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Hydrological modeling of the Congo River basin: Asoil-water balance approach

( Télécharger le fichier original )
par Bahati Chishugi Josue
University of Botswana - Masters of Sciences (M.Sc.) 2008
  

précédent sommaire

APPENDICES

APPENDIX 1: METEOROLOGICAL STATIONS COVERING THE STUDY AREA (FROM FAO/UNESCO CLIMWAT DATBASE)

ANG: Angola, CAF: Cantral Africa, CMR, Cameroon, PRC: People Republic of the Congo, URT: United Republic of Tanzania ZAI = Zaire (D.R.Congo), ZAM: Zambia .

COUNTRY

STATION NAME

LONGITUDE
(degree)

LATITUDE
(degree)

ELEVATION
(m)

ZAI.

Bafwasende

27.28

1.05

524

ZAI.

Bambesa

25.43

3.27

621

ZAI.

Banana

12.35

-6

2

ZAI.

Bandundu

17.21

-3.18

324

ZAI.

Basankusu

19.48

1.13

353

ZAI.

Basoko

23.36

1.15

366

ZAI.

Bena-Longo

21.4

-4.51

578

ZAI.

Binga

20.3

2.18

400

ZAI.

Boende

20.51

-0.13

351

ZAI.

Boketa

19.46

3.11

475

ZAI.

Bokondji

21.26

-0.43

365

ZAI.

Bongabo

20.32

3.06

450

ZAI.

Bukavu

28.52

-2.3 1

1612

ZAI.

Bumba

22.33

2.11

361

ZAI.

Bunia

30.13

1.3

1239

ZAI.

Buta

24.47

2.5

410

ZAI.

Butembo

29.16

0.08

1840

ZAI.

Eala

18.18

0.03

350

ZAI.

Gandajika

23.57

-6.45

780

ZAI.

Gemena

19.47

3.17

446

ZAI.

Gimbi-Plateau

13.22

-5.3 1

480

ZAI.

Goma

29.14

-1.41

1552

ZAI.

Ilebo

20.35

-4.2

420

ZAI.

Inongo

18.16

-1.58

299

ZAI.

Irumu

29.52

1.27

955

ZAI.

Isiro

27.39

2.46

764

ZAI.

Kalemie

29.11

-5.53

776

ZAI.

Kamina

25

-8.44

1105

ZAI.

Kamina - Base

25.15

-8.38

1106

ZAI.

Kananga

22.25

-5.53

657

ZAI.

Kaniama

24.09

-7.25

949

ZAI.

Kibangula

27.04

-4.52

685

ZAI.

Kikwit

18.48

-5.02

449

ZAI.

Kindu

25.55

-2.57

497

ZAI.

Kinshasa

15.22

-4.22

310

ZAI.

Kisanga-Plateau

27.25

-11.44

1187

ZAI.

Kisangani

25.11

0.31

396

ZAI.

Kiyaka-Plateau

18.57

-5.16

739

ZAI.

Kolwezi

25.28

-10.45

1526

ZAI.

Kondo

12.58

-5.34

230

ZAI.

Kongolo

27

-5.2 1

561

ZAI.

Kutubongo

19.53

-4.37

550

ZAI.

Libenge

18.38

3.38

359

ZAI.

Lisala

21.34

2.19

463

ZAI.

Lodja

23.28

-3.29

479

ZAI.

Loeka

22.42

2.12

380

ZAI.

Lomela

23.17

-2.18

427

ZAI.

Lubao

25.45

-5.18

694

ZAI.

Lubarika

28.57

-2.5

980

ZAI.

Lubumbashi Luano

27.29

-11.4

1298

ZAI.

Luki-Plateau

13.06

-5.37

350

ZAI.

Lukolela

17.1

-1.04

318

ZAI.

Luputa

23.44

-7.08

877

ZAI.

Lusambo

23.26

-4.58

424

ZAI.

M'Vuazi-Poste

14.54

-5.27

505

ZAI.

Magombo

27.54

3.42

705

ZAI.

Manono

27.26

-7.17

633

ZAI.

Mbandaka

18.16

0.03

317

ZAI.

Mbuji-Mayi

23.37

-6.1

677

ZAI.

Mitwaba

27.2

-8.56

1579

ZAI.

Mont Delele

29.47

4.22

900

ZAI.

Mont Hawa

30.45

2.49

1350

ZAI.

Mukumari

23.11

-2.5

535

ZAI.

Mulungu Bukulumisa

28.43

-2.2

2378

ZAI.

Mutombo - Yamfu

16.22

-5.19

700

ZAI.

Mutsora

29.44

0.19

1330

ZAI.

N'Dihira

29.1

-0.16

2190

ZAI.

Nioka-Drusi

30.39

2.09

1678

ZAI.

Opala

24.21

-0.35

398

ZAI.

Rumangabo

29.22

-1.21

1620

ZAI.

Rwindi

29.17

-0.47

1040

ZAI.

Simama

27.01

-9.37

852

ZAI.

Tshikapa

20.5 1

-6.25

481

ZAI.

Tukpwo

25.55

4.27

704

ZAI.

Watsa

29.3

3.04

1008

ZAI.

Yaligimba

22.51

2.17

435

ZAI.

Yangambi E.C.P.

24.31

0.53

491

ZAI.

Yangambi Km 5

24.29

0.49

470

ZAM.

Chipata

32.35

-13.33

1032

ZAM.

Kabompo

24.12

-13.36

1075

ZAM.

Kabwe

28.28

-14.27

1207

ZAM.

Kaoma

24.48

-14.48

1213

ZAM.

Kasama

31.08

-10.13

1384

ZAM.

Kasempa

25.51

-13.32

1234

ZAM.

Kawambwa

29.05

-9.48

1324

ZAM.

Lundazi

33.12

-12.17

1143

ZAM.

Mansa

28.51

-11.06

1259

ZAM.

Mbala

31.2

-8.51

1673

ZAM.

Mpika

31.36

-11.54

1402

ZAM.

Mwinilunga

24.26

-11.45

1363

ZAM.

Ndola

28.39

-13

1270

ZAM.

Petauke

31.17

-14.15

1036

ZAM.

Samfya

29.32

-11.21

1172

ZAM.

Serentje

30.13

-13.14

1384

ZAM.

Solwezi

26.23

-12.11

1386

ZAM.

