A Volterra Process Model for River Water Temperature

Water temperature as a key indicator of river environments evolves dynamically as well as stochastically. We introduce a new mathematical framework for modeling river water temperature at an observation station based on a Volterra process: a non-Markovian model. The non-Markovian nature arises from a non-exponential autocorrelation function, which is effectively captured by a completely monotone kernel. Parameters of the model are identified for a study site in Japan where the water temperature has been measured at a 10-min interval. We show that the observed time series of the water temperature is separated into seasonal and stochastic parts, and that the non-exponential autocorrelation function is fitted well by the proposed model. A brief application of the model to statistical evaluation of the river water temperature subject to misspecification is finally presented.