Assessing Scaling Behavior of Four Hydrological Variables Using Combined Fractal and Statistical Methods in Missouri River Basin

Evaluation of hydrological variables plays a vital role in watershed management studies. On top of that, Missouri River Basin system is well known as a large water storage capacity in the USA. In this study, multifractality, statistical features, and random behavior of daily flow discharge, suspended sediment discharge, precipitation, and groundwater level were analyzed in the two stations of Missouri River Basin, USA. Detrended fluctuation analysis and multifractal detrended fluctuation analysis were applied in order to evaluate seasonal trends, random behavior, self-affinity features, and the complexity of behavior types [fractional Brownian motion (fBm) and fractional Gaussian noise (fGn)] of time series. Statistical techniques, including the KPSS test, heteroscedasticity test, and autocorrelation function, were utilized to analyze statistical characteristics of repeating patterns of the datasets. Results of fractal and statistical analyses indicated that flow discharge, suspended sediment discharge, and groundwater time series were following self-affinity and fBm characteristics in a non-stationary and heteroscedastic state. Precipitation time series were not self-affine and represented fGn characteristics in a stationary and homoscedastic state. Eventually, this study can be proposed as an applicable method to distinguish the behavior of rivers and anthropogenic impacts in the watershed for effective hydrological planning management.