Zambezi

23.07

-13.32

1078

ANG.

Cabinda

12.11

-5.33

20

ANG.

Chitembo

16.46

-13.32

1500

ANG.

Cuemba

18.05

-12.08

1300

ANG.

Huambo

15.45

-12.48

1700

ANG.

Lobito

13.32

-12.22

3

ANG.

Luanda

13.14

-8.51

70

ANG.

Luau

22.15

-10.43

1100

ANG.

Lubango

13.34

-14.56

1758

ANG.

Luena

19.55

-11.47

1357

ANG.

Malanje

16.22

-9.33

1142

ANG.

Menongue

17.41

-14.39

1343

ANG.

Ndalatando

14.57

-9.19

690

ANG.

Nova Gaia

17.33

-10.04

1260

ANG.

Saurimo

20.24

-9.39

1080

ANG.

Soyo

12.21

-6.07

1

ANG.

Sunginge

16.47

-8.46

630

PRC.

Brazzaville

15.15

-4.15

316

PRC.

Djambala

14.46

-2.32

790

PRC.

Impfondo

18.04

1.37

326

PRC.

Loubomo

12.42

-4.12

330

PRC.

M'Pouya

16.13

-2.37

312

PRC.

Makoua

15.35

0.01

379

PRC.

Mouyondzi

13.55

-3.59

512

PRC.

Ouesso

16.03

1.37

352

PRC.

Pointe Noire

11.54

-4.49

17

URT.

Biharamulo

31.19

-2.38

1480

URT.

Bukoba

31.49

-1.2

1137

URT.

Chunya

33.26

-8.32

1500

URT.

Igawa

34.23

-8.46

1070

URT.

Igeri

34.4

-9.4

2250

URT.

Kigoma

29.38

-4.53

885

URT.

Mbeya Airfield

33.28

-8.56

1707

URT.

Musoma

33.48

-1.3

1147

URT.

Muze

3 1.33

-7.4

810

URT.

Mwanza Airfield

32.55

-2.28

1140

URT.

Njombe

34.45

-9.25

1890

URT.

Sumbawanga

31.36

-7.57

1710

URT.

Tabora Airport

32.5

-5.05

1190

URT.

Tabora Observatory

32.49

-5.02

1265

URT.

Urambo

32.03

-5.04

1106

CAF.

Bambari

20.39

5.51

475

CAF.

Bangassou

22.5

4.44

500

CAF.

Bangui

18.3 1

4.24

366

CAF.

Berberati

15.48

4.15

583

CAF.

Bossangoa

17.26

6.29

465

CAF.

Bouar

15.38

5.58

1020

CAF.

Bria

21.59

6.32

584

CAF.

N'Dele

20.39

8.24

510

CMR.

Batouri

14.22

4.28

656

CMR.

Garoua

13.23

9.2

244

CMR.

Koundja

10.45

5.39

1210

CMR.

Lomie

13.37

3.09

624

CMR.

Ngaoundere

13.34

7.21

1104

CMR.

Yaounde

11.31

3.5

760

APPENDIX 2: SPREADSHEET MODEL FOR THE PENMAN-MONTEITH CALCULATION METHOD OF ETo (After Allen et al, 1998)

PENMAN-MONTEITH CALCULATIONS

 

Grass

Alfalfa

Give :

Station name :

 

Gamma* Cff

Gamma*Cff

 

Latitude :

 

Lonitude

0.34

0.42

 

Altitude :

 
 
 

Parameters :

Short Wave Rad

 

a =

0.25

b = 0.50

alpha=

Albedo

 
 

alpha =

0.23

 
 
 

Long Wave Rad.

 

a =

0.90

b = 0.10

 
 

al =

0.34

bl = -0.139

 
 
 

Instrument height

 
 

wind

temp

Cropheight

AeroT Cff

 

AerDyn Resistance

ra * U =

206

200

190

12

900

 
 
 

Grass

Alfalfa

 
 
 

Canopy resistance

rc =

70

86

 

12

 
 
 

JAN

FEB

MAR

APR

MAY

JUN

JUL

AUG

SEP

OCT

NOV

DEC

YEAR

Tmax

12.3

13.6

15.6

19.8

23.0

28.0

31.0

31.2

28.1

22.7

17.1

4.8

 

Tmin

3.7

4.0

5.6

7.6

12.6

15.4

18.0

18.0

15.6

11.6

7.7

82

 

RHmean

81

77

72

74

69

65

59

61

70

77

81

58

 

RHmin

58

53

49

46

47

41

37

38

45

51

57

190

 

Wind (km/d)

190

190

190

156

156

156

156

121

121

121

190

3.50

 

Sunhours

4.20

4.30

5.80

7.00

8.40

9.00

10.60

9.70

8.00

6.00

4.00

1.47

 

ET fao

1.47

1.87

2.57

3.26

4.08

4.94

5.77

5.21

4.10

2.76

1.91

9.20

 

Avg Temp

8.00

8.80

10.60

13.70

17.80

21.70

24.50

24.60

21.85

17.15

12.40

34%

 

n/N

40%

39%

49%

55%

63%

65%

78%

75%

66%

53%

38%

2.20

 

Wind (m/s)

2.20

2.20

2.20

1.81

1.81

1.81

1.81

1.40

1.40

1.40

2.20

1.56

 

Ea(Tmax)

1.43

1.56

1.77

2.31

2.81

3.78

4.49

4.54

3.80

2.76

1.95

0.86

 

Ea(Tmin)

0.80

0.81

0.91

1.04

1.46

1.75

2.06

2.06

1.77

1.37

1.05

1.21

 

Ea(Tx)-Ea(Tn)

1.11

1.19

1.34

1.68

2.13

2.76

3.28

3.30

2.79

2.06

1.50

0.91

 

Edew

0.83

0.82

0.87

1.06

1.33

1.55

1.67

1.73

1.69

1.41

1.11

82%

 

RH(max-min)

81%

77%

72%

74%

69%

65%

59%

61%

70%

77%

81%

0.08

 

Dlt(ETx-ETn)

0.08

0.08

0.09

0.11

0.13

0.17

0.19

0.19

0.17

0.13

0.10

101.3

 

P-atm.

