Page 1
OFICINA GENERAL DE ESTADISTICA E INFORMATIVA
ESTACION : CHONTALI / 000250 /DRE - 02 LAT.: 5°38' 37'' "S" DPTO: CAJAMARCAPARAMETRO : PRECIPITACION MAXIMA EN 24 HORAS (mm) LONG. 79°5'5'' "W" PROV: JAEN
ALT: 1627 msnm DIST. CHONTALI
AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV
1993 16.8 22.6 28.4 22.4 14.6 16.4 8.4 4.2 8.8 36.8 20.2 38.2
1994 48.4 17.4 32.2 26.8 19 26.6 12 6.4 22.7 19 13 24.2
1995 28.8 8.8 22.6 12.8 16.2 10.2 16 10.1 8 8.8 46.8 44.2
1996 38.4 27 38.8 28.6 26.2 5.3 6.2 10 22.4 40.8 32
1997 47 20.2 12.3 50.4 15.8 9.4 10.4 6.6 20 22.8 29.8
1998 24.5 32.8 25.6 51.3 35.1 22.4 5.8 4 11 36.2 34.7 19.8
1999 23.8 43 24.4 25.5 21 29 9.3 8.3 16.2 51.6 27.2 42.3
2000 11.6 34.3 92.5 30.6 31.2 24.6 12.8 6 27 8.5 6.7 24.2
2001 70.5 13.3 21.7 31.9 13.3 4.7 11 6.6 30 13.4 43.3 20.5
2002 27.2 18.2 17.4 24.7 21.5 6 20.3 1.7 15.3 28.8 29 19.9
2003 30.9 24.6 22.6 32 23.9 30.5 10.8 3.1 9.2 48 28.7 22.2
2004 46.6 7.8 33.1 52.2 17.8 12.3 7.8 5.6 15.5 50.3 20.3 24.8
2005 34.4 47.3 41.9 66.3 25.8 15 4.3 5.8 29.1 23.8 32.6 33.3
2006 25.8 24.6 44.2 42 15.7 34.1 5.3 3.2 3.5 28 45.6 21.9
2007 17.2 10.7 34.8 28.7 20.7 22.7 13.3 10.8 4.6 37.9 51.6 20.8
2008 20.8 66.2 25.1 31.4 11.4 12.2 11.9 6.9 15 36.9 69.5 11.5
2009 49.5 20.2 48.2 42 27.4 17.3 15.2 10.2 12.4 22.3 20.2 25.8
2010 12.4 77.9 56.7 19.4 17.6 15.5 4.5 7.8 13.5 14.9 18 30.2
2011 42.5 39.4 44.1 38.2 21.5 8.6 14.9 3.5 44.4 23.7 30.7 44.5
Page 2
2012 42.1 46.6 38.8 83.7 48 12.3 13.6 6.4 3.7 46.4 46.9 24.3
2012 17.9 33.4 33.4 10.5 27.5 33.2 36.9 18.9 15.8 29.5 3.5 19.5
2014 29.1 19.6 52.3 20.9 27.4 23.3 12.7 12.4 5.3 27 22.3 19.6
OFICINA GENERAL DE ESTADISTICA E INFORMATIVA
ESTACION : LA CASCARILLA "CO" LAT.: 5°40'18.3'' "S" DPTO: CAJAMARCAPARAMETRO : PRECIPITACION MAXIMA EN 24 HORAS (mm) LONG. 78°53'51.6'' "W" PROV: JAEN
ALT: 2005 msnm DIST. JAEN
INFORMACIÓN PLUVIOMETRICA
AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC
1993 43 32.4 36.4 45.3 26.2 66 52 80 13.6 71.3 39.1 60.4
1994 22.8 29.4 26.5 39.4 49.5 13.6 8.6 13.5 32.3 21.8 70 56.9
1995 26.8 21.4 32.2 13.9 77.4 23.6 25.62 4.6 6.3 50 38.5 43.3
1996 31.2 37 33.4 57.2 26.9 30.7 3.8 24.2 29.4 41.2 15.4 17.1
1997 18.5 32.4 29.4 47.8 40.6 53.8 29.6 11.1 16.5 61.1 29.5 27.2
1998 49.9 41.1 32.4 65.3 82.6 29.8 10 8.9 23 43.1 42.2 35.9
Page 3
1999 44.3 66.8 44.4 30.8 36.2 46 34.3 12.4 41 66.4 53 54.4
2000 42 59.8 65.8 41.8 45 40.7 17.3 15.4 83.2 13.2 20.7 19
2001 39.2 26.8 25.2 44.9 32.3 8.2 13 11 67.6 30.8 110.5 36
2002 24.3 43.2 23.2 36.6 67 13.8 33.7 30.9 23.8 52.6 25.8 23.9
2003 24.8 31.2 51.5 36.6 29.5 30.4 19 15.7 14.1 55.2 41.8 33
2004 72.7 25.3 27.7 29.1 49.7 24.5 12.4 12.2 28.6 30.3 45.3 45.6
2005 19.5 32.5 47.6 51.6 25.8 16.6 10.7 18.3 30.8 54 73.9 35.4
2006 45 47.2 39 33.3 24.5 98.6 3.3 8.3 9.7 41.1 67.6 50.4
2007 17.7 21.9 31.9 48.5 49.3 15.8 28.1 26 26.5 80.5 53.7 45.9
2008 36.9 67.9 41.8 20.2 42.6 34 28.4 17.3 8.2 52.5 38.3 5.2
2009 56.1 26.7 73.6 43.6 46.8 19.4 23.8 33 23.3 87.9 27.2 42.9
2010 23.8 50.2 17.7 66.7 17.7 14 3.8 11.4 14.2 38.3 15.6 36
2011 78.6 34.6 31.7 83 27.7 16.8 15.6 10.4 41.5 32 56 53.6
2012 70.3 49 67.3 61 17.7 25.1 27.4 12.6 8.2 27.7 40.5 47.7
2013 18.3 44.5 31.1 14.6 52.2 30 23.3 29 18.1 80.5 11 38.6
2014 25 40.1 58.7 23.1 90.2 24.6 8.8 12.3 14.1 29.3 33.3 28.1
Page 4
OFICINA GENERAL DE ESTADISTICA E INFORMATIVA
ESTACION : JAEN / CP - 252/DRE - 02 LAT.: 5°40'39" "S" DPTO: CAJAMARCAPARAMETRO : PRECIPITACION MAXIMA EN 24 HORAS (mm) LONG. 78°46'46" "W" PROV: JAEN
ALT: 654 msnm DIST. JAENINFORMACIÓN PLUVIOMETRICA
AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC
1993 7.87 62.56 45.19 11.78 18.82 7.73 4.67 36.10 72.94 24.81 38.85 30.44
1994 14.70 58.46 35.44 57.94 13.87 12.24 6.56 4.75 48.20 7.54 17.39 14.06
