Persistence statistics of marine environmental parameters from Markov theory, part 2: analysis in continuous time

Abstract

Part 1 of the present investigation dealt with the derivation of reliable estimates of the persistence statistics of marine environmental parameters from relatively short records, treating the process as a Markov chain in discrete time. In part 2 of the work the marine environmental parameters are treated as Markov chains in continuous time, and the theoretical distribution of the persistence is established in terms of the long term probability distribution of each parameter of interest, and the mean persistence duration above or below each one of the threshold levels which define its states. The mean persistence durations of parameters like the wave height or wind speed, if they are not known, are established using the empirical relationships of Kuwashima-Hogben [Kuwashima, S. & Hogben, N., The estimation of wave height and wind speed persistence statistics from cumulative probability distributions. Coastal Engng, 9 (1986) 563–590]. It is shown that, in contrast with the discrete time case, the persistence distribution in continuous time is a weighted sum of exponential distributions. Theoretical predictions are compared with observed persistence distribution curves, those derived from the discrete Markov model, and those based on the Kuwashima-Hogben methodology. The presented results show close agreement in general between the two Markov models (discrete and continuous) and the observed persistence distribution curves, while the Kuwashima-Hogben model tends to overestimate observed behaviour.