ULADECH CURSO: HIDROLOGIA

ULADECHCURSO: HIDROLOGIA

TEMA: ANALISIS DE CONSISTENCIA DE DATOS HIDROLOGICOS

DOCENTE: ING GILBER GONZALES LIZARME

ANALISIS DE CONSISTENCIA DE DATOS HIDROLOGICOS

La inconsistencia de una serie de tiempo hidrolgica, est dada por la produccin de errores sistemticos (dficit en la toma de datos, cambio de estacin de registro o cambio de ubicacin de la estacin hidromtrica, etc.); y la no homogeneidad es una serie de tiempo hidrolgica, se debe a factores humanos (tala indiscriminada de una cuenca, construccin de estructuras hidrulicas, etc.) o a factores naturales de gran significancia como los desastres naturales. Esta inconsistencia y no homogeneidad se manifiesta con la presencia de saltos y/o tendencias en las series, afectando las caractersticas estadsticas de dichas series, tales como la media, desviacin estndar y correlacin serial. Villn [27].

ANALISIS DE SALTOS

Los saltos son formas determinsticas transitorias que permiten a una serie hidrolgica peridica o no peridica pasar desde un estado a otro, como respuesta a cambios hechos por el hombre debido al continuo desarrollo de los recursos hdricos en la cuenca o a cambios naturales que pueden ocurrir. Aliaga [3], ejemplo: deficiencia y error en la toma de datos de las estaciones hidromtricas, cambio de la ubicacin de la estacin, cambio en la posicin de la instrumentacin de recopilacin de datos.

1. IDENTIFICACIN.

La identificacin del salto tiene por objeto detectar la presencia del mismo y evaluar la causa que puede ser por errores naturales u ocasionados por la intervencin de la mano del hombre. La identificacin se realiza mediante la combinacin de los siguientes criterios:

Anlisis Visual de la Serie Histrica.

Esta fase consiste en analizar visualmente la distribucin temporal de toda la informacin, mediante el anlisis visual de la serie histrica es posible detectar regularidades como irregularidad de los mismos. Se debe aclarar que este anlisis es nicamente con fines de identificacin de las posibles inconsistencias, las mismas que debern ser evaluadas estadsticamente mediante el test respectivo. Aguirre [1].

