«25110 Record Number: Author, Monographic: Ouarda, T. B. M. J.//Bobée, B. Author Role: Regional estimation of floods and droughts in the State of ...»
Author, Monographic: Ouarda, T. B. M. J.//Bobée, B.
Regional estimation of floods and droughts in the State of Minas Gerais, Brazil
Place of Publication: Québec INRS-Eau, Terre & Environnement
Date of Publication: 2003 Septembre 2003
Original Publication Date:
Extent of Work:
Series Editor Role:
INRS-Eau, Terre & Environnement, rapport de recherche
Series Volume ID:
Rapport annuel 2002-2003
Numéro de rapport et ISBN fourni par Geneviève le 7 juin 2002. Confirmé par jdb, 20030917
REGIONAL ESTIMATION OF FLOODS AND
DROUGHTS IN THE STATE OF MINAS GERAIS,
BRAZILSeptember 2003 Research Report No R-619 Regional estimation of floods and droughts in the State of Minas Gerais, Brazil T.B.M.J. Ouarda B. Bobée
submitted to :
SYNEXUS GLOBAL INC.1801 McGill College, Suite 1060, Montréal, Québec H3A 2N4 Canada NSERClHydro-Québec Chair in Statistical Hydrology Institut National de la Recherche Scientifique, INRS-ETE 2800 Einstein, C.P. 7500, Sainte-Foy (Québec) GIV 4C7 Researeh Report No. R-619 ISBN: 2-89146-482-6 September 2003 3
SYNEXUS GLOBAL INC.A. Robitaille Chair in Statistical Hydrology INRS-ETE Taha B.M.J. Ouarda Bernard Bobée 4 Table of contents TABLE OF CONTENTS
CHAPITER 1: Introduction
CHAPITER 2: Evaluation of the method currently used by IGAM
CHAPITER 3: Proposition of alternative regional estimation methodologies
3.1 Brief literature review
10 3.1.1 Homogeneous region delineation
3.1.2 Regional estimation
3.2 Selection of methods
3.3 Adaptation of currently available tools and software
3.4 An alternative methodology for the regional estimation of drought characteristics
CHAPITER 4: Conclusions
CHAPITER 5: References
1. Introduction In regional flood/drought frequency analysis, the objective is to estimate flood/drought characteristics, such as the T-year events QT at any location in a given region, mainly at ungauged sites. In the coming sections we will focus on regional flood frequency analysis, without loss of generality. Indeed, regional flood and drought frequency analysis methodologies are very similar and are based on the same principles.
In regional flood frequency analysis, the flood characteristics of ungauged basins are estimated by using relationships between physiographical and meteorological variables and characteristics of the maximum annual floods or the partial duration series of a set of gauged basins with hydrological regimes similar to those of the ungauged basin.
The usual steps of the estimation are:
(1) Determination of a set of similar basins (homogeneous region»).
(2) Regional estimation of the flood distribution of the ungauged basin.
Several methods for the determination of homogeneous regions and for regional estimation have been proposed in the literature. The objective of the present report is to critically evaluate the method currently used by the IGAM (Instituto Mineiro de Gestao das Aguas) in the state of Minas Gerais, Brazil, for the regional estimation of floods and droughts. The present report ai ms also at presenting a brief review of the various methodologies that are available for regional estimation of floods and droughts, and proposing sorne alternatives to the methodology currently used by IGAM. The report makes also sorne recommendations concerning the methodologies that could be adopted in the state of Minas Gerais, and concerning future efforts aiming at the development of 7 regional estimation tools that are up-to-date and that utilise the most prominent and powerful methods that are eurrently available in the literature.
2. Evaluation of the method currently used by IGAM IGAM currently uses a procedure for the estimation of drought flows and design flows, that relies on previous experience and on a series of maps that define a set of geomorphological, meteorological and hydrological characteristics for the State of Minas Gerais. A very elaborate set of maps provides a geographic subdivision of the State of Minas Gerais into a large number of small regions for which the characteristics are the same.
One of the most important maps pro vides a family of iso-lines for which the minimum specific monthly streamflow is constant (corresponding to a return period of 10 years). The second map defines, in a fine resolution, a subdivision of the State Înto regions for which three characteristics P, D, and 1 are homogeneous; where P is the precipitation, D is the slope and 1 is the permeability. These maps pro vide a relatively refined description of the rainfall regime, the geomorphologic characteristics and the hydrologic regime in each location in the State.
The empirical approach currently used in the State of Minas Gerais allows to ob tain a very fast and relatively reliable estimates of drought flows and design flows. However, these values remain rough estimates of the desired streamflows. It is possible to obtain more accurate estimates of these variables by using more sophisticated but widely accepted regional estimation techniques. These new techniques are nowadays standard approaches for the estimation of streamflow characteristics in ungauged locations. It is also possible to use more recent approaches (such as the canonical correlation analysis method) which were shown to lead to an even better accuracy. This aspect will become apparent as we review, 9 in chapter 3, the state of the art of hydrological regional frequency analysis. Indeed, the approaches presented in chapter 3 are straight forward, easy to use, accepted by the hydrological community aIl over the world, and are already available in the form of a user friendly software.
