Estimating Daily Reference Evapotranspiration in a Semi-Arid Region Using Remote Sensing Data

Abstract

Estimating daily evapotranspiration is challenging when ground observation data are not available or scarce. Remote sensing can be used to estimate the meteorological data necessary for calculating reference evapotranspiration ETₒ. Here, we assessed the accuracy of daily ETₒ estimates derived from remote sensing (ETₒ_-RS) compared with those derived from four ground-based stations (ETₒ_-G) in Kurdistan (Iraq) over the period 2010–2014. Near surface air temperature, relative humidity and cloud cover fraction were derived from the Atmospheric Infrared Sounder/Advanced Microwave Sounding Unit (AIRS/AMSU), and wind speed at 10 m height from MERRA (Modern-Era Retrospective Analysis for Research and Application). Four methods were used to estimate ETₒ: Hargreaves–Samani (HS), Jensen–Haise (JH), McGuinness–Bordne (MB) and the FAO Penman Monteith equation (PM). ETₒ_-G (PM) was adopted as the main benchmark. HS underestimated ETₒ by 2%–3% (R² = 0.86 to 0.90; RMSE = 0.95 to 1.2 mm day⁻¹ at different stations). JH and MB overestimated ETₒ by 8% to 40% (R² = 0.85 to 0.92; RMSE from 1.18 to 2.18 mm day⁻¹). The annual average values of ETₒ estimated using RS data and ground-based data were similar to one another reflecting low bias in daily estimates. They ranged between 1153 and 1893 mm year⁻¹ for ETₒ_-G and between 1176 and 1859 mm year⁻¹ for ETₒ_-RS for the different stations. Our results suggest that ETₒ_-RS (HS) can yield accurate and unbiased ETₒ estimates for semi-arid regions which can be usefully employed in water resources management.

1. Introduction

Evapotranspiration (ET) is one of the main components of the hydrological cycle. Its quantification is essential for water resource management [1]. However, it is arguably the most difficult process to measure, especially in arid and semi-arid areas where losses of water tend to be spatially and temporally highly variable [2,3].

Evapotranspiration (ET) consists of two main component processes: evaporation and transpiration [4,5]. Evaporation (E) is the loss of water from open water surfaces such as oceans, lakes, reservoirs, and rivers, and from soil pores directly to the atmosphere. In the evaporation process, energy is required to convert liquid water to the vapour state. Most of this energy comes from absorbed radiation which depends (inter alia) on latitude, season, cloud cover, air temperature and surface albedo (the fraction of solar shortwave radiation reflected from the earth back into space, which is affected by surface conditions and soil moisture [4,6]). Transpiration (T) occurs when water absorbed by plant roots is transferred to the leaves via the vascular system and returned to the atmosphere through their stomata [7]. It is noteworthy to highlight that evaporation and transpiration occur simultaneously and it is complex to differentiate them. There are three different expressions for ET: potential evapotranspiration (ET_p), reference evapotranspiration (ETₒ) and actual evapotranspiration (ET_a). ET_p is the water loss which would occur from a vegetated surface when sufficient moisture is available in the soil such that stomata are fully open and resistance to water vapour transport from bare soil to the atmosphere is minimal [8]. ETₒ is defined as the evapotranspiration rate from a hypothetical reference surface with unlimited soil moisture availability [9]. The reference surface is assumed to be a grass sward with a height of 0.12 m, a fixed surface resistance (representing the ease with which water vapour is transferred between the surface layer and the atmosphere) of 70 s m⁻¹ and an albedo of 0.23 [9]. ET_a is the loss of water from a vegetated surface under ambient soil moisture conditions (i.e., soil moisture may be limiting to the evapotranspiration rate). ETₒ can vary significantly on a daily time scale (which is the most commonly applied input data time step for hydrological modelling). In contrast to precipitation (which is notoriously variable), several studies have reported that variation of ETₒ is likely to be relatively uniform spatially at the basin scale, except where there are topographic complexities or strong gradients in relief [10,11,12].

ET has a crucial role in the long term terrestrial water balance. Its estimation is essential for water resources management. However, this can be a problem when observed data are sparse or unavailable, as is often the case in low and middle income countries [13,14]. Fortunately, remote sensing (RS) has the potential to provide estimates of the meteorological variables required to calculate ET at different scales. Over the last decade, significant improvements in dynamic atmospheric retrieval techniques from RS have been made for several relevant variables with different spatial and temporal resolutions. Examples include the Atmospheric Infrared Sounder (AIRS)/Advanced Microwave Sounding (AMSU) and the MODerate resolution Imaging Spectroradiometer (MODIS) which are mounted on NASA’s Earth Observing System (EOS) Aqua satellite [15].

