Abstract

Several models have been developed to estimate evapotranspiration. Among those, the complementary relationship has been the subject of many recent studies because it relies on meteorological data only. Recently, the modified Granger and Gray (GG) model showed its applicability across 34 diverse global sites. While the modified GG model showed better performances compared to the recently published studies, it can be improved for dry conditions and the relative evaporation parameter in the original GG model needs to be further investigated. This parameter was empirically derived from limited data from wet environments in Canada – a possible reason for decreasing performance with dry conditions. This study proposed a refined GG model to overcome the limitation using the Budyko framework and vegetation cover to describe relative evaporation. This study used 75 eddy covariance sites in the USA from AmeriFlux, representing 36 dry and 39 wet sites. The proposed model produced better results with decreasing monthly mean root mean square error of about 30% for dry sites and 15% for wet sites compared to the modified GG model. The proposed model in this study maintains the characteristics of the Budyko framework and the complementary relationship and produced improved evapotranspiration estimates under dry conditions.

INTRODUCTION

Estimating evapotranspiration (ET) is an essential part of agricultural water management and there are many classical methods available for ET estimation based on data availability and required accuracy. The original models include the Penman (1948) and Penman–Monteith (Monteith 1965) equations that combine energy balance and aerodynamic water vapor mass transfer principles. In recent years, the Food and Agriculture Organization (FAO) version of the Penman–Monteith equation (Allen et al. 1998) has been widely used to estimate ET. According to Morton (1994), the Penman–Monteith equation is limited for hydrologic purposes. For example, meteorological data are not measured at 2 m elevation from ground level and not at crop elevation, as required by the Penman–Monteith equation (Shuttleworth 2006). Also, the FAO method is primarily used to estimate crop ET from agricultural lands using crop coefficients which are estimated under specific environmental conditions and at specific times of the growing cycle. According to Shuttleworth & Wallace (2009), this extrapolation is questionable while information of crop coefficients and growing cycles are not readily available worldwide.

Another approach to estimate ET directly is the complementary relationship developed by Bouchet (1963). This approach proposed the first complementary function of potential evapotranspiration (EP) and wet environment evapotranspiration (EW) for a wide range of available energy to estimate regional ET. Bouchet (1963) postulated that as a wet surface dries, the decrease in evapotranspiration is matched by an equivalent increase in potential evapotranspiration. EP is evaporation from a saturated surface while energy and atmospheric conditions do not change. EW is the value of potential evaporation when actual evaporation is equal to the potential rate. Bouchet's idea has been widely tested in conjunction with the models of Priestley & Taylor (1972) and Penman (1948). Examples of widely known models using the complementary relationship are the advection-aridity (AA) model of Brutsaert & Stricker (1979), the complementary relationship areal evapotranspiration (CRAE) model of Morton (1983), and the complementary relationship model proposed by Granger & Gray (1989) which is named as the GG model hereafter. In these three models, ET is usually calculated by Equation (1), developed by Bouchet (1963):  
formula
(1)
The procedure to calculate ET, which requires only meteorological data, was proposed by Brutsaert & Stricker (1979).

In the AA model, EP is estimated by combining information from the energy budget and water vapor transfer in the Penman (1948) equation. The partial equilibrium evapotranspiration equation of Priestley & Taylor (1972) was used to calculate EW. In the CRAE model of Morton (1983), the Penman equation is divided into two separate terms representing the energy balance and the vapor transfer process to calculate EP. A refinement to this approach is proposed through the definition of ‘equilibrium temperature’, TP, which is the temperature at which the energy budget method and the mass transfer method for a moist surface yields the same EP. In the calculation of EW, Morton (1983) modified the Priestley & Taylor equilibrium evapotranspiration to explain the temperature dependence of both net radiation and the slope of the saturated vapor pressure curve. In the GG model of Granger & Gray (1989), they proposed a revised version of the Penman's equation for estimating ET from different saturated and non-saturated surfaces using a dimensionless relative evaporation parameter for a given set of atmospheric and surface conditions. Later, they showed that relative evaporation, the ratio of actual to potential evapotranspiration, has a unique relationship with a parameter which they called relative drying power using 158 measurement data points from Canada. This relationship is independent of surface parameters (temperature and vapor pressure). The primary advantage of the GG model is that ET can be directly estimated without the surface parameters or prior estimates of EP. The original GG model has been successfully applied to a wide range of physical and surface conditions (Hobbins et al. 2001; Szilagyi & Jozsa 2008).

Although Equation (1) of Bouchet (1963) has been widely used in conjunction with Penman (1948) and Priestley & Taylor (1972) (Brutsaert & Stricker 1979; Morton 1983; Hobbins et al. 2001), Bouchet (1963) assumed that EP decreases by the same amount as ET increases. Granger (1989) argued that the symmetrical relationship of Equation (1) lacked a theoretical background and showed the symmetrical relationship only occurs near a temperature of 6 °C. This earlier study showed that ET and EP contribute to EW with different coefficients that depend on the psychrometric constant and the slope of the saturation vapor pressure curve. Later, Crago & Crowley (2005) evaluated the Granger (1989) equation by comparing it to measured latent heat fluxes and determined that the radiometric surface temperature measurements can be successfully incorporated into a complementary approach of Granger (1989). Kahler & Brutsaert (2006) incorporated a constant parameter, b, into the energy balance equation. The parameter b is dependent on the response of natural evaporation from the surrounding landscape. They showed that b values around 5 may be appropriate for the complementary relationship. Venturini et al. (2008, 2011) evaluated the approach of Granger & Gray (1989) along with the Priestly and Taylor equation. In their studies, the relative evaporation parameter in the GG model was derived from surface temperature of MODIS data and produced errors of about 15% compared to observed ET. In essence, these studies support the complementary relationship, but confirmed that it requires improvements to better predict ET.

Recently, Anayah & Kaluarachchi (2014) developed a modified method using the complementary method proposed by the GG model with meteorological data from 34 global eddy covariance (EC) sites. These sites were distributed as follows: North America (17), Europe (11), Asia (5), and Africa (1). The results of this modified GG model showed that the average root mean square error decreased from 20% to as much as 80% compared to the recently published work of Suleiman & Crago (2004), Mu et al. (2007, 2011), Szilagyi & Kovacs (2010), Han et al. (2011), and Thompson et al. (2011). While the results of Anayah & Kaluarachchi (2014) were very good, the results also showed that further refinements can improve performance under dry conditions. A probable reason for this limitation is that the relative evaporation equation of the original GG model was empirically derived from 158 sites under wet environments in Canada. Thus, the complementary relationship in the GG model still needs improvements under dry conditions. The purpose of this study is, therefore, to extend the modified GG model of Anayah & Kaluarachchi (2014) to propose refinements to the relative evaporation equation in the original GG model to better predict regional ET, especially under dry conditions and different land cover conditions. In addressing this goal, this work is still committed to use minimal data such as meteorological data and other readily accessible information with no local calibration.

Other classical approaches for estimating long-term ET assume that evaporation is controlled by the availability of both energy and water (Pike 1964; Budyko 1974). For example, the Budyko hypothesis (1974) and the corresponding Budyko curve has been broadly used for estimating annual ET as a function of the ratio of EP to precipitation. Usually, potential evapotranspiration (EP) which measures the availability of energy and precipitation is a measure of availability of water. According to the Budyko hypothesis (1974), actual evapotranspiration in humid regions is controlled by potential evapotranspiration, while in arid regions, it is controlled by precipitation. However, the Budyko hypothesis (1974) makes no attempt to consider the impact of land surface characteristics such as vegetation cover. Later, other authors attempted to incorporate these characteristics into the Budyko hypothesis (1974). Examples of such widely used studies are Fu (1981) and Choudhury (1999). Choudhury (1999) developed an empirical equation by introducing the water equivalent of annual net radiation and an adjustable parameter which was estimated from field observations at eight locations with different vegetation types. Fu (1981) developed differential forms of the Budyko (1974) hypothesis through a dimensional analysis and introduced a single parameter that determines the shape of the Budyko curve. This parameter can be calibrated from local data and represents land surface conditions such as vegetation cover, soil properties, and topography (Yang et al. 2006). This also supports the Penman hypothesis (1948) that ET is proportional to EP. Furthermore, Yang et al. (2008) derived the corresponding equivalence of Fu (1981) and Choudhury (1999) equations. While these expressions were not identical, their numerical values are the same. Thereafter, several studies used land surface characteristics including vegetation, soil types, and topography in the Budyko hypothesis using the work of Choudhury (1999) and Fu (1981) (Zhang et al. 2001, 2004; Yang et al. 2006, 2007, 2009; Li et al. 2013).

