Canopy Resistance and Actual Evapotranspiration over an Olive Orchard
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Abstract
Τhis study evaluates the hourly actual evapotranspiration (AΕT), predicted either by the two modified PenmanMonteith models (PM) which take into account the canopy resistance (r_{c}) from the KaterjiPerrier (KP) or Todorovic (TD) models, or the simplified PM model with zero r_{c}, as proposed by Priestley and Taylor (PT). The evaluation is based on comparisons with experimental measurements of AΕT applying the ‘Bowen ratio’ method. Hourly experimental data, of air temperature, humidity, wind speed and radiation balance measurements, taken at a 0.5 ha olive orchard in the rural area of Sparta (37° 04΄ N, 22°05΄ E), during the period from June 2010 up to July 2014, are used. The r_{c} estimated by KP model is parameterized by a semiempirical approach which requires a simple calibration procedure, while r_{c} from TD model is parameterized using a theoretical approach. For estimating AET from minimum data (air temperature, humidity and radiation balance components) the PT model is also employed, since r_{c} is not required and the aerodynamic term of PM is taken into account in the empirical parameter of the model. The results show that PT and KP models are the most appropriate [Refined Index of Agreement (RIA) equal to 0.89 or 0.88, respectively] followed by the TD model (RIA = 0.78). PT or KP models underestimate AET by 9.3% or 9.8%, respectively, while TD model overestimates AET by 15.0%, increased up to 25.8%, during warm period.
Keywords
Actual evapotranspiration Canopy resistance PenmanMonteith method KaterjiPerrier method Todorovic method Priestley and Taylor method1 Introduction
The accurate evaluation of actual evapotranspiration (AET) at different scales is considered as a subject of high interest for hydrology, for determining the water requirement in irrigated areas and analyzing the impacts of climate change on water resources. AET is a component of the water balance of the considered surface and its energy equivalent is the latent heat flux (λΕ) (Penman 1948). Several techniques provide direct measurements of λΕ, such as the Bowen ratio energy balance method (BREB method) or the eddy covariance system. The BREB method has been used to quantify λΕ over various surfaces, such as open water (Burba et al. 1999), grassland (Pauwels and Samson 2006), crop land (Todd et al. 2000; Zhang et al. 2008) and forest (Dawson 1996). Furthermore, λΕ is estimated, using empirical or mechanistic models, based upon in situ observed meteorological variables. Among them, the Penman–Monteith combination equation (Monteith 1965) is commonly used. The model is based upon the assumption that the water has to diffuse firstly through leaves against a canopy resistance (r_{c}), before diffusing into the atmosphere against an aerodynamic resistance (r_{a}), in order to have all λΕ accessible by the plant canopy. According to several researchers, the sensible heat flux (H) only has to diffuse into the atmosphere against the aerodynamic resistance (Shuttleworth 1993; Pauwels and Samson 2006). Canopy resistance expressed as a function of external conditions is usually difficult to be calculated accurately. Thus, a semiempirical approach has been suggested by Katerji and Perrier (1983), with r_{c} depending on climate variables and the aerodynamic resistance, and requiring in situ calibration of its parameters (KP model). A mechanistic model (not requiring in situ calibration) for determining λΕ was also developed by Todorovic (1999) with the r_{c} being also a function of climatic variables and aerodynamic resistance (TD model). The PriestleyTaylor (PT) model (Priestley and Taylor 1972) has been also used for estimating λΕ (Flint and Childs 1991), as a simplified form of PM method. The PT method has been reported as successfully simulating λΕ over forest ecosystems (Fisher et al. 2005; Kumagai et al. 2005), crop fields (Utset et al. 2004; Liu and Lin 2005) and grassland (Sumner and Jacobs 2005; Pauwels and Samson 2006). The model has been quite often used for calculating potential evapotranspiration. Priestley and Taylor (analysing data over water surfaces and saturated land areas after rainfall) recommended the value of 1.26 as the most appropriate for parameter α (of the respective equation) and thereafter, this value has been used in many studies referring to wet or irrigated crops and grass (Stewart and Rouse 1977; Liu and Lin 2005). When the method is used for estimating λΕ, values of α have been reported as equal to 1.18 over temperate forest during the development period (Shi et al. 2008) or 0.83 or 0.74 (values different for each year of the measurements) above alpine grass (Zhu et al. 2014). Pauwels and Samson (2006) reported an average daily value of α equal to 1.21 for the whole year (with great annual fluctuation) over a natural meadow. They also found α as decreasing with the increase of the water vapour deficit and as increasing with the increase of the soil moisture. Gavin and Agnew (2004) found the value of α equal to 1.25 for periods characterized by floods and equal to 0.80 for periods without surface water, when working over wet meadow during the period March–September. In addition, they concluded that the use of a single value for α throughout the year leads to an underestimation of the λΕ under wet ground conditions and overestimation under dry conditions.
