Estimation of crop water requirements in arid region
using Penman±Monteith equation with derived
crop coef®cients: a case study on Acala cotton
in Sudan Gezira irrigated scheme
A.W. Abdelhadi
*, Takeshi Hata, Haruya Tanakamaru,
Akio Tada, M.A. Tariq
Graduate School of Science and Technology, Department of Regional Environment, Kobe University, Rokkodai, Nada-ku, Kobe 657-8501, Japan
Accepted 10 September 1999
Abstract
The recommended Penman±Monteith reference crop evapotranspiration (ET0) with derived crop
coef®cients (Kc) from the phenomenological stages of Acala cotton is used to estimate the crop water
requirements (CWRs) of Acala cotton in the Gezira area of Sudan. The published basal crop factors of Acala cotton were used with Penman±Monteith equation as well to estimate ET. The results were compared with the current practice that uses Penman evaporation (E0) from free water surface and crop
factors (Kf) derived by Farbrother [Farbrother, H.G., 1970. Irrigation practices on Gezira clay-rates and
intervals. Gezira miscellaneous paper no. 94. Gezira Research Station, Wad Medani, Sudan] and still in use in Sudan. The two methods were compared with the actual ET of Acala cotton measured by Fadl [Fadl, O.A., 1987. Water use of Acala cotton. Annual report 1978±1979. Gezira Research Station, Wad Medani, Sudan, pp. 143±147]. Penman±Monteith equation was found to be better than Farbrother method in terms of the total predicted CWR, coef®cient of determination (r2), the slope of the linear regression line and the standard error of estimate with both basal and derived (Kc) values. The trends of
weather examined for the period 1966±1993 showed an increasing ET0during the rainy season due to
the recent drought conditions that prevailed in the region. Care must be taken when predicting CWR during such period.#2000 Elsevier Science B.V. All rights reserved.
Keywords:Penman evaporation; Penman±Monteith; Reference crop evapotranspiration; Crop water require-ments; Crop factors; Crop coef®cients; Acala cotton; Gezira scheme
*Corresponding author.
E-mail address: hadi@ans.ans.kobe-u.ac.jp (A.W. Abdelhadi)
1. Introduction
Sudan (Africa's largest country) is overwhelmingly dependent on agriculture, where more than one quarter of its population are involved in agricultural activities. Most of the country's foreign exchange earnings come from the irrigated sector. Cotton, wheat, groundnut, sorghum, vegetables and forage crops are produced under full or supplementary irrigation. Sudan possesses the third largest irrigated area in Africa with 1.3 million hectare at present irrigated from the Blue Nile. The Blue Nile flow pattern is marked by a pronounced seasonality. Its normal annual flow (1912±1989) is 49.2 billion cubic meters. About 71% of this flow occur during the short flood season (July± September), while this figure drops to 4% during the driest period (January±April). The lack of proper storage facilities renders the utilization of the country's water share uncompleted. The combined capacities of the two reservoirs of the Blue Nile (Roseires and Sennar) fall short of half the irrigation requirements during the dry season. Moreover, the capacities of the reservoirs are decreasing due to siltation.
Prediction of crop water requirement (CWR) is of vital importance in water resources management and planning in Sudan. Since the intensification of the cropping pattern of the Gezira scheme (882 000 ha), the empirical method of water indenting that assumes the requirements of all crops at 71.4 m3haÿ1per day was proved to be inappropriate by Farbrother (1984). A more scientific method was introduced in the early 1970s by Farbrother (1970, 1979) and Adam and Farbrother (1977). The method is based on the calculation of water needed by plants to satisfy evapotranspiration losses measured from soil moisture depletion via daily gravimetric sampling. The sampling was done on 10± 20 cm depth intervals up to 1 m. The calculated ET values were related to the original Penman evaporation from free water surface via a crop factor (Kf). On the other hand,
Doorenbos and Pruitt (1977) presented a similar method for the prediction of CWR. Both methods were based on Penman evaporation equation. Farbrother used the original Penman (1948) evaporation equation with the wind function suggested by Penman (1956) which was never calibrated for the Gezira conditions. Doorenbos and Pruitt (1977) method used a slightly modified version of the equation with a revised wind function where the evapotranspiration (ET0) from reference short grass was determined. Allen et
al. (1994) argued that Doorenbos and Pruitt (1977) method tends to overestimate ET and instead he presented another equation based on Penman±Monteith that determines ET0of
a hypothetical grass. The Penman±Monteith equation with its new definition of ET0is
recommended by FAO experts as the standard method of CWR calculation. This will solve the problem of estimating crop ET with respect to different kinds of reference grass (warm or cool-season grass) as shown by Fadl (1978) and discussed by Ahmed and Ahmed (1989). The only remaining difficulty would be the absence of calculated Kc
values for most of the arable crops in areas where the Penman±Monteith was not adopted. The determination ofKc is of more importance for large irrigated projects such as the
Gezira scheme that is considered as one of the largest of its kind under a single administration body.
