Flood frequency analysis by a bivariate model based on copulas

La adecuada estimación de avenidas de diseño asociadas a altos periodos de retorno es necesaria para el diseño y gestión de estructuras hidráulicas como presas. En la práctica, la estimación de estos cuantiles se realiza normalmente a través de análisis de frecuencia univariados, basados en su mayoría en el estudio de caudales punta. Sin embargo, la naturaleza de las avenidas es multivariada, siendo esencial tener en cuenta características representativas de las avenidas, tales como caudal punta, volumen y duración del hidrograma, con el fin de llevar a cabo un análisis apropiado; especialmente cuando el caudal de entrada se transforma en un caudal de salida diferente durante el proceso de laminación en un embalse o llanura de inundación. Los análisis de frecuencia de avenidas multivariados han sido tradicionalmente llevados a cabo mediante el uso de distribuciones bivariadas estándar con el fin de modelar variables correlacionadas. Sin embargo, su uso conlleva limitaciones como la necesidad de usar el mismo tipo de distribuciones marginales para todas las variables y la existencia de una relación de dependencia lineal entre ellas. Recientemente, el uso de cópulas se ha extendido en hidrología debido a sus beneficios en relación al contexto multivariado, permitiendo superar los inconvenientes de las técnicas tradicionales. Una copula es una función que representa la estructura de dependencia de las variables de estudio, y permite obtener la distribución de frecuencia multivariada de dichas variables mediante sus distribuciones marginales, sin importar el tipo de distribución marginal utilizada. La estimación de periodos de retorno multivariados, y por lo tanto, de cuantiles multivariados, también se facilita debido a la manera en la que las cópulas están formuladas. La presente tesis doctoral busca proporcionar metodologías que mejoren las técnicas tradicionales usadas por profesionales para estimar cuantiles de avenida más adecuados para el diseño y la gestión de presas, así como para la evaluación del riesgo de avenida, mediante análisis de frecuencia de avenidas bivariados basados en cópulas. Las variables consideradas para ello son el caudal punta y el volumen del hidrograma. Con el objetivo de llevar a cabo un estudio completo, la presente investigación abarca: (i) el análisis de frecuencia de avenidas local bivariado centrado en examinar y comparar los periodos de retorno teóricos basados en la probabilidad natural de ocurrencia de una avenida, con el periodo de retorno asociado al riesgo de sobrevertido de la presa bajo análisis, con el fin de proporcionar cuantiles en una estación de aforo determinada; (ii) la extensión del enfoque local al regional, proporcionando un procedimiento completo para llevar a cabo un análisis de frecuencia de avenidas regional bivariado para proporcionar cuantiles en estaciones sin aforar o para mejorar la estimación de dichos cuantiles en estaciones aforadas; (iii) el uso de cópulas para investigar tendencias bivariadas en avenidas debido al aumento de los niveles de urbanización en una cuenca; y (iv) la extensión de series de avenida observadas mediante la combinación de los beneficios de un modelo basado en cópulas y de un modelo hidrometeorológico. Accurate design flood estimates associated with high return periods are necessary to design and manage hydraulic structures such as dams. In practice, the estimate of such quantiles is usually done via univariate flood frequency analyses, mostly based on the study of peak flows. Nevertheless, the nature of floods is multivariate, being essential to consider representative flood characteristics, such as flood peak, hydrograph volume and hydrograph duration to carry out an appropriate analysis; especially when the inflow peak is transformed into a different outflow peak during the routing process in a reservoir or floodplain. Multivariate flood frequency analyses have been traditionally performed by using standard bivariate distributions to model correlated variables, yet they entail some shortcomings such as the need of using the same kind of marginal distribution for all variables and the assumption of a linear dependence relation between them. Recently, the use of copulas has been extended in hydrology because of their benefits regarding dealing with the multivariate context, as they overcome the drawbacks of the traditional approach. A copula is a function that represents the dependence structure of the studied variables, and allows obtaining the multivariate frequency distribution of them by using their marginal distributions, regardless of the kind of marginal distributions considered. The estimate of multivariate return periods, and therefore multivariate quantiles, is also facilitated by the way in which copulas are formulated. The present doctoral thesis seeks to provide methodologies that improve traditional techniques used by practitioners, in order to estimate more appropriate flood quantiles for dam design, dam management and flood risk assessment, through bivariate flood frequency analyses based on the copula approach. The flood variables considered for that goal are peak flow and hydrograph volume. In order to accomplish a complete study, the present research addresses: (i) a bivariate local flood frequency analysis focused on examining and comparing theoretical return periods based on the natural probability of occurrence of a flood, with the return period associated with the risk of dam overtopping, to estimate quantiles at a given gauged site; (ii) the extension of the local to the regional approach, supplying a complete procedure for performing a bivariate regional flood frequency analysis to either estimate quantiles at ungauged sites or improve at-site estimates at gauged sites; (iii) the use of copulas to investigate bivariate flood trends due to increasing urbanisation levels in a catchment; and (iv) the extension of observed flood series by combining the benefits of a copula-based model and a hydro-meteorological model.

