https://orcid.org/0000-0002-6550-2189
Abstract
Accurate estimation of actual evapotranspiration (
) is a critical component in improving agricultural water management and water use efficiency. Remote sensing (RS) techniques provide a promising inexpensive tool for reliable crop water consumption estimations compared to conventional field measurements. Having agricultural land fragmentation and mixed cropping systems in the Nile River Delta, traditional methods of estimating 
are seemingly challenging. The present study aims to improve agricultural water management at the meso scale using RS-based techniques. Four RS-based methods were employed to estimate 
in mixed cropping farms at the Nile River Delta. The adopted methods include: (i) the Surface Energy Balance Algorithm for Land (SEBAL), (ii) the Simplified Surface Energy Balance algorithm (SSEB), (iii) Earth Engine Evapotranspiration Flux (EEFLUX) product, and (iv) the crop coefficient (
) method. The analysis of variance (ANOVA) test showed a significant difference between the employed RS-based techniques. During the winter season 2018–2019, the estimated 
varied from 331.33 mm/season to 389.34 mm/season, with an average of 358.76 mm/season. The irrigation efficiency was estimated to be about 55–63%, with an average of 59.55%. The study developed an algorithm to schedule the operation hours of irrigation pumps in the study area based on actual water requirements and pump capacity. The study highlights the relevance of RS methods and the importance of the equitable distribution of water in small farms to enhance water management.
HIGHLIGHTS
A remote sensing-based approach is developed to estimate actual crop evapotranspiration in arid regions.
The developed approach is tested on small scale farms with mixed vegetation in the Nile Delta.
Irrigation efficiency and irrigation schedule are determined based on estimated actual evapotranspiration.
Remote sensing-based methods can be adopted to enhance irrigation water management in small farms.
NOTATION
- ET
Evapotranspiration
Actual evapotranspiration
Crop coefficient
Instantaneous evapotranspiration flux
Latent heat flux
Net radiation flux
Soil heat flux
Sensible heat flux
- α
Surface albedo
Incoming shortwave radiation
Incoming longwave radiation
Outgoing longwave radiation
Surface emissivity
- ETo
Reference evapotranspiration
Instantaneous reference evapotranspiration at the satellite overpass time
Evapotranspiration fraction
Temperature of the hot pixel
Temperature of the cold pixel
Mean daily air temperature
Wind speed at 2 m height
Saturation vapor pressure
Actual vapor pressure
Saturation vapor pressure deficit
Slope vapor pressure curve
Psychometric constant
Spectral radiance
Spectral reflectance
Crop evapotranspiration
Difference between the maximum and the minimum value of NDVI
Minimum value of NDVI
Wavelength reflectivity for bands 5
Wavelength reflectivity for bands 4
Irrigation water supply
Discharge of the field pump
Actual operation hours
Required water supply
- V
Velocity
- H
Head
INTRODUCTION
Population growth and economic development, among other factors, are increasing pressure on water resources in Egypt. Growing pressure from socio-economic drivers increases the water supply and demand gap in the Egyptian water budget which is currently estimated at 19.5 
(MWRI 2014). The agricultural sector is the largest consumer of water in Egypt, accounting for approximately 80% of water use (El Bedawy 2014). Therefore, improving agricultural water use efficiency is fundamental for effective water management and productive agricultural systems. Accurate estimation of consumptive water use that is also known as actual evapotranspiration (
) is key to adjusting water supply and optimizing water use in irrigated agriculture (Mokhtari et al. 2019; Ghaderi et al. 2020; Xue et al. 2020). A proper estimation of 
plays a significant role that ranges from enhancing operation and management of irrigation systems to the broader perspective of managing and modelling water resource systems (KhazaiPoul et al. 2019; Akbari et al. 2022; Hatamkhani et al. 2022). Furthermore, this significance extends to the interdisciplinary analysis of the water, energy, and food nexus interactions at both local and regional scales (Elsayed et al. 2022; Zamani et al. 2022). From this perspective, a better understanding and assessment of actual agricultural water consumption are strongly required (Ghiat et al. 2021).
Factors affecting 
include climate, topography, crop type, soil type, and irrigation practices (Allen et al. 1998a). Methods for estimating 
can be divided into four categories: (i) hydrological methods (water balance), (ii) direct measurements, (iii) micrometeorological methods (energy balance methods), and (iv) empirical methods. Traditional methods provide point estimates of 
which are not sufficient for the analysis of system-level water management (Nouri et al. 2013). Moreover, such methods are often expensive, time-consuming to implement, and require well-trained staff (Liou & Kar 2014). Specifically, the lysimeter requires regular maintenance and it is time-consuming and labour-intensive (Liou & Kar 2014). Other approaches of estimating 
(such as Bowen ratio method, eddy correlation method, evaporation pans, scintillometers, sap flow methods) are based on a variety of complex models that can be applied at local, field, and landscape scales (Elhag et al. 2011). However, these techniques cannot be directly applied to large-scale areas due to the land surface complexity of hydrologic processes and the need for a variety of surface measurements and land surface parameters (Liou & Kar 2014). Another class of methods to estimate 
is the use of hydrological models such as Soil and Water Assessment Tool (SWAT). The application of SWAT has been widely adopted to explore and better understand water management aspects of irrigated agriculture in arid regions (Yazdi & Moridi 2017). However, model set up and calibration of SWAT is particularly challenging due to availability of observed data and poor quality of data together with inherited model limitations (Samimi et al. 2020). On the other hand, remote sensing (RS) based methods offer an alternative approach to estimate 
for various types of land cover. Furthermore, RS-based techniques can be employed at various spatial and temporal scales under different hydrological conditions (Mahmoud & Alazba 2016; Santos et al. 2017; Awada et al. 2022; Shekar & Raju 2022).
In Egypt, smallholdings of land (<1.26 ha) are estimated at 35% of the total agricultural land and distributed among 69% of farmers (CAPMAS 2019). Existing Egyptian agriculture practices indicate that land fragmentation and free cropping-pattern strategy are prevailing. These make the estimation of actual agricultural water consumption with traditional methods challenging. In contrast, RS-based techniques provide a useful alternative approach to estimate actual consumptive water use for mixed crop agriculture in Egypt. Remote sensing-based methods provide the same spatial data at a low cost compared to conventional methods where field measurements are difficult to obtain. Available satellite images provide a promising source of data for mapping 
at wide-ranging scales from regional to meso scale level. Therefore, RS techniques can thus provide estimates for 
without the need to quantify other complex hydrological processes (Bastiaanssen et al. 1998).
