Multiperiod Optimisation of Irrigated Crops under Different Conditions of Water Availability
Abstract
:1. Introduction
2. Methodology
2.1. Multiperiod Crop Yield Function
2.2. Optimisation of Irrigated Crops
- Water availability: Assuming that the farmer has the infrastructure to store water at monthly scale ( m3 of capacity), available water is defined as:
- Land availability: This constraint defines the area to be cultivated.
- Labour availability: Assuming that the labour availability can change for each month, this constraint is defined as:
- Capital availability: Assuming that farmers can save money if it is not spent, the monthly capital availability is considered as:
- Crop area considerations: It is necessary to consider agricultural, market and productive diversity management criteria to restrict the maximum or minimum crop areas. This is due to marketing situations, rotations, or other agricultural limitations. These constraints are expressed as:
- Complementary considerations: To force the crop water requirement to be zero when the cultivated area is also zero, the constraint is expressed as:Finally, there are non-negativity constraints expressed as:
2.3. Case Study
2.3.1. Model Inputs
2.3.2. Model Application
- Scenario 1: Optimisation subject to seasonal constraints. This scenario assumes that resources are available for the season, but does not consider intraseasonal variability. In this scenario, for the whole growing period, only one value of and for each crop i was considered. Water storage and water transactions were not considered.
- Scenario 2: Optimisation subject to seasonal constraints. For the whole growing period, monthly values of and for each crop i were considered. In this scenario, water storage and water transactions were not considered.
- Scenario 3: Optimisation subject to monthly constraints, i.e., water and other resources availability at a monthly scale are considered. In this scenario, water storage and water transactions were not considered.
- Scenario 4: Optimisation subject to monthly constraints with water transactions.
- Scenario 5: Optimisation subject to monthly constraints with water storage.
- Scenario 6: Optimisation subject to monthly constraints with water storage and transactions. This scenario is the most complete, considering all possible factors involved in the process.
3. Results and Discussion
3.1. Seasonal Use of Resources and Profits
3.1.1. Situation a
3.1.2. Situation b
3.2. Crop Allocation
3.2.1. Situation a
3.2.2. Situation b
3.3. Monthly Limiting Resource
3.3.1. Situation a
3.3.2. Situation b
3.4. Sensitivity Analysis
3.4.1. Scenario 1
3.4.2. Scenario 6, Situation a
3.4.3. Scenario 6, Situation b
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Crop | Parameter | Month | Sowing | ||||||
---|---|---|---|---|---|---|---|---|---|
Sep | Oct | Nov | Dec | Jan | Feb | Mar | |||
Alfalfa | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 01-Sep | |
30.0 | 31.0 | 30.0 | 31.0 | 31.0 | 28.0 | 15.0 | |||
49.0 | 49.0 | 49.0 | 49.0 | 49.0 | 49.0 | 49.0 | |||
Maize | - | - | 0.5 | 0.7 | 1.2 | 0.5 | 0.1 | 01-Nov | |
- | - | 30.0 | 31.0 | 31.0 | 28.0 | 5.0 | |||
- | - | 28.4 | 35.1 | 35.6 | 34.3 | 33.4 | |||
Wheat | 0.4 | 0.6 | 0.7 | 0.5 | 0.1 | - | - | 01-Sep | |
30.0 | 31.0 | 30.0 | 31.0 | 8.0 | - | - | |||
30.0 | 30.9 | 32.5 | 32.6 | 8.5 | - | - | |||
Sugar beet | 0.6 | 0.8 | 1.0 | 1.0 | 0.9 | 0.6 | - | 01-Sep | |
30.0 | 31.0 | 30.0 | 31.0 | 31.0 | 7.0 | - | |||
29.5 | 31.5 | 35.2 | 37.3 | 38.8 | 38.4 | - |
Crop | Price | Maximum Yield | Source | ||