According to Zhang et al. (2004), the Fu equation can be restated that any change in evapotranspiration is a function of potential evapotranspiration and precipitation when precipitation is the only source of water. When there is no precipitation, evapotranspiration becomes zero and the atmospheric conditions are dry allowing potential evapotranspiration to reach the maximum. As precipitation increases, evapotranspiration increases and the atmosphere becomes cooler allowing potential evapotranspiration to decrease. This statement is similar to the complementary relationship introduced by Bouchet (1963). Yang et al. (2006) examined the complementary relationship using the long-term water balance data from 108 dry regions in China, and attempted to explain the consistency between the Budyko hypothesis and Bouchet hypothesis.

Recently, Li et al. (2013) focused on the vegetation impact and examined the conditions under which the vegetation index plays a major role in controlling the parameter which represents the land surface characteristics and climate seasonality, and they proposed a simple process to estimate using remote sensing vegetation information. Using data from 26 major global river basins, the basin-specific was found to be a linear relationship with the long-term average annual vegetation cover. Vegetation cover is derived from the normalized difference vegetation index (NDVI). As a result, the new parameterization of ω reduces the root mean square error (ERMS) by approximately 40% compared to the original Budyko framework.

As discussed earlier, the Budyko frameworks provide an opportunity to consider land surface characteristics, especially the vegetation cover to improve ET prediction. In this work, we proposed to upgrade the modified GG model of Anayah & Kaluarachchi (2014) to better predict ET under dry conditions using the Budyko framework. As mentioned before, one possible reason for poor performance of the original GG model is the use of data from wet regions of Canada, thus the GG model does not properly capture the prevailing dry conditions in arid regions. This work will use the approach in line with the earlier studies of Yang et al. (2006) and Zhang et al. (2004).

METHODOLOGY AND DATA

Methodology

Modified GG model

Anayah & Kaluarachchi (2014) developed their universal model using a three-step approach. First, they evaluated the original complementary methods under a variety of physical and climate conditions and developed 39 different model combinations. Second, three models' variations were identified based on performance compared to observed data from a set of global sites. Third, a statistical analysis was conducted to contrast and compare the three models to identify the best. The results showed that average ERMS, mean absolute bias, and R2 across the 34 global sites were 20.6 mm/month, 10.6 mm/month, and 0.64, respectively. More importantly, the performance of this modified GG model increased partly due to the use of the Priestley & Taylor (1972) equation shown in Equation (2) to calculate EW instead of the Penman (1948) equation.  
formula
(2)
where is in mm/d, is a coefficient equal to 1.28, is net radiation (mm/d), is the psychrometric constant (kPa/°C), is the rate of change of saturation vapor pressure with temperature (kPa/°C), and is soil heat flux density (mm/d).
Also, two parameters were considered similar to the original GG (Granger & Gray 1989): relative drying power () and relative evaporation (). D and G are described in Equations (3) and (5), respectively:  
formula
(3)
where is drying power of air (mm/d) given in Equation (4):  
formula
(4)
where U is wind speed at 2 m above ground level (m/s) that needs adjustments and conducted using the procedure described by Allen et al. (1998), is saturation vapor pressure (mmHg), is vapor pressure of air (mmHg).  
formula
(5)
where . The effect of is negligible compared to when calculated at monthly or higher timescale (e.g., Hobbins et al. 2001).
Solving Equation (5) for and substituting in Equation (1), the modified GG model is given in Equation (6):  
formula
(6)
Therefore, the modified GG model of Anayah & Kaluarachchi (2014) can estimate directly without calculating .

Budyko framework

Fu (1981) proposed the differential forms of the Budyko framework through a dimensional analysis. The corresponding analytical solution of the Budyko framework is given in Equation (7) or (8):  
formula
(7)
 
formula
(8)
where P is precipitation (mm) and is estimated using the Priestly and Taylor equation (1972). Parameter is a constant and represents the land surface conditions of the basin, especially the vegetation cover (Li et al. 2013). Li et al. (2013) showed that is linearly correlated with the long-term average annual vegetation cover and a model using NDVI can improve the estimation of . In that study, vegetation cover defined by M is calculated as (Yang et al. 2009):  
formula
(9)
where is minimum NDVI and is maximum NDVI. The values of and are constants at 0.05 and 0.8, respectively (Yang et al. 2009). Then, an optimal value for the basin can be derived through a curve fitting procedure that minimizes the mean squared error between the measured and predicted evaporation ratio (Li et al. 2013). The objective function used to find optimal is:  
formula
(10)
where i is year. Li et al. (2013) proposed parameterization that is simply a linear regression between optimal and long-term average M given as:  
formula
(11)
where a and b are constants that are found for each site.

Proposed GG model refinements

Figure 1 illustrates a schematic of the complementary relationship and the Budyko framework. Figure 1(a) shows the original complementary relationship proposed by Bouchet (1963) which translates to Figure 1(b) if all variables are divided by . Figure 1(c) is the original curve describing the Budyko hypothesis on the basis of Equation (7), where is the curve shape factor of the Fu equation. Figure 1(d) shows the other form of the Fu equation, as given in Equation (8). Comparing Figure 1(b) and 1(d), it can be concluded that the complementary relationship is consistent with the Budyko hypothesis through the Fu equation.

Figure 1

A schematic of the complementary relationship and the Fu equation: (a) original complementary relationship of Bouchet (1963), (b) updated complementary relationship with division by Ep, (c) Budyko hypothesis on the basis of Equation (7), and (d) Budyko hypothesis on the basis of Equation (8).

Figure 1

A schematic of the complementary relationship and the Fu equation: (a) original complementary relationship of Bouchet (1963), (b) updated complementary relationship with division by Ep, (c) Budyko hypothesis on the basis of Equation (7), and (d) Budyko hypothesis on the basis of Equation (8).

In the modified GG model (Anayah & Kaluarachchi 2014), the ratio of ET to EP is defined as relative evaporation (G), as shown in Equation (5). Parameter G was empirically derived using limited data from wet environments in western Canada (Granger & Gray 1989). As discussed earlier, this bias towards wet region data may be the reason for relatively poor predictions with the GG model under dry conditions. In order to improve the predictions of the modified GG model (Anayah & Kaluarachchi 2014), given by Equation (6), parameter G needs improvements. If this ratio can be improved and used appropriately in the modified GG model with the Fu equation, it would bring about the Budyko framework which works well in dry conditions and maintains the complementary relationship. For this purpose, we used the theoretical framework of the Fu equation developed by Li et al. (2013) on the basis of the work of Yang et al. (2006) and Zhang et al. (2004). Equation (12) shows the Fu equation where the ratio of is now defined as :  
formula
(12)
Note in Equation (12) is the new (updated) definition of relative evaporation, G, which includes the Budyko hypothesis and vegetation index. To estimate , is required and can be estimated using the equation from Penman (1948), given in Equation (13):  
formula
(13)
Having found from Equation (12) and estimating from Equation (2), we can estimate of the proposed model from Equation (14):  
formula
(14)

Hereafter, this proposed model will be referred to as the GG-NDVI model. Essentially, GG-NDVI is a combination of the complementary relationship through the modified GG model and the Budyko hypothesis that uses NDVI to describe the vegetation cover.

