MANAGING WATER PRODUCTIVITY IN SEMI-ARID AREAS
Heping Zhang
CSIRO Plant Industry
Private Bag 5, Wembley 6913, Australia
Abstract
Water is the major factor limiting crop production in many regions of the world. Improving
water productivity is urgently needed in water scarce dry areas. This paper outlines crop water
production functions and water productivity. Using the data from Syria, North China Plain, and
Oregon, US, this paper developed crop water production functions from which the water
productivity was derived. The results show that after an initial sharp increase, water productivity
reaches its maximum at a given amount of supplied water to plant and then decreases or remains
at a relative high level with further increasing water supply. This paper demonstrates that deficit
irrigation produces higher overall grain yield with the same amount of water resources compared
with full irrigation and therefore has higher water productivity. Deficit irrigation can be
considered as a key strategy for increasing on-farm water productivity in water scarce dry areas.
The risk with deficit irrigation can be minimised through proper irrigation scheduling (when and
how much to irrigate) and avoiding water stress in water-stress sensitive stages.
This paper also illustrated that a regional database of precipitation, irrigation, and yield for a
region in North China Plain was developed using a Geographic Information System (GIS) to
calculate regional water productivity of winter wheat and summer corn by dividing grain yield
by water available to the crops. For both wheat and corn, there were strong spatial as well as
temporal variations in the productivity of water.
Water scarcity is a real threat to food production for millions of people in arid and semi-arid
areas. As world population continues to grow, the area of arable land area per capita will
decrease. Future population will need to be fed from higher food production per unit land area.
The FAO (1988) estimated that almost two-third of the increase in crop production needed in the
upcoming decades must come from an increased yield per unit land areas. Thus, for improving
food production, rainfall and irrigation water have to be used more efficiently. Improving water
productivity by producing more food with less water is essential for future food production and
sustainable agriculture.
This paper developed crop water production functions from irrigation experiments in Syria,
North China Plain. From these functions, on-farm water productivity is derived and relation of
water productivity to applied water is analysed. This paper demonstrated that deficit irrigation
produces higher overall grain yield with the same amount of water resources compared with full
irrigation and therefore has higher water productivity. Deficit irrigation can be considered as a
key strategy for increasing on-farm water productivity in water scarce dry areas. The risk with
deficit irrigation can be minimised through proper irrigation scheduling (when and how much to
1
irrigate) and avoiding water stress in water-stress sensitive stages. In addition, this paper
illustrated that a regional database of precipitation, irrigation, and yield for a region in North
China Plain was developed using a Geographic Information System (GIS) to calculate regional
water productivity.
Theory of crop water production function
The relationship between crop production and water received is called as crop water production
function. According to Vaux and Pruit (1983), research aimed at illustrating this function can be
categorized into three groups by various notions of a desirable level of water use: (1) The work
of agronomists and other production-oriented scientists is frequently directed at the goal of
establishing the level of water inputs necessary to achieve maximum yield per unit land. (2)
Desirability of irrigation engineers whose goal is to maximise water use efficiency. (3) Another
definition of desirable levels of water use is advanced by economists who argued that water, to
be used efficiently, should be applied up to the point where the price of the last unit of water
applied is just equal to the revenue obtained as a result of its application. A simple model of
production can be used to demonstrate these three various goals and these three goals are
presented in Figure 1.
A production function in which crop production (Y) is a function of the amount of water
received by the crop in terms of rainfall (P) and irrigation (I) can be defined as follows:
Y  f ( P, I )
(1)
The average production Y which is output divided by input, can be written as
Y  Y /( P  I )
(2)
The marginal production is defined as the change in production associated with the addition of
one unit input. It can be written as

(3)
Y  Y / ( P  I )
The maximum production is achieved when the marginal production is equal to zero. Maximum
water use efficiency requires that the derivative of the average productivity be to zero,
( P  I ) 1[Y / ( P  I )  (Y /( P  I )]  0
(4)
Equation (4) shows that as long as some quantity of water is applied, water use efficiency is
maximized where it is equal to the marginal production.
2
8000
25.0
Marginal WP
Average WP
20.0
6000
15.0
4000
10.0
5.0
2000
Average or marginal
productivity (kg/m3)
Crop production (kg/ha)
Yield
0.0
0
-5.0
250
350
450
550
650
750
Rainfall + Irrigation (mm)
Figure 1. Relation of crop production, water productivity and marginal water productivity to
water supply to crop
Case studies of crop water production functions
Crop water production functions for wheat were derived from supplemental irrigation
experiments conducted in Syria (Zhang and Oweis, 1999), North China Plain (Zhang et al.,
1999) and Oregon state, US (English and Nakamura, 1989) (Figure 2ad). The quadratic
production function was used to describe the response of crop production to total applied water
Y  b0  b1 ( P  I )  b2 ( P  I ) 2
(5)
where Y is grain yield (kg/ha), I the irrigation water (mm), P the precipitation (mm) during the
growing season, and b0, b1 and b2 the regression coefficients. The response of yield to total
applied water showed very similar characteristics for wheat at all three locations. Yield linearly
increases with increasing water supply initially. As water supply increases further, yield shows a
plateau and finally approached the maximum. Unlike wheat crop, the response of chickpea and
lentil to total amount of water received in northern Syria is linear (Figure 2ef).
