Hidrologia, Pruebas de Bondad de Ajuste Chi Cuadrado

 

N 1 2 3 4 5 6

Pmax 37.00 33.50 33.20 31.20 28.80 28.40

7 8 9 10 11 12 13 14 15 16 17 18

28.00 27.20 24.60 24.00 24.00 23.40 23.20 22.40 22.00 21.10 20.00 20.00

1.447 1.435 1.391 1. 1.380 1. 1.380 1.369 1.365 1.350 1.342 1.324 1.301 1.301

19 20 21 22 23 24 25 26

19.50 19.50 18.80 17.50 17.20 17.00 14.20 13.60

1.290 1.290 1.274 1.243 1.236 1.230 1.152 1.134

N

LOG(Pmax) 1.568 1.525 1.521 1.494 1.459 1.453

 

1 2 3 4 5 6  

DISTRIBUCION DE FRECUENCIAS Valor maximo Valor minimo Rango Nro de datos Nro intervalos

a) Medidas de tendencia central: µ= 23.434615385 n= 26

b) Medidas de dispersion Desviacion estandar:

Sx= 6.04522570 57068

c) Medida de simetria y asimetria:

Coeciente de sesgo:

k=

5.333

∆x=

4.68

∆x/2=

2.34

Amplitud de Intervalos

PARAMETROS ESTADISTICOS Valores normales Precipitaciones x= P [mm]

Media aritmeca: Candad de valores:

Intervalos de clase Inferior (LI) Superior (LS) 11.26 15.94 15.94 20.62 20.62 25.3 25.3 29.98 29.98 34.66 34.66 39.34

Cs= 0.50355663 66322 f(x): con sesgo a la derecha

 

Marcas cas de Frecuenci Frecue ncia a Frecue Fre cuenci ncia a Mar Clase Cla se (LI (LI+LS +LS)/ )/2 2 Abs Absolu oluta ta Absolu Absoluta ta Acu Acum. m. 13.60 2 2 18.28 8 10 22.96 8 18 27.64 4 22 32.32 3 25 37.00 1 26

37 13.6 23.4 26 6

(R/(k-1))/2

>Xmin

2.34 SI: R/k 3.9

13.6   NO: R/(k-1) 4.68

NO CUMPLE

PARAMETROS ESTADISTICOS Valores normales Precipitaciones

Yi= LO LOG(P [mm])

a) Medidas de tendencia central: Media aritmeca: Candad de valores:

µ= 1.35604313 n= 26

b) Medidas de dispersion Desviacion estandar:

Sx= 0.1120636

c) Medida de simetria y asimetria:

Coeciente de sesgo:

Cs= -0.03977509 f(x): con sesgo a la izquierda

 

NORMAL µ= Sx= Si Sign gni ica canc ncia ia= =

N°

 

1 2 3 4 5 6

23.435 6.045 0. 0.05 050 0 Interv Inte rval alos os de cl clas ase e Inferior Superior 11.26 15.94 20.62 25.3 29.98 34.66

15.94 20.62 25.3 29.98 34.66 39.34

Marcas Marc as de Ꝋi:Frecuencia Clase Absoluta 13.6 18.28 22.96 27.64 32.32 37

2 8 8 4 3 1

Zinf  -2.01 -1.24 -0.47 0.31 1.08 1.86

Grados de libertad Nro parametros

Tabla chi Ingresamos:

v=k-1-m m= v=

v= sign signi ica canc ncia ia:: X²=

2 3

3 0. 0.05 05 7.81

 

D=xt) 1-P(X>=xt) 0.99009901 0.0099 0.9009009 0.0991 0.5 0.5000 0.2 0.8000 0.1 0.9000 0.04 0.9600 0.02 0.9800 0.01 0.9900 0.0001 0.9999

 

α= β=

z -2.33 -1.29 0.00 0.84 1.28 1.75 2.05 2.33 3.72

0.18123393 20.490575

P(X>=xt) 1-P(X>=xt) 0.99009901 0.0099 0.9009009 0.0991 0.5 0.5000 0.2 0.8000 0.1 0.9000 0.04 0.9600 0.02 0.9800 0.01 0.9900 0.0001 0.9999

P [mm] 12.052 15.867 22.513 28.767 32.907 38.139 42.020 45.873 71.310

P [mm] 12.443 16.287 22.701 28.207 31.598 35.664 38.565 41.375 59.267

 

k= m= n= b=

821.751 0.211 0.803 5.614

T [Años] 2 5 10 25 50 100 promedio

_=/

I: T: D:

5 102. 102.76 7686 8637 37 124. 124.68 6883 8367 67 144. 144.32 3255 5566 66 175. 175.10 1090 9057 57 202. 202.68 6870 7021 21 234. 234.60 6082 8243 43

 

10 79 79.4 .480 8058 5848 48 96 96.4 .433 3315 1594 94 11 111. 1.62 6204 0439 39 135 135.4 .428 28188 188 15 156. 6.75 7568 6802 02 181.4 181.444 44465 465

