DATOS HIDROMETEOROLOGICOS DE LA ESTACIN

1. Datos generalesNombre de la estacin: AricotaDepartamento: TacnaProvincia: CandaraveDistrito: QuilahuaniFuente de informacin: Pagina de ANANmero de aos tomados para el clculo: 43 aos

2. Ubicacin geogrficaLatitud: 1720Longitud: 1724Altitud: 2825 msnm

De la pgina del ANA, se puede ver 7 estaciones en la cuenca Locumba; de las cuales las de color blanco, que son 6, ya no existen.

Podemos ver la ubicacin de la estacin ARICOTA, la cual se Encuentra cercana a la laguna ARICOTA.3. Tipo de cultivo

Cultivo: TrigoTiempo de cultivo: 5 mesesrea: 4000m2

4. Calculo de la Oferta hdrica

Para el clculo de la oferta hdrica se tom en cuenta 43 aos de datos hidrometeorologicos, con la cual se procedio a ordenar en forma descendente y hallar la frecuencia para cada uno de los 43 aos.

Se ubic la frecuencia perteneciente al 0.75 y se procedi a interpolar si fuera necesario.

AOQPROM-MENSUAL

EFMAMJJASOND

19631.602.531.081.251.251.241.101.171.371.181.151.38

19641.582.141.781.421.251.191.211.201.211.021.021.14

19651.002.061.051.001.051.191.091.001.121.041.080.99

19660.870.950.960.940.940.940.920.960.840.830.810.82

19670.792.504.461.501.141.071.030.920.980.910.860.84

19682.512.239.521.781.091.011.010.960.770.750.840.78

19691.033.022.650.870.780.780.810.980.730.690.680.68

19703.551.973.760.910.900.880.860.900.860.810.830.95

19711.745.303.191.001.021.040.940.920.990.780.760.75

19725.187.068.774.691.361.181.181.091.030.940.951.84

19734.719.438.445.461.760.971.101.161.041.000.942.56

19746.059.086.883.521.210.730.951.111.071.181.030.94

19754.469.028.466.381.710.920.861.631.401.160.842.91

19765.287.335.563.571.391.201.141.410.831.801.291.22

19773.609.876.914.951.031.031.241.571.071.070.892.23

19782.852.812.271.811.491.501.081.181.381.161.371.47

19791.552.391.551.621.301.141.221.461.421.140.982.43

19801.321.301.661.271.311.230.710.730.931.341.461.01

19812.016.203.181.701.250.931.140.820.810.980.841.15

19821.671.851.181.391.221.021.101.020.960.920.911.07

19831.271.641.260.861.211.040.740.940.820.980.971.32

19841.305.534.111.490.840.850.981.211.091.081.181.19

19852.148.655.091.681.080.990.961.041.001.130.921.28

19866.517.375.162.801.281.121.041.461.120.870.891.49

19878.405.673.272.191.051.031.041.091.120.900.841.30

19882.602.151.511.341.151.191.031.130.930.970.931.50

19892.533.623.842.241.191.201.181.161.191.000.991.21

19901.962.221.281.231.201.081.091.010.911.020.961.38

19912.202.732.091.631.211.151.131.060.970.981.091.13

19921.451.891.651.371.201.101.101.281.181.361.282.32

19934.612.132.551.521.711.811.731.841.621.661.471.51

19944.1611.002.641.871.661.711.631.541.551.201.121.29

19952.191.623.901.381.251.391.391.521.321.060.951.10

19961.923.412.621.331.211.181.261.351.150.920.910.95

19972.349.206.081.831.731.581.371.351.441.221.011.13

19983.112.241.161.241.301.511.341.251.121.011.011.12

19991.0511.8010.762.302.121.671.171.301.071.031.031.02