On-farm water productivity
The average water productivity is estimated by dividing crop yield by total applied water
(rainfall plus irrigation) following Molden (1997). Figure 3 shows the relationship between water
productivity and the level of water application for wheat crop in northern Syria, North China
Plain and Oregon, US, for chickpea and lentil in northern Syria. The crop production functions in
Figure 2 were used to derive the water productivity. For wheat crop, WP from three locations
representing different climate conditions increases sharply at low water supply level and reaches
a maximum at certain level of water supply. After the maximum WP, WP shows either a steady
value or a decrease with increasing water supply, depending on the response of yield to water.
The level of water application at the maximum WP is considerable different for the three
locations. Most productive use of water is reached with about 440500 mm of water supply level
(140180 mm irrigation) in northern Syria, 400 mm (120160 mm irrigation) in North China
3
Plain, and 750850 mm (350450 mm irrigation) in Oregon, US. For grain legume crops in
northern Syria, WP gradually increases with increasing water supply and reaches a plateau at a
maximum WP. The maximum WP is about 0.5 kg m-3 for chickpea and 0.4 kg m-3 for lentil.
Significant differences in water productivity may occur between crops. In north Syria, wheat
crop has water productivity (1 kg m-3) twice as much as grain legume crops (0.40.5 kg m-3)
(Zhang and Oweis, 1999; Zhang et al. 2000). Wheat crop has similar water productivity to corn
in North China Plain (Mcvicar et al. 2001). Although the three experiments represent very
different climatic conditions, the maximum WP for wheat crop is about 11.2 kg m-3. Rice has
relative low water productivity of about 0.370.68 kg m-3 (Tuong and Bhuiyan, 1999). Corn has
relative high water productivity of about 1.21.5 kg m-3 (Howell, 2001). Water productivity of
0.4 kg/m3 was reported for cotton (Droogers et al., 2000).
Regional water productivity
A considerable of research work has been done on on-farm water use efficiency. However, little
attention has been given to water use efficiency or water productivity at basin and regional level
due to difficulties in quantifying crop production and water usage in spatial scale. Drooges and
Kite (2001) used a hydrological model to obtain the water balance components for the Gediz
Basin in western Turkey and calculated the productivity of water at field, irrigation scheme, and
basin scales. In a project funded by Australian Center for International Agricultural Research,
McViar et al. (2000) established regional database of precipitation, irrigation, and yield for a
region in North China Plain using a Geographic Information System (GIS) to calculate
agricultural productivity of water for both winter wheat and summer corn. The authors used an
‘inputoutput’ definition of regional agricultural water productivity.
4
10
12
10
a
2
y = -3E-05x + 0.0378x - 6.4335
R2 = 0.84
8
y = -2E-05x2 + 0.0329x - 5.8556
R2 = 0.87
8
y = -1E-05x2 + 0.0329x - 9.2699
R2 = 0.92
b
10
c
8
6
6
6
4
4
4
2
2
Syria: Durum wheat
Crop yield (t/ha)
Syria: Bread wheat
0
0
0
200
400
600
8
0
0
800
200
400
600
800
1000
6
d
0
200
400
600
800
800
1000
1200
f
y = 0.0052x - 0.54
R2 = 0.7094
3
2
2
1
1
0
0
600
Syria: Chickpea
y = 0.0061x - 0.715
R2 = 0.609
3
China
Wheat
2
e
Syria: lentil
4
400
4
4
y = -3E-05x2 + 0.0296x - 2.313
R2 = 0.77
Wheat, Oregon, US
2
0
0
200
400
600
800
0
200
Water supplied to crops (P+I, mm)
Figure 2. Crop production functions for wheat in China, Oragon, US, and Syria and for Chickpea and lentil in Syria.
5
400
600
800
1.20
1.20
1.00
1.00
0.80
0.80
0.60
Water productivity (kg/m3)
0.60
0.40
0.40
Bread wheat
Durum wheat
0.20
0.00
200
400
600
0.20
0.00
200
800
1.20
0.60
1.00
0.50
0.80
0.40
0.60
0.30
0.40
0.20
Wheat in China
0.20
Wheat in Oregon
400
600
800
1200
Chickpea
Lentil
0.10
0.00
1000
0.00
0
200
400
600
800
0
200
400
600
800
Water supplied to crops (P+I, mm)
Figure 3. Water productivity for wheat and legumes from Figure 2.