Furthermore, it must mentioned that the maps currently used by IGAM need to be constantly updated with new information (every few years). Indeed, land use parameters, for example, change constantly and this information needs to be fed to the maps. New precipitation information is available ever year, and should be used toupdate the precipitation index map. This aIlows to avoid any bias resulting from previous wet periods or drought spells that may have taken place in the past and were used in defining the current map. This systematic updating of these maps can be quite costly and unjustified compared to the costs of using other regionalisation approaches as will be presented in chapter 3.
3. Proposition of alternative regional estimationmethodologies
3.1 Brief literature review As indicated in chapter 1, The two main steps of a hydrological regional estimation methodology are the identification of groups of hydrologically homogeneous basins (or "homogeneous regions") and the application of a regional estimation method within each delineated region. These two steps will be considered separately in the following two sections.
3.1.1 Homogeneous region delineation
Homogeneous regions may be defined in the space of geographical coordinates. This definition, however, has the disadvantage that it is not applicable to small areas and that contiguous basins may not be hydrologically similar (Linsley 1982, Cunnane 1986, Wiltshire 1986). To overcome this difficulty, sorne researchers have defined homogeneous regions in the space of flood-related variables (Mosley 1981, Gottschalk 1985, Wiltshire 1986). This definition has both advantages and disadvantages. The primary advantage is that it is based on variables directly related to the flood phenomenon; its disadvantages are firstly the difficulty of relating the characteristics of hydrologically defined homogeneous regions to the topographical, physiographical and meteorological conditions of the area and secondly the fact that homogeneous regions in this definition are usually determined by cluster analysis, the purpose of which is to discover «natural clusters» (Dillon and Goldstein 1984) based on the assumption that such clusters exist; however, the existence of 11 such clusters cannot be taken for granted without prior testing (Rogers 1974, Dubes and Zeng 1987). The final set of homogeneous regions depends on the clustering method, the initial partitioning of the space and the me tric used. For this reason, sorne researchers attempted to relate this type of homogeneous region to the geographical coordinates empirically (Mosley 1981, Gottschalk 1985), or to introduce the concept of fractional membership of a basin to a homogeneous region (Wiltshire 1986).
An entirely different concept of homogeneous region is the «neighbourhood» or «region of influence». Here, a homogeneous region is defined in the space of physiographical, meteorological and hydrological variables and centered on the basin under investigation (Acreman and Wiltshire, 1989, Bum, 1990ab, Zrinji and Bum, 1994, Ouarda et al., 1998, 2000, 2001). This type of region avoids the difficulties related to the existence of «real» clusters but, in contrast to a priori regions, it has to be determined specifically for each basin under investigation. Two specifie methods can be identified: the region of influence method (Bum, 1990ab) and the canonical correlation analysis method (Ouarda et al., 1998, 2000, 2001).
According to the region of influence method, the gauged basins enter the region of influence in the order of their weighted Euclidean distances from the ungauged basin in the space of the physiographieal and meteorologieal variables where the weights of the variables are selected by the user. At every step, a homogeneity test, based on the flood distributions of the gauged basins of the homogeneous region is used to determine whether the boundary of the homogeneous region has been reached. The «region of influence»
approach has the following limitations:
(a) It requires a choice of an arbitrary weight for each basin variable.
(b) It uses weighted Euclidean distances that do not take into account the
(c) The region of influence is determined using both the basin and the flood variables without taking into account the relations between these two sets of variables.
The otherapproach for determining basin-centered homogeneous regions, uses the multivariate method of canonical correlation analysis which takes into account the relationships between the physiographical and meteorological variables and the characteristics of the distribution of the maximum annual floods (Ouarda et al., 1998,2000, 2001). This approaches has several strengths compared to all other methods of delineation of homogeneous regions. Among these strengths is the limited number of assumptions the method makes (only one hypothesis, and absolutely no assumptions concerning the statistical distribution of floods/droughts), the robustness of the method to changes in the configuration of the hydrometric network and to at-site estimation, the solid mathematical background of the method, and the capacity to jointly estimate several variables at the same time (for ex ample flood peak and flood volume quantiles). A detailed description of the mathematical background of the method and its characteristics is available in Ouarda et al.
•• • • • 0 •• ••
Figure 1. Various approaches for the determination of homogeneous regions 3.
1.2 Regional estimation Essentially, a regional estimation method is a technique for transferring information from the sites deemed to possess pertinent hydrological information to the site at which a quantile estimate is needed. Many regional estimation methods have been suggested in the literature.
The index flood method for regional flood estimation was devised by Dalrymple (1960).
The main assumption is that floods at different sites within a region are identically distributed except for a scale factor which is a function of the physiographical basin characteristics. Usually, the catchment area is the most important factor for explaining the scale of floods.. The index flood method was abandoned for sorne years, mainly because it was found that the catchment area affected not only the scale, but also other· characteristics of' flood distributions, such as the coefficient of variation and the coefficient of skewness, which according to the assumptions should be constant. In the last decade, however, the index flood method has regained its early popularity, 14 and today it is judged to be one of the most efficient regionalisation techniques (Cunnane, 1986;
Potter and Lettenmaier, 1990).