AIRS is a passive sensing system which uses infrared hyperspectral sensing to measure temperature and humidity [16]. The density profile of constituent atmospheric gases responsible for infrared absorption is used to define a weighting function for each of the 2378 AIRS channels, with wavelengths between 3.7 and 15.4 μm [16]. By measuring the infrared radiance (IR) in each of the AIRS channels, atmospheric temperature can be calculated using the Planck equation [17]. When cloud cover prevents accurate IR temperature retrieval from the lower atmosphere, measurements can be made by its partner, AMSU. This is a passive multi-channel microwave radiometer measuring atmospheric temperature with a 15-channel microwave sounder with a frequency range of 15–90 GHz. AMSU can provide atmospheric temperature measurements from the land surface up to an altitude of 40 km, as well as cloud filtering for the AIRS infrared channel at altitude to increase the accuracy of measurements [16]. This allows NASA to provide an integrated dataset (AIRS/AMSU, hereafter AIRS). AIRS contributes to studies of the atmospheric temperature profile, sea-surface temperature, relative humidity, land surface temperature and emissivity and fractional cloud cover [16].

Zhang et al. [18] used remotely sensed leaf area indices from MODIS with the Penman–Monteith equation, gridded meteorology and a two -parameter biophysical model for surface conductance (G_s) to estimate eight-day average evaporation (E_RS) at a 1 km spatial resolution. A steady-state water balance (precipitation–runoff) approach was used to calibrate E_RS which was then applied to estimate mean annual runoff, for 120 gauged sub-catchments in the Murray-Darling Basin of Australia. The results suggest that the evaporation model can be applied to estimate steady-state evaporation and E_RS could be used with a hydrological model to generate runoff with an RMSE as low as 79 mm year⁻¹.

Mu et al. [19] developed an algorithm to estimate ET using the Penman–Monteith method driven by MODIS-derived vegetation data and daily surface meteorological inputs. They also applied the model with different meteorological inputs from ground-based stations and vapour pressure deficit and air temperature from the Advanced Microwave Scanning Radiometer (AMSR-E) and Global Modelling and Assimilation Office (GMAO) meteorological reanalysis-based humidity, solar radiation and near-surface air temperature data. Their results were validated using data from six flux towers across the northern USA. Simulated ET__RS derived from MODIS, AMSR-E and GMAO agreed well with tower-observed fluxes (r > 0.7 and RMSE of latent heat flux <30 Wm⁻² (i.e., ETₒ < 1.05 mm day⁻¹).

Rahimi et al. [20] compared the Surface Energy Balance Algorithm for Land (SEBAL) with the Penman–Monteith equation to investigate the accuracy of actual evapotranspiration (ET_a) estimation using MODIS data. The results show that there was no significant difference between the SEBAL and PM methods for estimating hourly and daily ET_a (RMSE ranged from 0.091 mm day⁻¹ to 1.49 mm day⁻¹). Peng et al. [21] compared six existing RS-derived ET products at different spatial and temporal resolutions over the Tibetan Plateau. They used one product (LandFlux-EVAL) as a benchmark due to the lack of availability of in situ measurements. Their results showed that although existing ET products capture the seasonal variability well, validation against in situ measurements are still needed in order to confirm the accuracy of calculated ET, at least in this region and probably in general. Despite the fact that other studies have used RS data to estimate ET, few previous attempts have been made, to our knowledge, to use AIRS data to estimate ET in a data-scarce semi-arid area, such as northern Iraq. Existing ET-_RS and reanalysis data products with global spatial coverage include the MODIS 1km PM data [19,22] and reanalysis data such as MERRA-2 [23]. However, these data have temporal resolutions of eight days and one month, respectively—which are too course for many hydrological applications. Whilst attempts have been made elsewhere to obtain accurate evapotranspiration estimates from RS (ETₒ_-RS) at higher temporal resolutions (e.g., daily), for example in South Africa [24] and the USA [25], this has not been performed for many areas of the world where resources are limited and where ground observations are often very scarce. The main objective of this paper is to evaluate the accuracy of daily ETₒ estimates derived using remote sensing data against ETₒ calculated using ground observations based on the PM method as a benchmark. Our aim was to focus on the value of RS data while minimising the use of reanalysis data products (i.e., products derived from the reprocessing of historical observed RS data using a consistent analysis system, often involving models and incorporating or “assimilating” ground based observations, where available).

2. Materials and Methods

2.1. Study AREA

The study was conducted in the Kurdistan Region of northeastern Iraq (36°49′14′′N, 44°51′39′′E to 36°12′03′′N, 44°28′48′′E; Figure 1). The altitude in the study area ranges from 399 m to 3061 m above mean sea level. The land use is mainly extensive grazing of sparsely vegetated areas. There are also some irrigated and rain-fed arable areas, woodland, open water and urban areas [26].

The climate of the study area can be described as Mediterranean with hot and dry weather in summer (June to September) and cool and relatively moist conditions in winter (October to May) [27]. The transitions from winter to summer and vice versa are marked and often rapid [8]. The major moisture sources are the Mediterranean, Black and Caspian Seas [8]. Precipitation is varied and mostly falls as rain in winter and autumn (Figure 2) with mean annual precipitation ranging from 500 mm to ca. 1000 mm (

Table 1. Elevation, mean daily temperature, relative humidity and average annual rainfall for the four stations located in the study area from 2010 to 2014 (Sulaimani Meteorological Office, 2015).

