Avenidas Maximas Belempata

ESTACION : QUILLABAMBA LAT :

PARAMETRO : PRECIPITACION MAXIMA 24 HORAS (mm) LONG :

ALT :

AÑO ENE. FEB. MAR. ABR. MAY. JUN. JUL AGO.

1996 22.0 21.0 18.0 15.4 21.0 2.5 6.1 16.7

1997 30.7 40.2 20.2 17.2 11.0 16.8 3.0 29.5

1998 39.4 24.5 38.4 19.2 4.2 4.8 1.0

1999 27.5 59.0 46.4 49.5 26.5 6.4 6.6

2000 57.9 44.7 20.0 15.5 7.6 15.8 0.6 14.2

2001 44.7 44.3 30.3 14.0 10.6 2.2 15.0 9.5

2002 21.8 54.5 47.1 10.3 9.2 5.5 12.9 23.1

2003 46.2 36.0 30.0 24.6 5.6 3.4 5.0 27.5

2004 21.2 31.0 21.8 18.4 6.6 38.1 14.5

2005 29.4 28.3 28.2 26.2 24.6 6.9 20.3 5.2

2006 49.0 23.4 43.6 39.2 4.2 8.2 4.5 14.8

2007 52.6 18.9 20.3 31.5 17.3 10.2 7.1

2008 53.1 22.8 15.6 34.0 7.9 0.6 10.8 19.2

2009 38.2 28.0 9.8 6.5 2.3 7.8 4.0

2010 18.4 83.8 36.8 26.8 7.6 9.4 9.0 13.4

2011 24.2 34.6 30.4 28.0 15.2 12.0 12.4 26.8

MAXIMO 57.90 83.80 47.10 49.50 26.50 16.80 38.10 29.50

PROMEDIO 35.87 37.83 29.69 24.08 12.34 7.10 10.61 15.67

MINIMO 18.40 18.90 15.60 9.80 4.20 0.60 0.60 1.00

1996 22 21 18 15.4 21 2.5 6.1 16.71997 30.7 40.2 20.2 17.2 11 16.8 3 29.51998 39.4 24.5 38.4 19.2 4.2 4.8 11999 27.5 59 46.4 49.5 26.5 6.4 6.62000 57.9 44.7 20 15.5 7.6 15.8 0.6 14.22001 44.7 44.3 30.3 14 10.6 2.2 15 9.52002 21.8 54.5 47.1 10.3 9.2 5.5 12.9 23.12003 46.2 36 30 24.6 5.6 3.4 5 27.52004 21.2 31 21.8 18.4 6.6 38.1 14.52005 29.4 28.3 28.2 26.2 24.6 6.9 20.3 5.22006 49 23.4 43.6 39.2 4.2 8.2 4.5 14.82007 52.6 18.9 20.3 31.5 17.3 10.2 7.12008 53.1 22.8 15.6 34 7.9 0.6 10.8 19.22009 26.2 38.2 28 9.8 6.5 2.3 7.8 4

2010 18.4 83.8 36.8 26.8 7.6 9.4 9 13.42011 24.2 34.6 30.4 28 15.2 12 12.4 26.8

12° 51' 21" DPTO : CUSCO

72° 41' 30" PROV : LA CONVENCION

990 m.s.n.m. DIST : SANTA ANA

SET. OCT. NOV. DIC. MAXIMA

17.8 17.5 17.0 20.5 22.00

20.0 32.4 32.0 20.9 40.20

63.8 24.8 12.0 34.3 63.80

13.7 26.5 20.5 25.9 59.00

17.0 25.3 13.1 20.0 57.90

11.2 25.3 33.2 16.5 44.70

8.0 25.3 25.2 57.1 57.10

22.3 20.4 22.3 27.0 46.20

14.0 19.2 28.9 20.0 38.10

15.7 18.5 8.1 40.6 40.60

5.9 18.8 25.9 26.9 49.00

5.5 38.0 32.3 19.7 52.60

18.5 24.2 16.2 27.8 53.10

5.0 33.2 54.0 25.2 54.00

22.2 54.6 25.4 26.6 83.80

7.8 49.0 34.0 31.0 49.00

63.80 54.60 54.00 57.10 83.80

16.78 28.31 25.01 27.50 50.69

5.00 17.50 8.10 16.50 22.00

17.8 17.5 17 20.520 32.4 32 20.9

63.8 24.8 12 34.313.7 26.5 20.5 25.9

17 25.3 13.1 20 0.0 0.0 0.011.2 33.2 16.5 0.0 0.0 0.0

8 25.3 25.2 57.1 0.0 0.0 0.022.3 20.4 22.3 27 0.0 0.0 0.0

14 19.2 28.9 20 0.0 0.0 0.015.7 18.5 8.1 40.6 0.0 0.0 0.0

5.9 18.8 25.9 26.9 0.0 0.0 0.05.5 38 32.3 19.7 0.0 0.0 0.0

18.5 24.2 16.2 27.8 0.0 0.0 0.05 33.2 54 25.2 -26.2 0.0 0.0

22.2 54.6 25.4 26.6 0.0 0.0 0.07.8 49 34 31 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 25.30.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.00.0 0.00.0 0.00.0 0.00.0 0.00.0 0.00.0 0.00.0 0.00.0 0.00.0 0.0