101.3

101.3

101.3

101.3

101.3

101.3

101.3

101.3

101.3

101.3

101.3

2.48

 

lambda

2.48

2.48

2.48

2.47

2.46

2.45

2.44

2.44

2.45

2.46

2.47

0.07

 

gamma

0.07

0.07

0.07

0.07

0.07

0.07

0.07

0.07

0.07

0.07

0.07

70

 

rc

70

70

70

70

70

70

70

70

70

70

70

94

 

ra

94

94

94

114

114

114

114

147

147

147

94

0.12

 

gamma*

0.12

0.12

0.12

0.11

0.11

0.11

0.11

0.10

0.10

0.10

0.12

0.41

 

dl/dl+gm*

0.39

0.41

0.43

0.50

0.55

0.61

0.64

0.66

0.63

0.57

0.46

0.34

 

gm/dl+gm*

0.35

0.34

0.33

0.31

0.28

0.25

0.22

0.23

0.25

0.29

0.31

0.71

 

Aeroterm

0.70

0.87

1.08

1.08

1.26

1.64

1.97

1.53

1.18

0.84

0.85

12

 

Month

1

2

3

4

5

6

7

8

9

10

11

351

 

dayno

15

46

76

107

137

168

198

229

259

290

320

-0.408

 

soldeclin

-0.370

-0.230

-0.033

0.179

0.334

0.408

0.372

0.233

0.036

-0.176

-0.336

-0.186

 

xx

-0.170

-0.107

-0.016

0.083

0.154

0.186

0.170

0.108

0.017

-0.082

-0.155

0.810

 

yy

0.823

0.860

0.882

0.869

0.834

0.811

0.823

0.859

0.882

0.869

0.834

1.34

 

omega

1.36

1.45

1.55

1.67

1.76

1.80

1.78

1.70

1.59

1.48

1.38

1.03

 

dr

1.03

1.02

1.01

0.99

0.98

0.97

0.97

0.98

0.99

1.01

1.02

20.92

 

Ra

22.25

26.84

32.52

37.40

40.01

40.91

40.33

38.04

33.89

28.21

23.28

10.23

 

N

10.41

11.04

11.86

12.73

13.42

13.77

13.59

12.96

12.15

11.27

10.57

6.8

 

Rns

7.7

9.2

12.4

15.1

17.3

18.2

19.9

18.3

15.1

11.2

7.9

0.41

 

4.oe

2.oe

7.00

6.00

5.oe

3.oe

0.00

1.oe

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

FAO Penman-Monteith - ETo
Rei. Evapotranspiration Rome

ETo (-G) ETo

f(n/N)

0.46

0.45

0.54

0.59

0.66

0.69

0.80

0.77

0.69

0.58

0.44

31.19

 

sigma(TxTn)

30.66

31.02

31.83

33.27

35.19

37.14

38.58

38.63

37.21

34.88

32.64

0.21

 

emissivity

0.21

0.21

0.21

0.20

0.18

0.17

0.16

0.16

0.16

0.18

0.19

6.46

 

Rbo

6.53

6.62

6.69

6.53

6.32

6.18

6.18

6.06

5.91

6.10

6.31

2.64

 

LWR

3.03

2.99

3.62

3.89

4.20

4.26

4.96

4.69

4.10

3.54

2.79

4.14

 

Rn (Rns-Rl)

4.71

6.20

8.76

11.23

13.14

13.91

14.91

13.59

11.01

7.67

5.09

-0.45

 

G

-0.17

0.11

0.25

0.43

0.57

0.55

0.39

0.01

-0.39

-0.66

-0.67

4.59

 

Rn-G

4.88

6.09

8.51

10.79

12.57

13.36

14.51

13.57

11.40

8.33

5.75

0.69

 

Rad Term

0.75

1.02

1.53

2.27

2.95

3.44

3.90

3.68

2.82

1.77

0.94

0.76

 

Rad Term(-G)

0.77

1.00

1.49

2.18

2.82

3.30

3.80

3.67

2.92

1.92

1.06

1.40

 

ETcomb

1.44

1.88

2.61

3.35

4.21

5.07

5.87

5.21

4.01

2.60

1.79

-5.3%

 
 

-1.8%

1.0%

1.7%

2.6%

3.1%

2.7%

1.7%

0.1%

-2.5%

-5.8%

-6.9%

1.47

 

ET (-G)

1.47

1.87

2.57

3.26

4.08

4.94

5.77

5.21

4.10

2.76

1.91

13.6

 

