Irrigation in the Zambezi River Basin:Flexibility under Climate Uncertainty

Arthur Gueneau

December 13, 2011

The Zambezi River Basin

The Zambezi River Basin

Irrigation in the Zambezi Basin

Climate Change Uncertainty Uncertainty in precipitation patterns

drive uncertainty in irrigation need for the crops.

We can quantify this uncertainty using a hybridized frequency distribution model of regional climate (Schlosser et al., 2011) coupled to the MIT Integrated Global System Model (Sokolov et al., 2005).

Climate Change Uncertainty

Change in the 10-day average precipitation in 2050 versus 2000 obtained using the HFD method (Schlosser et al., 2011)

Crop Irrigation Uncertainty

The resulting distribution of the change in crop irrigation need follows the pattern of a log-normal distribution.

Lattice modeling of the uncertainty

We use the standard formula to fit the lattice to the lognormal distribution of the irrigation need in 2050.

The farm

System Designs Short-term vision Project: This project has no

flexibility; it invests in 2011, to maximize the Net Present Value considering that the irrigation need stays constant over the whole period. The level of investment is chosen at the first time period so as to maximize the discounted return of the project and investments are zero for all following years.

World-Bank led 2010 infrastructure project: This project has no flexibility; it invests in 2011 using the best guess for the irrigation need over the years (no change to precipitations). This path has the advantage to ensure that the irrigation capacity design chosen at the beginning will be optimal by maximizing the net present value of the project. The level of investment is chosen at the first time period so as to maximize the discounted return of the project and investments are zero for all following years. 

Flexible irrigation project with possibility of extension: The same project as previously is built at the first time-step as it maximizes the Net Present Value. However, we now allow flexibility. To be precise we allow the farmer who owns the land to expand the irrigation system by another 100 ha if she thinks it is necessary.

Net Present Value Calculation

We use the lattice analysis with no flexibility first. The short-term vision project would lead to an investment of 400ha irrigated.

A project maximizing ENPV would build for 450ha of irrigation.

Flexibility implementation

We use dynamic programming to calculate the NEPV in each cell for the future with and without investment and decide whether it is beneficial or not.

The lattice above shows in which cell we decide to make the supplemental investment.

Flexibility implementationUnder flexibility, the system becomes path-dependent as the choice to exercise flexibility is not reversible.

As there are too many path to explore one by one on the lattice we use a Monte-Carlo simulation that goes through the lattice to compute an output using the decision rule drawn from the lattice analysis.

Findings – VARG curves

Table of findings

ENPV: The flexible design is clearly better, by the design of the decision ruleStandard Deviation: the benefit being smaller, the “no anticipation design does better – not really pertinent here as ENPVs are differentValue at 10%: Less irrigation does better if climate actually becomes wetter, interesting to notice that non-flexible and flexible do the sameValue at 90%: The flexible design does better as it is designed to improve the performance under a dry climate (and high irrigation need)Benefit-Cost Ratio: Less investment gives a higher B-C ratio as the benefits are heavily discounted in the future.

Real Value of Flexibility

Total benefit of the farm (including rainfed crops): System flexibility acts as an insurance against bad climate outcome

Conclusions Flexibility acts as an insurance

against bad climate outcomes: there is a possibility of irrigating more if the climate becomes drier.

The difference in ENPV ($15,000) gives an indication on how much the farmer should be willing to pay to get a more powerful pump, but is not a limit as she may be risk-averse.

Questions

Irrigated farmland in Kenya