Data

The complementary method requires meteorological data for estimating ET and these include temperature, pressure or elevation, net radiation, and wind speed. As seen from Table 1, the GG-NDVI model requires two additional data strings, precipitation and NDVI, compared to the modified GG model proposed by Anayah & Kaluarachchi (2014). FLUXNET is a global network of micrometeorological tower sites. A flux tower uses the EC method to measure ecosystem-scale mass and energy fluxes. This study proposes to use data from AmeriFlux EC tower sites in the USA, a part of FLUXNET, because the US sites have a wide variety of climatic and physical conditions and land cover, especially in dry regions. At present, there are over 110 sites where data are collected at 30-minute intervals. In some cases, data are not available at monthly intervals and for such instances mean monthly data were aggregated from 30-minute time-scale that are available from Level 2 data of AmeriFlux. This study selected 75 sites with less than 50% missing data and the selected sites are shown in Figure 2. These data were obtained from the Oak Ridge National Laboratory's AmeriFlux website (http://ameriflux.ornl.gov/, last accessed: November 2015). These sites provide ten land cover types and a wide range of climates. The land cover types developed by the International Geosphere-Biosphere Programme (IGBP) include evergreen needleleaf forests (ENF), evergreen broadleaf forests (EBF), deciduous broadleaf forests (DBF), mixed forests (MF), closed shrublands (CSH), open shrublands (OSH), woody savannas (WSA), grasslands (GRA), permanent wetlands (WET), and croplands (CRO). Table 2 shows that the largest portion of land cover in the dry sites is GRA at 31% and the wet sites have ENF at 44%. The observed ET to validate the proposed model was calculated from measured latent heat flux (LE) data from EC towers using the equation where is latent heat of vaporization ( J/kg).

Table 1

Required meteorological data for different ET estimation methods including the GG-NDVI model proposed in this study

  CRAE Modified GGa GG-NDVIb ASCEc 
Temperature (min, max) ● ● ● ● 
Pressure (or elevation) ● ● ● ● 
Net radiation ● ● ● ● 
Wind speed  ● ● ● 
Precipitation   ●  
NDVI   ●  
Cn, Cdd    ● 
  CRAE Modified GGa GG-NDVIb ASCEc 
Temperature (min, max) ● ● ● ● 
Pressure (or elevation) ● ● ● ● 
Net radiation ● ● ● ● 
Wind speed  ● ● ● 
Precipitation   ●  
NDVI   ●  
Cn, Cdd    ● 

bProposed in this work.

dCn and Cd are constants that change with reference crop and time step.

Table 2

Land cover class distribution of the 75 EC sites from the AmeriFlux database used in this study with IGBP (International Geosphere-Biosphere Program)

IGBP Land cover class Dry (36 sites) Wet (39 sites) 
Evergreen needleleaf forests (ENF) 11% (4 sites) 44% (17 sites) 
Evergreen broadleaf forests (EBF) 3% (1 site) – 
Deciduous broadleaf forests (DBF) – 28% (11 sites) 
Mixed forests (MF) 8% (3 sites) 3% (1 site) 
Closed shrublands (CSH) 14% (5 sites) 5% (2 sites) 
Open shrublands (OSH) 11% (4 sites) – 
Woody savannas (WSA) 6% (2 sites) 3% (1 site) 
Grasslands (GRA) 31% (11 sites) 10% (4 sites) 
Permanent wetlands (WET) 3% (1 site) – 
Croplands (CRO) 14% (5 sites) 8% (3 sites) 
IGBP Land cover class Dry (36 sites) Wet (39 sites) 
Evergreen needleleaf forests (ENF) 11% (4 sites) 44% (17 sites) 
Evergreen broadleaf forests (EBF) 3% (1 site) – 
Deciduous broadleaf forests (DBF) – 28% (11 sites) 
Mixed forests (MF) 8% (3 sites) 3% (1 site) 
Closed shrublands (CSH) 14% (5 sites) 5% (2 sites) 
Open shrublands (OSH) 11% (4 sites) – 
Woody savannas (WSA) 6% (2 sites) 3% (1 site) 
Grasslands (GRA) 31% (11 sites) 10% (4 sites) 
Permanent wetlands (WET) 3% (1 site) – 
Croplands (CRO) 14% (5 sites) 8% (3 sites) 
Figure 2

Locations of 75 AmeriFlux EC towers used in this study.

Figure 2

Locations of 75 AmeriFlux EC towers used in this study.

To classify the climatic conditions, the ratio of , which is called the aridity index of the United Nations Environment Program (AIU) was used (Barrow 1992). AIU divides climatic conditions into six classes: hyper-arid regimes (AIU < 0.05), arid (0.05 ≤ AIU < 0.20), semi-arid (0.20 ≤ AIU < 0.50), dry sub-humid (0.50 ≤ AIU < 0.65), wet sub-humid (0.65 ≤ AIU < 0.75), and humid (AIU ≥ 0.75). Similar to Anayah & Kaluarachchi (2014), this work simplified the climatic class definitions into two classes, simply combining hyper-arid regimes, arid, semi-arid, and dry sub-humid to define the dry class and wet sub-humid and humid as the wet class. Using this simplified and updated definition, 36 sites fall to the dry class and 39 sites fall to the wet class. Mean AIU of the dry and wet sites are 0.41 and 0.92, respectively. The details of AIU values and additional details of 75 sites are given in Table 3.

Table 3

Details of the 75 AmeriFlux EC sites selected for this study; P is mean annual precipitation, T is mean annual temperature, AIU is aridity index of UNEP, and EL is elevation

