**4.4 Nitrate**

Mean and median values and standard deviation are approximately equal; thus data exhibit normal behavior. This suggests that the sample data are close to each other. The skewness value (1.011) and kurtosis are less than 3; hence the curve is not symmetrical and platykurtic. Nitrate has persistent behavior with turbidity, chloride, fluoride, TDS, alkalinity, hardness, and sulfate and anti-persistent behavior with Ca, Mg, Fe, and PH parameters.

#### *4.4.1 pH*

Average and median are almost same, i.e., 7.189 and 7.20, respectively, whereas the mode of pH is 0.25. These values are approximately equal and hence exhibit the normal behavior. Standard deviation (SD) is 0.691, and skewness is close to 0, and all values are also close to each other; thus pH is symmetrical. The curve is not platykurtic, as kurtosis is very large 74.92. It shows the Brownian time series behavior with fluoride (Fl) parameter; persistent behavior with Ca, Mg, Fe, and nitrate; and anti-persistent performance with different parameters, i.e., turbidity, chloride, TDS, alkalinity, hardness, and sulfate.

### *4.4.2 Calcium*

Mean, median, and mode values are not close to each other; thus the curve does not show normal behavior. High standard deviation (40) indicates that the Ca values are very much distributed from each other. It is positively skewed, and the

of the statistical and fractal analysis is shown in **Table 2**, and each WQI analysis is

*Regression equation, coefficient of correlation, Hurst exponent, fractal dimension, and probability index*

The turbidity sample datasets exhibit normal behavior as the mean, median, and mode values are approximately equal. Standard deviation is found to be 1.5 and

discussed subsequently.

*between water parameters at Tehri District.*

**Y Parameters-**

*Fractal Analysis - Selected Examples*

**X**

**Regression equation r<sup>2</sup> H D**

pH y = 0.0003732\*x + 7.1463 0.001183 1.2073 0.79271 1.4146 Calcium y = 0.24353\*x + 12.683 0.1511 1.4105 0.58949 1.821 Magnesium y = 0.10221\*x + 19.0295 0.01671 1.4381 0.56193 1.8761 Fluoride y = 0.0011091\*x + 0.1554 0.070809 1.0896 0.91044 1.1791 TDS y = 0.67597\*x + 29.1685 0.13638 1.0559 0.94412 1.1118 Hardness y = 0.53406\*x + 75.1633 0.1099 1.4326 0.56739 1.8652 Sulfate y = 0.12922\*x + 0.30058 0.23032 1.0907 0.9093 1.1814

Nitrate y = 0.00040404\*x + 2.6254 0.000151 0.98687 1.0031

Hardness Turbidity y = 0.0027505\*x + 1.2446 0.035196 0.73752 1.2625 0.47503

Sulfate Turbidity y = 0.0066538\*x + 1.5236 0.005754 0.93736 1.0626 0.87472

Chloride y = 0.13279\*x + 1.1384 0.20972 0.89036 1.1096 0.78071 Ferrous y = 0.00823\*x + 0.14631 0.018721 1.6664 0.33359 2.3328 Nitrate y = 0.0061497\*x + 2.7619 0.002539 1.0315 0.96846 1.0631 pH y = 0.0034876\*x + 7.1384 0.007486 1.3298 0.67025 1.6595 Calcium y = 0.48637\*x + 33.6799 0.043691 1.3417 0.65832 1.6834 Magnesium y = 0.085194\*x + 29.5794 0.000842 1.3882 0.61179 1.7764 Fluoride y = 0.004982\*x + 0.21061 0.1036 1.051 0.94905 1.1019 TDS y = 1.7448\*x + 81.682 0.06587 0.8804 1.1196 0.76081 Alkalinity y = 1.7825\*x + 89.3566 0.23032 0.82887 1.1711 0.65774 Hardness y = 1.6107\*x + 113.2606 0.072467 1.2378 0.76216 1.4757

Chloride y = 0.0077766\*x + 2.0148 0.02575 0.6886 1.3114 0.37721 Ferrous y = 0.0005587\*x + 0.19012 0.00309 1.1735 0.82654 1.3469 Nitrate y = 0.0013699\*x + 2.4847 0.004511 0.69629 1.3037 0.39259 pH y = 0.0001197\*x + 7.1729 0.000316 0.91947 1.0805 0.83895 Calcium y = 0.10221\*x + 26.8046 0.069075 0.97954 1.0205 0.95908 Magnesium y = 0.2265\*x + 0.15996 0.21297 1.0545 0.9455 1.109 Fluoride y = 0.0002939\*x + 0.2432 0.012907 0.74932 1.2507 0.49865 TDS y = 0.34256\*x + 60.3158 0.090894 0.68805 1.312 0.3761 Alkalinity y = 0.20579\*x + 87.25 0.1099 0.64706 1.3529 0.29411 Sulfate y = 0.044992\*x + 8.4565 0.072467 0.73569 1.2643 0.47139

**(Fractal)**

**PI**

**4.1 Turbidity**

**Table 2.**

**30**

curve is not platykurtic. With few parameters, i.e., turbidity, chloride, TDS, alkalinity, hardness, Mg, Fl, TDS, and sulfate, it shows persistent behavior and antipersistent behavior with Fe and pH parameters.