Stations	Elevation (m)	Mean Daily Temperature (°C)	Relative Humidity (%)	Rainfall (mm year−1)
Dukan	650	23.1	44.2	586.3
Sulaimani	885	20.1	45.2	646.7
Chwarta	1128	19.6	46.1	693.2
Penjween	1300	14	57.1	951

). Winter snowfall is common at elevations above 1000 m above mean sea level [28]. Higher temperatures are usually recorded at lower altitudes (Dukan and Sulaimani) compared with the high mountains (Penjween and Chwarta), see Table 1.

In addition, the study area experiences extreme seasonal variations in relative humidity (RH) due to the large variation in climate and altitude. The annual average RH in the study area is about 48%. It is high in winter and exceeds 70% but is only 22% on average in August. RH tends to be higher in the high mountains (Penjween and Chwarta) compared with at lower altitudes (Dukan and Sulaimani). The mean wind speed over the study area during 2010–2014 was 1.8 m s⁻¹. Southerly winds from the lowlands bring increased temperatures and northerly winds tend to bring cooler air [8].

2.2. Data Acquisition

Meteorological data were obtained for the four stations from Sulaimani Meteorological Office. These data all have daily temporal resolution from 2010 to 2014 and include maximum, minimum and average air temperature (°C), relative humidity (%), sunshine hours, wind speed (m s⁻¹) and rainfall (mm day⁻¹).

2.3. Remote Sensing Data

Daily time series of near-surface air temperature (°C), RH (%) and cloud cover fraction were obtained from Aqua AIRS/AMSU Level 3 Daily Standard Physical Retrieval (AIRS + AMSU) 1 degree × 1 degree V006 (short name AIRX3STD) for 2010–2014 at 1° spatial resolution. Data gaps were filled using cubic spline interpolation [29]. Although this can be problematic if temporal gaps in the data are wide, in our study, AIRS data were available for 99% of the period of interest (2010–2014) and the maximum data gap was just four days. Cubic splines are considered to be a reasonable interpolation method at this resolution and have often been reported to be better than simple linear interpolation for oscillating data, provided the temporal gaps are not too wide [30].

Cloud cover fraction data from AIRS were used to estimate sunshine duration using:

$$DS=H\cdot C_f$$

(1)

where $DS$ is sunshine duration (hours), $C_f$ is the cloud cover fraction (established from the AIRS/Aqua L3 Daily Standard Physical Retrieval (AIRS + AMSU) 1 degree × 1 degree V006 cloud-cover fraction data (AIRX3STD)) and H is the maximum possible sunshine hours, calculated as [9]:

$$H=\frac{24}{\pi } {\omega }_s$$

(2)

where ${\omega }_s$ is the sunset hour angle which is calculated by:

$${\omega }_s=\arccos [-\tan \left(\phi \right)\tan \left(\delta \right)]$$

(3)

in which $\phi$ is the latitude and $\delta$ is the solar declination i.e.,:

$$\delta =0.409\sin \left(\frac{2\pi }{365} J-1.39\right)$$

(4)

in which $J$ is the Julian day of the year (1 to 365, or 366 in a leap year).

2.4. Reanalysis Data

Combination methods such as the Penman–Monteith equation usually require wind speed measurements at 2 m height above ground [9]. Hourly estimates of wind speed at 10 m height were obtained from MERRA (Modern-Era Retrospective analysis for Research and Applications) [23] at 0.5° × 0.6° spatial resolution. These data were aggregated to compute daily values and then adjusted to the standard 2 m height using [9];

$$U_2=U_z\frac{4.87}{\ln \left(67.8 z-5.42\right)}$$

(5)

where $U_2$ is wind speed at 2 m (m s⁻¹) and $U_z$ is wind speed at z m above ground (m s⁻¹).

MERRA) is a NASA project which supplies consistent hydro-meteorological analyses of historical remote sensing data [31]. It assimilates atmospheric observations into a numerical model called the Goddard Earth Observation System Data Assimilation System Version 5 (GEOS-5). Data products (including monthly surface pressure, relative humidity and air temperature and hourly wind speed) are offered at a broad range of spatiotemporal scales, from 1979 to the present [31]. The output of interest for this study is wind speed. It should be noted that the spatial resolution of MERRA and AIRS is different. Therefore, bilinear interpolation was applied to resample the MERRA data to a 1° spatial grid using the four orthogonal MERRA cells surrounding a given pixel.