Numerous studies have applied RS-based methods to estimate 
at different spatial scales across regions, (see Papadavid et al. 2011; Sun et al. 2011; Deus et al. 2013; Bezerra et al. 2015; Samani & Bawazir 2015; Mahmoud & Alazba 2016; Ghaderi et al. 2020; Xue et al. 2020). In Egypt, several studies have been carried out to estimate 
using RS techniques at a different scale, e.g., at the national level (Droogers et al. 2009), and in the Nile Delta (Elhag et al. 2011; El-Shirbeny et al. 2014; Ayyad et al. 2019; Elnmer et al. 2019). Samani & Bawazir (2015) compared three RS-based ET models (Regional ET Estimation Model (REEM), Simplified Surface Energy Balance (SSEB) model, and Atmosphere Land Exchange Inverse (ALEXI) model) with ground measurement to estimate 
in New Mexico. Models' results showed varying estimations of 
, and the SSEB model provided adequate estimates for low ET rates. Mahmoud & Alazba (2016) estimated the spatial and temporal distribution of 
for different land use covers in the western and southern regions of Saudi Arabia during 1992–2014 using the Surface Energy Balance Algorithm for Land (SEBAL) model. The irrigated croplands recorded the highest 
rates, followed by forests and shrublands, and then water bodies. Bezerra et al. (2015) evaluated RS-based 
in a cotton field in Brazil using SEBAL and SSEB models for seven TM Landsat-5 images in 2005 and 2008. The estimated values of 
from SEBAL and SSEB algorithms were compared with Bowen ratio measurements. Results of the two algorithms showed a strong correlation with field measurements, and the SEBAL algorithm performed well compared to the SSEB algorithm.
Elhag et al. (2011) estimated daily 
and an evaporative fraction over the Nile Delta in August 2007 using the Surface Energy Balance System (SEBS) model. The simulated daily 
were compared with 92 field lysmiter data points covering the Nile Delta region. Model results showed a satisfactory agreement with field observations, indicating the skill of the SEBS model in estimating 
. Droogers et al. (2009) evaluated national water plans in Egypt, Saudi Arabia, and Tunisia using RS techniques. In Egypt, 
was estimated using the SEBAL model throughout the year 2008 and compared with 
from ET-Look model in 2007, ET-Look model is similar to SEBAL model but based on microwave satellite data which is less affected by cloud cover (Peña-Arancibia et al. 2020). Results of SEBAL were higher than ET-Look by (20–30%), due to using larger pixels in ET-Look, and using an old version of SEBAL. Ayyad et al. (2019) analyzed and evaluated three open-source RS 
products using Earth Engine Evapotranspiration Flux (EEFLUX), USGS-FEWS NET SSEBop 
monthly product, and MODIS 
monthly product (MOD16A2) in the Nile Valley and the Nile Delta. Results of the three products were compared with 
observations across Egypt. The monthly SSEBop algorithm was the best-performing product, while EEFLUX overestimated 
by about 36%. Elnmer et al. (2019) examined the performance of SEBAL algorithm using Landsat-8 images for the Nile Delta region. The algorithm showed a good agreement with the Penman-Monteith method (Allen et al. 1998b).
While to some extent most of the previous studies were conducted to estimate 
at a large scale ranging from sub-national to the national and regional level, the analysis of spatio-temporal 
at small scale, i.e., farm level, are lacking (Foster et al. 2019). Such an understanding of 
at the local scale is required for improving water management, particularly in arid areas where water is becoming scarce. Applying RS techniques to estimate 
is useful where field measurements are costly or unavailable and small landholdings with mixed cropping systems are dominant (Folhes et al. 2009). The method can be further integrated with existing modelling frameworks to enhance water resource system modelling and analysis from local scale (Yazdi & Moridi 2017) to regional scale (Avarideh et al. 2017; Elsayed et al. 2020). To fill these gaps in knowledge, this paper aims to develop a novel framework to estimate 
in small farms using multi-remote sensing techniques. This will be explored through a case study located at El-Atf canal, Menoufia governorate, Egypt. The rest of the paper is organized as follows: (a) methods, (b) study area description, (c) results and discussions, and (d) conclusions.
METHODS
method. These methods were selected because of their high accuracy in estimating 
and their suitability for small-scale farm applications (Gobbo et al. 2019; Elkatoury et al. 2020; Ghaderi et al. 2020). The RS application procedure includes four main steps as follows and as shown in Figure 1: - (i)
Data acquisition, in this step, the type of satellite images is chosen based on reasonable spatial and temporal resolution at the field scale (Landsat-8 and Sentinel-2 images). Meteorological parameters were collected from reliable weather stations covering the study area,
- (ii)
Data processing, where
is calculated according to Penman-Montieth equation. The selected methods are employed to obtain 
maps. Then, zonal statistical analysis is applied to obtain the mean 
for each mesqa, - (iii)
Preliminary evaluation, where the Analysis of Variance (ANOVA) test is conducted to identify the significance between the adopted methods,
- (iv)
Performance evaluation, in this step, the best method is defined according to ease, accuracy, and availability of data. Then, the irrigation efficiency (IE) is calculated and the required irrigation hours for each mesqa.
A flow chart illustrates the main steps of the adopted methodology.
Selection of satellite images
Satellite images are an easy, low-cost, and quick way to acquire data. It can provide useful information on land use cover, vegetation indices, and temperature (Shahrokhnia & Ahmadi 2019). Landsat-8 and Sentinel-2 are used in the present study to estimate 
with adequate spatial resolution at the farm level. Landsat-8 images contain nine bands from the Operational Land Imager (OLI) and two bands from Thermal Infrared Sensor (TIRS) instruments. Landsat-8 provides images with a spatial resolution of 30×30 m every 16 days (Earth Observing System 2019a). Landsat-8 images were downloaded from the United States Geological Survey (USGS) data site (U.S. Geological Survey 2019). Eight Landsat-8 images for the 2018–2019 winter season were obtained. The images are having slight clouds away from the study area for appropriate application of SEBAL and SSEB models (Figure 1).
Sentinel-2 images provide a high spatial resolution from 10 m to 60 m. They comprise two satellites (Sentinel-2A and Sentinel-2B) to monitor vegetation, land cover, and environmental parameters. The two satellites cover the entire surface of the earth; large islands, inland, and coastal waters every five days. Each satellite works in a sun-synchronous orbit with a 10-day repeat cycle (Earth Observing System 2019b). Sentinel-2 images were obtained from the Copernicus Open Access Hub (Sentinel images 2019). Eight Sentinel-2 images were selected and downloaded on the same dates as Landsat-8 images with slight clouds away from the study area in order to apply 
method (Figure 1).
Description of remote sensing methods
The actual evapotranspiration can not be directly obtained from satellite images but it can be estimated based on surface radiation fields through semi-empirical RS approaches. The adopted methods are explained below in detail.
Surface energy balance algorithm for land (SEBAL)
for heterogeneous areas at different spatial and temporal scales. It requires a small amount of ground-based climatic data without the need for crop classification maps (Silva et al. 2018). It is essential to validate SEBAL outcomes by in-field direct and indirect measurements of plant water status before using the algorithm as an irrigation scheduling tool (Gobbo et al. 2019). SEBAL computes the instantaneous evapotranspiration flux (
) from satellite images and weather data using an energy balance equation without information on soil, crop, and management practices. It is important to use an image with a clear sky as a thin cloud layer may cause large errors in calculations. Cloud-free images lead to accurate land surface temperature maps. The algorithm computes 
through a series of computational works that estimate net surface radiation, soil heat flux, and sensible heat flux to the air using satellite images and meteorological data. Then, ET flux is computed as a residual term of the surface energy budget equation. The basic equations of the algorithm can be described but the detailed equations can be found in (Bastiaanssen et al. 1998). Figure 2 shows the computational steps to calculate 
using the SEBAL algorithm.
is the latent heat flux (
), 
is the net radiation flux at the surface (
), G is the soil heat flux (
) and H is the sensible heat flux to the air (
). 
is calculated as follows:
is the surface emissivity, 
is the incoming shortwave radiation (
), 
is the outgoing longwave radiation (
) and 
is the incoming longwave radiation (
). The surface albedo (
) was calculated using the corrected radiance of the satellite images. SEBAL computes the ratio 
using the following empirical equation representing values near midday. G is then readily calculated by multiplying 
by the value for 
.
is the land surface temperature (
), 
is the surface albedo, and 
is the Normalized Difference Vegetation Index. If 
is less than zero, the surface is assumed water, and 
equals 0.5. H is computed according to the following equation:
is the air density (1.25 
), 
is the specific heat of the air (1,004 J/kg.K), 
(K) is the difference in temperature (
) between two heights (
and 
) respectively, and 
is the aerodynamic resistance to heat transport (
). 