Site ID T (°C) P (mm) AIU EL. (m) Site ID T (°C) P (mm) AIU EL. (m) 
Dry 
 1 US-Seg 13.4 250 0.15 1,622 19 US-Ne3 10.1 784 0.45 363 
 2 US-Ses 17.7 250 0.16 1,593 20 US-Kon 12.8 867 0.46 330 
 3 US-Ctn 9.7 278 0.16 744 21 US-Ne2 10.1 789 0.46 362 
 4 US-Wjs 12.1 249 0.16 1,926 22 US-Ivo −8.3 304 0.47 568 
 5 US-Whs 17.1 355 0.20 1,372 23 US-Wlr 13.5 881 0.49 408 
 6 US-FPe 5.5 335 0.22 364 24 US-PFa 4.3 823 0.49 470 
 7 US-SRM 17.9 380 0.22 1,120 25 US-Blk 6.2 574 0.50 1,718 
 8 US-Wkg 15.6 407 0.24 1,531 26 US-Syv 3.8 826 0.50 540 
 9 US-Mpj 10.4 330 0.25 2,138 27 US-FR2 19.5 864 0.51 272 
 10 US-Aud 14.9 438 0.26 1,469 28 US-KUT 8.0 701 0.52 301 
 11 US-SP1 20.1 1,310 0.26 50 29 US-FR3 19.6 869 0.52 232 
 12 US-SO4 14.7 484 0.34 1,429 30 US-Skr 23.8 1,259 0.53 
 13 US-SO3 13.3 576 0.37 1,429 31 US-KFS 12.0 1,014 0.58 310 
 14 US-SO2 13.6 553 0.39 1,394 32 US-Ro1 6.9 806 0.60 260 
 15 US-Bkg 6.0 586 0.41 510 33 US-Bo1 11.0 991 0.61 219 
 16 US-LWW 16.1 805 0.43 365 34 US-Me3 7.1 719 0.61 1,005 
 17 US-GMF 6.1 1,259 0.44 380 35 US-KS2 21.7 1,294 0.64 
 18 US-Ne1 10.1 790 0.45 361 36 US-SP3 20.3 1,312 0.64 50 
Wet 
 1 US-IB1 9.0 929 0.65 227 21 US-Ced 11.0 1,138 0.83 58 
 2 US-Ton 15.8 559 0.65 177 22 US-LPH 7.0 1,071 0.87 378 
 3 US-Var 15.8 559 0.65 129 23 US-NC2 16.0 1,294 0.89 12 
 4 US-Moz 12.0 986 0.65 220 24 US-Me4 8.0 1,039 0.9 922 
 5 US-Oho 9.0 843 0.66 230 25 US-Me5 6.0 591 0.91 1,188 
 6 US-IB2 9.0 930 0.66 227 26 US-Vcm 6.0 646 0.91 3,003 
 7 US-UMB 6.0 803 0.68 234 27 US-Ho2 5.0 1,064 0.93 91 
 8 US-Vcp 7.0 693 0.68 2,542 28 US-Ho1 5.0 1,070 0.94 60 
 9 US-Bo2 11.0 991 0.69 219 29 US-Goo 16.0 1,426 0.94 87 
 10 US-Los 4.0 828 0.69 480 30 US-Ho3 5.0 1,072 0.94 61 
 11 US-WCr 4.0 787 0.71 520 31 US-Ha1 7.0 1,071 0.97 340 
 12 US-Me6 7.6 494 0.71 998 32 US-ChR 14.0 1,359 1.00 286 
 13 US-Me2 6.3 523 0.71 1,253 33 US-WBW 14.0 1,372 1.09 283 
 14 US-Pon 14.9 866 0.74 310 34 US-Blo 11.0 1,226 1.06 1,315 
 15 US-MMS 11.0 1,032 0.75 275 35 US-Bar 6.0 1,246 1.14 272 
 16 US-NC1 16.0 1,282 0.81 36 US-CaV 8.0 1,317 1.15 994 
 17 US-Dix 11.0 1,127 0.81 48 37 US-MRf 10.0 1,820 1.75 263 
 18 US-SP2 20.0 1,314 0.81 43 38 US-GLE 1.0 525 2.08 3,190 
 19 US-Slt 11.0 1,152 0.82 30 39 US-Wrc 9.0 2,452 2.31 371 
 20 US-NR1 2.0 800 0.82 3,050       
Site ID T (°C) P (mm) AIU EL. (m) Site ID T (°C) P (mm) AIU EL. (m) 
Dry 
 1 US-Seg 13.4 250 0.15 1,622 19 US-Ne3 10.1 784 0.45 363 
 2 US-Ses 17.7 250 0.16 1,593 20 US-Kon 12.8 867 0.46 330 
 3 US-Ctn 9.7 278 0.16 744 21 US-Ne2 10.1 789 0.46 362 
 4 US-Wjs 12.1 249 0.16 1,926 22 US-Ivo −8.3 304 0.47 568 
 5 US-Whs 17.1 355 0.20 1,372 23 US-Wlr 13.5 881 0.49 408 
 6 US-FPe 5.5 335 0.22 364 24 US-PFa 4.3 823 0.49 470 
 7 US-SRM 17.9 380 0.22 1,120 25 US-Blk 6.2 574 0.50 1,718 
 8 US-Wkg 15.6 407 0.24 1,531 26 US-Syv 3.8 826 0.50 540 
 9 US-Mpj 10.4 330 0.25 2,138 27 US-FR2 19.5 864 0.51 272 
 10 US-Aud 14.9 438 0.26 1,469 28 US-KUT 8.0 701 0.52 301 
 11 US-SP1 20.1 1,310 0.26 50 29 US-FR3 19.6 869 0.52 232 
 12 US-SO4 14.7 484 0.34 1,429 30 US-Skr 23.8 1,259 0.53 
 13 US-SO3 13.3 576 0.37 1,429 31 US-KFS 12.0 1,014 0.58 310 
 14 US-SO2 13.6 553 0.39 1,394 32 US-Ro1 6.9 806 0.60 260 
 15 US-Bkg 6.0 586 0.41 510 33 US-Bo1 11.0 991 0.61 219 
 16 US-LWW 16.1 805 0.43 365 34 US-Me3 7.1 719 0.61 1,005 
 17 US-GMF 6.1 1,259 0.44 380 35 US-KS2 21.7 1,294 0.64 
 18 US-Ne1 10.1 790 0.45 361 36 US-SP3 20.3 1,312 0.64 50 
Wet 
 1 US-IB1 9.0 929 0.65 227 21 US-Ced 11.0 1,138 0.83 58 
 2 US-Ton 15.8 559 0.65 177 22 US-LPH 7.0 1,071 0.87 378 
 3 US-Var 15.8 559 0.65 129 23 US-NC2 16.0 1,294 0.89 12 
 4 US-Moz 12.0 986 0.65 220 24 US-Me4 8.0 1,039 0.9 922 
 5 US-Oho 9.0 843 0.66 230 25 US-Me5 6.0 591 0.91 1,188 
 6 US-IB2 9.0 930 0.66 227 26 US-Vcm 6.0 646 0.91 3,003 
 7 US-UMB 6.0 803 0.68 234 27 US-Ho2 5.0 1,064 0.93 91 
 8 US-Vcp 7.0 693 0.68 2,542 28 US-Ho1 5.0 1,070 0.94 60 
 9 US-Bo2 11.0 991 0.69 219 29 US-Goo 16.0 1,426 0.94 87 
 10 US-Los 4.0 828 0.69 480 30 US-Ho3 5.0 1,072 0.94 61 
 11 US-WCr 4.0 787 0.71 520 31 US-Ha1 7.0 1,071 0.97 340 
 12 US-Me6 7.6 494 0.71 998 32 US-ChR 14.0 1,359 1.00 286 
 13 US-Me2 6.3 523 0.71 1,253 33 US-WBW 14.0 1,372 1.09 283 
 14 US-Pon 14.9 866 0.74 310 34 US-Blo 11.0 1,226 1.06 1,315 
 15 US-MMS 11.0 1,032 0.75 275 35 US-Bar 6.0 1,246 1.14 272 
 16 US-NC1 16.0 1,282 0.81 36 US-CaV 8.0 1,317 1.15 994 
 17 US-Dix 11.0 1,127 0.81 48 37 US-MRf 10.0 1,820 1.75 263 
 18 US-SP2 20.0 1,314 0.81 43 38 US-GLE 1.0 525 2.08 3,190 
 19 US-Slt 11.0 1,152 0.82 30 39 US-Wrc 9.0 2,452 2.31 371 
 20 US-NR1 2.0 800 0.82 3,050       

There are two methods available to compute net radiation: Morton (1983) and Allen et al. (2005). Morton (1983) proposed net radiation for soil-plant surfaces at an equilibrium temperature that is derived from the solution to the water vapor transfer and energy-balance equations under a small moist surface. On the other hand, Allen et al. (2005) predicted net radiation from observed short wave radiation, vapor pressure, and air temperature; this method is routine and generally accurate. Anayah & Kaluarachchi (2014) found that the method described by Allen et al. (2005) is better than that of Morton (1983). In this study, we used mean of daily maximum and minimum temperatures to define mean daily air temperature in order to standardize air temperature. For NDVI, we retrieved 16-Day L3 Global 250 m SIN Grid (http://daac.ornl.gov/MODIS/modis.shtml) of MODIS. Generally, NDVI values are between −1 and 1, with values >0.5 indicating dense vegetation and <0 indicating water surface. The NDVI values of this study varied between 0.18 and 0.76. The mean NDVI is 0.44 for dry sites and 0.60 for wet sites and the distribution of NDVI is shown in Figure 3(a). The average annual precipitation varied from 249 mm to 1,312 mm with a mean of 703.1 mm for dry sites and from 494 mm to 2,452 mm with a mean of 1,033.3 mm for wet sites and the distribution of precipitation is shown in Figure 3(b). Data were available from 1995 to 2013. The shortest data available period is 3 years at one of the sites and the longest period is 19 years.

Figure 3

Distribution of (a) NDVI and (b) precipitation for dry and wet sites.

Figure 3

Distribution of (a) NDVI and (b) precipitation for dry and wet sites.

RESULTS AND DISCUSSION

This study used two scenarios to evaluate the performance of the proposed GG-NDVI model. In Scenario 1, the modified GG model of Anayah & Kaluarachchi (2014) is used for direct comparison and this scenario used all 75 AmeriFlux sites (36 dry and 39 wet sites). In Scenario 2, the original GG model described by Han et al. (2012) (also called the normalized complementary method) and the CRAE method of Morton (1983) are used for comparison. Scenario 2 used only 59 sites (29 dry and 30 wet sites) since only these 59 sites have incident global radiation data required by the CRAE model.