HIDROGRAMAS DE CAUDALES HISTORICOS1956 a 1995 m3/s

CONDORCERRO195619561956195619561956195619561956195619561956195719571957195719571957195719571957195719571957195819581958195819581958195819581958195819581958195919591959195919591959195919591959195919591959196019601960196019601960196019601960196019601960196119611961196119611961196119611961196119611961196219621962196219621962196219621962196219621962196319631963196319631963196319631963196319631963196419641964196419641964196419641964196419641964196519651965196519651965196519651965196519651965196619661966196619661966196619661966196619661966196719671967196719671967196719671967196719671967196819681968196819681968196819681968196819681968196919691969196919691969196919691969196919691969197019701970197019701970197019701970197019701970197119711971197119711971197119711971197119711971197219721972197219721972197219721972197219721972197319731973197319731973197319731973197319731973197419741974197419741974197419741974197419741974197519751975197519751975197519751975197519751975197619761976197619761976197619761976197619761976197719771977197719771977197719771977197719771977197819781978197819781978197819781978197819781978197919791979197919791979197919791979197919791979198019801980198019801980198019801980198019801980198119811981198119811981198119811981198119811981198219821982198219821982198219821982198219821982198319831983198319831983198319831983198319831983198419841984198419841984198419841984198419841984198519851985198519851985198519851985198519851985198619861986198619861986198619861986198619861986198719871987198719871987198719871987198719871987198819881988198819881988198819881988198819881988198919891989198919891989198919891989198919891989199019901990199019901990199019901990199019901990199119911991199119911991199119911991199119911991199219921992199219921992199219921992199219921992199319931993199319931993199319931993199319931993199419941994199419941994199419941994199419941994199519951995199519951995199519951995199519951995166.12216.11356.27366.02105.6864.3945.1745.8946.0571.51000000000000566.8774.62116.7139.54295.32538.79999999999995135.0500000000000195.9259.8453.4862.9786.9566.900000000000006119.73136.97999999999999195.25289.98239.8880.68000000000000758.2947.8648.4276.01000000000000595.97108.91124.39132.19999999999999137.19336.44252.8283.5661.9548.5650.6150.6891.695.14191.83194.27243.15318.95999999999998314.97000000000003117.868.1349.5648.9648.3461.1997.18102.39233.18197.44390.16313.06114.7282.0642.0439.9755.861.09166.9288253.58241.34515.44000000000005370.23106.2972.5656.2653.967.70999999999999459.6881.40000000000000687.4153.96291.64999999999998471.65290.62100.7753.4942.342.0248.7963.55130.15237.5196.47252.72312.22000000000003277.68118.7961.5665.4147.6844.3573.94103.64144.05000000000001115.43126.65415.48223.697.2350.3342.1344.8334.1795.0499.02139.99235.32208.38176.72124.5289.9857.3953.5452.0457.34115.66125.78124.4185.49168.32499.4173.2796.0460.4649.7547.5349.31116.63102.37110.08136.71143.38999999999999180.28109.0363.1446.6133.22999999999999737.3950.3282.4494.76100111.05137.76212.72216.1610068.5851.7449.5353.2185.85106.32150.51254.79171.61184.54224.4677.51000000000000559.4548.152.7766.25104.42164.89285.66000000000003344.96294.38811.19483.22126.0689.6959.7453.3560.9584.5966.8764.8172.49262.41000000000003511.84548.0700000000000596.5451.7467.8360.1760.5570.7893.52134.58000000000001220.6295.85000000000002403.18415.39158.9199999999999984.4868.9761.372.040000000000006131.69999999999999164.83233298.89224.81412.72253.9699.9876.40000000000000657.8752.4468.23999999999999598.04229.84431.27228.83235.39377.61324.5899999999999797.7171.6652.551.8966.7795.04160.97276.75232.62304.99352.13166.2573.8963.3348.4343.7146.2468.2275.5385.92159.71424.44297.8186.6993.7668.68000000000000752.0453.2453.8666.73113.72127111.81192.81152.44124.3285.0357.7753.4345.463.5564.7893.34108.76128.86000000000001226.86386.26195.2496.4461.6450.4249.5557.5968.6693.77104.39117.39128.93118.26117.6753.6648.263739.2967.510000000000005102.68128.33000000000001221.14159.38477.12394.02177.7486.7566.8654.7347.5944.0989.26171.02195.03175.78316.33190.04192.7897.7465.5648.8743.0448.69107.13181.83257.07338.18202.61386.13330.83153.589.4863.7853.3653.9670.45999999999999494.29176.88137.38999999999999711.05599.96346.45171.9893.558.6345.0445.14106.6878.790000000000006144.01142.56158.51172.45174.4283.546.6535.2634.452.2253.216389.88169.67165.61198.15269.23105.8652.4840.77000000000000338.2239.7457.0182.96131.62301.58999999999997292.70999999999998215.41159.07113.7155.1746.341.3748.8862.4114.26173.58254.42314.39999999999998191.03243.25124.0262.1646.1341.3831.3848.4861.8185.66203.24339.42345.22312.69106.0161.2939.88000000000000333.7837.450000000000003100.5390.5467.33133.24131.26116.688.752.0247.9638.79999999999999738.3637.77000000000000384.72144.04113.1120.5143.84357.97134.7589.9849.2238.8138.5639.34000000000000354.261.6178.09999999999999491.1776.16116.6108.7759.1338.15999999999999730.5438.3637.77000000000000348.1554.160.0696.39317.74867.54253.76169.1561.6444.0938.7456.8496.22191.99276.92376.37522.91347.15202.1166.93000000000000739.27000000000000332.1430.4652.1656.0981.0369.11148.13154.87250.44277.72000000000003108.6974.8464.3167.9160.5965.88107.11143.5PUENTE