In this research, a Python script (Wolff 2016) was employed to solve the SEBAL algorithm after image pre-processing and customizing the parameters of the study area using Grass GIS (OSGeo 2019) environment and QGIS (QGIS 2019). The employed Landsat-8 images are projected at UTM-WGS1984-ZONE36. Digital Elevation Model (DEM) is used at the same projection with a spatial resolution of 30 m of Shuttle Radar Topography Mission (NASA SRTM v3.0, 1 arcsec) (U.S. Geological Survey 2019). Input parameters include wind speed 
(m/s) at 2 m height measured at the weather station, 
(
) and instantaneous value of reference evapotranspiration from the weather station for the time of the satellite overpass (
) (
).
and 
are prepared in an EXCEL spreadsheet according to equations mentioned in (Allen et al. 1998a; Bastiaanssen et al. 1998). The cold pixel was selcted using the histogram of the cold pixel mask. The cold pixel should be a well-irrigated field where the leaf area index should be greater than 4 and the surface albedo should range between 0.22–0.24. If the region does not have these values, another value is selected on the map by prioritizing a well-irrigated field with a temperature close to minimum air temperature. In contrast, the hot pixel was chosen using the histogram of the hot pixel mask. The hot pixel should be a dry bare agricultural field where latent heat flux 
is assumed to be 0. The leaf area index should range between 0 and 0.4. If the region does not have these values, another value is selected on the map by prioritizing a dry field with a temperature close to maximum air temperature. The anchor pixels links the calculations for all other pixels between these two points (Sun et al. 2011).
Simplified surface energy balance (SSEB) algorithm
in semi-arid regions. It depends on the crop coefficient method proposed by Food and Agriculture Organization (FAO)-56 (Allen et al. 1998a). It is simpler than the SEBAL algorithm as it only requires the average temperature of the hot and cold pixels to solve the energy balance. The algorithm was applied for Landsat-8 images using ENVI5.3 software (ENVI 2019). The following equation is used to calculate 
:
is the evapotranspiration fraction and 
is the reference evapotranspiration (
). 
can be calculated from Landsat-8 images based on the following formula according to Bezerra et al. (2015):
is the temperature of the hot pixel,
is the estimated land surface temperature raster map, and 
is the temperature of the cold pixel. 
is calculated using Penman-Monteith equation as follows:
is the net radiation at the crop surface (
),
is the soil heat flux density (
),
is the mean daily air temperature at 2 m height (
),
is the wind speed at 2 m height (
),
is the saturation vapour pressure (
), 
actual vapour pressure (
), 
saturation vapour pressure deficit (
), 
is the slope vapour pressure curve (
), 
is the psychometric constant (
). The above-described steps are summarized in Figure 3. 
Flowchart of SSEB computational steps.
The earth engine evapotranspiration flux (EEFLUX)
The EEFLUX images are a valid RS product. They provide a daily 
estimated by METRIC algorithm with Landsat images. METRIC algorithm was originally developed by (Allen et al. 2007). The product operates on Google Earth Engine system for regional-scale estimates of the 
using Landsat-8 data (Allen et al. 2015; Ayyad et al. 2019; METRIC-EEFLUX 2019). The algorithm depends on the North American Land Data Assimilation System (NLDAS) hourly gridded weather data collection for energy balance calibration and time integration of ET. It calculates 
using the Standardized American Society of Civil Engineers (ASCE) Penman-Monteith (Irmak et al. 2005) and Gridded Surface Meteorological (gridMET) dataset (GridMET 2019). Selected EEFLUX images are downloaded from (METRIC-EEFLUX 2019) on the same dates used for Landsat-8 and Sentinel-2 images for comparison purposes.
Crop coefficient (![]()
method
) method (Allen et al. 1998a) is similar to the SSEB method. The method is classified as a spectral vegetation indices approach (Pôças et al. 2020). It has the advantage of enhancing the integration of multiple sensors to obtain reliable estimates of 
. Sentinel-2 and Landsat-8 images can be used together to map 
. The crop coefficient is estimated from Sentinel-2 images and the following equation is used to calculate 
.
is the water deficit index and is estimated from land surface temperature. 
is the crop evapotranspiration and calculated as follows:
is the crop coefficient and 
is the reference evapotranspiration.
is the maximum 
value for the Egyptian conditions, NDVI is the normalized difference vegetation index, 
is the difference between the maximum and the minimum value of NDVI, and 
is the minimum value of NDVI. The term of 
in Equation (8) was neglected as it was too small. Since 
and 
are equal, 
is assumed to be equal to 
according to Equation (5).
is the wavelength reflectivity for bands 5, and 
is the wavelength reflectivity for bands 4.The SEBAL algorithm requires more input data compared to other methods. It requires Landsat-8 image, digital elevation model (DEM), and meteorological data including the instantaneous reference evapotranspiration for the time of the satellite overpass. In contrast, SSEB model requires Landsat-8 image and meteorological data. The 
method alos requires Sentinel-2 image, Landsat-8 image, and meteorological data. However, it is simpler than SEBAL and SSEB models. Both SEBAL and SSEB algorithms require the determination of cold and hot pixels. However, SSEB is simpler than SEBAL as it does not apply an iterative process to calculate the sensible heat flux. EEFLUX images are freely available and provide 
maps at 
resolution that do not require data processing.
Evaluation criteria of remote sensing methods
To assess the performance of RS methods, the One-Way ANOVA test is adopted here (Omar et al. 2019). The ANOVA test measures the statistical significance of the difference between two different methods or more. The null hypothesis assumes that there is no difference between the groups; while the alternative hypothesis assumes that there is a difference between the groups. If the significance value is below .05 and 
, the null hypothesis is rejected and the alternative hypothesis is accepted. The ANOVA test is a parametric statistical method that requires approximately a normally distributed dependent variable for each category of the independent variable (George & Mallery 2019). The Shapiro-Wilk test P-value labeled sig., is used to check the deviation from normality. The data is normally distributed when the P-value is above .05 (Hanusz et al. 2016). The average 
in each mesqa was calculated as a pre-processing process in order to run the ANOVA test on equal size samples. Eleven samples representing the estimated mean 
at each mesqa are used for each RS method.
at 10 permanent citrus fields. The estimated 
from RS-based techniques is compared to actual water consumption from previous studies for the 10 citrus fields using the Root Mean Square Error (RMSE). The RMSE was calculated as follows:
is measured 
(
), 
is estimated 
(
), and N is the number of observations.Estimating the irrigation efficiency (IE)
) at the mesqa level can be estimated based on the calculated 
and the actual irrigation water withdrawal as follows:
Generally, 
varies between 30% and 70% with an average value of 60% for surface irrigation. To assess the performance of 
; 50–60% is good; 40% is reasonable, and 20–30% is poor (Rai et al. 2017).
