# Model Documentation

### | Version 4.0

created with goxygen 0.21.1

# 41_area_equipped_for_irrigation

# Area equipped for irrigation (41_area_equipped_for_irrigation)

## Description

The area equipped for irrigation module constrains irrigated crop production to those areas that are equipped with irrigation infrastructure and simulates the evolution of areas equipped for irrigation. The module receives information about the area actually irrigated from the 30_crop module.

## Interfaces

Interfaces to other modules

### Input

module inputs (A: endo_apr13 | B: static)
| Description | Unit | A | B
--- | --- | --- | --- | ---
pm_interest (i) | Current interest rate in each region | \(\%/yr\) | x |
vm_area (j, kcr, w) | Agricultural production area | \(10^6 ha\) | x | x

### Output

module outputs
| Description | Unit
--- | --- | ---
vm_cost_AEI (i) | Irrigation expansion costs | \(10^6 USD_{04MER}/yr\)

## Realizations

### (A) endo_apr13

This realization allows the model to endogenously decide on investments to deploy additional irrigation infrastructure, i.e. to increase the area equipped for irrigation (AEI). Initial values for AEI in 1995 are taken from Siebert et al. (2007). Contraction of AEI is not possible. Irrigated crop production can only take place where irrigation infrastructure is present.

Unit costs per hectare for AEI expansion are derived from a World Bank study (Jones (1995)) and adjusted for the regions used in MAgPIE. The region mapping is as follows:

Mapping between MAgPIE regions and the regions in (Jones 1995)

The regional unit costs converge linearly towards the European level until 2050.

Unit costs for AEI expansion in MAgPIE

\[\begin{multline*} \sum_{kcr} vm\_area(j2,kcr,"irrigated") \leq v41\_AEI(j2) \end{multline*}\] \[\begin{multline*} v41\_cost\_AEI\_annuity(i2) = \sum_{cell(i2,j2)}\left(v41\_AEI(j2)-pc41\_AEI\_start(j2)\right) \cdot pc41\_unitcost\_AEI(i2) \cdot \frac{pm\_interest(i2)}{\left(1+pm\_interest(i2)\right)} \end{multline*}\]

Investment costs in the current time step for each region are calculated by multiplying the AEI expansion in each cluster of the region by the regional unit cost per hectare. MAgPIE has a common planning horizon to which all one time investments are distributed using an annuity approach. Due to this distribution, part of the costs from previous investments in AEI still entail costs in the current time step.

\[\begin{multline*} vm\_cost\_AEI(i2) = v41\_cost\_AEI\_annuity(i2) + pc41\_cost\_AEI\_past(i2) \end{multline*}\]

> Limitations This realization increases model complexity.

### (B) static

In this realization, area equipped for irrigation is fixed to input data (around the year 2000) for all time steps. The source of the input data is Siebert et al. (2007).

\[\begin{multline*} \sum_{kcr} vm\_area(j2,kcr,"irrigated") \leq v41\_AEI(j2) \end{multline*}\]

This realization assures that irrigated crop production can only take place where irrigation infrastructure is present, i.e. the sum of irrigated cropland `vm_area(j,kcr,"irrigated")` over all crops in each grid cell has to be less than or equal to the area in this grid cell that is equipped with irrigation infrastructure (`v41_AEI(j)`).

> Limitations No irrigation is possible on areas that have not been equipped for irrigation in the past.

## Definitions

### Objects

module-internal objects (A: endo_apr13 | B: static)
| Description | Unit | A | B
--- | --- | --- | --- | ---
f41_c_irrig (t_all, i) | Irrigation investment costs | \(USD_{04MER}/ha\) | x |
f41_irrig (j) | Available area equipped for irrigation [AVL] | \(10^6 ha\) | x | x
p41_AEI_start (t, j) | Area equipped for irrigation at the beginning of each time step | \(10^6 ha\) | x |
p41_cost_AEI_past (t, i) | Costs for AEI expansion from the past | \(10^6 USD_{04MER}\) | x |
pc41_AEI_start (j) | Area equipped for irrigation at the beginning of current time step | \(10^6 ha\) | x |
pc41_cost_AEI_past (i) | Current costs for AEI expansion from the past | \(10^6 USD_{04MER}\) | x |
pc41_unitcost_AEI (i) | Unit cost of AEI expansion | \(USD_{04MER}/ha\) | x |
q41_area_irrig (j) | Irrigation area constraint | \(10^6 ha\) | x | x
q41_cost_AEI_annuity (i) | Calculation of annuity costs of AEI expansion | \(10^6 USD_{04MER}\) | x |
q41_cost_AEI (i) | Calculation of costs of irrigation area expansion | \(10^6 USD_{04MER}\) | x |
v41_AEI (j) | Area equipped for irrigation in each grid cell | \(10^6 ha\) | x | x
v41_cost_AEI_annuity (i) | Annuity costs of AEI expansion in the current time step | \(10^6 USD_{04MER}/yr\) | x |

### Sets

sets in use
| description
--- | ---
i | World regions
kcr(kve) | Cropping activities
t_all | 5-year time periods
t(t_all) | Simulated time periods
w | Water supply type

## Authors

Anne Biewald, Markus Bonsch, Christoph Schmitz

## See Also

11_costs, 12_interest_rate, 30_crop, 41_area_equipped_for_irrigation

## References

Jones, William I. 1995. “World Bank and Irrigation.” Washington, D.C.: World Bank.

Siebert, Stefan, Petra Döll, Sebastian Feick, Jippe Hoogeveen, and Karen Frenken. 2007. “Global Map of Irrigation Areas Version 4.0.1.” Johann Wolfgang Goethe University, Frankfurt Am Main, Germany / Food and Agriculture Organization of the United Nations, Rome, Italy. http://www.fao.org/nr/water/aquastat/irrigationmap/index10.stm.