short (July±September) with moderate temperature and high humidity. The summer (April±June) is hot and the winter (November±February) is dry and cool. The rest of the period is transitional. Cotton is the main crop grown in Gezira representing one of the most important cash crops for the country. The seasonal amount of total water releases from Sennar dam to Gezira scheme is about 6109±7109m3. This means an error of 10% in the calculation of CWR would be very large (about the current capacity of Sennar dam).
The prediction of CWR represents an important tool for pre-season planning of the year's hydraulic schedule and water indenting in large irrigated schemes in Sudan. Adam (1984) calibrated the wind function of the original Penman evaporation under the Gezira condition. The new wind function obtained would increase Penman evaporation by about
Fig. 1. Major irrigation schemes of the Blue Nile dominated by the Gezira scheme.
27%. This leads to the supposition that Farbrother crop factors were thought to be high. Never the less the predicted CWR would not be affected as long as the original Penman evaporation is used to predict the CWR. The objective of this paper is to examine the performance of the recommended method under arid climate and heavy cracking vertisol represented by the Gezira area compared with the current method of Farbrother. The lack of actually measured Kc values also provides an opportunity to examine the
recommended method with derived Kc values compared with the published ones by
Ahmed and Ahmed (1989) citing Doorenbos and Kassam (1979). Furthermore, the trends of weather changes with respect to Penman±Monteith monthly ET0values for the period
1966±1993 were studied.
2. Methodology
Farbrother method defined CWR as the amount of water that is equal to the maximum crop water use (CWU) when soil moisture is adequate and good husbandry practices are followed. A crop factor (Kf) was defined as the ratio between CWU and Penman
evaporation (E0). CWR is predicted by multiplying the crop factor during the specified
period by the relevantE0normalized means obtained from the Gezira Meteorological
Station (GMS). Crop factors of the main crops grown in the Gezira region were published by Adam and Farbrother (1977). Penman equation used in Sudan by Farbrother takes the form
E0D
Rng eaÿedf u Dg
; (1)
whereE0is the Penman evaporation (mm per day) from open water,Dthe slope of the
saturation vapor pressure (kPa8Cÿ1), Rn the net solar radiation (mm per day), g the
psychrometric constant (kPa8Cÿ1),eathe saturation vapor pressure at mean temperature
(kPa),edthe mean actual vapor pressure (kPa), andf(u) is the wind function suggested by
Penman (1956), whereuis the wind speed (m sÿ1) at 2 m height. For the calculation of Penman±Monteith ET0monthly values, the actual mean monthly relevant weather data
were used in the computer program CropWat 4 Windows Version 4.00 Beta of the Food and Agriculture Organization of the United Nations (FAO). The same program was used to calculate the mean monthly ET0values for the period 1966±1993 to study the trends of
ET0. The climatological normals of the weather data obtained from the GMS for the
period 1961±1990 were also used to calculate ET0 according to Penman±Monteith
equation through the CropWat program. These normalized weather data are currently in use for the prediction of CWR in Sudan. However, for the comparison of the two methods with the actual ET values the actual weather data were used.
