from Wikipedia:
A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network. In a regular Markov model, the state is directly visible to the observer, and therefore the state transition probabilities are the only parameters. In a hidden Markov model, the state is not directly visible, but output, dependent on the state, is visible. Each state has a probability distribution over the possible output tokens. Therefore the sequence of tokens generated by an HMM gives some information about the sequence of states. Note that the adjective ‘hidden’ refers to the state sequence through which the model passes, not to the parameters of the model; even if the model parameters are known exactly, the model is still ‘hidden’. Hidden Markov models are especially known for their application in temporal pattern recognition such as speech, handwriting, gesture recognition, part-of-speech tagging, musical score following, partial discharges and bioinformatics.
A hidden Markov model can be considered a generalization of a mixture model where the hidden variables (or latent variables), which control the mixture component to be selected for each observation, are related through a Markov process rather than independent of each other.
Climate models. See the papers by Lambert, Hughes.
M Lambert, J.Whiting, A.Metcalfe, 2003 A non Parametric Hidden Markov Model for Climate State Identification
James P. Hughes , Peter Guttorp , Stephen P. Charles, 1998 A Nonhomogeneous Hidden Markov Model for Precipitation Occurrence