Scenario 1: comparison with the modified GG model

Table 4 shows the comparison of results between the proposed GG-NDVI and the modified GG models. The GG-NDVI model reduces the mean ERMS by about 32% and 15% for dry and wet sites, respectively. In the dry sites, the GG-NDVI model showed higher maximum ERMS values compared to the modified GG model but the mean is much lower at 13.9 mm/month compared to 20.5 mm/month. On the other hand, the wet class values are comparable. Although the maximum increased with GG-NDVI for the dry sites, the lower mean value indicates more occurrence of lower values with GG-NDVI. Figure 4 confirms this observation where the occurrences of less than 10 mm/month is more frequent than the modified GG model. Similar results are seen with the wet sites as well, except, even higher occurrences of low ERMS values. The results also show that ET estimates of both models improve with wetness similar to other previous studies discussed earlier.

Table 4

Comparison of performance using ERMS (mm/month) of GG-NDVI compared to other models described in Scenarios 1 and 2

Method Min Mean Max Min Mean Max 
Dry sites Wet sites 
Scenario 1: All 75 sites (36 dry and 39 wet sites) 
 Modified GG 0.3 20.5 42.7 0.6 12.5 36.0 
 GG-NDVI 0.4 13.9 56.6 0.3 10.7 31.5 
Scenario 2: 59 sites only (29 dry and 30 wet sites) 
 Modified GG 1.7 21.4 42.7 0.6 12.9 36.0 
 GG-NDVI 0.4 14.7 56.6 0.3 11.6 28.5 
 CRAE 0.5 18.9 53.9 0.8 22.3 62.3 
 GG 0.1 32.3 75.1 1.1 19.6 60.1 
Method Min Mean Max Min Mean Max 
Dry sites Wet sites 
Scenario 1: All 75 sites (36 dry and 39 wet sites) 
 Modified GG 0.3 20.5 42.7 0.6 12.5 36.0 
 GG-NDVI 0.4 13.9 56.6 0.3 10.7 31.5 
Scenario 2: 59 sites only (29 dry and 30 wet sites) 
 Modified GG 1.7 21.4 42.7 0.6 12.9 36.0 
 GG-NDVI 0.4 14.7 56.6 0.3 11.6 28.5 
 CRAE 0.5 18.9 53.9 0.8 22.3 62.3 
 GG 0.1 32.3 75.1 1.1 19.6 60.1 
Figure 4

Histogram of ERMS of GG-NDVI and the modified GG models for (a) dry and (b) wet sites.

Figure 4

Histogram of ERMS of GG-NDVI and the modified GG models for (a) dry and (b) wet sites.

The major difference between the two models is the use of vegetation to estimate ET in the GG-NDVI model. To assess the contribution of NDVI on GG-NDVI, the variation of NDVI with ERMS was studied but is not shown here. The ERMS distribution of the GG-NDVI model that uses NDVI is consistently below 25 mm/month with 92% (33 sites) of the dry sites compared to 58% (21 sites) with the modified GG model that does not account for NDVI.

Most dry sites used in this work have hot summer and warm winter seasons with low vegetation density (low NDVI). For instance, the mean annual temperature at the Freeman Ranch in Texas is 20 °C and there is significant precipitation during summer. The minimum, maximum, and mean ERMS of the GG-NDVI model were 0.01, 48.4, and 14.0 mm/month, respectively. Figure 5 shows a comparison of monthly ET of the modified GG and GG-NDVI models with observed ET from 2005 to 2008. The mean ERMS of the modified GG model is 20.6 mm/month. While the modified GG model showed a regular and periodic performance and significant deviation from observed ET, the pattern of GG-NDVI is similar to the observed values. We observe similar results at the Goodwin Creek site in Mississippi, as shown in Figure 6. A reasonable conclusion would be that GG-NDVI is improved by using the vegetation cover information in the model. On the other hand, the method that uses only climatic data seems incomplete in estimating ET. This conclusion is supported by Bethenod et al. (2000) and Potter et al. (2005). Even under low vegetation cover (low NDVI) conditions, plant transpiration accounts for most ET from 20% to as much as 80%. Moreover, hot summer and warm winter months are producing high fluctuation of plant transpiration and, therefore, high fluctuation of ET (Hsiao & Henderson 1985). In this regard, the GG-NDVI model can be expected to be more accurate than the modified GG model due to the use of NDVI to better represent plant transpiration, whereas meteorological data alone may not be sufficient to estimate ET under dry conditions.

Figure 5

Comparison of monthly ET distribution and observed ET at Freeman Ranch in Texas for the period 2005–2008.

Figure 5

Comparison of monthly ET distribution and observed ET at Freeman Ranch in Texas for the period 2005–2008.

Figure 6

Comparison of monthly ET distribution and observed ET at Goodwin Creek in Mississippi for the period 2003–2006.

Figure 6

Comparison of monthly ET distribution and observed ET at Goodwin Creek in Mississippi for the period 2003–2006.

Meanwhile, the simulated patterns of ET from the modified GG model may be representing the principles of the complementary relationship. First, the complementary relationship assumes a homogeneous surface layer that assumes the mixing of the effects of surface environmental discontinuities. When surface discontinuities are prevalent, such as in the western United States where vegetation is less flourishing than other regions, this assumption may not be valid. Second, given the heterogeneity of surface conditions, the approaches used in identifying and calculating the various input data may not be perfect in the modified GG model. For these reasons, the modified GG model probably showed a regular and periodic performance in estimated ET and therefore the differences with observed ET.

Among the results of GG-NDVI, it should be noted that there are two sites with relatively large ERMS (higher than 40 mm/month). One is Brookings in South Dakota and the other is Florida Shark River in Florida. The IGBP land cover class of Brookings site is grassland which is representative of the north central United States. The mean annual precipitation from 2005 to 2009 is 586 mm at this site. The mean NDVI of Brookings is 0.41 and this site has a large seasonal vegetation cover, as shown in Figure 7. Although not shown here, the Florida Shark River site has a mean annual precipitation of 1,259 mm from 2007 to 2010 and the annual rainfall is high during the summer season. This site has a high dense vegetation cover with NDVI of 0.75.

Figure 7

Comparisons of monthly ET and observed ET and corresponding time-series of NDVI at the Brookings site in South Dakota.

Figure 7

Comparisons of monthly ET and observed ET and corresponding time-series of NDVI at the Brookings site in South Dakota.

A possible reason for high ERMS could be that NDVI is not the best index to represent the vegetation cover in this site given the large seasonal variation and dense vegetation cover. According to Pettorelli et al. (2005), the soil-adjusted vegetation index (SAVI) is recommended instead of NDVI for areas with leaf area index (LAI) less than 3. It should be noted that the LAI of Brookings and Florida sites is 2.5 and 2.9, respectively. However, a limitation of SAVI is it requires soil brightness correction with local calibration (Huete 1988). Mu et al. (2007) modified their algorithm to include vapor pressure deficit, minimum air temperature, and LAI, and replaced NDVI with the enhanced vegetation index (EVI) to represent dense vegetation conditions. Prior studies have also demonstrated that NDVI is insufficient to account for transpiration under dense vegetation cover conditions (Pettorelli et al. 2005; Yuan et al. 2010; Mu et al. 2011). For these reasons, the modified GG model showed better performance than GG-NDVI at both sites; ERMS of the modified GG for the Brookings site is 33 mm/month compared to 44 mm/month with GG-NDVI and 15 mm/month for the Florida site compared to 56 mm/month with GG-NDVI.

These results suggest that models using the complementary relationship may not predict ET accurately as the vegetation cover becomes dense. Beyond a given level of vegetation cover density and seasonality, NDVI is not capturing plant transpiration correctly, as seen with the Florida Shark River site. In essence, these results suggest that a different vegetation index, such as EVI, may be needed to better predict ET.