A simple model for estimating irrigation operating hours
from the meteorological data using the Penman-Montieth equation. After applying RS-based methods, the best outcomes of 
are selected to calculate the 
for each mesqa. Simultaneously, the actual volume of water pumped for irrigation (
) is calculated by multiplying the discharge of the field pump (
) by its actual operation hours (
). Then, 
of the mesqa is divided by 
to obtain 
. Knowing 
for each mesqa and 
, the required water supply (
) can be obtained. After that, the required operating hours for each mesqa (
) is calculated by dividing 
by 
. Figure 4 shows a flowchart of the computational steps for obtaining an irrigation schedule based on RS-based 
. 
Flowchart of calculating irrigation scheduling.
Study area description
Map of the study area: (a) map of Egypt, (b) location of El-Atf canal, and (c) small farms served by the El- Atf canal.
Map of the study area: (a) map of Egypt, (b) location of El-Atf canal, and (c) small farms served by the El- Atf canal.
El-Atf canal is a developed canal with available measured data of cropping patterns and irrigation water withdrawals. Also, it has fixed valves every 2.10 ha, and uses electricity to raise water to mesqas. Each mesqa has two pumps at its intake. To improve the irrigation condition in the command area, the open mesqas were replaced with pipelines. The area from km 2.7 to km 5.1 was selected as a monitoring area. This area was selected because: (i) the existence of minimum illegal irrigation from drains or other canals which is necessary for model calibration, and (ii) the presence of the Water Users Association (WUA) where research findings could raise their awareness about crop selection and lead to better irrigation practices. The area has eleven improved mesqas as shown in Figure 5(b), and the general information and characteristics of these mesqas, e.g., area, intake location, and the installed capacity of water pumps are provided in Table 1. Farmers follow a free cropping system. The main grown crops in the winter season are wheat, berseem (clover), citrus, orchard, and vegetables, e.g., taro, onion, potatoes, and green beans. The main grown crops in the summer season are maize, orchard, and vegetables, e.g., taro, and potatoes.
The general information of the selected improved mesqas
| Mesqa code | Location of mesqa intake | Command area (ha) | Installed capacity ( ) | Number of pumps | ||
|---|---|---|---|---|---|---|
| Numbering (km) | Right (R)/Left (L) | 0.06 ( ) | 0.09 ( ) | |||
| 9-9 | 2.95 | R | 18.83 | 0.12 | 2 | n/a |
| 10-10 | 3.37 | R | 41.16 | 0.15 | 1 | 1 |
| 11-11 | 3.32 | L | 20.09 | 0.12 | 2 | n/a |
| 12-12 | 3.38 | L | 16.01 | 0.12 | 2 | n/a |
| 13-13 | 3.81 | R | 20.11 | 0.12 | 2 | n/a |
| 14 | 4.10 | R | 28.04 | 0.18 | n/a | 2 |
| 15 | 4.16 | R | 28.25 | 0.15 | 1 | 1 |
| 16-15 | 4.06 | L | 19.11 | 0.12 | 2 | n/a |
| 17-16 | 4.50 | R | 22.94 | 0.12 | 2 | n/a |
| 18-16 | 4.80 | R | 50.44 | 0.12 | 2 | n/a |
| 19-17 | 4.92 | L | 26.60 | 0.12 | 2 | n/a |
| Mesqa code | Location of mesqa intake | Command area (ha) | Installed capacity () | Number of pumps | ||
|---|---|---|---|---|---|---|
| Numbering (km) | Right (R)/Left (L) | 0.06 () | 0.09 () | |||
| 9-9 | 2.95 | R | 18.83 | 0.12 | 2 | n/a |
| 10-10 | 3.37 | R | 41.16 | 0.15 | 1 | 1 |
| 11-11 | 3.32 | L | 20.09 | 0.12 | 2 | n/a |
| 12-12 | 3.38 | L | 16.01 | 0.12 | 2 | n/a |
| 13-13 | 3.81 | R | 20.11 | 0.12 | 2 | n/a |
| 14 | 4.10 | R | 28.04 | 0.18 | n/a | 2 |
| 15 | 4.16 | R | 28.25 | 0.15 | 1 | 1 |
| 16-15 | 4.06 | L | 19.11 | 0.12 | 2 | n/a |
| 17-16 | 4.50 | R | 22.94 | 0.12 | 2 | n/a |
| 18-16 | 4.80 | R | 50.44 | 0.12 | 2 | n/a |
| 19-17 | 4.92 | L | 26.60 | 0.12 | 2 | n/a |
Data requirements
The calibration of water pumps were conducted by Water Management Research Institute (WMRI) to determine the actual discharge, velocity and pumping head. The actual output power of the pumps ranged from 6,266 to 16,710 
with an actual discharge of 0.02–0.11 
. The characteristics of water pumps are shown in Tables 2 and 3. The climatic data were collected from the nearest weather station in the study area that is Shebin El-Kom weather station, the Egyptian Meteorological Authority (EMA). The station is located at Latitude: 30° 36′, Longitude: 31 °01′, and Altitude: 1.5 m. The collected data includes information about minimum and maximum temperatures, relative humidity, wind speed at 1.5 m, sunshine hours, and radiation. The data were collected on all dates for which suitable satellite images were available, as shown in Table 4.