APPENDIX 3: CONGO RIVER DISCHARGE DATA AT KINSHASA

Station: Kinshasa

Latitude: 4.3o S/ Longitude: 15.3o E River: Zaire

Country: Zaire

Elevation: m

Area: 3475000 km2

-

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Ann

m 3 /c

47494

37649

34713

37172

39150

36717

31703

31087

36366

43172

51708

56082

40251

mm

36.6

26.4

26.8

27.7

30.2

27.4

24.4

24

27.1

33.3

38.6

43.2

366

km 3

127

91.9

93

96.3

105

95.2

84.9

83.3

94.3

116

134

150

1270

l/s/km 2

13.7

10.8

9.99

10.7

11.3

10.6

9.12

8.95

10.5

12.4

14.9

16.1

11.6

%%

9.83

7.79

7.19

7.7

8.11

7.6

6.56

6.44

7.53

8.94

10.7

11.6

100

Year

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Annual

1903

45250

34860

32410

32820

34970

34060

30850

31160

36900

41280

48300

51020

37823

1904

42390

34510

33760

39600

40510

36810

28700

31960

38950

45330

52340

53850

39893

1905

46230

36340

33320

33460

29970

26080

22350

24180

28120

34450

42420

49960

33907

1906

47700

37050

36550

37620

36910

34410

30660

27280

30910

40750

46980

48310

37928

1907

37680

33130

31490

31900

35110

30730

24100

23980

29390

35610

42180

45680

33415

1908

38270

30120

28350

31350

34390

33840

31320

30410

37370

44340

55350

65760

38406

1909

53560

38810

35460

42050

50530

48140

37290

36560

37940

48170

53600

54350

44705

1910

49470

39480

34890

34120

41150

37400

29960

33800

36260

44380

53550

60160

41218

1911

47110

34390

30640

34150

36560

39260

30290

26080

31460

37200

46500

55440

37423

1912

47720

38260

34750

35870

33930

30660

30930

31320

37580

46680

52490

53260

39454

1913

42280

34110

34170

34160

39650

37930

29690

27730

29040

35120

42220

40930

35586

1914

33330

26910

30320

34750

32310

31780

28950

26280

29980

40460

49340

56810

35102

1915

47450

31100

28730

29230

29470

28440

25220

25360

30420

35730

41010

47170

33278

1916

41840

31490

30370

31980

37570

32240

29100

27760

33810

43340

54960

59680

37845

1917

49120

38390

35010

37150

42470

41220

32990

29270

35990

44720

55480

55920

41477

1918

39130

29280

27900

33170

34090

29790

27440

29550

35470

37520

41500

43840

34057

1919

39500

33620

30380

30890

30240

26380

23740

26810

30550

36220

41510

44630

32873

1920

39060

30780

27230

29740

34670

32090

29370

32750

38460

42530

50110

59540

37194

1921

52780

37570

32740

32900

37460

34180

32650

30590

38200

44720

53430

55850

40256

1922

43250

36260

33300

33260

32760

29720

26750

25830

33390

41970

53000

58140

37303

1923

44370

33990

29540

34370

41650

40550

32370

33700

39390

44010

50440

59870

40354

1924

49770

38820

30880

36310

42360

41450

30620

30610

37450

44910

57970

63370

42043

1925

49950

34770

32720

34610

34580

34160

34020

32180

37050

44900

55210

64170

40693

1926

60480

40870

34900

39780

43090

38090

31770

31820

38150

44480

55730

61660

43402

1927

46500

34440

32250

38020

38370

33660

27000

27650

31860

38480

46720

47350

36858

1928

39920

34680

31430

35800

40480

42290

37830

33530

40740

45280

49460

51730

40264

1929

42270

35310

34090

34930

36640

32940

29080

30200

36110

41530

51730

57930

38563

1930

47420

37460

33870

40460

44480

40740

31160

27860

31850

40360

48210

47100

39248

1931

40220

35530

34170

36940

37550

34530

29020

28850

31750

36970

44480

49130

36595

1932

45380

32600

29860

34370

35470

38280

35610

30820

38200

46820

56200

56380

39999

1933

49740

46510

42730

42240

37350

32560

27700

28720

34020

41630

46820

50950

40081

1934

47320

33860

31090

34180

35870

33330

31160

32580

39030

43950

54800

63670

40070

1935

57310

43300

40510

43650

44760

42300

38350

31830

35580

40450

45820

49040

42742

1936

44870

37780

35270

36520

37890

35490

32900

32640

39350

47430

53580

56770

40874

1937

45880

37740

37620

40810

44140

41460

31740

31400

34770

40660

52490

57900

41384

1938

49140

34130

34410

34580

35920

32880

30100

32250

36710

42420

52350

56790

39307

1939

45860

39080

37250

38080

40880

37470

29990

29040

32020

42340

52950

62380

40612

1940

49580

41420

38640

40380

42230

38920

30210

32480

36500

42110

50240

52780

41291

1941

44440

34870

34620

35000

34180

35270

34730

31370

38020

41360

47720

57110

39058

1942

55200

45070

38440

37180

36650

36500

31190

33170

41280

46570

47860

46450

41297

1943

39330

32430

29690

30200

32200

32050

27340

28170

33840

41060

45800

43730

34653

1944

39590

35670

31670

39990

40790

36460

27090

28520

36420

43840

50270

52030

38528

1945

42080

32720

31840

31010

31360

34560

30960

30080

36830

46180

54580

56250

38204

1946

43730

31860

29340

30580

34250

31740

28120

29270

36840

46120

54850

61300

38167

1947

50350

39850

36080

39060

45990

44510

36910

34900

36730

44220

49820

49540

42330

1948

46590

39350

37990

36180

37100

35080

33560

34630

42040

50620

60170

62740

43004

1949

47360

34630

31920

33970

32800

29350

29080

32870

38140

46990

53960

51030

38508

1950

39860

33800

31250

37410

36820

32500

29480

32830

38270

45720

56940

56150

39253

1951

44720

36500

34040

41700

37730

34170

31650

28150

34240

39310

53840

62780

39903

1952

55020

38160

33000

33900

39350

38650

32250

31900

37050

43150

51020

51520

40414

1953

42748

34920

34230

35760

36900

33800

28840

25850

31910

37540

45250

49370

36427

1954

36920

29160

31780

36470

39280

35860

31830

27690

33620

40560

50180

51450

37067

1955

46760

41590

37680

41340

45350

39190

32220

32570

37440

47740

59470

60790

43512

1956

48930

38300

34460

38850

46620

41840

34750

30490

35440

42630

50390

55490

41516

1957

49770

37530

36150

44050

44230

40840

35120

32840

35380

39480

48280

54520

41516

1958

50870

37780

29820

29960

34110

30660

26130

26010

29880

35000

42100

42900

34602

1959

38510

34590

30180

30660

31260

29920

25440

25940

33870

42700

49590

57720

35865

1960

51820

40650

41510

45450

48730

43540

37560

35380

38900

46860

56680

59540

45552

1961

48220

41240

39900

42650

44510

37530

35060

36700

41410

52190

65900

80830

47178

1962

76300

61200

47280

51290

53230

48710

44760

40420

44240

52930

64320

74890

54964

1963

67950

55860

47560

47220

53230

51800

44830

39630

40690

44010

51180

58540

50208

1964

57750

47440

41830

43990

47130

46750

38790

32930

38810

47700

61390

69410

47827

1965

54640

40590

37580

43360

43370

35590

28370

30020

35980

41670

51380

62350

42075

1966

55580

43690

41880

46980

50550

47930

39300

36670

41690

48190

55550

63040

47588

1967

49130

35900

33130

35030

35220

33030

30550

31420

38050

45900

60160

