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Patricio Alejandro González Loyola

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Patricio Alejandro González Loyola UNIVERSIDAD DE TALCA FACULTAD DE CIENCIAS FORESTALES ESCUELA DE INGENIERÍA FORESTAL CONSTRUCCIÓN DE HERRAMIENTAS MATEMÁTICAS PARA LA PREDICCIÓN DEL COMPORTAMIENTO DE LOS CAUDALES PUNTA EN LA REGIÓN DEL MAULE. PATRICIO ALEJANDRO GONZÁLEZ LOYOLA Memoria para optar al título de: INGENIERO FORESTAL Profesor Guía: DR. ING. ROBERTO PIZARRO TAPIA TALCA – CHILE 2009 0 ÍNDICE 1. INTRODUCCIÓN.......................................................................................................1 2. OBJETIVOS……………………………………………..................................................3 2.1. Objetivo General................................................................................................3 2.2. Objetivos Específicos........................................................................................3 3. REVISIÓN BIBLIOGRÁFICA…………………………......…........................................4 3.1 Hidrograma de crecida……………………………………....................................4 3.1.2. Caudal máximo o punta................................................................................5 3.1.3. Medición del nivel de aguas……………………………………..................….6 3.2. Las crecidas………………………………………………………….….....…..............7 3.2.1. Predicción de crecidas..................................................................................8 3.2.2 Método de predicción del caudal punta…………………………...…...........10 3.3. Modelos matemáticos.........................................................................................11 3.4. Métodos no paramétricos..................................................................................12 3.5. Antecedentes de las cuencas a estudiar..........................................................13 3.5.1. Cuenca del río Maule...................................................................................13 3.5.2. Cuenca del río Mataquito............................................................................14 4. METODOLOGÍA ......................................................................................................16 4.1. Revisión Bibliográfica................................................................................…16 4.2. Obtención de datos........................................................................................16 4.3. Selección de estaciones...............................................................................16 4.4. Selección de las crecidas..............................................................................21 4.5. Índice del caudal punta..................................................................................21 4.6. Modelación del caudal punta.........................................................................22 4.6.1. Tratamiento de las Variables.................................................................23 4.6.2 Relaciones entre Variables dependientes e independientes...............24 1 4.7. Calibración del modelo....................................................................................26 4.8. Validación del modelo......................................................................................26 4.9. Análisis de los desfases temporales de los hidrogramas............................29 4.9.1. Desfase entre caudales punta.....................................................................29 4.9.2. Desfase al inicio de la crecida.....................................................................30 4.10. Materiales……………….……..…………….......................................................30 5. PRESENTACIÓN DE RESULTADOS……………….………………..........................32 5.1. Selección de las crecidas....................................................................................32 5.1.2. Selección de crecidas con dos estaciones predictoras...........................35 5.1.3. Selección de crecidas con tres estaciones predictoras...........................36 5.1.4. Resumen de la selección de crecidas en cada punto...........................36 5.2 Modelos generados para la estimación del caudal punta.................................43 5.3. Desfase temporal de los hidrogramas................................................................54 5.3.1. Desfase del caudal punta.............................................................................54 5.3.2. Desfase del caudal inicial............................................................................56 6. ANÁLISIS Y DISCUSIÓN DE LOS RESULTADOS..................................................60 6.1. Selección de crecidas........................................................................................60 6.2. Caudales punta................................................................................................61 6.2.1.Coeficiente de variación..............................................................................61 6.2.2. Correlación entre caudales punta.............................................................62 6.2.3. Índice del caudal punta..............................................................................63 6.2.4. Comportamiento del Índice del caudal punta..........................................64 6.3. Análisis de la Validación de los modelos …………………………….….......65 6.4. Análisis para los Diferencial de tiempo…….................................................70 7. CONCLUSIONES Y RECOMENDACIONES...........................................................72 8. BIBLIOGRAFÍA………………………………………………………..….......................76 APÉNDICES……………………………………………………………………....................81 2 RESUMEN Este estudio investiga el comportamiento de las crecidas por medio del análisis de los caudales punta en cuatro estaciones fluviométricas, distribuidas en las cuencas del río Maule y el Mataquito. Estas estaciones fueron Maule en Forel, Claro en Rauquén, Loncomilla en Bodega y Mataquito en Licantén, las cuales se ubican aguas abajo de la cuenca. Para cada una de ellas, se escogieron tres estaciones ubicadas aguas arriba, denominadas como estaciones predictoras de las estaciones aguas abajo. A partir de la relación de los caudales punta aguas arriba, con los caudales punta aguas abajo, se obtuvo un Índice, a través del cual se observó la relación que existe entre los valores de la crecida de ambos caudales. De igual forma, fue posible generar modelos matemáticos capaces de predecir el caudal punta aguas abajo, a partir de los caudales punta de las estaciones ubicada aguas arriba. Se probó una gran variedad de modelos, escogiendo aquellos que presentaron un mejor el ajuste en cada caso, para la modelación con una, con dos y con tres estaciones predictoras. Para validar la calidad de los modelos seleccionados, se utilizaron el Coeficiente de Determinación (R 2), el Error estándar de estimación (EEE) y el Test de concordancia de Bland y Altman (ACBA), con lo cual se escogió finalmente el mejor para cada caso. Los resultados obtenidos con el Error estándar de estimación y el Test de Bland y Altman, indican que la mayoría de los modelos seleccionados con dos estaciones predictoras son capaces de realizar una mejor predicción. Por otro lado, se calculó el tiempo que demora en producirse la crecida en la estación ubicada aguas abajo, luego de producirse en la estación aguas arriba, concluyendo que, de las cuatro estaciones observadas, la estación mataquito en Licantén, es la que posee un mayor margen de tiempo para anticipar una crecida. 3 SUMMARY This research shows the behavior of flooding through the peak flows analysis in four fluvial stations distributed in the basins of the Maule river and the Mataquito river. These stations were Maule en Forel, Claro en Rauquén, Loncomilla en las Brisas, and Mataquito en Licantén which are located downstream of the basin. For each basin it was chosen three stations upstream called themselves predictor stations of the downstream stations. From the relation between upstream peak flows and downstream peak flows there was an indicator that noticed the relationship that existed between the values of both peak flows. Similarly it was possible to generate mathematical models capable of predicting the downstream peak flow from the upstream peak flows of the stations located upstream. Tested a variety of models choosing those that presented a better adjustment in each case for the modeling with one, two, and three predictor stations. To assess the quality of the selected models was used the coefficient of determination (R2), standard error of estimate (EEE) and the conformity test of Bland and Altman (ACBA), in order to choose the best for each case. The results obtained with the standard error of estimation and test of Bland and Altman indicate that most of the selected models with two predictor stations are capable to make a better prediction. Finally, it was calculated the time that takes to produce the flood located downstream station, following in the upstream station. In conclusion, the four stations observed, the Mataquito en Licantén station possesed a bit more time to anticipate a flood. 4 1.- INTRODUCCIÓN Las crecidas corresponden a procesos naturales, sin periodicidad, constituidos por un incremento importante y repentino del caudal, el cual lleva consigo un ascenso del nivel de la corriente hasta alcanzar un máximo o caudal punta y descender a continuación (Ollero, 1996 citado por Vera, 2008). Los episodios relacionados con las crecidas, han provocado innumerables pérdidas, sobretodo para las actividades humanas y los bienes públicos, siendo consideradas en todo el mundo como un riesgo natural importante. De este modo, se verifican
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