| Summary: | The main objective of this research was to develop models and procedures that would allow
water managers to evaluate the impact of alternative water conservation and demand
management principles in irrigated agriculture over the long-run and the short-run while taking
risk into account.
One specific objective was to develop a generalised whole-farm stochastic dynamic linear
programming (DLP) model to evaluate the impact of price incentives to conserve water when
irrigators have the option to adopt more efficient irrigation technology or cultivate high-value
crops over the long-run. The DLP model could be characterised as a disequilibrium known life
type of model where terminal values were calculated with a normative approach. MOTAD
(Minimising Of Total Absolute Deviations) was used to model risk. Another specific objective
was to develop an expected utility optimisation model to economically evaluate deficit irrigation
within a multi-crop setting while taking into account the increasing production risk of deficit
irrigation in the short-run.
The dynamic problem of optimising water use between multiple crops within a whole-farm
setting when intraseasonal water supply may be limited was approximated by the inclusion of
multiple irrigation schedules into the short-run model. The SAPWAT model (South African Plant
WATer) was further developed to quantify crop yield variability of deficit irrigation while taking
the non-uniformity of irrigation applications into account. Stochastic budgeting procedures were
used to generate appropriately correlated inter- and intra-temporal matrixes of gross margins
necessary to incorporate risk into the long-run and short-run water use optimisation models. A
new procedure (standard risk aversion) was developed to standardise values of absolute risk
aversion with the objective of establishing a plausible range of risk aversion levels for use with
stochastic efficiency analysis techniques. A procedure was developed to conduct stochastic
efficiency with respect to a negative exponential utility function using standard risk aversion. The
standardised risk aversion measure produced consistent answers when the risk premium was
expressed as a percentage of the range of the data.
Long-run results showed that the elasticity of irrigation water demand was low. Overall risk
aversion and the individual farming situation will have an important impact on the effectiveness
of water tariff increases when it comes to water conservation. Although the more efficient
irrigation technology scenario had a higher net present value when compared to flood irrigation,
the ability to pay for water with the first mentioned scenario was lower because the lumpy
irrigation technology needs to be financed. Failure to take risk into account would cause an
over- or underestimation of the shadow value of water, depending on whether water was valued
as relatively abundant or scarce. The conclusion was that care should be taken when interpreting the derived demand for irrigation water (elasticity) without knowing the conditions
under which they were derived. Cognisance should also be taken of the fact that higher gross
margins per unit of applied water would not necessarily result in greater willingness to pay for
water when the alternatives were evaluated on a whole-farm level.
The main conclusion from the short-run analyses was that although deficit irrigation was
stochastically more efficient than full irrigation under limited water supply conditions, irrigation
farmers would not willingly choose to conserve water through deficit irrigation and would be
expected to be compensated to do so. Deficit irrigation would not save water if the water that
was saved through deficit irrigation were used to plant larger areas to increase the overall
profitability of the strategy. Standard risk aversion was used to explain the simultaneous
increasing and decreasing relationship between the utility-weighted premiums and increasing
levels of absolute risk aversion and was shown to be more consistent than when constant
absolute risk aversion was assumed.
The modelling framework and the models that were developed in this research provide powerful
tools to evaluate water allocation problems that are identified while busy implementing the
National Water Act. Only through the application of these type of models linked to hydrological
models will a better understanding of the mutual interaction amongst water legislation, water
policy administration, technology, hydrology, human value systems and the environment be
gained to enhance water policy formulation and implementation.
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