Satellite-based evapotranspiration and crop coefficient for irrigated sorghum in the Gezira scheme, Sudan

Papers published in Hydrology and Earth System Sciences Discussions are under open-access review for the journal Hydrology and Earth System Sciences Abstract The availability of the actual water use from agricultural crops is considered as the key factor for irrigation water management, water resources planning, and water allocation. Traditionally, evapotranspiration (ET) has been estimated in the Gezira scheme by multiplying the reference evapotranspiration (ET o) by crop coefficient (k c) which is 5 derived from the phenomenological crop stages. Recently, advanced developed energy balance models assist to estimate ET through remotely sensed data. In this study Enhanced Thematic Mapper Plus (ETM+) images were used to estimate spatial distribution of daily, monthly and seasonal ET for irrigated sorghum in the Gezira scheme, Sudan. The daily ET maps were also used to estimate k c over time and space. Results 10 of remotely sensed based energy balance were compared with actual measurements conducted during 2004/05 season. The daily actual ET values estimated using the energy balance model during the satellite acquisition dates 15 remotely estimated k c values in the initial, crop development, mid-season and late-season stages were 0.62, 0.85, 1.15, and 0.48 respectively. On the other hand the widely used tradition k c values during the pervious mention stages are 0.55, 0.94, 1.21 and 0.65, respectively. This research shows that remotely sensed measurements can help objectively analyzed the irrigation water requirement for different field crops on 20 daily and seasonal time step. Moreover, the remotely sensed real-time data availability provides the system managers with information that not previously available.

EGU increase the acreage to meet the population food demand. Moreover, it estimated that by 2025 cereal production will have to increase by 38% to meet world food demands (Seckler et al., 1999), putting even more stress on the scarce water resources. However, the limited quantity of water available and the cost of its pumping make it mandatory irrigation water be used efficiency. Therefore, balancing the limited water 5 resources is a big challenge facing the irrigation system managers and engineers in the coming years. Accurate estimate of evapotranspiration is considered as the key factor in water resources management. Recently computer simulation models are being used to estimate evapotranspiration from heterogeneous natural landscapes, which are in dynamic 10 state due to spatial and temporal variations of interactions between soil, vegetation and atmosphere (Allen, 2000b). Such models require complex and high quality input data to obtain precise results. One of the most important developments in the field of remote sensing hydrology is the determination of distributed areal actual evapotranspiration from spectral satellite data, based on the energy balance approach (Menenti, 1984;15 Parodi, 1993;Bastiaanssen, 1995;Bastiaanssen et al., 1998;Su, 2002). The main advantage of the energy balance based on remotely sensed data is that large areas are covered, and that data is easily obtainable without extensive monitoring networks in the field.
In this study, a satellite-based energy balance model for surface fluxes, known as 20 surface energy balance algorithm for land (SEBAL) developed by Bastiaanssen et al. (1998) has been used with ETM+ data to estimate actual evapotranspiration for irrigated sorghum on daily and seasonal basis. SEBAL enables the calculation of the actual evapotranspiration during the time of satellite over pass, it involves complex procedures and determination of a number of variables such as surface temperature, Introduction

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The objectives of this study were (i) to estimate the spatial seasonal actual evapotranspiration of irrigated sorghum in the Gezira scheme and compare the results as determined with the actual measurements (ii) to apply SEBAL to derive actual k c for sorghum (iii) to compare sorghum remotely derived k c with the widely used k c in the Gezira scheme.

Study area and conditions
The study was carried out in the Gezira scheme during 2004/05 season. The scheme is located between latitudes 13 • 30 N and 15 •  EGU by Landsat 7 were processed. Images with zero percent cloud cover were selected for the processing. The four image dates selected are 28 July, 29 August, 16 October, and 17 November. The Landsat overpass time was approximately 09:58:07 a.m. local standard time (LT). Images were radiometrically and geometrically corrected and georegistered. An overview of some parameters (e.g. inverse relative distance Earth-Sun 5 dr, solar incidence angle θ, incoming shortwave radiation Rs ↓ and incoming longwave radiation L ↓) of the images used in this study are provided in Table 1. Due to an instrument malfunction occurred onboard Landsat 7 on 31 May 2003, the total loss of the image data has been estimated to be approximately 22% over any given scene. The impacts are most pronounced along the edge of the scene and gradually diminish 10 toward the center of the scene. The middle of the scene (approximately 22 km) should be very similar in quality to pervious Landsat image data that acquired prior to the failure of scan line corrector, in this study, the analysis were applied to middle part of the scene using four Landsat ETM+ images acquired on different dates to estimate seasonal actual evapotranspiration for summer sorghum crop during 2004 season.