0.0 0.00.0 0.0

Precipitación Máxima

Nº Año Mes Nº

1 1996 Enero 22.0 1

2 1997 Febrero 40.2 2

3 1998 Setiembre 63.8 3

4 1999 Febrero 59.0 4

5 2000 Enero 57.9 5

6 2001 Enero 44.7 6

7 2002 Diciembre 57.1 7

8 2003 Enero 46.2 8

9 2004 Julio 38.1 9

10 2005 Diciembre 40.6 10

11 2006 Enero 49.0 11

12 2007 Enero 52.6 12

13 2008 Enero 53.1 13

14 2009 Noviembre 54.0 14

15 2010 Febrero 83.8 15

16 2011 Octubre 49.0 16

Pp max. 24 horas (mm)

Dato excluido

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

Año

Prec

ipit

acio

n (m

m)

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

Año

Prec

ipit

acio

n (m

m)

Año

1996 24.9

1997 45.4

1998 72.1

1999 66.7

2000 65.4

2001 50.5

2002 64.5

2003 52.2

2004 43.1

2005 45.9

2006 55.4

2007 59.4

2008 60.0

2009 61.0

2010 94.7

2011 55.4

Pp max. 24 horas corregida

(mm)

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

Año

Prec

ipit

acio

n (m

m)

J5

Datos de ingreso a smada

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

Año

Prec

ipit

acio

n (m

m)

Precipitación Máxima

Nº Año

Quillabamba

Quillabamba Quillabamba LS LI

1 1996 22.0 1.342 94.532 25.289

2 1997 40.2 1.604 94.532 25.289

3 1998 63.8 1.805 94.532 25.289

4 1999 59.0 1.771 94.532 25.289

5 2000 57.9 1.763 94.532 25.289

6 2001 44.7 1.650 94.532 25.289

7 2002 57.1 1.757 94.532 25.289

8 2003 46.2 1.665 94.532 25.289

9 2004 38.1 1.581 94.532 25.289

10 2005 40.6 1.609 94.532 25.289

11 2006 49.0 1.690 94.532 25.289

12 2007 52.6 1.721 94.532 25.289

13 2008 53.1 1.725 94.532 25.289

14 2009 54.0 1.732 94.532 25.289

15 2010 83.8 1.923 94.532 25.289

16 2011 49.0 1.690 94.532 25.289

Pp max. 24 horas (mm)

Log Pp max. 24 horas (mm)

Quillabamba

Media 1.689

Desviacion Estandar 0.1256

n 16

Kn 2.279

1.98

1.40

Limite Superior 94.53

Limite Inferior 25.29

YL (superior)

YL (inferior)

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

Año

Prec

ipit

acio

n (m

m)

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

Año

Prec

ipit

acio

n (m

m)

PRECIPITACION MAXIMA EN 24 HORAS (mm)ESTACION QUILLABAMBA

Distribution Analysis: Normal Distribution First Moment (mean) = 55.7064 Second Moment = 5.261e01 Skew = -3.007e-01

Numero

1 0.0833 43.10 45.672 0.1667 45.90 48.693 0.25 50.50 50.824 0.3333 52.20 52.595 0.4167 55.37 54.186 0.5 55.40 55.717 0.5833 59.40 57.238 0.6667 60.00 58.839 0.75 61.00 60.60

10 0.8333 64.50 62.7211 0.9167 65.40 65.74

Predicciones

0.98 50 70.61 4.9960.96 25 68.41 4.4100.95 20 67.64 4.211

0.9 10 65.00 3.5550.8 5 61.81 2.858

Weibull Probabilidad

Valor Actual

Valor Previsto

Prob. de no Excedencia

Perido de Retorno

Valor Calculado

Desviación Standard

Fuente: Resultados obtenidos en base al Software SMADA ver. 6.3

Actual Data

Distribution

Normal Distribution

Weibull Probability

Value

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0

PRECIPITACION MAXIMA EN 24 HORAS (mm)ESTACION QUILLABAMBA Distribution Analysis: Normal Distribution