2.5. Reference Evapotranspiration (ETₒ) Estimation Methods

ET is commonly estimated indirectly from meteorological data [9,32,33] using a variety of different methods [34,35,36]. These methods can be grouped into three categories: (i) those based on energy balance and mass transfer concepts, often referred to as the combination equation or Penman–Monteith (PM) method [9]; (ii) those based on empirical relationships between ETₒ and temperature- (e.g., Thornthwaite [37] and Hargreaves and Samani (HS) [38]); and (iii) and radiation-based approach which utilise measured or estimated solar radiation flux density at the surface (e.g., Jensen and Haise [39]; McGuinness and Bordne [40]; and Priestley and Taylor [41]). The PM method is widely considered to be the most reliable indirect method [9,42,43]. However, its main shortcoming is that it requires a complete weather data set (net radiation flux density, temperature, relative humidity and wind speed) which is not always available for many areas [13,32]. The other methods have fewer meteorological data requirements [32] and are, hence, widely applied—particularly those based solely on temperature. The performance of temperature- and radiation-based methods, relative to the PM method, is spatially and temporally variable [44,45]. The HS method is generally agreed to be the best temperature-based approach [46,47] but has been reported to perform poorly in some semi-arid contexts [45] where radiation-based methods may be more suitable [43]. Several alternative approaches to the PM method were, therefore considered here.

Four methods were considered: (1) the Penman–Monteith (PM) equation [9] which was used as a benchmark for comparison with the other methods; (2) the Hargreaves and Samani equation (HS) [38]; (3) the radiation-based method of Jensen and Haise (JH) [39]; and (4) the radiation-based method of McGuinness and Bordne (MB) [40]. The JH and MB methods have been successfully applied in humid and arid environments [32,48] but the main drawback of these equations is underestimation in humid areas [35] and overestimation in semi-arid areas [32].

All methods require temperature data, the PM also requires RH, wind speed and sunshine hours data. JH and MB also require sunshine data. The equations are as follows.

$$\mathrm{PM}:E{T}_o=\frac{0.408∆\left(R_n-G\right)+\gamma \frac{900}{T_a+273}{U}_2\left(e_s-e_a\right)}{∆+\gamma \left(1+0.34U_2\right)}$$

(6)

$$\mathrm{HS}:E{T}_o=0.0023 {(T_{max}-T_{min})}^{0.5}\left(T_a+17.8\right)\frac{R_a}{\lambda }$$

(7)

$$\mathrm{JH}:E{T}_o=\frac{0.025\left(T_a+3\right) R_s}{\lambda }$$

(8)

$$\mathrm{MB}:E{T}_o=\frac{R_s}{\lambda } \frac{\left(T_a+5\right)}{68}$$

(9)

where $E{T}_o$ is the reference evapotranspiration rate (mm day⁻¹), $U_2$ is mean daily wind speed at 2 m height (m s⁻¹) (Equation (5)), $∆$ is the slope of the vapour pressure versus temperature curve (kPa °C⁻¹) (Equation (10)), $R_n$ is the net radiation flux density at the vegetation surface (MJ m⁻² day⁻¹) (Equation (11)), $G$ is the soil heat flux density (MJ m⁻² day⁻¹)—assumed to be zero because it is very small at the daily time scale [9], $T_a$ is mean daily air temperature at 2 m height (°C), $T_{min}$ is minimum air temperature (°C), $T_{max}$ is maximum air temperature (°C), $R_s$ is the solar radiation flux density at the surface (MJ m⁻² day⁻¹) (Equation (13)), $R_a$ is the extraterrestrial radiation (i.e., the theoretical radiation flux density at the top of the atmosphere) [MJ m⁻² day⁻¹] (Equation (14)), $e_s$ is the saturation vapour pressure (kPa) (Equation (18)), $e_a$ is the actual vapour pressure (kPa) (Equation (19)), $e_s-e_a$ is the saturation vapour pressure deficit (kPa), $\lambda$ is the latent heat of vaporization (i.e., 2.45 (MJ kg⁻¹)) and $\gamma$ is the psychrometric constant (kPa °C⁻¹) (Equation (22)).

Further definitions of variables used in Equations (6)–(9) are given [9] as follows:

$$∆=\frac{4096\left[0.6108ex{p}^{\left(\frac{17.27T_a}{T_a+273.3}\right)}\right]}{{(T_a+273.3)}^2}$$

(10)

$$R_n=R_{ns}-R_{nl}$$

(11)

in which $R_{ns}$ is the net shortwave radiation flux density (MJ m⁻² day⁻¹) (Equation (12)) and $R_{nl}$ is the net longwave radiation flux density (MJ m⁻² day⁻¹) (Equation (16)):

$$R_{ns}=\left(1-\mathrm{⍺}\right)R_s$$

(12)

where $\mathrm{⍺}$ is the surface albedo, assumed to be 0.23 for a hypothetical grass sward [9].

$$R_s=(a_s+b_s\frac{DS}{H})R_a$$

(13)

in which $DS$ is the actual duration of sunshine (hours), $H$ is the maximum possible duration of sunshine (hours) and $a_s+b_s$ are regression constants set to 0.25 and 0.5, respectively, as recommend by Allen et al. [9].

$$R_a=\frac{24\left(60\right)}{\pi } G_{sc} d_r\left[{\omega }_s\sin \left(\phi \right)\sin \left(\delta \right)+\cos \left(\phi \right)\cos \left(\delta \right)\sin \left({\omega }_s\right)\right]$$

