EJEMPLO _ Lutz Scholz.xlsx

Hoja1ESTACION 3AOENEFEBMARABRMAYJUNJULAGOSETOCTNOVDICTOT1197238.4777.16208.7642.5514.940.448.1811.107.420.2156.3061.90527.422197363.19138.8875.78132.579.560.068.181.943.3424.7510.4352.32521.003197450.41113.9172.3319.0931.337.180.273.272.569.6541.4517.54368.994197547.93194.33130.2287.9157.6139.508.1823.097.8650.283.2731.21681.395197697.06116.55137.7470.2420.437.128.186.612.809.605.4917.28499.106197780.28117.27111.4683.361.7524.248.1811.107.833.123.618.91461.117197821.8048.69113.1954.2845.171.770.1611.100.553.2425.046.03331.018197981.6264.31188.7152.3017.295.398.1817.882.177.2625.040.55470.709198021.8430.1471.13121.3215.8210.107.2011.107.8643.0831.8838.67410.1410198139.76100.46153.2594.042.042.532.334.027.8629.9122.7017.99476.8911198224.5936.7817.4789.5735.461.151.250.4414.6395.8353.52153.01523.70121983270.4198.00173.39107.89122.2816.279.773.063.0620.8512.6434.34871.9613198430.53179.12156.1257.7117.007.9019.2931.2810.1854.577.4632.96604.1214198537.3551.9450.5412.2354.924.123.4111.813.6011.197.299.48257.8815198665.77143.0766.1678.756.854.445.0312.538.7216.2167.5127.70502.74161987100.9956.9979.98119.4720.975.5628.8614.355.8416.546.037.62463.20171988120.0272.3133.8094.9038.496.686.787.7723.9615.4617.8531.64469.66181989127.14177.33126.4261.8212.917.817.907.9910.9935.7834.5741.97652.6219199033.8666.2527.0591.4439.0314.039.029.119.4147.5062.8916.49426.0820199124.4878.27214.0718.2615.3611.8510.1422.2412.9313.1219.3215.21455.2421199213.1051.80133.2980.2878.6833.8711.2611.3611.4511.5411.6432.63480.90TOTAL1390.602013.572340.861569.99657.90212.01171.75233.14165.00519.69525.92655.4410455.88PROM66.2295.88111.4774.7631.3310.108.1811.107.8624.7525.0431.21497.9041.49PRECIPITACION EFECTIVA (PE)En ele sentido hidrologico se denomina precipitacion efectiva a una parte de la precipitacion total mensual que produce escorrentia

CALCULO DE LA Pe POR EL METODO DE LA FAO (Organizacin de las Naciones Unidas para la Agricultura y Alimentacion))

CUADRO No. 3.7

DISTRIBUCION DE LA PRECIPITACION EFECTIVAFORMULASPe = 0.8 * P - 25 (cuando P > 75 mm/mes )Pe = 0.6 * P - 10 (cuando P < 75 mm/mes )

