A modelagem matemática da hidrologia de bacias hidrográficas é largamente utilizada em estudos de diversos tipos de problemas encontrados na engenharia hidráulica e de recursos hídricos. Nestes últimos 150 anos, muitos pesquisadores realizaram observações e experimentos sobre a natureza do ciclo hidrológico para que pudessem entender e equacionar seu comportamento. Diversos modelos diferentes surgiram baseando-se em equacionamentos físicos e empíricos, sendo que muitos destes modelos clássicos são utilizados até hoje. Para se ter uma visão mais abrangente do tema, uma revisão do estado da arte é apresentada, com uma perspectiva histórica destes modelos e seus criadores, assim como uma classificação fundamentada em suas características. Também são examinados alguns dos sistemas computacionais para modelagem hidrológica de bacias hidrográficas mais utilizados atualmente. São discutidas as hipóteses de uma simplificação do ciclo hidrológico para eventos intensos utilizados em projetos. Cada componente do ciclo hidrológico simplificado é modelado utilizando um dos diferentes modelos hidrológicos propostos, com graus de complexidade distintos. Para cada um destes modelos é realizada uma análise de sensibilidades dos seus parâmetros. Baseado nos avanços tecnológicos mais recentes na ciência da computação foi desenvolvido, em paralelo a esta pesquisa, uma ferramenta computacional que compila todos os conceitos aqui apresentados e tem distribuição acadêmica livre. / The mathematical modeling of the watershed hydrology is widely used in studies of several problems related to hydraulic and water resources engineering. On these last 150 years, many researchers accomplished observations and experiments on the nature of the hydrologic cycle in order to understand and equates its behavior. Several different models appeared basing on physical and empiric equating, and many of these classic models are being used until today. To get a more comprehensive view on the theme, a state of the art revision is presented, with an historical perspective about these models and its creators, such as a classification based on its characteristics are presented. Also some computational systems of hydrologic modeling of watershed are also examined more used now. The hypotheses of a simplification of the hydrologic cycle are discussed for intense events used in projects. Each component of the simplified hydrologic cycle is modeled using one of the different hydrologic models proposed, with distinct grades of complexity. For each one of these models a sensibility analysis of their parameter is performed. Based on the more recent technological progresses in the computational science was developed, parallel to this research, a computational tool that compiles all the concepts here presented and has free academic distribution.

A modelagem matemática da hidrologia de bacias hidrográficas é largamente utilizada em estudos de diversos tipos de problemas encontrados na engenharia hidráulica e de recursos hídricos. Nestes últimos 150 anos, muitos pesquisadores realizaram observações e experimentos sobre a natureza do ciclo hidrológico para que pudessem entender e equacionar seu comportamento. Diversos modelos diferentes surgiram baseando-se em equacionamentos físicos e empíricos, sendo que muitos destes modelos clássicos são utilizados até hoje. Para se ter uma visão mais abrangente do tema, uma revisão do estado da arte é apresentada, com uma perspectiva histórica destes modelos e seus criadores, assim como uma classificação fundamentada em suas características. Também são examinados alguns dos sistemas computacionais para modelagem hidrológica de bacias hidrográficas mais utilizados atualmente. São discutidas as hipóteses de uma simplificação do ciclo hidrológico para eventos intensos utilizados em projetos. Cada componente do ciclo hidrológico simplificado é modelado utilizando um dos diferentes modelos hidrológicos propostos, com graus de complexidade distintos. Para cada um destes modelos é realizada uma análise de sensibilidades dos seus parâmetros. Baseado nos avanços tecnológicos mais recentes na ciência da computação foi desenvolvido, em paralelo a esta pesquisa, uma ferramenta computacional que compila todos os conceitos aqui apresentados e tem distribuição acadêmica livre. / The mathematical modeling of the watershed hydrology is widely used in studies of several problems related to hydraulic and water resources engineering. On these last 150 years, many researchers accomplished observations and experiments on the nature of the hydrologic cycle in order to understand and equates its behavior. Several different models appeared basing on physical and empiric equating, and many of these classic models are being used until today. To get a more comprehensive view on the theme, a state of the art revision is presented, with an historical perspective about these models and its creators, such as a classification based on its characteristics are presented. Also some computational systems of hydrologic modeling of watershed are also examined more used now. The hypotheses of a simplification of the hydrologic cycle are discussed for intense events used in projects. Each component of the simplified hydrologic cycle is modeled using one of the different hydrologic models proposed, with distinct grades of complexity. For each one of these models a sensibility analysis of their parameter is performed. Based on the more recent technological progresses in the computational science was developed, parallel to this research, a computational tool that compiles all the concepts here presented and has free academic distribution.

From the Proceedings of the 1974 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 19-20, 1974, Flagstaff, Arizona / Semiarid environments exhibit certain hydrologic characteristics which must be taken into consideration for the effective modeling of the behavior of catchments in these areas. Convective storms, which cause most of the runoff, occur in high intensity and short duration during the summer months and are highly localized so that only a small portion of the catchment actually contributes flow to the storm hydrograph. Also, streams in semiarid catchments are ephemeral with flow occurring only about 1 percent of the time. This study attempts to develop a simple synthetic catchment model that reflects these features of the semiarid environment and for which (1) the simplifying assumptions do not preclude the inclusion of the important components of the runoff process, and (2) parameters of the equations representing the component processes have physical interpretation and are obtainable from basin characteristics so that the model may be applicable to ungaged sites. A reductionist approach is then applied in which the entire catchment is subdivided into a finite number of meshes and the various components of the runoff phenomenon are delineated within each mesh as independent functions of the catchment. Simplified forms of the hydrodynamic equations of flow are used to route flow generated from each mesh to obtain a complete hydrograph at the outlet point.

From the Proceedings of the 1974 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 19-20, 1974, Flagstaff, Arizona / A stochastic model is presented for the prediction of sediment yield in a semi-arid watershed based on rainfall data and watershed characteristics. Random variables which lead to uncertainty in the model are rainfall amount, storm duration, runoff, and peak flow. Soil conservation service formulas are used to compute the runoff and peak flow components of the universal soil loss equation, and a transformation of random variables is used to obtain the distribution function of sediment yield from the joint distribution of rainfall amount and storm duration. Applications of the model are in the planning of reservoirs and dams where the effective lifetime of the facility may be evaluated in terms of storage capacity as well as the effects of land management of the watershed. In order to calibrate the model and to evaluate the uncertainties involved, experimental data from the Atterbury watershed near Tucson, Arizona were used.