(14)

in which $d_r$ is the inverse of the relative distance between the Earth and the Sun ( Equation (15)), ${\omega }_s$ is defined by Equation (3), $\phi$ is the latitude, $\delta$ is given in Equation (4) and $G_{sc}$ is the solar constant = 0.0820 MJ m⁻¹ min⁻¹.

$$d_r=1+0.033\cos \frac{2\pi }{365}J$$

(15)

$$R_{nl}=\sigma \left[\frac{{(T_{max}+273.3)}^4+{(T_{min+}273.3)}^4}{2}\right]\left(0.34-0.14\ast \sqrt{e_a}\right)(1.35\frac{R_s}{R_{so}}-0.35)$$

(16)

in which $\mathsf{\sigma }$ is the Stefan–Boltzmann constant (4.903 × 10⁻⁹ MJ K⁻⁴ m⁻² day⁻¹), $\left(0.34-0.14\ast \sqrt{e_a}\right)$ expresses the correction for atmospheric humidity, and the cloudiness is expressed by $\left(1.35\frac{R_s}{R_{so}}-0.35\right)$ [9]; $R_{so}$ is the clear-sky solar radiation flux density (MJ m⁻² day⁻¹) which can be used when calibrated values for $a_s+b_s$ are not available [9] i.e.,

$$R_{so}=\left(0.75+2\ast {10}^{-5}\ast z\right)R_a$$

(17)

in which $z$ is the station elevation above sea level (m).

The vapour pressure terms are defined as follows:

$$e_s=(\frac{e^0\left(T_{max}\right)+e^0\left(T_{min}\right)}{2})$$

(18)

$$e_a=(\frac{e_{min}^0\frac{R{H}_{max}}{100}+e_{max}^0\frac{R{H}_{min}}{100}}{2})$$

(19)

where $R{H}_{min}$ and $R{H}_{max}$ are minimum and maximum relative humidity (%) and $e_{min}^0$ and $e_{max}^0$ are the saturation vapor pressure at the minimum and maximum air temperatures, respectively (Equations (20) and (21)):

$$e_{min}^0=0.6108 exp(\frac{17.27 T_{min}}{T_{min}+273.3})$$

(20)

$$e_{max}^0=0.6108 exp(\frac{17.27 T_{max}}{T_{max}+273.3})$$

(21)

The psychrometric constant is defined as:

$$\gamma =\frac{C_{p}P}{\epsilon \lambda }$$

(22)

in which $C_p$ is the specific heat capacity at constant pressure; 1.013 × 10⁻³ (MJ kg⁻¹ K⁻¹), $\epsilon$ is the ratio molecular weight of water vapour:dry air (i.e., 0.622); and $P$ is the atmospheric pressure (kPa).

Three statistical metrics were used to evaluate model performance in validation: the Pearson Product Moment Correlation Coefficient (r; Equation (23)), the root-mean-square error (RMSE; Equation (24)) and the bias (Equation (25)).

$$r=\frac{{\sum }_{i=1}^n(X_i^G-{\overline{X}}^G)(X_i^{RS}-{\overline{X}}^{RS})}{\sqrt{{\sum }_{i=1}^n{(X_i^G-{\overline{X}}^G)}^2}\sqrt{{\sum }_{i=1}^n{(X_i^{RS}-{\overline{X}}^{RS})}^2}}$$

(23)

$$RMSE=\sqrt{\frac{{\sum }_{i=1}^n{(X_i^{RS}-X_i^G)}^2}{N}}$$

(24)

$$Percent bias=\frac{{\sum }_{i=1}^N\left(X_i^{RS}-X_i^G\right)}{{\sum }_{i=1}^N{X}_i^G}\ast 100$$

(25)

where $X_i^G$ and $X_i^{RS}$ are the ground and RS values, respectively; ${\overline{X}}^G$ is the average ground value; ${\overline{X}}^{RS}$ is the average of RS value; and $N$ is the number of values recorded in the sample.

3. Results

3.1. Comparison between Meteorological Variables Estimated from Remote Sensing with Station Data

Satellite-derived and ground-measured values of mean daily air temperature ($T_a)$, RH, sunshine hours (DS) and U₂ are compared in Figure 3 for the four stations in the study area. A statistical summary of this comparison is shown in

Table 2. Statistical summary of the relationship between daily ground-measured and remotely-sensed values of $T_a$, RH %, $DS$ and $U_2$ for four different stations during the study period (2010–2014).

Station	Variable	RMSE	BIAS (%)	R
Sulaimani	$T_a$	3.5	−14.2	0.97
	RH %	12.7	−0.6	0.76
	$DS$	4.5	16.1	0.38
	$U_2$	1.4	27.8	0.03
Penjween	$T_a$	5.1	28.4	0.94
	RH %	13.8	−13.4	0.72
	$DS$	4.3	10.2	0.45
	$U_2$	1.7	34.8	0.02
Chwarta	$T_a$	3.3	−0.1	0.94
	RH %	24	−26	0.55
	$DS$	4.2	9.1	0.44
	$U_2$	1.5	24.5	0.03
Dukan	$T_a$	3.2	−2.8	0.95
	RH %	12.5	−7.3	0.80
	$DS$	5.1	21.8	0.40
	$U_2$	1.4	−47.7	0.03