VALOR DE PRECIPITACION PRECIPITACIONEFECTIVA0010020275Pe = 0.6 * P - 10 MAS DE 75Pe = 0.8 * P - 25 Fuente: F A O

CUADRO No. 3.8PRECIPITACION EFECTIVA MENSUAL

AOENEFEBMARABRMAYJUNJULAGOSETOCTNOVDICTOT197213.0836.73142.0015.532.000.000.002.000.000.0023.7827.14262197327.9186.1135.6281.060.000.000.000.000.004.852.0021.39259197420.2566.1233.402.008.800.000.000.000.000.0014.872.00147197518.76130.4679.1845.3324.5613.700.003.850.0020.170.008.73345197652.6468.2485.1932.142.260.000.000.000.000.000.002.00242197739.2268.8264.1741.690.004.550.002.000.000.000.000.0022019783.0819.2265.5522.5717.100.000.002.000.000.005.020.00135197940.3028.59125.9721.382.000.000.002.000.000.005.020.0022519803.118.0832.6872.062.002.000.002.000.0015.859.1313.20160198113.8655.3797.6050.240.000.000.000.000.007.943.622.0023119824.7512.072.0046.6511.280.000.000.002.0051.6622.1197.412501983191.3353.40113.7261.3172.832.000.000.000.002.512.0010.6051019848.32118.3099.8924.632.000.002.008.772.0022.740.009.77298198512.4121.1720.322.0022.950.000.002.000.002.000.000.0083198629.4689.4529.7038.000.000.000.002.000.002.0030.506.62228198755.8024.1938.9970.582.580.007.312.000.002.000.000.00203198871.0133.3910.2850.9213.090.000.000.004.382.002.008.99196198976.71116.8776.1427.092.000.000.000.002.0011.4710.7415.18338199010.3229.756.2348.1513.422.000.000.000.0018.5027.742.0015819914.6937.62146.252.002.002.002.003.342.002.002.002.0020819922.0021.0881.6339.2337.9410.322.002.002.002.002.009.58212TOTAL699.01125.01386.5794.5238.836.613.334.014.4167.7162.5238.6PROM33.2953.5766.0237.8411.371.740.631.620.687.997.7411.36233.8519.4984.6477.4973.5437.7710.107.134.5410.7320.4334.2548.5172.1140.1

19.5

COEFICIENTE DE AGOTAMIENTO

a = - 0.00252 Ln (A) + 0.026

a = Coeficiente de agotamientoA = Area de la subcuenca (km2)191.4km2191400000m2

a = 0.0128

RETENCION DE LA SUBCUENCA (Ri)

CUADRO 3.9(1)(2)(1) x (2)RETENCION POR LAS LAGUNA - PANTANOS Y NAPA FREATICA, CUENCA PRESA B-1

DESCRIPCIONAREA LAMINA ESPECIFICA VOLUMEN TOTAL(Km2)(mm/ao) (m3)Napa Freatica102500Lagunas y pantanos1.15500575000

Nevados9.14500

Total20.29575000

Ri = Volumen total (m3) / Area Cuenca (m2) =3.00mm/ao

575000/1914000000.003m=3.00mm

Esto es repartido en todo al subcuenca, al ao =3.00mm/ao

GASTO DE LA RETENCION (Gi )

go = e-a x 30

go = Descarga de la retencion del mes iniciala = Coeficiente de agotamiento0.0128

go =0.68197

gi = ( go) i

gi = Relacion de descarga del mes actual y del mes anteriori = Nmero de orden de los meses de la estacion seca, a partir de su inicio.

Los resultados de dicha relacion se ven en el Cuadro 3.10

Para el calculo del gasto de la retencion, de los meses de la estacion seca (abril - Setiembre) se aplica la siguiente relacin:

Gi = Ri x gi / Suma gi

Gi = Gasto de retencion mensual (mm/mes)


ABASTECIMIENTO DE LA RETENCION (Ai)

Para la cuenca alta del rio Grande (zona Ananea) de acuerdo a la geomorfologia los coeficientesde abastecimiento son 5%, 15%, 20%, 25%, 30% y 5% para los meses de Octubrea Marzo respectivamente.

La lmina de agua Ai, que ingresa a la reserva de la subcuenca se muestra en forma de deficit mensual de la precipitacion efectiva y se calcula con lasiguiente ecuacion:

Ai = ( ai x Ri )

Ai = Abastecimiento de la retencion mensual (mm)ai = Coeficiente de abastecimiento (%)Ri = Retencin de la subcuenca (m/ao)


CAUDAL MENSUAL PROMEDIO (CM)

Cmi = Pei + Gi - Ai

Cmi = Caudal de escorrenta mensual (mm/mes)Pei = Precipitacin efectiva (mm/mes)Gi = Gasto de la retencin (mm/mes)Ai = Abastecimiento de la retencin (mm/mes)


Dichos caudales estan expresados en mm, se transforman a m3/seg con la siguiente expresion:

Qi = 0.0115741 * ((Cmi x A) / ti)

factor: 0.0115741Qi = Caudal mensual (m3/seg)Cmi = Caudal de escorrentia mensual (mm/mes)A = Area de la subcuenca (Km2)ti = Tiempo del mes (das)