Distribution Analysis: Normal Distribution ------------------Summary of Data ----------------------- First Moment (mean) = 55.7064 Second Moment = 5.261e01 Skew = -3.007e-01--------------------------------------------------------- Point Weibull Actual Predicted Standard

3.7328 Number Probability Value Value Deviation3.0427 ---------------------------------------------------------2.6375 1 0.0833 43.1000 45.6735 3.73282.3808 2 0.1667 45.9000 48.6898 3.04272.2346 3 0.2500 50.5000 50.8163 2.63752.1869 4 0.3333 52.2000 52.5853 2.38082.2346 5 0.4167 55.3700 54.1828 2.23462.3808 6 0.5000 55.4000 55.7064 2.18692.6375 7 0.5833 59.4000 57.2299 2.23463.0427 8 0.6667 60.0000 58.8274 2.38083.7328 9 0.7500 61.0000 60.5964 2.6375

10 0.8333 64.5000 62.7229 3.0427 11 0.9167 65.4000 65.7393 3.7328-------------------------------------------------------------------------- Predictions -------------------------- Exceedence Return Calculated Standard Probability Period Value Deviation--------------------------------------------------------- 0.9800 50.0 70.6059 4.9964 0.9600 25.0 68.4073 4.4099 0.9500 20.0 67.6395 4.2105 0.9000 10.0 65.0031 3.5552 0.8000 5.0 61.8097 2.8581---------------------------------------------------------


Actual Data

Distribution

Normal Distribution

Weibull Probability

Value

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0

Distribution Analysis: Normal Distribution------------------Summary of Data -----------------------

--------------------------------------------------------- Point Weibull Actual Predicted Standard Number Probability Value Value Deviation--------------------------------------------------------- 1 0.0833 43.1000 45.6735 3.7328 2 0.1667 45.9000 48.6898 3.0427 3 0.2500 50.5000 50.8163 2.6375 4 0.3333 52.2000 52.5853 2.3808 5 0.4167 55.3700 54.1828 2.2346 6 0.5000 55.4000 55.7064 2.1869 7 0.5833 59.4000 57.2299 2.2346 8 0.6667 60.0000 58.8274 2.3808 9 0.7500 61.0000 60.5964 2.6375 10 0.8333 64.5000 62.7229 3.0427 11 0.9167 65.4000 65.7393 3.7328-------------------------------------------------------------------------- Predictions --------------------------

---------------------------------------------------------

---------------------------------------------------------


Distribution Analysis: 2 Parameter Log Normal First Moment (mean) = 55.7064 Second Moment = 5.261e01 Skew = -3.007e-01

Numero

1 0.0833 43.10 46.172 0.1667 45.90 48.733 0.25 50.50 50.624 0.3333 52.20 52.245 0.4167 55.37 53.766 0.5 55.40 55.247 0.5833 59.40 56.778 0.6667 60.00 58.419 0.75 61.00 60.29

10 0.8333 64.50 62.6211 0.9167 65.40 66.09

Predicciones

0.98 50 72.10 4.7880.96 25 69.32 4.2300.95 20 68.37 4.045

0.9 10 65.23 3.4550.8 5 61.61 2.848



Valor Actual

Valor Previsto


Perido de Retorno

Valor Calculado


Actual Data

Distribution

2 Parameter Log Normal

Weibull Probability

Value

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0

PRECIPITACION MAXIMA EN 24 HORAS (mm)ESTACION QUILLABAMBA Distribution Analysis: 2 Parameter Log Normal

Distribution Analysis: 2 Parameter Log Normal ------------------Summary of Data ----------------------- First Moment (mean) = 55.7064 Second Moment = 5.261e01 Skew = -3.007e-01--------------------------------------------------------- Point Weibull Actual Predicted Standard




Actual Data

Distribution

2 Parameter Log Normal

Weibull Probability

Value

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0

Distribution Analysis: 2 Parameter Log Normal------------------Summary of Data -----------------------


---------------------------------------------------------

---------------------------------------------------------


Distribution Analysis: Pearson Type III First Moment (mean) = 55.7064 Second Moment = 5.261e01 Skew = -3.007e-01

Numero

1 0.0833 43.10 45.092 0.1667 45.90 48.913 0.25 50.50 51.414 0.3333 52.20 53.375 0.4167 55.37 55.046 0.5 55.40 56.567 0.5833 59.40 58.008 0.6667 60.00 59.449 0.75 61.00 60.93