The KP model has been tested successfully by several researchers recommending it as a fairly reliable model for a large number of natural types of vegetation or crops: alfalfa (Katerji and Perrier 1983), grass (Rana et al. 2001), lettuce (Alves and Pereira 2000), tomato (Rana et al. 2012), sweet sorghum (Rana et al. 2001; Katerji et al. 2011), rice (Peterschmitt and Perrier 1991), sunflower (Rana et al. 1997a), soya bean (Rana et al. 1997b; Katerji et al. 2011), wheat (Amazirh et al. 2017), maize and vineyard (Li et al. 2015), overhead table grape vineyard (Rana and Katerji 2008), vineyards in rows (Li et al. 2009), clementine orchard (Rana et al. 2005), orange orchard (Ayyoub et al. 2017), forest (Shi et al. 2008). However, in situ calibration is required to determine the parameters of the KP model. The TD model has been reported (Katerji et al. 2011), as inadequate in correctly assessing λΕ over natural vegetation (prairie, forests) and annual crops (soya bean, sweet sorghum) or perennial crops (vines), as it leads to overestimation of the order of 30–50%, but instead it underestimates λΕ above irrigated grass, by about 20%. It must be noticed that the TD model is an attractive method for parameterization of r_{c} and estimation of λΕ, since it is a theoretical model that does not require the use of additional experimental data for its calibration.
The main objective of this study is to assess the evaluation of accurate hourly λΕ predictions, obtained either from the two modified PM models, with r_{c} estimated by the KP or TD models or the simplified model given by the PT method with zero r_{c}. The evaluation is based on comparisons with measurements of λΕ, taken over olive trees during the period June 2010 to July 2014. Furthermore, the discrepancies of the diurnal or annual variation of all estimated r_{c} and λΕ from the corresponding variations of the experimental r_{c} and λΕ are investigated. Additionally, the effect of r_{c} parameterization factors [water vapor deficit (D), wind speed (U), net radiation (R_{n}) and water status] on estimating λΕ by KP and TD model and the influence of D and soil moisture on the PT parameter are also examined.
2 Data and Methods
2.1 Data
Soil characteristics
Depth (cm)  0–30  30–60  60–90  
pH  –  7.19 ± 0.25  7.5 ± 0.17  7.66 ± 0.27 
EC  (μS /cm)  1963 ± 230  1677 ± 258  1683 ± 196 
Particle size class  –  SCL, CL, L  SCL, CL, L  SCL, CL, L 
Organic matter  (%)  6.3 ± 0.94  3.7 ± 0.28  2.5 ± 0.27 
N (Kjeldahl)  0.2 ± 0.015  0.1 ± 0.064  0.07 ± 0.02  
CaCO_{3}  0.51 ± 0.31  1.02 ± 1.45  2.02 ± 2.53 
The data belonging to days with rainfall or irrigation events were removed from the further analysis.
2.2 Methods
2.2.1 Measurement of Hourly Actual Evapotranspiration
Hourly values of all parameters were taken into account, after applying criteria for appropriate β values according to Ohmura (1982) and Tanner et al. (1987).
2.2.2 Estimation of Hourly Actual Evapotranspiration
In order to estimate hourly r_{c}, needed in the PM method, the KaterjiPerrier (Katerji and Perrier, 1983) and the Todorovic (Todorovic, 1999) models were applied over olive trees. For estimating λΕ without requiring r_{c}, the PT model was employed and the aerodynamic term of PM was taken into account in the dimensionless empirical parameter α of the model.
The difference between the two expressions of the aerodynamic resistances (Eqs. 7 and 8) is the additional aerodynamic resistance introduced by Perrier (1975) for taking into account the structure of vegetation, since he considered that the aerodynamic model of Thom (1972, 1975) ignores the role of plant architecture.
\( {r}_i=\frac{\rho {c}_pD}{\gamma A} \) is defined as a climatological resistance (s/m).
\( t=\frac{\gamma D}{\varDelta \left(\varDelta +\gamma \right)}\kern0.5em \)is the temperature difference in ^{0}C.