*4.4.8 Sulfate*

**5. Conclusion**

ity, chloride, TDS, and alkalinity.

**33**

behavior with hardness, Fe, PH, Ca, and Mg parameters.

Mean and median values are different and mode value is 0. Standard deviation (17.16) reveals that the dataset has distributed form. The skewness value is equal to 2.40 with larger kurtosis value, i.e., 7.22, which indicates that the curve is not symmetrical. It has true random walk flow with Fl and nitrate parameters. Sulfate has persistent behavior with turbidity, chloride, TDS, and alkalinity and anti-

persistent behavior with hardness, Fe, PH, Ca, and Mg parameters.

*Fractal Analysis for Time Series Datasets: A Case Study of Groundwater Quality*

*DOI: http://dx.doi.org/10.5772/intechopen.92865*

The water parameters from different sources in the Tehri District of Uttarakhand have shown the non-platykurtic curve. The analysis of most of the water parameter combinations has shown the Brownian time series behavior with each other. The irregular pattern in the WQI can be used for prediction purposes by deciding if its dynamic follows a chaotic, random, or deterministic structural pattern. Mostly all groundwater variables like turbidity, chloride, iron, nitrate, pH, calcium, magnesium, fluoride, TDS, alkalinity, hardness, sulfate, etc. are affected by each other. The pH of the sample datasets shows the Brownian time series behavior with fluoride (Fl) parameter; persistent behavior with Ca, Mg, Fe, and nitrate; and anti-persistent performance with turbidity, chloride, TDS, alkalinity, hardness, and sulfate. Turbidity, chloride, nitrate, fluoride, TDS, alkalinity, sulfate, and chloride have shown persistent behavior with each other. Fe has persistent behavior with pH, Ca, and Mg, and nitrate has persistent behavior with turbidity, chloride, fluoride, TDS, alkalinity, hardness, and sulfate. pH has persistent behavior with Ca, Mg, Fe, and nitrate. Turbidity, chloride, TDS, alkalinity, hardness, Mg, Fl, TDS, sulfate, and Ca show persistent behavior. Mg has persistent behavior with turbidity, chloride, nitrate, Ca, TDS, hardness, Fl, and sulfate. Fl has persistent behavior with turbidity, chloride, TDS, alkalinity, and sulfate. TDS has persistent behavior with alkalinity, nitrate, and chloride. Alkalinity has persistent behavior with nitrate only. Hardness has persistent behavior with turbidity, chloride, nitrate, pH, Ca, Fl, TDS, alkalinity, and sulfate. Sulfate has persistent behavior with turbid-

Turbidity and chloride have anti-persistent behavior with Fe, pH, Ca, Mg, and hardness parameters. Fe has anti-persistent behavior with chloride, TDS, alkalinity, and sulfate parameters. Nitrate has anti-persistent behavior with Ca, Mg, Fe, and pH parameters. pH has anti-persistent performance with different parameters, i.e., turbidity, chloride, TDS, alkalinity, hardness, and sulfate. Mg has anti-persistent behavior with Fe parameters only and Ca with Fe and pH parameters. Fl has antipersistent behavior with Fe, pH, Ca, and Mg parameters. TDS has anti-persistent behavior with Fe, Ca, Mg, and hardness parameters. Alkalinity has anti-persistent behavior with turbidity, Fe, pH, Ca, Mg, and hardness parameters. Hardness has anti-persistent behavior with Fe parameter only, and sulfate has anti-persistent

The persistent behavior is observed among the various indices which reveal that the variations of the water quality parameters are under an acceptable range with each other. This study is focused on the utility of the Hurst exponent, fractal dimension as an analysis tool, and predictability indices (PI) along with regression and coefficient of correlation among the water quality time series data points. 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.

#### *4.4.3 Magnesium*

Mean and mode values are 30.75 and 22.0, respectively, and median is 0, so the sample dataset are not same, and thus the curve does not show normal behavior. Standard deviation value is high (50.368); thus, the values of Mg are very much distributed with each other. It is positively skewed, and the curve is not platykurtic. Mg has Brownian time series (true random walk) behavior with pH and alkalinity parameters. Mg has persistent behavior with turbidity, chloride, nitrate, Ca, TDS, hardness, Fl, and sulfate and anti-persistent behavior with Fe parameters.