10 0.8333 64.50 62.6111 0.9167 65.40 64.77

Predicciones

0.98 50 67.73 3.7550.96 25 66.47 2.9160.95 20 66.00 2.680

0.9 10 64.26 2.1410.8 5 61.91 2.041



Valor Actual

Valor Previsto


Perido de Retorno

Valor Calculado


Actual Data

Distribution

Pearson Type III

Weibull Probability

Value

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0


Distribution Analysis: Pearson Type III

Distribution Analysis: Pearson Type III------------------Summary of Data ----------------------- First Moment (mean) = 55.7064 Second Moment = 5.261e01

4.2901 Skew = -3.007e-013.2226 ---------------------------------------------------------2.8325 Point Weibull Actual Predicted Standard2.6518 Number Probability Value Value Deviation2.542 ---------------------------------------------------------

2.4489 1 0.0833 43.1000 45.0865 4.29012.3486 2 0.1667 45.9000 48.9122 3.22262.2318 3 0.2500 50.5000 51.4100 2.83252.1049 4 0.3333 52.2000 53.3668 2.65182.0205 5 0.4167 55.3700 55.0419 2.54202.2465 6 0.5000 55.4000 56.5603 2.4489

7 0.5833 59.4000 58.0033 2.3486 8 0.6667 60.0000 59.4376 2.2318 9 0.7500 61.0000 60.9343 2.1049 10 0.8333 64.5000 62.6103 2.0205 11 0.9167 65.4000 64.7666 2.2465-------------------------------------------------------------------------- Predictions -------------------------- Exceedence Return Calculated Standard Probability Period Value Deviation--------------------------------------------------------- 0.9800 50.0 67.7336 3.7547 0.9600 25.0 66.4685 2.9162 0.9500 20.0 65.9978 2.6799 0.9000 10.0 64.2635 2.1409 0.8000 5.0 61.9067 2.0412---------------------------------------------------------


Actual Data

Distribution

Pearson Type III

Weibull Probability

Value

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0

------------------Summary of Data -----------------------


---------------------------------------------------------

---------------------------------------------------------


Distribution Analysis: Log Pearson Type III First Moment (mean) = 55.7064 Second Moment = 5.261e01 Skew = -3.007e-01

Numero

1 0.0833 43.10 44.392 0.1667 45.90 48.233 0.25 50.50 50.854 0.3333 52.20 52.975 0.4167 55.37 54.826 0.5 55.40 56.537 0.5833 59.40 58.178 0.6667 60.00 59.829 0.75 61.00 61.55

10 0.8333 64.50 63.5011 0.9167 65.40 66.00

Predicciones

0.98 50 69.36 5.6720.96 25 67.94 4.1690.95 20 67.41 3.728

0.9 10 65.42 2.6560.8 5 62.68 2.389



Valor Actual

Valor Previsto


Perido de Retorno

Valor Calculado


Actual Data

Distribution

Log Pearson Type III

Weibull Probability

Value

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0

PRECIPITACION MAXIMA EN 24 HORAS (mm)ESTACION QUILLABAMBA Distribution Analysis: Log Pearson Type III

Distribution Analysis: Log Pearson Type III ------------------Summary of Data ----------------------- First Moment (mean) = 55.7064 Second Moment = 5.261e01 Skew = -3.007e-01--------------------------------------------------------- Point Weibull Actual Predicted Standard




Actual Data

Distribution

Log Pearson Type III

Weibull Probability

Value

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0

Distribution Analysis: Log Pearson Type III------------------Summary of Data -----------------------


---------------------------------------------------------

---------------------------------------------------------


Distribution Analysis: Gumbel Extremal Type I First Moment (mean) = 55.7064 Second Moment = 5.261e01 Skew = -3.007e-01

Numero

1 0.0833 43.10 44.782 0.1667 45.90 47.323 0.25 50.50 49.314 0.3333 52.20 51.115 0.4167 55.37 52.876 0.5 55.40 54.687 0.5833 59.40 56.628 0.6667 60.00 58.839 0.75 61.00 61.49

10 0.8333 64.50 65.0211 0.9167 65.40 70.75

Predicciones

0.98 50 82.07 9.3680.96 25 76.62 7.7620.95 20 74.85 7.244

0.9 10 69.27 5.6300.8 5 63.46 4.008



Valor Actual

Valor Previsto


Perido de Retorno

Valor Calculado


Actual Data

Distribution

Gumbel Extremal Type I

Weibull Probability

Value

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0

PRECIPITACION MAXIMA EN 24 HORAS (mm)ESTACION QUILLABAMBA Distribution Analysis: Gumbel Extremal Type I

Distribution Analysis: Gumbel Extremal Type I ------------------Summary of Data ----------------------- First Moment (mean) = 55.7064 Second Moment = 5.261e01 Skew = -3.007e-01--------------------------------------------------------- Point Weibull Actual Predicted Standard

