verificaciones Pmax. Huarmaca (2).xls

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ANALISIS DE PRECIPITACIONES MAXIMAS EN 24 HORASESTACION CANCHAQUE

A. PRECIPITACIONES MAXIMAS EN 24 HORAS PARA DIFERENTES PERIODOS DE RETORNO

AÑO P máx (mm) Log P máx1964 31.00 1.491965 80.00 1.901966 61.00 1.791967 47.80 1.681968 33.20 1.521969 98.20 1.991970 37.50 1.571971 65.40 1.821972 72.80 1.861973 124.10 2.091974 31.10 1.491975 35.50 1.551976 58.70 1.771977 58.90 1.771978 74.40 1.871979 60.70 1.781980 49.10 1.691981 80.80 1.911982 116.80 2.071983 121.50 2.081984 81.20 1.911985 44.50 1.651986 32.50 1.511987 137.30 2.141988 39.10 1.591989 121.70 2.091990 24.20 1.381991 34.90 1.541992 33.20 1.52

1993 75.60 1.88Promedio m = 65.4 1.764Desv. Estánd s = 32.82 0.216Coef. Asimetr c.a. = 0.776 0.117c.a./6 k = 0.020

n = 30

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A.1. Distribuciones

A.1.1. Distribución Normal

TP w z

Pmax(años) (mm)

2 0.500 1.177 0.00 65.423 0.333 1.482 0.43 79.555 0.200 1.794 0.84 93.0410 0.100 2.146 1.28 107.4920 0.050 2.448 1.65 119.4225 0.040 2.537 1.75 122.8950 0.020 2.797 2.05 132.84

100 0.010 3.035 2.33 141.79200 0.005 3.255 2.58 149.98500 0.002 3.526 2.88 159.90

1000 0.001 3.717 3.09 166.86

Usando la metodologia del libro de Hidrologia Aplicada de Ven Te Chow, pag 401

A.2.2. Distribución Log Normal

TP w z Log Pmax

Pmax(años) (mm)

2 0.500 1.177 0.000 1.764 58.063 0.333 1.482 0.430 1.857 71.945 0.200 1.794 0.841 1.946 88.2910 0.100 2.146 1.282 2.041 109.9520 0.050 2.448 1.645 2.120 131.7725 0.040 2.537 1.751 2.143 138.9150 0.020 2.797 2.054 2.208 161.55

100 0.010 3.035 2.327 2.267 185.05200 0.005 3.255 2.576 2.321 209.54500 0.002 3.526 2.879 2.387 243.59

1000 0.001 3.717 3.091 2.433 270.72


Se debe tener en cuenta el ultimo párrafo de esta pagina; es decir que el procedimiento es el mismo excepto que este se

aplica a los logaritmos de las variables y su media y desviacion estándar son usadas para la generacion de caudales

A.2.3. Distribución Log Pearson III

Usando la metodologia del libro de Hidrologia Aplicada de Ven Te Chow, pag 401-403

TP w

KT Log Pmax Pmax(años) (mm)

2 0.500 1.1774 -0.020 1.76 57.503 0.333 1.4823 0.414 1.85 71.365 0.200 1.7941 0.835 1.94 88.0210 0.100 2.1460 1.294 2.04 110.6020 0.050 2.4477 1.678 2.13 133.9325 0.040 2.5373 1.791 2.15 141.6850 0.020 2.7971 2.117 2.22 166.65

100 0.010 3.0349 2.413 2.29 193.15200 0.005 3.2552 2.687 2.35 221.37500 0.002 3.5255 3.022 2.42 261.59

1000 0.001 3.7169 3.259 2.47 294.42

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A.2.4. Distribución Extrema Tipo I- Gumbel Original

TKT

Pmax(años) (mm)

2 -0.1478 60.573 0.3567 77.135 0.9186 95.5710 1.6247 118.7520 2.3020 140.9825 2.5169 148.03 (De tabla A-8, Pag. 583 del libro Engineering Hydrology

50 3.1787 169.75 de Victor Ponce, 1989)

100 3.8357 191.31200 4.4902 212.79500 5.3538 241.14

1000 6.0065 262.56

A.2.5. Distribución Extrema Tipo I- Gumbel Modificado

TKT

Pmax(años) (mm)

2 -0.1643 60.035 0.7195 89.046 0.8770 94.2110 1.3046 108.2420 1.8659 126.6625 2.0439 132.51 (Pag. 225 del libro Engineering Hydrology

50 2.5924 150.51 de Victor Ponce, 1989)

100 3.1368 168.37200 3.6792 186.18500 4.3949 209.66

1000 4.9357 227.42

PRECIPITACIONES MAXIMAS DIARIAS

Log Pearson III

Pmax Pmax Pmax Pmax PmaxT (mm) (mm) (mm) (mm) (mm)2 65.42 58.06 57.50 60.575 93.04 88.29 88.02 95.57 89.0410 107.49 109.95 110.60 118.75 108.2420 119.42 131.77 133.93 140.98 126.6625 122.89 138.91 141.68 148.03 132.5150 132.84 161.55 166.65 169.75 150.51

100 141.79 185.05 193.15 191.31 168.37200 149.98 209.54 221.37 212.79 186.18500 159.90 243.59 261.59 241.14 209.66

1000 166.86 270.72 294.42 262.56 227.42

0.1113 0.1471 0.6217 0.0942 0.1147

Período de Retorno

Distribución Normal

Distribución Log Normal

Gumbel Original

Gumbel Modificado

Delta c (Dc) =

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1 10 100 1000

0

50

100

150

200

250

300

350

Grafico N° 01: Precipitaciones Maximas Diariaspara diferentes Periodos de Retorno: Estacion Canchaque

Dist. Log Pearson IIIl

Dist. Gumbel Modificado

Dist. Normal

Dist. Log Normal

Dist. Gumbel

Periodo de Retorno (Años)

Pre

cip

ita

cio

n M

ax

ima

Dia

ria

(m

m)

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ANALISIS DE PRECIPITACIONES MAXIMAS DIARIAS: ESTACION CANCHAQUE

PRUEBA DE BONDAD DE AJUSTE

Distribucion Normal

N° P(x) Z F(Z)

1 24.20 0.0323 -1.26 0.1046 0.07232 31.00 0.0645 -1.05 0.1471 0.08263 31.10 0.0968 -1.05 0.1478 0.05114 32.50 0.1290 -1.00 0.1579 0.02895 33.20 0.1613 -0.98 0.1631 0.00186 33.20 0.1935 -0.98 0.1631 0.03057 34.90 0.2258 -0.93 0.1762 0.04968 35.50 0.2581 -0.91 0.1810 0.07719 37.50 0.2903 -0.85 0.1974 0.092910 39.10 0.3226 -0.80 0.2113 0.111311 44.50 0.3548 -0.64 0.2619 0.092912 47.80 0.3871 -0.54 0.2956 0.091413 49.10 0.4194 -0.50 0.3095 0.109914 58.70 0.4516 -0.20 0.4188 0.032815 58.90 0.4839 -0.20 0.4212 0.062616 60.70 0.5161 -0.14 0.4428 0.073317 61.00 0.5484 -0.13 0.4464 0.102018 65.40 0.5806 0.00 0.4997 0.080919 72.80 0.6129 0.22 0.5889 0.024020 74.40 0.6452 0.27 0.6078 0.037421 75.60 0.6774 0.31 0.6217 0.055722 80.00 0.7097 0.44 0.6715 0.038223 80.80 0.7419 0.47 0.6803 0.061624 81.20 0.7742 0.48 0.6846 0.089625 98.20 0.8065 1.00 0.8410 0.034626 116.80 0.8387 1.57 0.9413 0.102527 121.50 0.8710 1.71 0.9562 0.085328 121.70 0.9032 1.71 0.9568 0.053629 124.10 0.9355 1.79 0.9631 0.027630 137.30 0.9677 2.19 0.9857 0.0180

Suma (mm) 1962.70 Dmax = 0.1113Media (mm) 65.42D.Est. (mm) 32.82

Pmax (mm) (X)

DxF(Z)-P(x)

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Distribucion Log-Normal

N° P(x) Z F(Z)

1 24.20 3.1864 0.0323 -1.774 0.0380 0.00582 31.00 3.4340 0.0645 -1.216 0.1119 0.04743 31.10 3.4372 0.0968 -1.209 0.1133 0.01654 32.50 3.4812 0.1290 -1.110 0.1335 0.00455 33.20 3.5025 0.1613 -1.062 0.1441 0.01726 33.20 3.5025 0.1935 -1.062 0.1441 0.04947 34.90 3.5525 0.2258 -0.949 0.1712 0.05468 35.50 3.5695 0.2581 -0.911 0.1811 0.07699 37.50 3.6243 0.2903 -0.788 0.2155 0.074910 39.10 3.6661 0.3226 -0.694 0.2440 0.078611 44.50 3.7955 0.3548 -0.402 0.3438 0.011112 47.80 3.8670 0.3871 -0.241 0.4048 0.017713 49.10 3.8939 0.4194 -0.181 0.4283 0.009014 58.70 4.0724 0.4516 0.222 0.5877 0.136115 58.90 4.0758 0.4839 0.229 0.5907 0.106816 60.70 4.1059 0.5161 0.297 0.6168 0.100717 61.00 4.1109 0.5484 0.308 0.6210 0.072618 65.40 4.1805 0.5806 0.465 0.6790 0.098419 72.80 4.2877 0.6129 0.706 0.7601 0.147120 74.40 4.3095 0.6452 0.755 0.7750 0.129821 75.60 4.3255 0.6774 0.791 0.7857 0.108222 80.00 4.3820 0.7097 0.919 0.8209 0.111223 80.80 4.3920 0.7419 0.941 0.8267 0.084824 81.20 4.3969 0.7742 0.952 0.8296 0.055425 98.20 4.5870 0.8065 1.381 0.9163 0.109826 116.80 4.7605 0.8387 1.771 0.9617 0.123027 121.50 4.7999 0.8710 1.860 0.9686 0.097628 121.70 4.8016 0.9032 1.864 0.9688 0.065629 124.10 4.8211 0.9355 1.908 0.9718 0.036330 137.30 4.9222 0.9677 2.135 0.9836 0.0159

Suma (mm) 1962.70 107.30 Dmax = 0.1471Media (mm) 65.42 3.97D.Est. (mm) 32.82 0.44

Del libro de Máximo Villón, pag. 131Y=ln(X)

Pmax (mm) (X)

Ln Pmax (Y)

DxF(Z)-P(x)

Z=(Y-Ymedia)/YD.S.