1995 4.94 25.51 23.81 22.74 10.18 4.60 10.26 56.98 7.81 9.52 41.22 36.00
1996 7.90 25.70 18.00 11.20 16.50 14.70 0.50 6.70 13.70 19.80 18.40 38.00
1997 11.00 16.70 14.40 30.00 9.66 4.24 7.41 11.97 13.34 23.74 31.61 33.94
1998 26.59 76.25 41.16 37.27 31.44 18.50 3.10 21.82 23.25 29.68 35.65 15.39
1999 24.97 73.60 17.34 16.95 20.36 17.86 5.91 6.16 27.57 24.92 23.13 44.23
2000 7.10 70.45 49.15 39.80 67.99 18.06 8.18 75.14 40.81 3.61 10.89 18.02
2001 33.88 32.71 26.26 22.64 14.83 3.29 7.08 77.94 61.48 10.96 75.31 17.95
2002 7.26 31.63 38.37 18.24 27.04 4.05 12.70 1.26 8.14 25.28 34.01 29.71
2003 6.93 54.34 15.18 15.46 17.14 28.03 8.93 2.30 11.12 15.67 37.01 17.92
2004 7.50 6.80 17.70 30.60 38.10 18.00 2.40 7.20 17.00 19.40 18.20 12.00
2005 6.50 42.00 36.20 31.00 10.20 18.30 1.90 14.50 18.70 27.90 78.50 31.50
2006 18.50 38.70 23.00 9.40 13.50 26.50 1.30 8.50 5.60 11.70 15.50 16.00
2007 7.60 27.00 32.50 29.00 29.30 13.00 27.20 7.50 7.20 45.90 38.90 22.60
2008 17.00 37.20 63.70 10.20 15.80 26.90 17.40 3.40 9.93 24.57 77.48 9.96
Page 5
2009 21.47 54.12 29.48 13.67 22.19 8.30 8.30 14.64 14.52 20.23 59.48 23.59
2010 16.60 32.80 5.50 41.50 12.50 13.30 4.00 22.90 10.70 24.00 12.10 30.00
2011 25.50 39.50 48.90 39.80 70.60 4.50 21.80 5.80 2.50 30.80 23.50 38.70
2012 23.80 32.60 22.50 27.50 7.80 17.00 6.40 6.80 5.20 26.00 23.20 12.20
2013 9.40 47.00 10.30 18.80 12.90 9.00 6.40 7.40 14.00 56.90 0.70 18.60
2014 1.40 20.00 50.00 59.20 45.30 8.20 10.00 8.50 6.50 9.40 30.80 22.70
CÁLCULOS
Page 6
Año ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC TOTAL PRO. ANUAL
P. MAX
1995 28.8 8.8 22.6 12.8 16.2 10.2 16 10.1 8 8.8 46.8 44.2 233.3 19.44 46.81996 38.4 27 38.8 28.6 26.2 5.3 6.2 10 22.4 40.8 32 9.6 285.3 23.78 40.81997 47 20.2 12.3 50.4 15.8 9.4 10.4 6.6 20 22.8 29.8 35 279.7 23.31 50.41998 24.5 32.8 25.6 51.3 35.1 22.4 5.8 4 11 36.2 34.7 19.8 303.2 25.27 51.31999 23.8 43 24.4 25.5 21 29 9.3 8.3 16.2 51.6 27.2 42.3 321.6 26.80 51.62000 11.6 34.3 92.5 30.6 31.2 24.6 12.8 6 27 8.5 6.7 24.2 310 25.83 92.52001 70.5 13.3 21.7 31.9 13.3 4.7 11 6.6 30 13.4 43.3 20.5 280.2 23.35 70.52002 27.2 18.2 17.4 24.7 21.5 6 20.3 1.7 15.3 28.8 29 19.9 230 19.17 292003 30.9 24.6 22.6 32 23.9 30.5 10.8 3.1 9.2 48 28.7 22.2 286.5 23.88 482004 46.6 7.8 33.1 52.2 17.8 12.3 7.8 5.6 15.5 50.3 20.3 24.8 294.1 24.51 52.22005 34.4 47.3 41.9 66.3 25.8 15 4.3 5.8 29.1 23.8 32.6 33.3 359.6 29.97 66.32006 25.8 24.6 44.2 42 15.7 34.1 5.3 3.2 3.5 28 45.6 21.9 293.9 24.49 45.62007 17.2 10.7 34.8 28.7 20.7 22.7 13.3 10.8 4.6 37.9 51.6 20.8 273.8 22.82 51.62008 20.8 66.2 25.1 31.4 11.4 12.2 11.9 6.9 15 36.9 69.5 11.5 318.8 26.57 69.52009 49.5 20.2 48.2 42 27.4 17.3 15.2 10.2 12.4 22.3 20.2 25.8 310.7 25.89 49.52010 12.4 77.9 56.7 19.4 17.6 15.5 4.5 7.8 13.5 14.9 18 30.2 288.4 24.03 77.92011 42.5 39.4 44.1 38.2 21.5 8.6 14.9 3.5 44.4 23.7 30.7 44.5 356 29.67 44.52012 42.1 46.6 38.8 83.7 48 12.3 13.6 6.4 3.7 46.4 46.9 24.3 412.8 34.40 83.72012 17.9 33.4 33.4 10.5 27.5 33.2 36.9 18.9 15.8 29.5 3.5 19.5 280 23.33 36.92014 29.1 19.6 52.3 20.9 27.4 23.3 12.7 12.4 5.3 27 22.3 19.6 271.9 22.66 52.3
Promedio 32.05 30.795 36.525 36.155 23.25 17.43 12.15 7.395 16.095 29.98 31.97 25.695 299.49Máximo 70.5 77.9 92.5 83.7 48 34.1 36.9 18.9 44.4 51.6 69.5 44.5 672.5Mínimo 11.6 7.8 12.3 10.5 11.4 4.7 4.3 1.7 3.5 8.5 3.5 9.6 89.4
ESTACION : CHONTALI / 000250 /DRE - 02 LAT.: 5°38' 37'' "S" DPTO: CAJAMARCA
PARAMETRO : PRECIPITACION MAXIMA EN 24 HORAS (mm) LONG. 79°5'5'' "W" PROV: JAEN
ALT: 1627 msnm DIST. CHONTALI
Page 7
ESTACION : LA CASCARILLA "CO" LAT.: 5°40'18.3'' "S" DPTO:PARAMETRO : PRECIPITACION MAXIMA EN 24 HORAS (mm) LONG. 78°53'51.6'' "W" PROV:
ALT: 2005 msnm DIST.
AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC TOTAL PRO. ANUAL
P.MAX
1995 26.8 21.4 32.2 13.9 77.4 23.6 25.62 4.6 6.3 50 38.5 43.3 363.62 30.30 77.41996 31.2 37 33.4 57.2 26.9 30.7 3.8 24.2 29.4 41.2 15.4 17.1 347.5 28.96 57.21997 18.5 32.4 29.4 47.8 40.6 53.8 29.6 11.1 16.5 61.1 29.5 27.2 397.5 33.13 61.11998 49.9 41.1 32.4 65.3 82.6 29.8 10 8.9 23 43.1 42.2 35.9 464.2 38.68 82.61999 44.3 66.8 44.4 30.8 36.2 46 34.3 12.4 41 66.4 53 54.4 530 44.17 66.82000 42 59.8 65.8 41.8 45 40.7 17.3 15.4 83.2 13.2 20.7 19 463.9 38.66 83.22001 39.2 26.8 25.2 44.9 32.3 8.2 13 11 67.6 30.8 110.5 36 445.5 37.13 110.52002 24.3 43.2 23.2 36.6 67 13.8 33.7 30.9 23.8 52.6 25.8 23.9 398.8 33.23 672003 24.8 31.2 51.5 36.6 29.5 30.4 19 15.7 14.1 55.2 41.8 33 382.8 31.90 55.22004 72.7 25.3 27.7 29.1 49.7 24.5 12.4 12.2 28.6 30.3 45.3 45.6 403.4 33.62 72.72005 19.5 32.5 47.6 51.6 25.8 16.6 10.7 18.3 30.8 54 73.9 35.4 416.7 34.73 73.92006 45 47.2 39 33.3 24.5 98.6 3.3 8.3 9.7 41.1 67.6 50.4 468 39.00 98.62007 17.7 21.9 31.9 48.5 49.3 15.8 28.1 26 26.5 80.5 53.7 45.9 445.8 37.15 80.52008 36.9 67.9 41.8 20.2 42.6 34 28.4 17.3 8.2 52.5 38.3 5.2 393.3 32.78 67.92009 56.1 26.7 73.6 43.6 46.8 19.4 23.8 33 23.3 87.9 27.2 42.9 504.3 42.03 87.92010 23.8 50.2 17.7 66.7 17.7 14 3.8 11.4 14.2 38.3 15.6 36 309.4 25.78 66.72011 78.6 34.6 31.7 83 27.7 16.8 15.6 10.4 41.5 32 56 53.6 481.5 40.13 832012 70.3 49 67.3 61 17.7 25.1 27.4 12.6 8.2 27.7 40.5 47.7 454.5 37.88 70.32012 18.3 44.5 31.1 14.6 52.2 30 23.3 29 18.1 80.5 11 38.6 391.2 32.60 80.52014 25 40.1 58.7 23.1 90.2 24.6 8.8 12.3 14.1 29.3 33.3 28.1 387.6 32.30 90.2
Promedio 38.25 39.98 40.28 42.48 44.085 29.82 18.60 16.25 26.41 48.39 41.99 35.96 422.48Máximo 78.6 67.9 73.6 83 90.2 98.6 34.3 33 83.2 87.9 110.5 54.4 895.2Mínimo 17.7 21.4 17.7 13.9 17.7 8.2 3.3 4.6 6.3 13.2 11 5.2 140.2
ESTACION : JAEN / CP - 252/DRE - 02 LAT.: 5°40'39" "S" DPTO: CAJAMARCAPARAMETRO : PRECIPITACION MAXIMA EN 24 HORAS (mm) LONG. 78°46'46" "W" PROV: JAEN
ALT: 654 msnm DIST. JAEN
AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC TOTAL
1995 4.94 25.51 23.81 22.74 10.18 4.6 10.26 56.98 7.81 9.52 41.22 36 253.571996 7.9 25.7 18 11.2 16.5 14.7 0.5 6.7 13.7 19.8 18.4 38 191.11997 11 16.7 14.4 30 9.66 4.24 7.41 11.97 13.34 23.74 31.61 33.94 208.011998 26.59 76.25 41.16 37.27 31.44 18.5 3.1 21.82 23.25 29.68 35.65 15.39 360.11999 24.97 73.6 17.34 16.95 20.36 17.86 5.91 6.16 27.57 24.92 23.13 44.23 3032000 7.1 70.45 49.15 39.8 67.99 18.06 8.18 75.14 40.81 3.61 10.89 18.02 409.22001 33.88 32.71 26.26 22.64 14.83 3.29 7.08 77.94 61.48 10.96 75.31 17.95 384.332002 7.26 31.63 38.37 18.24 27.04 4.05 12.7 1.26 8.14 25.28 34.01 29.71 237.692003 6.93 54.34 15.18 15.46 17.14 28.03 8.93 2.3 11.12 15.67 37.01 17.92 230.032004 7.5 6.8 17.7 30.6 38.1 18 2.4 7.2 17 19.4 18.2 12 194.92005 6.5 42 36.2 31 10.2 18.3 1.9 14.5 18.7 27.9 78.5 31.5 317.22006 18.5 38.7 23 9.4 13.5 26.5 1.3 8.5 5.6 11.7 15.5 16 188.22007 7.6 27 32.5 29 29.3 13 27.2 7.5 7.2 45.9 38.9 22.6 287.72008 17 37.2 63.7 10.2 15.8 26.9 17.4 3.4 9.93 24.57 77.48 9.96 313.54
Page 8
2009 21.47 54.12 29.48 13.67 22.19 8.3 8.3 14.64 14.52 20.23 59.48 23.59 289.992010 16.6 32.8 5.5 41.5 12.5 13.3 4 22.9 10.7 24 12.1 30 225.92011 25.5 39.5 48.9 39.8 70.6 4.5 21.8 5.8 2.5 30.8 23.5 38.7 351.92012 23.8 32.6 22.5 27.5 7.8 17 6.4 6.8 5.2 26 23.2 12.2 2112012 9.4 47 10.3 18.8 12.9 9 6.4 7.4 14 56.9 0.7 18.6 211.42014 1.4 20 50 59.2 45.3 8.2 10 8.5 6.5 9.4 30.8 22.7 272