. The R² values between the ground-measured and AIRS-derived values of $T_a$ were high (R² > 0.88) and highly significant for all stations. The RMSE for $T_a$ ranged from 3.2 to 5.1 °C with a tendency of RS to underestimate the ground observations of $T_a$. For RH, the relationship between satellite-derived and ground-based measurements was also significant for all four stations (R² > 0.3; p < 0.05). For RH the RMSE ranged from 12.5% to 24% with negative bias for all stations. However, there was a weak but significant relationship for DS (0.15 < R² < 0.2; p < 0.05) and the relationship between measured $U_2$ and MERRA-derived wind speed is even weaker for all stations (Table 2). Remotely sensed DS and U₂ both had positive bias in all cases, except for wind speed at Dukan (Table 2).

Since ET is widely known to be driven by turbulent eddies, and is thus sensitive to wind speed, we conducted an extra analysis to evaluate the model sensitivity to the MERRA-wind speed data. We compared ET_o estimates derived using the PM equation for all four stations using U₂ derived from MERRA with PM estimates assuming a constant U₂ value (the mean measured daily value for each station during 2010–2014). The ET_o predictions produced with the constant wind velocity were actually better overall (closer match with PM estimates obtained using ground-measured data in terms of regression equation slope, R² and RMSE: see Supplementary Materials, Figures S1 and S2, Tables S1 and S3), although (as expected) high ET values (>ca 8 mm day⁻¹) which often arise on windy days are not well predicted. This implies that that the PM equation can still be used with RS data provided a reasonable estimate can be made for the mean wind speed for the locations of interest.

3.2. Comparison between Daily ETₒ-RS and ETₒ-G

The calculated daily ET_o-G and ETₒ_-RS estimates are shown in Figure 4. In all cases, the black line shows ET_o–G. For all stations, there is seasonal agreement between ET_o-G and ET_o–RS for all evapotranspiration methods. Estimated ET_o-G is plotted against ET_o-RS in Figure 5, along with the best-fit linear regression and the 1:1 line. Most of the points are scattered around the 1:1 line for the JH and MB methods which always have high R² and regression gradients close to unity. However, there is considerable variability in the slope of the ground-derived versus RS-derived regression lines (0.7 to 0.89) and in R² (0.64 to 0.9) when using the HS and PM methods—particularly for the Dukan and Sulaimani stations. These stations have relatively low elevations compared with the other two stations, with higher average temperatures (Table 1). Average annual ET₀ values estimated using the ground and RS data for all methods from 2010 to 2014 are presented in Figure 6. The MB method yielded highest average annual values for both ET_o-G and ET_o-RS (1670 mm year⁻¹ and 1677 mm year⁻¹, respectively), while the HS method yielded the lowest annual value of ET_o-RS (1198 mm year⁻¹) and the PM method yielded lowest annual values of ET_o-G (1337 mm year⁻¹). The average annual values of ET_o-RS were relatively similar to those of ET_o-G, which reflects low bias and hence small cumulative errors.

Goodness-of-fit statistics are presented in

Table 3. Statistical summary of comparisons between estimated daily reference evapotranspiration using ground-based measurements (ETₒ_-G) and remote sensing data (ETₒ_-RS) for four different methods at four different stations (Sulaimani, Penjween, Chwarta, and Dukan) over the study period 2010–2014.

Station	Methods	RMSE (mm day−1)	BIAS (%)	R
Sulaimani	PM	0.99	2.5	0.80
	HS	1.26	−17	0.95
	JH	0.82	−3.2	0.93
	MB	0.65	−10.5	0.99
Penjween	PM	1.59	17.7	0.81
	HS	1	−13	0.94
	JH	1.46	23.2	0.93
	MB	0.92	18.2	0.97
Chwarta	PM	1.26	12.8	0.86
	HS	0.95	−10	0.92
	JH	1.19	3.7	0.93
	MB	0.57	0.3	0.97
Dukan	PM	1.7	−13	0.81
	HS	1.1	−19.9	0.94
	JH	1.56	5.1	0.91
	MB	0.52	−1.8	0.98

. The MB method consistently performed better than other methods (in terms of the similarity of the ET_o-G and ETₒ_-RS data) for all stations and for all goodness-of-fit criteria, except for the bias at Sulaimani. The greatest differences were observed when the PM and HS methods are compared. The HS method consistently underestimated ground-based ET estimates when RS data were used as inputs (i.e., bias was always negative). Pearson correlation coefficients (r) between ET_ₒ-G and ETₒ_-RS were generally high and always highly significant (p < 0.05) for all stations.