The input is the water available over the crop-growing season and the output is grain yield. The
base unit of the region is the administrative county, which is the smallest geographic resolution
that the available dataset such as grain yield and water resources covered. Regional databases of
precipitation (P), irrigation (I), pre-sowing available soil water (Wo) and yield (Y) from 1984 to
1996 were established in a Geographic Information System (GIS) to calculate water productivity
of winter wheat and summer corn on a county basis (Figures 4 and 5). For 49 counties over 11
years, the average WP was 0.96 kg/m3 (3.8 kg/m3) for wheat and 0.95 kg/m3 (5.1 kg/m3) for
corn (Figure 6). For both wheat and corn, there are strong spatial variations in the productivity of
water. Crop yield and WP in the western counties were higher than those in the east. This is
primarily due to the irrigation water quality and the soil conditions in the west being more
favourable than the east.
6
WP
(kg/m3)
Y_wheat
(kg/ha)
P_wheat
(mm)
I_wheat
(mm)
1984
1984
1984
1984
1984
1996
1996
1996
1996
1996
1
40
380
(kg/m3)
Wo_wheat
(mm)
9000
(kg/ha)
0
900
(mm)
Figure 4. Wheat growing season WP (kg/m3), and its components: yield (Y_wheat kg/ha), growing
season rainfall (P_wheat, mm), irrigation (I_wheat, mm) and pre-sowing available soil water (Wo_wheat,
mm) annually for 1984 and 1996 (Adopted from McVicar et al. 2000).
WP
(kg/m3)
Y_corn
(kg/ha)
P_corn
(mm)
I_corn
(mm)
1984
1984
1984
1984
1996
1996
1996
1996
0.1
4.0
(kg/m3)
380
9000
(kg/ha)
0
900
(mm)
7
Figure 5. Corn growing season WP (kg/m3), and its components: yield (Y_wheat kg/ha), growing
season rainfall (P_wheat, mm), and irrigation (I_wheat, mm) annually for 1984 and 1996 (Adopted
from McVicar et al. 2000).
Wheat
Corn
3.5
20
(kg/m3)
(a) Mean
(b) Mean
1
8
(kg/m3)
(c) Std
(d) Std
Figure 6. County mean WP for both wheat (a) and corn (b) and their standard deviation (c and d)
(Adopted from McVicar et al. 2000).
Deficit irrigationan efficient way to increase water productivity
Increasing productivity of water in agriculture can be achieved by producing more agriculture
output with the same amount of water resources to crops. Many irrigation experiments involving
different irrigation levels showed that deficit irrigation usually has higher WP than full irrigation.
For example, 2/3 of full irrigation increases WP by 1928% for wheat crop and 8% for corn
(Table 1). Using the principle developed by English and Raja (1996) and Zhang and Oweis
(1999), we can derive different irrigation scenarios. Two of most important scenarios are those
for maximizing production (If) and maximizing farmers’ net profit under limited water resources
conditions (Id). The scenario for maximizing production is referred as full irrigation and the other
scenario that its water supply level is less than If is defined as deficit irrigation. The production,
water application, water productivity for these two scenarios is presented in Table 2 for wheat
and in Syria and Oregon, US, and maize in Zimbabwe. With the same amount of water available
to the crops, Id scenarios can improve the water productivity by 1220% for wheat.
8
Table 1 Comparison of water productivity of irrigation levels for wheat and corn
Irrigation level
Full
67%
33%
0
Yield
WP
(t/ha)
(kg/m3)
Wheat, Texas, US
4.76
0.64
4.74
0.76
3.88
0.80
2.19
0.61
Yield
WP
(t/ha)
(kg/m3)
Wheat, Syria
5.79
0.93
5.24
1.19
5.15
0.99
3.27
0.93
Yield
WP
(t/ha)
(kg/m3)
Corn, Texas, US ¶
13.95
1.42
11.36
1.53
6.62
1.21
1.36
0.43
 From Schneider and Howell (1996).
¶ From Howell et al. (1997).
Table 2 Scenario analysis of total production and water productivity at full (If) and deficit (Id)
irrigation
Irrigation Water
Yield Area
Total
WP
¶
scenarios
applied
irrigated
yield
(I)
(Y)
(A)
(mm)
(t/ha) (ha)
(t)
(kg/m3)
Wheat, Syria
Full
330
6.4
1.00
9.8
0.94
Deficit
160
5.6
2.06
11.8
1.12
Wheat, Oregon, US
Full
740
9.9
1.00
11.8
0.88
Deficit
520
9.2
1.43
13.3
0.98
Maize, Zimbabwe
Full
525
6.0
1.00
Deficit
215
4.1
2.44
10.1
¶ For full irrigation scenarios, total yield = Af × Yf + (Ad – Af ) × Yrainfed; For deficit irrigation scenarios, total yield =
Ad × Yd, where subscripts f and d represent full and deficit irrigation, respectively.