Canopy resistance r_{c} can be calculated from only one positive solution of the quadratic eq. 9.
2.2.3 Evaluation of Estimated Hourly Actual Evapotranspiration
In this study the percentage MBEs and RMSEs are estimated.
3 Results
3.1 Estimation of Hourly Canopy Resistance and Actual Evapotranspiration
3.1.1 Calibration of KP and PT Model
3.1.2 Evaluation of Estimated Hourly Actual Evapotranspiration
Results of the linear regressions [slope (a) and determination coefficient (R^{2})] and ‘difference measures’ [root mean square error (RMSE), mean bias error (MBE), refined index of agreement (RIA) and mean absolute error (MAE)] between estimated by TD or KP or PT methods and measured hourly actual evapotranspiration, for all or warm period data and for all or warm period data with β < 0.3
ΜETHOD  a  R^{2}  RMSE %  MBE %  RIA  MAE (W/m^{2}) 

All Data  
TD  1.17  0.96  34.55  15.04  0.78  57.91 
KP  0.92  0.98  19.19  −9.80  0.88  31.93 
PT  0.93  0.99  14.88  −9.33  0.89  27.36 
Warm Period Data  
TD  1.25  0.90  36.31  25.78  0.72  80.44 
KP  0.94  0.96  13.39  −6.39  0.90  28.61 
PT  0.95  0.97  11.27  −5.36  0.91  24.89 
All Data (β < 0.3)  
TD  1.15  0.90  32.35  12.67  0.80  53.57 
KP  0.90  0.95  19.46  −12.05  0.88  31.36 
PT  0.91  0.98  14.88  −11.31  0.90  27.08 
Warm Period Data (β < 0.3)  
TD  1.22  0.92  33.22  23.14  0.75  72.97 
KP  0.93  0.97  12.79  −8.45  0.91  27.21 
PT  0.94  0.98  10.33  −7.38  0.92  23.32 
It is well established, that as water availability decreases, the energy partitioning between λE and H is altered, resulting in an increase in H, and consequently in β. Thus, β has been sometimes used as an indicator of water stress (Peterschmitt and Perrier 1991; Frangi et al. 1996). The criterion β <0.3 is usually used, when applying ΚΡ or TD models, in order to exclude water stress situations (Alves and Pereira 2000). In this study, hourly λE_{TD} or λE_{KP} or λE_{PT} estimates based on all or warm period data satisfying the above criteria are also calculated and compared with λΕ_{M}. The results are shown in Table 2. Hourly λE_{TD} estimates from all periods data seem to be slightly improved (R^{2} = 0.90, RMSE = 32.35%, MBE = 12.67%, RIA = 0.80 and MAE = 53.57 W/m^{2}) indicating that the insufficiency of water rather enhances the overestimation of λΕ_{M} by the TD model.
The TD model based on a totally theoretical model for the determination of the r_{c}, compared to the KP model, which uses a semiempirical approach, employs a different parameterization of r_{a}, as well, in order to estimate λE_{TD}. The KP model uses eq. 7 for obtaining r_{aKP}, while the TD model uses eq. 8, for calculating r_{aTD}. To investigate the effect of the different form of r_{a}, employed by the TD model, λE_{TD} was recalculated by employing r_{aKP} instead of r_{aTD} and the new λE_{TD} was compared to λΕ_{M}. The results (not shown in Table 2) found from the linear regressions and the ‘difference measures’ for all data (R^{2} = 0.95, RMSE = 61.29%, MBE = 35.89%, RIA = 0.60 and MAE = 102.56 W/m^{2}) or for the warm period data (R^{2} = 0.88, RMSE = 65.89%, MBE = 51.35%, RIA = 0.47 and MAE = 151.45 W/m^{2}) show an even greater overestimation of λΕ_{M} from this TD approach. Therefore, it is noted that the use of a different form of r_{a} is not responsible for the overestimation of λΕ_{M} by the TD model and the cause must be searched in the different parameterization of r_{c} used by the two models.
3.1.3 Effect of Vapor Pressure Deficit and Wind Speed on the Estimation of Canopy Resistance and Actual Evapotranspiration by the KP and TD Models
Canopy resistance is primarily a function of D, U, R_{n} and water status of a crop (Katerji et al. 2011; Alves and Pereira 2000). Hence, in this part of the study, cases with maximized λΕ (being of great practical interest) and availability of water were considered in order to investigate the effect of D or U on the estimation of r_{c} or λΕ by the KP and TD models. Thus, only hourly data corresponding to high radiation values (R_{n} > 500 W / m^{2}) and high availability of water (β < 0.3) were taken into account. The experimental r_{cM} values were obtained by inversing eq. 3 and substituting as λE, the hourly λΕ_{M} values measured by the BREB method.