3. Determination ofKcfor Acala cotton
of Sudan. Acala cotton in the Gezira scheme is usually planted in August. The stages of growth development used in this study were approximated according to the phenomenological development of the crop obtained from the Gezira Research Station. Generally theKc orKf curve reflects an initial stage with low values and then a rising
limb during increased growth and a peak where the crop attains maximum cover and growth followed by a decreasing limb when leaves start shedding at the end of the growth cycle. Doorenbos and Pruitt (1977) divided the Kccurve into four stages: initial, crop
development, mid-season and late-season stages. The change in the slope of the curve reflects a change in the stage. Table 1 shows the length of each stage used in this study as compared with the ones obtained in a similar way from the graph of Farbrother's 10-day meanKfvalues. According to Doorenbos and Pruitt (1977) the initialKcfor two weeks
irrigation interval would be between 0.2 and 0.3. The value of 0.25 was taken as the initial Kc and the curve was drawn with mid and late-season values of 1.2 and 0.65,
respectively. From here on theKcvalues obtained by this method will be referred to as the
derivedKc.
On the other hand, Ahmed and Ahmed (1989) citing Doorenbos and Kassam (1979) presentedKc values of Acala cotton termed the basal Kc values. The resulting 10-day
means of the derivedKcare shown together with the 10-day means ofKfand basalKcof
Acala cotton in Fig. 2. It is worth mentioning that Acala varieties take about 200 days from sowing to final picking. As irrigation is usually stopped to induce polls ripening far before the final picking the period of 5 months was used for the derivation of the crop coefficients. Similar period was covered by the crop factors developed by Farbrother. Mean monthly values of crop factors were derived graphically from Farbrother's 10-day published crop factors of Acala cotton. The 10-day mean crop coefficients (derivedKc
and basal Kc) and crop factors were used to calculate Acala cotton CWR using the
following equations:
ETpKfE0; (2)
ETpKcET0; (3)
where ETpis the predicted CWR in mm per day,E0and ET0are the monthly or 10-day
mean Penman evaporation and Penman-Monteith reference crop evapotranspiration in mm per day, respectively. It is important to mention here that both the derived and the basalKcvalues were used in Eq. (3).
Table 1
Acala cotton development stages used for (Kc) derivation (adopted) compared with that obtained from the graph
of 10-day mean Farbrother crop factors (Kf)
Stage Number of days per stage
Fadl (1987) measured the actual ET of Acala cotton in the Gezira Research Station from daily soil moisture depletion readings using a Troxler's neutron probe at 10 cm depth intervals up to 160 cm. He published the results in 10-day periods together with the 10-day means ofE0values during the experiments. His values are referred to here as the
actual ET of Acala cotton. The experiments of Farbrother and Fadl were carried out in the Gezira Research Station that shares the same plot orientation and water distribution system of the Gezira scheme. The soil is known as the Gezira clay which is part of the central clay plain that covers about 25 million hectares of the flood plains of the Blue and White Niles. It is a heavy impermeable montomorrilitic vertisol with minor variations in physical and chemical characteristics. There are no deep drainage losses in this soil as reported by many researchers, e.g. Adam and Farbrother (1977), Farbrother (1984), Ibrahim (1984), Ahmed and Ahmed (1989), Elawad (1991) and Ibrahim et al. (1999). The technique of using the neutron probe for water relation studies has gained popularity in the Gezira area since 1971 due to the behavior of the cracking clay that renders other methods impracticable or cumbersome. More details of its application and sampling techniques were given recently by Ibrahim et al. (1999).
The effect of the recent weather trends was studied by plotting the 10-year moving averages of the mean monthly ET0values for the period 1966±1993.
4. Results and discussion
Fig. 3 shows the predicted mean monthly values of Acala cotton using the two methods and the actual ET. It is important to mention here that the actual 10-day mean E0and
mean monthly ET0values during the time of the experiment were used. Fig. 3 shows that
Penman±Monteith ET0combined with the derivedKcand the basalKcvalues were more
close to the actual values during the initial and development stages when compared with theE0combined with FarbrotherKfvalues. However, both methods underestimated the
Acala cotton peak ET in November and overestimated the actual requirements at the last stage. Fig. 4 shows the predicted versus the actual ET values on a 10-day basis. Farbrother method underestimated the peak CWR of Acala cotton on November first 10-day period by 0.9%, while the recommended method underestimation were 7.9% and 11.5% when the basal and derivedKcvalues were used, respectively. Farbrother method
clearly overestimated Acala cotton CWR during the initial and the development stages, coincided well during two 10-day periods during the actual ET peak and underestimated the decreasing limb before it overestimated the last period.
