed that the initial soil condition was dry. Figure 5a shows SWB-derived water stress coefficients (Ks) and crop coefficients (Kco) averaged over the five weather stations for three different initial conditions (dry, 25 and 50 mm), starting at 1 September, 2004. Differences in Kco only occurred during the first 3–4 months, and were nearly zero by the time of the first METRIC image, in April, 2005, when all additional initial water had been extracted by the model. The computed RMSE between FAO-SWB-estimated Kco and METRIC determined Kco were very similar for the three initial conditions (Table 3).

Fig. 5
figure 5

a) SWB-based water stress coefficients and crop coefficients produced using different soil water contents at the beginning of the simulation period and b) different depletion fraction (p) values

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A second sensitivity analysis was conducted on the influence of the depletion fraction (p) used to indicate the initiation of water stress on the Kc estimate from the SWB model. Figure 5b shows average SWB-based Ks and Kco averaged over the five weather stations for different values for p, where no important differences were found when compared with METRIC estimates. The relative insensitivity to p is expected, since, by midsummer, all available water was extracted, regardless of the value for p, and because Ks is so strongly influenced by total soil water holding capacity and rooting depth when time between wetting events is large.

A third sensitivity analysis was made on water holding capacity (WHC) and root zone depth (Rz), as these values impact the total water supply, and thus, control how low the value for Ks may become during summer (depending on water storage from winter; Table 3). However, insignificant change occurred in SWB-based Ks estimates when compared with METRIC estimates for the different WHC and root zone depth values, because total water in the root zone was constrained by precipitation input and initial available water.

The last sensitivity analysis examined the influence of Kcb (see Table 3) on soil water results and its agreement with METRIC estimates. Our initial values for Kcb were 0.42, 0.5 and 0.42 for Kcb ini, Kcb mid and Kcb end respectively. For the sensitivity analysis, we considered firstly 0.3, 0.35 and 0.3, as recommended by Allen and Pereira (2009) for a standard climate and then an average seasonal value for the basal crop coefficient of 0.54, based on sap flow measurements, obtained by Er-Raki et al. (2010) for similar semi-arid conditions. As expected, results were similar to those for the baseline conditions, as these changes only shifted the extraction of water in time, and soil water stress, via Ks, still dominated the process (data not shown in Figures).

The small differences produced by these sensitivity analysis showed that, due mainly to the scarce precipitation over the area during the 2005 study year, soil characteristics did not significantly influence the water balance-derived Kco estimates because rainfall inputs limited ET nearly all season, so that all likely values for soil parameters accommodated the storage and subsequent extraction of precipitation. Consequently the comparison of SWB-based results with METRIC estimations was considered to offer a relatively robust comparative basis for ET and Kco, which was the aim of this work.

4 Conclusions

Effective irrigation management and stress characterization in olive orchards requires an accurate methodology to quantify current evapotranspiration over large areas and at the spatial scale of individual orchards. Evapotranspiration from 22 non-irrigated olive fields under semi-arid conditions was assessed using the METRIC satellite-based energy balance model that until now had been mainly applied to agricultural fields having crops shorter and generally more dense than rainfed olives. The use of micrometeorological techniques was not feasible due to the large number of olive plots under study. Therefore, this study did not attempt to validate METRIC results using direct measurements of ET, but instead utilized a comparative approach between two independent models. The soil water balance model was based on the FAO 56 ET approach, where the crop coefficient (Kc) was estimated as a function of ground cover and height, a procedure that has been recently formalized in Allen and Pereira (2009). Some over-estimation of METRIC ET occurred for the non-irrigated olive orchards when crop height was estimated using a default METRIC algorithm intended for annual crops (RMSE = 1.12 mm/day).

METRIC-based ET estimates for olives was improved using a methodology that tailored zom estimation to the sparse tree crops by using a zom/h ratio of 0.12, similar to that defined by Villalobos et al. (2000) and Berni et al. (2009) for intensive irrigated olive orchards, but with improved estimates for tree height (RMSE = 0.34 mm/day). In our case this caused some underestimation of ET in comparison to the SWB-based estimates in the mid-spring and summer images due to the sparseness of our rainfed olives. On these dates the thermal signal of sparse olives was dominated by soil temperature and the large roughness value, and may have overstated sensible heat flux, and consequently the ET was underestimated. An alternative zom function developed by Perrier (1982) for tall and sparse vegetation produced the most accurate estimate of Kco as compared with the SWB-based estimates (RMSE = 0.25 mm/day).

This study provides a useful indication of the impact of estimation procedure for crop height and zom on aerodynamic behaviour of METRIC computations in application to sparse woody canopies. Results indicate that, with good estimates of zom, ET estimated by METRIC compares well with modelled ET under water shortage-induced stress of rainfed olives. This supports the value of continued study on the use of METRIC or similar models to monitor ET behaviour of olive orchards in Southern Europe for the design of customized irrigation schedules and means to take strong advantage of the spatial information and relatively good accuracy of satellite-based products. Particularly in large olive areas of Andalusia, this approach constitutes a useful tool for Irrigation Advisory Services to achieve an efficient use of irrigation water especially during drought periods, in contrast with the traditional fixed schedules based on average data that are commonly used (Lorite et al. 2012). Furthermore, the determination of ET via remote sensing techniques can help identify water stress in olive orchards, and can be useful to analyze deficit irrigation strategies.