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Distribucion Gumbel Modificado

N° P(X) y G(y)

1 24.20 0.0323 -1.03 0.0601 0.02792 31.00 0.0645 -0.77 0.1159 0.05133 31.10 0.0968 -0.76 0.1168 0.02014 32.50 0.1290 -0.71 0.1310 0.00205 33.20 0.1613 -0.68 0.1384 0.02296 33.20 0.1935 -0.68 0.1384 0.05527 34.90 0.2258 -0.62 0.1571 0.06878 35.50 0.2581 -0.59 0.1640 0.09419 37.50 0.2903 -0.51 0.1879 0.102410 39.10 0.3226 -0.45 0.2079 0.114711 44.50 0.3548 -0.24 0.2803 0.074512 47.80 0.3871 -0.11 0.3270 0.060113 49.10 0.4194 -0.06 0.3456 0.073814 58.70 0.4516 0.31 0.4818 0.030215 58.90 0.4839 0.32 0.4846 0.000716 60.70 0.5161 0.39 0.5090 0.007117 61.00 0.5484 0.40 0.5130 0.035318 65.40 0.5806 0.58 0.5701 0.010619 72.80 0.6129 0.87 0.6565 0.043620 74.40 0.6452 0.93 0.6734 0.028321 75.60 0.6774 0.97 0.6858 0.008322 80.00 0.7097 1.15 0.7279 0.018223 80.80 0.7419 1.18 0.7350 0.006924 81.20 0.7742 1.19 0.7385 0.035725 98.20 0.8065 1.86 0.8556 0.049126 116.80 0.8387 2.58 0.9274 0.088727 121.50 0.8710 2.77 0.9392 0.068228 121.70 0.9032 2.78 0.9396 0.036429 124.10 0.9355 2.87 0.9449 0.009430 137.30 0.9677 3.39 0.9667 0.0010

Suma (mm) 1962.70 Dmax = 0.1147Media (mm) 65.42D.Est. (S) 32.82 (Para N-1) muestral

25.59

50.65

Del libro de Máximo Villón, páginas: 210-216

Pmax (mm) (X)

DxG(y)-P(x)

α

μ

α=√6πS

μ=X−0 .5772156649αy=X−αμ G( y )=e−e

− y

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Distribucion Gumbel Original

N° P(X) z F(z)

1 24.20 0.0323 -0.83 0.1000 0.06772 31.00 0.0645 -0.61 0.1587 0.09423 31.10 0.0968 -0.61 0.1597 0.06294 32.50 0.1290 -0.56 0.1734 0.04445 33.20 0.1613 -0.54 0.1805 0.01926 33.20 0.1935 -0.54 0.1805 0.01317 34.90 0.2258 -0.48 0.1981 0.02778 35.50 0.2581 -0.46 0.2045 0.05369 37.50 0.2903 -0.40 0.2263 0.064010 39.10 0.3226 -0.34 0.2442 0.078411 44.50 0.3548 -0.17 0.3073 0.047612 47.80 0.3871 -0.06 0.3470 0.040113 49.10 0.4194 -0.01 0.3627 0.056614 58.70 0.4516 0.30 0.4775 0.025915 58.90 0.4839 0.31 0.4798 0.004116 60.70 0.5161 0.37 0.5005 0.015617 61.00 0.5484 0.38 0.5039 0.044418 65.40 0.5806 0.52 0.5528 0.027919 72.80 0.6129 0.77 0.6284 0.015520 74.40 0.6452 0.82 0.6435 0.001621 75.60 0.6774 0.86 0.6546 0.022822 80.00 0.7097 1.00 0.6931 0.016523 80.80 0.7419 1.03 0.6998 0.042224 81.20 0.7742 1.04 0.7031 0.071125 98.20 0.8065 1.60 0.8177 0.011226 116.80 0.8387 2.22 0.8967 0.058027 121.50 0.8710 2.37 0.9108 0.039828 121.70 0.9032 2.38 0.9114 0.008129 124.10 0.9355 2.46 0.9178 0.017730 137.30 0.9677 2.89 0.9460 0.0218

Suma (mm) 1962.70 Dmax = 0.0942Media (mm) 65.42D.Est. (S) 32.27 (Para N) poblacional

30.36 35.4900

49.53 183.1897

Del libro de Linsley, Hidrologia para Ingenieros y del boletin Nº 34, Analisis de Frecuencias de fenomenos en Hidrologia de Manuel Paulet

(De tabla A-8, Pag. 583 del libro Engineering Hydrology

de Victor Ponce, 1989)

Pmax (mm) (X)

DxF(z)-P(x)

n

S

s =

yn=0 .5236σ n=1.0628

μ=X− ynα

y=X−αμ

α

μ

B168

0.779696801*S

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Distribucion Log-Pearson III

N° Y=(x-δ1)/α1 2Y χ2 Fx Fo

1 24.20 3.1864 261.0217 522.0434 581.9741 0.9618 0.0382 0.0526 0.01442 31.00 3.4340 269.5011 539.0022 581.9741 0.8931 0.1069 0.1053 0.00163 31.10 3.4372 269.6114 539.2227 581.9741 0.8919 0.1081 0.1579 0.04984 32.50 3.4812 271.1191 542.2382 581.9741 0.8736 0.1264 0.2105 0.08425 33.20 3.5025 271.8488 543.6975 581.9741 0.8641 0.1359 0.2632 0.12736 33.20 3.5025 271.8488 543.6975 581.9741 0.8641 0.1359 0.3158 0.17997 34.90 3.5525 273.5587 547.1174 581.9741 0.8400 0.1600 0.3684 0.20848 35.50 3.5695 274.1424 548.2847 581.9741 0.8311 0.1689 0.4211 0.25229 37.50 3.6243 276.0191 552.0382 581.9741 0.8008 0.1992 0.4737 0.274510 39.10 3.6661 277.4497 554.8995 581.9741 0.7757 0.2243 0.5263 0.302011 44.50 3.7955 281.8794 563.7589 581.9741 0.6884 0.3116 0.5789 0.267312 47.80 3.8670 284.3290 568.6579 581.9741 0.6350 0.3650 0.6316 0.266613 49.10 3.8939 285.2478 570.4955 581.9741 0.6143 0.3857 0.6842 0.298514 58.70 4.0724 291.3626 582.7253 581.9741 0.4721 0.5279 0.7368 0.208915 58.90 4.0758 291.4791 582.9582 581.9741 0.4693 0.5307 0.7895 0.258816 60.70 4.1059 292.5099 585.0197 581.9741 0.4454 0.5546 0.8421 0.287517 61.00 4.1109 292.6787 585.3574 581.9741 0.4415 0.5585 0.8947 0.336318 65.40 4.1805 295.0635 590.1271 581.9741 0.3875 0.6125 0.9474 0.334819 72.80 4.2877 298.7340 597.4680 581.9741 0.3092 0.6908 1.0000 0.309220 74.40 4.3095 299.4784 598.9568 581.9741 0.2943 0.7057 1.0526 0.346921 75.60 4.3255 300.0263 600.0526 581.9741 0.2835 0.7165 1.1053 0.388822 80.00 4.3820 301.9634 603.9267 581.9741 0.2472 0.7528 1.1579 0.405123 80.80 4.3920 302.3041 604.6081 581.9741 0.2411 0.7589 1.2105 0.451624 81.20 4.3969 302.4732 604.9463 581.9741 0.2381 0.7619 1.2632 0.501225 98.20 4.5870 308.9822 617.9643 581.9741 0.1397 0.8603 1.3158 0.455526 116.80 4.7605 314.9216 629.8431 581.9741 0.0787 0.9213 1.3684 0.447127 121.50 4.7999 316.2724 632.5449 581.9741 0.0682 0.9318 1.4211 0.489328 121.70 4.8016 316.3288 632.6575 581.9741 0.0678 0.9322 1.4737 0.541529 124.10 4.8211 316.9974 633.9949 581.9741 0.0631 0.9369 1.5263 0.589430 137.30 4.9222 320.4586 640.9172 581.9741 0.0427 0.9573 1.5789 0.6217

Suma 121.844 Dmax = 0.62166Media 4.061Des.Est(S) 0.498sesgo(γ) 0.117

290.987

0.029

-4.437

(*): De Tabla 12.3.1 del Libro de Hidrologia Aplicada de Ven Te Chow, Pag. 404; por interpolacion

Pmax (mm) (X)

Log Pmax(Log X)

2β1Dx

F(z)-P(x)

β1=(2/γ)2

α1=S/√β1

δ1=X-α1β1

según el valor de kT

El valor de kT, se obtiene del libro de Hidrologia Aplicada de Ven Te Chow, pag. 400.

LogYTT SkLogYLogY = kT=LogY T−LogY

S LogY

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0.1113 0.1471 0.1147 0.0942 0.6217



Distribución Gumbel

Modificado

Distribución Gumbel Original

Distribución Log Pearson

III

Delta c (Dc) Delta c (Dc) Delta c (Dc) Delta c (Dc) Delta c (Dc)

0 20 40 60 80 100 120 140 160

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Grafico Nº 08: Ajuste de Distribuciones de Probabilidad a la Precipitacion Maxima Diaria en la Estacion Canchaque

Dist. Empírica

Dist. Normal

Dist. Log Normal


Dist. Gumbel

Dist. Log Pearson III

PRECIPITACION MAXIMA DIARIA EN MM

PR

OB

AB

ILID

AD

AC

UM

UL

AD

A

ESTACIONCANCHAQUE CHIGNIA TULUCE

Pmax Pmax Pmax Pmax(mm) (mm) (mm) (mm)

2 60.57 60.03 56.99 33.90 52.875 95.57 86.13 81.22 49.61 78.13

10 118.75 109.12 97.77 60.02 96.4220 140.98 131.19 113.94 70.00 114.0325 148.03 138.18 119.14 73.17 119.6350 169.75 159.74 135.36 82.92 136.94

100 191.31 181.14 151.83 92.61 154.22200 212.79 202.46 168.64 102.25 171.54500 241.14 230.59 191.54 114.98 194.56

1000 262.56 251.85 209.43 124.60 212.11

1000 262.56 251.85 209.43 124.60500 241.14 230.59 191.54 114.98200 212.79 202.46 168.64 102.25100 191.31 181.14 151.83 92.6150 169.75 159.74 135.36 82.9225 148.03 138.18 119.14 73.1720 140.98 131.19 113.94 70.0010 118.75 109.12 97.77 60.025 95.57 86.13 81.22 49.612 60.57 51.39 56.99 33.90