3.3. Cross-Comparison of the ET_ₒ Methods

In Figure 7, different ETₒ_-RS values calculated using the HS, JH, and MB methods are plotted against benchmark data (i.e., ETₒ_-G PM) for all stations. This comparison is based on the assumption that the PM method is most reliable [49], and that the ground-based measurements at each station best represent the atmospheric drivers for evapotranspiration (i.e., the ground-based data will best-predict ET_o using the PM method). There was considerable variation in model performance against the benchmark data for different stations. The JH and MB methods had regression slopes in the range between 0.95 and 1.4, with most slopes >1, indicating a slight tendency of these methods to overestimate the benchmark values. However, the slopes for the HS method ranged between 0.63 and 0.82, suggesting a tendency for the HS equation to under-predict ET when driven by RS data, particularly at the Dukan station Although the MB method yielded the best coefficient of determination for each station (0.74 < R² < 0.86), this was not always the best method in terms of proximity to the 1:1 line. At the two stations with higher elevation (Penjween and Chwarta) the HS method was the best predictor.

Table 4. Statistical bias, RMSE and Pearson Product Moment Correlation coefficient (r) for ETₒ_-RS values against the benchmark data set ETₒ_-G (PM) for the different stations over the study period 2010–2014.

Station	Methods	RMSE (mm day−1)	BIAS (%)	R
Sulaimani	HS	1.3	−9	0.83
	JH	2.1	21.4	0.83
	MB	1.6	24.5	0.85
Penjween	HS	1	−1.9	0.88
	JH	2.1	37	0.88
	MB	1.7	40	0.91
Chwarta	HS	0.98	−0.6	0.89
	JH	2	33.3	0.90
	MB	1.6	37	0.92
Dukan	HS	1.2	−2.6	0.89
	JH	1.8	11.2	0.89
	MB	1.81	8.6	0.92

summarises the results statistically. This confirms that the HS method tends to underestimate benchmark ET (−9 < bias% < −0.6) and that the other methods tend to overestimate it (bias ranged between 8.6 and 40%). At all stations the HS method had the lowest RMSE (1–1.3 mm day⁻¹). Despite the fact that the JH and MB methods had correlation coefficients which were often better than for the HS method, they had much higher RMSE values (1.8–2.1 mm day⁻¹).

4. Discussion

In this paper, reference evapotranspiration (ETₒ) was estimated based on four methods using ground-observed and RS-derived meteorological data (i.e., AIRS and reanalysis wind speed data from MERRA) at four stations in northeastern Iraq. For mean daily air temperature, AIRS and ground-based measurements were very similar for all sampled stations. The positive bias for $T_a$ increased with increasing station altitude. Similarly, for RH the relationship between AIRS and ground-based measurements was strong, albeit with a negative bias, for all stations. Despite the better spatial resolution of the MERRA data compared to AIRS data, we decided not to use the MERRA products because we wanted, explicitly, to focus on the value of the RS data and avoid reanalysis products as much as possible. Reanalysis data (which often integrate data from different sources) can be sensitive to observing system changes and there is often some uncertainty due to variations in both the models used and in the analysis techniques employed [31]. Unfortunately, we were not able to avoid using reanalysis products completely and MERRA wind speed data ($U_2$) was required because to date no RS wind speed data are available. The relationships for DS and $U_2$ were weak for all stations. The effect of differences between RS and ground-based meteorological variables on ETₒ rate will depend on the model sensitivity to the variable in question (i.e., if the model is sensitive to an input variable then predictions of ET will differ significantly if the RS estimate for that variable differs from the ground-based measurement; conversely, if the model is insensitive to the variable in question then ET will be relatively unaffected by errors in the RS estimates). Differences could be due to the different spatial reference frames employed, with meteorological stations recording point measurements and RS platforms observing spatially aggregated variables over large grid cells or pixels. As well as altering ET using empirical methods, differences in $T_a$ estimates will also affect other temperature-dependent values such as vapour pressure deficit and ∆.

There was generally reasonable agreement between ETₒ_-RS and ETₒ_-G for all the ETₒ methods evaluated, based on high R² values and regression line slopes close to unity compared with the predictions driven by ground-based measurements. However, there was some variation in model performance for individual stations. Regressions between the bias in input variables (RS versus ground) and the bias in ETₒ estimates (calculated using RS versus the benchmark) for all methods are shown in Table S2. Strong and significant relationships were observed between the bias in sunshine duration and the bias in ETₒ in the case of the JH and MB methods (R² > 0.95, p < 0.05) for all stations. This is not unexpected, given the dependence of these methods on solar radiation (and indirectly DS) suggesting high sensitivity. Other relationships were insignificant – even for the bias in ET from the HS method versus the bias in T_a, possibly because the HS method also depends on the theoretical radiation flux density at the top of the atmosphere. The bias in ETₒ_-RS for the PM equation was most sensitive to DS and wind speed, reflecting the high importance of both radiative and aerodynamic terms in this method (by definition).