65540

41088

1968

57600

44140

42800

44630

46590

46150

41570

36970

39700

43620

50420

58560

46063

1969

56690

48930

45360

52690

53070

50700

44510

43170

45980

50840

59180

66420

51462

1970

54910

44920

44300

45370

45020

42310

34480

36200

43330

51990

62820

62540

47349

1971

47930

38010

33630

35860

37540

33050

28180

32730

38690

44660

50590

54330

39600

1972

43510

34770

33130

35210

36450

33400

29580

29380

33000

36990

50140

55880

37620

1973

47060

37530

32340

32180

34650

32240

25760

26080

33170

40230

47200

50400

36570

1974

40840

34630

31530

34210

36700

35790

31530

33150

37410

44970

52150

52180

38757

1975

43490

37530

34490

34650

36450

32560

29970

29960

39110

49880

60170

63650

40993

1976

46450

38470

38300

40480

42240

38600

33940

32410

38950

44110

52040

59240

42103

1977

56190

46680

39680

43040

45650

38580

34210

33390

39260

48380

55690

57770

44877

1978

51640

37760

35800

37980

42250

41950

35860

33150

39440

44410

53640

62440

43027

1979

51920

45540

43540

45930

46870

47780

40980

33570

37600

39450

47430

52280

44408

1980

42440

35070

33340

35850

38170

37170

33780

34980

38050

45340

53790

59530

40626

1981

50000

39460

32940

36290

35540

38330

29680

30770

38900

44920

51040

52160

40003

1982

44050

35070

31400

29490

32610

34340

30680

29270

34040

41540

56690

61230

38367

1983

49020

36960

31360

31610

29980

27060

24360

25620

31250

36080

45260

47720

34690

APPENDIX 4: ATTRIBUTE TABLE FOR DRAINAGE NETWORK ORDERING

Domain

The IDs of the Table's domain, every record (ID) represents a certain stream.

UpstreamLinkID

The IDs of the streams that directly contribute to the current stream, e.g. when streams 5 and 7 flow together into stream 12, then the UpstreamLinkID column will read for the record with ID 12: {5,7}

UpstreamCoord

The XY-coordinate of the beginning of a stream segment (down-flow); these coordinates are shown as points in the third picture above. This column is a coordinate column.

UpstreamElevation

The elevation, as extracted from the DEM, at the position of the upstream coordinate. This column is a value column.

DownstreamLinkID

The ID of the stream segment into which the current stream will flow (down-flow). This column is a value column.

DownstreamCoord

The XY-coordinate of the end of a stream segment (down-flow).

DownstreamElevation

A column containing the elevation, as extracted from the DEM, at the position of the downstream coordinate.

ElevationDifference

Height difference between upstream coordinate and downstream coordinate, i.e. UpstreamElevation - DownstreamElevation.

Strahler

Strahler ordering number; the Strahler ordering number for a stream is calculated as follows: when streams of equal order join each other: the Strahler ordering number of one of the streams that directly contributes to this stream + 1 is assigned;

when streams of unequal order join each other: the largest Strahler ordering number of the streams that directly contribute to this stream is assigned;

In other words: the Strahler order values of the UpstreamLinkIDs are found, when these order values are equal, the value is increased by 1;

when these order values are unequal, the maximum value is assigned. The Strahler column is a value column.

Shreve

Shreve ordering number; the Shreve ordering number for a stream is calculated as the sum of the Shreve ordering numbers of the streams that directly contribute to this stream, i.e. the sum of the Shreve order values of the UpstreamLinkIDs. The Shreve column is a value column.

Length

The length of a stream measured along the drainage.

StraightLength

The length of a stream calculated as the difference between the upstream coordinate and the downstream coordinate, i.e. | UpstreamCoord - DownstreamCoord |

SlopeAlongDrainage%

The average slope in percentages between the upstream coordinate and the downstream coordinate, when the length is measured along the drainage, i.e. (ElevationDifference/Length)* 100%

SlopeAlongDrainageDegree

The average slope angle in degrees between the upstream coordinate and the downstream coordinate, when the length is measured along the drainage, i.e. tan- 1(ElevationDifference/Length)

SlopeDrainageStraight%

The average slope in percentages between the upstream coordinate and the downstream coordinate, when the length is the straight length between the upstream coordinate and the downstream coordinate, i.e. (ElevationDifference/StraightLength)* 100%

SlopeDrainageStraightDegree

The average slope angle in degrees between the upstream coordinate and the downstream coordinate, when the length is the straight length between the upstream coordinate and the downstream coordinate, i.e. tan1(ElevationDifference/StraightLength)

Sinuosity

A measure for meandering of the stream, i.e. Length / StraightLength

TotalUpstreamAlongDrainageLength

The total length of all (upstream) streams that contribute to the current stream

StrahlerClass

An additional class column to be able to display the Strahler ordering numbers as classes.

APPENDIX 5: HORTON STATISTICS FUNCTIONALITY: DEFINITION OF PARAMETERS

The Horton Statistics operation calculates for all streams with a certain (Strahler) stream order number i, located in merged catchment C with ID x:

Cx_N: the number of streams for catchment x, or The number of streams with a certain Strahler stream order number

Cx_L: the average stream length (km), or The average length (km) of the streams with this Strahler order number.

Cx_A: the average area of catchments (km2) or The average area (km2) of the catchments belonging to the streams with this Strahler order number.

Cx_N_LSq: expected values for Cx_N by means of a least squares fit through Cx_N, or The expected number of streams with a certain Strahler stream order number.

Cx_L_LSq: expected values for Cx_L by means of a least squares fit through Cx_L, or The expected average length (km) of the streams with this Strahler order number.

Cx_A_LSq: expected values for Cx_A by means of a least squares fit through Cx_A, or The expected average area (km2) of the catchments belonging to the streams with this Strahler order number.

APPENDIX 6: HORTON MORPHOLOGICAL PARAMETERS AND STATISTICS FOR SUBSEQUENT STRAHLER ORDER

 

strahler Order

HORTON MORPHOLOGICAL PARAMETERS

Calculated

Expected

C_N

C_L

C_A

C_N_LSq

C1_L_LSq

C_A_LSq

1

1

30

64.74

3322.57

25.751

69.607

4205.716

2

6

196.02

21035.86

8.143

169.59

14619.42

3

3

384.32

49761.68

2.575

413.19

50818.28

4

1

662.01

158672.2

0.814

1006.7

176648.5

5

 
 
 
 
 

1

6

 
 
 
 
 

1

7

 
 
 
 
 

1

2

1

26

64.76

3258.19

30.213

76.663

2964.718

2

8

183.8

14855.7

5.925

131.139

17944.58

3

1

189.49

119366.6

1.162

224.328

108613.4

4

1

664.74

132257.5

0.228

383.737

657405.5

5

 
 
 
 
 
 

6

 
 
 
 
 
 

7

 
 
 
 
 
 

