## 3.1. Volume estimation

The ArcGIS Surface Volume module and raster DEM were utilized for the calculation of the reservoir water volume. The capacity of water is calculated based on Lu et al. (2013), the relative surface, and base height or reference level.

\(V={\sum }_{i=1}^{n}\frac{Si({h}_{i} + {h}_{i}+1 + {h}_{i}+2)}{3}\) (3)

where the volume total (m3) is V, the area projected (m2) is Si of the submerged land on the surface of the water, distance (m) are hi, hi+1, and hi+2, the submerged of water, and n is the number of triangular grids (Lu et al. 2013).

## 3.2. Reservoir Level-Area-Volume relationship Curve Fitting

Linear, power, exponential, polynomial, and logarithmic models were used to determine the relationship between water surface area and the water level (Ling et al. 2012; Zhu et al. 2014). Five models are used to identify the relationship between water surface area computed from Landsat images, in-situ water levels acquired by WAPDA, and Volume estimated using bathymetry of the reservoir. Therefore, the optimal connection among them finds.

The linear trend line is the finest used with linear data sets when the data points in a chart bar and resemblance to a straight line. Characteristically, a linear function defines a constant increase or decrease over time. The least-squares equation is used to pursue the slope and intercept coefficients such as:

\(y=bx+\)a (4)

Where the trend line slope is b. The intercept-y is a. the projected-y mean-value where x variables are equal to 0.

The exponential model is a line that demonstrates the values of data at an increasing rate. Consequently, it is extra curved at one side. For this model,

\(y=a{e}^{bx}\) (5)

Where calculated coefficients are a, and b. e is the mathematical constant (the natural logarithm base). The logarithmic line is generally used to plot data on the chart, and represented increases or decreases and then levels off containing both negative and positive values. The logarithmic model equation is:

\(y=a*\text{ln}\left(x\right)+b\) (6)

Where constants are a and b and the natural logarithm function is ln.

The trendline of polynomial curvilinear suits fine with oscillating values of huge data sets having greater than one up and down. Normally, it is classified by the largest exponent degree. The trendline equation of polynomial used is:

\(y={b}_{6}{x}^{6}+{ \dots +b}_{2}{x}^{2}+{b}_{1}x+a\) (7)

Where constants are b1…b6 and a. It depends on the degree of your polynomial trend line which is one of the succeeding groups of formulas that can be used to get the constant.

Quadratic (2nd order) polynomial Equation:

\(y={b}_{2}{x}^{2}+{b}_{1}x+a\) (8)

Cubic (3rd order) polynomial Equation:

\(y={b}_{3}{x}^{3}+{b}_{2}{x}^{2}+{b}_{1}x+a\) (9)

The same pattern can be used to shape the formula for higher-degree polynomial trend lines. The power trend line and the exponential curve are very similar to each other, but only the later curve has a more symmetrical arc normally used to plot quantities that rises at a firm rate. A power trend line is plotted on the succeeding equation:

\(y=a{x}^{b}\) (10)

Where constants are a and b. For consistency, the same data values can be used for all the models. The water level, surface area, and volume relationship are determined through above mention models to find the best suitable method for our reservoir.

## 2.3 Accuracy assessment

The percentage difference (PD), the root means square errors (RMSE), and the coefficient of determination (R2) was calculated for validation.

\(PD=\frac{(estimated value-In situ value)}{In situ value}\) (11)

The model performance can quantify by the coefficient of determination (R

2) using the regression equation.

\(RMSE=\sqrt{\frac{1}{n}\sum _{i=1}^{n}{\left({y}_{i-}{ŷ}_{i}\right)}^{2}}\) (12)

Where yi is the in-situ measurement of water level, \({ŷ}_{i}\)is the estimated representing values using the approaches explained in this study, i is the ith observation, and n is the number of observations.

\({R}^{2}=\frac{\sum _{i=1}^{n}{\left({y}_{i-}{ŷ}_{i}\right)}^{2}}{\sum _{i=1}^{n}{\left({y}_{i-}{ŷ}_{i}\right)}^{2}}=1- \frac{\sum _{i=1}^{n}{\left({y}_{i-}{ŷ}_{i}\right)}^{2}}{\sum _{i=1}^{n}{\left({y}_{i-}{ŷ}_{i}\right)}^{2}}\) (13)

Where yi is the in-situ measurement of water level. Lastly, accuracy was evaluated by using the linear regression (estimated value vs in-situ value). The values obtained by the two approaches be in seamless arrangement where regression has ‘R2’ equivalent to 1, ‘b’ equal to 1, and ‘a’ equal to 0, as a degree of accuracy.