Energy balance approach
There are many remote sensing algorithms for estimating the energy balance fluxes on the surface, each algorithm has its own advantages and disadvantages. The surface energy balance algorithm for land (SEBAL) is the most promising algorithm that requires minimum input data of ground based variables and it has been widely applied 20 in several countries of the world due to its accurate estimation of actual evapotranspiration. SEBAL calculates both the instantaneous and 24-h integrated surface heat fluxes. The latent heat flux represents the energy required for ET, and is computed as the residual of the surface energy balance. The simplified form of the energy balance equation is given by

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where Rn is net radiation (W/m 2 ), H is sensible heat flux to warm or cool the atmosphere (W/m 2 ), G o is soil heat flux to warm or cool the soil (W/m 2 ), and λE is latent heat flux (W/m 2 ), the latent heat flux associated with the evaporation from soil, water and vegetation. SEBAL has been used to estimate monthly and seasonal ET by linearly interpolations the ET values for periods in between two adjacent images (Bas-5 tiaanssen, 2000). SEBAL is a one-layer approach that computes surface energy fluxes using both physical and semi-empirical relations. The net radiation is computed from spatially variable reflectance and emittance of radiation. This model requires spectral radiances in the visible, near infrared and thermal infrared regions of the spectrum to determine 10 the intermediate parameters such as surface albedo, normalized difference vegetation index (NDVI) and surface temperature. Net radiation Rn is computed as algebraic sum of the shortwave and the long wave radiation components. The soil heat flux is the energy engaged to soil warming, and it is computed as an empirical fraction of the net radiation using surface temperature, surface albedo and NDVI as the depending 15 variables.
In SEBAL method, the initial estimate of surface roughness length for momentum transport (z om ) is based upon the soil adjusted vegetation index (SAVI) using an empirical relation (Moran and Jackson, 1991). Observed wind speed measurements are used to determine the friction velocity (u * ) at each pixel based on the assumption that 20 the wind speed at blending height (200 m) is areally constant. Reference heights Z 1 and Z 2 (usually 0.01 and 2.0 m above the ground respectively) are defined as the vertical limits for specifying sensible heat flux (H) and near surface temperature difference dT. Then according to the sensible heat transfer equation these limits become applicable for aerodynamic resistance (r ah ) (Farah and Bastiaanssen, 2001). The extremes 25 wet (zero sensible heat flux assumed, Rn=G o +λE) and dry (zero latent heat flux assumed, Rn=G o +H) pixels within the image enable to partition the available energy on the surface. This implies that dT wet =0 and d T dry = (Rn−G o ) r ah /ρ a Cp and allows the estimation of dT dry using the initial estimate of r ah . It is assumed that dT is linearly EGU related to T o at all pixels and hence the determination of the relationship is possible with the aid of the extreme pixels. The first estimate of sensible heat flux is used to correct turbulent heat transport for buoyancy effects according to Monin-Obuhkov similarity hypothesis. The estimation of sensible heat flux requires internally iterative until H converges to the local non-neutral buoyancy for each pixel.

