  In the expeditionary sciences, spatiotemporally varying environments --
hydrothermal plumes, algal blooms, lava flows, or animal migrations -- are
ubiquitous. Mobile robots are uniquely well-suited to study these dynamic,
mesoscale natural environments. We formalize expeditionary science as a
sequential decision-making problem, modeled using the language of
partially-observable Markov decision processes (POMDPs). Solving the
expeditionary science POMDP under real-world constraints requires efficient
probabilistic modeling and decision-making in problems with complex dynamics
and observational models. Previous work in informative path planning, adaptive
sampling, and experimental design have shown compelling results, largely in
static environments, using data-driven models and information-based rewards.
However, these methodologies do not trivially extend to expeditionary science
in spatiotemporal environments: they generally do not make use of scientific
knowledge such as equations of state dynamics, they focus on information
gathering as opposed to scientific task execution, and they make use of
decision-making approaches that scale poorly to large, continuous problems with
long planning horizons and real-time operational constraints. In this work, we
discuss these and other challenges related to probabilistic modeling and
decision-making in expeditionary science, and present some of our preliminary
work that addresses these gaps. We ground our results in a real expeditionary
science deployment of an autonomous underwater vehicle (AUV) in the deep ocean
for hydrothermal vent discovery and characterization. Our concluding thoughts
highlight remaining work to be done, and the challenges that merit
consideration by the reinforcement learning and decision-making community.
