Directory UMM :Data Elmu:jurnal:A:Agricultural Water Management:Vol45.Issue2.Jul2000:
Agricultural Water Management 45 (2000) 203±214
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 ET0 during 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 requirements; Crop factors; Crop coef®cients; Acala cotton; Gezira scheme
*
Corresponding author.
E-mail address: hadi@ans.ans.kobe-u.ac.jp (A.W. Abdelhadi)
0378-3774/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 3 7 7 4 ( 9 9 ) 0 0 0 7 7 - 3
204
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
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 m3 haÿ1 per 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 ET0 of
a hypothetical grass. The Penman±Monteith equation with its new definition of ET0 is
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 of Kc 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.
The Gezira scheme is shown together with the major irrigation schemes on the Blue
Nile in Fig. 1. The climate of the region is arid and continental with low average annual
precipitation (472 mm at Sennar dam and 160 mm near Khartoum). The rainy season is
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
205
Fig. 1. Major irrigation schemes of the Blue Nile dominated by the Gezira scheme.
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 6 109±7 109 m3. 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
206
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
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 ET0 values 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 relevant E0 normalized 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
E0
DRn g ea ÿ ed f u
;
Dg
(1)
where E0 is the Penman evaporation (mm per day) from open water, D the slope of the
saturation vapor pressure (kPa 8Cÿ1), Rn the net solar radiation (mm per day), g the
psychrometric constant (kPa 8Cÿ1), ea the saturation vapor pressure at mean temperature
(kPa), ed the mean actual vapor pressure (kPa), and f(u) is the wind function suggested by
Penman (1956), where u is the wind speed (m sÿ1) at 2 m height. For the calculation of
Penman±Monteith ET0 monthly 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 ET0 values 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 of Kc for Acala cotton
The guideline for the calculation of the crop coefficient presented by Doorenbos and
Pruitt (1977) was followed to calculate the crop coefficients (Kc) of Acala cotton varieties
207
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
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
Adopted
Initial
Crop development
Mid-season
Late-season
Total
25
40
45
40
150
Farbrother
15
60
29
46
150
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 the Kc or Kf 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 Kc curve 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
mean Kf values. According to Doorenbos and Pruitt (1977) the initial Kc for 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 the Kc values obtained by this method will be referred to as the
derived Kc.
On the other hand, Ahmed and Ahmed (1989) citing Doorenbos and Kassam (1979)
presented Kc values of Acala cotton termed the basal Kc values. The resulting 10-day
means of the derived Kc are shown together with the 10-day means of Kf and basal Kc of
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 (derived Kc
and basal Kc) and crop factors were used to calculate Acala cotton CWR using the
following equations:
(2)
ETp Kf E0 ;
ETp Kc ET0 ;
(3)
where ETp is the predicted CWR in mm per day, E0 and ET0 are 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
basal Kc values were used in Eq. (3).
208
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
Fig. 2. 10-day mean derived and basal Kc and Kf of Acala cotton.
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 of E0 values 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 ET0 values 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 E0 and
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
209
Fig. 3. Mean monthly predicted and actual CWR of Acala cotton.
mean monthly ET0 values during the time of the experiment were used. Fig. 3 shows that
Penman±Monteith ET0 combined with the derived Kc and the basal Kc values were more
close to the actual values during the initial and development stages when compared with
the E0 combined with Farbrother Kf values. 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 10day period by 0.9%, while the recommended method underestimation were 7.9% and
11.5% when the basal and derived Kc values 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
basal Kc values) was better than Farbrother method in all the criteria. This means that
accurate estimates of ET can be obtained using Penman±Monteith ET0 combined 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
derived Kc values, while the use of the derived Kc values was ranked first in terms of the
210
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
Fig. 4. 10-day mean 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 estimate Kc values under arid conditions. It is of vital
importance for regions where the Penman±Monteith method was not adopted and the
determination of field-measured Kc 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.
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 (%)
Kf E0
Basal Kc ET0
Derived Kc ET0
1.15
0.59
0.89
0.60
0.94
0.86
1.15
1.11
1.04
120.0
103.4
102.5
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
211
Fig. 5. Total predicted and actual CWR of Acala cotton.
Examination of the 10-year moving averages of the monthly ET0 values 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. 6. 10-year moving average of mean monthly ET0 for July, August and September (1966±1993) with the
normalized means of the period 1961±1990.