CUADRO No. 3.10

CAUDAL DE APORTACION AO PROMEDIO DE LA CUENCA DE RECEPCION DE LA PRESA B-1

PRECIPITACION (mm) CONTRIBUCION DE RETENCION Q. APORTACIONNo.MEDIA EFECTIVAGASTO ABASTECIMIENTOCmiQiDasMES(mm)(mm)giGiaiAi(mm/mes)(m3/seg)(mm/mes)(mm/mes)31ENE66.233.290.250.75132.5352.32528FEB95.953.570.300.90152.6714.16731MAR111.566.020.050.15065.8744.70730ABR74.837.840.68201.062338.8982.87231MAY31.311.370.46510.724412.0970.86430JUN10.11.740.31720.49402.2350.16531JUL8.20.630.21630.33690.9710.06931AGO11.11.620.14750.22981.8470.13230SET7.90.680.10060.15670.8410.06231OCT24.77.990.050.1507.8350.56030NOV25.07.740.150.4517.2890.53831DIC31.211.360.200.60110.7620.769TOTAL497.9233.851.9293.0041.0003.004233.85517.232

Promedio =41.4919.491.44

CUADRO 3.11

PARAMETROS DEL MODELO DE GENERACION PARA PERIODOPARA CALCULOS CON MODELO HIDROESTAEXTENDIDOSYX1X2X1X2YQtQt-1PEtQt-1PEtQt(mm)(mm)(mm)(mm)(mm)(mm)32.53510.76233.2910.76233.2932.53552.67132.53553.5732.53553.5752.67165.87452.67166.0252.67166.0265.87438.89865.87437.8465.87437.8438.89812.09738.89811.3738.89811.3712.0972.23512.0971.7412.0971.742.2350.9712.2350.632.2350.630.9711.8470.9711.620.9711.621.8470.8411.8470.681.8470.680.8417.8350.8417.990.8417.997.8357.2897.8357.747.8357.747.28910.7627.28911.367.28911.3610.762233.855233.855233.85233.855233.855233.855

Nota : se ha usado el metodo FAO para el calculo de la Precipitacion Efectiva (PE)

CAUDALES MENSUALES GENERADOS METODO DE LUTZ

La generacion de caudales mensuales de la subcuenca en el punto de interes, se calculamediante el modelo hidrologico que consiste en una combinacion de un procesoCuadro No. 3.12: Resultados de la Regresin Multiple entre Qt, Qt-1 y PEt MARKOVIANO de primer orden con una variable de impuldo, que en este caso es Usando MODELO HIDROESTAla PRECIPITACION EFECTIVA, la ecuacin es la siguiente:

Qt = B1 + ( B2 * Qt-1 ) + ( B3 * PEt ) + ( S * ( 1 - R2 )1/2 * Z )

Qt = Caudal del mes t (mm/mes)Qt-1 =Caudal del mes anterior (mm/mes)Pet =Precipitacin efectiva del mes t (mm)B1 = Factor constante (caudal base)B2 , B3 =Constante de la regresinS = Desviscion estndarR = Coeficiente de RegresinZ = Variable aleatorio con media = 0 y variazncia 2

Los valores B1, B2, B3, S y R, se determinan a partir de la ecuacin de regresin linealMultiple con los valores de Qt, Qt-1 y Pet, que figuran en el CUADRO 3.11

B1 =-0.01590.0141417821B2 =0.0344B3 =0.9666S =1.6594R =0.9999

Con estos valores se conformo la ecuacion general para generar los caudales mensualesen la subcuenca del ro Cunas, siendo la siguiente:

Qt = -0.0159 + ( 0.03344 * Qt-1 ) + ( 0.9666 * PEt ) + ( 1.6594 * ( 1 - (0.9999)2 )1/2 * Z )

Qt = -0.0159 + ( 0.03344 * Qt-1 ) + ( 0.9666 * PEt ) + ( 0.0141418 * Z )

