Table 3 Relationships between erosive rainfall thresholds and rainfall intensity under different erosion intensity classes on farmland slopes across the study regions.

Suide

Moderate

8 ~ 15

1.278 ± 0.214

6

y = 0.426x- 0.5378

0.91

1.3

0.788 ± 0.162

14

y = 0.264x − 2.628

0.92

10.0

0.461 ± 0.106

8

y = 0.119x − 2.479

0.91

20.9

Intense

15 ~ 25

1.221 ± 0.176

36

y = 0.737x − 4.017

0.90

5.5

0.781 ± 0.199

30

y = 0.426x − 4.899

0.92

11.5

0.489 ± 0.153

28

y = 0.246x − 4.506

0.91

18.4

0.330 ± 0.066

14

y = 0.195x − 5.949

0.91

30.6

Extremely intense

25 ~ 35

1.152 ± 0.144

36

y = 0.624x − 4.448

0.90

7.1

0.606 ± 0.116

22

y = 0.393x − 5.112

0.91

13.0

0.533 ± 0.106

43

y = 0.194x − 4.022

0.90

20.7

Severe

> 35

1.024 ± 0.132

6

y = 0.614x − 5.247

0.98

8.5

0.526 ± 0.073

11

y = 0.326x − 4.681

0.96

14.4

Xifeng

Moderate

8 ~ 15

1.370 ± 0.257

55

y = 0.615x − 1.786

0.90

2.9

1.090 ± 0.304

48

y = 0.507x − 2.137

0.92

4.2

0.565 ± 0.109

36

y = 0.181x − 3.246

0.91

18.0

0.264 ± 0.046

20

y = 0.076x − 2.347

0.90

30.8

Intense

15 ~ 25

1.307 ± 0.242

44

y = 0.761x − 2.707

0.90

3.6

0.938 ± 0.220

57

y = 0.463x − 4.073

0.92

8.8

0.783 ± 0.169

19

y = 0.258x − 2.847

0.90

11.0

0.599 ± 0.203

31

y = 0.211x − 2.741

0.90

13.0

Tianshui

Mild

5 ~ 8

0.590 ± 0.125

31

y = 0.426x − 1.681

0.91

3.9

0.409 ± 0.114

20

y = 0.390x − 5.669

0.94

14.6

Moderate

8 ~ 15

0.615 ± 0.137

44

y = 0.475x − 2.113

0.92

4.5

0.401 ± 0.096

27

y = 0.228x − 3.268

0.91

14.3

Intense

15 ~ 25

0.461 ± 0.105

14

y = 0.468x − 1.524

0.90

3.1

0.341 ± 0.102

21

y = 0.234x − 1.397

0.91

4.6