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Trend Analyses Methodologies in Hydro-meteorological Records

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Abstract

In recent years, global warming and climate change impacts on hydro-meteorological variables and water resources triggered extensive focus on trend analyses. Especially, in historical records and climate change model scenario projections, trend feature searches help for better predictions prior to mitigation and adaptation activities. Each trend identification technique has a set of restrictive assumptions and limitations, but they are not cared for by many researchers. The major problem with trend research is that the researchers do not care for the basic assumptions of any methodology but use ready software to solve their problems. Among these assumptions, the most significant ones are the normal (Gaussian) probability distribution function (PDF) and serially independent structure of a given time series. It is the main objective of this review paper to present each trend identification methodology including classical ones with the new alternatives so that any researcher in need of trend analysis can have concise and clear interpretations for the choice of the most convenient trend method. In general, parametric, non-parametric, classical and innovative trend methods are explained comparatively including the linear regression, Mann–Kendall (MK) trend test with Sen slope estimation, Spearman’s rho, innovative trend analysis (ITA), partial trend analysis (PTA) and crossing trend analysis (CTA). Pros and cons are given for each methodology. In addition, for improvement of serial independence requirement of the classical trend analyses, methods are introduced briefly by pre- and over-whitening processes. Finally, a set of recommendations is suggested for future research possibilities.

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Authors and Affiliations

  1. Department of Meteorology, Center of Excellence for Climate Change Research, King Abdulaziz University, PO Box 80234, Jeddah, 21589, Saudi Arabia

    Mansour Almazroui & Zekâi Şen

  2. Engineering and Natural Sciences Faculty, Istanbul Medipol University, Beykoz, 34810, Istanbul, Turkey

    Zekâi Şen

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Appendix

Appendix

In the following table, time series with 100 data are given and the regression trend analysis details are given numerically similar to Table 1 in the text. The necassary arithmetic mean values are given in tlast row in bold.

t

v

tv

t2

t

v

tv

t2

1

16.7008

16.7008

1

51

17.0601

870.065

2601

2

13.2639

26.5278

4

52

15.9999

831.995

2704

3

15.2602

45.7806

9

53

15.9905

847.497

2809

4

13.9909

55.9636

16

54

14.4837

782.12

2916

5

15.707

78.535

25

55

18.1374

997.557

3025

6

13.9193

83.5158

36

56

15.8536

887.802

3136

7

16.1199

112.839

49

57

14.7109

838.521

3249

8

16.6387

133.11

64

58

18.8628

1094.04

3364

9

18.6038

167.434

81

59

15.7305

928.1

3481

10

14.8118

148.118

100

60

15.0219

901.314

3600

11

10.9433

120.376

121

61

15.6325

953.583

3721

12

13.5608

162.73

144

62

14.5441

901.734

3844

13

17.9692

233.6

169

63

14.0197

883.241

3969

14

13.1357

183.9

196

64

21.332

1365.25

4096

15

17.2219

258.329

225

65

19.611

1274.72

4225

16

15.5681

249.09

256

66

16.9351

1117.72

4356

17

18.2134

309.628

289

67

13.8258

926.329

4489

18

11.4382

205.888

324

68

14.6291

994.779

4624

19

14.9846

284.707

361

69

16.0269

1105.86

4761

20

12.9843

259.686

400

70

17.9828

1258.8

4900

21

21.236

445.956

441

71

13.756

976.676

5041

22

17.0904

375.989

484

72

11.7803

848.182

5184

23

18.2179

419.012

529

73

13.5618

990.011

5329

24

13.3636

320.726

576

74

17.147

1268.88

5476

25

14.5628

364.07

625

75

17.2827

1296.2

5625

26

14.9751

389.353

676

76

17.4234

1324.18

5776

27

17.7368

478.894

729

77

16.2794

1253.51

5929

28

15.0043

420.12

784

78

16.9274

1320.34

6084

29

16.9831

492.51

841

79

15.6277

1234.59

6241

30

11.4964

344.892

900

80

18.324

1465.92

6400

31

14.9123

462.281

961

81

13.8966

1125.62

6561

32

13.9928

447.77

1024

82

17.5501

1439.11

6724

33

12.5059

412.695

1089

83

14.9626

1241.9

6889

34

16.6959

567.661

1156

84

16.0102

1344.86

7056

35

16.264

569.24

1225

85

17.8056

1513.48

7225

36

15.787

568.332

1296

86

18.7982

1616.65

7396

37

13.0726

483.686

1369

87

14.5047

1261.91

7569

38

18.015

684.57

1444

88

19.2813

1696.75

7744

39

16.4804

642.736

1521

89

18.1003

1610.93

7921

40

15.2019

608.076

1600

90

16.6643

1499.79

8100

41

15.8658

650.498

1681

91

16.4296

1495.09

8281

42

15.316

643.272

1764

92

16.4048

1509.24

8464

43

12.3596

531.463

1849

93

16.2538

1511.6

8649

44

15.3087

673.583

1936

94

16.9261

1591.05

8836

45

14.2373

640.679

2025

95

17.0026

1615.25

9025

46

13.9616

642.234

2116

96

18.5721

1782.92

9216

47

13.6272

640.478

2209

97

19.994

1939.42

9409

48

14.8929

714.859

2304

98

17.8938

1753.59

9604

49

11.9747

586.76

2401

99

16.5606

1639.5

9801

50

17.9285

896.425

2500

100

18.2504

1825.04

10,000

   

Means

25.5

15.202

385.11

858.5

The substitution of the mean values into Eqs. (3) and (4) yields the slope of the regression line as 0.022.

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Almazroui, M., Şen, Z. Trend Analyses Methodologies in Hydro-meteorological Records. Earth Syst Environ 4, 713–738 (2020). https://doi.org/10.1007/s41748-020-00190-6

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