20002.677.385.711.911.621.611.481.531.231.060.920.89

20012.2417.6817.092.632.322.352.492.411.731.671.501.74

20022.005.369.284.513.252.874.133.561.582.011.611.57

20031.701.632.941.691.751.691.611.591.451.201.081.05

20041.954.392.141.541.481.621.831.971.591.281.221.12

20062.7210.2310.176.172.542.191.971.951.681.531.581.41

CALCULO DE PROBABILIDAD DE EXCEDENCIA DE CAUDALES

ORDENCAUDALES ORDENADOSFRECUENCIA

EFMAMJJASOND

18.4017.6817.096.383.252.874.133.561.732.011.612.912.27

26.5111.8010.766.172.542.352.492.411.681.801.582.564.55

36.0511.0010.175.462.322.191.971.971.621.671.502.436.82

45.2810.239.524.952.121.811.831.951.591.661.472.329.09

55.189.879.284.691.761.711.731.841.581.531.462.2311.36

64.719.438.774.511.751.691.631.631.551.361.371.8413.64

74.619.208.463.571.731.671.611.591.451.341.291.7415.91

84.469.088.443.521.711.621.481.571.441.281.281.5718.18

94.169.026.912.801.711.611.391.541.421.221.221.5120.45

103.608.656.882.631.661.581.371.531.401.201.181.5022.73

113.557.386.082.301.621.511.341.521.381.201.151.4925.00

123.117.375.712.241.491.501.261.461.371.181.121.4727.27

132.857.335.562.191.481.391.241.461.321.181.091.4129.55

142.727.065.161.911.391.241.221.411.231.161.081.3831.82

152.676.205.091.871.361.231.211.351.211.161.081.3834.09

162.605.674.461.831.311.201.181.351.191.141.031.3236.36

172.535.534.111.811.301.201.181.301.181.131.031.3038.64

182.515.363.901.781.301.191.171.281.151.081.021.2940.91

192.345.303.841.701.281.191.141.251.121.071.011.2843.18

202.244.393.761.691.251.191.141.211.121.061.011.2245.45

212.203.623.271.681.251.181.131.201.121.060.991.2147.73

222.193.413.191.631.251.181.101.181.121.040.981.1950.00

232.143.023.181.621.251.151.101.171.091.030.971.1552.27

242.012.812.941.541.221.141.101.161.071.020.961.1454.55

252.002.732.651.521.211.121.101.161.071.020.951.1356.82

261.962.532.641.501.211.101.091.131.071.010.951.1359.09

271.952.502.621.491.211.081.091.111.041.000.941.1261.36

281.922.392.551.421.211.071.081.091.031.000.931.1263.64

291.742.242.271.391.201.041.041.091.000.980.921.1065.91

301.702.232.141.381.201.041.041.060.990.980.921.0768.18

311.672.222.091.371.191.031.031.040.980.980.911.0570.45

321.602.151.781.341.151.031.031.020.970.970.911.0272.73

331.582.141.661.331.141.021.011.010.960.940.891.0175.00

341.552.131.651.271.091.010.981.000.930.920.890.9977.27

351.452.061.551.251.080.990.960.980.930.920.860.9579.55

361.321.971.511.241.050.970.950.960.910.910.840.9581.82

371.301.891.281.231.050.940.940.960.860.900.840.9484.09

381.271.851.261.001.030.930.920.940.840.870.840.8986.36

391.051.641.181.001.020.920.860.920.830.830.840.8488.64

401.031.631.160.920.940.880.860.920.820.810.830.8290.91

411.001.621.080.910.900.850.810.900.810.780.810.7893.18

420.871.301.050.870.840.780.740.820.770.750.760.7595.45

430.790.950.960.860.780.730.710.730.730.690.680.6897.73

Ubicamos la frecuencia del 75%, y as encontraremos los valores mensuales de Q75%

CAUDAL CONPROB DE EXCEDCAUDALES (m3/s)FREC.