212
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
Fig. 7. 10-year moving average of mean monthly vapor pressure de®cit for July, August and September (1966±
1993).
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 ET0 means 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 and Kc values.
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 ET0 and Kc was found to be better than
Farbrother method that uses Penman E0 and Kf in the estimation of Acala cotton CWR
under arid conditions in the Gezira scheme. The former method overestimated the total
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
213
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 of Kc values
would allow for the utilization of the recommended method in the arid and semiarid region of the whole central clay plain. This is very useful especially when the
calculation of site-specific Kc is 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.
References
Adam, H.S., 1984. On the wind function in the Penman formula. In: F.O.A. Bailey (Ed.), Conference on Water
Distribution in Sudanese Irrigated Agriculture, pp. 53±58.
Adam, H.S., Farbrother, H.G., 1977. Crop-water use in irrigated and rainfed agriculture in the Democratic
Republic of Sudan. United Nations Water Conference, Mar del plata, Argentina. E/CONF. 70/TP 29. 20
January 1977, pp. 1±25.
Ahmed, S.A.H., Ahmed, K.E., 1989. Evapotranspiration in Sudan Gezira irrigation scheme. J. Irrigation
Drainage Eng. 115 (6), 1018±1033.
Ibrahim, A.A., Stigter, C.J., Ali, M.A., Hussein, S.A., Van Rheenen, W., 1999. On-farm sampling density and
correction requirements for soil moisture determination in irrigated heavy clay soils in the Gezira, Central
Sudan. Agric. Water Mgmt. 41, 93.
Allen, R.G., Smith, M., Perrier, A., Pereira, L.S., 1994. An update for the de®nition of reference
evapotranspiration. ICID Bull. 43 (2), 1±92.
Doorenbos, J., Pruitt, W.O., 1977. Guidelines for predicting crop water requirements. FAO irrigation and
drainage paper no. 24. Food and Agriculture Organization of the United Nations, Rome, pp. 15±29, 112±
115.
Doorenbos, J., Kassam, A.H., 1979. Yield response to water. FAO irrigation and drainage paper No. 33. Food
and Agriculture Organisation of the United Nations, Rome, pp. 19±36.
Elawad, O.M.A., 1991. Multicriterion approach to the evaluation of irrigation systems performance. Ph.D.
Thesis, University of Newcastle upon Tyne, UK.
Fadl, O.A., 1978. Evapotranspiration measured by a neutron probe on Sudan Gezira vertisols. Exp. Agric. 14,
341±347.
Fadl, O.A., 1987. Water use of Acala cotton. Annual report 1978±1979. Gezira Research Station, Wad Medani,
Sudan, pp. 143±147.
Farbrother, H.G., 1970. Irrigation practices on Gezira clay-rates and intervals. Gezira miscellaneous paper no.
94. Gezira Research Station, Wad Medani, Sudan.
Farbrother, H.G., 1979. Water requirements of crops in the Gezira. Annual report 1972±1973. Gezira Research
Station, Wad Medani, Sudan, pp. 39±65.
Farbrother, H.G., 1984. Modernization of indenting in the Gezira. In: Fadl, O.A., Charles, R.B., Conference on
Water Distribution in Sudanese Irrigated Agriculture, pp. 78±93.
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Ibrahim, A.M., 1984. Concepts of design and practice for irrigation distribution system in Sudan. In: Fadl, O.A.,
Charles, R.B., Conference on Water Distribution in Sudanese Irrigated Agriculture, pp. 107±116.
Mohamed, H.A., 1998. Rainfall in the Sudan: trend and agricultural implications. Sudan Journal of Agricultural
Research, 1, pp. 45±48.
Penman, H.L., 1948. Natural evaporation from open water, bare soil and grass. Proc. R. Soc. London A 193,
120±146.
Penman, H.L., 1956. Evaporation: an introductory survey. Neth. J. Agr. Sci. 4, 9±29.
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 ET0 during 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 requirements; Crop factors; Crop coef®cients; Acala cotton; Gezira scheme
*
Corresponding author.
E-mail address: hadi@ans.ans.kobe-u.ac.jp (A.W. Abdelhadi)
0378-3774/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 3 7 7 4 ( 9 9 ) 0 0 0 7 7 - 3
204
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
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 m3 haÿ1 per 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 ET0 of
a hypothetical grass. The Penman±Monteith equation with its new definition of ET0 is
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 of Kc 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.
