Distribucion Normal, Log - Normal, Gambel JABE

HIDROLOGIA

INGENIERIA CIVIL

Distribución de Gumbel Caudales Medios

Orden m P (x) Y=(X-u)/a F(y) F(y)-P(x)

1 360 0.0333 -0.5455 0.178100 0.1448

2 367 0.0667 -0.5323 0.182161 0.1155

3 418 0.1000 -0.4365 0.212824 0.11284 520 0.1333 -0.2449 0.278738 0.14545 522 0.1667 -0.2411 0.280077 0.11346 557 0.2000 -0.1754 0.303703 0.10377 563 0.2333 -0.1641 0.307787 0.07458 581 0.2667 -0.1303 0.320085 0.05349 610 0.3000 -0.0758 0.340014 0.040010 618 0.3333 -0.0608 0.345530 0.012211 658 0.3667 0.0144 0.373159 0.006512 683 0.4000 0.0613 0.390423 0.009613 740 0.4333 0.1684 0.429549 0.003814 779 0.4667 0.2417 0.455972 0.010715 818 0.5000 0.3149 0.481984 0.018016 824 0.5333 0.3262 0.485943 0.047417 824 0.5667 0.3262 0.485943 0.080718 876 0.6000 0.4239 0.519701 0.080319 917 0.6333 0.5009 0.545538 0.087820 921 0.6667 0.5084 0.548018 0.118621 934 0.7000 0.5328 0.556028 0.144022 1030 0.7333 0.7132 0.612576 0.120823 1120 0.7667 0.8823 0.661101 0.105624 1150 0.8000 0.9386 0.676265 0.123725 1230 0.8333 1.0889 0.714203 0.119126 1410 0.8667 1.4270 0.786614 0.080127 1660 0.9000 1.8967 0.860652 0.039328 2280 0.9333 3.0614 0.954257 0.020929 3800 0.9667 5.9168 0.997310 0.0306

957.586 m3/s 0.1454682.725 m3/s532.318 m3/s650.360 m3/s

Caudal (m3/s)

�� ̅��

∆_𝑚𝑎𝑥

HIDROLOGIA

INGENIERIA CIVIL

Método de Gumbel Precipitaciones Máximas

Orden m P (x) Y=(X-u)/a F(y) F(y)-P(x)

1 20.70 0.04762 -1.18268 0.03827 0.00935

2 25.40 0.09524 -0.68591 0.13730 0.04206

3 26.40 0.14286 -0.58022 0.16756 0.02470

4 27.10 0.19048 -0.50623 0.19032 0.00015

5 28.60 0.23810 -0.34769 0.24273 0.00464

6 30.00 0.28571 -0.19971 0.29492 0.00921

7 32.00 0.33333 0.01168 0.37218 0.03884

8 33.10 0.38095 0.12794 0.41482 0.03387

9 33.90 0.42857 0.21250 0.44550 0.01693

10 33.90 0.47619 0.21250 0.44550 0.03069

11 34.60 0.52381 0.28649 0.47194 0.05187

12 35.10 0.57143 0.33933 0.49054 0.08089

13 35.30 0.61905 0.36047 0.49790 0.12114

14 41.10 0.66667 0.97351 0.68540 0.01873

15 41.10 0.71429 0.97351 0.68540 0.02889

16 43.70 0.76190 1.24831 0.75052 0.01138

17 47.40 0.80952 1.63939 0.82358 0.01405

18 51.70 0.85714 2.09388 0.88408 0.02694

19 51.80 0.90476 2.10445 0.88523 0.01954

20 74.10 0.95238 4.46145 0.98852 0.03614

37.350 mm12.134 mm 0.12119.461 mm31.890 mm

PRECIPITACIONES PARA CADA TIEMPO DE RETORNO - CUEVA BLANCA

TR - Años F(z) Z YPRECIPITACIÓN - CUEVA BLANCA

NORMAL GUMBEL

5 0.80000 0.84164 1.49994 47.563 50.090

Precipit. (mm)

�� ̅ ��∆_𝑚𝑎𝑥

HIDROLOGIA

INGENIERIA CIVIL

10 0.90000 1.28155 2.25037 52.901 59.19620 0.95000 1.64485 2.97020 57.309 67.93125 0.96000 1.75070 3.19853 58.594 70.70250 0.98000 2.05375 3.90194 62.271 79.237

100 0.99000 2.32630 4.60015 65.578 87.710

Dt TR, Añosmin 5 10 20 25 50

5 15.61716 18.26668 20.91621 21.76917 24.4187015 28.57994 33.42867 38.27740 39.83834 44.6870730 38.79233 45.37364 51.95495 54.07366 60.6549845 45.63993 53.38297 61.12601 63.61871 71.3617560 1 50.93698 59.57869 68.22040 71.00241 79.64412120 2 65.37947 76.47143 87.56338 91.13419 102.22615240 4 82.55460 96.56039 110.56619 115.07505 129.08085360 6 94.07084 110.03042 125.99001 131.12785 147.08743480 8 102.97937 120.45034 137.92130 143.54569 161.01666600 10 110.34436 129.06483 147.78530 153.81194 172.53241720 12 116.67457 136.46899 156.26341 162.63579 182.43021840 14 122.25645 142.99787 163.73928 170.41653 191.15794