2.7242 Number Probability Value Value Deviation2.2084 ---------------------------------------------------------1.923 1 0.0833 43.1000 44.7837 2.7242

1.8027 2 0.1667 45.9000 47.3174 2.20841.839 3 0.2500 50.5000 49.3051 1.9230

2.0259 4 0.3333 52.2000 51.1070 1.80272.3555 5 0.4167 55.3700 52.8660 1.83902.8312 6 0.5000 55.4000 54.6752 2.02593.488 7 0.5833 59.4000 56.6239 2.3555

4.4351 8 0.6667 60.0000 58.8294 2.83126.0555 9 0.7500 61.0000 61.4881 3.4880



Actual Data

Distribution

Gumbel Extremal Type I

Weibull Probability

Value

0

20

40

60

80

0.0 0.2 0.4 0.6 0.8 1.0

Distribution Analysis: Gumbel Extremal Type I------------------Summary of Data -----------------------


---------------------------------------------------------

---------------------------------------------------------

PRUEBA DE KOLMOGOROV-SMIRNOVDistribución Normal.- Precipitación Máxima en 24 horas

Estación Quillabamba

m P(mm) z Abs(Fo-Fz)

1 43.10 -1.738 0.041 0.083 0.042

2 45.90 -1.352 0.088 0.167 0.078

3 50.50 -0.718 0.236 0.250 0.014

4 52.20 -0.483 0.314 0.333 0.019

5 55.37 -0.046 0.482 0.417 0.065

6 55.40 -0.042 0.483 0.500 0.017

7 59.40 0.509 0.695 0.583 0.111

8 60.00 0.592 0.723 0.667 0.056

9 61.00 0.730 0.767 0.750 0.017

10 64.50 1.212 0.887 0.833 0.054

11 65.40 1.336 0.909 0.917 0.007

Media 55.706 0.111Desv. Est(S) 7.253

0.391

n= 11

α=0.05

Normal Gumbel

50 70.61 72.10 67.73 69.36 82.07

25 68.41 69.32 66.47 67.94 76.62

20 67.64 68.37 66.00 67.41 74.85

10 65.00 65.23 64.26 65.42 69.27

5 61.81 61.61 61.91 62.68 63.46

Maximo Registrado: 65.40 mm N° Datos: 11

Probabilidad teórica

F(z)

Fo probabilidad

empírica (m/n+1)

Dmax

d crítico =

T (años)

Log Normal

Pearson Tipo III

Log Pearson Tipo III

PRUEBA DE KOLMOGOROV-SMIRNOVDistribución Log Normal.- Precipitación Máxima en 24 horas


m P (mm) LnP z

1 43.10 3.764 -1.844 0.033 0.083

2 45.90 3.826 -1.377 0.084 0.167

3 50.50 3.922 -0.668 0.252 0.250

4 52.20 3.955 -0.423 0.336 0.333

5 55.37 4.014 0.015 0.506 0.417

6 55.40 4.015 0.019 0.508 0.500

7 59.40 4.084 0.536 0.704 0.583

8 60.00 4.094 0.611 0.729 0.667

9 61.00 4.111 0.733 0.768 0.750

10 64.50 4.167 1.147 0.874 0.833

11 65.40 4.181 1.250 0.894 0.917

Media 4.012Desv. Est(S) 0.135

0.391

n= 11

α=0.05

Probabilidad teórica

F(z)

Fo probabilidad

empírica (m/n+1)

Dmax

d crítico =

PRUEBA DE KOLMOGOROV-SMIRNOV PRUEBA DE KOLMOGOROV-SMIRNOVDistribución Log Normal.- Precipitación Máxima en 24 horas Distribución Pearson Tipo III- Precipitación Máxima en 24 horas

Estación Quillabamba Estación Quillabamba

Abs(Fo-Fz) N X 2Y

0.051 1 43.10 15.882 31.763 48.963

0.082 2 45.90 17.792 35.584 48.963

0.002 3 50.50 20.930 41.859 48.963

0.003 4 52.20 22.089 44.179 48.963

0.089 5 55.37 24.252 48.504 48.963

0.008 6 55.40 24.272 48.545 48.963

0.121 7 59.40 27.001 54.002 48.963

0.063 8 60.00 27.410 54.820 48.963

0.018 9 61.00 28.092 56.185 48.963

0.041 10 64.50 30.480 60.960 48.963

0.022 11 65.40 31.094 62.188 48.963

0.121 Media 55.71Desv.Est(S) 7.25

sesgo(γ) -0.4042 0.391

24.4813 n= 11

1.4659 α=0.05

19.8186

Y=(x-δ1)/α1 2β1

d crítico =

β1=(2/γ)2

α1=S/√β1

δ1=X-α1β1

PRUEBA DE KOLMOGOROV-SMIRNOV PRUEBA DE KOLMOGOROV-SMIRNOVDistribución Pearson Tipo III- Precipitación Máxima en 24 horas Distribución Log Pearson Tipo III- Precipitación Máxima en 24 horas