The Gezira scheme is shown together with the major irrigation schemes on the Blue
Nile in Fig. 1. The climate of the region is arid and continental with low average annual
precipitation (472 mm at Sennar dam and 160 mm near Khartoum). The rainy season is
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
205
Fig. 1. Major irrigation schemes of the Blue Nile dominated by the Gezira scheme.
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 6 109±7 109 m3. 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
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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 ET0 values 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 relevant E0 normalized 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
E0
DRn g ea ÿ ed f u
;
Dg
(1)
where E0 is the Penman evaporation (mm per day) from open water, D the slope of the
saturation vapor pressure (kPa 8Cÿ1), Rn the net solar radiation (mm per day), g the
psychrometric constant (kPa 8Cÿ1), ea the saturation vapor pressure at mean temperature
(kPa), ed the mean actual vapor pressure (kPa), and f(u) is the wind function suggested by
Penman (1956), where u is the wind speed (m sÿ1) at 2 m height. For the calculation of
Penman±Monteith ET0 monthly 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 ET0 values 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 of Kc for Acala cotton
The guideline for the calculation of the crop coefficient presented by Doorenbos and
Pruitt (1977) was followed to calculate the crop coefficients (Kc) of Acala cotton varieties
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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
Adopted
Initial
Crop development
Mid-season
Late-season
Total
25
40
45
40
150
Farbrother
15
60
29
46
150
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 the Kc or Kf 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 Kc curve 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
mean Kf values. According to Doorenbos and Pruitt (1977) the initial Kc for 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 the Kc values obtained by this method will be referred to as the
derived Kc.
On the other hand, Ahmed and Ahmed (1989) citing Doorenbos and Kassam (1979)
presented Kc values of Acala cotton termed the basal Kc values. The resulting 10-day
means of the derived Kc are shown together with the 10-day means of Kf and basal Kc of
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 (derived Kc
and basal Kc) and crop factors were used to calculate Acala cotton CWR using the
following equations:
(2)
ETp Kf E0 ;
ETp Kc ET0 ;
(3)
where ETp is the predicted CWR in mm per day, E0 and ET0 are 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
basal Kc values were used in Eq. (3).
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A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
Fig. 2. 10-day mean derived and basal Kc and Kf of Acala cotton.
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 of E0 values 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 ET0 values 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 E0 and
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
209
Fig. 3. Mean monthly predicted and actual CWR of Acala cotton.
mean monthly ET0 values during the time of the experiment were used. Fig. 3 shows that
Penman±Monteith ET0 combined with the derived Kc and the basal Kc values were more
close to the actual values during the initial and development stages when compared with
the E0 combined with Farbrother Kf values. 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 10day period by 0.9%, while the recommended method underestimation were 7.9% and
11.5% when the basal and derived Kc values 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
basal Kc values) was better than Farbrother method in all the criteria. This means that
accurate estimates of ET can be obtained using Penman±Monteith ET0 combined 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
derived Kc values, while the use of the derived Kc values was ranked first in terms of the
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A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
Fig. 4. 10-day mean 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 estimate Kc values under arid conditions. It is of vital
importance for regions where the Penman±Monteith method was not adopted and the
determination of field-measured Kc 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.
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 (%)
Kf E0
Basal Kc ET0
Derived Kc ET0
1.15
0.59
0.89
0.60
0.94
0.86
1.15
1.11
1.04
120.0
103.4
102.5
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
211
Fig. 5. Total predicted and actual CWR of Acala cotton.
Examination of the 10-year moving averages of the monthly ET0 values 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. 6. 10-year moving average of mean monthly ET0 for July, August and September (1966±1993) with the
normalized means of the period 1961±1990.
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A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
Fig. 7. 10-year moving average of mean monthly vapor pressure de®cit for July, August and September (1966±
1993).
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 ET0 means 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 and Kc values.
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 ET0 and Kc was found to be better than
Farbrother method that uses Penman E0 and Kf in the estimation of Acala cotton CWR
under arid conditions in the Gezira scheme. The former method overestimated the total
A.W. Abdelhadi et al. / Agricultural Water Management 45 (2000) 203±214
213
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 of Kc values
would allow for the utilization of the recommended method in the arid and semiarid region of the whole central clay plain. This is very useful especially when the
calculation of site-specific Kc is 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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