Scenario 2: comparison with other complementary methods

The CRAE method is considered to be simple, practical and a reliable method to estimate monthly ET (Hobbins et al. 2001). Han et al. (2012) developed the normalized complementary method which is based on the CRAE method. This study found that the method performed better than the AA model in predicting ET under dry and wet conditions. However, the normalized complementary method was tested using only four sites with different land covers. Therefore, this study provides the opportunity to test both models, CRAE and GG models, compared to the proposed GG-NDVI model. This comparison used only 59 sites from the 75 sites due to the reason described earlier.

The results of the comparison are given in Table 4. Again, all models showed high maximum ERMS values in dry sites in the order of more than 40 mm/month. However, the GG-NDVI model showed the lowest mean ERMS across all models at 14.7 mm/month for the dry and 11.6 mm/month for the wet sites. The modified GG model was the third best for mean values for the dry sites. The GG-NDVI model performed much better in the wet category too. The GG-NDVI model produced the lowest mean ERMS for the dry sites and lowest mean and maximum ERMS for the wet sites. The results in general indicate that GG-NDVI can perform well in the dry regions and even better in the wet sites. These results also confirm the observation of Xu & Singh (2005) that showed the estimation capability of ET reduces with increased aridity.

The CRAE model assumes that the vapor transfer coefficient is independent of wind speed and this may lead to errors in calculating ET. The complementary relationship-driven models do not directly use soil moisture information and hence may overestimate ET as aridity increases (Xu & Singh 2005). This reason may cause decreased predictive power of these methods using the complementary method. To evaluate this concern, this study used the 59 sites and simulated ET using the CRAE method, modified GG model of Anayah & Kaluarachchi (2014), original GG model, and the proposed GG-NDVI model. Figure 8 presents a comparison of the ERMS distribution of these four models and the corresponding boxplots are shown in Figure 9. The results indicate better performance of the GG-NDVI model compared to the other models. For example, most values of ERMS of the GG-NDVI model are at less than 20 mm/month interval. The number of less than 20 mm/month contributed 72% of the 29 dry sites in the GG-NDVI model in comparison with 48% with GG, 55% with CRAE, and 45% with the modified GG. Figure 9 shows that the GG-NDVI model has the lowest mean error across all four methods especially in the dry sites while maintaining a low range of ERMS values.

Figure 8

Histogram of ERMS for GG-NDVI and other complementary methods. GG refers to the normalized complementary method of Han et al. (2012).

Figure 8

Histogram of ERMS for GG-NDVI and other complementary methods. GG refers to the normalized complementary method of Han et al. (2012).

Figure 9

Boxplots of ERMS between different complementary methods of Scenario 2. GG refers to the normalized complementary method of Han et al. (2012).

Figure 9

Boxplots of ERMS between different complementary methods of Scenario 2. GG refers to the normalized complementary method of Han et al. (2012).

GG-NDVI underestimates ET in most dry sites during the rainy months. For example, the Audubon Research Ranch site in Arizona is considered dry with an annual precipitation of about 438 mm. About 70% of annual precipitation is present in the rainy months from July to September. In this period, the GG-NDVI model underestimated ET, as shown in Figure 10. A possible explanation was mentioned by Budyko (1974) and Gerrits et al. (2009). They found that locations where monthly EP and precipitation are out of phase, for example in a dry site, ET is generally underestimated. Similarly, ET decreases with increasing EP on the basis of the complementary relationship and EP is overestimated in regions of decreasing moisture availability. According to Hobbins et al. (2001), a negative relationship between wind speed and EP and the mean monthly values of wind speed are lowest in the summer months. Hence, higher EP estimates and correspondingly lower ET estimates should be expected for these summer months with higher precipitation.

Figure 10

Comparison of mean monthly ET of GG-NDVI and observed values at the Audubon site in Arizona.

Figure 10

Comparison of mean monthly ET of GG-NDVI and observed values at the Audubon site in Arizona.

Although not shown here, we plotted monthly ERMS and precipitation to evaluate the relationship between model accuracy and wetness. The results showed a weak relationship for dry sites. Figure 11(a) shows the relationship between the correlation coefficient between precipitation and ERMS versus mean annual precipitation. Results indicate that GG-NDVI produce errors that increase in variability with increasing precipitation and this trend decreases with increasing precipitation based on the negative slope of least fit (dashed-line in Figure 11(a)). Accordingly, the R-square for this relationship from GG-NDVI across all 75 sites is 0.322. While this value is not high, it is still better than the results obtained from the CRAE and AA models by Hobbins et al. (2001) which were 0.148 and 0.314, respectively.

Figure 11

(a) Correlation coefficient between precipitation and ERMS versus mean annual precipitation. (b) Correlation coefficient between AIU and ET versus AIU.

Figure 11

(a) Correlation coefficient between precipitation and ERMS versus mean annual precipitation. (b) Correlation coefficient between AIU and ET versus AIU.

Figure 11(b) shows the relationship between the correlation coefficient between AIU and ET, and AIU. The correlation coefficients for the wet sites are mostly negative and ranged from −0.68 to −0.11. On the contrary, many dry sites have positive correlation coefficients. This implies that increasing AIU decreased ET for most wet sites but increased for most dry sites. These trends are characteristics of the complementary relationship and have been observed by Roderick et al. (2009) and Han et al. (2014).

For a clear relationship between vegetation cover and ET, Figure 12 displays the estimated ET with NDVI for all 75 sites. In a linear regression analysis between both, NDVI explains 51% of the variance in the estimated ET and similar observations have been made by Hsiao & Henderson (1985), Bethenod et al. (2000), and Hsiao & Xu (2005).

Figure 12

Scatter plot of monthly GG-NDVI ET and NDVI from all 75 sites. The dashed line indicates a linear fit to the data.

Figure 12

Scatter plot of monthly GG-NDVI ET and NDVI from all 75 sites. The dashed line indicates a linear fit to the data.

Comparison with other published studies

Table 5 shows a comparison between the results of the proposed GG-NDVI model and the results from recently published studies. The mean ERMS of GG-NDVI across the 75 sites produced the lowest ERMS of 12.3 mm/month compared to 25.6 mm/month from a remote sensing method and 20.6 mm/month from the modified GG. It should be noted that both studies by Han et al. (2011, 2012) have only four sites. Although these studies evaluated other methods and were applied at different study sites, Mu et al. (2011) used the same data from AmeriFlux similar to this study and Li et al. (2013) used the Fu equation across 26 global river basins. A comparison of GG, the Fu equation, CRAE, and remote sensing methods with the GG-NDVI model shows that the proposed GG-NDVI is an enhancement to the modified GG model, providing improved predictions of ET especially under dry conditions.

Table 5

Comparison of performance using ERMS (mm/month) between GG-NDVI and recently published results

Study # of sites Method ERMS [mm/month]
 
R2
 
Min Max Mean Min Max Mean 
This study 75 GG-NDVI 0.3 56.6 12.3 0.01 0.94 0.60 
This study 75 Modified GGa 0.3 42.7 16.4 0.01 0.94 0.64 
Mu et al. (2011)  46 MODISb 9.4 52.0 25.6 0.02 0.93 0.65 
Anayah & Kaluarachchi (2014)  34 Modified GG 10.3 59.9 20.6 0.01 0.94 0.64 
Anayah & Kaluarachchi (2014)  34 CRAE 7.4 50.0 18.3 0.02 0.94 0.67 
Han et al. (2011)  GG 3.7 16.0 10.7 0.82 0.98 0.92 
Han et al. (2012)  GG 11.8 18.3 14.8    
Li et al. (2013)  26 Budyko 1.8 18.8 –    
Study # of sites Method ERMS [mm/month]
 
R2
 
Min Max Mean Min Max Mean 
This study 75 GG-NDVI 0.3 56.6 12.3 0.01 0.94 0.60 
This study 75 Modified GGa 0.3 42.7 16.4 0.01 0.94 0.64 
Mu et al. (2011)  46 MODISb 9.4 52.0 25.6 0.02 0.93 0.65 
Anayah & Kaluarachchi (2014)  34 Modified GG 10.3 59.9 20.6 0.01 0.94 0.64 
Anayah & Kaluarachchi (2014)  34 CRAE 7.4 50.0 18.3 0.02 0.94 0.67 
Han et al. (2011)  GG 3.7 16.0 10.7 0.82 0.98 0.92 
Han et al. (2012)  GG 11.8 18.3 14.8    
Li et al. (2013)  26 Budyko 1.8 18.8 –    

bRemote sensing method.

