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Model for optimal cropping patterns within the farm based on crop water production functions and irrigation uniformity II: A case study of irrigation scheduling in Albacete, Spain
Agricultural watermanagement ELSEVIER
Agricultural
Water Management
3 1 ( 1996) 145- 163
Model for optimal cropping patterns within the farm based on crop water production functions and irrigation uniformity II: A case study of irrigation scheduling in Albacete, Spain J.M. Tarjuelo Department
*, J.A. de Juan, M. Valiente, P. Garcia
oj’Plant Production and Agrarian Technology, School of Agricultural Engineering, Muncha Uniuersity, Ctra. de Las Peiias, Km. 3.2, 02071 Alhacete, Spain Received
Castillu-La
I March 1995; accepted 25 August 1995
Abstract A model has been developed to determine optimal irrigation strategies for a single season. Application of the model to a case study is presented and then analysed to illustrate the use of the technique and to develop some general guidelines. The multiple results prove that the normal strategy of adopting a single value to the ‘gross water depth applied/water depth needed’ which depends on the irrigation system is not acceptable. This is because agronomic and economic factors should also be taken into account, plus the volume of available water on the farm and the price per cubic metre of water placed in the field. Keywords:
Irrigation;
Water requirements;
Farm management;
Crop rotation;
Crop-water
use; Economic
1. Introduction Castilla-La Mancha, the third largest region in Spain with 80000 km2, has only 20 inhabitants km-* in contrast to the national average of 70 inhabitants km-*, thus making it one of the least populated regions in the country. In spite of favourable conditions relating to topography, soils and water availability, (Castilla-La Mancha
’ Corresponding
author.
0378-3774/96/$15.00 SSDI 037%3774(95)0
0 1996 Elsevier Science B.V. All rights reserved 1220-6
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being the source of important Iberian rivers such as the Tajo, Guadiana and the J&car), the regional irrigated surface is only 7% of the total cultivated surface, a figure which is below the national average of 14% and very much below the average of other neighbouring regions such as Valencia or Murcia. In general, the climatic conditions of Castilla-La Mancha can be defined as appropriate to a Mediterranean climate, with continental degradation, noticeable fluctuations in daily and seasonal temperatures and an unequal distribution of scant rains. According to Kiippen’s weather classification, the major part of the region is adapted to the Csa, climate, but an extensive area in the province of Albacete shows a Bs, climate, steppic with rainfall under 400 mm, cold winters (under 6°C) and hot summers (more than 24°C). Water is a highly limiting factor in all means of production since Castilla-La Mancha is an arid region with a mean annual rainfall of 370 mm and with frequent and intense periods of drought, thus making unirrigated crops hardly profitable. For this reason, one of the permanent and most important objectives of the regional government’s farming policy is to promote the transformation and upgrading of irrigation fields. The production systems set up in irrigated fields of Castilla-La Mancha require high volumes of seasonal irrigation water and are quite sensitive to hydric restrictions. The repeated droughts of recent years and the growth in the diverse uses of water now question both newly created irrigation systems and also the older systems for irrigating mainly corn and barley. A few years ago, an additional worry arose due to the new Community Agriculture Policy (CAP), which produced a radical change in philosophy directly affecting farmers. The CAP fundamentally modifies classic economic reasoning, up to the point that farmers are unsure of what they can produce and for how long, especially when they must increase their investments in irrigation systems. Knowledge of when irrigation is needed and of the likely response of crop yields to irrigation is desirable for both irrigation scheme planners and farm managers. Irrigation scheme planners need such information to estimate the likely demand for water and to carry out economic analyses of proposed irrigation schemes. Farm managers also need this information in order to maximize returns from available irrigation water. Computer programs can be good tools in solving these problems. A method of analysing decision making in irrigated agriculture is through the development of an adequate model of a farmer’s planning process. With a good model the farmer can apply the latest information to his/her specific needs and conditions to find the biologically and economically optimal levels of available irrigation water. A computer model for on-farm irrigation system planning has been developed by the Department of Plant Production and Agrarian Technology, University of Castilla-La Mancha, Spain. A detail description of the model is provided by De Juan et al. (1996). The model consists of an assembly of submodels (see Figs. I-3) so that it can be executed on a microcomputer with Windows 3.1 or posterior with 4 MB or more of RAM memory. A small prototype was first programmed and then given to the experts in the field (agronomist) for evaluation. The model was developed according to the results of this evaluation. This cycle was repeated several times improving and expanding the model each time.
J.M. Tarjuelo et al./Agricultural
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147
Lrl START
4 CLIMATE DATA
.
I ...___ E!6fEEl.._ :...: “‘.....“““I’ i iGrowing Cycle ! ~Soil-Crop Unit : & !Growing Root (GRi) :_:Charaetensnes : i..... .. . m\ i iCfOp Stages (CSi) ... ?.. ....... $ropCoefficient (kCi)i :.. . .r.. .. .... ,_... . .. I
: . ......m=h ... iTotiAv ailable Water (TAW) {RootZone Depth : CW Y..............................
Times Series +-Seasonal Irrigation Water CslWj>
from SIWj= 0 t0 SIWj = SIWm
I
x
I
SIWj = SIWj + A(SIW)
Maximum Crop Yield
Yield response Factors
4
No
Actual yield yij,C= Yij.t(SIWj)
I
Yes
b
STOP
Fig. I. General submodel.
flow and components
handled
by actual evapotranspiration
and actual crop yield in
first
In the first phase, by means of the schematic illustration of the submodel shown in Fig. 1, the maximum evapotranspiration of crops (crop water requirements for maximum production) in different types of soils is estimated. In order to analyse climatic variability, agroclimatic data over a board period of time is used. Under conditions of
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maximum evapotranspiration, and also for distinct evapotranspiration deficits, the submodel will also give us the net irrigation needs, irrigation schedules, the losses in crop yield and effective rainfall in each type of soil and each year of the climatic series. FAO guidelines were mainly followed in the construction of the submodel (Doorenbos and Pruitt, 1977; Doorenbos and Kassam, 1979). The methods used in the development of the software for reference evapotranspiration (ETr) estimation were FAO-Penman given by Doorenbos and Pruitt (1977) and Penman-Monteith given by Hatfield (1985) and Allen et al. (1989). The actual yield, for each year is determined by Stewart’s formula, expressed in multiplicative form. In the second phase, a new submodel (Fig. 2) incorporates the water distribution function for the irrigation system into Stewart’s production function of a crop in relation to water (Stewart et al., 1977), generating a new function that relates attainable crop production with the water application uniformity by irrigation system in the field (Orgaz et al., 1992; Mantovani, 1993). With this submodel, the effects of water application uniformity on yields for each crop and the irrigation depth needed can be analysed. In order to determine optimum irrigation which leads to highest economic profits, the submodel calculated the gross margin of each crop for different uniformities of water distribution in the irrigation system (CU) and ‘a’ values (fraction of total area which received water in excess of crop water requirements (Hr)). Fixing the water and production prices would allow us to determine the optimum application of irrigation which maximizes the economic returns. This situation does not always coincide with maximum production. In the third phase, by mean of the schematic illustration of the submodel shown in Fig. 3, the model provides a procedure by which farms could evaluate and compare alternative assumptions on expected water regimes for the coming year in order to optimize crop rotations, crop production, and farm resources. The fundamental objective of this paper is describe the application of the model and nature of the results.
2. Example
application
The model was applied to the case of farm rehabilitation so as to evaluate and demonstrate its use. The farm used consists of approximately 300 ha located near Albacete, Castilla-La Mancha, Spain. The irrigable area is divided into three areas, each equipped with buried fixed sprinkler systems of 18 m X 18 m spacing. Two-nozzle sprinklers (4.8 + 2.4 mm) operating at 350 kPa were employed. This irrigable perimeter contains soil with a loamy and a loam-clay-sand texture, a depth of 1.2 m and a water-retention capacity of 1.1 mm cm- ’. Two crops were rotated on this farm: corn being cultivated on 84% of the area and barley on the remaining 16%. The crops selected to test the model were: barley, proteaginous pea, oleaginous sunflower, corn and sugar-beet. These crops are in harmony with the tendencies observed during the last two harvests. The basic data is shown in Table 1. Since decisions had to be made before the beginning of the 1994 season, it was
J.M. Tarjuelo et ul./Agricultural
t ECONOMIC DATA Ps = sale price of yield S = subvention C, = cost of production varying with crop yield pw = price of water
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4 Soil-Crop Unit Characteristics (Ui)
31 (1996) 145-163
149
4 CLIMATE DATA Maximum ET Crop @Tmi.J Efective Precipitation (EPS
I-
I Water that represents the contributions different to the irrigation @j,J
v Maximum crop water requeriment (Hr~J
Sprinkler irrigation equipment: * Funtion of normal distribution (ak)
Applied depth/Required
depth
oIbm)i)ij.kr r Fraction of area fully irrigated (aij.k_t)
Gross depth applied
+iisqz$w Bij.k
Fig. 2. General flow and component
= (psi
yij.k
+ Si)-
handled of optimal irrigation
(CIi yi.k+ Hbaij,kb)
depth according
to the second submodel.
