Multifractal Applications in Hydro-Climatology: A Comprehensive Review of Modern Methods - Shamseena Vahab; Adarsh Sankaran (Fractal and Fractional)
Complexity evaluation of hydro-climatic datasets is a challenging but essential pre-requisite for accurate modeling and subsequent planning. Changes in climate and anthropogenic interventions amplify the complexity of hydro-climatic time-series. Understanding persistence and fractal features may help us to develop new and robust modeling frameworks which can work well under non-stationary and non-linear environments. Classical fractal hydrology, rooted in statistical physics, has been developed since the 1980s and the modern alternatives based on de-trending, complex network, and time–frequency principles have been developed since 2002. More specifically, this review presents the procedures of Multifractal Detrended Fluctuation Analysis (MFDFA) and Arbitrary Order Hilbert Spectral Analysis (AOHSA), along with their applications in the field of hydro-climatology. Moreover, this study proposes a complex network-based fractal analysis (CNFA) framework for the multifractal analysis of daily streamflows as an alternative. The case study proves the efficacy of CNMFA and shows that it has the flexibility to be applied in visibility and inverted visibility schemes, which is effective in complex datasets comprising both high- and low-amplitude fluctuations. The comprehensive review showed that more than 75% of the literature focuses on characteristic analysis of the time-series using MFDFA rather than modeling. Among the variables, about 70% of studies focused on analyzing fine-resolution streamflow and rainfall datasets. This study recommends the use of CNMF in hydro-climatology and advocates the necessity of knowledge integration from multiple fields to enhance the multifractal modeling applications. This study further asserts that transforming the characterization into operational hydrology is highly warranted.