Los valores de la variable a leatoria ( Z ) se ven en el Cuadro 3.13

CUADRO 3.13

GENERACION DE NUMEROS ALEATORIOS NORMALES CON MEDIA = 0 Y VARIANCIA = 1GENERACION DE NUMEROS ALEATORIOS NORMALES CON MEDIA = 0 y DESVEST = 1 CON EXCEL AOENEFEBMARABRMAYJUNJULAGOSETOCTNOVDIC119720.5658-0.2931-0.2501-2.1201-0.1886-0.9150-0.70520.8240-0.54350.5390-1.49440.625521973-0.43200.4082-1.52081.71750.45750.36001.5040-0.4123-0.72540.8481-1.39800.2546319740.14611.15420.35251.0209-0.4771-0.30832.28250.3070-0.5592-0.65311.72391.885841975-0.59410.7054-0.50630.18471.07290.94200.5398-0.1221-0.33940.71600.9592-0.512151976-2.1172-0.03510.66482.43500.1980-1.1310-0.7668-0.83140.0173-0.5929-1.05110.9404619771.50860.29850.5327-1.3996-0.1830-0.5435-0.15941.32531.40410.61021.28220.4572719780.5964-0.7767-2.26520.6046-1.8486-1.59610.82370.78050.8528-0.04430.38120.696481979-0.1098-0.67910.8690-2.8440-0.6268-1.6734-1.03710.03221.10290.3100-2.6680-1.1443919800.75310.9112-1.2001-0.6788-0.3973-0.3322-0.1834-1.0925-1.73140.47180.9692-0.6099101981-0.1244-0.20630.14100.99071.5693-1.0064-0.50831.1825-0.32491.25331.2009-1.22641119820.67110.5002-0.29221.5788-0.6854-0.74470.34010.78050.00440.1611-1.6391-1.47411219830.18701.12490.1879-1.0527-0.0233-0.19540.8396-0.13070.75660.36232.7137-1.41991319841.1340-0.1403-0.9667-0.61051.09810.55080.77760.8208-0.2432-1.1742-0.32900.8775141985-0.6797-0.91790.2882-0.7345-0.48420.4279-1.3889-1.25400.4059-0.4608-0.4960-1.6548151986-0.5719-1.5947-0.4727-0.5825-0.8718-0.2014-0.5825-0.64710.15810.4782-0.0957-0.0361161987-0.0055-0.7123-1.2496-0.0538-0.81240.3845-0.2331-0.0904-1.4703-1.1566-0.67880.8816171988-0.13320.43180.95800.64850.46520.60861.1890-0.3915-0.97750.25290.2040-0.13771819891.3760-0.36811.0406-0.52950.04160.3107-0.83560.65261.14101.51790.66620.65481919900.4427-2.74880.19361.34811.60240.2958-1.1548-2.14920.43240.04460.5178-1.95072522019910.68472.54310.92870.5270-0.2361-0.04550.1488-0.5899-0.86221.7297-0.1635-0.61702119920.7236-0.2235-0.92091.38030.3054-0.99191.1633-0.45080.9634-0.49790.64440.8922Media =-0.0Desvest =1.0

Qt = -0.0159 + ( 0.03344 * Qt-1 ) + ( 0.9666 * PEt ) + ( 0.0141418 * Z )