CARRETERA195619561956195619561956195619561956195619561956195719571957195719571957195719571957195719571957195819581958195819581958195819581958195819581958195919591959195919591959195919591959195919591959196019601960196019601960196019601960196019601960196119611961196119611961196119611961196119611961196219621962196219621962196219621962196219621962196319631963196319631963196319631963196319631963196419641964196419641964196419641964196419641964196519651965196519651965196519651965196519651965196619661966196619661966196619661966196619661966196719671967196719671967196719671967196719671967196819681968196819681968196819681968196819681968196919691969196919691969196919691969196919691969197019701970197019701970197019701970197019701970197119711971197119711971197119711971197119711971197219721972197219721972197219721972197219721972197319731973197319731973197319731973197319731973197419741974197419741974197419741974197419741974197519751975197519751975197519751975197519751975197619761976197619761976197619761976197619761976197719771977197719771977197719771977197719771977197819781978197819781978197819781978197819781978197919791979197919791979197919791979197919791979198019801980198019801980198019801980198019801980198119811981198119811981198119811981198119811981198219821982198219821982198219821982198219821982198319831983198319831983198319831983198319831983198419841984198419841984198419841984198419841984198519851985198519851985198519851985198519851985198619861986198619861986198619861986198619861986198719871987198719871987198719871987198719871987198819881988198819881988198819881988198819881988198919891989198919891989198919891989198919891989199019901990199019901990199019901990199019901990199119911991199119911991199119911991199119911991199219921992199219921992199219921992199219921992199319931993199319931993199319931993199319931993199419941994199419941994199419941994199419941994199519951995199519951995199519951995199519951995185.005415.13616.255503.447227.625139.75168.30100000000000267.47599999999999975.28700000000000693.72799999999999478.64400000000000579.515000000000001118.617302.495221.399158.714120.48873.49762.8860.1175.49299999999999591.87600000000000575.492999999999995130.12200000000001275.30099999999999292.93400000000003593.17600000000004263.90699999999998136.00200000000001108.1280.72199999999999463.71500000000000362.01299999999999885.89499999999999672.61390.015000000000001153.67599999999999332.46618.279348.32100000000003195.4929999999999985.32200000000000364.54900000000000763.25964.06100000000000765.5570.597999999999999266.286293.02199999999999277.38600000000002432.93700000000001241.53593.62574.9766.22100000000000464.51600000000000567.75499999999999567.01000000000000581.51287.334000000000003233.011204.49799999999999264.31400000000002233.284.8876.2561.92499999999999764.49299999999999562.29399999999999754.75200000000000275.629000000000005194.191431.96440.31099999999998512.65288.95499999999998102.9355.6563.98899999999999749.43800000000000251.81600000000000353.73878.28799999999999789.23107.919192.10599999999999447.80900000000003288.14299999999997100.3589999999999958.3647.41799999999999941.70600000000000357.70600000000000365.64107.306238.88900000000001241.52500000000001274.84699999999998313.661234.4619999999999964.03400000000000639.86328.58899999999999928.86700000000000132.6974.685000000000002112.107120.16129.62799999999999188.72900000000001365.904171.6440000000000158.92499999999999727.61625.50400000000000126.43700000000000126.1238.79200000000000255.436105.66800000000001256.11799999999999259.7285.16800000000001173.2570000000000162.83599999999999936.75930.00928.76500000000000128.30300000000000162.734000000000002124.28100000000001128.42400000000001200.63499999999999442.79599999999999508.1190000000000397.59900000000000441.77400000000000134.70600000000000328.25799999999999926.91400000000000126.68926.75199999999999924.93375.119162.541163.041250.74600000000001321.4309999999999847.82500000000000323.66100000000000122.92399999999999925.17599999999999830.71243.53099999999999952.77900000000000336.7450.42600000000000262.46174.14400000000001326.8480000000000185.17199999999999749.35399999999999939.23499999999999928.92299999999999824.26500000000000155.64099999999999885.59288.32499999999999334.22500000000002208.761255.155247.185197.642103.3110000000000164.30599999999999752.58100000000000344.58100000000000348.14500000000000364.167000000000002130.03158.49799999999999176.87799999999999571.64700000000005734.303279.3170000000000166.4259.7951.23700000000000241.72399999999999770.779.558999999999997228.11099999999999283.98500000000001385.04700000000003829.28800000000001414.77300000000002187.15700000000001107.09259.93399999999999749.62299999999999851.14300000000000163.93665.492999999999995113.355256.82297.178611.43700000000001583.93399999999997110.61957.28900000000000144.68941.07800000000000353.14200000000000386.698999999999998157.006200.31200000000001449.91699999999997490.47399999999999507.74799999999999282.42861.94851.55548.59400000000000152.6351.889000000