Estación Quillabamba Estación Quillabamba

χ2 Fx Fo Abs(Fo-Fx) N X LnX

0.966 0.034 0.083 0.049 1 43.10 3.7635

0.908 0.092 0.167 0.074 2 45.90 3.8265

0.721 0.279 0.250 0.029 3 50.50 3.9220

0.630 0.370 0.333 0.037 4 52.20 3.9551

0.453 0.547 0.417 0.131 5 55.37 4.0140

0.451 0.549 0.500 0.049 6 55.40 4.0146

0.256 0.744 0.583 0.161 7 59.40 4.0843

0.232 0.768 0.667 0.102 8 60.00 4.0943

0.195 0.805 0.750 0.055 9 61.00 4.1109

0.099 0.901 0.833 0.067 10 64.50 4.1667

0.082 0.918 0.917 0.001 11 65.40 4.1805

0.161 Media 4.01Desv.Est(S) 0.1348

sesgo(γ) -0.6127

10.654

0.0413

3.5722

Dmax

β1=(2/γ)2

α1=S/√β1

δ1=X-α1β1

PRUEBA DE KOLMOGOROV-SMIRNOVDistribución Log Pearson Tipo III- Precipitación Máxima en 24 horas


2Y χ2 Fx Fo Abs(Fo-Fx)

4.6349 9.2698 21.3073 0.9869 0.0131 0.0833 0.0703

6.1593 12.3187 21.3073 0.9306 0.0694 0.1667 0.0973

8.4725 16.9450 21.3073 0.7144 0.2856 0.2500 0.0356

9.2744 18.5487 21.3073 0.6141 0.3859 0.3333 0.0526

10.7022 21.4045 21.3073 0.4345 0.5655 0.4167 0.1488

10.7153 21.4307 21.3073 0.4329 0.5671 0.5000 0.0671

12.4038 24.8076 21.3073 0.2556 0.7444 0.5833 0.1611

12.6472 25.2944 21.3073 0.2346 0.7654 0.6667 0.0987

13.0475 26.0951 21.3073 0.2028 0.7972 0.7500 0.0472

14.3988 28.7975 21.3073 0.1189 0.8811 0.8333 0.0477

14.7344 29.4688 21.3073 0.1032 0.8968 0.9167 0.0199

0.161

0.391

n= 11

α=0.05

Y=(x-δ1)/α1 2β1

Dmax

d crítico =

PRUEBA DE KOLMOGOROV-SMIRNOVDistribución Gumbel.- Precipitación Máxima en 24 horas


N X Fx Fo Abs(Fo-Fx)

1 43.10 0.0418 0.0833 0.0415

2 45.90 0.1108 0.1667 0.0559

3 50.50 0.2997 0.2500 0.0497

4 52.20 0.3812 0.3333 0.0478

5 55.37 0.5289 0.4167 0.1123

6 55.40 0.5303 0.5000 0.0303

7 59.40 0.6868 0.5833 0.1034

8 60.00 0.7065 0.6667 0.0399

9 61.00 0.7373 0.7500 0.0127

10 64.50 0.8247 0.8333 0.0086

11 65.40 0.8426 0.9167 0.0741

Media 55.71 0.112Desv.Est(S) 7.25

uy 0.4952 0.391

σy 0.9496 n= 11

Alfa 0.13092 α=0.05

Beta 51.92395exp(1) 2.71828

TABLA DE GUMBEL

n my sy

10 0.4952 0.9496

15 0.5128 1.0206

20 0.5236 1.0628

25 0.5309 1.0914

Dmax

d crítico =

30 0.5362 1.1124

35 0.5403 1.128537 0.54162 1.1336240 0.5436 1.141345 0.5463 1.151850 0.5485 1.160755 0.5504 1.168260 0.5521 1.174765 0.5535 1.180370 0.5548 1.185475 0.5559 1.189880 0.5569 1.193885 0.5578 1.197490 0.5586 1.200795 0.5593 1.2037