PERIODO DE

RETORNO

PROMEDIO

(mm)

HUARMACA

Gumbel Original

Gumbel Modificado

Log Normal

Gumbel Modificado

12.91 105 SC1 6315.69 112 SC2 67.213.75 106 SC3 63.6

15.6 58 SC4 34.836.69 98 SC5 58.8

7.5 73 SC6 43.858.91 52 SC7 31.268.64 58 IC1 34.847.89 131 IC2 78.6

277.58

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ANALISIS DE PRECIPITACIONES MAXIMAS EN 24 HORASESTACION CHIGNIA


AÑO P máx (mm) Log P máx1973 61.20 1.791974 13.10 1.121975 67.00 1.831976 63.30 1.801977 46.30 1.671978 164.40 2.221979 34.60 1.541980 41.60 1.621981 106.70 2.031982 38.60 1.591983 76.00 1.881984 53.30 1.731985 30.70 1.491986 19.30 1.291987 73.70 1.871988 26.80 1.431989 67.50 1.831990 9.60 0.981991 32.40 1.51

1992 130.80 2.12Promedio m = 57.8 1.665Desv. Estánd s = 39.31 0.313Coef. Asimetr c.a. = 1.325 -0.426c.a./6 k = -0.071

n = 20

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A.1. Distribuciones


TP w z

Pmax(años) (mm)

2 0.500 1.177 0.00 57.843 0.333 1.482 0.43 74.765 0.200 1.794 0.84 90.9210 0.100 2.146 1.28 108.2220 0.050 2.448 1.65 122.5125 0.040 2.537 1.75 126.6750 0.020 2.797 2.05 138.59

100 0.010 3.035 2.33 149.30200 0.005 3.255 2.58 159.11500 0.002 3.526 2.88 170.99

1000 0.001 3.717 3.09 179.32



TP w z Log Pmax

Pmax(años) (mm)

2 0.500 1.177 0.000 1.665 46.243 0.333 1.482 0.430 1.800 63.065 0.200 1.794 0.841 1.929 84.8210 0.100 2.146 1.282 2.066 116.5120 0.050 2.448 1.645 2.180 151.4225 0.040 2.537 1.751 2.213 163.4350 0.020 2.797 2.054 2.308 203.35

100 0.010 3.035 2.327 2.394 247.51200 0.005 3.255 2.576 2.472 296.28500 0.002 3.526 2.879 2.566 368.43

1000 0.001 3.717 3.091 2.633 429.28






TP w z KT

Pmax(años) (mm)

2 0.500 1.1774 0.000 0.071 48.663 0.333 1.4823 0.430 0.484 65.545 0.200 1.7941 0.841 0.855 85.6310 0.100 2.1460 1.282 1.227 112.0020 0.050 2.4477 1.645 1.516 137.9025 0.040 2.5373 1.751 1.596 146.1950 0.020 2.7971 2.054 1.821 171.82

100 0.010 3.0349 2.327 2.013 197.34200 0.005 3.2552 2.576 2.181 222.76500 0.002 3.5255 2.879 2.375 256.21

1000 0.001 3.7169 3.091 2.505 281.39

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TKT

Pmax(años) (mm)


50 3.1787 182.79 de Victor Ponce, 1989)

100 3.8357 208.61200 4.4902 234.34500 5.3538 268.28

1000 6.0065 293.93

A.2.5. Distribución Extrema Tipo I- Gumbel Modificado

TKT

Pmax(años) (mm)


50 2.5924 159.74 de Victor Ponce, 1989)

100 3.1368 181.14200 3.6792 202.46500 4.3949 230.59

1000 4.9357 251.85


Log Pearson III

Pmax Pmax Pmax Pmax PmaxT (mm) (mm) (mm) (mm) (mm)2 57.84 46.24 48.66 52.04 51.395 90.92 84.82 85.63 93.95 86.1310 108.22 116.51 112.00 121.71 109.1220 122.51 151.42 137.90 148.33 131.1925 126.67 163.43 146.19 156.77 138.1850 138.59 203.35 171.82 182.79 159.74

100 149.30 247.51 197.34 208.61 181.14200 159.11 296.28 222.76 234.34 202.46500 170.99 368.43 256.21 268.28 230.59

1000 179.32 429.28 281.39 293.93 251.85

Período de Retorno



Gumbel Original

Gumbel Modificado

16 de 46


1 10 100 1000

0

50

100

150

200

250

300

350

400

450

500

Grafico N° 02: Precipitaciones Maximas en 24 Horaspara diferentes Periodos de Retorno: Estacion Chignia



Dist. Normal

Dist. Log Normal

Dist. Gumbel


Pre

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(m

m)

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ANALISIS DE PRECIPITACIONES MAXIMAS EN 24 HORASESTACION HUARMACA


AÑO P máx (mm) Log P máx1964 46.10 1.661965 52.80 1.721966 22.30 1.351967 39.80 1.601968 40.90 1.611969 70.60 1.851970 27.00 1.431971 51.40 1.711972 57.00 1.761973 63.30 1.801974 33.70 1.531975 59.10 1.771976 36.30 1.561977 68.20 1.831978 90.30 1.961979 61.00 1.791980 39.30 1.591981 82.80 1.921982 89.80 1.951983 111.00 2.051984 61.70 1.791985 53.50 1.731986 54.80 1.741987 50.50 1.701988 41.60 1.621989 84.10 1.921990 36.90 1.571991 52.10 1.721992 78.10 1.891993 43.80 1.641994 34.50 1.541995 76.80 1.891996 26.20 1.421997 71.70 1.861998 92.10 1.961999 78.70 1.902000 99.00 2.002001 68.30 1.832002 111.40 2.052003 39.90 1.602004 37.70 1.582005 48.10 1.682006 80.90 1.912007 39.20 1.592008 113.80 2.062009 55.80 1.75


n = 47

18 de 46


A.1. Distribuciones


TP w z

Pmax(años) (mm)

2 0.500 1.177 0.00 62.113 0.333 1.482 0.43 73.525 0.200 1.794 0.84 84.4310 0.100 2.146 1.28 96.1120 0.050 2.448 1.65 105.7625 0.040 2.537 1.75 108.5750 0.020 2.797 2.05 116.61

100 0.010 3.035 2.33 123.84200 0.005 3.255 2.58 130.46500 0.002 3.526 2.88 138.48

1000 0.001 3.717 3.09 144.10



TP w z Log Pmax

Pmax(años) (mm)

2 0.500 1.177 0.000 1.756 56.993 0.333 1.482 0.430 1.834 68.315 0.200 1.794 0.841 1.910 81.2210 0.100 2.146 1.282 1.990 97.7720 0.050 2.448 1.645 2.057 113.9425 0.040 2.537 1.751 2.076 119.1450 0.020 2.797 2.054 2.131 135.36

100 0.010 3.035 2.327 2.181 151.83200 0.005 3.255 2.576 2.227 168.64500 0.002 3.526 2.879 2.282 191.54

1000 0.001 3.717 3.091 2.321 209.43






TP w z KT

Pmax(años) (mm)

2 0.500 1.1774 0.000 0.001 57.023 0.333 1.4823 0.430 0.432 68.345 0.200 1.7941 0.841 0.842 81.2410 0.100 2.1460 1.282 1.281 97.7320 0.050 2.4477 1.645 1.643 113.8225 0.040 2.5373 1.751 1.748 118.9850 0.020 2.7971 2.054 2.049 135.09

100 0.010 3.0349 2.327 2.320 151.41200 0.005 3.2552 2.576 2.568 168.05500 0.002 3.5255 2.879 2.868 190.66

1000 0.001 3.7169 3.091 3.078 208.31

19 de 46



TKT

Pmax(años) (mm)


50 3.1787 146.44 de Victor Ponce, 1989)

100 3.8357 163.87200 4.4902 181.24500 5.3538 204.15

1000 6.0065 221.46

A.2.5. Distribución Extrema Tipo I - Gumbel Modificado

TKT

Pmax(años) (mm)

5 0.7195 81.206 0.8770 85.3810 1.3046 96.7220 1.8659 111.6125 2.0439 116.34 (Pag. 225 del libro Engineering Hydrology

50 2.5924 130.89 de Victor Ponce, 1989)

100 3.1368 145.33200 3.6792 159.72500 4.3949 178.71

1000 4.9357 193.06


Log Pearson III


100 123.84 151.83 151.41 163.87 145.33200 130.46 168.64 168.05 181.24 159.72500 138.48 191.54 190.66 204.15 178.71

1000 144.10 209.43 208.31 221.46 193.06

Período de Retorno



Gumbel Original

Gumbel Modificado

20 de 46


1 10 100 1000

0

50

100

150

200

250

Grafico N° 03: Precipitaciones Maximas en 24 Horaspara diferentes Periodos de Retorno: Estacion Huarmaca



Dist. Normal

Dist. Log Normal

Dist. Gumbel


Pre

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m)

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AÑO P máx (mm) Log P máx1964 10.00 1.001965 10.00 1.001966 15.70 1.201967 18.60 1.271968 15.40 1.191969 28.70 1.461970 40.90 1.611971 59.60 1.781972 46.40 1.671973 47.40 1.681974 39.30 1.591975 36.90 1.571976 38.60 1.591977 36.80 1.571978 39.90 1.601979 35.30 1.551980 38.20 1.581981 38.90 1.591982 28.60 1.461983 75.10 1.881984 25.80 1.411985 25.30 1.401986 18.12 1.261987 32.20 1.511988 16.30 1.211989 17.30 1.241990 19.40 1.291991 16.90 1.231992 16.40 1.211993 34.80 1.541994 32.30 1.511995 23.90 1.381996 32.50 1.511997 36.60 1.561998 34.50 1.541999 64.60 1.812000 41.10 1.612001 37.40 1.572002 34.50 1.542003 37.30 1.572004 37.80 1.582005 52.50 1.722006 56.30 1.752007 76.70 1.882008 81.80 1.912009 52.80 1.72


n = 47

22 de 46


A.1. Distribuciones


TP w z

Pmax(años) (mm)

2 0.500 1.177 0.00 36.823 0.333 1.482 0.43 44.475 0.200 1.794 0.84 51.7810 0.100 2.146 1.28 59.6120 0.050 2.448 1.65 66.0825 0.040 2.537 1.75 67.9650 0.020 2.797 2.05 73.35

100 0.010 3.035 2.33 78.20200 0.005 3.255 2.58 82.64500 0.002 3.526 2.88 88.01

1000 0.001 3.717 3.09 91.78



TP w z Log Pmax

Pmax(años) (mm)