Promedio 14.29 39.23 29.17 26.25 24.67 13.82 8.56 18.37 15.95 23.00 34.28 24.45 272.04Máximo 33.88 76.25 63.7 59.2 70.6 28.03 27.2 77.94 61.48 56.9 78.5 44.23 677.91Mínimo 1.4 6.8 5.5 9.4 7.8 3.29 0.5 1.26 2.5 3.61 0.7 9.96 52.72
Page 9
PARA PRECIPITACIONES MAXIMAS ANUALES EN 24 HORAS
ESTACION p. promedio
AÑO CHONTALI CASCARILLA JAEN PP. MAX 24 HORAS
1995 46.8 77.4 56.98 60.391996 40.8 57.2 38 45.33
1997 50.4 61.1 33.94 48.481998 51.3 82.6 76.25 70.05
1999 51.6 66.8 73.6 64.002000 92.5 83.2 75.14 83.61
2001 70.5 110.5 77.94 86.312002 29 67 38.37 44.79
2003 48 55.2 54.34 52.512004 52.2 72.7 38.1 54.33
2005 66.3 73.9 78.5 72.902006 45.6 98.6 38.7 60.97
2007 51.6 80.5 45.9 59.332008 69.5 67.9 77.48 71.63
2009 49.5 87.9 59.48 65.632010 77.9 66.7 41.5 62.03
2011 44.5 83 70.6 66.032012 83.7 70.3 32.6 62.20
2012 36.9 80.5 56.9 58.102014 52.3 90.2 59.2 67.23
A) ANALISIS DE DISTRIBUCION
Page 10
I. ANALISIS CON DISTRIBUCION NORMAL
ANALISIS CON DISTRIBUCION NORMALAÑO PRECIPITACION P ORDENADOS F(x) f(x)1995 69.39 86.31 0.982 0.0041996 45.33 83.61 0.969 0.0061997 48.48 72.90 0.815 0.0241998 70.05 71.63 0.783 0.0261999 64.00 70.05 0.739 0.0292000 83.61 69.39 0.720 0.0302001 86.31 67.23 0.651 0.0332002 44.79 66.03 0.610 0.0352003 52.51 65.63 0.596 0.0352004 54.33 64.00 0.539 0.0362005 72.90 62.20 0.474 0.0362006 60.97 62.03 0.468 0.0362007 59.33 60.97 0.430 0.0352008 71.63 59.33 0.373 0.0342009 65.63 58.10 0.332 0.0332010 62.03 54.33 0.220 0.0272011 66.03 52.51 0.175 0.0232012 62.20 48.48 0.097 0.0152013 58.10 45.33 0.057 0.0102014 67.23 44.79 0.051 0.009
MEDIA 63.24DESV.EST. 11.12
N 20
Page 11
Media 63.24 63.24 0.5042 0.025857Des.Est 11.12 11.12 0.288192 0.010841Coef.As 0.23 0.23 -0.065282 -0.952898
Tr Pexc. Pno-exc valor Z y=x+z*desv.est
10 0.100 0.900 1.28 77.49
20 0.050 0.950 1.64 81.53
30 0.033 0.967 1.83 83.63
40 0.025 0.975 1.96 85.03
50 0.020 0.980 2.05 86.07
100 0.010 0.990 2.33 89.10
II. ANALISIS LOG. NORMAL 2 PARAMETROS
ANALISIS CON DISTRIBUCION LOG - NORMAL DE 2 PARAMETROS
Page 12
AÑO P P ORDENADOS y = ln (x) F(x) f(x)1995 69.39 86.31 4.458 0.966 0.4211996 45.33 83.61 4.426 0.951 0.5741997 48.48 72.90 4.289 0.811 1.5181998 70.05 71.63 4.272 0.783 1.6481999 64.00 70.05 4.249 0.744 1.8042000 83.61 69.39 4.240 0.727 1.8652001 86.31 67.23 4.208 0.665 2.0442002 44.79 66.03 4.190 0.628 2.1232003 52.51 65.63 4.184 0.615 2.1452004 54.33 64.00 4.159 0.560 2.2132005 72.90 62.20 4.130 0.496 2.2382006 60.97 62.03 4.128 0.490 2.2382007 59.33 60.97 4.110 0.452 2.2222008 71.63 59.33 4.083 0.392 2.1552009 65.63 58.10 4.062 0.347 2.0732010 62.03 54.33 3.995 0.221 1.6662011 66.03 52.51 3.961 0.169 1.4122012 62.20 48.48 3.881 0.080 0.8312013 58.10 45.33 3.814 0.037 0.4552014 67.23 44.79 3.802 0.032 0.403
III. ANALISIS LOG NORMAL 3 PARAMETROS
ANALISIS CON DISTRIBUCION LOG - NORMAL DE 3 PARAMETROS
Media 63.24 4.13Desv.stand 11.12 0.18Coef.asimet 0.23 -0.22
Pexc. Tr x=LN I0.100 10 78.300.050 20 83.530.033 30 86.400.025 40 88.360.020 50 89.850.010 100 94.32
Page 13
AÑO P P ORDENADOS y = ln (x-a) F(x) f(x)1995 69.39 86.31 4.747 0.972 0.5381996 45.33 83.61 4.723 0.956 0.7671997 48.48 72.90 4.623 0.811 2.2371998 70.05 71.63 4.610 0.782 2.4381999 64.00 70.05 4.595 0.741 2.6762000 83.61 69.39 4.588 0.723 2.7692001 86.31 67.23 4.566 0.658 3.0352002 44.79 66.03 4.553 0.619 3.1492003 52.51 65.63 4.549 0.606 3.1812004 54.33 64.00 4.531 0.550 3.2722005 72.90 62.20 4.512 0.485 3.2962006 60.97 62.03 4.510 0.479 3.2932007 59.33 60.97 4.498 0.441 3.2612008 71.63 59.33 4.480 0.382 3.1512009 65.63 58.10 4.466 0.338 3.0232010 62.03 54.33 4.421 0.217 2.4262011 66.03 52.51 4.399 0.167 2.0672012 62.20 48.48 4.349 0.083 1.2622013 58.10 45.33 4.307 0.042 0.7392014 67.23 44.79 4.300 0.037 0.664
