By A. Ramachandra Rao, V.V. Srinivas (auth.)

Design of water regulate constructions, reservoir administration, monetary assessment of flood security initiatives, land use making plans and administration, flood coverage evaluation, and different tasks depend upon wisdom of significance and frequency of floods. frequently, estimation of floods isn't effortless due to loss of flood documents on the objective websites. local flood frequency research (RFFA) alleviates this challenge through the use of flood documents pooled from different watersheds, that are just like the watershed of the objective web site in flood characteristics.

Clustering ideas are used to spot group(s) of watersheds that have comparable flood features. This booklet is a complete reference on how you can use those concepts for RFFA and is the 1st of its style. It offers a close account of a number of lately constructed clustering suggestions, together with these according to fuzzy set thought and synthetic neural networks. It additionally files study findings on software of clustering recommendations to RFFA that stay scattered in a variety of hydrology and water assets journals.

The optimum variety of teams outlined in a space relies on cluster validation measures and L-moment dependent homogeneity exams. those shape the bases to ascertain the areas for homogeneity.

The subjectivity concerned and the trouble had to determine homogeneous teams of watersheds with traditional methods are significantly lowered by utilizing effective clustering strategies mentioned during this e-book. additionally, higher flood estimates with smaller self belief periods are bought through research of information from homogeneous watersheds. for that reason, the matter of over- or under-designing through the use of those flood estimates is diminished. This ends up in optimum fiscal layout of constructions. the benefits of higher regionalization of watersheds and their software are stepping into hydrologic perform.

*Audience*This booklet can be of curiosity to researchers in stochastic hydrology, practitioners in hydrology and graduate students.

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**Extra resources for Regionalization of Watersheds: An Approach Based on Cluster Analysis**

**Example text**

2004), have been used in examples presented in this book. The Davies-Bouldin index is computed using Eq. 18). A small value for DB indicates good partition, which corresponds to compact clusters with their centers far apart. 18) Dunn’s index is computed by using Eq. 19) 1≤k≤K where δ(Ci , C j ) denotes the distance between clusters Ci and C j (intercluster distance) computed using Eq. 20); Δ(Ck ) represents the intracluster distance of cluster Ck defined by Eq. 21). The value of K for which D is maximized is taken as the optimal number of clusters.

To understand this point Eq. 5) k=1 j=1 i=1 where, x• j denotes the mean value of j-th attribute over all feature vectors. 7) (xikj − x• j )(x• j − x•k j ) From Eq. 8) i=1 The value x• j is unique for a given set of feature vectors. 9) i=1 Substituting the values of Eqs. 3 Clustering Algorithms and Performance Assessment 27 Let us consider two clusters labeled 1 and 2, before and after merger. Let N1 and N2 denote the number of feature vectors in clusters 1 and 2 respectively. The value of objective function before merger is obtained by substituting K=2 in Eq.

The feature vectors of X are divided into two subsets I and O, which are composed of inliers and outliers, respectively. Inliers are feature vectors assigned to clusters, whereas outliers are those which are not allocated to any cluster. 25) where Z represents the set of cluster centroids Z = {z1 , z2 , . . , z K }. The complexity of the entire model is evaluated by the term mod L(I, Z). The length of encoding mod L(I, Z) is given by the sum of: (i) the length of encoding Z, denoted by L(Z); and (ii) the length of encoding all the indices of I, given by L(I(Z)).