2 0.500 1.177 0.000 1.514 32.663 0.333 1.482 0.430 1.610 40.715 0.200 1.794 0.841 1.701 50.2610 0.100 2.146 1.282 1.799 62.9620 0.050 2.448 1.645 1.880 75.8425 0.040 2.537 1.751 1.903 80.0750 0.020 2.797 2.054 1.971 93.51

100 0.010 3.035 2.327 2.031 107.52200 0.005 3.255 2.576 2.087 122.17500 0.002 3.526 2.879 2.154 142.62

1000 0.001 3.717 3.091 2.201 158.98






TP w z KT

Pmax(años) (mm)

2 0.500 1.1774 0.000 0.065 33.763 0.333 1.4823 0.430 0.480 41.755 0.200 1.7941 0.841 0.854 50.5810 0.100 2.1460 1.282 1.232 61.3920 0.050 2.4477 1.645 1.527 71.3925 0.040 2.5373 1.751 1.610 74.4950 0.020 2.7971 2.054 1.841 83.82

100 0.010 3.0349 2.327 2.039 92.79200 0.005 3.2552 2.576 2.213 101.46500 0.002 3.5255 2.879 2.416 112.54

1000 0.001 3.7169 3.091 2.552 120.67

23 de 46



TKT

Pmax(años) (mm)


50 3.1787 93.35 de Victor Ponce, 1989)

100 3.8357 105.03200 4.4902 116.68500 5.3538 132.03

1000 6.0065 143.64

A.2.5. Distribución Extrema Tipo I - Gumbel Modificado

TKT

Pmax(años) (mm)


50 2.5924 82.92 de Victor Ponce, 1989)

100 3.1368 92.61200 3.6792 102.25500 4.3949 114.98

1000 4.9357 124.60


Log Pearson III


100 78.20 107.52 92.79 105.03 92.61200 82.64 122.17 101.46 116.68 102.25500 88.01 142.62 112.54 132.03 114.98

1000 91.78 158.98 120.67 143.64 124.60

0.1549 0.1347 0.3952 0.1170 0.1027

Período de Retorno



Gumbel Original

Gumbel Modificado

Delta c (Dc) =

24 de 46


1 10 100 1000

0

20

40

60

80

100

120

140

160

180

Grafico N° 02: Precipitaciones Maximas en 24 Horaspara diferentes Periodos de Retorno: Estacion Tuluce



Dist. Normal

Dist. Log Normal

Dist. Gumbel


Pre

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ANALISIS DE PRECIPITACIONES MAXIMAS DIARIAS: ESTACION CHIGNIA


Distribucion Normal

N° P(x) Z F(Z)

1 9.60 0.0476 -1.23 0.1098 0.06222 13.10 0.0952 -1.14 0.1275 0.03223 19.30 0.1429 -0.98 0.1634 0.02054 26.80 0.1905 -0.79 0.2148 0.02435 30.70 0.2381 -0.69 0.2449 0.00686 32.40 0.2857 -0.65 0.2587 0.02707 34.60 0.3333 -0.59 0.2771 0.05628 38.60 0.3810 -0.49 0.3122 0.06889 41.60 0.4286 -0.41 0.3397 0.088910 46.30 0.4762 -0.29 0.3845 0.091711 53.30 0.5238 -0.12 0.4540 0.069812 61.20 0.5714 0.09 0.5340 0.037413 63.30 0.6190 0.14 0.5552 0.063914 67.00 0.6667 0.23 0.5921 0.074615 67.50 0.7143 0.25 0.5970 0.117316 73.70 0.7619 0.40 0.6567 0.105217 76.00 0.8095 0.46 0.6779 0.131618 106.70 0.8571 1.24 0.8931 0.035919 130.80 0.9048 1.86 0.9683 0.063520 164.40 0.9524 2.71 0.9966 0.0443


Pmax (mm) (X)

DxF(Z)-P(x)

26 de 46




N° P(x) Z F(Z)

1 9.60 2.2618 0.0476 -2.180 0.0146 0.03302 13.10 2.5726 0.0952 -1.749 0.0401 0.05513 19.30 2.9601 0.1429 -1.212 0.1128 0.03014 26.80 3.2884 0.1905 -0.757 0.2247 0.03425 30.70 3.4243 0.2381 -0.568 0.2850 0.04696 32.40 3.4782 0.2857 -0.493 0.3109 0.02527 34.60 3.5439 0.3333 -0.402 0.3438 0.01048 38.60 3.6533 0.3810 -0.250 0.4011 0.02019 41.60 3.7281 0.4286 -0.147 0.4417 0.013110 46.30 3.8351 0.4762 0.002 0.5007 0.024511 53.30 3.9759 0.5238 0.197 0.5781 0.054312 61.20 4.1141 0.5714 0.389 0.6513 0.079813 63.30 4.1479 0.6190 0.436 0.6684 0.049414 67.00 4.2047 0.6667 0.514 0.6965 0.029815 67.50 4.2121 0.7143 0.525 0.7001 0.014216 73.70 4.3000 0.7619 0.647 0.7410 0.020917 76.00 4.3307 0.8095 0.689 0.7546 0.054918 106.70 4.6700 0.8571 1.160 0.8769 0.019819 130.80 4.8737 0.9048 1.442 0.9254 0.020620 164.40 5.1023 0.9524 1.759 0.9607 0.0084



Pmax (mm) (X)

Ln Pmax (Y)

DxF(Z)-P(x)

Z=(Y-Ymedia)/YD.S.

27 de 46




N° P(X) y G(y)

1 9.60 0.0476 -1.00 0.0665 0.01892 13.10 0.0952 -0.88 0.0891 0.00613 19.30 0.1429 -0.68 0.1388 0.00414 26.80 0.1905 -0.44 0.2131 0.02265 30.70 0.2381 -0.31 0.2563 0.01826 32.40 0.2857 -0.25 0.2758 0.00997 34.60 0.3333 -0.18 0.3016 0.03188 38.60 0.3810 -0.05 0.3492 0.03179 41.60 0.4286 0.05 0.3852 0.043410 46.30 0.4762 0.20 0.4412 0.035011 53.30 0.5238 0.43 0.5214 0.002412 61.20 0.5714 0.69 0.6046 0.033113 63.30 0.6190 0.76 0.6251 0.006014 67.00 0.6667 0.88 0.6594 0.007315 67.50 0.7143 0.89 0.6638 0.050516 73.70 0.7619 1.09 0.7156 0.046317 76.00 0.8095 1.17 0.7331 0.076418 106.70 0.8571 2.17 0.8922 0.035119 130.80 0.9048 2.96 0.9494 0.044620 164.40 0.9524 4.05 0.9828 0.0304


30.65

40.16


Pmax (mm) (X)

DxG(y)-P(x)

α

μ

α=√6πS

μ=X−0 .5772156649αy=X−αμ G( y )=e−e

− y

28 de 46




N° P(X) z F(z)

1 9.60 0.0476 -0.81 0.1045 0.05692 13.10 0.0952 -0.72 0.1288 0.03353 19.30 0.1429 -0.55 0.1780 0.03524 26.80 0.1905 -0.34 0.2462 0.05575 30.70 0.2381 -0.23 0.2843 0.04626 32.40 0.2857 -0.18 0.3012 0.01557 34.60 0.3333 -0.12 0.3234 0.00998 38.60 0.3810 -0.01 0.3641 0.01699 41.60 0.4286 0.07 0.3947 0.033910 46.30 0.4762 0.20 0.4422 0.034011 53.30 0.5238 0.40 0.5107 0.013112 61.20 0.5714 0.62 0.5829 0.011513 63.30 0.6190 0.67 0.6010 0.018114 67.00 0.6667 0.78 0.6316 0.035115 67.50 0.7143 0.79 0.6356 0.078716 73.70 0.7619 0.96 0.6828 0.079117 76.00 0.8095 1.03 0.6991 0.110418 106.70 0.8571 1.88 0.8583 0.001219 130.80 0.9048 2.55 0.9247 0.019920 164.40 0.9524 3.48 0.9697 0.0173


36.05 35.4900

38.97 183.1897




Pmax (mm) (X)

DxF(z)-P(x)

n

S

s =

yn=0 .5236σ n=1.0628

μ=X− ynα

y=X−αμ

α

μ

B128

0.779696801*S

29 de 46





1 9.60 2.2618 11.7881 23.5762 44.0399 0.9950 0.0050 0.0526 0.04762 13.10 2.5726 13.8112 27.6225 44.0399 0.9746 0.0254 0.1053 0.07993 19.30 2.9601 16.3332 32.6664 44.0399 0.8958 0.1042 0.1579 0.05374 26.80 3.2884 18.4699 36.9398 44.0399 0.7658 0.2342 0.2105 0.02375 30.70 3.4243 19.3541 38.7083 44.0399 0.6973 0.3027 0.2632 0.03966 32.40 3.4782 19.7049 39.4098 44.0399 0.6685 0.3315 0.3158 0.01577 34.60 3.5439 20.1325 40.2650 44.0399 0.6325 0.3675 0.3684 0.00098 38.60 3.6533 20.8445 41.6890 44.0399 0.5712 0.4288 0.4211 0.00789 41.60 3.7281 21.3316 42.6633 44.0399 0.5290 0.4710 0.4737 0.002610 46.30 3.8351 22.0283 44.0566 44.0399 0.4692 0.5308 0.5263 0.004411 53.30 3.9759 22.9447 45.8893 44.0399 0.3938 0.6062 0.5789 0.027312 61.20 4.1141 23.8442 47.6884 44.0399 0.3251 0.6749 0.6316 0.043313 63.30 4.1479 24.0638 48.1276 44.0399 0.3094 0.6906 0.6842 0.006414 67.00 4.2047 24.4335 48.8670 44.0399 0.2839 0.7161 0.7368 0.020715 67.50 4.2121 24.4819 48.9638 44.0399 0.2806 0.7194 0.7895 0.070116 73.70 4.3000 25.0538 50.1076 44.0399 0.2440 0.7560 0.8421 0.086117 76.00 4.3307 25.2538 50.5077 44.0399 0.2319 0.7681 0.8947 0.126718 106.70 4.6700 27.4621 54.9241 44.0399 0.1251 0.8749 0.9474 0.072519 130.80 4.8737 28.7875 57.5750 44.0399 0.0823 0.9177 1.0000 0.082320 164.40 5.1023 30.2755 60.5510 44.0399 0.0494 0.9506 1.0526 0.1020