AS: Asimetría
Si As < 0 Indica que existe presencia de la minoría de datos en la parte izquierda de la media, aunque en algunos casos no necesariamente indicará que la distribución sea asimétrica negativaSi As = 0 la distribución será simétricaSi As > 0 Indica que existe presencia de la minoría de datos en la parte derecha de la media, aunque en algunos casos no necesariamente indicará que la distribución sea asimétrica positiva
a= (Extremomayor∗extremomenor−(media≺.)2)(Extremomayor+extremomenor−(2∗media≺.))
Precipitación YMedia 63.24 4.52
Desv.stand 11.12 0.12Coef.asimet
. 0.23 -0.08
a -28.8900
Page 14
Tr Pexc. 1-Pexc. z = f ( Pexc) y = ln (x - a) x10 0.100 0.900 1.28 4.67 77.9520 0.050 0.950 1.64 4.72 82.7530 0.033 0.967 1.83 4.74 85.3340 0.025 0.975 1.96 4.75 87.0950 0.020 0.980 2.05 4.76 88.41100 0.010 0.990 2.33 4.80 92.34
IV. ANALISIS POR METODO GUMBEL
VALORES GUMBELMedia reducida Yn
Page 15
n 0 1 2 3 4 5 6 7 8 910 0.4952 0.4996 0.5035 0.5070 0.5100 0.5128 0.5157 0.5181 0.5202 0.522020 0.5230 0.5252 0.5268 0.5283 0.5296 0.5309 0.5320 0.5332 0.5343 0.535330 0.5362 0.5371 0.5380 0.5388 0.5396 0.5402 0.5410 0.5418 0.5424 0.543040 0.5436 0.5442 0.5448 0.5453 0.5458 0.5463 0.5468 0.5473 0.5477 0.548150 0.5485 0.5489 0.5493 0.5497 0.5501 0.5504 0.5508 0.5511 0.5515 0.551860 0.5521 0.5524 0.5527 0.5530 0.5533 0.5535 0.5538 0.5540 0.5543 0.554570 0.5548 0.5550 0.5552 0.5555 0.5557 0.5559 0.5561 0.5563 0.5565 0.556780 0.5569 0.5570 0.5572 0.5574 0.5576 0.5578 0.5580 0.5581 0.5583 0.558590 0.5586 0.5587 0.5589 0.5591 0.5592 0.5593 0.5595 0.5596 0.5598 0.5599
100 0.5600
Desviación típica reducida Sn
n 0 1 2 3 4 5 6 7 8 910 0.9496 0.9676 0.9833 0.9971 1.0095 1.0206 1.0316 1.0411 1.0493 1.056520 1.0628 1.0696 1.0754 1.0811 1.0864 1.0915 1.0961 1.1004 1.1047 1.108630 1.1124 1.1159 1.1193 1.2260 1.1255 1.1285 1.1313 1.1339 1.1363 1.388040 1.1413 1.1430 1.1458 1.1480 1.1499 1.1519 1.1538 1.1557 1.1574 1.159050 1.1607 1.1623 1.1638 1.1658 1.1667 1.1681 1.1696 1.1708 1.1721 1.173460 1.1747 1.1759 1.1770 1.1782 1.1793 1.1803 1.1814 1.1824 1.1834 1.184470 1.1854 1.1863 1.1873 1.1881 1.1890 1.1898 1.1906 1.1915 1.1923 1.193080 1.1938 1.1945 1.1953 1.1959 1.1967 1.1973 1.1980 1.1987 1.1994 1.200190 1.2007 1.2013 1.2020 1.2026 1.2032 1.2038 1.2044 1.2049 1.2055 1.2060
100 1.2065
ANALISIS CON DISTRIBUCION GUMBELVar. Reducida
AÑO P P ORDENADOS y = (x - u)/a Tr1995 69.39 86.31 2.73 15.811996 45.33 83.61 2.47 12.33
Page 16
1997 48.48 72.90 1.45 4.771998 70.05 71.63 1.32 4.281999 64.00 70.05 1.17 3.762000 83.61 69.39 1.11 3.562001 86.31 67.23 0.90 3.002002 44.79 66.03 0.79 2.742003 52.51 65.63 0.75 2.662004 54.33 64.00 0.60 2.362005 72.90 62.20 0.42 2.082006 60.97 62.03 0.41 2.062007 59.33 60.97 0.31 1.922008 71.63 59.33 0.15 1.732009 65.63 58.10 0.03 1.612010 62.03 54.33 (0.33) 1.332011 66.03 52.51 (0.50) 1.242012 62.20 48.48 (0.89) 1.102013 58.10 45.33 (1.19) 1.042014 67.23 44.79 (1.24) 1.03
Tr Pexc.(1/Tr) Pno exc. ln(1-1/Tr) e(-y) y=-(LN(e(-y))) x=u+a*y
10 0.100 0.900 -0.105 0.105 2.250 81.31020 0.050 0.950 -0.051 0.051 2.970 88.840
