Publication: ESTIMACIÓN DE CAUDALES MEDIOS ANUALES DE CUENCAS NIVO-PLUVIALES SIN INFORMACIÓN FLUVIOMÉTRICA
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Date
2017
Authors
FLORES FLORES, JOSÉ LUIS
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Abstract
Una cuenca hidrográfica es un sistema que conjuga distintos elementos esenciales para el desarrollo de las actividades humanas, entre las cuales y de manera especial, las vinculadas a las actividades agropecuarias, mineras y económicas en general. Considerando este aspecto, es que se desprende la importancia y la utilidad que tiene la estimación de caudales de estos sistemas hídricos, en el ámbito de la ingeniería.Teniendo presente lo anterior, en el presente estudio se planteó desarrollar una ecuación que permita estimar el caudal medio anual de cuencas de régimen nival o nivo-pluvial sin información fluviométrica, mediante una simple relación de sus variables fisiográficas e hidrológicas generales, y de fácil aplicación. La principal complejidad se debe a considerar cuencas de régimen mixto (nivo-pluvial), lo que en la práctica se traduce en incorporar la superposición de los efectos de ambos regímenes en la fluviometría, caracterizado por los flujos del período invernal, principalmente, producto de las precipitaciones líquidas, y por otro lado, la magnitud del flujo en el período estival, ocurrido entre los meses de septiembre y abril.La formulación de la ecuación se llevó a cabo en base a la construcción de índices adimensionales, con los cuales fuera posible introducir la información geomorfológica e hidrológica de manera simple, para lo cual se utilizó el procedimiento del Teorema Pi de Buckinham. Posterior a la formación de los índices adimensionales, la generación de la ecuación se realizó siguiendo la metodología para regresiones lineales múltiples.El estudio configuró como base un conjunto de 10 cuencas, desde las cuales se obtuvieron las variables finalmente seleccionadas por el procedimiento estadístico, corresponden básicamente a características físicas de la cuenca de fácil estimación, como lo son el área total (A), el área cubierta por nieve (An), la altura media (H) y la altura media de la zona cubierta por nieve (Hn). Respecto de las variables meteorológicas incluidas, se consideró a la precipitación media anual (Pp).En relación a los resultados obtenidos con el modelo, se pudo observar que su aplicación sobre las cuencas del estudio, utilizando las características físicas de las propia cuencas y la estimación de sus precipitaciones medias anuales, en base a estaciones cercanas, arrojó un error relativo (ER) promedio de 27,6%.Complementariamente y con el objetivo de obtener una mejor medida de la calidad de las estimaciones, se realizó una comparación de la ecuación formulada con otras relaciones. Dicha comparación, consiste en aplicar la ecuación generada en este estudio y los modelos de la comparación, a un conjunto de 23 cuencas, conformado por las 10 cuencas de la base de datos, y por otras 13 cuencas distintas, de las cuales 11 pertenecen al estudio [10] de las relaciones que servirán para la comparación y 2 cuencas del mismo trabajo de donde se obtuvo la base de datos original [2].Los resultados de aplicar las ecuaciones comparadas sobre el conjunto de las 23 cuencas, fueron muy similares en magnitud, lo que se verificó con el cálculo del error relativo (ER) promedio. El menor ER se consiguió con la fórmula de Turc ajustada, alcanzando un 40,1%, a este lo siguen Turc-Pike ajustado y el modelo de Coutagne ajustado, con un ER de 41,2% y ER de 41,9%, respectivamente.El resultado con la ecuación seleccionada promedia un ER de 41,9%, levemente superior a los ER promedios obtenidos con los modelos ajustados, sin embargo la diferencia no es significativa. Por otra parte, dicha ecuación presenta el error cuadrático medio (ECM) más bajo de todos, correspondiente a 0,70, en comparación con el 1,55 para Turc-Pike ajustado, 1,65 para Coutagne ajustado y 1,61 obtenido para Turc ajustado. En estos términos, la ecuación elaborada en este trabajo resulta competitiva y recomendable de utilizar.
