  Causal structure discovery (CSD) models are making inroads into several
domains, including Earth system sciences. Their widespread adaptation is
however hampered by the fact that the resulting models often do not take into
account the domain knowledge of the experts and that it is often necessary to
modify the resulting models iteratively. We present a workflow that is required
to take this knowledge into account and to apply CSD algorithms in Earth system
sciences. At the same time, we describe open research questions that still need
to be addressed. We present a way to interactively modify the outputs of the
CSD algorithms and argue that the user interaction can be modelled as a greedy
finding of the local maximum-a-posteriori solution of the likelihood function,
which is composed of the likelihood of the causal model and the prior
distribution representing the knowledge of the expert user. We use a real-world
data set for examples constructed in collaboration with our co-authors, who are
the domain area experts. We show that finding maximally usable causal models in
the Earth system sciences or other similar domains is a difficult task which
contains many interesting open research questions. We argue that taking the
domain knowledge into account has a substantial effect on the final causal
models discovered.