TreXxF
ye 11)(
PRECIPITACION YMEDIA 63.24 0.5230DES. ESTA 11.12 1.0628N 20Yn= 0.523Sn= 1.0628a= 10.46u= 57.7
Page 17
30 0.033 0.967 -0.034 0.034 3.384 93.17140 0.025 0.975 -0.025 0.025 3.676 96.22550 0.020 0.980 -0.020 0.020 3.902 98.585100 0.010 0.990 -0.010 0.010 4.600 105.889
Probabilidad de excedencia F(x) Diferencia Delta DDATO
S EmpíricaNorma
l LN2 LN3 GumbelNorma
l LN2 LN3 Gumbel
Page 18
1 0.0476 0.0190 0.0338 0.0284 0.0632 0.0286 0.0139 0.0192 0.01562 0.0952 0.0335 0.0495 0.0438 0.0811 0.0618 0.0458 0.0514 0.01413 0.1429 0.1925 0.1892 0.1891 0.2098 0.0496 0.0463 0.0462 0.06694 0.1905 0.2253 0.2170 0.2184 0.2334 0.0348 0.0265 0.0279 0.04305 0.2381 0.2701 0.2555 0.2590 0.2660 0.0321 0.0174 0.0209 0.02796 0.2857 0.2901 0.2729 0.2772 0.2806 0.0044 0.0128 0.0085 0.00517 0.3333 0.3599 0.3348 0.3418 0.3329 0.0266 0.0015 0.0085 0.00048 0.3810 0.4010 0.3724 0.3807 0.3650 0.0201 0.0086 0.0003 0.01609 0.4286 0.4150 0.3853 0.3941 0.3761 0.0136 0.0432 0.0345 0.052510 0.4762 0.4728 0.4402 0.4503 0.4238 0.0034 0.0360 0.0259 0.052411 0.5238 0.5374 0.5039 0.5147 0.4805 0.0135 0.0199 0.0091 0.043312 0.5714 0.5434 0.5100 0.5208 0.4860 0.0280 0.0614 0.0506 0.085413 0.6190 0.5810 0.5485 0.5593 0.5213 0.0381 0.0706 0.0597 0.097814 0.6667 0.6376 0.6082 0.6185 0.5775 0.0291 0.0584 0.0482 0.089115 0.7143 0.6782 0.6526 0.6619 0.6206 0.0361 0.0617 0.0524 0.093716 0.7619 0.7886 0.7790 0.7834 0.7508 0.0267 0.0171 0.0215 0.011117 0.8095 0.8328 0.8314 0.8331 0.8087 0.0233 0.0219 0.0236 0.000818 0.8571 0.9079 0.9204 0.9172 0.9121 0.0508 0.0633 0.0600 0.054919 0.9048 0.9464 0.9629 0.9582 0.9626 0.0417 0.0581 0.0534 0.057820 0.9524 0.9515 0.9680 0.9633 0.9686 0.0008 0.0156 0.0109 0.0162
B) PRUEBAS DE BONDAD DE AJUSTE SMIRNOV-KOLMOGOROV
Max. Normal Max. LN2 Max.LN3 Max. Gumbel0.06177 0.07060 0.06003 0.09780
VERDADERO VERDADERO VERDADERO VERDADERO0.3041
Los datos de ajustan a la función Log Normal 3, siendo este dato 0,06003 menor a 0,3041
C) INTENSIDAD DE PRECIPITACIONES
T R PRECIP. MÁX LN3
10 77.9520 82.7530 85.3340 87.0950 88.41
100 92.34
Page 19
Con los datos ajustados hacemos:
Tr N°P. Max 24 h. mm
I24Intensidad de lluvias en (mm/hr)
Duración de lluvias (min)10 30 60 120 180 240 480
10 1 77.95 3.25 38.98 22.50 15.91 11.25 9.19 7.96 5.6320 2 82.75 3.45 41.38 23.89 16.89 11.94 9.75 8.45 5.9730 3 85.33 3.56 42.67 24.63 17.42 12.32 10.06 8.71 6.1640 4 87.09 3.63 43.55 25.14 17.78 12.57 10.26 8.89 6.2950 5 88.41 3.68 44.21 25.52 18.05 12.76 10.42 9.02 6.38
100 6 92.34 3.85 46.17 26.66 18.85 13.33 10.88 9.42 6.66
El tiempo de concentración = 1.63 horas
Page 20
Graficamos nuestra curva IDF
D. CALCULO DEL CAUDAL
Para esto se tendrá en cuenta la fórmula:
Q= CIA/360
C: coeficiente de escorrentía
I: Intensidad para un determinado tiempo de retorno de acuerdo a un tiempo de concentración.
A: Área de la cuenca en Has
Page 21
-Precipitación máxima corregida sobre la cuenca (P):
Donde: KA = Factor reductor
A=Área de la cuenca en km2 = 156.12 km2
KA = 0.85376943
Pd = Precipitación máxima diaria (mm)
ESTACIÓN ARIAL CUENCA AMOJÚ
T R PRECIP. MÁX LN3 P
10 77.949 66.5520 82.750 70.6530 85.332 72.8540 87.087 74.3550 88.410 75.48100 92.343 78.84
-Intensidad:
T R Precipitación Intensidad
10 66.55 14.68920 70.65 15.59330 72.85 16.08040 74.35 16.41150 75.48 16.660100 78.87 17.401
Page 22
Como la pendiente es 10 %
C= 0.6
Se tendrá en cuenta el Tc= 1.63 horas = 97.8 min lo cual representa un flujo lento.