J.M. Turjuelo et ul./Agricultural
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i=l * 0 iAi,t <&
(SW *
Fig. 3. General flow and component
Inigable area CL41
handled by optimal crop rotation in third submodel.
decided that an analysis of climatic variability over the last 20 years (1974- 1993) would be made to analyse the risks, using data registered at the Los Llanos meteorological station, located near the farm in question. Fig. 4 shows the interannual variations of the net irrigation requirements under maximum crop evapotranspiration (ETm) conditions, calculated by means of the first submodel (Fig. 1). These results clearly demonstrate the complexity of trying to predict the irrigation needs of the following year. Since decisions about what crops to cultivate must be based on these predictions, it seems logical to analyse the results both for the
Table 1 Selected crops crops
Barley Protean pea Sunflower Corn Sugar-beet Set aside
Date
sowing
Harvest
15/02 01/02 01/05 24/04 25/03 -
28/06 29/06 15/10 15/11 28/11 _
ETm (mm) a (Aver. year, 1974-93)
Grants CAP b (ECU ha-
393’ 1 432‘4 701’7 881’8 1083’0 _
268 500 1170 350 _ 533
c ;a-
t)
Direct costs d (ECU ha- ‘)
crop price e (ECU t- ‘)
673 737 398 1138 1865
150 180 210 180 60 _
’) 7’0 6’0 5’0 15’0 90’0 _
a ETm = maximum evapotranspiration per average year in the 1974- I993 climatic series. b CAP grants in the central region of the Province of Albacete for 1994. ’ ym = maximum yields reached in the Province of Albacete. d Crop price = average prices obtained by area farmers for the 1993 harvest. I ECU=150pta.
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1 .ooo
900 800 700 600 600 400 300 200 100
ok,,,,,,,,,,,,,,,,,,, 74
75
76
77
78
79
80
81
82
83
84
85
8%
07
88
09
90
91
92
93
MD
YEAR
-
BARLEY
PEA +-SUNFLOWER
Fig. 4. Net irrigation
requirements
-CORN
of crops under maximum
*SUGAR
evapotranspiration
BEET
conditions.
average year and for the humid and dry years, including even the most extreme years. With this information, one will have at least an idea of the limits which affect our decision and the risks that can be run. The difference between the extreme values in barley is 71% of the greatest value, 77% in proteaginous peas, 42% in corn and 29% in sugar-beets. Barley and peas are spring crops, corn and sunflowers are grown in summer, and sugar-beets are spring-summer crops. Assuming that there is no limitation on water availability, we analyzed the effect of two coefficients of uniformity values (CU = 70% and CU = 85%) and three different costs of water (Pw = 10 pta rne3, 17 pta rnm3, 25 pta m- 3> (1 ECU = 150 pta) on the profits of each of the five crops selected. Each crop was dealt with independently by the application of a second submodel (Fig. 2). Table 2 shows the results obtained for the average year in the 1974-1993 climatic cycle. The economic optimum did not correspond to the maximum production goal in any of the cases analysed, as can be observed in columns 6 and 7 of Table 2. rate is reduced in all the For both uniformity coefficients analysed, the Hba/Hr crops when the cost of a cubic metre of water increases (Hba = depth of water applied to ground). Therefore, when water prices are low, the economic optimum is obtained by increasing the irrigation depth to compensate for the water deficits caused by lack of uniformity.
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Table 2 Optimum profits climatic series
depending
crop Barley
Protean pea
Sunflower
Corn
Sugar-beet
70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85
on uniformity
Pw b (ptamm3)
Hha/Hr
10
1’23 1’16 0’73 1’05 0’73 0’70 1’23 1’16 0’78 I’IO 0’78 1’00 0’54 0’75 0’54 0’75 0’47 0’64 1’23 1’16 1’00 1’05 0’78 1’00 1’39 1’23 I’10 I’10 0’84 1’05
10
17 17 25 25 10 IO 17 17 25 25 10 10 17 17 25 25 10 IO 17 17 25 25 10 IO 17 17 25 25
Water Management 31 (1996) 145-163
coefficient =
and water
price.
Average
Cd d
Hhu e (mm)
Y/Ym (%)
t
0’09 0’03 0’30 0’06 0’30 0’30 0’09 0’03 0’26 0’04 0’26 0’08 0’46 0’25 0’46 0’25 0’53 0’36 0’09 0’03 0’15 0’06 0’26 0’08 0’07 0’02 0’12 0’04 0’22 0’06
282 266 166 240 166 161 290 274 183 260 183 235 261 362 261 362 226 308 757 715 614 645 479 614 III9 990 887 887 676 843
93’73 98’04 79’74 96’13 79’74 79’62 94’09 98’15 83’32 97’35 83’32 95’16 69’86 83’60 69’86 83’60 65’20 76’33 92’02 97’50 86’93 95’08 77’48 93’46 94’37 98’42 90’27 96’64 81’91 95’37
year for the 1974-1993
ET,‘ETm (%)
g
94’55 98’29 82’38 96’64 82’38 82’28 94’86 98’39 85’50 97’70 85’50 95’79 68’28 82’74 68’28 82’74 63’37 75’08 93’61 98’00 89’54 96’06 81’98 94’77 94’89 98’56 91’15 96’94 83’56 95’79
OB h (ECU ha- ‘) 535 596 445 479 356 364 962 1033 855 909 757 779 1341 1354 1219 1185 1095 1015 1100 1270 775 953 491 618 2253 2548 1782 2110 1321 I645
a Cci = uniformity coefficient of sprinkler system. b Pw = price of water (1 ECU = 150 pta). ’ Hba/ Hr = relationship between gross depth of water applied and depth of water required. d Cd = deficit coefficient. e Hb = seasonal volume of applied water. f y/ ym = relationship between actual and maximum yields. g ET/ ETm = relationships between actual and maximum evapotranspiration. ’ OB = optimum economic profits.
When water is expensive (2.5 pta mm3), an increase in the optimum rate between the gross depth and the depth required with irrigation uniformity can be observed in most cases. The values of this relation range from 0.64 (sunflower) to 0.84 (sugar-beet) when the value of the uniformity coefficient is high (CU = 85%); and between 0.47 (sunflower) and 0.84 (sugar-beet) when the CU value is low (70%). The same occurs when the price of a cubic metre of water is 17 pta rne3, although with higher values in the
J.M. Tarjuelo et al./Agricultural Table 3 Optimal annual pattern. Average
Water Management 31 (1996) 145-163
year for the 1974- 1993 climatic
1.53
series
Option
CC/ Pw (%I (ptam-‘1
Barley (ha)
Pea (ha)
Sunflower (ha)
Corn (ha)
Sugarbeet (ha)
OB Set aside (ECU ha- ‘) (ha)
Water (m3 ha- ‘)
A C E B D F
7010
_ _ _
108’37 108’37 108’37
108’38 108’38 108’38 108’38 108’38 108’38
108’37 108’37 108’37 -
45’00 45’00 45’00 45’00 45’00 45’00
1427 1201 1037 1549 1277 1061
5356 2934 2581 5375 4968 3226
17 25 8510 17 25
38’25 38’25 38’25 38’25 38’25 38’25
Hba/Hr
relation. This proves that the higher the CU value is, the more water is needed, even though part of the water is lost. This is because the increase in production which results from adequate or excessive irrigation on the major portion of the field makes up for greater water expenditures. The economic optimum is always reduced when the price of a cubic metre of water increases, but, generally speaking, this optimum normally rises along with the CU.