Looking for a more comprehensive approach

The necessity/convenience for improving accuracy in determining the flood frequency is widely accepted further than among hydrologists, and is increasingly deepened in relationship with the statement of different thresholds related to the respective management systems. And both Scientific and Management Communities fully accept the necessity of living with determined levels of flood risk. Most of the approaches for “Advancing Methods” improving concentrate on the statistical ways, even since Climate in fact is not a Stationary process. The question is here reflected since the SMARTeST research and final highlights, policy and recommendations. The paper looks at a better agreement between Hydrology and the whole Climate as the result of the Global Thermal Machine and takes mainly into account a historical approach, trying to show the necessity of a wider collection and analysis of climate data for statistical approaches.

Looking for a more comprehensive approach

The necessity/convenience for improving accuracy in determining the flood frequency is widely accepted further than among hydrologists, and is increasingly deepened in relationship with the statement of different thresholds related to the respective management systems. And both Scientific and Management Communities fully accept the necessity of living with determined levels of flood risk. Most of the approaches for “Advancing Methods” improving concentrate on the statistical ways, even since Climate in fact is not a Stationary process. The question is here reflected since the SMARTeST research and final highlights, policy and recommendations. The paper looks at a better agreement between Hydrology and the whole Climate as the result of the Global Thermal Machine and takes mainly into account a historical approach, trying to show the necessity of a wider collection and analysis of climate data for statistical approaches.

Coastal Urban Flood Resislience versus Climate Change

Processes of founding and expanding cities in coastal areas have undergone great changes over time driven by environmental conditions. Coastal settlements looked for places above flood levels and away from swamps and other wetlands whenever possible. As populations grew, cities were extending trying to avoid low and wet lands. No city has been able to limit its growth. The risk of flooding can never be eliminated, but only reduced to the extent possible. Flooding of coastal areas is today dramatically attributed to eustasic sea level rise caused by global climate change. This can be inaccurate. Current climate change is generating an average sea level upward trend, but other regional and local factors result in this trend being accentuated in some places or attenuated, and even reversed, in others. Then, the intensity and frequency of coastal flooding around the planet, although not so much as a unique result of this general eustasic elevation, but rather of the superposition of marine and crustal dynamic elements, the former also climate-related, which give rise to a temporary raising in average sea level in the short term. Since the Little Ice Age the planet has been suffering a global warming change leading to sea level rise. The idea of being too obeying to anthropogenic factors may be attributed to Arrhenius (1896), though it is of much later highlight after the sixties of the last century. Never before, the human factor had been able of such an influence on climate. However, other types of changes in sea levels became apparent, resulting from vertical movements of the crust, modifications of sea basins due to continents fracturing, drifting and coming together, or to different types of climate patterns. Coastal zones are then doubly susceptible to floods. Precipitation immediately triggers pluvial flooding. If it continues upland or when snow and glaciers melt eventually fluvial flooding can occur. The urban development presence represents modifying factors. Additional interference is caused by river and waste water drainage systems. Climate also influences sea levels in coastal areas, where tides as well as the structure and dynamic of the geoid and its crust come into play. From the sea, waters can flood and break or push back berms and other coastline borders. The sea level, controlling the mouth of the main channel of the basin's drainage system, is ultimately what governs flood levels. A temporary rise in sea level acts as a dam at the mouth. Even in absence of that global change, so, floods are likely going to increase in many urban coastal areas. Some kind of innovative methodologies and practices should be needed to get more flood resilience cities