Ejemplo de Clculo de Mximas Avenidas Mediante uso de Factor de frecuencia

Ao Q Q Posicin P >= Q (%) T (aos) X=Q/Q

m3/s m3/s m m/(N+1) (N+1)/m

1 2 3 4 5 6 7

1970 71 120 1 1.96 51.0 1.742

1971 45 120 2 3.92 25.5 1.742

1972 25 118 3 5.88 17.0 1.713

1973 83 118 4 7.84 12.8 1.713

1974 60 117 5 9.80 10.2 1.699

1975 105 117 6 11.76 8.5 1.699

1976 47 113 7 13.73 7.3 1.641

1977 43 106 8 15.69 6.4 1.539

1978 28 105 9 17.65 5.7 1.524

1979 23 102 10 19.61 5.1 1.481

1980 32 102 11 21.57 4.6 1.481

1981 31 101 12 23.53 4.3 1.466

1982 113 99 13 25.49 3.9 1.437

1983 78 89 14 27.45 3.6 1.292

1984 37 87 15 29.41 3.4 1.263

1985 76 87 16 31.37 3.2 1.263

1986 21 83 17 33.33 3.0 1.205

1987 81 83 18 35.29 2.8 1.205

1988 66 82 19 37.25 2.7 1.190

1989 44 81 20 39.22 2.6 1.176

1990 118 78 21 41.18 2.4 1.132

1991 117 76 22 43.14 2.3 1.103

1992 82 71 23 45.10 2.2 1.031

1993 21 70 24 47.06 2.1 1.016

1994 60 68 25 49.02 2.0 0.987

1995 83 67 26 50.98 2.0 0.973

1996 54 66 27 52.94 1.9 0.958

1997 101 65 28 54.90 1.8 0.944

1998 99 62 29 56.86 1.8 0.900

1999 120 61 30 58.82 1.7 0.886

2000 102 60 31 60.78 1.6 0.871

2001 61 60 32 62.75 1.6 0.871

2002 65 54 33 64.71 1.5 0.784

2003 87 47 34 66.67 1.5 0.682

2004 117 45 35 68.63 1.5 0.653

2005 102 44 36 70.59 1.4 0.639

2006 120 44 37 72.55 1.4 0.639

2007 68 43 38 74.51 1.3 0.624

2008 19 39 39 76.47 1.3 0.566

2009 106 37 40 78.43 1.3 0.537

2010 118 34 41 80.39 1.2 0.494

2011 62 32 42 82.35 1.2 0.465

2012 89 31 43 84.31 1.2 0.450

2013 67 28 44 86.27 1.2 0.407

2014 70 25 45 88.24 1.1 0.363

2015 23 23 46 90.20 1.1 0.334

2016 34 23 47 92.16 1.1 0.334

2017 44 21 48 94.12 1.1 0.305

2018 87 21 49 96.08 1.0 0.305

2019 39 19 50 98.04 1.0 0.276

Media 68.88 media

desvi. Est 31.83 desvi.est

cof. Asim 0.0671 cof.asim

ANALISIS DE MAXIMAS AVENIDAS-METODO log-normal

X

antilog

2 0.50000 0.0000 -0.0562 0.8787 60.522

5 0.20000 0.8415 0.1438 1.3927 95.927

10 0.10000 1.2817 0.2485 1.7722 122.068

25 0.04000 1.7511 0.3601 2.2913 157.824

50 0.02000 2.0542 0.4321 2.7048 186.306

75 0.01333 2.2168 0.4708 2.9566 203.650

100 0.01000 2.3268 0.4969 3.1400 216.286

150 0.00667 2.4752 0.5322 3.4057 234.585

200 0.00500 2.5762 0.5562 3.5994 247.929

300 0.00333 2.7134 0.5888 3.8802 267.265

400 0.00250 2.8074 0.6112 4.0849 281.370

500 0.00200 2.8785 0.6281 4.2471 292.538

1000 0.00100 3.0905 0.6785 4.7697 328.536

Comparacin de los Valores de Caudales Mximos Obtenidos

T P Q (m3/s) Q (m3/s)

aos Log-Normal Gumbel

2 0.50000 60.522 63.65

5 0.20000 95.927 91.78

10 0.10000 122.068 110.40

25 0.04000 157.824 133.93

50 0.02000 186.306 151.39

75 0.01333 203.650 161.53

100 0.01000 216.286 168.71

150 0.00667 234.585 178.82

200 0.00500 247.929 185.98

300 0.00333 267.265 196.06

400 0.00250 281.370 203.21

500 0.00200 292.538 208.75

1000 0.00100 328.536 225.97

Periodo

Retorno: T

aos

Probabilid.