CUADRO No. 3.14

CAUDALES MENSUALES GENERADOS EN LA ZONA DE UBICACIN DE LA PRESA B1 , RIO GRANDE - ANANEA (mm/mes) AOENEFEBMARABRMAYJUNJULAGOSETOCTNOVDICTOTAL10.762197213.0135.48137.2414.951.911.050.531.940.47-0.0022.9426.23253.49197327.8691.9534.3878.37-0.01-0.010.021.120.514.691.8820.67261.44197420.2772.9232.271.948.481.130.04-0.010.575.9814.401.96159.95197518.17131.6176.5043.8123.7513.25-0.003.710.6119.490.018.41339.31197651.1177.6282.3531.112.171.200.531.19-0.026.295.671.94261.16197738.0075.4962.0240.258.704.370.531.950.02-0.000.01-0.01231.3319782.9726.5063.2921.8116.471.300.001.940.006.614.850.00145.75197938.9332.62121.7620.581.901.420.531.920.01-0.014.788.17232.6219803.2815.8231.5469.621.911.910.531.890.6615.328.8312.73164.04198113.8159.1494.3348.570.021.550.530.010.757.693.511.89231.8019824.6619.631.9145.1210.871.66-0.010.001.9249.9221.3294.11251.111983188.1660.27109.9159.2270.381.910.001.270.002.421.9810.20505.7219848.40131.7296.5223.771.94-0.001.948.481.9121.945.989.45312.06198512.2931.1619.631.9022.16-0.010.811.89-0.011.916.288.60106.61198628.7590.0828.6836.708.271.760.811.90-0.011.9329.476.38234.71198754.1431.4337.6468.212.46-0.017.051.920.801.896.600.00212.12198868.6239.569.9449.2212.65-0.000.011.344.191.921.928.67198.05198974.46119.7573.6126.161.92-0.010.96-0.001.9411.1010.3814.67334.95199010.4740.206.0146.5612.991.921.041.42-0.0117.8726.819.07174.3519914.8442.40141.381.931.911.921.923.201.901.961.911.90207.1719922.0027.4878.8737.9336.679.941.941.911.941.911.939.26211.78SUMA TOT684.221252.821339.78767.72247.5346.2519.7138.9718.17180.82181.46254.31PROM32.5859.6663.8036.5611.792.200.941.860.878.618.6412.11

No dias312831303130313130313031horas242424242424242424242424min606060606060606060606060seg606060606060606060606060Factor (seg)267840024192002678400259200026784002592000267840026784002592000267840025920002678400Area cuenca191.4km2

CUADRO No. 3.15

CAUDALES MENSUALES GENERADOS EN LA ZONA DE UBICACIN DE LA PRESA B1 , RIO GRANDE - ANANEA (m3/seg) AOENEFEBMARABRMAYJUNJULAGOSETOCTNOVDICPROM19720.932.549.811.070.140.080.040.140.03-0.001.641.871.5219731.996.572.465.60-0.00-0.000.000.080.040.340.131.481.5619741.455.212.310.140.610.080.00-0.000.040.431.030.140.9519751.309.405.473.131.700.95-0.000.260.041.390.000.602.0219763.655.555.882.220.160.090.040.09-0.000.450.410.141.5619772.725.394.432.880.620.310.040.140.00-0.000.00-0.001.3819780.211.894.521.561.180.090.000.140.000.470.350.000.8719792.782.338.701.470.140.100.040.140.00-0.000.340.581.3919800.231.132.254.980.140.140.040.140.051.090.630.910.9819810.994.236.743.470.000.110.040.000.050.550.250.131.3819820.331.400.143.220.780.12-0.000.000.143.571.526.721.50198313.454.317.854.235.030.140.000.090.000.170.140.733.0119840.609.416.901.700.14-0.000.140.610.141.570.430.681.8619850.882.231.400.141.58-0.000.060.13-0.000.140.450.610.6319862.056.442.052.620.590.130.060.14-0.000.142.110.461.4019873.872.252.694.870.18-0.000.500.140.060.140.470.001.2619884.902.830.713.520.90-0.000.000.100.300.140.140.621.1819895.328.565.261.870.14-0.000.07-0.000.140.790.741.051.9919900.752.870.433.330.930.140.070.10-0.001.281.920.651.0419910.353.0310.100.140.140.140.140.230.140.140.140.141.2319920.141.965.642.712.620.710.140.140.140.140.140.661.26

PROM2.334.264.562.610.840.160.070.130.060.620.620.871.43MAXIMO13.459.4110.105.605.030.950.500.610.303.572.116.723.01MINIMO0.141.130.140.14-0.00-0.00-0.00-0.00-0.00-0.000.00-0.000.63Nota : Metodo LUTS SCHOTZ. Se usa el metodo de la FAO para el clculo de la Precipitacion Efectiva (PE)

6.06.65.63.62.00.160.100.160.082.7

MesPromQmaxQminE2.3313.450.14F4.269.411.13M4.5610.100.14A2.615.600.14M0.845.03-0.00J0.160.95-0.00J0.070.50-0.00A0.130.61-0.00S0.060.30-0.00O0.623.57-0.00N0.622.110.00D0.876.72-0.00promed1.434.860.13

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EJEMPLO _ Lutz Scholz.xlsx