Characteristics of pump1
| Mesqa code | Calibration date | Nominal values | Measurements | |||
|---|---|---|---|---|---|---|
Discharge ( ) | Power (W) | Discharge ( ) | Velocity (m/s) | Head (m) | ||
| 9-9 | n/a | 0.06 | n/a | n/a | n/a | n/a |
| 10-10 | 21/11/2018 | 0.06 | 7,385 | 0.06 | 1.12 | 2.25 |
| 11-11 | 16/04/2018 | 0.06 | 6,266 | 0.05 | 1.35 | 2.17 |
| 12-12 | 09/10/2018 | 0.06 | 7,385 | 0.05 | 1.49 | 2.12 |
| 13-13 | 09/10/2018 | 0.06 | n/a | n/a | n/a | n/a |
| 14 | 03/10/2018 | 0.09 | 11,190 | 0.09 | 2.55 | 1.93 |
| 15 | 03/10/2018 | 0.09 | 16,710 | 0.07 | 1.24 | 2.00 |
| 16-15 | 21/11/2018 | 0.06 | 11,190 | 0.11 | 2.98 | 1.92 |
| 17-16 | 03/10/2018 | 0.06 | 7,385 | 0.08 | 2.18 | 2.05 |
| 18-16 | 03/10/2018 | 0.06 | 14,920 | 0.10 | 2.79 | 2.00 |
| 19-17 | 09/10/2018 | 0.06 | 14,920 | 0.09 | 2.41 | 2.20 |
| Mesqa code | Calibration date | Nominal values | Measurements | |||
|---|---|---|---|---|---|---|
| Discharge () | Power (W) | Discharge () | Velocity (m/s) | Head (m) | ||
| 9-9 | n/a | 0.06 | n/a | n/a | n/a | n/a |
| 10-10 | 21/11/2018 | 0.06 | 7,385 | 0.06 | 1.12 | 2.25 |
| 11-11 | 16/04/2018 | 0.06 | 6,266 | 0.05 | 1.35 | 2.17 |
| 12-12 | 09/10/2018 | 0.06 | 7,385 | 0.05 | 1.49 | 2.12 |
| 13-13 | 09/10/2018 | 0.06 | n/a | n/a | n/a | n/a |
| 14 | 03/10/2018 | 0.09 | 11,190 | 0.09 | 2.55 | 1.93 |
| 15 | 03/10/2018 | 0.09 | 16,710 | 0.07 | 1.24 | 2.00 |
| 16-15 | 21/11/2018 | 0.06 | 11,190 | 0.11 | 2.98 | 1.92 |
| 17-16 | 03/10/2018 | 0.06 | 7,385 | 0.08 | 2.18 | 2.05 |
| 18-16 | 03/10/2018 | 0.06 | 14,920 | 0.10 | 2.79 | 2.00 |
| 19-17 | 09/10/2018 | 0.06 | 14,920 | 0.09 | 2.41 | 2.20 |
Characteristics of pump2
| Mesqa code | Calibration date | Nominal values | Measurements | |||
|---|---|---|---|---|---|---|
Discharge ( ) | Power (W) | Discharge ( ) | Velocity (m/s) | Head (m) | ||
| 9-9 | n/a | 0.06 | n/a | n/a | n/a | n/a |
| 10-10 | 21/11/2018 | 0.09 | 14,920 | 0.10 | 1.85 | 2.00 |
| 11-11 | 16/04/2018 | 0.06 | 11,190 | 0.07 | 2.01 | 2.18 |
| 12-12 | 09/10/2018 | 0.06 | 11,190 | 0.05 | 1.36 | 2.05 |
| 13-13 | 09/10/2018 | 0.06 | 7,385 | 0.04 | 1.04 | 2.05 |
| 14 | 03/10/2018 | 0.09 | 14,920 | n/a | n/a | n/a |
| 15 | 03/10/2018 | 0.06 | 11,563 | 0.09 | 2.60 | 1.96 |
| 16-15 | 21/11/2018 | 0.06 | 7,385 | 0.02 | 0.43 | 2.15 |
| 17-16 | 03/10/2018 | 0.06 | 7,385 | 0.06 | 1.72 | 2.04 |
| 18-16 | 03/10/2018 | 0.06 | 11,190 | 0.06 | 1.51 | 1.96 |
| 19-17 | 09/10/2018 | 0.06 | 7385 | 0.04 | 1.17 | 2.15 |
| Mesqa code | Calibration date | Nominal values | Measurements | |||
|---|---|---|---|---|---|---|
| Discharge () | Power (W) | Discharge () | Velocity (m/s) | Head (m) | ||
| 9-9 | n/a | 0.06 | n/a | n/a | n/a | n/a |
| 10-10 | 21/11/2018 | 0.09 | 14,920 | 0.10 | 1.85 | 2.00 |
| 11-11 | 16/04/2018 | 0.06 | 11,190 | 0.07 | 2.01 | 2.18 |
| 12-12 | 09/10/2018 | 0.06 | 11,190 | 0.05 | 1.36 | 2.05 |
| 13-13 | 09/10/2018 | 0.06 | 7,385 | 0.04 | 1.04 | 2.05 |
| 14 | 03/10/2018 | 0.09 | 14,920 | n/a | n/a | n/a |
| 15 | 03/10/2018 | 0.06 | 11,563 | 0.09 | 2.60 | 1.96 |
| 16-15 | 21/11/2018 | 0.06 | 7,385 | 0.02 | 0.43 | 2.15 |
| 17-16 | 03/10/2018 | 0.06 | 7,385 | 0.06 | 1.72 | 2.04 |
| 18-16 | 03/10/2018 | 0.06 | 11,190 | 0.06 | 1.51 | 1.96 |
| 19-17 | 09/10/2018 | 0.06 | 7385 | 0.04 | 1.17 | 2.15 |
Climatic parameters of the study area
| Date | Maximum temperaturea (C) | Minimum temperaturea (C) | Relative humiditya (%) | Wind speeda at 1.5 m ( ) | Sunshine hoursb | Radiationc ( ) |
|---|---|---|---|---|---|---|
| 28/11/2018 | 24.60 | 14.20 | 67.50 | 2.57 | 10:24 | 15.45 |
| 14/12/2018 | 22.28 | 9.09 | 59.08 | 1.64 | 10:13 | 12.39 |
| 15/12/2018 | 23.90 | 8.45 | 59.73 | 1.31 | 10:12 | 12.40 |
| 23/12/2018 | 20.24 | 8.37 | 70.99 | 1.62 | 10:10 | 12.25 |
| 30/12/2018 | 18.20 | 9.00 | 74.50 | 2.06 | 10:11 | 14.77 |
| 04/01/2019 | 19.29 | 5.50 | 48.41 | 1.87 | 10:14 | 15.00 |
| 08/01/2019 | 15.94 | 5.41 | 63.44 | 4.33 | 10:16 | 15.20 |
| 15/01/2019 | 17.12 | 4.48 | 43.06 | 4.66 | 10:21 | 13.50 |
| 24/01/2019 | 19.54 | 7.88 | 32.69 | 3.41 | 10:31 | 16.50 |
| 29/01/2019 | 19.64 | 4.93 | 44.87 | 1.87 | 10:38 | 17.10 |
| 31/01/2019 | 20.20 | 7.20 | 63.50 | 2.57 | 10:40 | 17.27 |
| 01/02/2019 | 22.50 | 6.37 | 35.12 | 1.57 | 10:41 | 14.71 |
| 16/02/2019 | 19.80 | 8.00 | 49.50 | 2.06 | 11:05 | 19.41 |
| 25/02/2019 | 28.11 | 8.62 | 36.90 | 3.20 | 11:21 | 18.47 |
| 13/03/2019 | 21.65 | 10.77 | 34.45 | 4.14 | 11:50 | 23.20 |
| 20/03/2019 | 25.00 | 8.20 | 65.00 | 2.57 | 12:03 | 24.29 |
| Date | Maximum temperaturea (C) | Minimum temperaturea (C) | Relative humiditya (%) | Wind speeda at 1.5 m () | Sunshine hoursb | Radiationc () |
|---|---|---|---|---|---|---|
| 28/11/2018 | 24.60 | 14.20 | 67.50 | 2.57 | 10:24 | 15.45 |
| 14/12/2018 | 22.28 | 9.09 | 59.08 | 1.64 | 10:13 | 12.39 |
| 15/12/2018 | 23.90 | 8.45 | 59.73 | 1.31 | 10:12 | 12.40 |
| 23/12/2018 | 20.24 | 8.37 | 70.99 | 1.62 | 10:10 | 12.25 |
| 30/12/2018 | 18.20 | 9.00 | 74.50 | 2.06 | 10:11 | 14.77 |
| 04/01/2019 | 19.29 | 5.50 | 48.41 | 1.87 | 10:14 | 15.00 |
| 08/01/2019 | 15.94 | 5.41 | 63.44 | 4.33 | 10:16 | 15.20 |
| 15/01/2019 | 17.12 | 4.48 | 43.06 | 4.66 | 10:21 | 13.50 |
| 24/01/2019 | 19.54 | 7.88 | 32.69 | 3.41 | 10:31 | 16.50 |
| 29/01/2019 | 19.64 | 4.93 | 44.87 | 1.87 | 10:38 | 17.10 |
| 31/01/2019 | 20.20 | 7.20 | 63.50 | 2.57 | 10:40 | 17.27 |
| 01/02/2019 | 22.50 | 6.37 | 35.12 | 1.57 | 10:41 | 14.71 |
| 16/02/2019 | 19.80 | 8.00 | 49.50 | 2.06 | 11:05 | 19.41 |
| 25/02/2019 | 28.11 | 8.62 | 36.90 | 3.20 | 11:21 | 18.47 |
| 13/03/2019 | 21.65 | 10.77 | 34.45 | 4.14 | 11:50 | 23.20 |
| 20/03/2019 | 25.00 | 8.20 | 65.00 | 2.57 | 12:03 | 24.29 |
aCollected from Shebin El-Kom weather station.
bCollected from: https://en.tutiempo.net/shibin-al-kawm.html?data=calendar#cal.
cCalculated.