100 0.56 1.2065

formula de bellCuadro N°04: Lluvias máximas (mm).- Estación Quillabamba

T (años)Duración en minutos

5 10 15 20 30 60 120

50 70.61 7.35 11.01 13.46 15.35 18.27 23.98 30.79

25 68.41 6.56 9.81 12.00 13.69 16.28 21.38 27.44

20 67.64 6.30 9.43 11.53 13.15 15.65 20.54 26.37

10 65.00 5.50 8.23 10.07 11.48 13.66 17.83 23.03

5 61.81 4.70 7.04 8.61 9.82 11.68 15.34 19.69

Fuente: Elaboración propia

Cuadro N°05: Intensidades máximas (mm/hora).- Estación Quillabamba

T (años)Duración en minutos

5 10 15 20 30 60 120

50 70.61 88.20 66.00 53.80 46.10 36.50 24.00 15.40

25 68.41 78.70 58.90 48.00 41.10 32.60 21.40 13.70

20 67.64 75.60 56.60 46.10 39.50 31.30 20.50 13.20

10 65.00 66.00 49.40 40.30 34.50 27.30 17.80 11.50

5 61.81 56.40 42.20 34.40 29.50 23.40 15.30 9.80

Fuente: Elaboración propia

Resultado del Análisis de Regresión:

0.9967K= 110.63

0.9934m= 0.195

R^2 ajustado 0.9930 n= 0.557

Error típico 0.0213

Observaciones 35 Donde:

Log (K) 2.0439 I= mm/h

m 0.1951 T= años

n -0.5568 t= minutos

Resumen

Resumen

P.Max 24 horas

P.Max 24 horas

Coeficiente de correlación múltiple

Coeficiente de determinación R^2 I = 110.63 T 0.195

t0.557

Estadísticas de la regresiónCoeficiente 0.9967042Coeficiente 0.9934194R^2 ajusta 0.9930081Error típico 0.0212771Observacio 35

ANÁLISIS DE VARIANZAGrados de libertadSuma de cuadradosPromedio de los cuadradosF Valor crítico de F

Regresión 2 2.186945 1.093473 2415.373 1.24E-35Residuos 32 0.014487 0.000453Total 34 2.201432

CoeficientesError típicoEstadístico tProbabilidadInferior 95%Superior 95%Inferior 95.0%Superior 95.0%Intercepció 2.0438743 0.017442 117.1795 1.02E-43 2.008346 2.079403 2.008346 2.079403Log (T) 0.1950899 0.010492 18.5943 1.03E-18 0.173719 0.216461 0.173719 0.216461Log (t) -0.5568426 0.008315 -66.97012 5.65E-36 -0.573779 -0.539906 -0.573779 -0.539906

3.31

198.6

Y X1 X2

Log (I) Log (T) Log (t)

1.945469 1.698970 0.698970

1.895975 1.397940 0.698970

1.878522 1.301030 0.698970

1.819544 1.000000 0.698970

1.751279 0.698970 0.698970

1.819544 1.698970 1.000000

1.770115 1.397940 1.000000

1.752816 1.301030 1.000000

1.693727 1.000000 1.000000

1.625312 0.698970 1.000000

1.730782 1.698970 1.176091

1.681241 1.397940 1.176091

1.663701 1.301030 1.176091

1.605305 1.000000 1.176091

1.536558 0.698970 1.176091

1.663701 1.698970 1.301030

1.613842 1.397940 1.301030

1.596597 1.301030 1.301030

1.537819 1.000000 1.301030

1.469822 0.698970 1.301030

1.562293 1.698970 1.477121

1.513218 1.397940 1.477121

1.495544 1.301030 1.477121

1.436163 1.000000 1.477121

1.369216 0.698970 1.477121

1.380211 1.698970 1.778151

1.330414 1.397940 1.778151

1.311754 1.301030 1.778151

1.250420 1.000000 1.778151

1.184691 0.698970 1.778151

1.187521 1.698970 2.079181

1.136721 1.397940 2.079181

1.120574 1.301030 2.079181

1.060698 1.000000 2.079181

0.991226 0.698970 2.079181

Superior 95.0%

Intensidades máximas.- Estación Quillabamba (mm/h)

I= K=

m=n=

Período de Retorno (T) en años

10 20 25

2 117.85 134.92 140.92

4 80.11 91.71 95.80

6 63.92 73.18 76.43

8 54.46 62.35 65.12

10 48.10 55.06 57.51

12 43.45 49.75 51.96

14 39.88 45.65 47.69

16 37.02 42.38 44.27

18 34.67 39.69 41.46

20 32.70 37.43 39.10

22 31.01 35.50 37.07

24 29.54 33.82 35.32

K T m

tn

Duración (t) (minutos)

2 4 6 8 10 12 14 16 18 20 22 240

20

40

60

80

100

120

140

160

Estacion Quillabamba

Tr = 10 Años

Tr = 20 Años

Tr = 25 Años

Tr = 50 Años

Duración (min)