5
The evaporative fraction (EF) describes the partitioning of the surface energy balance as the latent heat flux/net available energy, with the net available energy being defined as the difference in net radiation and soil heat flux. In this study we used the concept "ETr fraction" (ETrF), which represents the ratio of ET of each pixel to the reference ET (ETr) as computed by Penman-Monteith method (ETrF is the same as the 10 crop coefficient, k c ), ETrF is calculated and applied instead of EF: The instantaneous EF and ETrF are shown in the literature to be similar to the 24-h evaporative fraction and 24-h ETrF respectively, (Shuttleworth et al., 1989;Brutsaert and Chen, 1996;Trezza et al., 2003) and this allows estimating the latent heat flux at 15 a 24-h basis.
In this study the daily values of actual evapotranspiration was simulated to get an accurate estimation of seasonal ET. The monthly and seasonal ETrF and ET are estimated by linear interpolating the ETrF values for periods in between two adjacent images. ETr or crop reference evapotranspiration is estimated using Penman-Monteith 20 method as follows: method for the whole period represented by each image (iii) computation of multiplier K m for each period to used to convert ET for the day of the image into ET for the period and (iv) computation of accumulative seasonal actual ET using the following equation: where ET SEBAL is the daily ET predicted by SEBAL, and K m is the multiplier factor for 10 ET for the representative period, n is the number of satellite images processed. For more details description and calculations of SEBAL refer to Bastiaanssen et al. (1998) and Tasumi et al. (2000).

Calculation of actual crop evapotranspiration
The water content in the effective root zone is estimated by using the water balance 15 equation, for the Gezira clay soil due to negligible values of runoff, deep percolation and capillary rise, water balance equation reads in its most simplified form as: where ∆S is the change in soil moisture storage (mm), I is the irrigation applied (mm), P is the precipitation (mm) and ET is the evapotranspiration (mm). Irrigation and pre-20 cipitation are the deposits in water balance and are measured or calculated values. In this study irrigation water applied was measured using intensive gravimetric samples just before each irrigation and 2-3 days after irrigation. Rainfall was measured using the rain gauges. During the short post irrigation periods the roots suffer from temporary anaerobic conditions and consequently ET was very small and hence neglected EGU (Fadl, 1978). Slight modification has to be made to cater for the evaporation from free water surface as water was expected to pond between the ridges on the first day of irrigation before the crop emerged and during the early growing stages. The data of the soil volume weight ratios introduced by Abdine and Farbrother (1969) were used to generate regression equations that relate soil bulk density to soil depth and mois-5 ture content. Second degree polynomial equations were used in the regression for the 0-60 cm depth while linear regression was used for the 60-100 cm depth. The generated regression equations were used to transform the gravimetric moisture contents to volumetric values. The actual evapotranspiration during each irrigation cycle was calculated from soil moisture depletion between each post and pre-irrigation moisture 10 sampling cycles (Abdelhadi et al., 2006).