A Hydrographic Basin is a system that combines different essential elements for the development of human activities, especially those linked to farming, mining and economical activities. Taking this aspect into account, we can realize the importance and usefulness of the flow estimations of these water systems in the engineering area.Considering what was mentioned before, in this study we set out the development of an equation that allows us to estimate the annual average flow of the basins during the rainfall regime or snow-rain regime, without the need of recorded data from streamgage measurements. Just only by a simple connection of its physiographic and hydrological variables, throughout easy application. One of the main complications to consider in mix regime basins (nivo-pluvial), which means, to incorporate the overlapping effects of both regimes in the streamgage measurements, known for the flows during winter season. Mainly, are a product from the rains, and on the other hand, the magnitude of the flow during summer season, which manifests between the months of September and April.The formulation for the equation was carried out by creating dimensionless indexes, which allow us the possibility of adding geomorphological and hydrological information in a simple way. For this procedure, we used Buckingham’s Pi Theorem. After the formation of the dimensionless indexes, the creation of the equation was done per the linear multiple regression theories methodology.The study included 10 basins, in which from these, we could obtain the variables that were finally selected by the statistical procedure. This basically corresponds to the physical features of the basin, which are easy to estimate. Like the total surface (A), the surface covered by snow (An), the average height (H) and the average height of the area covered by snow (Hn). About the meteorological variables that were included, we took into consideration the annual average rainfall (Pp).Per the outcome obtained from our model, we could observe its application in those basins that were part of the research, using the physical features of the basins and the estimation of the annual average rainfall, per the nearest seasons, which gave as relative error (RE) of 27.6% average.Complementary to this, and with the goal of having a better-quality measurement of the estimations, we did a comparison between the formulated equation and other connections involved. Such comparison consisted of applying the created equation in this study and the models of comparison in a group of 23 basins, where 10 of these basins were part of our data base, and by other 13 different basins, from which 11 belonged to our study [10] of the connections that will help us to do the comparison; and where two of the basins of this research gave us part of the original data base [2].The outcome of applying the compared equations on the group of 23 basins, was similar in magnitude, which was verified in the relative error (RE) average calculation. The lowest RE was obtained with the adjusted Turc formula, reaching a 40.1%, which was followed by the adjusted Turc-Pike’s and Coutagne’s model, with a RE of 41.2% and 41.9% each.The outcome with the selected equation, gave us an RE average of 41.9%, slightly higher to the RE averages obtained with the adjusted models. However, this is not a significant difference. On the other hand, such equation presents the lowest mean square error (MSE) of them all, corresponding to a 0.70, in comparison with the 1.55 for the Turc-Pike’s model; the 1.65 for the adjusted Coutagne’s; and the 1.61 obtained to Turc’s models. That is why we consider that the equation developed during this study, is highly competitive and recommendable to use.
A Hydrographic Basin is a system that combines different essential elements for the development of human activities, especially those linked to farming, mining and economical activities. Taking this aspect into account, we can realize the importance and usefulness of the flow estimations of these water systems in the engineering area.Considering what was mentioned before, in this study we set out the development of an equation that allows us to estimate the annual average flow of the basins during the rainfall regime or snow-rain regime, without the need of recorded data from streamgage measurements. Just only by a simple connection of its physiographic and hydrological variables, throughout easy application. One of the main complications to consider in mix regime basins (nivo-pluvial), which means, to incorporate the overlapping effects of both regimes in the streamgage measurements, known for the flows during winter season. Mainly, are a product from the rains, and on the other hand, the magnitude of the flow during summer season, which manifests between the months of September and April.The formulation for the equation was carried out by creating dimensionless indexes, which allow us the possibility of adding geomorphological and hydrological information in a simple way. For this procedure, we used Buckingham’s Pi Theorem. After the formation of the dimensionless indexes, the creation of the equation was done per the linear multiple regression theories methodology.The study included 10 basins, in which from these, we could obtain the variables that were finally selected by the statistical procedure. This basically corresponds to the physical features of the basin, which are easy to estimate. Like the total surface (A), the surface covered by snow (An), the average height (H) and the average height of the area covered by snow (Hn). About the meteorological variables that were included, we took into consideration the annual average rainfall (Pp).Per the outcome obtained from our model, we could observe its application in those basins that were part of the research, using the physical features of the basins and the estimation of the annual average rainfall, per the nearest seasons, which gave as relative error (RE) of 27.6% average.Complementary to this, and with the goal of having a better-quality measurement of the estimations, we did a comparison between the formulated equation and other connections involved. Such comparison consisted of applying the created equation in this study and the models of comparison in a group of 23 basins, where 10 of these basins were part of our data base, and by other 13 different basins, from which 11 belonged to our study [10] of the connections that will help us to do the comparison; and where two of the basins of this research gave us part of the original data base [2].The outcome of applying the compared equations on the group of 23 basins, was similar in magnitude, which was verified in the relative error (RE) average calculation. The lowest RE was obtained with the adjusted Turc formula, reaching a 40.1%, which was followed by the adjusted Turc-Pike’s and Coutagne’s model, with a RE of 41.2% and 41.9% each.The outcome with the selected equation, gave us an RE average of 41.9%, slightly higher to the RE averages obtained with the adjusted models. However, this is not a significant difference. On the other hand, such equation presents the lowest mean square error (MSE) of them all, corresponding to a 0.70, in comparison with the 1.55 for the Turc-Pike’s model; the 1.65 for the adjusted Coutagne’s; and the 1.61 obtained to Turc’s models. That is why we consider that the equation developed during this study, is highly competitive and recommendable to use.
Description
Catalogado desde la version PDF de la tesis.
Keywords
CAUDAL MEDIO ANUAL , CUENCA HIDROGRAFICA , CUENCAS NIVO-PLUVIALES