Table 4 Protits for corn crops with distinct amounts of seasonal irrigation Hba/Hr 70
10
70
17
70
25
85
10
85
17
85
25
B = profits corresponding
0’54 0’68 1’00 1’23 0’54 0’68 1’00 0’54 0’64 0’78 0’64 0’73 1’00 1’00 1’16 0’64 0’73 0’84 1’00 1’05 0’64 0’73 0’84 1’00
Cd 0’46
0’33 0’15 0’09 0’46 0’33 0’15 0’46 0’37 0’26 0’36 0’27 0’84 0’08 0’03 0’36 0’27 0’17 0’08 0’06 0’36 0’27 0’17 0’08
333 418 614 757 333 418 614 333 393 479 393 446 517 614 715 393 446 517 614 645 393 446 517 614
to each Hba / Hr restriction.
ET/ETm
Y/Ym (o/o)
(%I
B(I) (ECU ha- ‘)
59’98 71’01 86’93 92’02 59’98 71’01 86’93 5998 67’96 77’48 68’57 76’09 85’06 93’46 97’50 68’57 76’09 85’06 93’46 95’08 68’57 76’09 85’06 93’46
67’99 76’81 89’54 93’61 67’99 76’81 8954 67’99 74l37 81’98 74!85 80’87 88’05 94’77 98’00 74’85 80’87 88’08 94’77 96’06 74’85 80’87 88’08 94l77
673 843 1062 1100 458 648 775 280 388 491 796 956 1078 1232 1270 613 748 837 945 953 403 509 561 618
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The application of the third submodel (Fig. 3) allowed us to select crop rotations that lead to higher profits, depending on the different CU values and Pw for the average year of the climatic series. In addition to the restrictions imposed by the CAP reform for land surface set aside and maximum surface for sunflower, the sugar-beet quota for each farm can vary from 0 to 15% of the irrigable perimeter. First of all we have determined the crop rotations that give the best economic returns, with no water restrictions, for the different combinations of CU and Pw values (Table 3). In a similar situation, where available water is not a limiting factor, the most profitable crop rotations include sugar-beet (with its maximum quotas), oleaginous sunflower and corn or proteaginous peas. For the same CU values, maximum benefits diminish as Pw increases. Whatever the Pw may be, the highest profits are obtained when CU = 85%, even though these crop rotations require a greater volume of irrigation water. The highest prices per cubic metre of water exclude corn from the crop rotation in favour of a spring crop such as proteaginous peas. Since limitations on water availability can exist on farms, we have begun with the maximum volume of water utilized in crop rotation that will lead to optimum profits without water limitations (as can be seen in Table 3, corresponding to a CU = 85% and a Pw = 10 pta rnm3> and available water has been reduced by different percentages of the maximum volume. Since lack of water on a farm would imply that some crops
Table 5 Yield variation situation
in crops with deficit levels (ET/ETm)
Crop
ET (% ETd
Yield (kg ha-
Barley
100 80 60 40 100 80 60 40 100 80 60 40 100 80 60 40 100 80 60 40
7000 5474 3941 3700 6000 4848 3606 1687 5000 4165 3215 2335 15000 11250 7500 3750 9OQOo 71550 52290 31590
Pea
Sunflower
Corn
Sugar-beet
’)
and direct cost of production Direct cost, excluding 673 594 565 488 737 670 523 498 398 342 295 243 1138 1075 807 739 1865 1773 1153 1109
associated
with each
water (ECU ha- ‘)
J.M. Tarjuelo et al./Agricultural
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31 (1996) 145-163
155
*Seasonal irrigation water (1000 m3)
Fig. 5. Optimum crop rotations with no water limitation but with various water supplies possible for the six combinations of CU and Pw (A, B, ... . F). The figures in parentheses correspond to the relation Hba / Hr and the figures above the bars indicate seasonal volumes of water.
would not receive sufficient irrigation or that the irrigable perimeter would be reduced, different water restriction levels for the five crops have been studied: from the value that gives optimum benefits without water restrictions (Table 2) down to approximately 50% of this value. Taking corn as an example, in Table 4, we can see each of these situations as if it were a different crop when the third submodel is applied, thus determining the crop rotation that produces the highest profits. When managing crops with different levels of hydric deficit, the expected yield will vary. It is therefore logical that production costs will also vary. In Table 5 the variations in yields estimated by the model according to the ET/ETm relation and the direct costs associated with each situation are presented. Fig. 5 shows crop rotations that lead to highest profits when no water limitations exist on farms. When distinct amounts of water are applied to a single crop, we have considered this crop as two different ones, as shown in Table 4 for the six possible combinations between CU and Pw (A, B, . . . . F). In Fig. 5 we can observe the appearance of the same crop with a different Hba/Hr relation, considered as a distinct agricultural activity. The seasonal volumes of irrigation water for each crop are expressed in thousands of cubic metres. The optimum profits for these crop rotations can be seen in Fig. 6.
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Wetter Munugement 31 (19961 145-163
5a) i..__...____ . . _... .~.
Fig. 6. Optimum economic limitations on farms.
benefits of crop rotations for the different
CU and Pw combinations
with no water
*Seasonal irrigation water (1000 m3)
fzj -
Sunaower(O.47)
Fig. 7. Optimum crop rotations when only 60% of fixed maximum
water volume is available.
J.M. Tarjuelo et al./Agricultural
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31 (1996) 14.5-163
157
(1000m3)
Fig. 8. Optimum crop rotations when only 40% of fixed maximum
for water volume is available.
Figs. 7-9 are examples of crop rotations that give maximum profits when only 60%, 40% and 20% of the maximum water volume already mentioned are available on the farm. From the results obtained, we should point out the appearance, within the same crop pattern, of different irrigation programmes for the same crop. The irrigation fields which are set aside also increase when water availability on the farm lessens. In Fig. 10 we can see how optimum benefits (OB) vary in relation to diminishing Note that the OB is water availability for the different ClJ and Pw combinations. greater when CU values are higher, although this ceases to occur when the water availability is reduced past 50% of the maximum volume fixed for the farm. This coincides perfectly with the setting aside of a greater perimeter of irrigable land than the minimum required by the CAP. Fig. 11 shows the variation in seasonal volume of irrigation water with respect to the maximum value (with no water limitations) contrasted to water availability for the distinct crop rotations for different CU and Pw combinations. Likewise, Fig. 12 represents the optimum benefit (OB) variations with water availability for different crop rotations, in distinct Pw and CU combinations. We can gather from Figs. 11 and 12 that neither reference parameter is reduced until water availability is less than the optimum water needs for each of the CU and Pw combinations. It is also apparent that there is a much more rapid descent in OB after a 50% reduction in water availability is reached.
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*Seasonal irrigation water (1000 m3)
A
C
B
F
E
D
Fig. 9. Optimum crop rotations when only 20% of fixed maximum
for water volume is available
80 i 1.
\,”
’ ..&-
0
L -
i.
i-l
0
. ..--I
)_
1~
20
40
--A--_--
..A
60
c--m
-*_
.-_
80
100
WATER AVALAIBLE (%)
Fig. 10. Optimum restrictions.
economic
benefit (OB) for six possible
CL’ and Pw combinations
with varying
water
J.M. Tarjuelo et al./Agricultural
I -t
(A) I CU=70% PA=10
/ r. (B) ICU=M%
PA=10
159
Water Management 31 (1996) 145-163
(C) / CU=70% PA=17
.
(D) / CU=BS% PA=17 -i-
(E) / CU=70% PA=25 (F) I C&85%
PA=25 I
Fig. 11. Variation in seasonal irrigation water (SW) with the lessening of water availability for different CC/ and Pw combinations.
____ _._ 1 I
10
17 Pw (pta*m-3)
25
1 ECU=150 pta m -J m
. ~._____ CU=70% (100%) cuds% (I-) m CU=7@%(40%) cu=tW% (40%) m cu=70% (5%) cu-BJ# (5%)
~~-70% (60%) ic cu=70% (20%) -
~~-85% (M)%) cu-85% (20%)
Fig. 12. UB variations with the reduction of water availability for distinct CC/ and Pw combinations.
