How to Adjust the fGn Stochastic Model for Statistical Bias when Handling a Single Time Series; Application to Annual Flood Inundation

Abstract

A simple scaling model known as the fractional Gaussian noise is often chosen for the description of several annual (and of larger) scale hydroclimatic processes exhibiting the Hurst phenomenon. An important characteristic of such model is the induced large statistical bias, i.e. the deviation of a statistical characteristic (e.g. variance) from its theoretical discretized value. Most studies in literature perform stochastic modelling by equating the sampling second order dependence structure with the expected value of the estimator of a stochastic model. However, this is justified only when many realizations (i.e. many time series) of a single process are available. In case where we have a single realization we should model the mode estimator of the dependence structure of the desired stochastic model instead, otherwise we may overestimate the extremeness of a realization, e.g. flood event. In this study, we show an innovative way of handling the statistical bias for an fGn process when analyzing one time series. Particularly, we conduct a thorough Monte-Carlo analysis based on the climacogram (i.e., marginal distribution of a scaled process, with focus on the second central moment of variance that is shown to be the least uncertain from the rest central moments) of an fGn process and we propose to equate the 25% quartile (and not the expected) value of the modeled climacogram with the sampling one to correctly adjust the model for bias.