3

1

118

65.19

3137.12

133.107

80.73

3510.212

2

32

191.43

15777.09

33.277

178.149

15224.16

3

9

340.46

61493.83

8.32

393.127

66028.79

4

2

932.09

296725.4

2.08

867.528

286373.8

5

1

2130.4

646792.4

0.52

1914.403

1242034

6

 
 
 
 
 
 

7

 
 
 
 
 
 

4

1

168

77.44

2986.6

107.066

160.972

5432.712

2

42

234.59

16796.23

39.039

263.615

17644.8

3

13

476.94

63232.86

14.235

431.708

57308.19

4

5

821.84

177175

5.19

706.985

186130.1

5

2

1013.09

450879.8

1.893

1157.791

604528.3

6

1

1152.81

905331.4

0.69

1896.051

1963436

7

 
 
 
 
 
 

5

1

261

57.51

2591.04

236.501

75.237

3126.151

2

54

185.49

16541.88

55.742

173.055

14315.61

3

14

346.48

70292.39

13.138

398.046

65555.63

4

3

981.2

358082.7

3.097

915.553

300199.5

5

1

2265.76

1121600

0.73

2105.879

1374707

6

 
 
 

0.172

4843.768

6295207

7

 
 
 
 
 

1

6

1

151

63.27

3080.17

25.159

195.664

27871.48

2

26

297.12

27360.17

12.592

312.666

57809.6

3

6

589.78

129887.4

6.302

499.632

119905.7

4

1

605.16

779475.3

3.154

798.399

248702.4

5

1

1655.82

823385.2

1.578

1275.822

515845.9

6

2

1847.5

417141.4

0.79

2038.731

1069941

7

1

2445.2

859575.2

0.395

3257.842

2219218

APPENDIX 7 PEARSON PRODUCT MOMENT CORRELATION BETWEEN
HORTON AND GIUH

Friday, June 27, 2008, 3:52:27 AM
Data source:
Data 1 in Notebook 1

Pearson Product Moment Correlation Friday, June 27, 2008, 3:52:27 AM

Data source: Data 1 in Notebook 1

Cell Contents:

Correlation Coefficient

P Value Number of

Samples

 

Rb

Rl

Ra

LHSOr

Tpg

Qpg

Tpg

 
 
 
 
 
 
 
 

Rb

 

0.903

0.952

-0.284

-0.464

0.504

-0.464

 
 

0.0137

0.00345

0.585

0.354

0.308

0.354

 
 

6

6

6

6

6

6

 
 
 
 
 
 
 
 

Rl

 
 

0.958

-0.287

-0.494

0.532

-0.494

 
 
 

0.00267

0.582

0.32

0.277

0.32

 
 
 

6

6

6

6

6

 
 
 
 
 
 
 
 

Ra

 
 
 

-0.386

-0.586

0.598

-0.586

 
 
 
 

0.45

0.222

0.209

0.222

 
 
 
 

6

6

6

6

 
 
 
 
 
 
 
 

LHSOr

 
 
 
 

0.965

-0.96

0.965

 
 
 
 
 

0.00182

0.00243

0.00182

 
 
 
 
 

6

6

6

 
 
 
 
 
 
 
 

Tpg

 
 
 
 
 

-0.975

1

 
 
 
 
 
 

0.000899

0

 
 
 
 
 
 

6

6

 
 
 
 
 
 
 
 

Qpg

 
 
 
 
 
 

-0.975

 
 
 
 
 
 
 

0.000899

 
 
 
 
 
 
 

6

APPENDIX 8.a. LOCAL WATER BALANCE FOR SELECTED GRID CELLS IN THE CONGO RIVER BASIN (TABLE)

PPT = Precipitation, PEH= Effective Precipitation, PET= Potential Evapotranspiration, AET = Actual Evapotranspiration, SOM= Soil Moisture, ROF= Runoff, C= Vertical Integrated Moisture Convergence

Long Lat

Item

Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DJF MAM JJA SON

Ann.

