Periodo de retorno

CALCULO DE LA ECUACIÓN DE INTENCIDAD DURACIÓN PERIODO DE RETORNO
Cuadro 3.10.1
AÑO | DURACIÒN (min) |
| 5 | 10 | 20 | 30 | 60 | 120 |
1945 | 4.5 | 7.2 | 12.1 | 14.5 | 19.1 | 26.7 |
1946 | 4 | 7 | 12 | 16.5 | 27.6 | 31.5 |
1947 | 10 | 20 | 30.5 | 33 | 36 | 38.9 |
1948 | 14 | 21 | 27 | 32 | 35.3 | 40.4 |
1950 | 3.5 | 6 | 9.9 | 13.7 | 23.1 | 24 |
1951 | 5 | 7 | 8 | 9 | 12 | 15 |1952 | 7 | 11.5 | 20 | 22.8 | 30.5 | 32.7 |
1954 | 15 | 24 | 33 | 40 | 43.2 | 45.7 |
1955 | 5.5 | 10 | 17 | 21.5 | 32.5 | 35.1 |
1956 | 5.5 | 10 | 20 | 24.5 | 27 | 29.58 |
1957 | 10 | 14 | 21 | 23.3 | 29 | 33.4 |
1958 | 5.5 | 7.5 | 11.1 | 14.7 | 21.5 | 27.6 |
1959 | 15 | 22.3 | 31.8 | 37.1 | 37.7 | 38.9 |
1960 | 10 | 18 | 30 | 32 | 35 | 38.6 |
1969 | 10 | 20 | 21 | 22 | 23.5 | 25 |1970 | 10 | 17 | 27 | 28.5 | 33 | 37.2 |
1971 | 10 | 20 | 24 | 27 | 31.5 | 35.6 |
1972 | 5.5 | 11 | 21 | 25 | 32.2 | 34.1 |
1973 | 10 | 17 | 19 | 20.3 | 24 | 31.5 |

Ordenando estos valores del cuadro anterior, en forma descendente y obteniendo el periodo de retorno de la siguiente expresión:
Tr= (n+1)/m
Donde:
n= numero de datos por duración = 19
m= numero de orden en la lista, porlo tanto es variable

Cuadro 3.10.2
AÑO | DURACIÒN (min) |
| 5 | 10 | 20 | 30 | 60 | 120 |
45 | 17 | 54 | 16 | 43.2 | 15 | 36.3 | 17 | 29 | 18 | 19.1 | 16 | 13.35 |
46 | 18 | 48 | 17 | 42 | 16 | 36 | 15 | 33 | 12 | 27.6 | 12 | 15.75 |
47 | 10 | 12 | 4 | 120 | 3 | 91.5 | 3 | 66 | 3 | 36 | 3 | 19.45 |
48 | 13 | 168 | 3 | 126 | 5 | 81 | 4 | 64 | 4 | 35.3 | 2 | 20.2 |
50 | 19 | 42 |19 | 36 | 18 | 29.7 | 18 | 27.4 | 16 | 23.1 | 18 | 12 |
51 | 16 | 60 | 18 | 42 | 19 | 24 | 19 | 18 | 19 | 12 | 19 | 7.5 |
52 | 11 | 84 | 11 | 69 | 11 | 60 | 11 | 45.6 | 10 | 30.5 | 11 | 16.35 |
54 | 2 | 180 | 1 | 144 | 1 | 99 | 1 | 80 | 1 | 43.2 | 1 | 22.85 |
55 | 15 | 66 | 14 | 60 | 14 | 51 | 13 | 43 | 7 | 32.5 | 8 | 17.55 |
56 | 14 | 66 | 13 | 63 | 12 | 60 | 9 | 49 | 13 | 27 | 14 |14.75 |
57 | 9 | 120 | 140 | 84 | 8 | 63 | 10 | 46.6 | 11 | 29 | 10 | 16.7 |
58 | 13 | 66 | 15 | 45 | 17 | 33.3 | 16 | 29.4 | 17 | 21.5 | 15 | 13.8 |
59 | 1 | 180 | 2 | 133.8 | 2 | 95.4 | 2 | 74.2 | 2 | 37.7 | 4 | 19.45 |
60 | 8 | 120 | 7 | 108 | 4 | 90 | 5 | 64 | 5 | 35 | 5 | 19.3 |
69 | 7 | 120 | 5 | 120 | 9 | 63 | 12 | 44 | 15 | 23.5 | 17 | 12.5 |
70 | 6 | 120 | 8 | 102 | 6 | 81 | 6 |57 | 6 | 33 | 6 | 18.6 |
71 | 5 | 120 | 6 | 120 | 7 | 72 | 7 | 54 | 9 | 31.5 | 7 | 17.8 |
72 | 12 | 66 | 12 | 66 | 10 | 63 | 8 | 50 | 8 | 32.2 | 9 | 17.05 |
73 | 4 | 120 | 9 | 102 | 13 | 57 | 14 | 40.6 | 14 | 24 | 13 | 15.75 |

Cuadro 3.10.3
ORDEN | DURACIÒN (min) | Tr |
| 5 | 10 | 20 | 30 | 60 | 120 |   |
1 | 180 | 144 | 99 | 80 | 43.2 | 22.9 | 20 |
2 | 180 | 133.8 | 95.4 | 74.2| 37.7 | 20.2 | 10 |
3 | 168 | 126 | 91.5 | 66 | 36 | 19.5 | 6.7 |
4 | 120 | 120 | 90 | 64 | 35.3 | 19.5 | 5 |
5 | 120 | 120 | 81 | 64 | 35 | 19.3 | 4 |
6 | 120 | 120 | 81 | 57 | 33 | 18.6 | 3.3 |
7 | 120 | 108 | 72 | 54 | 32.5 | 17.8 | 2.9 |
8 | 120 | 102 | 63 | 50 | 32.3 | 17.6 | 2.5 |
9 | 120 | 102 | 63 | 49 | 31.5 | 17.1 | 2.2 |
10 | 120 | 84 | 63 | 46.6 | 30.5 | 16.7 | 2 |11 | 84 | 69 | 60 | 45.8 | 29 | 16.4 | 1.8 |
12 | 66 | 66 | 60 | 44 | 27.6 | 15.6 | 1.7 |
13 | 66 | 63 | 57 | 43 | 27.6 | 15.6 | 1.5 |
14 | 66 | 60 | 51 | 40.6 | 24 | 14.8 | 1.4 |
15 | 66 | 45 | 36.3 | 33 | 23.5 | 13.8 | 1.3 |
16 | 60 | 43.2 | 36 | 29.4 | 23.1 | 13.4 | 1.2 |
17 | 54 | 42 | 33.3 | 29 | 21.5 | 12.5 | 1.2 |
18 | 48 | 42 | 29.7 | 27.4 | 19.1 | 12 | 1.1 |
19 | 42 | 36 |24 | 18 | 12 | 7.5 | 1.1 |
  | 1920 | 1626 | 1186.2 | 915 | 554.4 | 310.8 |   |

Para obtener la ecuación hace falta aplicar el método estadístico de Gumbell, cuya expresión es:
1-1Tr=e-e-i+ac
Calculo de la intensidad para el periodo de retorno de 400 años
Se sustituye el periodo de retorno de Tr = 400 y despejando “i”:
i=5.990213243c-a

i | ( i-ī ) | ( i-ī ) |
180 | 78.95 |...