Using Multiple Stochastic Tools in Identification of Scaling in Hydrometeorology

Abstract:

The identification and quantification of stochastic scaling laws has been an important task in modelling of hydrometeorological processes. Stochastic tools such as the power spectrum, autocovariance function, structure and climacogram have been among the most powerful. However, the common practice of using solely one of them may lead to process misinterpretation. We introduce a methodology that compares these stochastic tools and seeks the optimal one for different scales in terms of minimizing fitting errors. For validation and illustration purposes, we apply this methodology to various fundamental stochastic processes, such as Markovian, Hurst-Kolmogorov and Cauchy type ones. For each one, we produce Gaussian synthetic time series, we estimate the uncertainty of their expected values and finally, we conclude upon the ones with the smallest uncertainty. Furthermore, we apply this method to a real case time-series of high resolution turbulent flow velocities.