---|---|---|---|---|---|
Value | Units | Value | Units | ||
Alfalfa | 5.1 | US$ bale−1 | 400 | bales ha−1 | INIA [45] |
Maize | 22.3 | US$ qqm−1 | 150 | qqm ha−1 | ODEPA [46] |
Wheat | 22.5 | US$ qqm−1 | 70 | qqm ha−1 | ODEPA [46] |
Sugar beet | 62.7 | US$ ton−1 | 100 | ton ha−1 | ODEPA [47] |
Function or Constraint | Equation | Scenarios |
---|---|---|
Objective | 1 | |
2, 3, 5 | ||
4, 6 | ||
Capital | 1, 2 | |
3–6 | ||
Water | 1 | |
2 | ||
3 | ||
4 | ||
5 | ||
6 |
Crop Allocation | Use of Resources | ||||||||
---|---|---|---|---|---|---|---|---|---|
Alfalfa | Maize | Wheat | Sugar Beet | Land | Water | Labor | Capital | Profits | |
(ha) | (ha) | (m3) | (Person-d) | (US$) | (US$) | ||||
1. Optimum cropping pattern | 0 | 0 | 0 | 20 | 20 | 167,477 | 120 | 80,000 | 45,917 |
2. Export prices | |||||||||
2.1 Decrease in 50% for sugar beet | 0 | 25 | 0 | 0 | 25 | 172,417 | 267 | 57,114 | 26,671 |
2.2 Decrease in 50% for maize | 0 | 0 | 0 | 20 | 20 | 167,477 | 120 | 80,000 | 45,917 |
2.3 Increase in 50% for alfalfa | 8 | 0 | 0 | 17 | 25 | 201,623 | 192 | 80,000 | 51,708 |
2.4 Increase in 50% for wheat | 0 | 0 | 0 | 20 | 20 | 167,477 | 120 | 80,000 | 45,917 |
3. Agronomic management | |||||||||
3.1 Minimum area to be sowed corresponds to 3 ha | 3 | 3 | 3 | 16 | 25 | 196,754 | 178 | 79,578 | 41,695 |
4. Application efficiency of the irrigation system | |||||||||
4.1 Sugar beet is irrigated by furrow () and | |||||||||
wheat by sprinkler () | 0 | 0 | 0 | 20 | 20 | 209,346 | 120 | 80,000 | 45,917 |
5. Water costs | |||||||||
5.1 Costs of water rights increase to 0.05 US$/m3 | 0 | 0 | 0 | 16 | 16 | 131,010 | 94 | 80,000 | 18,500 |
6. Labour | |||||||||
6.1 Costs increase to 30 US$/person-d | 0 | 0 | 0 | 20 | 20 | 164,974 | 119 | 80,000 | 44,036 |
6.2 Availability decreases to 100 person-d | 0 | 0 | 0 | 17 | 17 | 139,015 | 100 | 66,502 | 38,017 |
7. Other costs | |||||||||
7.1 Increase in 50% for sugar beet | 0 | 25 | 0 | 0 | 25 | 172,417 | 267 | 57,114 | 26,671 |
7.2 Increase in 50% for maize | 0 | 0 | 0 | 20 | 20 | 167,477 | 120 | 80,000 | 45,917 |
7.3 Decrease in 50% for alfalfa | 6 | 0 | 0 | 19 | 25 | 203,014 | 184 | 80,000 | 50,321 |
7.4 Decrease in 50% for wheat | 0 | 0 | 6 | 19 | 25 | 198,643 | 146 | 80,000 | 47,781 |
8. Capital | |||||||||
8.1 Availability decreases to 50% | 0 | 0 | 0 | 10 | 10 | 83,136 | 60 | 40,000 | 22,506 |
Crop Allocation | Use of Resources | ||||||||
---|---|---|---|---|---|---|---|---|---|
Alfalfa | Maize | Wheat | Sugar Beet | Land | Water | Labor | Capital | Profits | |
(ha) | (ha) | (m3) | (Person-d) | (US$) | (US$) | ||||
1. Optimum cropping pattern | 3 | 4 | 0 | 6 | 13 | 96,212 | 109 | 36,000 | 18,754 |
2. Export prices | |||||||||
2.1 Decrease in 50% for sugar beet | 5 | 0 | 0 | 0 | 5 | 37,995 | 58 | 8098 | 2805 |
2.2 Decrease in 50% for maize | 5 | 0 | 0 | 6 | 11 | 89,835 | 95 | 32,687 | 17,122 |
2.3 Increase in 50% for alfalfa | 5 | 0 | 0 | 6 | 11 | 89,835 | 95 | 32,687 | 22,349 |
2.4 Increase in 50% for wheat | 3 | 4 | 5 | 4 | 16 | 114,625 | 125 | 36,687 | 19,046 |
3. Agronomic management | |||||||||
3.1 Minimum area to be sowed corresponds to 3 ha | 3 | 4 | 3 | 5 | 14 | 107,854 | 119 | 36,434 | 16,578 |
4. Application efficiency of the irrigation system | |||||||||
4.1 Sugar beet is irrigated by furrow () and | |||||||||
wheat by sprinkler () | 3 | 4 | 0 | 6 | 13 | 108,040 | 109 | 36,000 | 18,737 |
5. Water costs | |||||||||
5.1 Costs of water rights increase to 0.05 US$/m3 | 3 | 4 | 0 | 6 | 13 | 96,212 | 109 | 53,350 | 12,505 |
6. Labour | |||||||||
