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Table 7 Quantitative relationship between spectral indices and NO3−–N content

From: Estimation of nitrate nitrogen content in cotton petioles under drip irrigation based on wavelet neural network approach using spectral indices

Type of reflectivity

Vegetation indices

Functional model

Regression equation

R2

RMSE (g/L)

First derivative

RD

Linear

y = − 8116.9x + 13,150

0.71

1.77

Exponential

y = 17,860e−1.306x

0.73

2.01

Quadratic

y = 3178.2x2 − 13,332x + 15,120

0.72

1.88

CIred-edge

Linear

y = − 76,288x − 66,089

0.80

0.92

Exponential

y = 0.067e−12.01x

0.78

0.98

Quadratic

y = − 169,389x2 − 400,646x − 221,261

0.80

0.93

NDRE

Linear

y = − 27,424x − 18,368

0.63

1.14

Exponential

y = 147.75e−4.115x

0.56

1.23

Quadratic

y = 126,872x2 + 207,536x + 89,944

0.67

1.18

ND705

Linear

y = − 18,527x + 3265

0.82

1.52

Exponential

y = 3707.4e−2.893x

0.78

1.35

Quadratic

y = − 29,935x2 − 30,687x + 2342.8

0.83

1.69

NIR

Linear

y = − 85,125x + 10,408

0.39

1.45

Exponential

y = 11,137e−12.9x

0.35

1.55

Quadratic

y = − 2E + 06x2 + 47,910x + 8644.1

0.44

1.44

RI-1 dB

Linear

y = − 19,373x + 22,583

0.52

2.37

Exponential

y = 78,853e−3.076x

0.52

2.91

Quadratic

y = 126,872x2 + 207,536x + 89,944

0.59

2.83

Original

RD

Linear

y = − 8564.7x + 25,826

0.65

1.50

Exponential

y = 131,902e−1.36x

0.65

1.57

Quadratic

y = − 10,788x2 + 39,287x − 26,804

0.67

1.47

CIred-edge

Linear

y = − 3415.6x + 14,222

0.54

1.69

Exponential

y = 19,774e−0.516x

0.49

1.81

Quadratic

y = − 357.75x2 − 1914.2x + 12,720

0.54

1.67

NDRE

Linear

y = − 28,351x + 17,684

0.59

1.70

Exponential

y = 34,790e−4.394x

0.56

1.81

Quadratic

y = − 202,849x2 + 124,311x − 10,381

0.63

1.60

ND705

Linear

y = − 2745.6x + 16,233

0.58

2.38

Exponential

y = 29,232e−0.441x

0.59

2.41

Quadratic

y = − 35.761x2 − 2493x + 15,800

0.58

2.34

NIR

Linear

y = − 28,744x + 38,765

0.62

1.66

Exponential

y = 946,939e−4.488x

0.60

1.81

Quadratic

y = − 180,524x2 + 369,826x − 180,634

0.66

1.53

RI-1 dB

Linear

y = − 10,960x + 28,560

0.59

1.58

Exponential

y = 199,238e−1.729x

0.58

1.67

Quadratic

y = − 26,273x2 + 92,468x − 72,663

0.64

1.52

  1. E stands for scientific counting; e is the base of natural logarithm