Number

of river

PDF

Equation

Parameters for Equations

R² in %

y₀

a

b

c

d

x₀

Subarnarekha

Rational (7P)

$Y=\frac{a+bx+c{x}^2+d{x}^3}{1+ex+f{x}^2+g{x}^3}$

6.434

−1.33

0.081

d = −1.5E−7

e = −0.20

f = −0.012

g = −2.2E−4

54

Baitarani

Log Normal

$Y=y_0+\frac{a}{x}{\text{e}}^{{\left[-0.5\frac{\ln \frac{x}{x_0}}{b}\right]}^2}$

2.88

42.2

0.05

.17.3

38

Brahmani

Sine (4P)

$Y=y_0+a\sin \left(\frac{2\text{π}x}{b}+c\right)$

1.79

4.22

2.23

0.601

30

Mahanadi

Rational (6P)

$Y=\frac{a+bx+c{x}^2}{1+dx+e{x}^2+f{x}^3}$

39.6

−6.67

−0.25

d = −0.177

e = 0.008

f = −4.88E−5

60

Vansadhara

Damped Sine

$Y=y_0+a{\text{e}}^{-\frac{x}{d}}\sin \left[\frac{2\text{π}\left(x\right)}{b}+c\right]$

2.76

1.52

1463

4.85

117.1

36

Nagavali

Rational (5P)

$Y=\frac{a+bx+c{x}^2}{1+dx+e{x}^2}$

2.47

−0.34

0.01

d = −0.138

e = 0.0042

43

Godavari

Rational (6P)

$Y=\frac{a+bx+c{x}^2}{1+dx+e{x}^2+f{x}^3}$

108

−17.7

0.52

d = −0.139

e = 8.04E−5

32

Krishna

Gaussian(mod)

$Y=y_0+a{\text{e}}^{0.5{\left(\frac{x-x_0}{b}\right)}^c}$

21.9

35.2

1.495

18.4

21.47

50

Pennar

Gaussian(4P)

$Y=y_0+a{\text{e}}^{0.5{\left(\frac{x-x_0}{b}\right)}^2}$

1.01

17.5

22.38

8.321

55

Ponniayar

Weilbull (5P)

$Y=y_0+\cdots +\frac{c-1}{c}$

0.38

5.7

1.35

4.87

7.609

69

Cauvery

Gaussian(4P)

$Y=y_0+a{\text{e}}^{0.5{\left(\frac{x-x_0}{b}\right)}^2}$

9.05

−7.8

1.013

14.6

4.11

46

Vaigai

Rational (8P)

$Y=\frac{a+bx+c{x}^2+d{x}^3}{1+ex+f{x}^2+g{x}^3+h{x}^4}$

0.02

−8E−2

9E−4

d = 2.77E−5

e = −0.446

f = 0.068

g = −0.003

h = 5.15E−5

92

Tambarparani

Log Normal

$Y=y_0+\frac{a}{x}{\text{e}}^{{\left[-0.5\frac{\ln \frac{x}{x_0}}{b}\right]}^2}$

4.66

4.57

0.12

4.64

61