Methodological Framework

Although, El Niño phenomenon mainly affects the precipitation regime of central Chile, the study is carried out considering crops that are grown during the austral spring and summer (October to March). Being a Mediterranean climate, only the effects of ENSO on atmospheric water demands are considered. Following the definition of El Niño given by Trenberth (1997), daily meteorological records for the period 1976 to 2003 at the location of Pudahuel (33.27° S) were classified in the different phases of El Niño. A "weather generator" conditioned on El Niño phases (Wilks and Wilby 1999) was fitted and used to generate synthetic series of daily meteorological variables that were combined to generate estimates of reference evapotranspiration using Pen-man-Monteith formula (Monteith and Unsworth 1990), more details of the weather generator algorithm can be found in Meza (2005).

The soil unit selected corresponds to the Maipo soil with the following characteristics: 1.2 m depth, 34.8% sand, 21.2% clay, bulk density equal to 1.3 g cm-3, and a water holding capacity of 80 mm. Due to the lack of information about saturated hydraulic conductivity, water flow in the soil was simulated at a daily time step using a tipping bucket approach.

A farming system composed by 1 ha of tomato, 1 ha of watermelon, and 1 ha of potato is used in this example. The problem corresponds to an optimal allocation of limited water resources among the different crops with the general objective of maximizing the net benefits of the farm.

It is assumed here that all crops have the same growing period with sowing date set to 1 October, and with an extension of 182 days (exactly six months). The yield at the end of the growing season is simulated by the Jensen's model (Eq. 9.2). Each crop is grown in the same type of soil with maximum water holding capacity of 80 mm and initial water content of 50 mm.

For simplification it is assumed that water for irrigation (Q¡ in mm) is available in fixed and known amounts and can be applied as a discrete variable to each crop irrigated (0, 5, 10, ...,X). The irrigation is made on fixed dates with a frequency of 10 days and without the possibility to store it for subsequent periods. In this way there are 18 times 3 possible irrigation amounts represented by X¡,k (l dates and k crops). Since the Doorenbos and Kassam work contains information about the Ky factor for several crops that are relevant to this study, it is necessary to adapt their method into a simpler one like the Jensen's model. The solution to this problem is presented by Kipkorir and Raes (2002) transforming the Ky factor into the Jensen's sensitivity index (A) as:

The nonlinear mathematical model is represented as:

For each irrigation moment, the constraints of the system are represented by the following equation:

The parameters used in this example are presented in Table 9.1 and the mean values of reference evapotranspiration are presented in Table 9.2. Note the differences between the sensitivity of different crops to water stress and the mean values of crop potential evapotranspiration between El Niño phases.

In the absence of information a farmer will select an irrigation strategy based on the expected value of crop evapotranspiration (i.e. the weighted average of ETc across all El Niño phases) and water availability, creating a Qc function as:

To estimate the potential use of El Niño-driven climate forecasts, it is necessary to compare the performance of the farmer described above with one that has some information about the future possible states of ETc. This farmer will choose an irrigation strategy conditioned on the expected value of crop potential evapotranspiration under the correspondent El Niño scenario and water availability (Qe under El Niño events, Qn under normal events, and Qa under La Niña events). These functions are represented by:

with o = e, n, a following the notation described above.

It is assumed here that El Niño conditions for the whole growing season are known at the beginning, in that sense it represents a case of perfect information about El Niño phases, although there is uncertainty about crop evapotranspiration within each phase. Under maximization criteria if the irrigation strategies selected in Eqs. 9.6 and 9.7 do differ, the information about future El Niño conditions has a potential economic value (i.e. there is an economic incentive for the farmer to use climate forecasts based on El Niño events). The relative frequencies of the phases of El Niño for the growing season considered here are: P(e) = 0.33; P(n) = 0.41; P(a) = 0.26.

Using approximate moments analysis, the expected value of the use of ENSO information (EVI) in this optimum irrigation problem is calculated as:

Table 9.1. Parameters used in the mathematical programming model for each crop

Tomato

Potato

Watermelon

Price (U.S.S t"1)

250

220

320

Vm (t ha-1)

65

50

40

0.33

0.37

0.62

¿2

1.15

0.74

0.74

0.74

0.62

0.74

a4

0.33

0.15

0.24

Table 9.2. Mean values of crop potential évapotranspiration (ETc in mm.) for the different phases of El Niño. T = Tomato, P = Potato, W = Watermelon

Period

La Niña T

P

W

Normal T

P

W

El Niño T

P

W

1

13.4

13.5

13.3

14.0

14.1

13.9

12.2

12.3

12.1

2

15.8

16.2

15.4

16.9

17.4

16.5

14.9

15.3

14.6

3

17.5

18.3

16.9

19.2

20.0

18.6

17.2

17.9

16.6

4

25.5

26.9

24.5

26.8

28.3

25.7

23.0

24.3

22.0

5

28.1

30.0

26.8

29.7

31.7

28.3

26.9

28.7

25.6

6

31.1

33.7

29.4

33.3

36.1

31.5

30.8

33.4

29.1

7

36.9

40.2

34.2

39.0

42.5

36.1

36.7

40.0

34.0

8

42.1

45.5

38.4

44.0

47.6

40.2

40.8

44.2

37.3

9

44.4

47.7

40.5

47.7

51.3

43.5

45.0

48.4

41.0

10

50.6

54.1

46.0

51.7

55.4

47.1

50.5

54.0

46.0

11

51.4

51.9

46.8

55.3

55.8

50.3

54.9

55.4

50.0

12

50.8

48.9

46.1

54.0

52.0

49.1

53.0

51.0

48.1

13

49.0

47.1

44.5

51.7

49.7

46.9

50.4

48.5

45.8

14

46.3

44.5

42.0

48.0

46.1

43.5

43.9

42.2

39.8

15

41.9

40.2

37.9

43.3

41.5

39.2

41.2

39.5

37.3

16

34.6

32.9

31.0

35.4

33.6

31.7

34.7

33.0

31.1

17

28.4

28.1

26.4

29.2

28.9

27.1

29.8

29.5

27.7

18

21.6

23.6

22.1

22.3

24.3

22.7

21.6

23.6

22.1

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