EFMAMJJASOND

Q50%2.193.413.191.631.251.181.101.181.121.040.981.191.62

Q75%1.582.141.661.331.141.021.011.010.960.940.891.011.22

Q95%0.891.371.070.870.850.790.750.840.780.760.780.760.88

Entonces la oferta hdrica en MMC ser:OFERTA HIDRICA - ESTACION ARICOTA (PROBABILIDAD AL 75%)

MESEFMAMJJASONDPROM

Q (m3/s)1.582.141.661.331.141.021.011.010.960.940.891.011.22

VOL (MMC)4.235.184.453.443.052.642.712.712.492.522.312.713.20

5. Calculo de la DemandaPara el clculo de oferta hdrica se ha realizado con el mtodo de Blaney, en la cual se ha usado las siguientes expresiones para su clculo mensual.MesTEMP PROMC%p(15)%p(20)%p(17 20')KcKtU(mm/mes)

ENERO17.39.059.249.210.720.7882.75

FEBRERO17.27.988.098.080.930.7893.03

MARZO15.18.558.578.570.930.7184.95

ABRIL14.38.027.947.950.800.6863.84

MAYO19.18.027.857.870.580.8364.19

JUNIO13.67.657.437.460.000.660.00

JULIO10.17.957.767.790.000.550.00

AGOSTO16.508.158.038.050.720.7568.35

SEPTIEMBRE11.008.158.138.130.930.5857.89

OCTUBRE12.208.688.768.750.930.6269.04

NOVIEMBRE20.408.708.878.850.800.87108.01

DICIEMBRE14.309.109.339.300.580.6854.14

Para el cultivo de la ecuacin de Blaney:

MesENEROFEBMARZOABRILMAYOJUNIOJULIOAGSEPTOCTNOVDICIEM

Dias312931303130313130313031

U(mm/mes)82.7593.0384.9563.8464.190.000.0068.3557.8969.04108.0154.14

Area400040004000400040004000400040004000400040004000

Qu(m3/s)1.241.491.270.990.960.000.001.020.891.031.670.81

n (conduc. + aplicac.)0.480.480.480.480.480.480.480.480.480.480.480.48

Qbocatoma (m3/s)2.573.092.642.052.000.000.002.131.862.153.471.68

V(MMC)6.907.757.085.325.350.000.005.704.825.759.004.51

Entonces la demanda hdrica del proyecto para las 4000 Ha proyectadas es:DEMANDA HIDRICA DEL PROYECTO

MESENEROFEBMARZOABRILMAYOJUNIOJULIOAGSEPTOCTNOVDICIEM

VOLUMEN (MMC)6.90 7.75 7.08 5.32 5.35 0.00 0.00 5.70 4.82 5.75 9.00 4.51

6. Balance hdrico

BALANCE HIDRICO

ITEMEFMAMJJASONDTOTAL

DEMANDA TOTAL6.907.757.085.325.350.000.005.704.825.759.004.5162.18

OFERTA AL 75%4.23 5.18 4.45 3.44 3.05 2.64 2.71 2.71 2.49 2.52 2.31 2.62 38.34

BALANCE (MMC)-2.66 -2.58 -2.63 -1.88 -2.30 2.64 2.71 -2.99 -2.34 -3.24 -6.69 -1.89 -23.85

DEFICIT (MMC)-2.7-2.6-2.6-1.9-2.32.62.7-3.0-2.3-3.2-6.7-1.9-23.8

Haciendo el balance hdrico se determinara que el volumen til ser de:

VOLUMEN UTIL DEL EMBALSE (MMC)24.0

7. Clculo de caudales de avenidas

Para determinar los caudales de avenidas procederemos a establecer el modelo probabilstico que mejor represente el comportamiento hidrolgico, para esto usaremos la prueba de bondad de ajuste del chi cuadrado.

Factor de fuller

Caudal mximo instantneo

Numero de intervalos de clase

Amplitud del intervalo de clase

Amplitud intervalo de clase

Qmax25.81

Qmin1.40

Q4.88078817

Calculo del primer intervalo de clase

AOQPROM-MENSUALQmaxANUALQmaxINSTANT.