Suma 76.677 Dmax = 0.12667Media 3.834Des.Est(S) 0.721sesgo(γ) -0.426

22.020

0.154

0.451


Pmax (mm) (X)

Log Pmax(Log X)

2β1Dx

F(z)-P(x)

β1=(2/γ)2

α1=S/√β1

δ1=X-α1β1




S LogY

30 de 46



0.1316 0.0798 0.0764 0.1104 0.1267

Calculo de interpolacion para el coeficiente de asimetria igual a 0.0523




Modificado



III


0 20 40 60 80 100 120 140 160 180

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Grafico Nº 03: Ajuste de Distribuciones de Probabilidad a la Precipitacion Maxima Diaria en la Estacion Chignia

Dist. EmpíricaDist. NormalDist. Log NormalDist. Gumbel Modificado

PRECIPITACION MAXIMA DIARIA EN MM

PR

OB

AB

ILID

AD

AC

UM

UL

AD

A

31 de 46

ANALISIS DE PRECIPITACIONES MAXIMAS DIARIA: ESTACION HUARMACA


Distribucion Normal

N° P(x) Z F(Z)

1 22.30 0.0208 -1.50 0.0667 0.04592 26.20 0.0417 -1.35 0.0880 0.04633 27.00 0.0625 -1.32 0.0929 0.03044 33.70 0.0833 -1.07 0.1421 0.05885 34.50 0.1042 -1.04 0.1490 0.04496 36.30 0.1250 -0.97 0.1653 0.04037 36.90 0.1458 -0.95 0.1710 0.02528 37.70 0.1667 -0.92 0.1788 0.01219 39.20 0.1875 -0.86 0.1939 0.0064

10 39.30 0.2083 -0.86 0.1950 0.013411 39.80 0.2292 -0.84 0.2002 0.029012 39.90 0.2500 -0.84 0.2013 0.048713 40.90 0.2708 -0.80 0.2120 0.058814 41.60 0.2917 -0.77 0.2198 0.071915 43.80 0.3125 -0.69 0.2451 0.067416 46.10 0.3333 -0.60 0.2731 0.060217 48.10 0.3542 -0.53 0.2987 0.055418 50.50 0.3750 -0.44 0.3309 0.044119 51.40 0.3958 -0.40 0.3432 0.052620 52.10 0.4167 -0.38 0.3530 0.063721 52.80 0.4375 -0.35 0.3628 0.074722 53.50 0.4583 -0.32 0.3728 0.085523 54.80 0.4792 -0.28 0.3915 0.087724 55.80 0.5000 -0.24 0.4060 0.094025 57.00 0.5208 -0.19 0.4237 0.097226 59.10 0.5417 -0.11 0.4549 0.086827 61.00 0.5625 -0.04 0.4833 0.079228 61.70 0.5833 -0.02 0.4939 0.089529 63.30 0.6042 0.04 0.5179 0.086330 68.20 0.6250 0.23 0.5908 0.034231 68.30 0.6458 0.23 0.5923 0.053632 70.60 0.6667 0.32 0.6255 0.041133 71.70 0.6875 0.36 0.6411 0.046434 76.80 0.7083 0.55 0.7101 0.001835 78.10 0.7292 0.60 0.7267 0.002536 78.70 0.7500 0.63 0.7341 0.015937 80.90 0.7708 0.71 0.7606 0.010238 82.80 0.7917 0.78 0.7823 0.009439 84.10 0.8125 0.83 0.7964 0.016140 89.80 0.8333 1.04 0.8517 0.018441 90.30 0.8542 1.06 0.8560 0.001942 92.10 0.8750 1.13 0.8709 0.004143 99.00 0.8958 1.39 0.9178 0.022044 111.00 0.9167 1.84 0.9673 0.050745 111.40 0.9375 1.86 0.9684 0.030946 113.80 0.9583 1.95 0.9743 0.016047 145.20 0.9792 3.13 0.9991 0.0200


Pmax (mm) (X)

DxF(Z)-P(x)

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N° P(x) Z F(Z)

1 22.30 3.1046 0.0208 -2.228 0.0129 0.00792 26.20 3.2658 0.0417 -1.845 0.0325 0.00923 27.00 3.2958 0.0625 -1.774 0.0381 0.02444 33.70 3.5175 0.0833 -1.247 0.1061 0.02285 34.50 3.5410 0.1042 -1.192 0.1167 0.01256 36.30 3.5918 0.1250 -1.071 0.1421 0.01717 36.90 3.6082 0.1458 -1.032 0.1510 0.00528 37.70 3.6297 0.1667 -0.981 0.1633 0.00349 39.20 3.6687 0.1875 -0.888 0.1871 0.0004

10 39.30 3.6712 0.2083 -0.882 0.1888 0.019611 39.80 3.6839 0.2292 -0.852 0.1970 0.032212 39.90 3.6864 0.2500 -0.846 0.1987 0.051313 40.90 3.7111 0.2708 -0.788 0.2155 0.055414 41.60 3.7281 0.2917 -0.747 0.2274 0.064215 43.80 3.7796 0.3125 -0.625 0.2660 0.046516 46.10 3.8308 0.3333 -0.503 0.3073 0.026017 48.10 3.8733 0.3542 -0.403 0.3436 0.010618 50.50 3.9220 0.3750 -0.287 0.3871 0.012119 51.40 3.9396 0.3958 -0.245 0.4032 0.007420 52.10 3.9532 0.4167 -0.213 0.4157 0.001021 52.80 3.9665 0.4375 -0.181 0.4281 0.009422 53.50 3.9797 0.4583 -0.150 0.4404 0.017923 54.80 4.0037 0.4792 -0.093 0.4630 0.016224 55.80 4.0218 0.5000 -0.050 0.4801 0.019925 57.00 4.0431 0.5208 0.001 0.5002 0.020626 59.10 4.0792 0.5417 0.086 0.5344 0.007227 61.00 4.1109 0.5625 0.162 0.5642 0.001728 61.70 4.1223 0.5833 0.189 0.5748 0.008529 63.30 4.1479 0.6042 0.249 0.5985 0.005730 68.20 4.2224 0.6250 0.426 0.6651 0.040131 68.30 4.2239 0.6458 0.430 0.6664 0.020632 70.60 4.2570 0.6667 0.509 0.6945 0.027833 71.70 4.2725 0.6875 0.545 0.7072 0.019734 76.80 4.3412 0.7083 0.708 0.7607 0.052335 78.10 4.3580 0.7292 0.748 0.7729 0.043736 78.70 4.3656 0.7500 0.766 0.7783 0.028337 80.90 4.3932 0.7708 0.832 0.7973 0.026538 82.80 4.4164 0.7917 0.887 0.8125 0.020839 84.10 4.4320 0.8125 0.924 0.8223 0.009840 89.80 4.4976 0.8333 1.080 0.8599 0.026641 90.30 4.5031 0.8542 1.093 0.8628 0.008642 92.10 4.5229 0.8750 1.140 0.8728 0.002243 99.00 4.5951 0.8958 1.311 0.9051 0.009344 111.00 4.7095 0.9167 1.583 0.9433 0.026645 111.40 4.7131 0.9375 1.592 0.9443 0.006846 113.80 4.7344 0.9583 1.642 0.9497 0.008647 145.20 4.9781 0.9792 2.221 0.9868 0.0077



Pmax (mm) (X)

Ln Pmax (Y)

DxF(Z)-P(x)

Z=(Y-Ymedia)/YD.S.

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N° P(X) y G(y)

1 22.30 0.0208 -1.35 0.0214 0.00052 26.20 0.0417 -1.16 0.0413 0.00033 27.00 0.0625 -1.12 0.0467 0.01584 33.70 0.0833 -0.80 0.1089 0.02565 34.50 0.1042 -0.76 0.1185 0.01436 36.30 0.1250 -0.67 0.1416 0.01667 36.90 0.1458 -0.64 0.1497 0.00398 37.70 0.1667 -0.60 0.1609 0.00589 39.20 0.1875 -0.53 0.1828 0.0047

10 39.30 0.2083 -0.53 0.1843 0.024011 39.80 0.2292 -0.50 0.1919 0.037312 39.90 0.2500 -0.50 0.1934 0.056613 40.90 0.2708 -0.45 0.2090 0.061814 41.60 0.2917 -0.41 0.2202 0.071515 43.80 0.3125 -0.31 0.2565 0.056016 46.10 0.3333 -0.20 0.2960 0.037317 48.10 0.3542 -0.10 0.3312 0.023018 50.50 0.3750 0.02 0.3738 0.001219 51.40 0.3958 0.06 0.3898 0.006120 52.10 0.4167 0.09 0.4022 0.014521 52.80 0.4375 0.13 0.4146 0.022922 53.50 0.4583 0.16 0.4269 0.031423 54.80 0.4792 0.22 0.4496 0.029624 55.80 0.5000 0.27 0.4669 0.033125 57.00 0.5208 0.33 0.4874 0.033526 59.10 0.5417 0.43 0.5224 0.019327 61.00 0.5625 0.52 0.5530 0.009528 61.70 0.5833 0.56 0.5640 0.019329 63.30 0.6042 0.63 0.5886 0.015630 68.20 0.6250 0.87 0.6582 0.033231 68.30 0.6458 0.88 0.6595 0.013732 70.60 0.6667 0.99 0.6891 0.022433 71.70 0.6875 1.04 0.7025 0.015034 76.80 0.7083 1.29 0.7588 0.050535 78.10 0.7292 1.35 0.7717 0.042536 78.70 0.7500 1.38 0.7774 0.027437 80.90 0.7708 1.49 0.7974 0.026638 82.80 0.7917 1.58 0.8134 0.021839 84.10 0.8125 1.64 0.8237 0.011240 89.80 0.8333 1.92 0.8631 0.029841 90.30 0.8542 1.94 0.8662 0.012042 92.10 0.8750 2.03 0.8766 0.001643 99.00 0.8958 2.36 0.9100 0.014144 111.00 0.9167 2.94 0.9485 0.031945 111.40 0.9375 2.96 0.9495 0.012046 113.80 0.9583 3.08 0.9549 0.003447 145.20 0.9792 4.59 0.9899 0.0108


20.69

50.17


Pmax (mm) (X)

DxG(y)-P(x)

α

μ

α=√6πS

μ=X−0 .5772156649αy=X−αμ G( y )=e−e

− y

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N° P(X) z F(z)

