Precipitaciones Estacion Sallique

PRECIPITACIONES HIDROLOGIA

DATOS DE PRECIPITACIONES

INFORMACION PLUVIOMETRICA

ESTACION: SALLIQUE

CATEGORIA: "CO"

AÑO ENERO FEBRERO MARZO ABRIL MAYO JUNIO JULIO AGOSTO

SEPTIEMBRE OCTUBRE NOVIEMBRE

DICIEMBREPmax anual

(mm)2002 19.6 26.0 29.4 41.4 15.8 4.2 3.8 0.0 4.6 22.0 19.7 10.0 41.42003 10.8 17.8 23.0 12.6 11.2 10.6 5.4 0.0 9.4 3.8 9.6 10.5 23.02004 7.0 4.5 17.4 17.8 12.2 5.6 3.2 0.0 3.8 23.3 17.2 18.2 23.32005 5.0 15.6 36.0 20.2 3.4 2.2 0.0 0.0 14.0 11.0 8.1 27.6 36.02006 14.5 42.9 36.2 51.2 6.0 17.8 6.4 1.4 5.5 13.8 20.0 33.6 51.22007 28.2 23.8 53.0 19.0 8.8 15.8 1.2 5.8 2.5 24.8 18.4 13.0 53.02008 14.4 36.2 30.4 22.4 5.2 9.4 10.4 2.8 2.3 30.8 23.4 0.0 36.22009 24.4 16.0 48.7 16.0 11.2 3.0 0.6 4.6 10.5 17.4 14.8 18.6 48.72010 15.6 27.0 36.0 15.4 6.9 5.0 6.2 9.5 7.4 19.4 9.0 20.4 36.02011 11.7 16.8 12.5 36.8 4.5 16.2 6.4 1.8 11.4 8.8 23.8 10.4 36.82012 25.7 25.7 14.0 13.9 7.0 2.8 0.3 3.0 0.4 31.6 23.5 12.0 31.62013 9.9 6.6 13.2 2.8 13.8 2.5 20.8 2.2 2.0 20.0 0.2 6.8 20.8

P.max. Mes 28.2 42.9 53.0 51.2 15.8 17.8 20.8 9.5 14.0 31.6 23.8 33.6 53.0

LAT.: 05°39'32''LONG.: 79°18'45''ALT.: 1789 m.s.n.m.

DPTO: CAJAMARCAPROV: JAENDIST.: SALLIQUE


2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 20140.0

10.0

20.0

30.0

40.0

50.0

60.0

Series2

AÑOS DE LA ESTACION SALLIQUE

Pmax

.en

24h

Anu

ales

(mm

)


PRUEBA DE SMIRNOV-KOLMOGOROV

Datos Conocidos:

N=12

x=36.50mm

s=10.82mm

Obtención del Estadístico S-K y Verificación de la Confiabilidad

Para la distribución normal con N = 12 datos de Precipitación máxima 24h de la estación Tinajones, procedemos a Calcular el estadístico S-k, con un nivel de significancia de 0.05.

N α=0 .05

10 0.41

12 S-K

15 0.34

S−K=12−1510−15

(0.41−0.34 )+0.34

S−K=0.382


ANALISIS DE CONFIABILIDAD: PRUEBA DE BONDAD DE AJUSTE ''DISTRIBUCION NORMAL''

AÑO mPmax anual

(mm)Pmax anual

(mm)P(x)=m/N+1 ( X−X )2 z F(z) |F(z)-P(x)|

2002 1 41.4 20.8 0.07692 246.49000 -1.45042 0.07347 0.003452003 2 23.0 23.0 0.15385 182.25000 -1.24717 0.10617 0.047682004 3 23.3 23.3 0.23077 174.24000 -1.21946 0.11133 0.119432005 4 36.0 31.6 0.30769 24.01000 -0.45268 0.32539 0.017702006 5 51.2 36.0 0.38462 0.25000 -0.04619 0.48158 0.096962007 6 53.0 36.0 0.46154 0.25000 -0.04619 0.48158 0.020042008 7 36.2 36.2 0.53846 0.09000 -0.02771 0.48894 0.049522009 8 48.7 36.8 0.61538 0.09000 0.02771 0.51106 0.104332010 9 36.0 41.4 0.69231 24.01000 0.45268 0.67461 0.017702011 10 36.8 48.7 0.76923 148.84000 1.12708 0.87014 0.100912012 11 31.6 51.2 0.84615 216.09000 1.35803 0.91277 0.066622013 12 20.8 53.0 0.92308 272.25000 1.52432 0.93629 0.01321

SUMA 438.0 438.0 1288.86000

ANALISIS DE CONFIABILIDAD: "DISTRIBUCION LOG - NORMAL DE 2 PARAMETROS"

X S36.50 10.82

Δ = |F(z)-P(x)|max 0.11943

¡DATOS SON CONFIABLES!