PFactor

frecuenciaK

= Z

Y Estimado Caudal Q

(m3/s)

calculo de los limites de confianza-metodo de gumbel

T AOS P K=z Q(M3/S)

2 0.50000 -0.1643 63.65

5 0.20000 0.7195 91.78

10 0.10000 1.3046 110.40

25 0.04000 2.0438 133.93

50 0.02000 2.5923 151.39

75 0.01333 2.9111 161.53

100 0.01000 3.1367 168.71

150 0.00667 3.4541 178.82

200 0.00500 3.6791 185.98

300 0.00333 3.9959 196.06

400 0.00250 4.2205 203.21

500 0.00200 4.3947 208.75

1000 0.00100 4.9355 225.97

T AOS Q (m3/s) LCI(Q) LCS(Q)

2 161.52 147.87 175.17

5 192.35 177.14 207.56

10 212.77 194.32 231.21

25 238.56 214.74 262.39

50 257.70 229.39 286.00

75 268.82 237.80 299.84

100 276.69 243.71 309.68

150 287.77 251.99 323.55

200 295.62 257.83 333.40

300 306.67 266.04 347.30

400 314.51 271.84 357.18

500 320.58 276.33 364.84

1000 339.46 290.24 388.67

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00

1 10 100

METODO DE GUMBEL

1 10 100

Q LCI(Q) LCS(

Y=Log Q

8

0.2411

0.2411

0.2338

0.2338

0.2301

0.2301

0.2150

0.1872

0.1831

0.1705

0.1705

0.1662

0.1575

0.1113

0.1014

0.1014

0.0810

0.0810

0.0757

0.0704

0.0540

0.0427

0.0132

0.0070

-0.0056

-0.0120

-0.0185

-0.0252

-0.0457

-0.0528

-0.0599

-0.0599

-0.1057

-0.1660

-0.1849

-0.1946

-0.1946

-0.2046

-0.2470

-0.2699

-0.3066

-0.3329

-0.3467

-0.3909

-0.4402

-0.4764

-0.4764

-0.5159

-0.5159

-0.5593

-0.0562

0.2377

-0.6154

Anlisis de Mximas Avenidas - Mtodo de Gumbel Anlisis de Mximas Avenidas - Mtodo Log-Pearson Tipo III

T P K Q (m3/s) T P

aos aos

2 0.50000 -0.1643 63.65 2 0.50000

5 0.20000 0.7195 91.78 5 0.20000

10 0.10000 1.3046 110.40 10 0.10000

25 0.04000 2.0438 133.93 25 0.04000

50 0.02000 2.5923 151.39 50 0.02000

75 0.01333 2.9111 161.53 75 0.01333

100 0.01000 3.1367 168.71 100 0.01000

150 0.00667 3.4541 178.82 150 0.00667

200 0.00500 3.6791 185.98 200 0.00500

300 0.00333 3.9959 196.06 300 0.00333

400 0.00250 4.2205 203.21 400 0.00250

500 0.00200 4.3947 208.75 500 0.00200

1000 0.00100 4.9355 225.97 1000 0.00100

Comparacin de los Valores de Caudales Mximos Obtenidos

calculo de los limites de confianza- metodo Log-Normal

Q (m3/s) Q (m3/s)

Log-Pearson observado T AOS P K=z

63.98 2 0.50000 0.0000

96.67 5 0.20000 0.8415

116.54 10 0.10000 1.2817

139.34 25 0.04000 1.7511

154.72 50 0.02000 2.0542

163.12 75 0.01333 2.2168

168.83 100 0.01000 2.3268

176.58 150 0.00667 2.4752

181.87 200 0.00500 2.5762

189.05 300 0.00333 2.7134

193.97 400 0.00250 2.8074

197.68 500 0.00200 2.8785

208.69 1000 0.00100 3.0905

Grados de libertad: 28-2=26

CALCXULO DE LOS LIMITES DE CONFIANZA-METODO DE LOG-PERSON TIPO III

2.056

IC(Q) LCI(Q) LCS(Q) T AOS P K=z

12.45 51.20 76.10 2 0.50000 0.0184

13.87 77.90 105.65 5 0.20000 0.8463

16.82 93.58 127.23 10 0.10000 1.2693

21.73 112.20 155.66 25 0.04000 1.7125

25.82 125.56 177.21 50 0.02000 1.9945

28.30 133.23 189.83 75 0.01333 2.1445

30.09 138.63 198.80 100 0.01000 2.2454

32.64 146.18 211.46 150 0.00667 2.3809

34.47 151.51 220.44 200 0.00500 2.4727

37.07 158.99 233.13 300 0.00333 2.5968

38.92 164.29 242.13 400 0.00250 2.6814

40.37 168.38 249.12 500 0.00200 2.7452

44.90 181.07 270.86 1000 0.00100 2.9344

T AOS Q (m3/s) LCI(Q)

2 164.44 151.64

5 195.37 177.76

10 213.34 191.34

25 233.96 206.01

50 248.10 215.67

75 255.97 220.94

100 261.40 224.53

150 268.88 229.43

200 274.07 232.80

300 281.24 237.41

400 286.23 240.60

500 290.06 243.02

1000 301.71 250.34

1000

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

1 10 100

METODO LOG-PERSON TIPO III

Q (m3/s) LCI(Q) LCS(Q)