18.31

4.24

AET

32.2

18.8

34.6

89.3

106.5

121.2

102.3

102.5

102.5

105.2

105.6

91.3

85.5

317.1

307.2

302.1

1011.9

18.31

4.24

PET

114.7

117.9

117.8

136.4

128.8

121.0

102.2

102.4

102.4

105.2

105.8

105.2

350.5

386.2

307.0

316.2

1359.8

18.31

4.24

PPT

31.3

20.4

37.5

108.9

137.1

170.8

140.0

178.4

227.3

192.8

195.6

92.6

89.3

416.8

545.7

480.9

1532.7

18.31

4.24

ROF

1.2

0.4

0.1

0.0

0.0

0.0

0.0

11.8

33.2

29.3

13.7

4.1

1.7

0.0

45.0

47.1

93.9

18.31

4.24

SOM

0.0

0.0

0.0

0.0

0.0

2.9

9.3

17.6

17.6

17.6

17.6

3.9

0.0

2.9

44.5

39.1

86.6

18.31

4.24

C

-0.1

0.0

0.0

0.0

0.0

0.1

0.2

0.7

1.1

1.0

0.4

-0.3

-0.1

0.1

1.9

1.1

3.1

21.04

-0.04

AET

105.8

108.7

108.3

122.3

112.5

110.2

100.1

96.2

105.1

107.8

110.1

103.5

322.8

345.0

301.3

321.4

1290.5

21.04

-0.04

PET

105.8

113.8

113.6

122.3

112.5

110.2

100.1

96.2

105.1

107.8

110.1

103.5

333.2

345.0

301.3

321.4

1300.9

21.04

-0.04

PPT

165.0

123.3

135.7

181.5

159.0

189.1

143.1

146.5

184.7

192.2

233.7

210.9

424.0

529.6

474.3

636.8

2064.7

21.04

-0.04

ROF

7.4

2.2

0.7

0.2

0.1

0.0

0.0

0.0

0.0

8.0

23.4

24.5

10.2

0.3

0.0

55.9

66.4

21.04

-0.04

SOM

17.6

7.4

4.7

10.9

16.6

17.6

17.6

17.6

17.6

17.6

17.6

17.6

29.7

45.1

52.8

52.8

180.4

21.04

-0.04

C

0.1

-0.3

-0.1

0.2

0.2

0.5

0.4

0.5

0.7

0.8

1.0

1.2

-0.2

0.9

1.6

3.0

5.2

28.52

-2.31

PET

115.2

122.4

118.4

136.3

123.4

119.8

103.5

100.9

103.5

109.8

111.6

107.2

356.0

379.5

307.9

328.5

1371.9

28.52

-2.31

PPT

165.4

136.1

133.8

181.2

170.2

107.1

32.4

16.6

57.3

105.9

134.9

175.5

435.3

458.4

106.3

416.3

1416.4

28.52

-2.31

ROF

1.2

0.4

0.1

0.0

0.0

0.0

1.8

14.9

29.2

21.7

13.0

3.9

1.6

0.0

45.9

38.6

86.2

28.52

-2.31

SOM

1.2

0.0

0.0

0.0

0.0

11.3

28.2

28.2

28.2

28.2

28.2

17.4

1.2

11.3

84.5

73.7

170.6

28.52

-2.3 1

C

0.9

0.5

0.6

0.9

0.9

0.0

-0.4

0.0

0.0

0.0

0.3

1.0

2.0

1.8

-0.4

1.2

4.6

28.52

-2.30

AET

95.2

100.5

93.6

102.9

92.9

91.0

41.3

16.7

51.4

86.6

99.7

97.5

289.2

286.9

109.4

283.8

969.4

22.25

-5.56

AET

112.0

114.6

109.7

122.9

110.8

87.7

12.3

7.6

19.8

65.2

122.1

106.5

336.3

321.4

39.8

293.9

991.4

22.25

-5.56

PET

108.7

111.7

103.6

114.9

108.2

118.1

114.5

112.2

112.1

114.4

124.4

111.3

324.1

341.2

338.8

350.1

1354.2

22.25

-5.56

PPT

232.2

137.5

125.6

204.4

177.5

76.5

17.6

15.6

49.6

126.5

171.6

235.3

495.3

458.3

82.7

533.4

1569.7

22.25

-5.56

ROF

0.0

0.0

0.0

0.0

1.4

0.4

0.1

0.0

0.0

0.0

0.0

0.0

0.0

1.8

0.2

0.0

2.0

22.25

-5.56

SOM

28.2

23.6

20.9

28.2

28.2

4.7

0.1

0.0

0.0

0.0

0.4

28.2

72.7

61.0

0.2

28.6

162.4

22.25

-5.56

C

0.9

0.1

0.0

0.6

0.1

-0.7

-0.1

0.0

0.0

0.0

0.0

1.1

1.0

0.0

-0.1

1.1

2.0

15.22

-4.22

AET

105.5

109.8

107.2

122.2

114.1

105.4

25.8

2.8

3.6

35.9

98.4

107.8

322.6

341.6

32.1

242.1

938.4

15.22

-4.22

PET

105.5

109.8

109.4

122.2

114.1

106.0

90.5

93.6

106.7

113.8

116.0

107.8

324.8

342.2

290.9

337.7

1295.6

15.22

-4.22

PPT

162.8

142.4

121.1

180.9

213.7

125.1

4.5

1.8

3.5

38.6

123.6

246.2

426.2

519.8

9.7

408.4

1364.2

15.22

-4.22

ROF

13.1

4.1

1.2

0.4

8.4

2.5

0.8

0.2

0.1

0.0

0.0

8.5

18.4

11.3

1.0

8.5

39.2

15.22

-4.22

SOM

27.7

27.7

18.1

24.2

27.7

22.2

1.0

0.0

0.0

0.0

0.0

27.7

73.6

74.1

1.0

27.7

176.5

15.22

-4.22

C

0.4

0.1

-0.3

0.2

0.4

-0.1

-0.7

0.0

0.0

0.0

0.0

1.2

0.3

0.5

-0.7

1.2

1.3

25.11

0.31

AET

101.2

82.1

88.8

119.3

112.3

108.6

94.5

79.5

98.5

102.1

108.9

101.9

272.1

340.2

272.5

312.9

1197.7

25.11

0.31

PET

108.4

114.6

114.7

123.8

116.8

111.6

96.2

96.0

99.1

108.0

114.5

107.9

337.8

352.1

291.3

330.3

1311.5

25.11

0.31

PPT

101.7

71.5

96.2

164.0

179.1

161.7

109.2

119.5

156.0

184.9

214.1

196.3

269.4

504.8

384.7

595.4

1754.2

25.11

0.31

ROF

7.8

2.3

0.7

0.2

0.6

1.5

0.4

3.3

11.6

16.8

24.6

25.9

10.8

2.3

15.3

67.3

95.7

25.11

0.31

SOM

4.7

0.3

0.0

0.0

11.2

17.0

11.8

12.3

17.6

17.6

17.6

17.6

5.0

28.3

41.7

52.8

127.8

25.11

0.31

C

-0.2

-0.1

0.0

0.0

0.4

0.2

-0.2

0.0

0.5

0.6

0.8

0.9

-0.2

0.6

0.3

2.2

2.9

27.29

-11.40

AET

109.6

112.4

104.4

106.2

99.1

17.0

0.2

0.0

1.3

20.1

78.2

112.1

326.3

222.4

1.5

210.4

760.5

27.29

-11.40

PET

113.3

111.6

98.0

117.1

118.7

119.7

108.5

118.4

142.4

163.4

175.5

135.3

322.9

355.4

369.3

474.2

1521.9

27.29

-11.40

PPT

259.2

247.5

267.6