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From the global analysis of optimum crop rotations for different levels of water restrictions, the following should be pointed out: - Sugar-beet and oleaginous sunflower are valid for all the solutions with the maximum surface possible, although with application levels which use less water as water availability diminishes. This is especially true for sugar-beet. Both crops begin to disappear only under severely restricted water availability, around 40% of the fixed maximum value. With such low levels, both crops, and especially sugar-beet, are replaced by proteaginous peas. - Corn is a possibility for crop rotations when water is cheap and CU values are high. Corn disappears when water restrictions surpass 25% of available water. * Proteaginous pea as a component of crop rotations is seen more and more as water availability decreases, when water is costly and CU is lower. * Barley, due to its cost-earning structure, did not participate in any of the crop rotations selected. Since barley has an agronomic cycle similar to proteaginous peas, it seems that barley cannot compete with them. * When water restrictions surpass 50% of the maximum fixed volume for a farm, the setting aside of more irrigable land becomes feasible.
3. Conclusions We have developed a model to help the farmer evaluate the effects that lack of sprinkler irrigation uniformity can have on crop productivity. This model also permits the selection of optimum irrigation treatments using a small amount of information which is available to the farmer. In areas where water availability is limited, the model can also aid in evaluating system management strategies, economic returns and sensibilities water availability, fluctuation and cost. The model was applied to a farm in order to evaluate its capacity and method of use. From the results obtained, we can conclude that the higher the uniformity of water application, the greater the economic benefits even though benefits decrease as the price of water goes up. Given the yearly differences in climate, the proposed process guides the farmer in his choice of crop rotations which give maximum profits in relation to water availability, the CU of his irrigation system, and the cost of water placed in the ground and ready to be used by his crop. In addition, the model developed allows a farmer to analyse any crop rotations he wishes, even for different levels of hydric deficit. It can also be used to study optimum utilization in the case of limited water resources for large irrigable zones or for catchment areas. When water availability is unlimited, crop rotations that give agricultural activities the best profits include sugar-beet (with the maximum surface area possible), oleaginous sunflowers and corn. This last crop is substituted by proteaginous peas when the cost of the cubic metre of water rises and the CU of the irrigation system falls. When the volume of available water becomes a limiting factor, the first crop that disappears from the rotation is corn, which is substituted by proteaginous peas. In this
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161
situation, the crop rotations include crops managed with hydric deficit, especially sugar-beet. The best economic results are achieved with the highest CV values, whatever the price of water may be, even though the crop rotations require a higher volume of water for irrigation. The results of this study prove that it is erroneous to use a single gross depth/redepending on the irrigation system, since agronomic and quired depth rate (Hba/Hr) economic factors should also be taken into account, as well as water availability and the price of a cubic metre of water available to a crop. This model, designed with a prototype methodology, has been developed step-by-step on the basis of successive evaluations carried out by agronomic experts. During the elaboration process new information was incorporated and, also as a result of the successive evaluations, the development of the model had to be redirected. The methodology shown in the model allows us to satisfactorily reach the planned objectives, even though a series of limitations can be seen. These, which have already been commented on partially (De Juan et al., 1996) give way to a certain degree of doubt with respect to the results obtained on application. The main limitations are centred around the following points: (1) the empirical nature of the relation between yield and water consumed; (2) doubt as to the crop’s response factor to hydric deficit (ky); (3) with sprinkler irrigation, the uniformity coefficient (CV) not only depends on the irrigation system, but also on wind, a factor which is not taken into account in the methodology indicated and (4) with this method we assume that the gross depth applied each time is such that the deficit coefficient (Cd) is the same for all the irrigation sessions carried out during the crop’s growing season, although obviously this is not always so. The method must be further developed to correct some of its most relevant limitations. For instance, functional simulation models of crops can be developed to determine the doses needed for optimum irrigation. Also, strategies can be established in which the deficit coefficient varies with each irrigation, thus implying a needed knowledge of the impact on production of a Cd variable based on the stage of crop development. Another of the model’s limitations is that there has not been any consideration of risk. Farmers want to maximize returns but simultaneously they also want to minimize risk. Risk in irrigated agriculture with a stochastic supply of water has a multidimensional character.
4. List of symbols a A B B CSb
fraction of total area which received sional) area under cultivation, [L12 benefit per unit area (ECU ha- I> Koppen’s climatic classification Community Agriculture Policy
water in excess
of Hr (nondimen-
162
Cd CP CS Cs,, CU EP ET ETm ETr ET/ETm GR Hb Hba Hr IA Iw IWb kc ky iL1 m N OB OHba P PS Pw Ra RD s SIW SIWm u Y ym
J.M. Turjuelo et al./Agriculturul
Wrrter Management 31 (1996) 145-163
deficit coefficient (nondimensional) crop rotation crop stages Koppen’s climatic classification Christiansen’s coefficient of uniformity (%) effective rainfall during the growing season, [L] crop evapotranspiration, [L] maximum crop evapotranspiration during the growing season, [L] reference evapotranspiration, [L] relative evapotranspiration (nondimensional) growing root, [L] gross water depth applied from irrigation system, [L] depth of water applied to ground (gross dose, Dba), [L] crop water requirements, [Ll irrigable area of farm, [L12 irrigation water, [L13 gross contribution of irrigation during the growing season, [L] crop coefficient (nondimensional) crop or yield response factor (nondimensional) crop number (nondimensional) symbol of long dimension the number of growth stages considered (nondimensional) year number in climatic series (nondimensional) optimum benefit per unit area (ECU ha-’ ) optimum depth of water applied to ground, [L] water that represents the applications distinct to the irrigation during growing season, [L] sale price of yield (ECU t- ’) price of water (ECU me3) application efficiency (nondimensional) root zone depth, [L] subvention (ECU ha- ’> available seasonal irrigation water for the whole area, [L13 maximum available seasonal irrigation water for the whole area, [L13 soil-crop unit characteristics actual yield per unit area (t ha-‘) maximum yield of the crop (t ha-‘)
4.1 .I. Greek symbols variable factor between - 3 y + the participation coefficient of ; according to CAP demands and mensional) ostandard deviation of application A increment
the
3 the crop in relation to the farm surface, /or conditions of another nature (nondidepth
J.M. Tarjuelo et al./Agricultural
4.1.2. i
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31 (1996) 145-163
163
Subscripts
j k 1
max min n P
t
refers to each one of the crops being discussed refers to the different assumptions of seasonal volumes of irrigation interval used for the (Y value between - 3 and + 3 number of crops considered in the study maximum minimum refers to the stage of growth of the crop under consideration period in which water balance in the soil is reached refers to the year in the climatic series considered
water
Acknowledgements The writers wish to thank the Consejeria de Agricultura y Medio Ambiente de la Junta de Comunidades de Castilla-La Mancha for partly funding this research. The authors would like to express their gratitude to the anonymous reviewers for the many good suggestions.
References Allen, R.G., Jensen, M.E., Wright, J.J. and Burman, R.D., 1989. Operational estimates of reference evapotmnspiration. Agron. J., 81: 650-662. De Juan, J.A., Tarjuelo, J.M., Valiente, M. and Garcia, P., 1996. Model for optimal cropping patterns within the farm based on crop water production functions and irrigation uniformity. I: Development of a decision model. Agric. Water Manage., 31: I S-143. Doorenbos, J. and Kassam, A.H., 1979. Yield response to water. Inig. Drain. Pap. 33, FAO, Rome, Italy, 179 PP. Doorenbos, J. and Pruitt, W.O., 1977. Guidelines for predicting crop water requirements. Irrig. Dram. Pap. 24, FAO, Rome, Italy, 144 pp. Hatfield, J.L., 1985. Wheat canopy resistance determined by energy balance techniques. Agron. J., 77: 279-283. Mantovani, E.C., 1993. Desarrollo y evaluacidn de modelos para el manejo de1 riego: estimaci6n de la evapotranspiraci6n y efectos de la uniformidad de aplicacidn de1 riego sobre la producci6n de cultivos. Tesis Doctoral, Universidad de C6rdoba. Andalucia, Espaiia, 184 pp. Orgaz, F., Mateos, L. and Fereres, E., 1992. Season length and cultivar determine the optimum evapotranspiration deficit in cotton. Agron. J., 84: 700-706. Stewart, II., Hagan, R.M., Pruitt, W.O., Hanks, R.J., Riley, J.P., Danilson, R.E., Franklin, W.T. and Jackson, E.B., 1977. Optimizing crop production through control of water and salinity levels. Utah Water Res. Lab. PRWG 1.5 1- 1, September.