3.1.4 Effect of Vapor Pressure Deficit and Soil Moisture on the PriestleyTaylor Parameter
In order to investigate any dependence of the PriestleyTaylor parameter α upon D or soil moisture, hourly experimental values of α were obtained from the reversal of the eq. 10, when substituting as λE, the hourly λΕ_{M} values. The analysis was applied on all hourly data measured during the year 2011, which was selected as a year with no missing data.
3.2 Diurnal and Annual Variation of Canopy Resistance and Actual Evapotranspiration
4 Discussion
4.1 Estimation of Hourly Canopy Resistance and Actual Evapotranspiration
The evaluation of the three methods employed for estimating λΕ over olive trees on hourly basis (Table 2), suggests that PT and KP models are the most appropriate (RIA equal to 0.89 or 0.88, respectively) followed by the TD model (RIA = 0.78). These results are in agreement with those reported by Shi et al. (2008), when the three methods were used over a forest ecosystem, on a daily scale. PT or KP model underestimates λΕ by 9.3% or 9.8%, respectively, while TD model overestimates λΕ by 15.0%, increased up to 25.8%, during warm period.
This study shows that the KP model seems to be a robust and reliable model for predicting λΕ and this has already been reported for other cultivated or natural crops, subjected to contrasting water conditions (Katerji and Rana 2006; Katerji et al. 2011; Lecina et al. 2003; Pauwels and Samson 2006; Rana et al. 1994; Rana et al. 2005; Rana and Katerji 2008; Shi et al. 2008; Steduto et al. 2003; Zhu et al. 2014; Rana et al. 2012; Li et al. 2015; Ayyoub et al. 2017; Amazirh et al. 2017).
On the other hand, the use of TD model has been shown as not recommended for the estimation of λΕ above olive trees. The model has already been referred as not suitable over other crops (overestimating up to 30–50%). It has been though referred as underestimating λΕ above irrigated grass, by about 20% (Katerji et al. 2011). During conditions of no water stress and maximized λΕ, it may be used only for low values of D or low values of U [Fig. 6 (a, b)]. The disagreement between estimated by the TD model and measured λΕ is mainly due to the parameterization of r_{c} by the model. r_{cTD} is mainly a function of D, but the variables associated with soil and plant water deficit are not taken into account and consequently, its value is assumed to be the same for all surfaces, which is not applicable (Katerji et al. 2011). In this study, this is evident from the increasing MBE of the model, as D increases (Fig. 6b), and the especially great disagreement between λE_{TD} and λΕ_{M}, during the warm period, which is usually associated with higher values of D (Table 2). It is also supported from a better agreement between λE_{TD} and λΕ_{M}, when the data from no water stress cases are considered in the analysis (Table 2). When D increases, higher values of measured r_{c} are expected (due to stomata closure), as already reported over olive trees (Bongi and Loreto 1989; Fernandez et al. 1993, 1997) or other crops (ElSharkawy and Cock 1984; Hernández et al. 1989; Mansfield and Davies 1981; Schulze et al. 1972; Schulze and Hall 1982). Great increases of wind velocity have been also referred, as furthermore speeding up the stomata closure caused by D increases, through a feedback mechanism (ElSharkawy 1990) and thus resulting in increasing measured r_{c}. The effect of r_{a} on λΕ through r_{c} has also been discussed (Alves and Pereira 2000; Katerji et al. 2011), but the parameterization of r_{cTD} does not incorporate the effect of r_{a}. This results in greater underestimations of experimental r_{cM} (and greater overestimations of λE, respectively) by the TD model, when U increases and thus r_{a} decreases. This is shown in Fig. 6a by the increasing MBE of the λE_{TD} predictions, when U increases. It must be also noticed that the employment of a different r_{a} (as the one used by the KP model) in the analysis, resulted in worse predictions (RIA = 0.60) and an even greater overestimation (MBE = 35.9%) in agreement with the findings presented by Katerji et al. (2011) for other crops.
