**Abstract**

Fractal dimension (FD) is a highly used mathematical tool to measure long-term memory of time series dataset in various research areas and also applied in chaos theory and fractal and spectral analysis. FD analysis has been applied in various disciplines, e.g., from biophysics, hydrology to computer networking. In developing countries like India, the water quality parameter characterization is very much challenging due to the increase of the contaminated substances in groundwater. In view of health issues and drinking water standards, water quality assurance is a requisite on the region basis. In order to quantify the same, a numerical index known as water quality index (WQI) well adopted by worldwide researchers has been recognized for its significance and applicability for water characterization. Further, the water quality parameters, such as turbidity, chloride, ferrous (Fe), nitrate, pH, calcium (Ca), magnesium (Mg) fluoride (Fl), total dissolved salts **(**TDS), alkalinity, hardness, and sulfate, could significantly improve the understanding through statistical and fractal modeling. Especially in the high mountainous regions of the Himalayas where there is scarcity of observed dataset, the predictability estimation will be highly applicable in WQI modeling. In the current study, statistical relationship among the sample datasets is obtained by regression equation, coefficient of correlation, Hurst exponent, and FD and probability index between water parameters for Tehri District. It is concluded that the fractal analysis is a better statistical and mathematical tool to calculate water quality indices. Fractal analysis among the various parameters suggested that the water samples are good for drinking and the health.

**Keywords:** water quality index, fractals, Hurst exponent, Himalayan region