1080 18 131.83079 154.19654 176.56229 183.76245 206.128201440 24 143.55509 167.90992 192.26476 200.10526 224.46010

Grafico de Precipitacion y Periodo de Duración

ESTACION CUEVA BLANCA AÑO 1990 - 2011

0 200 400 600 800 1000 1200 14000

50

100

150

200

250

PRECIPITACIÓN - CUEVA BLANCA

5 AÑOS10 AÑOS20 AÑOS25 AÑOS50 AÑOS100 AÑOS

Dt (min)

P (m

m)

HIDROLOGIA

INGENIERIA CIVIL

Orden m

1 20.7 7.994342 25.40 9.809483 26.40 10.195684 27.10 10.466025 28.60 11.045326 30.00 11.5867 32.00 12.35848 33.10 12.783229 33.90 13.0921810 33.90 13.0921811 34.60 13.36252 Curso:12 35.10 13.55562 Hidrología13 35.30 13.63286 Docente:

14 41.10 15.87282 Dr. Walter Morales Uchofen

15 41.10 15.87282 Alumno:16 43.70 16.87694 Edwin Jabe Paredes17 47.40 18.3058818 51.70 19.9665419 51.8 20.0051620 74.10 28.61742

ESTACION CUEVA BLANCA AÑO 1990 - 2011

Precipit. (mm)

.3862 Pmax 24 Hr

HIDROLOGIA

INGENIERIA CIVIL

DISTRIBUCION DE GUMBEL

TR - Años F(z) Y

5 0.80000 1.49994 1448.8110 0.90000 2.25037 1848.2720 0.95000 2.97020 2231.4525 0.96000 3.19853 2353.0050 0.98000 3.90194 2727.43

100 0.99000 4.60015 3099.10

DISTRIBUCIÓNTR - Años

5 10 20

GUMBEL 1448.81 1848.27 2231.45

QAUDAL MEDIO

HIDROLOGIA

INGENIERIA CIVIL

Distribución normal Precipitaciones Máximas

Orden m P (x) z

1 20.70 0.047619 -1.372132

2 25.40 0.095238 -0.984803

3 26.40 0.142857 -0.902393

4 27.10 0.190476 -0.844706

5 28.60 0.238095 -0.721090

6 30.00 0.285714 -0.605716

7 32.00 0.333333 -0.440895

8 33.10 0.380952 -0.350244

9 33.90 0.428571 -0.284316

10 33.90 0.476190 -0.284316

11 34.60 0.523810 -0.226628

12 35.10 0.571429 -0.185423

13 35.30 0.619048 -0.168941

14 41.10 0.666667 0.309039

15 41.10 0.714286 0.309039

16 43.70 0.761905 0.523306

17 47.40 0.809524 0.828224

18 51.70 0.857143 1.182588

19 51.80 0.904762 1.190829

20 74.10 0.952381 3.028580

37.350 mm12.134 mm

PRECIPITACIONES PARA CADA TIEMPO DE RETORNO - CUEVA BLANCA ESTACION CUEVA BLANCAAÑO 1990 - 2011

PRECIPITACIÓN - CUEVA BLANCADISTRIBUCIÓN TR - Años

LOG. NORMAL 546.375 NORMAL 47.563

Precipit. (mm)

�� ̅��

HIDROLOGIA

INGENIERIA CIVIL

53.310 GUMBEL 50.09059.812 LOG NORMAL 46.37561.85168.08374.222

TR, Años Dt I (mm/h)100 min 5

27.06823 5 187.4058749.53580 15 114.3197767.23629 30 77.5846679.10479 45 60.8532488.28583 60 1 50.93698113.31810 120 2 32.68974143.08665 240 4 20.63865163.04702 360 6 15.67847178.48762 480 8 12.87242191.25288 600 10 11.03444202.22463 720 12 9.72288211.89936 840 14 8.73260228.49395 1080 18 7.32393248.81493 1440 24 5.98146

Grafico Intensidad – Periodo de Duración – Tiempo Retorno

0 20 40 60 80 100 1200

50

100

150

200

250

300

INTENSIDAD - CUEVA BLANCA

TR = 5 AÑOSTR = 10 AÑOSTR = 20 AÑOSTR = 25 AÑOS TR = 50 AÑOSTR = 10 AÑOS

Dt (min)

I (m

m/h

r)

