A simple method for calculating the probability of quiescent periods in random seas for maritime search and rescue operations

The identification of quiescent periods in oceans and regional waters is an important task that ensures safer operations in the marine environment. If such identification is done through a probabilistic approach on a geographical scale, it can be used for quick planning of search and rescue operations. This paper aims to present a simple equation that can be universally used for calculating the waiting time for a desired quiescent period to emerge. This is achieved through monitoring various low-run waves occurring in different sea states. The related data is numerically generated using a high fidelity code that permits the fully nonlinear solution of water waves propagating in a computational domain under nonlinear conditions set for the upper layer of the fluid. The probability distributions of quiescent runs are found and then formulated using a modified geometric distribution function. This function is identified by one parameter. The subtraction of this parameter from unity is equivalent to the probability of two successive low waves. This parameter is observed to decrease with an increase in the wave height threshold and is found to be nearly insensitive to variables representing sea states. An equation is established for calculating the parameter used in the calculation of quiescent period probabilities. The probability curves of quiescent runs constructed using a geometric distribution function are observed to be in fair agreement with those found in the numerical data. The suggested method for calculating quiescent period probabilities is straightforward and can be easily used to compute the waiting time for desired quiescent periods on a geographical scale.