Caudales Máximos:
Tr Intensidad mm/h Área C Q (m3/Seg)10 14.69 15612 0.6 382.2020 15.59 15612 0.6 405.7430 16.08 15612 0.6 418.4040 16.41 15612 0.6 427.0150 16.66 15612 0.6 433.49100 17.40 15612 0.6 452.78
Page 23
PRECIPITACIONES 24 HORAS
Page 24
PRECIPITACIONES MINIMAS EN 24 HORAS
AÑO MIN1998 1.011999 0.932000 0.342001 0.82002 1.492003 1.52004 0.992005 1.012006 0.832007 2.43
Page 25
ANALISIS DE DISTRIBUCION DE PRECIPITACIONES MINIMAS
I. ANALISIS CON DISTRIBUCION NORMAL
ANALISIS CON DISTRIBUCION NORMALAÑO PRECIPITACION P ORDENADOS F(x) f(x)
1998 1.01 2.43 0.989 0.050
1999 0.93 1.50 0.742 0.572
2000 0.34 1.49 0.736 0.579
2001 0.8 1.01 0.414 0.690
2002 1.49 1.01 0.414 0.690
2003 1.5 0.99 0.400 0.684
2004 0.99 0.93 0.360 0.662
2005 1.01 0.83 0.296 0.612
2006 0.83 0.80 0.278 0.594
2007 2.43 0.34 0.080 0.263
Page 26
MEDIA 1.13DESV.EST. 0.56N 10
Media 1.13 1.13 0.4708 0.539763Des.Est 0.56 0.56 0.270295 0.212832Coef.As 1.31 1.31 0.728996 -1.814385
Tr Pexc. Pno-exc valor Z y=x+z*desv.est10 0.100 0.900 1.28 1.8620 0.050 0.950 1.64 2.0630 0.033 0.967 1.83 2.1740 0.025 0.975 1.96 2.2450 0.020 0.980 2.05 2.29
100 0.010 0.990 2.33 2.45
II. ANALISIS LOG. NORMAL 2 PARAMETROS
ANALISIS CON DISTRIBUCION LOG - NORMAL DE 2 PARAMETROSAÑO P P ORDENADOS y = ln (x) F(x) f(x)1998 1.01 2.43 0.888 0.956 0.182
1999 0.93 1.50 0.405 0.777 0.582
2000 0.34 1.49 0.399 0.774 0.587
2001 0.8 1.01 0.010 0.497 0.778
2002 1.49 1.01 0.010 0.497 0.778
2003 1.5 0.99 -0.010 0.481 0.778
2004 0.99 0.93 -0.073 0.433 0.767
2005 1.01 0.83 -0.186 0.348 0.721
2006 0.83 0.80 -0.223 0.322 0.699
2007 2.43 0.34 -1.079 0.016 0.080
Page 27
media 1.13 0.01desv.stand 0.56 0.51
coef.asim 1.31 -0.56
Pexc. Tr x=LN I0.100 10 1.960.050 20 2.360.033 30 2.600.025 40 2.770.020 50 2.910.010 100 3.34
MEDIA 1.13 MEDIA 0.014DESV.EST. 0.56 DESV.EST. 0.512
N 10 C.ASIMETRIA -0.561
III. ANALISIS LOG NORMAL 3 PARÁMETROS
ANALISIS CON DISTRIBUCION LOG - NORMAL DE 3 PARAMETROSAÑO P P ORDENADOS y = ln (x-a) F(x) f(x)1998 1.01 2.43 3.444 0.989 1.5951999 0.93 1.50 3.414 0.746 17.2192000 0.34 1.49 3.414 0.740 17.4182001 0.80 1.01 3.398 0.416 20.9432002 1.49 1.01 3.398 0.416 20.9432003 1.50 0.99 3.397 0.402 20.7712004 0.99 0.93 3.395 0.361 20.1052005 1.01 0.83 3.392 0.296 18.5512006 0.83 0.80 3.391 0.277 17.9932007 2.43 0.34 3.375 0.077 7.719
Precipitación Ymedia 1.13 3.40
desv.stand 0.56 0.02coef.asimet. 1.31 1.26
a -28.8900
Page 28
AS: Asimetría
Si As < 0 Indica que existe presencia de la minoría de datos en la parte izquierda de la media, aunque en algunos casos no necesariamente indicará que la distribución sea asimétrica negativaSi As = 0 la distribución será simétricaSi As > 0 Indica que existe presencia de la minoría de datos en la parte derecha de la media, aunque en algunos casos no necesariamente indicará que la distribución sea asimétrica positiva
a= (Extremomayor∗extremomenor−(media≺.)2)(Extremomayor+extremomenor−(2∗media≺.))