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BALSA195619561956195619561956195619561956195619561956195719571957195719571957195719571957195719571957195819581958195819581958195819581958195819581958195919591959195919591959195919591959195919591959196019601960196019601960196019601960196019601960196119611961196119611961196119611961196119611961196219621962196219621962196219621962196219621962196319631963196319631963196319631963196319631963196419641964196419641964196419641964196419641964196519651965196519651965196519651965196519651965196619661966196619661966196619661966196619661966196719671967196719671967196719671967196719671967196819681968196819681968196819681968196819681968196919691969196919691969196919691969196919691969197019701970197019701970197019701970197019701970197119711971197119711971197119711971197119711971197219721972197219721972197219721972197219721972197319731973197319731973197319731973197319731973197419741974197419741974197419741974197419741974197519751975197519751975197519751975197519751975197619761976197619761976197619761976197619761976197719771977197719771977197719771977197719771977197819781978197819781978197819781978197819781978197919791979197919791979197919791979197919791979198019801980198019801980198019801980198019801980198119811981198119811981198119811981198119811981198219821982198219821982198219821982198219821982198319831983198319831983198319831983198319831983198419841984198419841984198419841984198419841984198519851985198519851985198519851985198519851985198619861986198619861986198619861986198619861986198719871987198719871987198719871987198719871987198819881988198819881988198819881988198819881988198919891989198919891989198919891989198919891989199019901990199019901990199019901990199019901990199119911991199119911991199119911991199119911991199219921992199219921992199219921992199219921992199319931993199319931993199319931993199319931993199419941994199419941994199419941994199419941994199519951995199519951995199519951995199519951995100.46190.12200.87204.6881.54000000000000644.330.9227.532.3351.8753.0870.0685.65165.95192.58134.5769.839.04999999999999733.3232.86999999999999738.1962.3389.11101.04123.62119.52209139.8772.8743.8233.632.7842.849.574.3969.5877.27106.91176.68124.5782.9248.1236.52000000000000342.7638.2163.8164.13103.16188.27254.44313.72000000000003179.4572.1751.0741.094342.3549.164.372.069999999999993160.82114.49184.02186.471.79000000000000639.29999999999999728.5725.6424.0334.95000000000000376.62128.36000000000001147.31170.22359.24169.3248.5838.20000000000000332.1133.3137.9437.564.5873.09127.14145.44279.24187.0167.4437.6429.6230.1236.6743.1386.49142.07126.37170.37206.21166.2179.7337.90999999999999733.9631.3228.6350.5871.18000000000000759.9670.95100.38228.89104.896033.6727.3127.843.5364.18000000000000768.6393.07154.9147.4118.5977.90000000000000658.1341.3838.6139.7645.5883.2890.2194.09131.16999999999999364.12315.2397.7158.1236.9929.0427.9332.8271.4466.48999999999999570.34999999999999492.9396.24126.44667.34600000000000439.69100000000000331.92800000000000127.9625.48199999999999936.32600000000000158.2667.0876.583.7198.16135.624131.6362.95499999999999847.76500000000000135.20600000000000337.03799999999999737.53099999999999966.65900000000000683.313000000000002149.24182.17117.48123.62158.19999999999999123.4444.2233.4730.6842.461.5473.900000000000006107.52142.04215.15234.21154.2269.5942.9731.1833.4631.0355.6659.35106.07133.47999999999999163.21267.44196.9196.1156.1936.5833.15999999999999735.6446.6367.76000000000000595.2122.2121.65219.77229.8397.741.431.9931.6537.52000000000000379.7113.37135.77000000000001198.48293.25272.37161.6660.142.6829.6126.4526.1940.65999999999999759.8680.41116.52133.88999999999999276.08999999999997148.6887.6142.5829.2530.333.8149.4661.0333.9114.91157.77000000000001171.8894.8947.3533.7923.5922.1125.8444.6249.9963.98114.82184.14185.4584.5752.9234.429.434.7136.2845.1190.0593.6296.77136.91999999999999109.8781.1752.4136.13000000000000331.9631.4741.2142.5476.4889.4492.28144.69256.7110.4660.442.1334.7834.8638.2648.563.0671.4490.0986.7182.1668.2740.2935.8328.4431.2346.5763.8878.08116.5485.7992.09185.494.1946.3834.02000000000000329.2426.1124.4353.5584.6281.3385.91141.7555.6680.09999999999999447.4834.5728.0525.0727.0157.0988.35112.39134.0695.27157.47170.657.7242.4833.7530.4431.0944.0960.7189.1467.12249.79303.27999999999997167.9991.1143.6127.524.4126.9661.0849.481.89106.64112.3124.56109.1353.8529.1224.1625.5668.3361.4887.2977.17184.3155.38141.6138.2657.1632.1926.2724.3631.8749.0771.6790.4193.56174.47138.3300000000000192.858.2833.61999999999999728.4622.6142.857.9484.17120.11167.51163.25110.92131.2467.04000000000000635.36999999999999727.8627.9540.5753.7267.1763.72133.63199.08211.26184.4862.4935.3226.0425.3627.958.361.9253.97103.3596.6193.9572.1748.6829.3522.022326.663.5296.9582.2686.51100.25234.0670.7263.8235.8228.8829.9127.4242.2342.9567.0975.4267.31999999999999395.7481.8643.7429.8223.5125.8739.450.5654.4452.4189.6173.6193.24180.9571.9300000000000073427.9626.2842.1364.459999999999994126.35147.84211.38287.98262.79000000000002172.7169.1440.3632.931.2227.8330.9948.0967.91103.46100.32164.51154.2157.5836.5728.0933.3137.1842.3271.2896.85