HIDROLOGIA

INGENIERIA CIVIL

Hidrología

Dr. Walter Morales Uchofen

Edwin Jabe Paredes

HIDROLOGIA

INGENIERIA CIVIL

TR - Años25 50 100

2353.00 2727.43 3099.10

HIDROLOGIA

INGENIERIA CIVIL

Distribución normal Precipitaciones Máximas

F(z) F(z)-P(x) Orden m P (x) y

0.085011 0.037392 1 20.70 0.04762 3.03013

0.162360 0.067122 2 25.40 0.09524 3.23475

0.183424 0.040567 3 26.40 0.14286 3.27336

0.199138 0.008661 4 27.10 0.19048 3.29953

0.235427 0.002668 5 28.60 0.23810 3.35341

0.272352 0.013363 6 30.00 0.28571 3.40120

0.329644 0.003689 7 32.00 0.33333 3.46574

0.363078 0.017875 8 33.10 0.38095 3.49953

0.388084 0.040487 9 33.90 0.42857 3.52342

0.388084 0.088106 10 33.90 0.47619 3.52342

0.410356 0.113453 11 34.60 0.52381 3.54385

0.426449 0.144980 12 35.10 0.57143 3.55820

0.432921 0.186126 13 35.30 0.61905 3.56388

0.621354 0.045313 14 41.10 0.66667 3.71601

0.621354 0.092932 15 41.10 0.71429 3.71601

0.699619 0.062286 16 43.70 0.76190 3.77735

0.796228 0.013296 17 47.40 0.80952 3.85862

0.881514 0.024371 18 51.70 0.85714 3.94546

0.883140 0.021622 19 51.80 0.90476 3.94739

0.998771 0.046391 20 74.10 0.95238 4.30542

37.350 mm0.1861 12.134 mm

C 0.325 mm0.317 mm3.570 mm

TR - Años10 20 25 50 100

52.901 57.309 58.594 62.271 65.578

Distribución log - normal de 2 Parámetros Precipitaciones Máximas

Precipit. (mm)

∆_𝑚𝑎𝑥 �� ̅ ��𝜎_𝑦𝑢_𝑦

1 10 10045

50

55

60

65

70

75

80

85

90

TR, AÑOS

Dist. NormalDist. gumbelDist. Log - Nomal 2 P.

PROBABILIDAD (%)

PR

EC

IPIT

AC

ION

(m

m)

HIDROLOGIA

INGENIERIA CIVIL

59.196 67.931 70.702 79.237 87.71053.310 59.812 61.851 68.083 74.222

I (mm/h)10 20 25 50 100

219.20021 250.99455 261.23004 293.02438 324.81872133.71469 153.10960 159.35337 178.74829 198.1432190.74729 103.90991 108.14733 121.30995 134.4725871.17729 81.50135 84.82495 95.14900 105.4730659.57869 68.22040 71.00241 79.64412 88.2858338.23571 43.78169 45.56710 51.11307 56.6590524.14010 27.64155 28.76876 32.27021 35.7716618.33840 20.99833 21.85464 24.51457 27.1745015.05629 17.24016 17.94321 20.12708 22.3109512.90648 14.77853 15.38119 17.25324 19.1252911.37242 13.02195 13.55298 15.20252 16.8520510.21413 11.69566 12.17261 13.65414 15.135678.56647 9.80902 10.20903 11.45157 12.694116.99625 8.01103 8.33772 9.35250 10.36729

Grafico Intensidad – Periodo de Duración – Tiempo Retorno

0 20 40 60 80 100 1200

50

100

150

200

250

300

INTENSIDAD - CUEVA BLANCA

TR = 5 AÑOSTR = 10 AÑOSTR = 20 AÑOSTR = 25 AÑOS TR = 50 AÑOSTR = 10 AÑOS

Dt (min)

I (m

m/h

r)

1 10 10045

50

55

60

65

70

75

80

85

90

TR, AÑOS


PROBABILIDAD (%)

PR

EC

IPIT

AC

ION

(m

m)

HIDROLOGIA

INGENIERIA CIVIL

1 10 10045

50

55

60

65

70

75

80

85

90

TR, AÑOS


PROBABILIDAD (%)

PR

EC

IPIT

AC

ION

(m

m)

HIDROLOGIA

INGENIERIA CIVIL

z F(z) F(z)-P(x)

-1.70480 0.04412 0.00350

-1.05886 0.14483 0.04959

-0.93695 0.17439 0.03153

-0.85434 0.19646 0.00598

-0.68427 0.24690 0.00881

-0.53340 0.29688 0.01116

-0.32966 0.37083 0.03750

-0.22297 0.41178 0.03083

-0.14757 0.44134 0.01277

-0.14757 0.44134 0.03485

-0.08305 0.46691 0.05690

-0.03776 0.48494 0.08649

-0.01982 0.49209 0.12695

0.46042 0.67739 0.01073

0.46042 0.67739 0.03689

0.65406 0.74346 0.01844

0.91063 0.81876 0.00923

1.18476 0.88194 0.02480

1.19086 0.88315 0.02162

2.32111 0.98986 0.03748

0.1270

Distribución log - normal de 2 Parámetros Precipitaciones

∆_𝑚𝑎𝑥

1 10 10045

50

55

60

65

70

75

80

85

90

TR, AÑOS


PROBABILIDAD (%)

PR

EC

IPIT

AC

ION

(m

m)

HIDROLOGIA

INGENIERIA CIVIL

1 10 10045

50

55

60

65

70

75

80

85

90

TR, AÑOS


PROBABILIDAD (%)

PR

EC

IPIT

AC

ION

(m

m)

Distribucion Normal, Log - Normal, Gambel JABE

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