Inte

nsid

ad (m

m/h

)

Intensidades máximas.- Estación Quillabamba (mm/h)

I= K=

m=n=T=

I (mm/h) P (mm)

2 161.32 5.38 5.38

4 109.67 7.31 1.93

6 87.50 8.75 1.44

8 74.55 9.94 1.19

10 65.84 10.97 1.03

12 59.48 11.90 0.92

14 54.59 12.74 0.84

16 50.68 13.51 0.78

18 47.46 14.24 0.72

20 44.76 14.92 0.68

22 42.44 15.56 0.64

24 40.44 16.18 0.61

26 38.67 16.76 0.58

28 37.11 17.32 0.56

30 35.71 17.86 0.54

K T m

tn

(t) (min)

∆ P

2 4 6 8 10 12 14 16 18 20 22 24 26 28 300.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00 Hietograma Estacion Quillabamba

T=50 años

T=25 años

T=20 años

T=10 años

Tiempo (min)

Prec

ipita

cion

(mm

)

Cuadro Nº12:Caudales máximos Método Racional K= 110.630m= 0.195n= 0.557T= 20 añosT= 25 añosT= 50 años

Nº Nombre C

horas minutos T=20 T=25 T=50 T=20 T=25 T=50

1 Rio Sicrimayo 0.30 1.95 1.70 0.3676 0.473 28.36 30.81 32.19 36.85 5.01 5.23 5.99

2 Rio Picchu Alto 0.35 1.97 1.73 0.3468 0.486 29.17 30.34 31.69 36.27 5.81 6.07 6.95

3 Rio Ucurimayoc 0.40 4.50 3.34 0.4311 0.827 49.64 22.56 23.57 26.98 11.28 11.78 13.49

K C1 30 10 5 5 50 0.502 30 10 5 5 50 0.503 30 10 5 5 50 0.50

Area(km2)

Longitud del cauce L

(Km)

Pendiente del cauce S

(m/m)

Tiempo de Concentración Tc

Intensidadmm/hora

Caudal Máximo(m3/s)

K1 K2 K3 K4

K=K1+K2+K3+K4 C100 0.8075 0.6550 0.5030 0.3525 0.20

Fuente: Manual para el diseño de caminos no pavimentados de bajo volumen de tránsito, MTC.

Coeficiente de EscorrentíaCondiciónK1=40 K1=30 K1=20 K1=10

Muy accidentado pendiente superior al 30%

Accidentado pendiente entre 10% y 30%

Ondulado pendiente entre 5% y 10%

Llano pendiente inferior al 5%

K2=20 K2=15 K2=10 K2=5

Muy impermeable Roca sana

Bastante impermeable Arcilla

Permeable Muy permeable

K3=20 K3=15 K3=10 K3=5

Sin vegetaciónPoca menos del 10% de la superficie

Bastante hasta el 50% de la superficie

Mucha hasta el 90% de la superficie

K4=20 K4=15 K4=10 K4=5

Ninguna Poca Bastante MuchaFuente: Manual para el diseño de caminos no pavimentados de bajo volumen de tránsito, MTC.

ValoresValores para la determinación del Coeficiente de Escorrentía

1. Relieve del terreno

2. Permeabilidad del suelo

3. Vegetación

4. Capacidad de retención

6.3

CIAQ

n

m

t

KTI

K=K1+K2+K3+K4 C100 0.8075 0.6550 0.5030 0.3525 0.20


Coeficiente de EscorrentíaCondiciónK1=40 K1=30 K1=20 K1=10

Muy accidentado pendiente superior al 30%

Accidentado pendiente entre 10% y 30%

Ondulado pendiente entre 5% y 10%

Llano pendiente inferior al 5%

K2=20 K2=15 K2=10 K2=5

Muy impermeable Roca sana

Bastante impermeable Arcilla

Permeable Muy permeable

K3=20 K3=15 K3=10 K3=5

Sin vegetaciónPoca menos del 10% de la superficie

Bastante hasta el 50% de la superficie

Mucha hasta el 90% de la superficie

K4=20 K4=15 K4=10 K4=5

Ninguna Poca Bastante MuchaFuente: Manual para el diseño de caminos no pavimentados de bajo volumen de tránsito, MTC.

ValoresValores para la determinación del Coeficiente de Escorrentía

1. Relieve del terreno

2. Permeabilidad del suelo

3. Vegetación

4. Capacidad de retención

K=K1+K2+K3+K4 C100 0.8075 0.6550 0.5030 0.3525 0.20


Coeficiente de Escorrentía

K=K1+K2+K3+K4 C100 0.8075 0.6550 0.5030 0.3525 0.20


Coeficiente de Escorrentía

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