Tr Pexc. 1-Pexc. z = f ( Pexc) y = ln (x - a) x10 0.100 0.900 1.28 3.43 1.8520 0.050 0.950 1.64 3.43 2.0630 0.033 0.967 1.83 3.44 2.1740 0.025 0.975 1.96 3.44 2.2450 0.020 0.980 2.05 3.44 2.30
100 0.010 0.990 2.33 3.45 2.46
IV. ANALISIS POR METODO GUMBEL
VALORES GUMBELMedia reducida Yn
n 0 1 2 3 4 5 6 7 8 910 0.4952 0.4996 0.5035 0.5070 0.5100 0.5128 0.5157 0.5181 0.5202 0.522020 0.5230 0.5252 0.5268 0.5283 0.5296 0.5309 0.5320 0.5332 0.5343 0.535330 0.5362 0.5371 0.5380 0.5388 0.5396 0.5402 0.5410 0.5418 0.5424 0.543040 0.5436 0.5442 0.5448 0.5453 0.5458 0.5463 0.5468 0.5473 0.5477 0.548150 0.5485 0.5489 0.5493 0.5497 0.5501 0.5504 0.5508 0.5511 0.5515 0.551860 0.5521 0.5524 0.5527 0.5530 0.5533 0.5535 0.5538 0.5540 0.5543 0.554570 0.5548 0.5550 0.5552 0.5555 0.5557 0.5559 0.5561 0.5563 0.5565 0.556780 0.5569 0.5570 0.5572 0.5574 0.5576 0.5578 0.5580 0.5581 0.5583 0.558590 0.5586 0.5587 0.5589 0.5591 0.5592 0.5593 0.5595 0.5596 0.5598 0.5599
100 0.5600
Page 29
Desviación típica reducida Sn
n 0 1 2 3 4 5 6 7 8 910 0.9496 0.9676 0.9833 0.9971 1.0095 1.0206 1.0316 1.0411 1.0493 1.056520 1.0628 1.0696 1.0754 1.0811 1.0864 1.0915 1.0961 1.1004 1.1047 1.108630 1.1124 1.1159 1.1193 1.2260 1.1255 1.1285 1.1313 1.1339 1.1363 1.388040 1.1413 1.1430 1.1458 1.1480 1.1499 1.1519 1.1538 1.1557 1.1574 1.159050 1.1607 1.1623 1.1638 1.1658 1.1667 1.1681 1.1696 1.1708 1.1721 1.173460 1.1747 1.1759 1.1770 1.1782 1.1793 1.1803 1.1814 1.1824 1.1834 1.184470 1.1854 1.1863 1.1873 1.1881 1.1890 1.1898 1.1906 1.1915 1.1923 1.193080 1.1938 1.1945 1.1953 1.1959 1.1967 1.1973 1.1980 1.1987 1.1994 1.200190 1.2007 1.2013 1.2020 1.2026 1.2032 1.2038 1.2044 1.2049 1.2055 1.2060
100 1.2065
ANALISIS CON DISTRIBUCION GUMBELAÑO P P ORDENADOS y = (x - u)/a Tr1998 1.01 2.43 2.96 19.901999 0.93 1.50 1.21 3.892000 0.34 1.49 1.20 3.832001 0.80 1.01 0.29 1.902002 1.49 1.01 0.29 1.902003 1.50 0.99 0.25 1.852004 0.99 0.93 0.14 1.722005 1.01 0.83 (0.05) 1.542006 0.83 0.80 (0.10) 1.492007 2.43 0.34 (0.97) 1.08
MEDIA 1.13 0.5230DES. ESTA 0.56 1.0628N 10Yn= 0.523Sn= 1.0628a= 0.53
u= 0.86 TreXxF
ye 11)(
Page 30
PRUEBAS DE BONDAD DE AJUSTE SMIRNOV-KOLMOGOROV
Probabilidad de excedencia F(x) Diferencia Delta DDATOS Empírica Normal LN2 LN3 Gumbel Normal LN2 LN3 Gumbel
1 0.0909 0.0108 0.0441 0.0113 0.0503 0.0801 0.0468 0.0796 0.04072 0.1818 0.2578 0.2225 0.2544 0.2570 0.0760 0.0407 0.0726 0.07513 0.2727 0.2636 0.2264 0.2601 0.2611 0.0092 0.0463 0.0126 0.01164 0.3636 0.5862 0.5032 0.5839 0.5263 0.2226 0.1396 0.2203 0.16275 0.4545 0.5862 0.5032 0.5839 0.5263 0.1317 0.0487 0.1294 0.07186 0.5455 0.6000 0.5188 0.5979 0.5397 0.0545 0.0267 0.0524 0.00587 0.6364 0.6404 0.5672 0.6390 0.5805 0.0041 0.0692 0.0026 0.05598 0.7273 0.7043 0.6521 0.7041 0.6496 0.0230 0.0751 0.0232 0.07779 0.8182 0.7224 0.6783 0.7225 0.6703 0.0958 0.1399 0.0956 0.1479
10 0.9091 0.9200 0.9835 0.9235 0.9285 0.0109 0.0744 0.0144 0.01940.22261 0.13988 0.22030 0.16267
VERDADERO VERDADERO VERDADERO VERDADERO
0.4301
Los datos de ajustan a la función Log Normal 3, siendo este dato 0,13988 menor a 0,4301
Page 31
INTENSIDAD DE PRECIPITACIONES
Con los datos ajustados hacemos:
Donde el tiempo de concentración es de 1,63 horas.
Page 33
Precipitación mínima corregida sobre la cuenca (P):
Donde: KA = Factor reductor
A=Área de la cuenca en km2 = 156.12 km2
KA = 0.85376943
Pd = Precipitación máxima diaria (mm)
ESTACIÓN ARIAL CUENCA AMOJÚ
T R PRECIP. MÁX LN3 P
10 1.956 1.6720 2.356 2.0130 2.596 2.2240 2.769 2.3650 2.906 2.48100 3.341 2.85
D. CALCULO DEL CAUDAL
Para esto se tendrá en cuenta la fórmula:
Q= CIA/360
C: coeficiente de escorrentía
I: Intensidad para un determinado tiempo de retorno de acuerdo a un tiempo de concentración.
A: Área de la cuenca en Has
Page 34
-Intensidad:
Donde:P = Precipitación máxima corregida (mm)
Tc= Tiempo de concentración (horas)
T R P I
10 1.67 0.36920 2.01 0.44430 2.22 0.49040 2.36 0.52150 2.48 0.547100 2.85 0.629
Page 35
Como la pendiente es 10 %
C= 0.6
Se tendrá en cuenta el Tc= 1.63 horas = 97.8 min lo cual representa un flujo lento.
Caudales Máximos:
Tr Intensidad mm/h Area C Q (m3/Seg)10 0.369 15612 0.6 9.60
20 0.444 15612 0.6 11.55
30 0.49 15612 0.6 12.75
40 0.521 15612 0.6 13.56
50 0.547 15612 0.6 14.23100 0.629 15612 0.6 16.37