Agricultural
Water Management
3 1 ( 1996) 145- 163
Model for optimal cropping patterns within the farm based on crop water production functions and irrigation uniformity II: A case study of irrigation scheduling in Albacete, Spain J.M. Tarjuelo Department
*, J.A. de Juan, M. Valiente, P. Garcia
oj’Plant Production and Agrarian Technology, School of Agricultural Engineering, Muncha Uniuersity, Ctra. de Las Peiias, Km. 3.2, 02071 Alhacete, Spain Received
Castillu-La
I March 1995; accepted 25 August 1995
Abstract A model has been developed to determine optimal irrigation strategies for a single season. Application of the model to a case study is presented and then analysed to illustrate the use of the technique and to develop some general guidelines. The multiple results prove that the normal strategy of adopting a single value to the ‘gross water depth applied/water depth needed’ which depends on the irrigation system is not acceptable. This is because agronomic and economic factors should also be taken into account, plus the volume of available water on the farm and the price per cubic metre of water placed in the field. Keywords:
Irrigation;
Water requirements;
Farm management;
Crop rotation;
Crop-water
use; Economic
1. Introduction Castilla-La Mancha, the third largest region in Spain with 80000 km2, has only 20 inhabitants km-* in contrast to the national average of 70 inhabitants km-*, thus making it one of the least populated regions in the country. In spite of favourable conditions relating to topography, soils and water availability, (Castilla-La Mancha
’ Corresponding
author.
0378-3774/96/$15.00 SSDI 037%3774(95)0
0 1996 Elsevier Science B.V. All rights reserved 1220-6
146
J.M. Tarjudo
et al./Agriculturul
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being the source of important Iberian rivers such as the Tajo, Guadiana and the J&car), the regional irrigated surface is only 7% of the total cultivated surface, a figure which is below the national average of 14% and very much below the average of other neighbouring regions such as Valencia or Murcia. In general, the climatic conditions of Castilla-La Mancha can be defined as appropriate to a Mediterranean climate, with continental degradation, noticeable fluctuations in daily and seasonal temperatures and an unequal distribution of scant rains. According to Kiippen’s weather classification, the major part of the region is adapted to the Csa, climate, but an extensive area in the province of Albacete shows a Bs, climate, steppic with rainfall under 400 mm, cold winters (under 6°C) and hot summers (more than 24°C). Water is a highly limiting factor in all means of production since Castilla-La Mancha is an arid region with a mean annual rainfall of 370 mm and with frequent and intense periods of drought, thus making unirrigated crops hardly profitable. For this reason, one of the permanent and most important objectives of the regional government’s farming policy is to promote the transformation and upgrading of irrigation fields. The production systems set up in irrigated fields of Castilla-La Mancha require high volumes of seasonal irrigation water and are quite sensitive to hydric restrictions. The repeated droughts of recent years and the growth in the diverse uses of water now question both newly created irrigation systems and also the older systems for irrigating mainly corn and barley. A few years ago, an additional worry arose due to the new Community Agriculture Policy (CAP), which produced a radical change in philosophy directly affecting farmers. The CAP fundamentally modifies classic economic reasoning, up to the point that farmers are unsure of what they can produce and for how long, especially when they must increase their investments in irrigation systems. Knowledge of when irrigation is needed and of the likely response of crop yields to irrigation is desirable for both irrigation scheme planners and farm managers. Irrigation scheme planners need such information to estimate the likely demand for water and to carry out economic analyses of proposed irrigation schemes. Farm managers also need this information in order to maximize returns from available irrigation water. Computer programs can be good tools in solving these problems. A method of analysing decision making in irrigated agriculture is through the development of an adequate model of a farmer’s planning process. With a good model the farmer can apply the latest information to his/her specific needs and conditions to find the biologically and economically optimal levels of available irrigation water. A computer model for on-farm irrigation system planning has been developed by the Department of Plant Production and Agrarian Technology, University of Castilla-La Mancha, Spain. A detail description of the model is provided by De Juan et al. (1996). The model consists of an assembly of submodels (see Figs. I-3) so that it can be executed on a microcomputer with Windows 3.1 or posterior with 4 MB or more of RAM memory. A small prototype was first programmed and then given to the experts in the field (agronomist) for evaluation. The model was developed according to the results of this evaluation. This cycle was repeated several times improving and expanding the model each time.
J.M. Tarjuelo et al./Agricultural
Water Management 31 (1996) 145-163
147
Lrl START
4 CLIMATE DATA
.
I ...___ E!6fEEl.._ :...: “‘.....“““I’ i iGrowing Cycle ! ~Soil-Crop Unit : & !Growing Root (GRi) :_:Charaetensnes : i..... .. . m\ i iCfOp Stages (CSi) ... ?.. ....... $ropCoefficient (kCi)i :.. . .r.. .. .... ,_... . .. I
: . ......m=h ... iTotiAv ailable Water (TAW) {RootZone Depth : CW Y..............................
Times Series +-Seasonal Irrigation Water CslWj>
from SIWj= 0 t0 SIWj = SIWm
I
x
I
SIWj = SIWj + A(SIW)
Maximum Crop Yield
Yield response Factors
4
No
Actual yield yij,C= Yij.t(SIWj)
I
Yes
b
STOP
Fig. I. General submodel.
flow and components
handled
by actual evapotranspiration
and actual crop yield in
first
In the first phase, by means of the schematic illustration of the submodel shown in Fig. 1, the maximum evapotranspiration of crops (crop water requirements for maximum production) in different types of soils is estimated. In order to analyse climatic variability, agroclimatic data over a board period of time is used. Under conditions of
148
J.M. Turjuelo et ul./Agriculturul
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31 (1996) 145-163
maximum evapotranspiration, and also for distinct evapotranspiration deficits, the submodel will also give us the net irrigation needs, irrigation schedules, the losses in crop yield and effective rainfall in each type of soil and each year of the climatic series. FAO guidelines were mainly followed in the construction of the submodel (Doorenbos and Pruitt, 1977; Doorenbos and Kassam, 1979). The methods used in the development of the software for reference evapotranspiration (ETr) estimation were FAO-Penman given by Doorenbos and Pruitt (1977) and Penman-Monteith given by Hatfield (1985) and Allen et al. (1989). The actual yield, for each year is determined by Stewart’s formula, expressed in multiplicative form. In the second phase, a new submodel (Fig. 2) incorporates the water distribution function for the irrigation system into Stewart’s production function of a crop in relation to water (Stewart et al., 1977), generating a new function that relates attainable crop production with the water application uniformity by irrigation system in the field (Orgaz et al., 1992; Mantovani, 1993). With this submodel, the effects of water application uniformity on yields for each crop and the irrigation depth needed can be analysed. In order to determine optimum irrigation which leads to highest economic profits, the submodel calculated the gross margin of each crop for different uniformities of water distribution in the irrigation system (CU) and ‘a’ values (fraction of total area which received water in excess of crop water requirements (Hr)). Fixing the water and production prices would allow us to determine the optimum application of irrigation which maximizes the economic returns. This situation does not always coincide with maximum production. In the third phase, by mean of the schematic illustration of the submodel shown in Fig. 3, the model provides a procedure by which farms could evaluate and compare alternative assumptions on expected water regimes for the coming year in order to optimize crop rotations, crop production, and farm resources. The fundamental objective of this paper is describe the application of the model and nature of the results.
2. Example
application
The model was applied to the case of farm rehabilitation so as to evaluate and demonstrate its use. The farm used consists of approximately 300 ha located near Albacete, Castilla-La Mancha, Spain. The irrigable area is divided into three areas, each equipped with buried fixed sprinkler systems of 18 m X 18 m spacing. Two-nozzle sprinklers (4.8 + 2.4 mm) operating at 350 kPa were employed. This irrigable perimeter contains soil with a loamy and a loam-clay-sand texture, a depth of 1.2 m and a water-retention capacity of 1.1 mm cm- ’. Two crops were rotated on this farm: corn being cultivated on 84% of the area and barley on the remaining 16%. The crops selected to test the model were: barley, proteaginous pea, oleaginous sunflower, corn and sugar-beet. These crops are in harmony with the tendencies observed during the last two harvests. The basic data is shown in Table 1. Since decisions had to be made before the beginning of the 1994 season, it was
J.M. Tarjuelo et ul./Agricultural
t ECONOMIC DATA Ps = sale price of yield S = subvention C, = cost of production varying with crop yield pw = price of water
Wuter h4unqement
4 Soil-Crop Unit Characteristics (Ui)
31 (1996) 145-163
149
4 CLIMATE DATA Maximum ET Crop @Tmi.J Efective Precipitation (EPS
I-
I Water that represents the contributions different to the irrigation @j,J
v Maximum crop water requeriment (Hr~J
Sprinkler irrigation equipment: * Funtion of normal distribution (ak)
Applied depth/Required
depth
oIbm)i)ij.kr r Fraction of area fully irrigated (aij.k_t)
Gross depth applied
+iisqz$w Bij.k
Fig. 2. General flow and component
= (psi
yij.k
+ Si)-
handled of optimal irrigation
(CIi yi.k+ Hbaij,kb)
depth according
to the second submodel.