206.0

55.9

2.6

1.0

1.6

0.0

2.1

33.6

164.2

774.3

264.6

2.6

200.0

1241.5

27.29

-11.40

ROF

12.7

23.8

24.3

12.0

3.6

1.1

0.3

0.1

0.0

0.0

0.0

0.0

60.7

16.7

0.5

0.0

77.9

27.29

-11.40

SOM

28.2

28.2

28.2

28.2

2.5

0.0

0.0

0.0

0.0

0.0

0.0

0.0

84.5

30.7

0.0

0.0

115.2

27.29

-11.40

C

1.1

0.9

1.6

0.2

-0.8

-0.1

0.0

0.0

0.0

0.0

0.0

0.0

3.6

-0.7

0.0

0.0

2.9

16.03

1.37

AET

81.0

55.8

81.2

111.7

105.0

102.3

87.1

86.6

93.0

99.0

105.4

99.0

218.0

319.0

266.7

303.4

1107.1

16.03

1.37

PET

105.4

99.3

98.1

111.7

105.0

102.3

87.1

89.9

93.0

99.0

105.4

99.0

302.7

319.0

270.0

303.4

1195.2

16.03

1.37

PPT

74.2

60.3

96.1

151.0

134.3

179.0

143.7

91.7

144.0

223.0

237.1

172.1

230.6

464.3

379.3

632.1

1706.3

16.03

1.37

ROF

9.0

2.7

0.8

0.2

0.1

8.1

10.5

3.1

7.4

33.0

39.0

29.9

12.5

8.4

20.9

102.0

143.8

16.03

1.37

SOM

1.8

0.1

0.1

3.4

3.5

17.6

17.6

8.8

17.6

17.6

17.6

17.6

2.0

24.5

44.1

52.9

123.5

16.03

1.37

C

-0.2

0.0

0.0

0.1

0.0

0.7

0.3

-0.2

0.5

1.1

1.3

1.0

-0.2

0.8

0.7

3.4

4.7

20.04

-11.04

AET

114.2

115.8

107.6

109.9

101.8

18.3

0.0

-0.1

2.6

23.5

78.7

117.2

337.6

229.9

2.5

219.4

789.4

20.04

-11.04

PET

114.2

115.8

107.6

109.9

110.9

122.0

113.3

125.5

144.0

148.1

140.2

117.2

337.6

342.8

382.8

405.5

1468.6

20.04

-11.04

PPT

214.3

212.3

182.1

205.0

101.1

7.2

-0.2

-0.2

2.6

24.9

92.1

172.3

608.6

313.3

2.2

289.3

1213.4

20.04

-11.04

ROF

4.1

18.5

20.3

9.4

2.8

0.8

0.3

0.1

0.0

0.0

0.0

0.0

42.9

13.1

0.4

0.0

56.3

20.04

-11.04

SOM

28.2

28.2

28.2

11.1

0.2

0.0

0.0

0.0

0.0

0.0

7.3

21.2

84.5

11.3

0.0

28.5

124.3

20.04

-11.04

C

0.8

0.6

0.7

0.3

-0.5

-0.3

0.0

0.0

0.0

0.0

0.0

0.2

2.1

-0.5

0.0

0.2

1.9

23.05

8.00

AET

4.5

0.8

7.0

51.5

88.7

123.5

113.4

103.4

108.0

109.7

116.9

43.6

12.3

263.7

324.8

270.2

871.0

23.05

8.00

PET

114.2

114.6

99.7

112.7

110.1

123.6

128.4

133.2

136.1

131.7

136.6

121.3

328.5

346.4

397.7

389.6

1462.1

23.05

8.00

PPT

258.2

195.3

188.0

232.0

181.6

48.5

3.5

0.5

18.8

81.6

161.4

242.9

641.5

462.0

22.7

486.0

1612.2

23.05

8.00

ROF

8.8

8.2

12.0

8.5

2.5

0.8

0.2

0.1

0.0

0.0

0.0

0.0

29.1

11.7

0.3

0.0

41.2

23.05

8.00

SOM

28.2

28.2

28.2

28.2

28.2

1.6

0.0

0.0

0.0

0.0

0.0

26.6

84.5

58.0

0.0

26.6

169.0

23.05

8.00

C

0.8

0.7

1.0

1.0

0.0

-0.8

-0.1

0.0

0.0

0.0

0.0

0.9

2.5

0.2

-0.1

0.9

3.6

32.03

-5.05

AET

113.1

114.6

107.9

125.2

119.0

79.7

17.7

8.3

59.4

95.5

124.4

115.3

335.7

324.0

85.3

335.3

1080.3

32.03

-5.05

PET

116.9

116.0

110.8

123.0

118.8

126.5

129.4

143.0

158.8

158.8

159.8

122.9

343.7

368.4

431.2

441.5

1584.8

32.03

-5.05

PPT

164.1

127.6

121.8

152.5

168.9

55.1

4.2

0.0

-0.1

12.5

46.0

130.7

413.6

376.4

4.2

189.2

983.3

32.03

-5.05

ROF

25.3

10.0

5.0

15.6

3.5

1.0

0.3

0.1

0.0

0.0

0.0

6.5

40.3

20.2

0.4

6.5

67.4

32.03

-5.05

SOM

-5.1

5.2

2.1

0.9

0.6

12.2

0.1

0.0

0.0

0.0

0.0

0.0

2.3

13.6

0.1

0.0

16.0

32.03

-5.05

C

0.1

0.0

0.0

0.0

0.1

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.1

0.0

0.0

0.2

300

260

220

300

260

220

300

260

220

300

260

220

300

260

220

300

260

220

180

140

100

180

140

100

180

140

100

180

140

100

180

140

100

180

140

100

-20

-20

-20

-20

-20

-20

60

20

60

20

60

20

60

20

60

20

60

20

LUBUMBASHI(-14, 27)

UP-NORTH

BOYENDE

URAMBO

KINSHASA

OUESSO

AET PET PPT ROF SOM

AET PET PPT ROF SOM

AET PET PPT ROF SOM

AET PET PPT ROF SOM

AET PET PPT ROF SOM

AET PET PPT ROF SOM

300

260

220

300

260

220

300

260

220

300

260

220

180

140

100

180

140

100

300

260

220

180

140

100

180

140

100

180

140

100

-20

-20

-20

-20

20

60

20

60

20

60

20

60

20

60

20

BUKAVU (28.52, -2.30)

SOUTH-WEST

KANANGA

BANGUI

KISANGANI

AET PET PPT ROF SOM

AET PET PPT ROF SOM

AET PET PPT ROF SOM

AET PET PPT ROF SOM

AET PET PPT ROF SOM

APPENDIX 8.b. LOCAL WATER BALANCE FOR SELECTED GRID CELLS IN THE CONGO RIVER BASIN (GRAPHS)

APPENDIX 9: SEASONAL DISTRIBUTION OF THE CONVERGENCE MOISTURE SAMPLES FOR SELECTED GRID CELLES OVER THE CONGO BASIN (C)

4

3

3

2

2

1

1

0

-1

-1

DJF MAM JJA SON

BOYENDE LUBUMBASHI KINSHASA

SOUTH-WEST BUKAVU

4

3

3

2

2

1

1

0

-1

-1

DJF MAM JJA SON

KISANGANI OUESSO BANGUI UP-NORTH

The first graph shows stations in the southern hemisphere. The second corresponds to the northern hemisphere.

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