15 65.9 65.9967 96779 792 2 80.0 80.0733 73365 657 7 92.6 92.6841 84137 374 4 112. 112.452 45292 924 4 130.1 130.1631 6316 6 150. 150.662 66258 584 4

Intensidad de precipitacio Periodo de retorno [a;os Duracion [min]

30 45.3 45.3700 70000 005 5 55. 55.04 04705 70596 96 63.71 63.71643 6433 3 77.3 77.3066 06639 398 8 89.4 89.4816 81679 793 3 103.574 103.57416 168 8

DURACION [mi 45 60 35 35.3 .3958 95809 094 4 29.359 29.35998 989 9 42 42.9 .9454 45453 531 1 35. 35.62 62224 22404 04 49 49.7 .7089 08941 418 8 41 41.2 .2323 32394 948 8 60.3 60.3114 11462 625 5 50.0 50.0269 26935 357 7 69 69.8 .8099 09927 279 9 57 57.9 .9056 05688 886 6 80.80 80.80430 43086 86 67.0 67.0252 25268 681 1

30 0.347 0.347 0.347 0.347 0.347 0.347 0.34711 0.3471137 37

COEFICIENTE Kd DURACION [mi 45 60 0.406 0.449 0.406 0.449 0.406 0.449 0.406 0.449 0.406 0.449 0.406 0.449 0.4062057 0.40620575 5 0.4492507 0.44925079 9

_=(_^)/(_25^ _=(_^)/(_25^ )

T [Años] 2 5 10 25 50 100 PROMED PRO MEDIO IO

0.131 0.131 0.131 0.131 0.131 0.299 0.1590 0.15906114 6114

DESV. EST.

0.06863126

5

GUMBEL

 

N 1 2 3 4

T [años] 1.01 1.11 2 5

5 6 7

10 25 50

10 15 0.203 0.252 0.203 0.252 0.203 0.252 0.203 0.252 0.203 0.252 0.203 0.252 0.2026 0.20269487 9487 0.25246 0.25246182 182 0

α= β=

0

0

0

0.18123393 20.490575

P(X>=xt) 1-P(X>=xt) 0.99009901 0. 0.0099 0.9009009 0.0991 0.5 0.5000 0.2 0.8000 0.1 0.04 0.02

0

0.9000 0.9600 0.9800

P [mm] 12.052 15.867 22.513 28.767 32.907 38.139 42.020

 

T [Años] 2 5 10 25 50 100

 

8 9

100 10000

0.01 0.0001

0.9900 0.9999

45.873 71.310

100

90

80

70

    ]    r    H     /    m    m     [    D    A    D    I    S    N    E    T    N    I

60

50

40

30

20

10

0

0

 

 [mm/hr]

 

=(821.751∗^0.211)/ (^0.803+5.614)

n] 120 18.1719898 22.0479302 25.5202635 30.9635321 35.8399855 41.4844326

180 13.52516509 16.4099749 18.99438541 23.04573627 26.67521428 30.87629956

360 8.02549358 9.73726733 11.2707917 13.6747616 15.8284028 18.3212214

720 4.6947835 5.69614336 6.59323021 7.99951361 9.25935875 10.7176172

1440 2.72305114 3.30385622 3.82418125 4.6398486 5.37057937 6.21639308

120 180 360 720 0.556 0.621 0.737 0.862 0.556 0.621 0.737 0.862 0.556 0.621 0.737 0.862 0.556 0.621 0.737 0.862 0.556 0.621 0.737 0.862 0.556 0.621 0.737 0.862 0.55 556 611606 0.62 620 086444 446 6 0.7368107 077 7 0.8620446 468 8

1440 1.000 1.000 1.000 1.000 1.000 1.000 1

T [Años] 2 5 10 25 50 100

  n]

0

0

0

0

0

PRECIPITACION MEJOR DISTRIBUCION DURACION [min] 5 10 15 30 45 60 120 180 3.58092664 3.5809 2664 4.563248321 5.68364638 5.68364638 7.81453404 7.81453404 9.14486734 9.14486734 10.1139357 10.1139357 12.5197823 12.5197823 13.9774558 13.9774558 4.5756 4.5 756863 863 5.8308 5.83089096 90966 6 7.2625 7.26252879 2879 9.98536 9.9853641 41 11.6852 11.6852559 559 12.9235 12.9235255 255 15.9977 15.9977018 018 17.8603 17.8603081 081 5.2343 5.2 3430375 0375 6.67018069 6.670180698 8 8.3078 8.30788633 8633 11.422 11.4226425 6425 13.3672 13.3672142 142 14.7837 14.7837185 185 18.3003 18.300387 87 20.4310 20.4310942 942 6.06646864 6.0664 6864 7.73062 7.7306255 55 9.62869 9.62869836 836 13.238 13.2386475 6475 15.49 15.492372 23729 9 17.134077 17.1340772 2 21.2098 21.209836 36 23.67928 23.6792892 92 6.68381609 6.6838 1609 8.517324032 10.6085522 10.6085522 14.5858638 14.5858638 17.0689371 17.0689371 18.8777076 18.8777076 23.3682314 23.3682314 26.0889858 26.0889858 7.29660515 7.2966 0515 9.298213706 11.5811709 11.5811709 15.9231325 15.9231325 18.6338601 18.6338601 20.6084633 20.6084633 25.5106896 25.5106896 28.4808896 28.4808896