J.M. Turjuelo et ul./Agricultural
150
Water Managrment
31 (1996) 145-163
i=l * 0 iAi,t <&
(SW *
Fig. 3. General flow and component
Inigable area CL41
handled by optimal crop rotation in third submodel.
decided that an analysis of climatic variability over the last 20 years (1974- 1993) would be made to analyse the risks, using data registered at the Los Llanos meteorological station, located near the farm in question. Fig. 4 shows the interannual variations of the net irrigation requirements under maximum crop evapotranspiration (ETm) conditions, calculated by means of the first submodel (Fig. 1). These results clearly demonstrate the complexity of trying to predict the irrigation needs of the following year. Since decisions about what crops to cultivate must be based on these predictions, it seems logical to analyse the results both for the
Table 1 Selected crops crops
Barley Protean pea Sunflower Corn Sugar-beet Set aside
Date
sowing
Harvest
15/02 01/02 01/05 24/04 25/03 -
28/06 29/06 15/10 15/11 28/11 _
ETm (mm) a (Aver. year, 1974-93)
Grants CAP b (ECU ha-
393’ 1 432‘4 701’7 881’8 1083’0 _
268 500 1170 350 _ 533
c ;a-
t)
Direct costs d (ECU ha- ‘)
crop price e (ECU t- ‘)
673 737 398 1138 1865
150 180 210 180 60 _
’) 7’0 6’0 5’0 15’0 90’0 _
a ETm = maximum evapotranspiration per average year in the 1974- I993 climatic series. b CAP grants in the central region of the Province of Albacete for 1994. ’ ym = maximum yields reached in the Province of Albacete. d Crop price = average prices obtained by area farmers for the 1993 harvest. I ECU=150pta.
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151
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1 .ooo
900 800 700 600 600 400 300 200 100
ok,,,,,,,,,,,,,,,,,,, 74
75
76
77
78
79
80
81
82
83
84
85
8%
07
88
09
90
91
92
93
MD
YEAR
-
BARLEY
PEA +-SUNFLOWER
Fig. 4. Net irrigation
requirements
-CORN
of crops under maximum
*SUGAR
evapotranspiration
BEET
conditions.
average year and for the humid and dry years, including even the most extreme years. With this information, one will have at least an idea of the limits which affect our decision and the risks that can be run. The difference between the extreme values in barley is 71% of the greatest value, 77% in proteaginous peas, 42% in corn and 29% in sugar-beets. Barley and peas are spring crops, corn and sunflowers are grown in summer, and sugar-beets are spring-summer crops. Assuming that there is no limitation on water availability, we analyzed the effect of two coefficients of uniformity values (CU = 70% and CU = 85%) and three different costs of water (Pw = 10 pta rne3, 17 pta rnm3, 25 pta m- 3> (1 ECU = 150 pta) on the profits of each of the five crops selected. Each crop was dealt with independently by the application of a second submodel (Fig. 2). Table 2 shows the results obtained for the average year in the 1974-1993 climatic cycle. The economic optimum did not correspond to the maximum production goal in any of the cases analysed, as can be observed in columns 6 and 7 of Table 2. rate is reduced in all the For both uniformity coefficients analysed, the Hba/Hr crops when the cost of a cubic metre of water increases (Hba = depth of water applied to ground). Therefore, when water prices are low, the economic optimum is obtained by increasing the irrigation depth to compensate for the water deficits caused by lack of uniformity.
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J.M. Tarjuelo et al./Agricultural
Table 2 Optimum profits climatic series
depending
crop Barley
Protean pea
Sunflower
Corn
Sugar-beet
70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85 70 85
on uniformity
Pw b (ptamm3)
Hha/Hr
10
1’23 1’16 0’73 1’05 0’73 0’70 1’23 1’16 0’78 I’IO 0’78 1’00 0’54 0’75 0’54 0’75 0’47 0’64 1’23 1’16 1’00 1’05 0’78 1’00 1’39 1’23 I’10 I’10 0’84 1’05
10
17 17 25 25 10 IO 17 17 25 25 10 10 17 17 25 25 10 IO 17 17 25 25 10 IO 17 17 25 25
Water Management 31 (1996) 145-163
coefficient =
and water
price.
Average
Cd d
Hhu e (mm)
Y/Ym (%)
t
0’09 0’03 0’30 0’06 0’30 0’30 0’09 0’03 0’26 0’04 0’26 0’08 0’46 0’25 0’46 0’25 0’53 0’36 0’09 0’03 0’15 0’06 0’26 0’08 0’07 0’02 0’12 0’04 0’22 0’06
282 266 166 240 166 161 290 274 183 260 183 235 261 362 261 362 226 308 757 715 614 645 479 614 III9 990 887 887 676 843
93’73 98’04 79’74 96’13 79’74 79’62 94’09 98’15 83’32 97’35 83’32 95’16 69’86 83’60 69’86 83’60 65’20 76’33 92’02 97’50 86’93 95’08 77’48 93’46 94’37 98’42 90’27 96’64 81’91 95’37
year for the 1974-1993
ET,‘ETm (%)
g
94’55 98’29 82’38 96’64 82’38 82’28 94’86 98’39 85’50 97’70 85’50 95’79 68’28 82’74 68’28 82’74 63’37 75’08 93’61 98’00 89’54 96’06 81’98 94’77 94’89 98’56 91’15 96’94 83’56 95’79
OB h (ECU ha- ‘) 535 596 445 479 356 364 962 1033 855 909 757 779 1341 1354 1219 1185 1095 1015 1100 1270 775 953 491 618 2253 2548 1782 2110 1321 I645
a Cci = uniformity coefficient of sprinkler system. b Pw = price of water (1 ECU = 150 pta). ’ Hba/ Hr = relationship between gross depth of water applied and depth of water required. d Cd = deficit coefficient. e Hb = seasonal volume of applied water. f y/ ym = relationship between actual and maximum yields. g ET/ ETm = relationships between actual and maximum evapotranspiration. ’ OB = optimum economic profits.
When water is expensive (2.5 pta mm3), an increase in the optimum rate between the gross depth and the depth required with irrigation uniformity can be observed in most cases. The values of this relation range from 0.64 (sunflower) to 0.84 (sugar-beet) when the value of the uniformity coefficient is high (CU = 85%); and between 0.47 (sunflower) and 0.84 (sugar-beet) when the CU value is low (70%). The same occurs when the price of a cubic metre of water is 17 pta rne3, although with higher values in the
J.M. Tarjuelo et al./Agricultural Table 3 Optimal annual pattern. Average
Water Management 31 (1996) 145-163
year for the 1974- 1993 climatic
1.53
series
Option
CC/ Pw (%I (ptam-‘1
Barley (ha)
Pea (ha)
Sunflower (ha)
Corn (ha)
Sugarbeet (ha)
OB Set aside (ECU ha- ‘) (ha)
Water (m3 ha- ‘)
A C E B D F
7010
_ _ _
108’37 108’37 108’37
108’38 108’38 108’38 108’38 108’38 108’38
108’37 108’37 108’37 -
45’00 45’00 45’00 45’00 45’00 45’00
1427 1201 1037 1549 1277 1061
5356 2934 2581 5375 4968 3226
17 25 8510 17 25
38’25 38’25 38’25 38’25 38’25 38’25
Hba/Hr
relation. This proves that the higher the CU value is, the more water is needed, even though part of the water is lost. This is because the increase in production which results from adequate or excessive irrigation on the major portion of the field makes up for greater water expenditures. The economic optimum is always reduced when the price of a cubic metre of water increases, but, generally speaking, this optimum normally rises along with the CU.