CAUDAL m3/seg

Anlisis Doble Masa.

Este anlisis se utiliza para tener una cierta confiabilidad en la informacin, as como tambin, para realizar la consistencia en lo relacionado a errores, que pueden producirse durante la obtencin de los mismos; y no para correccin a partir de la recta doble masa. Villn [27].

Para construir el patrn se convierten los caudales en magnitudes que sean comparables (gastos por unidad de rea, escorrenta en mm o en porcentaje del gasto medio). Chereque [7].

Un quiebre de la recta de doble masa o un cambio de pendiente, puede o no ser significativo, ya que si dicho cambio est dentro de los lmites de confianza de la variacin de la recta para un nivel de probabilidades dado, entonces el salto no es significativo, el mismo que se comprobar mediante la prueba estadstico. Chereque [7].

DIAGRAMA DOBLE MASA

PUENTE CARRETERA521.9098719421612970.494345937716391436.93581195961021912.49759932527382437.42554832193582918.27461880520473467.06747569552823978.39685499538974429.54854815716864811.97831797492025219.95883850451815708.69673936590246021.77688770255196404.23789309415686875.17732627814897487.94699489498098082.56150080878348690.44502956541339280.37707704085919803.734450145015210172.73026918274810611.99938851579110960.60370404127211389.64100101388411857.70398871122112402.67339404247712863.19642273328113556.94996211359314228.4635895799814631.18714468856915215.47216519997915813.47051590020216584.71975324990117010.8549008613717415.02385652427317805.33288834367718149.38427157870718719.29339207466219280.87601435916119659.690923699152562.70621259445841891.743286649873991360.50544987405531874.1578690176322281.88909017632252637.01926952141053126.6425894206553513.53030629722933858.96336423173814128.25128060453434454.01604231738024792.56554962216615053.18261057934525333.49885944584375719.66459345088156275.31426196473516851.40584282115837403.08791536523867886.54922619647288372.47414911838688621.23233249370248973.01826599496239277.34419647355219637.050979345089210324.62508440577211006.54496752919811524.89344474467712580.9586648958113302.70918681016713752.52260948019314618.01038882528215431.07943144492916843.76407507213317094.87642570185617634.97433602931118049.06284585298618541.00745542477318983.68301264941319495.49649375772419742.471123480645CONDORCERRO521.9098719421612970.494345937716391436.93581195961021912.49759932527382437.42554832193582918.27461880520473467.06747569552823978.39685499538974429.54854815716864811.97831797492025219.95883850451815708.69673936590246021.77688770255196404.23789309415686875.17732627814897487.94699489498098082.56150080878348690.44502956541339280.37707704085919803.734450145015210172.73026918274810611.99938851579110960.60370404127211389.64100101388411857.70398871122112402.67339404247712863.19642273328113556.94996211359314228.4635895799814631.18714468856915215.47216519997915813.47051590020216584.71975324990117010.8549008613717415.02385652427317805.33288834367718149.38427157870718719.29339207466219280.87601435916119659.690923699152412.41298174442193862.013445378151351243.43770501303971632.46699507389172055.08432338452622558.8084381338743057.80352361634283546.81256447406533977.9614372645614354.63382208055654715.35747319617535136.38830483917725409.84956244566825750.8651173572886180.98340191248926825.68487974500117366.49494059692827952.93010721529948537.89300492610719055.65190379600069451.96130976528559882.89695740365110175.68555201390910561.44031295276710861.00134453781511359.43798319327811797.27552593451212308.37113880034812952.77308606201213233.53476673428113576.5531150391213988.90263691683714370.70765575195814811.72326861779415072.30725007244515378.66102578962815571.31756592292416198.55996522747216674.69426832802117061.543077368879LA BALSA521.9098719421612970.494345937716391436.93581195961021912.49759932527382437.42554832193582918.27461880520473467.06747569552823978.39685499538974429.54854815716864811.97831797492025219.95883850451815708.69673936590246021.77688770255196404.23789309415686875.17732627814897487.94699489498098082.56150080878348690.44502956541339280.37707704085919803.734450145015210172.73026918274810611.99938851579110960.60370404127211389.64100101388411857.70398871122112402.67339404247712863.19642273328113556.94996211359314228.4635895799814631.18714468856915215.47216519997915813.47051590020216584.71975324990117010.8549008613717415.02385652427317805.33288834367718149.38427157870718719.29339207466219280.87601435916119659.690923699152590.610421487603281157.72630578512421706.86428099173582230.86793388429762975.30323140495883558.99614876033054216.75631404958684874.84769421487545451.72084297520635953.04985123966896490.50299999999977197.13636363636317602.29849008264418128.34970247933878724.88398347107439362.841842975205510029.78371900826310715.317066115711416.68899999999811983.0772975206612444.99716528925512980.08294214875813428.78136363636113970.43171074379814387.48553719007914842.03723140495515267.42029752065715781.52008264462316429.90849586776316907.50405785123417451.85299173553418020.4294793388418539.68752892561719125.96500826445819537.7899834710719988.27479338842420335.82779338842420975.637198347121672.43728099172922175.058570247929