 For full irrigation scenarios. WP = Total yield /[If × Af + Rainfall × (Ad – Af )]; For deficit irrigation scenarios,
WP=Total yield/[(Id +rainfall) ×Ad].
The risk with deficit irrigation is usually low because the response curve of crop yield to water
supply has a wide plateau (Figure 2). Zhang and Oweis (1999) reported that Ww strategy can
save irrigation water by 4070% with a grain yield loss of only 13%. Similarly, English and Raja
(1996) reported that deficit averaging 64% were found to be economically equivalent to full
irrigation in the water limiting cases, and deficits averaging 30% were found to be equivalent to
full irrigation in the land-limiting cases. If the saved water resources are allocated to other
cropped areas, the total production and water productivity can be increased as indicated in Table
2. However, information is needed to guide farmers when and how much to irrigation with
deficit irrigation in order to reduce the unwanted effect of water stress on crop yield. Using
Jensen’s (1968) model, the sensitivity indexes ( values) of crop to water stress at different crop
growth stages were quantified for wheat in northern Syria (Zhang and Oweis, 1999) and in North
China Plain (Zhang et al. 1999). These authors concluded that most sensitive stages to water
stress for wheat crop are from stem-elongation to grain-filling stage (Figure 7). The variation of
 values indicates that crop grain yield depends not only on the total water use during the
growing season, but also on water use during different growth stages. For example, 40% deficit
in evaporation during the period from heading to milking reduced grain yield by 15% for winter
wheat in North China Plain, while this deficit in ET during the period from winter freezing to
9
reviving reduced grain yield by only 3%. Similarly, 40% deficit in ET during period of stem
elongation to grain-filling period reduces yield by 1520% for spring wheat in northern Syria,
while this deficit in ET at seedling stage and late grain-filling stage hardly affect the grain yield.
(a) North China Plain: winter wheat
0.4
(b) Northern Syria: spring wheat
0.4
Gaocheng
Bread wheat
0.3
Sensitivity index
Sensitivity index
Luancheng
Nanpi
0.2
0.1
0
Durum wheat
0.3
0.2
0.1
0
1
2
3
4
5
Growth stages
6
1
2 3 4 5
Growth stage
Figure 7. Sensitivity indexes ( value) of wheat to water stress during individual growing periods at three locations
in North China Plain (a) and in Northern Syria (b). The growth stages 1 to 6 represent sowing to tillering,
overwintering, reviving to stem elongation, stem elongation to heading, heading to grain filling, grain filling to
maturity for winter wheat in North China Plain. The growth stages 1 to 5 represent seedling, stem elongation to
booting, booting to anthesis, anthesis to soft dough, and soft dough to maturity for spring wheat in northern Syria.
Water stress sensitivity indexes have an important implication for irrigation scheduling, in
particular for deficit irrigation. Since water stress during growth stages with high  values has
much greater effect on final yield, irrigation to prevent stress during these stages would be
advisable and consequently higher WP could be achieved, especially in the areas where water
resources are limited. Based on the production functions and water productivity analysis, an
optimal irrigation scheduling for wheat crop in North China Plain and northern Syria is proposed
in Table 3.
10
Table 3 Amount (mm) and timing of supplemental irrigation for high water
productivity under different rainfall conditions
Rainfall
Northern Syria
North China
Plain
(mm)
250
Deficit
irrigation
(mm)
160260
300
350
400
110210
60160
0110
80
160240
120
160
120180
100160
Time of irrigation
Stem elongation, booting, flowering and grain
filling
Stem elongation, flowering and/or grain filling
Flowering and/or grain filling
Grain filling
Stem elongation, booting, flowering and grain
filling
Stem elongation, flowering and grain filling
Stem elongation, and flowering
Conclusions
This paper concludes that deficit irrigation has higher water productivity and can be
used for improving water productivity in semi-arid area. Deficit irrigation requires
more control over the amount and timing of water application than full irrigation
practice. Information on when and how much to irrigate is needed in order to reduce
unwanted effect of water stress on production. With established crop water production
functions and the sensitive stages of crop to water stress, optimal deficit irrigation can
be scheduled with a minimum yield reduction compared with full irrigation and
therefore limited water resources can be utilized more efficiently. In addition, the
established crop production functions make it possible to solve the problem of
allocation of limited water resources between crops where crops compete for limited
available water in dry areas.
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