Equitable water allocation in real-world irrigation systems is hampered
by supply fluctuations, posing a significant challenge to the goal of
promoting fairness among consumers. In this paper, we concern ourselves
with the limits of equity achievable for any water allocation scheme
across the entire spectrum of water supply conditions. In the process,
we develop a typology of canonical water allocation mechanisms that
categorizes mechanisms w.r.t. the distribution of fulfilled demand
across the users. Adopting specific notions of supply reliability and
distribution equity, we derive the theoretical performance limits for
all canonical mechanisms and extend the analysis to arbitrary allocation
mechanisms. We show that for any value of supply reliability, the best
possible equity is realized by mechanisms that uniformly distribute
water among users, whereas the worst possible equity is associated with
mechanisms that prioritize the demand of some users before allocating
water to others. We also show that any intermediate equity level can be
realized by adjusting the initial entitlements prior to allocating water
to fulfill demands, in an approach we categorize as hybrid allocation.
We parameterize the performance boundaries for such allocation schemes
based on the fraction of supply allocated to initial entitlements. We
discuss how this parameter can serve as a policy tool to balance the
goals of equitable water access with other system-level objectives. In
the end, we complement the analytical results with numerical simulations
of a selected agricultural district from a real-world irrigation system
and speculate about the application of our study to large-scale
hierarchical systems.