RESULTS AND DISCUSSION
Estimation of reference evapotranspiration (![]()
)
The above-described four RS-based methods were applied to the study area to estimate 
. First, 
is determined using the FAO-Penman-Monteith equation (Allen et al. 1998a) on 24-h time scale during the considered dates in the winter season (from November 2018 to March 2016) as shown in Table 5. The estimated 
for the study area are ranged from 1.9 to 5.8 
. The minimum 
was on 23/12/2018 while the maximum 
value occurred on 13/03/2019. The estimated 
values will be used to calculate 
in the study area.
Estimated 
according to the FAO-Penman-Monteith equation
| Date |  ( ) | Date |  ( ) |
|---|---|---|---|
| 28/11/2018 | 3.0 | 24/01/2019 | 4.3 |
| 14/12/2018 | 2.3 | 29/01/2019 | 2.8 |
| 15/12/2018 | 2.2 | 31/01/2019 | 3.0 |
| 23/12/2018 | 1.9 | 01/02/2019 | 3.2 |
| 30/12/2018 | 1.9 | 16/02/2019 | 3.5 |
| 04/01/2019 | 2.4 | 25/02/2019 | 5.7 |
| 08/01/2019 | 2.6 | 13/03/2019 | 5.8 |
| 15/01/2019 | 3.8 | 20/03/2019 | 4.6 |
| Date | () | Date | () |
|---|---|---|---|
| 28/11/2018 | 3.0 | 24/01/2019 | 4.3 |
| 14/12/2018 | 2.3 | 29/01/2019 | 2.8 |
| 15/12/2018 | 2.2 | 31/01/2019 | 3.0 |
| 23/12/2018 | 1.9 | 01/02/2019 | 3.2 |
| 30/12/2018 | 1.9 | 16/02/2019 | 3.5 |
| 04/01/2019 | 2.4 | 25/02/2019 | 5.7 |
| 08/01/2019 | 2.6 | 13/03/2019 | 5.8 |
| 15/01/2019 | 3.8 | 20/03/2019 | 4.6 |
Estimation of evapotranspiration using remote sensing methods
The estimated daily 
in the winter season (from November 2018 to March 2019) are analyzed here. During the winter season, 
increased depending on 
and the crop growth phases. SEBAL model showed that the average 
for the considered mesqas ranged from 1.50 to 2.62 
during November 2018, and from 1.74 to 2.14 
during December 2018. Furthermore, 
ranged from 2.36 to 4.06 
in January 2019, from 2.54 to 4.12 
in February 2019, and from 2.48 to 4.84 
in March 2019. On the other hand, the maximum values of 
were located in extensive agricultural zones and the minimum values of 
were located in residential dominant zones. Specifically, mesqa (10-10) recorded the highest values of 
as citrus and taro were dominantly grown there. Mesqa (12-12) showed the lowest values of 
as it had small agricultural areas compared to other mesqas.
The SSEB algorithm showed that the average 
for the considered mesqas ranged from 1.57 to 2.24 
in November 2018, and from 1.58 to 1.84 
in December 2018. Also, average 
were (2.57–3.05 
) in January 2019, (3.12–4.05 
) in February 2019, and (3.49–4.49 
) in March 2019. The METRIC algorithm showed an average 
value of (1.65–1.83 
) in November 2018, and (0.99–1.19 
) in December 2018. Furthermore, it ranged from 2.09 to 2.49 
in January 2019, from 3.03 to 3.65 
in February 2019, and from 3.88 to 4.53 
in March 2019. The 
method showed that the average 
ranged from 1.48 to 2.12 
in November 2018, and from 1.66 to 2.01 
in December 2019. As well, it ranged from 1.99 to 2.51 
on January 2019, from 2.60 to 3.36 
in February 2019, and from 3.66 to 5.04 
in March 2019. Table 6 summarizes the estimated 
(
) according to employed RS techniques during the winter season 2018–2019.
Estimated 
(
) during winter season 2018–2019 using RS methods
| Method | November 2018 | December 2018 | January 2019 | February 2019 | March 2019 |
|---|---|---|---|---|---|
| SEBAL | 1.50–2.62 | 1.74–2.14 | 2.36–4.06 | 2.54–4.12 | 2.48–4.84 |
| SSEB | 1.57–2.24 | 1.58–1.84 | 2.57–3.05 | 3.12–4.05 | 3.49–4.49 |
| EEFLUX | 1.65–1.83 | 0.99–1.19 | 2.09–2.49 | 3.03–3.65 | 3.88–4.53 |
 | 1.48–2.12 | 1.66–2.01 | 1.99–2.51 | 2.60–3.36 | 3.66–5.04 |
| Method | November 2018 | December 2018 | January 2019 | February 2019 | March 2019 |
|---|---|---|---|---|---|
| SEBAL | 1.50–2.62 | 1.74–2.14 | 2.36–4.06 | 2.54–4.12 | 2.48–4.84 |
| SSEB | 1.57–2.24 | 1.58–1.84 | 2.57–3.05 | 3.12–4.05 | 3.49–4.49 |
| EEFLUX | 1.65–1.83 | 0.99–1.19 | 2.09–2.49 | 3.03–3.65 | 3.88–4.53 |
| | 1.48–2.12 | 1.66–2.01 | 1.99–2.51 | 2.60–3.36 | 3.66–5.04 |
Evaluation of remote sensing methods
According to the Shapiro-Wilk test, the significance value is higher than 0.05, as shown in Table 7. Therefore, the estimated values of 
are normally distributed which is a necessary condition to apply the ANOVA test. There is a wide variance of Shapiro-Wilk 
-values between 0.94 (SEBAL method) and 0.07 (
method). The Sentinel-2 spatial resolution affected the normality of the results in the 
method. The normality of 
method is closer to reality as a result of the inhomogeneous cropping pattern in the study area. SEBAL algorithm has the most normally distributed results. This is because the application of SEBAL algorithm does not account for land use cover classification. This results in weak representation of land surface interaction with solar radiation elements.