1 22.30 0.0208 -1.09 0.0513 0.03052 26.20 0.0417 -0.93 0.0792 0.03753 27.00 0.0625 -0.90 0.0859 0.02344 33.70 0.0833 -0.63 0.1539 0.07065 34.50 0.1042 -0.59 0.1634 0.05926 36.30 0.1250 -0.52 0.1855 0.06057 36.90 0.1458 -0.50 0.1932 0.04748 37.70 0.1667 -0.46 0.2036 0.03699 39.20 0.1875 -0.40 0.2236 0.0361

10 39.30 0.2083 -0.40 0.2250 0.016611 39.80 0.2292 -0.38 0.2318 0.002612 39.90 0.2500 -0.38 0.2332 0.016813 40.90 0.2708 -0.34 0.2470 0.023814 41.60 0.2917 -0.31 0.2569 0.034815 43.80 0.3125 -0.22 0.2884 0.024116 46.10 0.3333 -0.12 0.3222 0.011217 48.10 0.3542 -0.04 0.3518 0.002318 50.50 0.3750 0.05 0.3876 0.012619 51.40 0.3958 0.09 0.4009 0.005120 52.10 0.4167 0.12 0.4113 0.005421 52.80 0.4375 0.15 0.4217 0.015822 53.50 0.4583 0.18 0.4320 0.026423 54.80 0.4792 0.23 0.4510 0.028224 55.80 0.5000 0.27 0.4654 0.034625 57.00 0.5208 0.32 0.4826 0.038226 59.10 0.5417 0.40 0.5122 0.029527 61.00 0.5625 0.48 0.5382 0.024328 61.70 0.5833 0.51 0.5476 0.035829 63.30 0.6042 0.57 0.5687 0.035530 68.20 0.6250 0.77 0.6295 0.004531 68.30 0.6458 0.77 0.6306 0.015232 70.60 0.6667 0.87 0.6570 0.009633 71.70 0.6875 0.91 0.6692 0.018334 76.80 0.7083 1.12 0.7212 0.012935 78.10 0.7292 1.17 0.7334 0.004336 78.70 0.7500 1.20 0.7389 0.011137 80.90 0.7708 1.28 0.7582 0.012638 82.80 0.7917 1.36 0.7739 0.017739 84.10 0.8125 1.41 0.7842 0.028340 89.80 0.8333 1.64 0.8245 0.008941 90.30 0.8542 1.67 0.8277 0.026542 92.10 0.8750 1.74 0.8387 0.036343 99.00 0.8958 2.02 0.8755 0.020444 111.00 0.9167 2.50 0.9214 0.004845 111.40 0.9375 2.52 0.9227 0.014846 113.80 0.9583 2.62 0.9296 0.028847 145.20 0.9792 3.89 0.9797 0.0006


24.70 35.4900

49.18 183.1897




Pmax (mm) (X)

DxF(z)-P(x)

n

S

s =

yn=0 .5236σ n=1.0628

μ=X− ynα

y=X−αμ

α

μ

B236

0.779696801*S

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1 22.30 3.1046 49420.2015 98840.4030 99835.9287 0.9872 0.0128 0.02862 26.20 3.2658 49505.7070 99011.4139 99835.9287 0.9676 0.0324 0.05713 27.00 3.2958 49521.6637 99043.3273 99835.9287 0.9620 0.0380 0.08574 33.70 3.5175 49639.2594 99278.5188 99835.9287 0.8937 0.1063 0.11435 34.50 3.5410 49651.7062 99303.4124 99835.9287 0.8830 0.1170 0.14296 36.30 3.5918 49678.6877 99357.3753 99835.9287 0.8575 0.1425 0.17147 36.90 3.6082 49687.3849 99374.7698 99835.9287 0.8485 0.1515 0.20008 37.70 3.6297 49698.7638 99397.5276 99835.9287 0.8362 0.1638 0.22869 39.20 3.6687 49719.4629 99438.9259 99835.9287 0.8122 0.1878 0.2571

10 39.30 3.6712 49720.8146 99441.6292 99835.9287 0.8106 0.1894 0.285711 39.80 3.6839 49727.5216 99455.0433 99835.9287 0.8023 0.1977 0.314312 39.90 3.6864 49728.8529 99457.7059 99835.9287 0.8006 0.1994 0.342913 40.90 3.7111 49741.9853 99483.9706 99835.9287 0.7838 0.2162 0.371414 41.60 3.7281 49750.9883 99501.9766 99835.9287 0.7717 0.2283 0.400015 43.80 3.7796 49778.3280 99556.6559 99835.9287 0.7330 0.2670 0.428616 46.10 3.8308 49805.4796 99610.9591 99835.9287 0.6916 0.3084 0.457117 48.10 3.8733 49828.0104 99656.0207 99835.9287 0.6552 0.3448 0.485718 50.50 3.9220 49853.8420 99707.6841 99835.9287 0.6116 0.3884 0.514319 51.40 3.9396 49863.2136 99726.4272 99835.9287 0.5954 0.4046 0.542920 52.10 3.9532 49870.3898 99740.7797 99835.9287 0.5829 0.4171 0.571421 52.80 3.9665 49877.4703 99754.9406 99835.9287 0.5705 0.4295 0.600022 53.50 3.9797 49884.4575 99768.9150 99835.9287 0.5582 0.4418 0.628623 54.80 4.0037 49897.1945 99794.3890 99835.9287 0.5356 0.4644 0.657124 55.80 4.0218 49906.7883 99813.5766 99835.9287 0.5185 0.4815 0.685725 57.00 4.0431 49918.0764 99836.1528 99835.9287 0.4984 0.5016 0.714326 59.10 4.0792 49937.2704 99874.5409 99835.9287 0.4642 0.5358 0.742927 61.00 4.1109 49954.0577 99908.1154 99835.9287 0.4344 0.5656 0.771428 61.70 4.1223 49960.1110 99920.2219 99835.9287 0.4238 0.5762 0.800029 63.30 4.1479 49973.6930 99947.3861 99835.9287 0.4002 0.5998 0.828630 68.20 4.2224 50013.2482 100026.4965 99835.9287 0.3337 0.6663 0.857131 68.30 4.2239 50014.0256 100028.0511 99835.9287 0.3324 0.6676 0.885732 70.60 4.2570 50031.5966 100063.1932 99835.9287 0.3044 0.6956 0.914333 71.70 4.2725 50039.7988 100079.5976 99835.9287 0.2917 0.7083 0.942934 76.80 4.3412 50076.2529 100152.5059 99835.9287 0.2385 0.7615 0.971435 78.10 4.3580 50085.1579 100170.3159 99835.9287 0.2263 0.7737 1.000036 78.70 4.3656 50089.2181 100178.4361 99835.9287 0.2209 0.7791 1.028637 80.90 4.3932 50103.8449 100207.6898 99835.9287 0.2020 0.7980 1.057138 82.80 4.4164 50116.1605 100232.3210 99835.9287 0.1869 0.8131 1.085739 84.10 4.4320 50124.4252 100248.8505 99835.9287 0.1771 0.8229 1.114340 89.80 4.4976 50159.2159 100318.4319 99835.9287 0.1397 0.8603 1.142941 90.30 4.5031 50162.1616 100324.3233 99835.9287 0.1368 0.8632 1.171442 92.10 4.5229 50172.6328 100345.2656 99835.9287 0.1268 0.8732 1.200043 99.00 4.5951 50210.9602 100421.9204 99835.9287 0.0947 0.9053 1.228644 111.00 4.7095 50271.6573 100543.3145 99835.9287 0.0567 0.9433 1.257145 111.40 4.7131 50273.5656 100547.1312 99835.9287 0.0558 0.9442 1.285746 113.80 4.7344 50284.8738 100569.7475 99835.9287 0.0503 0.9497 1.314347 145.20 4.9781 50414.1455 100828.2911 99835.9287 0.0133 0.9867 1.3429

Suma 190.013 Dmax =Media 4.043Des.Est(S) 0.421sesgo(γ) -0.009

49917.964

0.002

-90.050


Pmax (mm) (X)

Log Pmax(Log X)

2β1

β1=(2/γ)2

α1=S/√β1

δ1=X-α1β1




S LogY

36 de 46



0.0972 0.0642 0.0715 0.0706 0.3646




Modificado



III


0 20 40 60 80 100 120 140 160

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Grafico Nº 03: Ajuste de Distribuciones de Probabilidad a la Precipitacion Maxima Diaria en la Estacion Huarmaca

Column CColumn EColumn FDist. Gumbel ModificadoColumn EColumn H

PRECIPITACION MAXIMA EN 24 HORAS EN MM

PR

OB

AB

ILID

AD

AC

UM

UL

AD

A

37 de 46


0.01580.02470.04780.00790.02590.02890.04850.06480.06940.09630.11660.14350.15520.17170.16160.14870.14090.12590.13830.15440.17050.18680.19280.20420.21270.20700.20590.22380.22870.19080.21810.21870.23460.20990.22630.24950.25910.27260.29140.28260.30820.32680.32330.31390.34150.36460.3562

0.36460

DxF(z)-P(x)

38 de 46

ANALISIS DE PRECIPITACIONES MAXIMAS DIARIAS: ESTACION TULUCE


Distribucion Normal

N° P(x) Z F(Z)