The ranking of the two methods was done under four methods: two were obtained from linear regression of the actual values (Y) on the predicted ones (X). These are the slope and the coefficient of determination (r2). The other two were the total estimated CWR as percent from the actual value and the standard error of estimate (SEE). The result is shown in Table 2. Using the ranking method, Penman±Monteith (with both derived and basalKc values) was better than Farbrother method in all the criteria. This means that
accurate estimates of ET can be obtained using Penman±Monteith ET0combined with
derived or basal Kc values. However, the use of basal Kc values resulted in higher
coefficient of determination and smaller SEE compared with results obtained from derivedKcvalues, while the use of the derivedKcvalues was ranked first in terms of the
Fig. 3. Mean monthly predicted and actual CWR of Acala cotton.
slope and the total predicted CWR. This means that the phenomenological stages of the crop can be used successfully to estimateKcvalues under arid conditions. It is of vital
importance for regions where the Penman±Monteith method was not adopted and the determination of field-measuredKc values is expensive and time consuming. The total
CWR predicted by Farbrother method was 856 mm, a figure close to the 848 mm obtained from CWR tables by Farbrother for Acala cotton under research conditions. The predicted total CWR of Acala cotton by the two methods are compared with the actual one in Fig. 5. Generally, the recommended method with basal and derived Kc
overestimated the total ET of Acala cotton by about 3.4% and 2.5%, respectively, compared with 20% by Farbrother method.
Fig. 4. 10-day mean predicted and actual CWR of Acala cotton.
Table 2
Rating results for the two methods de®ned by Eqs. (2) and (3) Method SEE (mm
per day)
r2 Slope (mm per day)
Total CWR as percent of actual ET (%)
KfE0 1.15 0.60 1.15 120.0
BasalKcET0 0.59 0.94 1.11 103.4
Examination of the 10-year moving averages of the monthly ET0values for the period
1966±1993 revealed an increasing trend for the months July, August and September as shown in Fig. 6. No clear trend was found for the other months. Fig. 6 also shows the normalized means (1961±1990) of the mentioned months. The normalized means are in
Fig. 5. Total predicted and actual CWR of Acala cotton.
Fig. 6. 10-year moving average of mean monthly ET0for July, August and September (1966±1993) with the
normalized means of the period 1961±1990.
use for CWR prediction. The increasing trend during these months may be explained by the severe drought conditions that prevailed in the region from the late 1970s. As these months represent the rainy season, the resulting low relative humidity due to the lack of rain combined with high temperatures led to increased evapotranspiration. This is in agreement with Mohamed (1998) who reported that the decline in rainfall in the Gezira area was attributed to the decline in July and August rainfall. This may further be clarified when the mean monthly vapor pressure deficit (10-year moving average for the period 1966±1993) of the concerned months are plotted as shown in Fig. 7. It is clear from Figs. 6 and 7 that care should be taken when the normalized means are used to predict CWR during the rainy season. However, knowing the fact that the rainy season coincides with the Blue Nile flood where shortages in irrigation water is not common, care must be taken only during prolonged dry periods. This is clear in case of August as the normalized ET0means were far below the actual trend due to the recent drought. This
means that crops may need more water than what is estimated using the normalized means andKcvalues.
5. Conclusions
The recommended Penman±Monteith reference crop evapotranspiration may be combined successfully with crop coefficients derived from crop phenomenological stages to predict CWR. Penman±Monteith method using ET0andKcwas found to be better than
Farbrother method that uses PenmanE0andKfin the estimation of Acala cotton CWR
under arid conditions in the Gezira scheme. The former method overestimated the total
CWR of Acala cotton by 3.4% and 2.5% when basal and derived Kc were used,
respectively, while the later overestimation was about 20%. The derivation ofKcvalues
would allow for the utilization of the recommended method in the arid and semi-arid region of the whole central clay plain. This is very useful especially when the calculation of site-specific Kcis expensive and time consuming for the large proposed
irrigation projects along the Blue Nile. Examination of the recent weather trends showed that care must be taken when predicting the CWR in the Gezira region under drought conditions.
Acknowledgements
The author is indebted to the Japanese Government for the provision of the scholarship from the Ministry of Education, Science and Culture, which led to this work. Appreciation and gratitude are extended to the Director of the Agricultural Research Corporation, Gezira Meteorological Station staff and the scientists of the Gezira Research Station who provided the necessary information.
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