LA,MINA ESCURRIDA mm PROMEDIO

LAMINA ESCURRIDA mm

DIAGRAMA DOBLE MASA

CONDORCERRO590.610421487603281157.72630578512421706.86428099173582230.86793388429762975.30323140495883558.99614876033054216.75631404958684874.84769421487545451.72084297520635953.04985123966896490.50299999999977197.13636363636317602.29849008264418128.34970247933878724.88398347107439362.841842975205510029.78371900826310715.317066115711416.68899999999811983.0772975206612444.99716528925512980.08294214875813428.78136363636113970.43171074379814387.48553719007914842.03723140495515267.42029752065715781.52008264462316429.90849586776316907.50405785123417451.85299173553418020.4294793388418539.68752892561719125.96500826445819537.7899834710719988.27479338842420335.82779338842420975.637198347121672.43728099172922175.058570247929412.41298174442193862.013445378151351243.43770501303971632.46699507389172055.08432338452622558.8084381338743057.80352361634283546.81256447406533977.9614372645614354.63382208055654715.35747319617535136.38830483917725409.84956244566825750.8651173572886180.98340191248926825.68487974500117366.49494059692827952.93010721529948537.89300492610719055.65190379600069451.96130976528559882.89695740365110175.68555201390910561.44031295276710861.00134453781511359.43798319327811797.27552593451212308.37113880034812952.77308606201213233.53476673428113576.5531150391213988.90263691683714370.70765575195814811.72326861779415072.30725007244515378.66102578962815571.31756592292416198.55996522747216674.69426832802117061.543077368879PUENTE CARRETERA590.610421487603281157.72630578512421706.86428099173582230.86793388429762975.30323140495883558.99614876033054216.75631404958684874.84769421487545451.72084297520635953.04985123966896490.50299999999977197.13636363636317602.29849008264418128.34970247933878724.88398347107439362.841842975205510029.78371900826310715.317066115711416.68899999999811983.0772975206612444.99716528925512980.08294214875813428.78136363636113970.43171074379814387.48553719007914842.03723140495515267.42029752065715781.52008264462316429.90849586776316907.50405785123417451.85299173553418020.4294793388418539.68752892561719125.96500826445819537.7899834710719988.27479338842420335.82779338842420975.637198347121672.43728099172922175.058570247929562.70621259445841891.743286649873991360.50544987405531874.1578690176322281.88909017632252637.01926952141053126.6425894206553513.53030629722933858.96336423173814128.25128060453434454.01604231738024792.56554962216615053.18261057934525333.49885944584375719.66459345088156275.31426196473516851.40584282115837403.08791536523867886.54922619647288372.47414911838688621.23233249370248973.01826599496239277.34419647355219637.050979345089210324.62508440577211006.54496752919811524.89344474467712580.9586648958113302.70918681016713752.52260948019314618.01038882528215431.07943144492916843.76407507213317094.87642570185617634.97433602931118049.06284585298618541.00745542477318983.68301264941319495.49649375772419742.471123480645

LAMINA ESCURRIDA mm ESTACION LA BALSA

LA,ONA ESCURRIDA mm

2. EVALUACION Y CUANTIFICACION

La evaluacin y cuantificacin de los errores detectados en la forma de saltos, se realiza mediante un anlisis estadstico; vale decir un proceso de inferencia estadstica para las medias y desviacin estndar de ambos perodos identificados en la fase anterior.

SERIE ESTACIONPERODOSCONFIABLELONGITUD AOSDUDOSOLONGITUD (AOS)CONDORCERRO1956-1978231979-199517PUENTE CARRETERA1956-1971161972-19791980-19851986-1989864

Consistencia en la Media.

Este anlisis consiste en probar, mediante la prueba t (prueba de hiptesis), si los valores medios de las sub muestras, son estadsticamente iguales y diferentes con una probabilidad del 95% de confiabilidad o con 5% de nivel de significacin. Villn [27].

Consistencia en la Desviacin Estndar

Consiste en probar, mediante la prueba F (prueba de hiptesis), si los valores de las desviaciones estndar de la submuestras son estadsticamente iguales o diferentes con una probabilidad del 95% de confiabilidad o con 5% de nivel de significacin. Villn [27].

