  We deal with a new maximum principle-based stochastic control model for river
management through operating a dam and reservoir system. The model is based on
coupled forward-backward stochastic differential equations (FBSDEs) derived
from jump-driven streamflow dynamics and reservoir water balance. A
continuous-time branching process with immigration driven by a tempered stable
subordinator efficiently describes clustered inflow streamflow dynamics. This
is a completely new attempt in hydrology and control engineering. Applying a
stochastic maximum principle to the dynamics based on an objective functional
for designing cost-efficient control of dam and reservoir systems leads to the
FBSDEs as a system of optimality equations. The FBSDEs under a linear-quadratic
ansatz lead to a tractable model, while they are solved numerically in the
other cases using a least-squares Monte-Carlo method. Optimal controls are
found in the former, while only sub-optimal ones are computable in the latter
due to a hard state constraint. Model parameters are successfully identified
from a real data of a river in Japan having a dam and reservoir system. We also
show that the linear-quadratic case can capture the real operation data of the
system with underestimation of the outflow discharge. More complex cases with a
realistic time horizon are analyzed numerically to investigate impacts of
considering the environmental flows and seasonal operational purposes. Key
challenges towards more sophisticated modeling and analysis with jump-driven
FBSDEs are discussed as well.