Test of normality for the considered four RS methods
| Date | Method | Kolmogorov-Smirnova | Shapiro-Wilk | ||||
|---|---|---|---|---|---|---|---|
| Statistic | df | Significance | Statistic | df | Significance | ||
| 28-11-2018 | SEBAL | 0.118 | 11 | .200* | 0.976 | 11 | .940 |
| SSEB | 0.161 | 11 | .200* | 0.933 | 11 | .439 | |
| EEFLUX | 0.219 | 11 | .146 | 0.925 | 11 | .360 | |
 | 0.251 | 11 | .052 | 0.866 | 11 | .069 | |
| Date | Method | Kolmogorov-Smirnova | Shapiro-Wilk | ||||
|---|---|---|---|---|---|---|---|
| Statistic | df | Significance | Statistic | df | Significance | ||
| 28-11-2018 | SEBAL | 0.118 | 11 | .200* | 0.976 | 11 | .940 |
| SSEB | 0.161 | 11 | .200* | 0.933 | 11 | .439 | |
| EEFLUX | 0.219 | 11 | .146 | 0.925 | 11 | .360 | |
| | 0.251 | 11 | .052 | 0.866 | 11 | .069 | |
aLilliefors Significance Correction.
*This is a lower bound of the true significance.
was greater than 
. For example, on 28 November 2018 
= 6.868, 
= 2.84, and 
= .001, while on 16 February 2019, 
= 35.899, 
= 2.84, and 
= .000, as shown in Table 8 and Figure 6. Figure 7 shows the spatial distribution of 
on 28 November 2018. The figure indicates a difference between the estimated values of 
in the four RS-based techniques. The differences between the estimated values can be explained by the differences between the methods themselves. Mean values of 
using various RS techniques and the statistical significance for difference according to the ANOVA test
| Date | SEBAL | SSEB | EEFLUX |  | Significance |
|---|---|---|---|---|---|
| 28/11/2018 | 2.14 | 1.98 | 1.73 | 1.89 | .001 |
| 30/12/2018 | 1.91 | 1.57 | 1.07 | 1.89 | .000 |
| 08/01/2019 | 2.65 | 2.32 | 2.75 | 2.15 | .029 |
| 24/01/2019 | 3.91 | 3.61 | 4.04 | 2.46 | .000 |
| 31/01/2019 | 2.73 | 2.40 | 2.27 | 2.76 | .000 |
| 16/02/2019 | 3.51 | 2.63 | 3.32 | 3.4 | .000 |
| 13/03/2019 | 5.18 | 4.84 | 4.30 | 4.99 | .043 |
| 20/03/2019 | 2.92 | 3.41 | 4.19 | 4.18 | .000 |
| Date | SEBAL | SSEB | EEFLUX | | Significance |
|---|---|---|---|---|---|
| 28/11/2018 | 2.14 | 1.98 | 1.73 | 1.89 | .001 |
| 30/12/2018 | 1.91 | 1.57 | 1.07 | 1.89 | .000 |
| 08/01/2019 | 2.65 | 2.32 | 2.75 | 2.15 | .029 |
| 24/01/2019 | 3.91 | 3.61 | 4.04 | 2.46 | .000 |
| 31/01/2019 | 2.73 | 2.40 | 2.27 | 2.76 | .000 |
| 16/02/2019 | 3.51 | 2.63 | 3.32 | 3.4 | .000 |
| 13/03/2019 | 5.18 | 4.84 | 4.30 | 4.99 | .043 |
| 20/03/2019 | 2.92 | 3.41 | 4.19 | 4.18 | .000 |
Mean crop evapotranspiration per each RS technique and ANOVA test results on; (a) 28 November 2018 and (b) 16 February 2019.
Mean crop evapotranspiration per each RS technique and ANOVA test results on; (a) 28 November 2018 and (b) 16 February 2019.
Spatio-temporal distribution of 
(mm/ day) using RS based- methods at the same colormap scale; (a) SEBAL algorithm, (b) SSEB algorithm, (c) EEFLUX, and (d)
on 28 November 2018.
Spatio-temporal distribution of (mm/ day) using RS based- methods at the same colormap scale; (a) SEBAL algorithm, (b) SSEB algorithm, (c) EEFLUX, and (d) on 28 November 2018.
The spatial analysis of the results in Figure 7 shows the difference between the employed RS-methods. Table 9 shows the estimated actual evapotranspiration (mm/day) of all mesqas of the study area on 28 November 2018. Generally, SEBAL algorithm gave the highest 
among the four RS methods. For example, SEBAL results were higher than the SEEB estimates by about 7.83% for the whole study area. Furthermore, SEBAL results were higher than SSEB by 24.14% at mesqa (12-12) and 7.16% at mesqa (14). On the other hand, at mesqa (15), the mean 
estimated by SEBAL was lower than SSEB method by 4.36%. The 
results of EEFLUX were lower than SEBAL results by 17.76% over the study area. For instance, at mesqas (9-9) and (17-16), the EEFLUX results were lower than SEBAL outputs by 15.17% and 26.40%, respectively. The 
results of SEBAL were higher than those of 
method by about 13.45%. SEBAL results were higher than 
by 29.32% at mesqa (18-16), 12.32% at mesqa (13-13) and 6.89% at mesqa (16-15). Generally, the EEFLUX results gave the lowest 
among the four RS methods. For example, EEFLUX results were lower than the SEEB estimates by about 12.08% for the whole study area. Furthermore, EEFLUX results were lower than SSEB by 17.78% at mesqa (14) and 9.41% at mesqa (16-15). EEFLUX results were lower than 
method by about 7.33% for the whole study area. Also, the EEFLUX results were lower than 
outputs by 17.72% and 8.31% at mesqas (19-17) and (9-9), respectively.
The estimated actual evapotranspiration (
) of mesqas on 28 November 2018
| Mesqa code | SEBAL | SSEB | EEFLUX |  |
|---|---|---|---|---|
| 9-9 | 1.98 | 1.93 | 1.68 | 1.83 |
| 10-10 | 2.06 | 1.90 | 1.72 | 1.63 |
| 11-11 | 2.48 | 2.13 | 1.71 | 2.11 |
| 12-12 | 2.62 | 2.11 | 1.81 | 2.06 |
| 13-13 | 1.80 | 1.79 | 1.65 | 1.60 |
| 14 | 2.23 | 2.08 | 1.71 | 2.01 |
| 15 | 1.50 | 1.57 | 1.72 | 1.48 |
| 16-15 | 2.20 | 1.94 | 1.75 | 2.06 |
| 17-16 | 2.35 | 2.24 | 1.73 | 2.12 |
| 18-16 | 2.38 | 2.11 | 1.83 | 1.84 |
| 19-17 | 1.97 | 1.98 | 1.67 | 2.03 |
| Mesqa code | SEBAL | SSEB | EEFLUX | |
|---|---|---|---|---|
| 9-9 | 1.98 | 1.93 | 1.68 | 1.83 |
| 10-10 | 2.06 | 1.90 | 1.72 | 1.63 |
| 11-11 | 2.48 | 2.13 | 1.71 | 2.11 |
| 12-12 | 2.62 | 2.11 | 1.81 | 2.06 |
| 13-13 | 1.80 | 1.79 | 1.65 | 1.60 |
| 14 | 2.23 | 2.08 | 1.71 | 2.01 |
| 15 | 1.50 | 1.57 | 1.72 | 1.48 |
| 16-15 | 2.20 | 1.94 | 1.75 | 2.06 |
| 17-16 | 2.35 | 2.24 | 1.73 | 2.12 |
| 18-16 | 2.38 | 2.11 | 1.83 | 1.84 |
| 19-17 | 1.97 | 1.98 | 1.67 | 2.03 |
There is a need to validate the results and confirm the accuracy of each method on the meso scale. As a result of the lack of ground measurements, we relied on spatial data of the study area and collected data from previous work. First, the percentage of residential areas was calculated from each estimated 
image and compared to the calculated percentage of residential areas using Google Earth Pro. The residential zones represent the minimum water consumption 8.10% (SEBAL), 9.54% (SSEB), 11.89% (EEFLUX images), and 15.93% (
method). The actual percentage is calculated by 9.60% from Google Earth Pro. It appears that SSEB is closer to the actual than other methods. Determining the residential zones using SSEB was more accurate than the SEBAL model. Second, 10 fields of permanent crops such as citrus were determined and the extracted values of 
from each method were compared to the water consumption of citrus crops (in previous studies (WMRI 2019)) using the RMSE. The estimated 
in those 10 fields is found to be 1.78 mm/day (SEBAL), 0.61 mm/day (SSEB), 1.10 mm/day (EEFLUX), and 1.36 mm/day (
method). The SSEB method gave the lowest RMSE.