Table 4 Protits for corn crops with distinct amounts of seasonal irrigation Hba/Hr 70
10
70
17
70
25
85
10
85
17
85
25
B = profits corresponding
0’54 0’68 1’00 1’23 0’54 0’68 1’00 0’54 0’64 0’78 0’64 0’73 1’00 1’00 1’16 0’64 0’73 0’84 1’00 1’05 0’64 0’73 0’84 1’00
Cd 0’46
0’33 0’15 0’09 0’46 0’33 0’15 0’46 0’37 0’26 0’36 0’27 0’84 0’08 0’03 0’36 0’27 0’17 0’08 0’06 0’36 0’27 0’17 0’08
333 418 614 757 333 418 614 333 393 479 393 446 517 614 715 393 446 517 614 645 393 446 517 614
to each Hba / Hr restriction.
ET/ETm
Y/Ym (o/o)
(%I
B(I) (ECU ha- ‘)
59’98 71’01 86’93 92’02 59’98 71’01 86’93 5998 67’96 77’48 68’57 76’09 85’06 93’46 97’50 68’57 76’09 85’06 93’46 95’08 68’57 76’09 85’06 93’46
67’99 76’81 89’54 93’61 67’99 76’81 8954 67’99 74l37 81’98 74!85 80’87 88’05 94’77 98’00 74’85 80’87 88’08 94’77 96’06 74’85 80’87 88’08 94l77
673 843 1062 1100 458 648 775 280 388 491 796 956 1078 1232 1270 613 748 837 945 953 403 509 561 618
154
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The application of the third submodel (Fig. 3) allowed us to select crop rotations that lead to higher profits, depending on the different CU values and Pw for the average year of the climatic series. In addition to the restrictions imposed by the CAP reform for land surface set aside and maximum surface for sunflower, the sugar-beet quota for each farm can vary from 0 to 15% of the irrigable perimeter. First of all we have determined the crop rotations that give the best economic returns, with no water restrictions, for the different combinations of CU and Pw values (Table 3). In a similar situation, where available water is not a limiting factor, the most profitable crop rotations include sugar-beet (with its maximum quotas), oleaginous sunflower and corn or proteaginous peas. For the same CU values, maximum benefits diminish as Pw increases. Whatever the Pw may be, the highest profits are obtained when CU = 85%, even though these crop rotations require a greater volume of irrigation water. The highest prices per cubic metre of water exclude corn from the crop rotation in favour of a spring crop such as proteaginous peas. Since limitations on water availability can exist on farms, we have begun with the maximum volume of water utilized in crop rotation that will lead to optimum profits without water limitations (as can be seen in Table 3, corresponding to a CU = 85% and a Pw = 10 pta rnm3> and available water has been reduced by different percentages of the maximum volume. Since lack of water on a farm would imply that some crops
Table 5 Yield variation situation
in crops with deficit levels (ET/ETm)
Crop
ET (% ETd
Yield (kg ha-
Barley
100 80 60 40 100 80 60 40 100 80 60 40 100 80 60 40 100 80 60 40
7000 5474 3941 3700 6000 4848 3606 1687 5000 4165 3215 2335 15000 11250 7500 3750 9OQOo 71550 52290 31590
Pea
Sunflower
Corn
Sugar-beet
’)
and direct cost of production Direct cost, excluding 673 594 565 488 737 670 523 498 398 342 295 243 1138 1075 807 739 1865 1773 1153 1109
associated
with each
water (ECU ha- ‘)
J.M. Tarjuelo et al./Agricultural
Water Management
31 (1996) 145-163
155
*Seasonal irrigation water (1000 m3)
Fig. 5. Optimum crop rotations with no water limitation but with various water supplies possible for the six combinations of CU and Pw (A, B, ... . F). The figures in parentheses correspond to the relation Hba / Hr and the figures above the bars indicate seasonal volumes of water.
would not receive sufficient irrigation or that the irrigable perimeter would be reduced, different water restriction levels for the five crops have been studied: from the value that gives optimum benefits without water restrictions (Table 2) down to approximately 50% of this value. Taking corn as an example, in Table 4, we can see each of these situations as if it were a different crop when the third submodel is applied, thus determining the crop rotation that produces the highest profits. When managing crops with different levels of hydric deficit, the expected yield will vary. It is therefore logical that production costs will also vary. In Table 5 the variations in yields estimated by the model according to the ET/ETm relation and the direct costs associated with each situation are presented. Fig. 5 shows crop rotations that lead to highest profits when no water limitations exist on farms. When distinct amounts of water are applied to a single crop, we have considered this crop as two different ones, as shown in Table 4 for the six possible combinations between CU and Pw (A, B, . . . . F). In Fig. 5 we can observe the appearance of the same crop with a different Hba/Hr relation, considered as a distinct agricultural activity. The seasonal volumes of irrigation water for each crop are expressed in thousands of cubic metres. The optimum profits for these crop rotations can be seen in Fig. 6.
156
J.M. Tarjudo rt ul./Agriculturcrl
Wetter Munugement 31 (19961 145-163
5a) i..__...____ . . _... .~.
Fig. 6. Optimum economic limitations on farms.
benefits of crop rotations for the different
CU and Pw combinations
with no water
*Seasonal irrigation water (1000 m3)
fzj -
Sunaower(O.47)
Fig. 7. Optimum crop rotations when only 60% of fixed maximum
water volume is available.
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?? Soaaonal irr@tkbn w&w
31 (1996) 14.5-163
157
(1000m3)
Fig. 8. Optimum crop rotations when only 40% of fixed maximum
for water volume is available.
Figs. 7-9 are examples of crop rotations that give maximum profits when only 60%, 40% and 20% of the maximum water volume already mentioned are available on the farm. From the results obtained, we should point out the appearance, within the same crop pattern, of different irrigation programmes for the same crop. The irrigation fields which are set aside also increase when water availability on the farm lessens. In Fig. 10 we can see how optimum benefits (OB) vary in relation to diminishing Note that the OB is water availability for the different ClJ and Pw combinations. greater when CU values are higher, although this ceases to occur when the water availability is reduced past 50% of the maximum volume fixed for the farm. This coincides perfectly with the setting aside of a greater perimeter of irrigable land than the minimum required by the CAP. Fig. 11 shows the variation in seasonal volume of irrigation water with respect to the maximum value (with no water limitations) contrasted to water availability for the distinct crop rotations for different CU and Pw combinations. Likewise, Fig. 12 represents the optimum benefit (OB) variations with water availability for different crop rotations, in distinct Pw and CU combinations. We can gather from Figs. 11 and 12 that neither reference parameter is reduced until water availability is less than the optimum water needs for each of the CU and Pw combinations. It is also apparent that there is a much more rapid descent in OB after a 50% reduction in water availability is reached.
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*Seasonal irrigation water (1000 m3)
A
C
B
F
E
D
Fig. 9. Optimum crop rotations when only 20% of fixed maximum
for water volume is available
80 i 1.
\,”
’ ..&-
0
L -
i.
i-l
0
. ..--I
)_
1~
20
40
--A--_--
..A
60
c--m
-*_
.-_
80
100
WATER AVALAIBLE (%)
Fig. 10. Optimum restrictions.
economic
benefit (OB) for six possible
CL’ and Pw combinations
with varying
water
J.M. Tarjuelo et al./Agricultural
I -t
(A) I CU=70% PA=10
/ r. (B) ICU=M%
PA=10
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Water Management 31 (1996) 145-163
(C) / CU=70% PA=17
.
(D) / CU=BS% PA=17 -i-
(E) / CU=70% PA=25 (F) I C&85%
PA=25 I
Fig. 11. Variation in seasonal irrigation water (SW) with the lessening of water availability for different CC/ and Pw combinations.
____ _._ 1 I
10
17 Pw (pta*m-3)
25
1 ECU=150 pta m -J m
. ~._____ CU=70% (100%) cuds% (I-) m CU=7@%(40%) cu=tW% (40%) m cu=70% (5%) cu-BJ# (5%)
~~-70% (60%) ic cu=70% (20%) -
~~-85% (M)%) cu-85% (20%)
Fig. 12. UB variations with the reduction of water availability for distinct CC/ and Pw combinations.