We plotted the GG-NDVI estimates of ET against observed ET and the same with the modified GG estimates for dry sites. The results are shown in Figure 13. In a linear regression analysis, the GG-NDVI model has greater strong agreement (R2 = 0.60) with observed ET than modified GG model (R2 = 0.46). The GG-NDVI is, therefore, shown to be a reasonably good predictor of ET and the R2 of 60% is much better than the recently published study of Allam et al. (2016) which is about 37%. In essence, the results show that GG-NDVI can improve performance under dry conditions.

Figure 13

Scatter plot of monthly observed ET and estimated ET across 36 dry sites: (a) GG-NDVI and (b) modified GG. The dashed line indicates a linear fit to the data.

Figure 13

Scatter plot of monthly observed ET and estimated ET across 36 dry sites: (a) GG-NDVI and (b) modified GG. The dashed line indicates a linear fit to the data.

SUMMARY AND CONCLUSIONS

Models using the complementary method to estimate ET are simple, practical, and provide valuable estimates of regional ET using point meteorological data only. The methods do not require data such as soil moisture, stomatal resistance properties of vegetation, or any other aridity measures. Since the original work of Bouchet (1963), the complementary relationship has been the subject of many studies. Among the recent methods, Anayah & Kaluarachchi (2014) developed the modified GG model that is an enhanced version of the original GG method. It can be universally applied under a variety of climatic conditions without local calibration. While that study showed excellent results compared to the recently published work, the accuracy could be improved under dry conditions.

The Budyko framework has been successfully used to predict the long-term annual water balance as a function of EP and precipitation. According to Yang et al. (2006), the Budyko hypothesis through the Fu equation is consistent with the Bouchet hypothesis which is based on the complementary relationship. Also, the Fu equation works well in dry conditions and it can be improved by using the vegetation cover represented by NDVI.

Given the limitation of not accurately predicting ET under dry conditions, the goal of this work is to extend the modified GG model (Anayah & Kaluarachchi 2014) to combine the complementary relationship and the Budyko approach for improved estimation of ET. The expectation is that this enhanced version of the GG model will produce better performance especially under dry conditions.

For the purpose of model development and application, 75 sites from the AmeriFlux database covering the United States were selected. These sites were divided based on an aridity index from UNEP (Barrow 1992), where 39 sites fall into the dry class and the remaining 36 the wet class. The GG-NDVI model shows better performance with both dry and wet sites compared to other methods. In general, the GG-NDVI model reduces mean ERMS by about 24% compared to the modified GG model while increasing wetness leads to increasing accuracy with the GG-NDVI model. Lastly, ET is directly proportional to the aridity index of dry sites. On the other hand, increasing of aridity index leads to decreasing ET in wet sites. These trends were seen in recent studies from Roderick et al. (2009) and Han et al. (2014). The GG-NDVI model is more correlated with observed ET than the modified GG model at values better than the work of Allam et al. (2016). Although this study applied the Budyko framework to the modified GG model, the GG-NDVI model shows similar results with other complementary relationship studies as well. We may therefore conclude that the GG-NDVI model maintains the characteristics of both the complementary relationship and Budyko hypothesis. We also observed that ET estimates of GG-NDVI have a good correlation coefficient with NDVI confirming conclusions from several previous studies (Hsiao & Henderson 1985; Bethenod et al. 2000; Hsiao & Xu 2005). However, when the vegetation cover is very dense or has a seasonal fluctuation, the proposed GG-NDVI model did not perform well. As a result, NDVI seems insufficient to represent plant transpiration, which suggests that other vegetation indices might be more suitable.

It is also noted that the GG-NDVI model requires NDVI and more computation than the modified GG model proposed by Anayah & Kaluarachchi (2014). However, NDVI data are readily available from satellite data from MODIS or similar outlets. On a positive note, both GG-NDVI and modified GG require no local calibration. Reference ET of FAO (Allen et al. 2005) is considered to be the best method and is widely used globally. Unfortunately, this method requires crop coefficients that vary depending on the growing season and crop type for different regions or countries. Lastly, this study will be the first to incorporate the vegetation cover to the complementary relationship through the Budyko framework to improve ET predictions, especially under dry conditions. Consequently, the GG-NDVI model can be used as a powerful tool to estimate ET with meteorological and remote sensing data at monthly time scale without local calibration.