3. CORRECCION DE DATOS.

En los casos en que los parmetros media y desviacin estndar de las sub muestras de series de tiempo, resultan estadsticamente iguales, la informacin no se corrige, por ser consistente; aun cuando se observen quiebres en el doble masa. En caso contrario, se corrige los valores con la siguiente ecuacin: Villn [27].

RESULTADO DE LOS ANLISIS DE CONSISTENCIA EN LOS SALTOSESTACIONPERIODOSPERIODO CONFIABLEPERIODO DUDOSOCONSISTENCIA EN LA MEDIACONSISTENCIA EN LA DESV. ESTANDARECUACIONCONFIABLESDUDOSOSN1X1S1N2X2S2TcalT95%CompDif.Sig.FcalF95%COMP.D.SIG.COEF. ACOEF. BCONDORRCERRO1956198419851993348146.631120.996108118.396111.3712.1581.965Tc>TtSI1.1801.308Fc>FtNO1.0864218.00241PUENTE CARRETERA1956197119721979192148.12137.8996158.70163.910.5761.968Tc>TtNO1.4131.330Tc>TtSi0.8412814.611281956197919801985288148.12137.6570259.94255.965.0171.967Tc>TtSI3.4571.345Tc>TtSi0.537808.326151956198519861989358148.12137.4646281.70242.255.5811.966Tc>TtSI3.1061.406Tc>TtSi0.56744-11.72550NOTA:X1: PROMEDIO DEL GRUPO 1T cal: ESTADISTICO T DE STUDENT CALCULADOCOEF. A: COEFICIENTE DE REGRESION AX2: PROMEDIO DEL GRUPO 2T 95%: ESTADISTICO T DE STUDENT TABULARCONST. B: TERMINO CONSTANTE DE REGRESION BS(X1): DESVIACION ESTANDAR DEL GRUPO 1Fcal: ESTADITICO F DE SNEDECOR CALCULADON1: NUMERO DE DATOS DEL GRUPO 1S(X2): DESVIACION ESTANDAR DEL GRUPO 2F 95%: ESTADISTICO F DE SNEDECOR TABULARN2: NUMERO DE DATOS DEL GRUPO 2

ANALISIS DE TENDENCIA

Las tendencias son componentes determinsticas transitorias que se definen como un cambio sistemtico y continuo sobre una muestra de informacin hidrometeorolgica en cualquier parmetro de la misma, que afecta las distribuciones y dependencias de las series. Aliaga [2]. Ejemplos: deforestacin o reforestacin de rboles en una cuenca., construccin de estructuras hidrulicas de regulacin en las cabeceras de las cuencas, construccin de canales, ampliacin de reas de cultivo. Antes de realizar el anlisis de tendencia, se realiza el anlisis de saltos con series libres de saltos.

1. IDENTIFICACION.

Tiene por objetivo identificar los perodos que presentan tendencias, para la identificacin se procede con:

Anlisis Visual de la Serie Histrica.

Obtenido la serie libre de saltos, se procede a identificar los posibles perodos con tendencias.

2. EVALUACION Y CUANTIFICACION

La evaluacin y cuantificacin de los errores detectados en la forma de tendencia, se realiza mediante un anlisis estadstico: vale decir un proceso de inferencia estadstica para las medias y desviacin estndar del perodo identificado en la fase anterior. Villn [27].

Tendencia en la Media.

La tendencia en la media Tm, puede ser expresada en forma particular por la ecuacin de regresin lineal simple:

Tendencia en la Desviacin Estndar.

La tendencia en la desviacin estndar Ts, se expresa en forma particular por la ecuacin de regresin lineal simple:

CORRECCION DE DATOS.

Si la prueba R resulta significativo, la tendencia en la desviacin estndar es significativa, por lo que se debe eliminar de la serie, aplicando la siguiente ecuacin:

RESULTADOS DE ANALISIS DE CONSISTENCIA EN LAS TENDENCIAS EN LA MEDIA Y DESVIACION ESTANDARESTACIONPERIODOTENDENCIACOEFICIENTEESTADISTICO TCOMPROVACIONTENDENCIA SIGNIFICATIVAINICIOFINALAmBmTcTt (95%)CONDORCERRO19561995MEDIA0.01218143.452980.305101.96494Tc>=TtNO19561995DES. ESTANDAR0.05814109.762590.084212.02439Tc>=TtNOPUENTE CARRETERA19561995MEDIA0.03430141.494100.726661.96521Tc>=TtNO19561965MEDIA-0.80793204.78879-2.292871.98027Tc>=TtSI19561995DES. ESTANDAR-0.13978126.48320-0.195392.02439Tc>=TtNOLA BALSA19561995MEDIA-0.0395094.58298-1.927491.96494Tc>=TtNO19561995DES. ESTANDAR-0.3761667.30793-1.282532.02439Tc>=TtNOTc: ESTADISTICO T DE STUDENT CALCULADOAm COEFICIENTE DE CORRELACION LINEAL SIMPLETt (95%): ESTADITICO T DE STUDENT TABULARBm COEFICIENTE CONSTANTE DE CORRELACION SIMPLE

21

,xx

Media de los perodos 1 y 2 respectivamente.