1000Q (m3/s) LCI(Q) LCS(Q)

Anlisis de Mximas Avenidas - Mtodo Log-Pearson Tipo III

K Y x Q (m3/s)

estimado antilog(Y) antilog(Y)

0.1015 -0.0321 0.92885 63.98

0.8556 0.1472 1.40346 96.67

1.1970 0.2284 1.69190 116.54

1.5235 0.3060 2.02296 139.34

1.7148 0.3515 2.24624 154.72

1.8113 0.3744 2.36811 163.12

1.8743 0.3894 2.45111 168.83

1.9562 0.4088 2.56357 176.58

2.0101 0.4217 2.64037 181.87

2.0809 0.4385 2.74465 189.05

2.1278 0.4496 2.81599 193.97

2.1624 0.4579 2.86988 197.68

2.2614 0.4814 3.02970 208.69

calculo de los limites de confianza- metodo Log-Normal

t(estad.)= 2.056

Y IC(Y) LCI(Y) LCS(Y) LCI(Q) LCS(Q)

-0.0562 0.0924 -0.1485 0.0362 48.93 74.86

0.1438 0.1075 0.0364 0.2513 74.90 122.86

0.2485 0.1247 0.1239 0.3732 91.61 162.65

0.3601 0.1470 0.2131 0.5071 112.50 221.40

0.4321 0.1629 0.2693 0.5950 128.04 271.09

0.4708 0.1717 0.2991 0.6425 137.13 302.43

0.4969 0.1778 0.3191 0.6748 143.61 325.73

0.5322 0.1862 0.3460 0.7184 152.80 360.15

0.5562 0.1919 0.3643 0.7482 159.36 385.72

0.5888 0.1998 0.3890 0.7887 168.69 423.43

0.6112 0.2053 0.4059 0.8165 175.38 451.42

0.6281 0.2095 0.4186 0.8376 180.60 473.86

0.6785 0.2220 0.4565 0.9005 197.06 547.72

Grados de libertad: 28-2=26

CALCXULO DE LOS LIMITES DE CONFIANZA-METODO DE LOG-PERSON TIPO III

2.06

Y IC(Y) LCI(Y) LCS(Y) LCI(Q) LCS(Q)

-0.0518 0.0926 -0.1444 0.0407 49.40 75.65

0.1450 0.1079 0.0372 0.2529 75.03 123.30

0.2455 0.1244 0.1212 0.3699 91.05 161.43

0.3509 0.1453 0.2056 0.4962 110.58 215.94

0.4180 0.1600 0.2580 0.5780 124.75 260.64

0.4536 0.1681 0.2855 0.6217 132.92 288.27

0.4776 0.1737 0.3039 0.6512 138.69 308.56

0.5098 0.1812 0.3286 0.6910 146.78 338.14

0.5316 0.1864 0.3452 0.7180 152.51 359.85

0.5611 0.1935 0.3676 0.7546 160.59 391.47

0.5812 0.1984 0.3829 0.7796 166.32 414.66

0.5964 0.2021 0.3943 0.7985 170.77 433.08

0.6414 0.2132 0.4282 0.8545 184.63 492.76

LCS(Q)

178.32

214.71

237.88

265.71

285.41

296.56

304.33

315.11

322.65

333.15

340.52

346.20

363.61

0.000

50.000

100.000

150.000

200.000

250.000

300.000

350.000

400.000

100 1000

PERSON TIPO III

LCS(Q)

LCS(Q)

T AOS Q LCI(Q) LCS(Q)

2 163.815 151.09 177.61

5 195.169 177.64 214.43

10 213.898 191.78 238.56

25 235.847 207.36 268.24

50 251.205 217.82 289.71

75 259.852 223.58 302.01

100 265.868 227.54 310.66

150 274.207 232.96 322.75

200 280.036 236.72 331.28

300 288.148 241.90 343.24

400 293.838 245.50 351.70

500 298.219 248.25 358.25

1000 311.673 256.62 378.53

100.000

150.000

200.000

250.000

300.000

350.000

1

350.000

0.000

50.000

100.000

150.000

200.000

250.000

300.000

350.000

400.000

1 10 100 1000

LOG-NORMAL

Q LCI(Q) LCS(Q)

0.000

50.000

100.000

150.000

200.000

250.000

300.000

350.000

0

1 10 100

CAUDALES MAXIMOS

LOG-NORMAL GUMBEL LOG-PEARSON350.000

LOG-NORMAL GUMBEL LOG-PEARSON

150.000

200.000

250.000

300.000

350.000

400.000

10 100

KISAME

LOGNO GUM,BEL PEARSON

0.000

50.000

100.000

150.000

200.000

250.000

300.000

350.000

0 200 400 600 800 1000 1200

LOG NORMAL

GUMBEL

LOG PEARSON

1000

1000