Evaporative depletion of the study area
During 2004/05 season the actual evapotranspiration (ET a ) via SEBAL model and soil moisture depletion approach (MD) has been quantified for irrigated sorghum in the 15 Gezira scheme, Sudan. In particular, the soil of the study area is a deep heavy soil with 58-66% clay, 0.5% organic matter, water infiltration rate of 1 mmh −1 and pH 8.5. Figure 2 shows the daily actual evapotranspiration estimated by SEBAL and calculated by MD method (ET a computed as a residual of soil water balance, Eq. 5). The results from Fig. 2  EGU and 3.0 mm/d. The comparison provides an indication of the amount of confident that can be given to ET estimated via remotely sensed based-energy balance model such as SEBAL.
The frequency distribution of daily actual ET and the basic statistics for different image dates including all land use types are presented in Fig. 3 and summarized in 5 Table 2, respectively. The histograms in Fig. 3 associate the higher ET to irrigated crop grown in the study area, while low ET was observed from bare soil and settlements. In 28 July irrigated crops showed relatively high ET, although most of the crops were at initial stage this could be attributed to high soil moisture at the root zone at the time of the satellite overpass. From the frequency distribution histograms the absolute min-10 imum and maximum actual ET values during 28 July, 29 August, 16 October and 17 November were 1.6-9 mm/d, 0.04-7.8, 1.0-9, and 0.03-8.9, respectively, with standard deviation 1.4, 1.93, 1.94, and 1.92, respectively. In Fig. 3 two clear peaks appear in the histograms distinguish between vegetation fields and fallow areas (sparse vegetation), on 28 July one peak around 3.5 mm/d (fallow soil) and the second one around 15 4.6 mm/d (irrigated crops), cotton crop obtained more than 4 mm/d during 29 August, during 16 October the first peak represents fallow soil (2.7 mm/d) and the other peak represent sorghum and cotton areas, while during 17 November the fallow soil shows very low ET a , it should be noted that during 17 November the high evaporation signature (greater than 6 mm/d) represents cotton field as sorghum was harvested or due to 20 harvest, its ET was reduced to less than 3 mm/d.
In this study, the monthly and seasonal evapotranspiration ET s maps on a pixel-bypixel basis were produced through the integration of all daily ET maps for the summer irrigated season of 2004/05. Figure 4 demonstrates the comparison of monthly ET (mm) estimated using SEBAL and monthly ET calculated using moisture depletion 25 approach (MD) for irrigated sorghum in the Gezira scheme. It is clear from Fig. 4 Figures 5 and 6 illustrate respectively the spatial distribution map and frequency distribution of ET s (mm/season) for the summer season (28 July to 27 November), whereas Table 3 represents the comparison of ET s as estimated by SEBAL and calculated by MD method for sorghum. In Fig. 5 the pattern of ET determined with SEBAL for all features in the image is compared to a simple false color composite of ETM+band 4, 5 3, and 2 (RGB) the degree of associations is noteworthy. However, such simple band combination gives a first approximate visual impression of the relative ET distribution in the study area. The estimated seasonal ET lie between 80-813 mm using the MD approach the accumulated ET of irrigated sorghum for a period of 92 days (28 August to 27 November) was 489 mm. SEBAL results for exactly the same period (92 days) were 468 mm. Consequently, the absolute error |ET SEBAL −ET MD | and relative error |ET SEBAL −ET MD | /ET MD ×100 values were 21 mm and 5%, respectively (Table 3). Owing to the fine resolution of ETM+ imagery different land cover classes can be easily distinguished and coincided ET s can be determined. The quantification of accurate daily and seasonal evapotranspiration for different land cover types in the irrigated 15 scheme will provide valuable information for the farmers and irrigation engineers to determine the delivered amount of water and hence enhanced the irrigation and application efficiencies for the whole system. Consequently, this will leads towards sustainable management of the limited water resources in the country.
3.2 Remotely derived crop coefficient, k c 20 SEBAL derived k c values were determined by dividing the actual ET on a pixel-based by reference crop evapotranspiration ET o , as estimated using Penman-Monteith equation. Table 4 demonstrates the comparison of SEBAL derived k c with wide use experimental crop coefficient by Farbrother (1973) for irrigated sorghum in the Gezira scheme at different crop stages. Farbrother and his co-workers during early 1970s According to the results of this study, the estimated value of crop coefficient by SE-BAL during mid-October looks similar to the k c values suggested by Farbrother (during early 1970s) with only 5% deviation. In the initial stage (late July), the derived k c value was overestimated the experimental value by 13%, while during crop development stage (late August) the SEBAL k c value underestimated the Farbrother by 10%. Significant differences were observed during the late season stage (mid November), SEBAL derived k c understated Farbrother by 26%. Above variations could be attributed to differences in crop varieties, differences in the date of sowing, change in the climatic conditions and cultural practices. Such variations explain the difficulties of interpolating traditional k c determined for specific crop variety and specific region to be used for 15 large scale region. Thus SEBAL can be used successfully to derive and update crop coefficient curves for large populations of crops in the Gezira arid conditions as the determination of field-measured k c is expensive and time consuming.

Conclusions and future remarks
This study focused on the evaluation of multi-temporal ETM+ data to calculate daily and 20 seasonal actual ET based upon satellite energy balance model such as SEBAL. The remotely sensed measurements and SEBAL provide the estimation of spatial distribution of instantaneous ET, which can be integrated into daily and seasonal ET values. The seasonal spatial distribution maps help to explain the water consumption for the different land use classes throughout the cropping season. 25 A comparison of the seasonal ET estimated by SEBAL with actual measurements for irrigated sorghum for a period of 92 days shows a deviation of 5%. Spatial daily maps varieties for specific locations. The study also shows that the real-time and accurate remotely sensed measurements provide irrigation managers and farmers with information that not previously available, that information can enhance irrigation performance for sustainable management of limited water resources.
Owing to low temporal resolution of high spatial resolution image and the cost in-  , 212-213, 198-212, 1998