  The ongoing California drought has highlighted the potential vulnerability of
state water management infrastructure to multi-year dry intervals. Due to the
high complexity of the network, dynamic storage changes across the California
reservoir system have been difficult to model using either conventional
statistical or physical approaches. Here, we analyze the interactions of
monthly volumes in a network of 55 large California reservoirs, over a period
of 136 months from 2004 to 2015, and we develop a latent-variable graphical
model of their joint fluctuations. We achieve reliable and tractable modeling
of the system because the model structure allows unique recovery of the
best-in-class model via convex optimization with control of the number of free
parameters. We extract a statewide `latent' influencing factor which turns out
to be highly correlated with both the Palmer Drought Severity Index (PDSI,
$\rho \approx 0.86$) and hydroelectric production ($\rho \approx 0.71$).
Further, the model allows us to determine system health measures such as
exhaustion probability and per-reservoir drought sensitivity. We find that as
PDSI approaches -6, there is a probability greater than 50\% of simultaneous
exhaustion of multiple large reservoirs.