EFMAMJJASOND

19631.602.531.081.251.251.241.101.171.371.181.151.382.533.69

19641.582.141.781.421.251.191.211.201.211.021.021.142.143.12

19651.002.061.051.001.051.191.091.001.121.041.080.992.063.01

19660.870.950.960.940.940.940.920.960.840.830.810.820.961.40

19670.792.504.461.501.141.071.030.920.980.910.860.844.466.51

19682.512.239.521.781.091.011.010.960.770.750.840.789.5213.90

19691.033.022.650.870.780.780.810.980.730.690.680.683.024.41

19703.551.973.760.910.900.880.860.900.860.810.830.953.765.49

19711.745.303.191.001.021.040.940.920.990.780.760.755.307.74

19725.187.068.774.691.361.181.181.091.030.940.951.848.7712.80

19734.719.438.445.461.760.971.101.161.041.000.942.569.4313.77

19746.059.086.883.521.210.730.951.111.071.181.030.949.0813.26

19754.469.028.466.381.710.920.861.631.401.160.842.919.0213.17

19765.287.335.563.571.391.201.141.410.831.801.291.227.3310.70

19773.609.876.914.951.031.031.241.571.071.070.892.239.8714.41

19782.852.812.271.811.491.501.081.181.381.161.371.472.854.16

19791.552.391.551.621.301.141.221.461.421.140.982.432.433.55

19801.321.301.661.271.311.230.710.730.931.341.461.011.662.42

19812.016.203.181.701.250.931.140.820.810.980.841.156.209.05

19821.671.851.181.391.221.021.101.020.960.920.911.071.852.70

19831.271.641.260.861.211.040.740.940.820.980.971.321.642.39

19841.305.534.111.490.840.850.981.211.091.081.181.195.538.07

19852.148.655.091.681.080.990.961.041.001.130.921.288.6512.62

19866.517.375.162.801.281.121.041.461.120.870.891.497.3710.76

19878.405.673.272.191.051.031.041.091.120.900.841.308.4012.26

19882.602.151.511.341.151.191.031.130.930.970.931.502.603.80

19892.533.623.842.241.191.201.181.161.191.000.991.213.845.61

19901.962.221.281.231.201.081.091.010.911.020.961.382.223.24

19912.202.732.091.631.211.151.131.060.970.981.091.132.733.99

19921.451.891.651.371.201.101.101.281.181.361.282.322.323.39

19934.612.132.551.521.711.811.731.841.621.661.471.514.616.73

19944.1611.002.641.871.661.711.631.541.551.201.121.2911.0016.05

19952.191.623.901.381.251.391.391.521.321.060.951.103.905.70

19961.923.412.621.331.211.181.261.351.150.920.910.953.414.98

19972.349.206.081.831.731.581.371.351.441.221.011.139.2013.43

19983.112.241.161.241.301.511.341.251.121.011.011.123.114.54

19991.0511.8010.762.302.121.671.171.301.071.031.031.0211.8017.22

20002.677.385.711.911.621.611.481.531.231.060.920.897.3810.78

20012.2417.6817.092.632.322.352.492.411.731.671.501.7417.6825.81

20022.005.369.284.513.252.874.133.561.582.011.611.579.2813.55

20031.701.632.941.691.751.691.611.591.451.201.081.052.944.29

20041.954.392.141.541.481.621.831.971.591.281.221.124.396.40

20062.7210.2310.176.172.542.191.971.951.681.531.581.4110.2314.93

Promedio de valores agrupados Desviacin estndar de valores agrupadosKLinfer.Lsuper.MclaseZinfZsup

1-1.743.841.0511-1.8183-0.7545

23.849.426.6315-0.75450.3092

39.4215.0012.21150.30921.3730

415.0020.5917.8011.37302.4367

520.5926.1723.3812.43673.5005

626.1731.7528.9603.50054.5643

KZinfZsupF(Z)infF(Z)supe

1-1.8183-0.75450.030990.210847.73351.3797

2-0.75450.30920.210840.6402018.46230.6493

30.30921.37300.640200.9224512.13680.6755

41.37302.43670.922450.993523.05631.3835

52.43673.50050.993520.999800.26991.9755

63.50054.56430.999801.000860.04570.0457

6.1092

De la tabla de distribucin Chi cuadrado:Grado de libertad=6-2-1=3Nivel de significacin 5%Obtenemos el valor de 7.81

Conclusin:

Entonces el registro de caudales se ajusta a una distribucin normal de probabilidades con un nivel de significacin de 5%.