The study clarified that the spatial distribution of 
using SEBAL algorithm was not the best compared to other methods, as the residential zones were not distinguished when compared to the actual survey using Google Earth Pro, see Figure 7. Also, the RMSE calculated by citrus fields was 1.78 mm/day. The model may provide good results in the case of a vegetated region without residential zones. The application of SEBAL model is complicated compared to other methods as it depends on an iterative process in estimating the sensible heat flux. According to previous studies, SEBAL is more complex and less accurate than SSEB. Therefore, the SSEB algorithm is recommended in the present study. The accuracy of its results emerges from the use of cloud-free images and proper observation of instantaneous climatic parameters from the weather station. However, it requires a careful selection of cold and hot pixels. It was noticed that SEBAL model was sensitive to instantaneous meteorological data, thus it is important to provide more meteorological stations close to the study area with advanced systems to monitor the instantaneous changes in the different climatic factors.
The use of EEFLUX images offers 
maps at 
resolution without image processing procedures. It provides accurate 
maps in the case of cloud-free images. However, it provides overestimated or underestimated values compared to the reference evapotranspiration. Therefore, they cannot be completely relied upon without checking 
values in other methods. One of its disadvantages is that images may require a gap-filling process. The 
method was the simplest method. It did not need detection of cold and hot pixels. The 
method depends on Sentinel-2 images, which are available every five days, and they have a high spatial resolution (
) that is suitable for the field scale.
Estimation of irrigation efficiency
) gradually increased during the winter season in mesqa (16-15) from 379.81 to 802.14 
as shown in Figure 8. The actual volume of pumped water for irrigation (
) increased during the winter season from 605.28 to 1,284.87 
. Irrigation efficiency (IE) fluctuated from 63% in November to 59% in December, 59% in January, 55% in February, and 62% in March. The irrigation efficiency (IE) of each method was found to be 67% (SEBAL), 57% (SSEB), 59% (EEFLUX), and 55% (
method). The estimated 
for the whole season varied from 331.33 mm/season to 389.34 mm/season, with an average of 358.76 mm/season. Our results are in agreement with the reported range of 
(81–700 mm/season) in the Nile Delta (Elnmer et al. 2019). The water consumption of the study area ranges from 11,748.48 
to 13,805.44 
with an average of 12,720.90 
during winter season 2018–2019. 
Relationship between actual canal discharge, actual evapotranspiration, and irrigation efficiency in mesqa (16-15) during the winter season (from November 2018 to March 2019).
Relationship between actual canal discharge, actual evapotranspiration, and irrigation efficiency in mesqa (16-15) during the winter season (from November 2018 to March 2019).
into water requirements using 
, Figure 9 shows a schematic for water distribution in November using SSEB algorithm. Then, the required operation hours for each mesqa are calculated according to the pumps' discharge. For example, water consumption for mesqa (18-16) was 929.68 
. Based on the irrigation efficiency (59.55%), the water requirements for this mesqa were 1,561.18 
. Based on pumps' discharge (0.1 
), the required operating hours for the mesqa was 4.28 h. A scenario for distributing irrigation water between the mesqas was extracted, considering that the withdrawal is changing throughout the day, and it reaches its peak during the morning and midday hours, especially from 8:00 AM to 11:00 AM. The total withdrawals every hour should not exceed a certain limit as a percentage of the canal's discharge. Figure 10 shows a suggested scenario for the withdrawals during the day. The scenario is checked by the HEC-RAS simulation model (Brunner 2016) to calculate water levels through the canal with the suggested irrigation scenario. The scenario might be adjusted if the HEC-RAS results referred to an undesirable change in water levels. In the present research, the impact of the withdrawal on water levels in the canal was found to be minor as the canal is a main branch canal, and its discharge is considerably high compared to the withdrawal value. 
Schematic for water distribution in the study area in November using SSEB.
Recommended pumping irrigation schedule in the study area.
CONCLUSIONS
In the present study, the spatial and temporal distribution of 
at the field scale was estimated over a mixed vegetation region in El-Atf canal, Menoufia governorate, Egypt using four RS-based techniques; SEBAL algorithm, SSEB algorithm, EEFLUX images, and 
method. The ANOVA test showed that there was a significant difference between the four methods. SSEB algorithm had more accurate results compared to other methods according to the spatial distribution of the residential zones and the RMSE. The spatial analysis showed that the determination of residential zones in SSEB (9.54%) was the closest to the actual survey using Google Earth Pro (9.60%). The estimated 
of 10 citrus fields was compared to other estimates from previous research and showed that the RMSE was 1.78 mm/day in SEBAL, 0.61 mm/day in SSEB, 1.10 in EEFLUX, and 1.36 in 
method. The more complex model was not the more accurate model. The average water consumption in the study area was calculated by 12,720.90 
during winter season 2018–2019. The irrigation efficiency was estimated at an average of 59.55% in the study area. Furthermore, the study developed an RS-based algorithm to improve water management in small-scale farms. The algorithm calculates the operation hours for different improved mesqas, based on actual water requirements, and pumping capacities for these mesqas. The results of the study suggest that mapping 
at 30 m and 10 m spatial resolution presents a useful approach to assessing water use and water availability at the field scale in the case of limited ground data.
The current study highlights the importance of local weather stations in providing climatic data that can be utilized in estimating actual irrigation consumption. The study recommends that there is an urgent need for reliable measured data to calibrate and obtain accurate estimates for 
. Also, it is important to use cloud-free sensor images of multi-spectral bands and greater spatial resolution. Furthermore, future research should be directed to applying a combination of different types of satellite images to improve the accuracy of the results. Future research should also test more different RS-based methods at the field scale and determine their efficiency in determining the actual water consumption. Automated models that determine cold and hot pixels automatically should be used to have more accurate results. Applying SEBAL algorithm with the land use cover map may provide more accurate results.
ACKNOWLEDGEMENTS
This research was supported by Science, Technology and Innovation Funding Authority–Egypt, Project title ‘Integrated Crop Irrigation Management System for the Nile Delta Scheme’, (Project ID 26318). Comments from two anonymous WS reviewers are gratefully acknowledged.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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