The PM model tended to predict lower ETₒ than when using ground-based data for the Dukan station, but higher ETₒ for the Sulaimani, Penjween and Charta stations. This is mainly due to the sensitivity of the PM method to meteorological input data (i.e., radiation, air temperature, humidity and wind speed [9]). Thus, the effects of disparities between ground-level measurements and RS estimates can be significant on ETₒ calculations especially in windy, warm and or dry conditions [9]. For instance, $T_a$ derived from RS overestimated ground-based measurements for the Penjween and Charta stations in the mountains (1284 and 1128 m ASL, respectively) but underestimated $T_a$ at Dukan, which is located at lower altitude (690 m ASL). These results agree with the results reported by Ferguson and Wood [50] which showed that the positive bias of near-surface air temperature from AIRS increased with increasing elevation. Similar to $T_a$, DS and $U_2$ also contributed significantly to the deviation of RS and ground-driven ET using the PM method due to high bias and RMSE for the RS-estimates of these variables compared to ground-based measurements.

In the cross-comparison of the ETₒ methods (i.e., when the RS-driven models were compared with the benchmark data set), ETₒ_-RS (HS) slightly underestimated ETₒ_-G (PM: Table 4). This could be due to: (i) The absence of humidity terms in the HS method [32,51] in contrast to the PM method in which ETₒ is positively correlated with vapour pressure deficit. This is especially important in semi-arid environments were humidity deficits can be high (i.e., when low relative humidity results in a steep gradient in vapour pressure between the surface and the bulk atmosphere). (ii) The fact that temperature-based methods (HS) tend to underestimate ETₒ at high wind speeds of >3 m s⁻¹ [49]. In the original PM method, wind speed is included via the aerodynamic resistance term (which is combined with the surface resistance, specific heat capacity and air density in the FAO version shown in Equation (6) via the constants 900 and 0.34). (iii) The fact that atmospheric transmissivity (the ratio of the global solar radiation at ground level to that received at the top of the atmosphere, [52,53]) in semi-arid area tends to differ from other areas due to lower atmospheric moisture content [52]. A number of other studies [54,55,56,57,58,59] have reported that the HS method can overestimate ETₒ in humid environments and under estimate it in semi-arid regions [47]. Although a slight negative bias was also observed here, the HS model yielded lower RMSE values overall compared with the other methods suggesting that it is a reasonable method for estimating ETₒ in semi-arid regions similar to our study area (even when driven by RS data). This result is in agreement with Lopez et al. [7], Tabari [47] and Tabari and Talaee [59] who concluded that the HS method can be successfully used in semi-arid areas.

The positive bias obtained from comparisons between ETₒ_-RS calculated using the JH and MB methods and ETₒ_-G PM is in accordance with both Jensen et al. [36] and Tabari et al. [32] who found that these models tend to overestimate ET_o compared with the PM method, by as much as 30% and 60%, respectively. In our study the JH and MB methods overestimated the benchmark average annual ETₒ at all stations (Figure 6) by between 9% and 40%. Instead, the average annual ETₒ predicted by the HS method was similar to that estimated by the PM method for all stations (e.g., bias ranged between −0.6% and −9%).

This study did not take into account the effects of vegetation factors on the ET rate and, instead, focussed on climatic factors. ETₒ expresses the evaporation power of the atmosphere at a specific location and time of the year and does not consider land cover characteristics and soil factors [9]. If required, crop-specific ETp can be calculated from ETₒ using crop-specific resistance terms in the PM equation or, more generally, using crop coefficients [9] which account for differences in vegetation canopy characteristics such as leaf area index, canopy height and stomatal resistance. ETa can be calculated from ETp (or ETₒ) if soil moisture content can be estimated, often via a linear reduction in ETa:ETp between a threshold moisture content and the permanent wilting point [13].

5. Conclusions

Obtaining accurate estimates of ETₒ is essential for well-informed water management. However, in many parts of the world, the meteorological data required to estimate it are not available or are very scarce. Satellite remote sensing offers an alternative data source to ground stations, provided it can be shown to provide robust and reliable estimates of water fluxes. In this study, we assessed the validity of using daily RS-derived meteorological variables for estimating daily ETₒ compared with ETₒ from the same models driven by ground-based meteorological variables, for four stations in northeastern Iraq. The results were also compared with a benchmark model (PM) driven by ground-based meteorological observations. The good agreement (i.e., low RMSE and bias and high r) between AIRS and ground-based data, particularly near-surface air temperature, and the generally good performance of the ET models compared to the benchmark data set, suggest that AIRS data can be used as alternatives to conventional meteorological data to estimate daily ETₒ with reasonable accuracy. Considering the low density of ground-based stations and the paucity of climatological records in regions such as Iraq, this is encouraging for future hydrological studies and for better-informed water management. The application of the PM method is limited in many semi-arid regions of the world by lack of required weather observations. In such circumstances, simpler models are often used to estimate ETₒ. In this case, the RS-driven HS method produced better ETₒ estimates (compared to the PM equation as a benchmark) than the other models. It is recommended that the HS model is used where complete weather observation data are lacking. This method can be successfully employed using RS data to yield accurate and useful daily ETₒ estimates. This, in turn, is valuable for better policy making and planning in order to ensure efficient use of water resources, to improve irrigation management and for hydrological modelling. Some reanalysis data products already exist which attempt to estimate ETₒ using a combination of RS and ground-based data and numerical models (e.g., MERRA-2). Future work could usefully compare ETₒ estimates generated here with those predicted by MERRA-2.