Calculo de f(z)123

ZF(Z)1-F(Z)ZF(Z)1-F(Z)ZF(Z)1-F(Z)

1.80.96780.70.77340.30.6368

1.81830.969006630.030993370.75450.789157810.2108421850.30920.640197260.35980274

1.90.97440.80.80230.40.6736

456

ZF(Z)1-F(Z)ZF(Z)1-F(Z)ZF(Z)1-F(Z)

1.30.91152.40.99292.60.996

1.37300.92244830.07755172.43670.993524680.0064753233.50051.00500503-0.00500503

1.40.92652.50.99462.70.997

6

ZF(Z)1-F(Z)ZF(Z)1-F(Z)

3.30.99963.30.9996

3.40.99970.00033.40.99970.0003

3.50050.99980054.56431.00086426

Aplicando Log normalSe procede a calcular el logaritmo natural de los mximos caudales instantneos, la cual denominaremos como Y: AOQmax.anualQmax.instY=Ln(Qm.inst)(Y-)2

19632.533.691.30560.3677

19642.143.121.13780.5994

19652.063.011.10190.6563

19660.961.40.33652.4824

19674.466.511.87330.0015

19689.5213.92.63190.5182

19693.024.411.48390.1833

19703.765.491.70290.0437

19715.37.742.04640.0181

19728.7712.82.54940.4063

19739.4313.772.62250.5048

19749.0813.262.58480.4525

19759.0213.172.57790.4434

19767.3310.72.37020.2100

19779.8714.412.66790.5714

19782.854.161.42550.2367

19792.433.551.26690.4161

19801.662.420.88381.0573

19816.29.052.20280.0845

19821.852.70.99330.8442

19831.642.390.87131.0831

19845.538.072.08820.0310

19858.6512.622.53530.3884

19867.3710.762.37580.2151

19878.412.262.50630.3532

19882.63.81.33500.3330

19893.845.611.72460.0352

19902.223.241.17560.5424

19912.733.991.38380.2790

19922.323.391.22080.4778

19934.616.731.90660.0000

19941116.052.77570.7459

19953.95.71.74050.0294

19963.414.981.60540.0940

19979.213.432.59750.4699

19983.114.541.51290.1593

199911.817.222.84610.8724

20007.3810.782.37770.2168

200117.6825.813.25081.7922

20029.2813.552.60640.4821

20032.944.291.45630.2077

20044.396.41.85630.0031

200610.2314.932.70340.6262

1.912019.5351

Con los valores de Y calculados se halla el promedio de estos valores

Por ultimo calculamos la desviacin estndar de los valores de Y

Calculo de los caudales de avenidas para 50, 100 y 500 aos:

Para periodo de retorno de 50 aos

De la tabla de distribucin normal: 0.9798182

0.982.0041

0.9842222.1

Remplazando en la expresin

Para periodo de retorno de 100 aos

De la tabla de distribucin normal: 0.9877762.2

0.992.2784

0.9906132.3

Remplazando en la expresin

Para periodo de retorno de 500 aos

De la tabla de distribucin normal: 0.9978142.8

0.9982.8312

0.9984112.9

Remplazando en la expresin

Aplicando gumbelComo el nmero de datos es 43 y es menor a 100, podemos hallar el de la siguiente tabla:

Interpolamos para el valor de 43 y obtenemos:

Calculo de las variables y :

Calculo de los caudales de avenidas para 50, 100 y 500 aos: Para 50 aos

Para 100 aos

Para 500 aos