160
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From the global analysis of optimum crop rotations for different levels of water restrictions, the following should be pointed out: - Sugar-beet and oleaginous sunflower are valid for all the solutions with the maximum surface possible, although with application levels which use less water as water availability diminishes. This is especially true for sugar-beet. Both crops begin to disappear only under severely restricted water availability, around 40% of the fixed maximum value. With such low levels, both crops, and especially sugar-beet, are replaced by proteaginous peas. - Corn is a possibility for crop rotations when water is cheap and CU values are high. Corn disappears when water restrictions surpass 25% of available water. * Proteaginous pea as a component of crop rotations is seen more and more as water availability decreases, when water is costly and CU is lower. * Barley, due to its cost-earning structure, did not participate in any of the crop rotations selected. Since barley has an agronomic cycle similar to proteaginous peas, it seems that barley cannot compete with them. * When water restrictions surpass 50% of the maximum fixed volume for a farm, the setting aside of more irrigable land becomes feasible.
3. Conclusions We have developed a model to help the farmer evaluate the effects that lack of sprinkler irrigation uniformity can have on crop productivity. This model also permits the selection of optimum irrigation treatments using a small amount of information which is available to the farmer. In areas where water availability is limited, the model can also aid in evaluating system management strategies, economic returns and sensibilities water availability, fluctuation and cost. The model was applied to a farm in order to evaluate its capacity and method of use. From the results obtained, we can conclude that the higher the uniformity of water application, the greater the economic benefits even though benefits decrease as the price of water goes up. Given the yearly differences in climate, the proposed process guides the farmer in his choice of crop rotations which give maximum profits in relation to water availability, the CU of his irrigation system, and the cost of water placed in the ground and ready to be used by his crop. In addition, the model developed allows a farmer to analyse any crop rotations he wishes, even for different levels of hydric deficit. It can also be used to study optimum utilization in the case of limited water resources for large irrigable zones or for catchment areas. When water availability is unlimited, crop rotations that give agricultural activities the best profits include sugar-beet (with the maximum surface area possible), oleaginous sunflowers and corn. This last crop is substituted by proteaginous peas when the cost of the cubic metre of water rises and the CU of the irrigation system falls. When the volume of available water becomes a limiting factor, the first crop that disappears from the rotation is corn, which is substituted by proteaginous peas. In this
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situation, the crop rotations include crops managed with hydric deficit, especially sugar-beet. The best economic results are achieved with the highest CV values, whatever the price of water may be, even though the crop rotations require a higher volume of water for irrigation. The results of this study prove that it is erroneous to use a single gross depth/redepending on the irrigation system, since agronomic and quired depth rate (Hba/Hr) economic factors should also be taken into account, as well as water availability and the price of a cubic metre of water available to a crop. This model, designed with a prototype methodology, has been developed step-by-step on the basis of successive evaluations carried out by agronomic experts. During the elaboration process new information was incorporated and, also as a result of the successive evaluations, the development of the model had to be redirected. The methodology shown in the model allows us to satisfactorily reach the planned objectives, even though a series of limitations can be seen. These, which have already been commented on partially (De Juan et al., 1996) give way to a certain degree of doubt with respect to the results obtained on application. The main limitations are centred around the following points: (1) the empirical nature of the relation between yield and water consumed; (2) doubt as to the crop’s response factor to hydric deficit (ky); (3) with sprinkler irrigation, the uniformity coefficient (CV) not only depends on the irrigation system, but also on wind, a factor which is not taken into account in the methodology indicated and (4) with this method we assume that the gross depth applied each time is such that the deficit coefficient (Cd) is the same for all the irrigation sessions carried out during the crop’s growing season, although obviously this is not always so. The method must be further developed to correct some of its most relevant limitations. For instance, functional simulation models of crops can be developed to determine the doses needed for optimum irrigation. Also, strategies can be established in which the deficit coefficient varies with each irrigation, thus implying a needed knowledge of the impact on production of a Cd variable based on the stage of crop development. Another of the model’s limitations is that there has not been any consideration of risk. Farmers want to maximize returns but simultaneously they also want to minimize risk. Risk in irrigated agriculture with a stochastic supply of water has a multidimensional character.
4. List of symbols a A B B CSb
fraction of total area which received sional) area under cultivation, [L12 benefit per unit area (ECU ha- I> Koppen’s climatic classification Community Agriculture Policy
water in excess
of Hr (nondimen-
162
Cd CP CS Cs,, CU EP ET ETm ETr ET/ETm GR Hb Hba Hr IA Iw IWb kc ky iL1 m N OB OHba P PS Pw Ra RD s SIW SIWm u Y ym
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deficit coefficient (nondimensional) crop rotation crop stages Koppen’s climatic classification Christiansen’s coefficient of uniformity (%) effective rainfall during the growing season, [L] crop evapotranspiration, [L] maximum crop evapotranspiration during the growing season, [L] reference evapotranspiration, [L] relative evapotranspiration (nondimensional) growing root, [L] gross water depth applied from irrigation system, [L] depth of water applied to ground (gross dose, Dba), [L] crop water requirements, [Ll irrigable area of farm, [L12 irrigation water, [L13 gross contribution of irrigation during the growing season, [L] crop coefficient (nondimensional) crop or yield response factor (nondimensional) crop number (nondimensional) symbol of long dimension the number of growth stages considered (nondimensional) year number in climatic series (nondimensional) optimum benefit per unit area (ECU ha-’ ) optimum depth of water applied to ground, [L] water that represents the applications distinct to the irrigation during growing season, [L] sale price of yield (ECU t- ’) price of water (ECU me3) application efficiency (nondimensional) root zone depth, [L] subvention (ECU ha- ’> available seasonal irrigation water for the whole area, [L13 maximum available seasonal irrigation water for the whole area, [L13 soil-crop unit characteristics actual yield per unit area (t ha-‘) maximum yield of the crop (t ha-‘)
4.1 .I. Greek symbols variable factor between - 3 y + the participation coefficient of ; according to CAP demands and mensional) ostandard deviation of application A increment
the
3 the crop in relation to the farm surface, /or conditions of another nature (nondidepth
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Subscripts
j k 1
max min n P
t
refers to each one of the crops being discussed refers to the different assumptions of seasonal volumes of irrigation interval used for the (Y value between - 3 and + 3 number of crops considered in the study maximum minimum refers to the stage of growth of the crop under consideration period in which water balance in the soil is reached refers to the year in the climatic series considered
water
Acknowledgements The writers wish to thank the Consejeria de Agricultura y Medio Ambiente de la Junta de Comunidades de Castilla-La Mancha for partly funding this research. The authors would like to express their gratitude to the anonymous reviewers for the many good suggestions.
References Allen, R.G., Jensen, M.E., Wright, J.J. and Burman, R.D., 1989. Operational estimates of reference evapotmnspiration. Agron. J., 81: 650-662. De Juan, J.A., Tarjuelo, J.M., Valiente, M. and Garcia, P., 1996. Model for optimal cropping patterns within the farm based on crop water production functions and irrigation uniformity. I: Development of a decision model. Agric. Water Manage., 31: I S-143. Doorenbos, J. and Kassam, A.H., 1979. Yield response to water. Inig. Drain. Pap. 33, FAO, Rome, Italy, 179 PP. Doorenbos, J. and Pruitt, W.O., 1977. Guidelines for predicting crop water requirements. Irrig. Dram. Pap. 24, FAO, Rome, Italy, 144 pp. Hatfield, J.L., 1985. Wheat canopy resistance determined by energy balance techniques. Agron. J., 77: 279-283. Mantovani, E.C., 1993. Desarrollo y evaluacidn de modelos para el manejo de1 riego: estimaci6n de la evapotranspiraci6n y efectos de la uniformidad de aplicacidn de1 riego sobre la producci6n de cultivos. Tesis Doctoral, Universidad de C6rdoba. Andalucia, Espaiia, 184 pp. Orgaz, F., Mateos, L. and Fereres, E., 1992. Season length and cultivar determine the optimum evapotranspiration deficit in cotton. Agron. J., 84: 700-706. Stewart, II., Hagan, R.M., Pruitt, W.O., Hanks, R.J., Riley, J.P., Danilson, R.E., Franklin, W.T. and Jackson, E.B., 1977. Optimizing crop production through control of water and salinity levels. Utah Water Res. Lab. PRWG 1.5 1- 1, September.