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