 

CUR T= 2 a ños

10

20

30

T= 5 años

40

T= 10 años

 

5 8.5640 8.5 6405309 5309 10.3906973 10.390 6973 12.027 12. 0271305 1305 14.5924214 14.592 4214 16.890 16. 890585 585 19.550687 19.550 687

10 13.24676 13.2467641 41 16.0721932 16.0721932 18.603 18.6034064 4064 22.5713646 22.5713646 26.12 26.12613 61337 37 30.2407442 30.2407442

15 16.499 16.4991948 1948 20.0183414 20.0183414 23.171 23.1710344 0344 28.1132311 28.1132311 32. 32.5407 54079 9 37.6656461 37.6656461

30 22.68500 22.6850002 02 27.5235298 27.5235298 31.858 31.8582165 2165 38.6533199 38.6533199 44.7408 44.7408396 396 51.7870842 51.7870842

PRECIPITACION [mm] DURACION [min] 45 60 120 26.5468 26.546857 57 29.3599 29.359989 89 36.3439 36.3439795 795 32.2090898 32.2090898 35.6222404 35.6222404 44.0958604 44.0958604 37.2817 37.2817064 064 41.2323 41.2323948 948 51.0405 51.040527 27 45.2335969 45.2335969 50.0269357 50.0269357 61.9270642 61.9270642 52.35 52.357445 74459 9 57.90568 57.9056886 86 71.6799 71.679971 71 60.6032314 60.6032314 67.0252681 67.0252681 82.9688652 82.9688652

180 40.575495 40.5754953 3 49.2299247 49.2299247 56.9831 56.9831562 562 69.1372088 69.1372088 80.0256 80.0256428 428 92.6288987 92.6288987

360 720 72 1440 16.5877431 19.407121 22.5128946 21.1957173 24.7983013 28.7668399 24.2465972 28.3677317 32.9074958

T [Años] 2 5 10

5 10 42.9711197 27.3794899 54.9082356 34.9853458 62.811645 40.0210842

28.101392 32.8777165 38.1392256 30.961099 36.2234809 42.0204216 33.7996904 39.5445407 45.8729594

25 50 100

72.7976237 46.383753 80.2057931 51.1039442 87.5592618 55.7892822

 

A I-D-F  

T= 25 años

50 T [años]

T= 50 años

60

T= 100 años

70

80

 

360 48.1529615 48.152 9615 58.423604 58.423 604 67.62475 67.6247 5 82.0485697 82.048 5697 94.9704167 94.970 4167 109.927328 109.92 7328

720 56.3374019 56.3374019 68.3537203 68.3537203 79.1187626 79.1187626 95.9941634 95.9941634 111.112305 111.112305 128.611406 128.611406

1440 65.3532273 65.3532273 79.2925493 79.2925493 91.7803501 91.7803501 111.356366 111.356366 128.893905 128.893905 149.193434 149.193434

INTENSIDAD [mm/hr] MEJOR DISTRIBUCION DURACION [min] 15 30 45 60 120 180 360 720 22.7345855 22.734 5855 15.6290681 15.6290681 12.1931565 12.1931565 10.1139357 10.1139357 6.25989116 6.25989116 4.65915195 4.65915195 2.76462385 2.76462385 1.61726009 1.61726009 29.0501152 29.050 1152 19.9707282 19.9707282 15.5803412 15.5803412 12.9235255 12.9235255 7.99885088 7.99885088 5.95343603 5.95343603 3.53261955 3.53261955 2.06652511 2.06652511 33.231 33. 2315453 5453 22.845 22.845285 285 17.822 17.8229522 9522 14.783 14.7837185 7185 9.15019 9.15019352 352 6.81036 6.81036472 472 4.04109 4.04109953 953 2.36397 2.36397764 764 38.5147934 38.514 7934 26.477 26.4772951 2951 20.656 20.6564972 4972 17.134 17.1340772 0772 10.6049 10.604918 18 7.89309 7.89309639 639 4.68356 4.68356533 533 2.73980 2.73980971 971 42.4342087 42.434 2087 29.1717276 29.1717276 22.7585827 22.7585827 18.8777076 18.8777076 11.6841157 11.6841157 8.69632859 8.69632859 5.16018317 5.16018317 3.01862341 3.01862341 46.324 46. 3246836 6836 31.846 31.846265 265 24.845 24.8451468 1468 20.608 20.6084633 4633 12.7553 12.7553448 448 9.49362 9.49362985 985 5.63328 5.63328173 173 3.29537 3.29537839 839

 

90

100

 

1440 0.93803727 1.19861833 1.37114566 1.5891344 1.7508509 1.91137331