REFERENCES

REFERENCES
Allam
,
M. M.
,
Jain-Figueroa
,
A.
,
McLaughlin
,
D. B.
&
Eltahir
,
E. A. B.
2016
Estimation of evaporation over the Upper Blue Nile basin by combining observations from satellites and river flow gauges
.
Water Resources Research
52
,
DOI:10.1002/2015WR017251
.
Allen
,
R. G.
,
Pereira
,
L. S.
,
Raes
,
D.
&
Smith
,
M.
1998
Crop Evapotranspiration: Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper No. 56
.
Food and Agriculture Organization of the United Nations
,
Rome
,
Italy
.
Allen
,
R. G.
,
Walter
,
I. A.
,
Elliot
,
R.
,
Howell
,
T.
,
Itenfisu
,
D.
&
Jensen
,
M.
2005
The ASCE Standardized Reference Evapotranspiration Equation
.
American Society of Civil Engineers Environmental and Water Resource Institute (ASCE-EWRI), American Society of Civil Engineers
,
Reston, VA
,
USA
.
Anayah
,
F. M.
&
Kaluarachchi
,
J. J.
2014
Improving the complementary methods to estimate evapotranspiration under diverse climatic and physical conditions
.
Hydrology and Earth System Sciences
18
,
2049
2064
.
DOI: 10.5194/hess-18-2049-2014
.
Barrow
,
C. J.
1992
World Atlas of Desertification (United Nations Environment Programme) Section one: Global
(
Middleton
,
N.
&
Thomas
,
D. S. G.
, eds).
Edward Arnold
,
London
,
UK
.
Bethenod
,
O.
,
Katerji
,
N.
,
Goujet
,
R.
,
Bertolini
,
J. M.
&
Rana
,
G.
2000
Determination and validation of corn crop transpiration by sap flow measurement under field conditions
.
Theoretical and Applied Climatology
67
,
153
160
.
Bouchet
,
R. J.
1963
Evapotranspiration reelle et potentielle, signification climatique (Actual and potential evapotranspiration climate service)
.
International Association of Hydrological Sciences
62
,
134
142
.
Brutsaert
,
W.
&
Stricker
,
H.
1979
An advection-aridity approach to estimate actual regional evapotranspiration
.
Water Resources Research
15
(
2
),
443
450
.
Budyko
,
M. I.
1974
Climate and Life. Xvii
.
Academic Press
,
New York
,
USA
.
Crago
,
R.
&
Crowley
,
R.
2005
Complementary relationship for near-instantaneous evaporation
.
Journal of Hydrology
300
,
199
211
.
Fu
,
B. P.
1981
On the calculation of the evaporation from land surface
.
Sci. Atmos. Sin.
5
(
1
),
23
31
(in Chinese)
.
Gerrits
,
A. M. J.
,
Savenije
,
H. H. G.
,
Veling
,
E. J. M.
&
Pfister
,
L.
2009
Analytical derivation of the Budyko curve based on rainfall characteristics and a simple evaporation model
.
Water Resources Research
45
,
W04403
.
DOI:10.1029/2008WR007308
.
Granger
,
R. J.
1989
A complementary relationship approach for evaporation from nonsaturated surfaces
.
Journal of Hydrology
111
,
31
38
.
DOI:10.1016/0022-1694(89)90250-3
.
Granger
,
R. J.
&
Gray
,
D. M.
1989
Evaporation from natural non-saturated surface
.
Journal of Hydrology
111
,
21
29
.
DOI:10.1016/0022-1694(89)90249-7
.
Hsiao
,
T. C.
&
Henderson
,
D. W.
1985
Improvement of Crop Coefficients for Evapotranspiration, Final Report. California Irrigation Management Information System project
,
Vol. 1, Land, Air & Water Resources Papers 10013-A
,
University of California Davis
,
CA, USA
, pp.
III3
III35
.
Hsiao
,
T. C.
&
Xu
,
L.
2005
Evapotranspiration and Relative Contribution by the Soil and the Plant. California Water Plan Update 2005
,
University of California Davis
,
CA, USA
.
Huete
,
A. R.
1988
A soil-adjusted vegetation index (SAVI)
.
Remote Sensing of Environment
25
,
295
309
.
Kahler
,
D. M.
&
Brutsaert
,
W.
2006
Complementary relationship between daily evaporation in the environment and pan evaporation
.
Water Resources Research
42
,
W05413. DOI:05410.01029/02005WR004541
.
Li
,
D.
,
Pan
,
M.
,
Cong
,
Z.
,
Zhang
,
L.
&
Wood
,
E.
2013
Vegetation control on water and energy balance within the Budyko framework
.
Water Resources Research
49
,
969
976
.
DOI:10.1002/wrcr.20107
.
Monteith
,
J. L.
1965
Evaporation and environment
. In:
19th Symp. Soc. Exp. Biol.
University Press
,
Cambridge
, pp.
205
234
.
Morton
,
F. I.
1994
Evaporation research – a critical review and its lessons for the environmental sciences
.
Critical Reviews in Environmental Science and Technology
24
(
3
),
237
280
.
Mu
,
Q.
,
Zhao
,
M.
&
Running
,
S. W.
2007
Development of a global evapotranspiration algorithm based on MODIS and global meteorological data
.
Remote Sensing of Environment
111
(
4
),
519
536
.
DOI:10.1016/J.RSE.2007.04.015
.
Mu
,
Q.
,
Zhao
,
M.
&
Running
,
S. W.
2011
Improvements to a MODIS global terrestrial evapotranspiration algorithm
.
Remote Sensing of Environment
115
,
1781
1800
.
DOI:10.1016/J.RSE.2011.02.019
.
Penman
,
H. L.
1948
Natural evaporation from open water, bare and grass
.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
193
(
1032
),
120
145
.
DOI:10.1098/rspa.1948.0037
.
Pettorelli
,
N.
,
Vik
,
J. O.
,
Mysterud
,
A.
,
Gaillard
,
J. M.
,
Tucker
,
C. J.
&
Stenseth
,
N. C.
2005
Using the satellite-derived NDVI to assess ecological responses to environmental change
.
Trends in Ecology and Evolution
20
(
9
),
503
510
.
DOI:10.1016/j.tree.2005.05.011
.
Potter
,
N. J.
,
Zhang
,
L.
,
Milly
,
P. C. D.
,
McMahon
,
T. A.
&
Jakeman
,
A. J.
2005
Effects of rainfall seasonality and soil moisture capacity on mean annual water balance for Australian catchments
.
Water Resources Research
41
,
W06007
.
DOI:10.1029/2004WR003697
.
Priestley
,
C. H. B.
&
Taylor
,
R. J.
1972
On the assessment of surface heat fluxes and evaporation using large-scale parameters
.
Monthly Weather Review
100
,
81
92
.
Roderick
,
M. L.
,
Hobbins
,
M. T.
&
Farquhar
,
G. D.
2009
Pan evaporation trends and the terrestrial water balance. II: Energy balance and interpretation
.
Geography Compass
3
(
2
),
761
780
.
Shuttleworth
,
W. J.
2006
Towards one-step estimation of crop water requirements
.
Transactions of the ASABE
49
(
4
),
925
935
.
Shuttleworth
,
W. J.
&
Wallace
,
J. S.
2009
Calculating the water requirements of irrigated crops in Australia using the Matt-Shuttleworth approach
.
Transactions of the ASABE
52
(
6
),
1895
1906
.
Szilagyi
,
J.
&
Kovacs
,
A.
2010
Complementary-relationship-based evapotranspiration mapping (cremap) technique for Hungary
.
Periodica Polytechnica: Civil Engineering
54
(
2
),
95
100
.
DOI:10.3311/pp.ci.2010-2.04
.
Thompson
,
S. E.
,
Harman
,
C. J.
,
Konings
,
A. G.
,
Sivapalan
,
M.
,
Neal
,
A.
&
Troch
,
P. A.
2011
Comparative hydrology across AmeriFlux sites: the variable roles of climate, vegetation, and groundwater
.
Water Resources Research
47
,
W00J07
.
DOI:10.1029/2010WR009797
.
Venturini
,
V.
,
Islam
,
S.
&
Rodríguez
,
L.
2008
Estimation of evaporative fraction and evapotranspiration from MODIS products using a complementary based model
.
Remote Sensing of Environment
112
,
132
141
.
Venturini
,
V.
,
Rodriguez
,
L.
&
Bisht
,
G.
2011
A comparison among different modified Priestley and Taylor's equation to calculate actual evapotranspiration
.
International Journal of Remote Sensing
32
(
5
),
1319
1338
.
DOI:10.1080/01431160903547965
.
Yang
,
D.
,
Sun
,
F.
,
Liu
,
Z.
,
Cong
,
Z.
&
Lei
,
Z.
2006
Interpreting the complementary relationship in non-humid environments based on the Budyko and Penman hypotheses
.
Geophysical Research Letters
33
,
L18402
.
DOI:10.1029/2006GL027657
.
Yang
,
D.
,
Sun
,
F.
,
Liu
,
Z.
,
Cong
,
Z.
,
Ni
,
G.
&
Lei
,
Z.
2007
Analyzing spatial and temporal variability of annual water energy balance in non humid regions of China using the Budyko hypothesis
.
Water Resources Research
43
,
W04426
.
DOI:10.1029/2006WR005224
.
Yang
,
H. B.
,
Yang
,
D. W.
,
Lei
,
Z. D.
&
Sun
,
F. B.
2008
New analytical derivation of the mean annual water-energy balance equation
.
Water Resources Research
44
(
3
),
W03410
.
DOI:10.1029/2007WR006135
.
Yang
,
D.
,
Shao
,
W.
,
Yeh
,
P. J. F.
,
Yang
,
H.
,
Kanae
,
S.
&
Oki
,
T.
2009
Impact of vegetation coverage on regional water balance in the nonhumid regions of China
.
Water Resources Research
45
,
W00A14
.
DOI:10.1029/2008WR006948
.
Yuan
,
W. P.
,
Liu
,
S. G.
,
Yu
,
G. R.
,
Bonnefond
,
J. M.
,
Chen
,
J. Q.
,
Davis
,
K.
,
Desai
,
A. R.
,
Goldstein
,
A. H.
,
Gianelle
,
D.
,
Rossi
,
F.
,
Suyker
,
A. E.
&
Verma
,
S. B.
2010
Global estimates of evapotranspiration and gross primary production based on MODIS and global meteorology data
.
Remote Sensing of Environment
114
(
7
),
1416
1431
.
Zhang
,
L.
,
Dawes
,
W. R.
&
Walker
,
G. R.
2001
Response of mean annual evapotranspiration to vegetation changes at catchment scale
.
Water Resources Research
37
(
3
),
701
708
.
Zhang
,
L.
,
Hickel
,
K.
,
Dawes
,
W. R.
,
Chiew
,
F. H. S.
,
Western
,
A. W.
&
Briggs
,
P. R.
2004
A rational function approach for estimating mean annual evapotranspiration
.
Water Resources Research
40
,
02502
.
DOI:10.1029/2003WR002710
.