1 10.00 0.0208 -1.51 0.0658 0.04502 10.00 0.0417 -1.51 0.0658 0.02413 15.40 0.0625 -1.20 0.1142 0.05174 15.70 0.0833 -1.19 0.1175 0.03425 16.30 0.1042 -1.15 0.1243 0.02026 16.40 0.1250 -1.15 0.1255 0.00057 16.90 0.1458 -1.12 0.1314 0.01458 17.30 0.1667 -1.10 0.1362 0.03049 18.12 0.1875 -1.05 0.1466 0.040910 18.60 0.2083 -1.02 0.1528 0.055511 19.40 0.2292 -0.98 0.1637 0.065512 23.90 0.2500 -0.73 0.2338 0.016213 25.30 0.2708 -0.65 0.2586 0.012214 25.80 0.2917 -0.62 0.2678 0.023915 28.60 0.3125 -0.46 0.3220 0.009516 28.70 0.3333 -0.46 0.3240 0.009317 32.20 0.3542 -0.26 0.3976 0.043418 32.30 0.3750 -0.25 0.3997 0.024719 32.50 0.3958 -0.24 0.4041 0.008320 34.50 0.4167 -0.13 0.4482 0.031521 34.50 0.4375 -0.13 0.4482 0.010722 34.80 0.4583 -0.11 0.4548 0.003523 35.30 0.4792 -0.09 0.4660 0.013224 36.60 0.5000 -0.01 0.4951 0.004925 36.80 0.5208 0.00 0.4996 0.021226 36.90 0.5417 0.00 0.5019 0.039827 37.30 0.5625 0.03 0.5108 0.051728 37.40 0.5833 0.03 0.5131 0.070329 37.80 0.6042 0.06 0.5220 0.082130 38.20 0.6250 0.08 0.5310 0.094031 38.60 0.6458 0.10 0.5399 0.105932 38.90 0.6667 0.12 0.5466 0.120133 39.30 0.6875 0.14 0.5555 0.132034 39.90 0.7083 0.17 0.5688 0.139535 40.90 0.7292 0.23 0.5908 0.138436 41.10 0.7500 0.24 0.5951 0.154937 46.40 0.7708 0.54 0.7050 0.065838 47.40 0.7917 0.60 0.7241 0.067639 52.50 0.8125 0.88 0.8111 0.001440 52.80 0.8333 0.90 0.8156 0.017841 56.30 0.8542 1.10 0.8633 0.009242 59.60 0.8750 1.28 0.8999 0.024943 64.60 0.8958 1.56 0.9409 0.045044 75.00 0.9167 2.15 0.9841 0.067445 75.10 0.9375 2.15 0.9843 0.046846 76.70 0.9583 2.24 0.9875 0.029247 81.80 0.9792 2.53 0.9943 0.0151


Pmax (mm) (X)

DxF(Z)-P(x)

39 de 46




N° P(x) Z F(Z)

1 10.00 2.3026 0.0208 -2.312 0.0104 0.01042 10.00 2.3026 0.0417 -2.312 0.0104 0.03133 15.40 2.7344 0.0625 -1.468 0.0710 0.00854 15.70 2.7537 0.0833 -1.431 0.0763 0.00715 16.30 2.7912 0.1042 -1.357 0.0873 0.01686 16.40 2.7973 0.1250 -1.345 0.0892 0.03587 16.90 2.8273 0.1458 -1.287 0.0991 0.04688 17.30 2.8507 0.1667 -1.241 0.1073 0.05949 18.12 2.8970 0.1875 -1.151 0.1249 0.062610 18.60 2.9232 0.2083 -1.100 0.1357 0.072611 19.40 2.9653 0.2292 -1.017 0.1545 0.074712 23.90 3.1739 0.2500 -0.610 0.2709 0.020913 25.30 3.2308 0.2708 -0.499 0.3090 0.038114 25.80 3.2504 0.2917 -0.461 0.3225 0.030915 28.60 3.3534 0.3125 -0.259 0.3977 0.085216 28.70 3.3569 0.3333 -0.253 0.4003 0.067017 32.20 3.4720 0.3542 -0.028 0.4889 0.134718 32.30 3.4751 0.3750 -0.022 0.4913 0.116319 32.50 3.4812 0.3958 -0.010 0.4961 0.100320 34.50 3.5410 0.4167 0.107 0.5426 0.125921 34.50 3.5410 0.4375 0.107 0.5426 0.105122 34.80 3.5496 0.4583 0.124 0.5493 0.090923 35.30 3.5639 0.4792 0.152 0.5603 0.081124 36.60 3.6000 0.5000 0.222 0.5879 0.087925 36.80 3.6055 0.5208 0.233 0.5921 0.071326 36.90 3.6082 0.5417 0.238 0.5941 0.052527 37.30 3.6190 0.5625 0.259 0.6023 0.039828 37.40 3.6217 0.5833 0.264 0.6043 0.021029 37.80 3.6323 0.6042 0.285 0.6123 0.008130 38.20 3.6428 0.6250 0.306 0.6201 0.004931 38.60 3.6533 0.6458 0.326 0.6279 0.018032 38.90 3.6610 0.6667 0.341 0.6336 0.033133 39.30 3.6712 0.6875 0.361 0.6410 0.046534 39.90 3.6864 0.7083 0.391 0.6520 0.056335 40.90 3.7111 0.7292 0.439 0.6697 0.059436 41.10 3.7160 0.7500 0.449 0.6732 0.076837 46.40 3.8373 0.7708 0.686 0.7535 0.017338 47.40 3.8586 0.7917 0.727 0.7665 0.025239 52.50 3.9608 0.8125 0.927 0.8230 0.010540 52.80 3.9665 0.8333 0.938 0.8259 0.007541 56.30 4.0307 0.8542 1.063 0.8562 0.002042 59.60 4.0877 0.8750 1.175 0.8799 0.004943 64.60 4.1682 0.8958 1.332 0.9085 0.012744 75.00 4.3175 0.9167 1.623 0.9477 0.031145 75.10 4.3188 0.9375 1.626 0.9480 0.010546 76.70 4.3399 0.9583 1.667 0.9523 0.006147 81.80 4.4043 0.9792 1.793 0.9635 0.0157



Pmax (mm) (X)

Ln Pmax (Y)

DxF(Z)-P(x)

Z=(Y-Ymedia)/YD.S.

40 de 46




N° P(X) y G(y)

1 10.00 0.0208 -1.36 0.0206 0.00032 10.00 0.0417 -1.36 0.0206 0.02113 15.40 0.0625 -0.97 0.0720 0.00954 15.70 0.0833 -0.95 0.0762 0.00715 16.30 0.1042 -0.90 0.0850 0.01926 16.40 0.1250 -0.90 0.0865 0.03857 16.90 0.1458 -0.86 0.0943 0.05158 17.30 0.1667 -0.83 0.1009 0.06589 18.12 0.1875 -0.77 0.1151 0.072410 18.60 0.2083 -0.74 0.1239 0.084511 19.40 0.2292 -0.68 0.1392 0.089912 23.90 0.2500 -0.35 0.2405 0.009513 25.30 0.2708 -0.25 0.2757 0.004914 25.80 0.2917 -0.22 0.2886 0.003115 28.60 0.3125 -0.02 0.3622 0.049716 28.70 0.3333 -0.01 0.3649 0.031517 32.20 0.3542 0.24 0.4569 0.102718 32.30 0.3750 0.25 0.4595 0.084519 32.50 0.3958 0.27 0.4646 0.068820 34.50 0.4167 0.41 0.5150 0.098321 34.50 0.4375 0.41 0.5150 0.077522 34.80 0.4583 0.43 0.5224 0.064023 35.30 0.4792 0.47 0.5345 0.055424 36.60 0.5000 0.56 0.5653 0.065325 36.80 0.5208 0.58 0.5700 0.049126 36.90 0.5417 0.58 0.5723 0.030627 37.30 0.5625 0.61 0.5814 0.018928 37.40 0.5833 0.62 0.5837 0.000429 37.80 0.6042 0.65 0.5927 0.011530 38.20 0.6250 0.68 0.6016 0.023431 38.60 0.6458 0.71 0.6103 0.035532 38.90 0.6667 0.73 0.6168 0.049833 39.30 0.6875 0.76 0.6254 0.062134 39.90 0.7083 0.80 0.6379 0.070435 40.90 0.7292 0.87 0.6582 0.071036 41.10 0.7500 0.89 0.6621 0.087937 46.40 0.7708 1.27 0.7548 0.016038 47.40 0.7917 1.34 0.7697 0.022039 52.50 0.8125 1.71 0.8343 0.021840 52.80 0.8333 1.73 0.8375 0.004241 56.30 0.8542 1.98 0.8713 0.017142 59.60 0.8750 2.22 0.8971 0.022143 64.60 0.8958 2.58 0.9271 0.031244 75.00 0.9167 3.33 0.9649 0.048245 75.10 0.9375 3.34 0.9651 0.027646 76.70 0.9583 3.45 0.9689 0.010547 81.80 0.9792 3.82 0.9783 0.0008


13.87

28.81


Pmax (mm) (X)

DxG(y)-P(x)

α

μ

α=√6πS

μ=X−0 .5772156649αy=X−αμ G( y )=e−e

− y

41 de 46




N° P(X) z F(z)

1 10.00 0.0208 -1.10 0.0501 0.02932 10.00 0.0417 -1.10 0.0501 0.00853 15.40 0.0625 -0.77 0.1153 0.05284 15.70 0.0833 -0.75 0.1199 0.03665 16.30 0.1042 -0.72 0.1293 0.02516 16.40 0.1250 -0.71 0.1309 0.00597 16.90 0.1458 -0.68 0.1391 0.00688 17.30 0.1667 -0.66 0.1458 0.02099 18.12 0.1875 -0.61 0.1600 0.027510 18.60 0.2083 -0.58 0.1686 0.039811 19.40 0.2292 -0.53 0.1833 0.045812 23.90 0.2500 -0.26 0.2746 0.024613 25.30 0.2708 -0.17 0.3049 0.034114 25.80 0.2917 -0.14 0.3159 0.024215 28.60 0.3125 0.03 0.3779 0.065416 28.70 0.3333 0.03 0.3801 0.046817 32.20 0.3542 0.24 0.4571 0.102918 32.30 0.3750 0.25 0.4592 0.084219 32.50 0.3958 0.26 0.4635 0.067720 34.50 0.4167 0.38 0.5059 0.089221 34.50 0.4375 0.38 0.5059 0.068422 34.80 0.4583 0.40 0.5121 0.053823 35.30 0.4792 0.43 0.5224 0.043324 36.60 0.5000 0.51 0.5487 0.048725 36.80 0.5208 0.52 0.5527 0.031826 36.90 0.5417 0.53 0.5546 0.013027 37.30 0.5625 0.55 0.5625 0.000028 37.40 0.5833 0.56 0.5645 0.018929 37.80 0.6042 0.58 0.5722 0.032030 38.20 0.6250 0.61 0.5799 0.045131 38.60 0.6458 0.63 0.5875 0.058432 38.90 0.6667 0.65 0.5931 0.073533 39.30 0.6875 0.67 0.6006 0.086934 39.90 0.7083 0.71 0.6116 0.096835 40.90 0.7292 0.77 0.6294 0.099736 41.10 0.7500 0.78 0.6330 0.117037 46.40 0.7708 1.10 0.7174 0.053438 47.40 0.7917 1.16 0.7315 0.060139 52.50 0.8125 1.47 0.7948 0.017740 52.80 0.8333 1.49 0.7980 0.035341 56.30 0.8542 1.70 0.8331 0.021142 59.60 0.8750 1.90 0.8610 0.014043 64.60 0.8958 2.20 0.8953 0.000544 75.00 0.9167 2.83 0.9427 0.026045 75.10 0.9375 2.84 0.9430 0.005546 76.70 0.9583 2.93 0.9481 0.010247 81.80 0.9792 3.24 0.9616 0.0175


