Download - 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
PRECIPITACIONES HIDROLOGIA
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
)
PRECIPITACIONES HIDROLOGIA
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
PRECIPITACIONES HIDROLOGIA
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!
PRECIPITACIONES HIDROLOGIA
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!
PRECIPITACIONES HIDROLOGIA
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
PRECIPITACIONES HIDROLOGIA
( 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
PRECIPITACIONES HIDROLOGIA
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
PRECIPITACIONES HIDROLOGIA
( 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
PRECIPITACIONES HIDROLOGIA
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)
PRECIPITACIONES HIDROLOGIA
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
PRECIPITACIONES HIDROLOGIA
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
PRECIPITACIONES HIDROLOGIA
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
PRECIPITACIONES HIDROLOGIA
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
PRECIPITACIONES HIDROLOGIA
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
PRECIPITACIONES HIDROLOGIA
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(
%)