6.1 Costs increase to 30 US$/person-d | 3 | 4 | 0 | 6 | 13 | 96,212 | 109 | 37,091 | 17,662 |
6.2 Availability decreases to 100 person-d | 1 | 1 | 0 | 2 | 4 | 32,071 | 36 | 12,380 | 6204 |
7. Other costs | |||||||||
7.1 Increase in 50% for sugar beet | 0 | 10 | 2 | 0 | 12 | 81,744 | 115 | 25,683 | 10,416 |
7.2 Increase in 50% for maize | 5 | 0 | 0 | 6 | 11 | 89,835 | 95 | 32,687 | 17,122 |
7.3 Decrease in 50% for alfalfa | 3 | 4 | 0 | 6 | 13 | 96,212 | 109 | 34,032 | 20,722 |
7.4 Decrease in 50% for wheat | 3 | 4 | 0 | 6 | 13 | 96,212 | 109 | 36,000 | 18,754 |
8. Capital | |||||||||
8.1 Availability decreases to 50% | 3 | 0 | 0 | 6 | 10 | 79,035 | 78 | 30,922 | 16,577 |
Crop Allocation | Use of Resources | ||||||||
---|---|---|---|---|---|---|---|---|---|
Alfalfa | Maize | Wheat | Sugar Beet | Land | Water | Labor | Capital | Profits | |
(ha) | (ha) | (m3) | (Person-d) | (US$) | (US$) | ||||
1. Optimum cropping pattern | 0 | 0 | 0 | 20 | 20 | 167,460 | 120 | 80,000 | 46,177 |
2. Export prices | |||||||||
2.1 Decrease in 50% for sugar beet | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 572 | −71 |
2.2 Decrease in 50% for maize | 0 | 0 | 0 | 20 | 20 | 167,460 | 120 | 80,000 | 46,177 |
2.3 Increase in 50% for alfalfa | 0 | 0 | 0 | 20 | 20 | 167,739 | 121 | 80,000 | 46,224 |
2.4 Increase in 50% for wheat | 0 | 0 | 0 | 20 | 20 | 167,760 | 121 | 79,958 | 46,135 |
3. Agronomic management | |||||||||
3.1 Minimum area to be sowed corresponds to 3 ha | 3 | 3 | 3 | 5 | 14 | 101,803 | 113 | 36,395 | 7464 |
4. Application efficiency of the irrigation system | |||||||||
4.1 Sugar beet is irrigated by furrow () and | |||||||||
wheat by sprinkler () | 0 | 0 | 0 | 20 | 20 | 209,292 | 120 | 80,000 | 46,108 |
5. Water costs | |||||||||
5.1 Costs of water rights increase to 0.05 US$/m3 | 0 | 0 | 0 | 17 | 17 | 143,133 | 103 | 77,493 | 32,014 |
6. Labour | |||||||||
6.1 Costs increase to 30 US$/person-d | 0 | 0 | 0 | 20 | 20 | 163,870 | 118 | 79,363 | 43,920 |
6.2 Availability decreases to 100 person-d | 0 | 0 | 0 | 16 | 16 | 137,558 | 99 | 65,815 | 37,919 |
7. Other costs | |||||||||
7.1 Increase in 50% for sugar beet | 0 | 0 | 0 | 13 | 14 | 112,451 | 82 | 79,277 | 5221 |
7.2 Increase in 50% for maize | 0 | 0 | 0 | 20 | 20 | 167,433 | 121 | 79,988 | 46,074 |
7.3 Decrease in 50% for alfalfa | 0 | 0 | 0 | 20 | 20 | 168,256 | 122 | 79,980 | 46,268 |
7.4 Decrease in 50% for wheat | 0 | 0 | 0 | 20 | 20 | 168,256 | 122 | 79,980 | 46,268 |
8. Capital | |||||||||
8.1 Availability decreases to 50% | 0 | 0 | 0 | 10 | 10 | 83,074 | 60 | 39,972 | 22,872 |
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Kuschel-Otárola, M.; Rivera, D.; Holzapfel, E.; Palma, C.D.; Godoy-Faúndez, A. Multiperiod Optimisation of Irrigated Crops under Different Conditions of Water Availability. Water 2018, 10, 1434. https://doi.org/10.3390/w10101434
Kuschel-Otárola M, Rivera D, Holzapfel E, Palma CD, Godoy-Faúndez A. Multiperiod Optimisation of Irrigated Crops under Different Conditions of Water Availability. Water. 2018; 10(10):1434. https://doi.org/10.3390/w10101434
Chicago/Turabian StyleKuschel-Otárola, Mathias, Diego Rivera, Eduardo Holzapfel, Cristian D. Palma, and Alex Godoy-Faúndez. 2018. "Multiperiod Optimisation of Irrigated Crops under Different Conditions of Water Availability" Water 10, no. 10: 1434. https://doi.org/10.3390/w10101434
APA StyleKuschel-Otárola, M., Rivera, D., Holzapfel, E., Palma, C. D., & Godoy-Faúndez, A. (2018). Multiperiod Optimisation of Irrigated Crops under Different Conditions of Water Availability. Water, 10(10), 1434. https://doi.org/10.3390/w10101434