Persistence statistics of marine environmental parameters from Markov theory, Part 1: analysis in discrete time

Abstract

Reliable persistence statistics of marine environmental parameters such as the wave height, wind speed and direction can be established from an available record provided the record is sufficiently long. This investigation presents an easily applied statistical methodology for deriving the theoretical distribution of the persistence of marine environmental parameters from relatively short records. The basic assumption made is that the process may be regarded as a stationary first order Markov process whose transition matrix may be established from the given record. The transition matrix is considered as the fingerprint of the process of which the given record is only a single realisation. The work deals with the persistence statistics of an r-state chain and is condensed from consisting of only two states (one above and the other below the specified threshold level). It is shown that generally the use of progressively higher numbers of appropriately selected states results in a better description of the persistence statistics. Results from the proposed methodology are compared with observed persistence curves and those derived using the empirical methodology by 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 mean persistence durations derived from the record are identical to those derived from the Markov model. Higher order moments may show a significant deviation from the observed values owing to the small sample size of the persistence durations that may be derived from a short record. It is also shown that for the cases considered the present methodology compares favourably with the approach of Kuwashima and Hogben.