)(),(

21

xSxS

Desviacin estndar de los perodos 1 y 2 respectivamente

21

nnn

, tamao de la muestra.

Determinacin de t calculada segn:

d

c

S

xx

t

2121

(2.1)

Donde:

0

21

, por hiptesis.

Quedando:

d

c

S

xx

t

21

(2.2)

Desviacin de las diferencias de los promedios:

2/1

21

11

nn

SS

pd

(2.3)

Desviacin estndar ponderada:

2/1

21

2

22

2

11

2

11

nn

SnSn

S

p

(2.4)

Comparacin del t calculado (t

c

) con el t tabular (t

t

) con n

1

+ n

2

-2 grados de libertad.

Si

)(%)95(

)(%)95(

21

21

amenteestadisticxxtt

amenteestadisticxxtt

tc

tc

, resultara diferente se debe corregir.

Los F calculado (F

c

) se calcula de la siguiente forma:

)x(S)x(Ssi,

)x(S

)x(S

F

2

2

2

1

2

2

2

1

c

(2.5)

)x(S)x(Ssi,

)x(S

)x(S

F

2

1

2

2

2

1

2

2

c

(2.6)

Comparacin del F

c

con el F tabular (F

t

) con los siguientes grado de libertad:

Grado de libertad del numerador = (n

1

-1)

Grado de libertad del denominador = (n

2

-1)

Si:

)()(

2

2

2

1

xSxS

Grado de libertad del numerador = (n

2

-1)

Grado de libertad del denominador = (n

1

-1)

Si:

)()(

2

1

2

2

xSxS

)amenteestadistic()x(S)x(S%)95(FF

)amenteestadistic()x(S)x(S%)95(FF

21tc

21tc

)1

2

n(),1

1

n(

)1

2

n(),1

1

n(

22

1

1t

'

)t(

x)x(S*

)x(S

xx

X

(2.7)

11

2

2t

'

)t(

x)x(S*

)x(S

xx

X

(2.8)

Donde:

'

)(t

X

= valor corregido de saltos.

X

t

= valor a ser corregido.

La ecuacin 2.7, se utiliza cuando se deben corregir los valores de la

submuestra de tamao n

1

, y la ecuacin 2.7, si se deben corregir la submuestra de

tamao n

2

.

tBAT

mmm

(2.9)

Donde:

t = tiempo en aos, tomado como la variable independiente de la tendencia.

t= 1, 2, 3, , n

Tm = tendencia en la media

Am, Bm = coeficiente de la ecuacin a ser estimados.

Para averiguar si la tendencia es significativa, se analiza el coeficiente de correlacin R

con el estadstico t

c

calculado:

2

1

2

R

nR

t

c

(2.10)

Donde:

t

c

= valor del estadstico t calculado.

n= numero total de datos.

R= coeficiente de correlacin.

Comparacin del t

c

con el t tabular (t

t

) con (n-2) grados de libertad.

ivosignificatesRtt

ivosignificatesnoRtt

tc

tc

%)95(

%)95(

tBAT

sss

(2.11)

Donde:

t = tiempo en aos, tomado como la variable independiente de la tendencia.

t= 1, 2, 3, , n

Ts = tendencia en la desviacin estndar, que es el valor corregido de tendencia en

la media.

A

s

, B

s

= coeficiente de la ecuacin a ser estimados.

Para calcular y probar si la tendencia en la desviacin es significativa se calcula la

desviacin estndar de cada ao, y luego, se calcula los parmetros de la ecuacin de

regresin 2.10; luego se realiza la evaluacin de Ts siguiendo el mismo proceso descrito

para Tm. Villn [27].

s

mt

T

T

TX

z

'

)(

(2.12)

Donde:

Z

t

= serie sin tendencia en la media ni en la desviacin estndar. Las dems

variables han sido definidas anteriormente.

Para que el proceso preservando la media y la desviacin estndar constante,

la ecuacin toma la forma:

ms

s

mt

T

TT

T

TX

z

*

'

)(

(2.13)

Donde:

ms

TT,

: son los promedios de la tendencia en la desviacin y media

respectivamente.

La serie Z

t

es una serie homognea y consistente al 95% de probabilidad.