AÑO mPmax anual

(mm)Pmax anual

(mm)P(x)=m/N+1 ( X−X )2 y z F(z) |F(z)-P(x)|

2002 1 41.4 20.8 0.07692 246.49000 3.03495 -1.79177 0.03658 0.040342003 2 23 23.0 0.15385 182.25000 3.13549 -1.44548 0.07416 0.079682004 3 23.3 23.3 0.23077 174.24000 3.14845 -1.40084 0.08063 0.150142005 4 36 31.6 0.30769 24.01000 3.45316 -0.35135 0.36266 0.054972006 5 51.2 36.0 0.38462 0.25000 3.58352 0.09766 0.53890 0.154282007 6 53 36.0 0.46154 0.25000 3.58352 0.09766 0.53890 0.077362008 7 36.2 36.2 0.53846 0.09000 3.58906 0.11674 0.54647 0.008012009 8 48.7 36.8 0.61538 0.09000 3.60550 0.17336 0.56882 0.046572010 9 36 41.4 0.69231 24.01000 3.72328 0.57904 0.71872 0.026412011 10 36.8 48.7 0.76923 148.84000 3.88568 1.13839 0.87252 0.103292012 11 31.6 51.2 0.84615 216.09000 3.93574 1.31082 0.90504 0.058892013 12 20.8 53.0 0.92308 272.25000 3.97029 1.42983 0.92362 0.00054

SUMA 438.0 1288.86000

X Sx

36.50 10.82

Cv σy µy

0.296561 0.2903336 3.555165

Δ = |F(z)-P(x)|max 0.15428

¡DATOS SON CONFIABLES!


TIEMPOS DE RETORNO

TIEMPOS DE RETORNO CON DISTRIBUCION NORMAL

Para 25 años:

1− 125

=P( X−36.5010.82 )=0,96=¿> X−36.50

10.82=1.7507=¿>55.45mm

( z )= 0.96−0.960800.95994−0.96080

(1.75−1.76 )+1.76

( z )=1.7507

Para 50 años:

1− 150

=P( X−36.510.82 )=0,98=¿> X−36.5

10.82=2.0537=¿>58.7307mm

P ( z )= 0.98−0.980300.97982−0.98030

(2.05−2.06 )+2.06

( z )=2.05375

Para 100 años:

1− 1100

=P( X−36.510.82 )=0,99=¿> X−36.5

10.82=2,3263=¿>61.6815mm

0.95994 1.75

0.96 (z)0.96080 1.76

0.97982 2.05

0.98 (z)0.98030 2.06


( z )= 0.99−0.990100.98983−0.99010

(2.05−2.06 )+2.06

( z )=2,3263

Para 200 años:

1− 1200

=P( X−36.510.82 )=0,995=¿> X−36.5

10.82=2.5758=¿>64.3820mm

P ( z )= 0.995−0.99010.98983−0.9901

(2.32−2.33 )+2.33

( z )=2.5758

TR F(Z) Z X25 0.96 1.7507 55.450250 0.98 2.0537 58.7307

100 0.99 2.3263 61.6815200 0.995 2.5758 64.3820

TIEMPOS DE RETORNO CON DISTRIBUCION NORMAL

0.98983 2.32

0.99 (z)0.99010 2.33

0.98983 2.32

0.995 (z)0.9901 2.33


PERIODOS DE RETORNO

Para 25 años:

1− 125

=P( ln (X )−3.55510.29033 )=0,96=¿>

ln(X)−3.55510.29033

=1.7507=¿>58.1746mm

P ( z )= 0.96−0.960800.95994−0.96080

(1.75−1.76 )+1.76

( z )=1.7507

Para 50 años:

1− 150

=P( ln (X )−3.55510.29033 )=0,98=¿>

ln(X )−3.55510.29033

=2.0537=¿>63.5253mm

P ( z )= 0.98−0.980300.97982−0.98030

(2.05−2.06 )+2.06

( z )=2.05375

Para 100 años:

1− 1100

=P( ln (X )−3.55510.29033 )=0,99=¿>

ln(X )−3.55510.29033

=2,3263=¿>68.7573mm

0.95994 1.75

0.96 (z)0.96080 1.76

0.97982 2.05

0.98 (z)0.98030 2.06

0.98983 2.32

0.99 (z)0.99010 2.33


( z )= 0.99−0.990100.98983−0.99010

(2.05−2.06 )+2.06

( z )=2,3263

Para 200 años:

1− 1200

=P( ln(X )−3.55510.29033 )=0,995=¿>

ln (X )−3.55510.29033

=2,5758=¿>73.9224mm

( z )= 0.995−0.99010.98983−0.9901

(2.32−2.33 )+2.33

( z )=2.5758

0.98983 2.32

0.995 (z)0.9901 2.33

TR F(Z) Z Y(lnx) x25 0.96 1.7507 4.0634 58.1745850 0.98 2.0537 4.1514 63.52527

100 0.99 2.3263 4.2306 68.75727200 0.995 2.5758 4.3030 73.92236


TIEMPOS DE RETORNO CON DISTRIBUCION NORMAL Y LOG NORM

10 100 100055.00000

57.00000

59.00000

61.00000

63.00000

65.00000

67.00000

69.00000

71.00000

73.00000

75.00000

Series2

TIEMPODE RETORNO (años)

Prec

ipit

acio

n(m

m)

10 100 100055.0000

57.0000

59.0000

61.0000

63.0000

65.0000

67.0000

69.0000

71.0000

73.0000

75.0000

Series2Series4

TIEMPODE RETORNO (años)

Prec

ipit

acio

n(m

m)


PROBABILIDAD DE OCURRENCIA

PROBABILIDAD DE OCURRENCIA CON DISTRIBUCION NORMAL

Para 10 mm:

z= X−Xσ

=¿> 10−36.510.82

=−2.4481

f (−z )=1−f (z)

f (−z )=1−0.99928=0.00718=0.72%

f ( z )=0.99928

0.99266 2.44

f(z) 2.44810.99286 2.45


Para 20 mm:

z= X−Xσ

=¿> 20−36.510.82

=−1.52432

f (−z )=1−f (z)

f (−z )=1−0.93629=0.06371=6.37%

f ( z )=0.93629

Para 30 mm:

z= X−Xσ

=¿> 30−36.510.82

=−0.60049

f (−z )=1−f (z)

f (−z )=1−0.72591=0.27409=27.41%

f ( z )=0.72591

Para 40 mm:

z= X−Xσ

=¿> 4 0−36.510.82

=0.32334

0.93574 1.52

f(z) 1.524320.93699 1.53

0.72575 0.60

f(z) 0.600490.72907 0.61


f ( z )=0.62678=62.68%

P max z f(z) Probabilidad(%)10 -2.44816 0.00718 0.7220 -1.52432 0.06371 6.3730 -0.60049 0.27409 27.4140 0.32334 0.62678 62.68

PROBABILIDAD DE OCURRENCIA CON DISTRIBUCION LOG-NORMAL

Para 10 mm:

z=ln (X )−μy

σ y=¿>

ln (x)−3.55510.29033

=−4.31428

f (−z )=1−f (z)

f (−z )=1−0.999992=0.00008=0.01%

f ( z )=0.999992

0.62551 0.32

f(z) 0.323340.62930 0.33


Para 20 mm:

z=ln (X )−μy

σ y=¿>

ln(x)−3.55510.29033

=−1.92686

f (−z )=1−f (z)

f (−z )=1−0.97300=0.026998=2.7%

f ( z )=0.97300

Para 30 mm:

z=ln (X )−μy

σ y=¿>

ln (x)−3.55510.29033

=−0.53031

f (−z )=1−f (z)

f (−z )=1−0.702053=0.297947=29.79%

f ( z )=0.702053

0.97257 1.92

f(z) 1.926860.97320 1.93

0.70194 0.53

f(z) 0.530310.70540 0.54


Para 40 mm:

z=ln (X )−μy

σ y=¿>

ln (x)−3.55510.29033

=0.46055

f ( z )=0.67744

0.0.67724 0.46

f(z) 0.460550.68082 0.47

P max Y Z F(Z) Probabilidad(%)10 2.30259 -4.31428 0.000008 0.00120 2.99573 -1.92686 0.026998 2.70030 3.40120 -0.53031 0.297947 29.79540 3.68888 0.46055 0.677440 67.744


5 10 15 20 25 30 35 40 450.000

10.000

20.000

30.000

40.000

50.000

60.000

70.000

80.000

Series2

Precipitacion(mm)

Prob

abili

dad(

%)

Precipitaciones Estacion Sallique

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