In this study, the PT model has been evaluated as a reliable model for predicting λΕ over olive trees, when based on the calibration of its parameter α during the warm and cold period. The parameter has been referred as depending upon D (Shi et al. 2008) and SM (Flint and Childs 1991; Fisher et al. 2005), but in the present study the experimental values of α were found as reducing when D increases but did not appear to be dependent on SM [Fig. 7 (a, b)]. These results are quite in agreement with findings presenting a greater dependence of α on D and a small dependence on SM, as referred for a forest by Shi et al. (2008). They are though, in coincidence with part of the results reported above a natural meadow by Pauwels and Samson (2006), who found that the parameter α decreases with the increase of D but increases with the increase of the soil moisture. Probably ‘the weak influence of soil moisture on α’ found in this work may be due to the absence of significant water stress during the study period as it has also been noticed by Shi et al. (2008).
4.2 Diurnal and Annual Variation of Canopy Resistance and Actual Evapotranspiration
The diurnal variations of predicted and measured λΕ follow the bellcurved shape, similarly to net radiation (Fig. 8b). A rapid increase in predicted and measured λΕ has been observed shortly after sunrise, reaching its peak at noon of solar time and followed by a slow decline at first and a more rapid one over the afternoon. However, λΕ_{M} is significantly overestimated by the TD model at noon, when high values of D are expected. Similar patterns of daily variation of λΕ_{M} were also reported over olive orchard (Villalobos et al. 2000; Berni et al. 2009), over alpine grass (Zhu et al. 2014) and over forest ecosystem (Shi et al. 2008).
The diurnal course of r_{cM}, r_{cTD} and r_{cKP} over olive trees (Fig. 8a) shows that the experimental r_{cM} and the estimated r_{cTD} and r_{cKP} attain similar variation, with the r_{cKP} values being in a very good agreement with r_{cM} values. However, r_{cTD} values are always significantly lower than those of r_{cM} and r_{cKP}, indicating that the TD model is rather unreliable over olive trees. The observed in this analysis, diurnal evolution of r_{c} is similar to the ones referred by other studies over olive orchard crops (Alves and Pereira 2000; Katerji and Rana 2006) and the ones reported over forest (Shi et al. 2008), irrigated grass (Rana et al., 1994) and alfalfa (Lascano et al. 2010).
According to the annual variation of r_{cM}, r_{cKP} and r_{cTD}, the underestimation from the TD model is large, during the warm period, while there is a high correlation between r_{cKP} and r_{cM}. The annual course of estimated λE_{ΚΡ}, λE_{ΡΤ} and λΕ_{M} traces the R_{n}. These results are in agreement with the findings reported by Erraki et al. (2008) or MartinezCob and Faci (2010) over olive trees, when using λΕ measured by Eddy covariance or estimated by PM method. As far as λE_{ΤD} concerns, its annual course seems to be particularly affected by the annual course of D. During the warm period, the overestimation of λΕ_{M} by TD model is large, while there is a high coincidence between λE_{KΡ} and λΕ_{M}. During the cold period the ΚP model underestimates λΕ_{M}.
5 Conclusions

The PT model (when based on the calibration of its parameter α during the warm and cold period) and the KP model are the most appropriate (RIA equal to 0.89 or 0.88, respectively), followed by the TD model (RIA = 0.78). PT or KP model underestimates λΕ_{M} by 9.3% or 9.8%, respectively, while TD model overestimates λΕ_{M} by 15.0%, increased up to 25.8%, during warm period.

In conditions of maximizing λΕ, the KP model satisfactorily evaluates λΕ_{M} while the TD model overestimates it. The overestimation of TD increases with the increase of D, with the increase of U and when the sufficiency of water is not ensured.

The experimental r_{cM} and the estimated r_{cTD} and r_{cKP} attain similar diurnal variation. The r_{cKP} values are in a very good agreement with r_{cM} values, while r_{cTD} values are always significantly lower than those of r_{cM} and r_{cKP}, indicating that the TD model is rather unreliable over olive trees. This is also evident from the annual variation of r_{cM}, r_{cKP} and r_{cTD.} The underestimation from the TD model is large, during the warm period, while there is a high coincidence between r_{cKP} and r_{cM}.

The experimental values of the PT parameter α were reducing with D increasing but they were not found as influenced by SM.
Notes
Acknowledgements
The National and Kapodistrian University of Athens, the Greek Ministry of Rural Development and Food and the former Prefecture of Laconia for funding the project are duly acknowledged. A previous shorter version of the paper has been presented in the 10th World Congress of EWRA “Panta Rei” Athens, Greece, 59 July 2017 and has been published in the European Water Journal (Margonis et al. 2017)
Compliance with ethical standards
Conflict of Interest
None.
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