16.56 35.4900

28.15 183.1897




Pmax (mm) (X)

DxF(z)-P(x)

n

S

s =

yn=0 .5236σ n=1.0628

μ=X− ynα

y=X−αμ

α

μ

B236

0.779696801*S

42 de 46





1 15.40 2.7344 295.6138 591.2276 655.1375 0.9644 0.0356 0.0303 0.00532 15.70 2.7537 296.3802 592.7603 655.1375 0.9607 0.0393 0.0606 0.02133 16.30 2.7912 297.8699 595.7398 655.1375 0.9526 0.0474 0.0909 0.04354 16.40 2.7973 298.1128 596.2257 655.1375 0.9512 0.0488 0.1212 0.07245 16.90 2.8273 299.3058 598.6115 655.1375 0.9437 0.0563 0.1515 0.09526 17.30 2.8507 300.2350 600.4699 655.1375 0.9372 0.0628 0.1818 0.11917 18.12 2.8970 302.0745 604.1489 655.1375 0.9229 0.0771 0.2121 0.13508 18.60 2.9232 303.1130 606.2260 655.1375 0.9137 0.0863 0.2424 0.15619 19.40 2.9653 304.7857 609.5715 655.1375 0.8974 0.1026 0.2727 0.170110 23.90 3.1739 313.0719 626.1437 655.1375 0.7855 0.2145 0.3030 0.088511 25.30 3.2308 315.3331 630.6661 655.1375 0.7461 0.2539 0.3333 0.079512 25.80 3.2504 316.1104 632.2208 655.1375 0.7318 0.2682 0.3636 0.095513 28.60 3.3534 320.2030 640.4060 655.1375 0.6509 0.3491 0.3939 0.044914 28.70 3.3569 320.3417 640.6833 655.1375 0.6480 0.3520 0.4242 0.072315 32.20 3.4720 324.9124 649.8248 655.1375 0.5497 0.4503 0.4545 0.004316 32.30 3.4751 325.0356 650.0711 655.1375 0.5470 0.4530 0.4848 0.031917 32.50 3.4812 325.2808 650.5615 655.1375 0.5416 0.4584 0.5152 0.056818 34.50 3.5410 327.6529 655.3058 655.1375 0.4893 0.5107 0.5455 0.034719 34.50 3.5410 327.6529 655.3058 655.1375 0.4893 0.5107 0.5758 0.065020 34.80 3.5496 327.9968 655.9936 655.1375 0.4817 0.5183 0.6061 0.087821 35.30 3.5639 328.5635 657.1269 655.1375 0.4693 0.5307 0.6364 0.105622 36.60 3.6000 330.0000 660.0000 655.1375 0.4379 0.5621 0.6667 0.104623 36.80 3.6055 330.2165 660.4329 655.1375 0.4333 0.5667 0.6970 0.130224 36.90 3.6082 330.3243 660.6485 655.1375 0.4309 0.5691 0.7273 0.158225 37.30 3.6190 330.7525 661.5051 655.1375 0.4217 0.5783 0.7576 0.179326 37.40 3.6217 330.8589 661.7178 655.1375 0.4194 0.5806 0.7879 0.207327 37.80 3.6323 331.2815 662.5629 655.1375 0.4104 0.5896 0.8182 0.228628 38.20 3.6428 331.6996 663.3992 655.1375 0.4015 0.5985 0.8485 0.250029 38.60 3.6533 332.1133 664.2267 655.1375 0.3928 0.6072 0.8788 0.271530 38.90 3.6610 332.4209 664.8417 655.1375 0.3863 0.6137 0.9091 0.295431 39.30 3.6712 332.8272 665.6545 655.1375 0.3778 0.6222 0.9394 0.317232 39.90 3.6864 333.4291 666.8582 655.1375 0.3654 0.6346 0.9697 0.335133 40.90 3.7111 334.4123 668.8247 655.1375 0.3454 0.6546 1.0000 0.345434 41.10 3.7160 334.6061 669.2122 655.1375 0.3415 0.6585 1.0303 0.371835 46.40 3.8373 339.4240 678.8480 655.1375 0.2516 0.7484 1.0606 0.312236 47.40 3.8586 340.2710 680.5419 655.1375 0.2373 0.7627 1.0909 0.328237 52.50 3.9608 344.3301 688.6603 655.1375 0.1754 0.8246 1.1212 0.296738 52.80 3.9665 344.5565 689.1130 655.1375 0.1723 0.8277 1.1515 0.323939 56.30 4.0307 347.1059 694.2119 655.1375 0.1399 0.8601 1.1818 0.321740 59.60 4.0877 349.3685 698.7371 655.1375 0.1149 0.8851 1.2121 0.327041 64.60 4.1682 352.5685 705.1369 655.1375 0.0854 0.9146 1.2424 0.327842 75.00 4.3175 358.4978 716.9957 655.1375 0.0465 0.9535 1.2727 0.319243 75.10 4.3188 358.5508 717.1015 655.1375 0.0462 0.9538 1.3030 0.349244 76.70 4.3399 359.3881 718.7763 655.1375 0.0422 0.9578 1.3333 0.375545 81.80 4.4043 361.9452 723.8905 655.1375 0.0315 0.9685 1.3636 0.3952

Suma 159.248 Dmax = 0.39517Media 3.539Des.Est(S) 0.456sesgo(γ) -0.111

327.569

0.025

-4.708


Pmax (mm) (X)

Log Pmax(Log X)

2β1Dx

F(z)-P(x)

β1=(2/γ)2

α1=S/√β1

δ1=X-α1β1




S LogY

43 de 46



0.1549 0.1347 0.1027 0.1170 0.3952

Calculo de interpolacion para el coeficiente de asimetria igual a 0.0523Coeficiente Periodo de retorno, añosde 1.0101 1.25 2 5 10 25 50 100Asimetria Nivel de probabilidad, porcentajeAg 99 80 50 20 10 4 2 1

0.99 0.80 0.50 0.20 0.10 0.04 0.02 0.01

0 -2.326 -0.842 0.000 0.842 1.282 1.751 2.054 2.3260.1 -2.253 -0.846 -0.017 0.836 1.292 1.785 2.107 2.400

-0.1105 -2.4067 -0.8376 0.0188 0.8486 1.2709 1.7134 1.9954 2.2442




Modificado



IIIDelta c (Dc) Delta c (Dc) Delta c (Dc) Delta c (Dc) Delta c (Dc)

0 10 20 30 40 50 60 70 80 90

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Grafico Nº 03: Ajuste de Distribuciones de Probabilidad a la Precipitacion Maxima Diaria en la Estacion Tuluce

Column CColumn EColumn FDist. Gumbel ModificadoColumn EColumn H

PRECIPITACION MAXIMA EN 24 HORAS EN MM

PR

OB

AB

ILID

AD

AC

UM

UL

AD

A

44 de 46

45 de 46

SC-1 68,64 50,1SC-2 47,89 27,9

J1 116,53 76,4TRAMO 1 116,53 57,1

SC-3 58,91 49,6IC-1 7,50 9,2J2 182,94 96,9

TRAMO 2 182,94 82,2SC-5 36,69 21,7SC-4 15,60 35,5

J3 235,23 97,8TRAMO 3 235,23 96,0

SC-6 15,69 22,3SC-7 13,75 22,5

J4 264,67 95,8TRAMO 4 264,67 90,1

IC-2 12,91 11,9J5 277,58 90,6

Hydrologic Element

Drainage Area (Km2)

Peak Discharge (m3/s) TR = 50 Años

Tr = 5 Tr = 10 Tr = 20 Tr = 40 Tr = 50 Tr = 100Tabloran 25.4 A1 1.1 2.9 5.8 9.7 11 17.4Araypite 12.3 A2 5.5 8.1 11.6 16.4 18.4 26.1

Tab + Aray 37.7 A3 6.3 10.6 16.8 25 28.1 41.3SC-1 68.6 9.9 17.7 28.8 43.7 49.2 73.2SC-2 47.9 5.4 10.0 16.5 25.4 28.5 42.9J -1 116.5 A4 15.1 27.4 44.8 68.5 76.9 114.8

Reach-1 116.5 11.0 20.2 33.4 51.2 57.6 86.7SC-3 58.9 11.6 19.6 30.4 45.1 50.0 72.8IC-1 7.5 2.3 3.7 5.6 8.1 9.0 12.8J -2 182.9 A5 20.0 35.3 57.0 86.4 96.6 144.1

Reach-2 182.9 16.8 29.8 48.2 73.2 81.9 122.3SC-4 15.6 5.9 9.2 13.6 19.6 21.9 30.8SC-5 36.7 8.8 14.5 22.1 32.3 35.9 51.9J -3 235.2 A6 21.0 36.5 58.2 87.8 98.0 146.0

Reach-3 235.2 20.5 35.6 56.8 85.6 95.6 142.3SC-6 15.7 6.0 9.3 13.7 19.7 21.9 31.1SC-7 13.8 6.2 9.4 13.7 19.9 22.3 31.1J -4 264.7 A7 20.6 35.8 57.1 86.0 96.1 142.9

Reach-4 264.7 19.3 33.5 53.4 80.4 89.8 133.5IC-2 12.9 3.0 4.8 7.2 10.3 11.5 16.6J -5 277.6 A8 19.4 33.7 53.7 80.8 90.2 134.1

Hydrologic Element

Peak Discharge (m3/s)Drainage Area (Km2)

Point Aforo

PGumbel

T Qmax Qmax Qmax Qmax Qmax2 0.500 #REF! #REF! #REF! #REF!5 0.200 #REF! #REF! #REF! #REF! #REF!

10 0.100 #REF! #REF! #REF! #REF! #REF!20 0.050 #REF! #REF! #REF! #REF! #REF!25 0.040 #REF! #REF! #REF! #REF! #REF!50 0.020 #REF! #REF! #REF! #REF! #REF!

100 0.010 #REF! #REF! #REF! #REF! #REF!200 0.005 #REF! #REF! #REF! #REF! #REF!500 0.002 #REF! #REF! #REF! #REF! #REF!

1000 0.001 #REF! #REF! #REF! #REF! #REF!

0.2500 #REF! #REF! 0.0000 0.0000 #REF!

Período de Retorno


Distribución Log

Normal

Log Pearson III

Gumbel Modificado

Delta c (Dc) =

Documents

verificaciones Pmax. Huarmaca (2).xls