Evaluation of flood risk in response to climate variability

Standard procedures for forecasting flood risk (Bulletin 17B) assume annual maximum flood (AMF) series are stationary, meaning the distribution of flood flows is not significantly affected by climatic trends/cycles, or anthropogenic activities within the watershed. Historical flood events are therefore considered representative of future flood occurrences, and the risk associated with a given flood magnitude is modeled as constant over time. However, in light of increasing evidence to the contrary, this assumption should be reconsidered, especially as the existence of nonstationarity in AMF series can have significant impacts on planning and management of water resources and relevant infrastructure. Research presented in this thesis quantifies the degree of nonstationarity evident in AMF series for unimpaired watersheds throughout the contiguous U.S., identifies meteorological, climatic, and anthropogenic causes of this nonstationarity, and proposes an extension of the Bulletin 17B methodology which yields forecasts of flood risk that reflect climatic influences on flood magnitude. To appropriately forecast flood risk, it is necessary to consider the driving causes of nonstationarity in AMF series. Herein, large-scale climate patterns—including El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), North Atlantic Oscillation (NAO), and Atlantic Multidecadal Oscillation (AMO)—are identified as influencing factors on flood magnitude at numerous stations across the U.S. Strong relationships between flood magnitude and associated precipitation series were also observed for the majority of sites analyzed in the Upper Midwest and Northeastern regions of the U.S. Although relationships between flood magnitude and associated temperature series are not apparent, results do indicate that temperature is highly correlated with the timing of flood peaks. Despite consideration of watersheds classified as unimpaired, analyses also suggest that identified change-points in AMF series are due to dam construction, and other types of regulation and diversion. Although not explored herein, trends in AMF series are also likely to be partially explained by changes in land use and land cover over time. Results obtained herein suggest that improved forecasts of flood risk may be obtained using a simple modification of the Bulletin 17B framework, wherein the mean and standard deviation of the log-transformed flows are modeled as functions of climate indices associated with oceanic-atmospheric patterns (e.g. AMO, ENSO, NAO, and PDO) with lead times between 3 and 9 months. Herein, one-year ahead forecasts of the mean and standard deviation, and subsequently flood risk, are obtained by applying site specific multivariate regression models, which reflect the phase and intensity of a given climate pattern, as well as possible impacts of coupling of the climate cycles. These forecasts of flood risk are compared with forecasts derived using the existing Bulletin 17B model; large differences in the one-year ahead forecasts are observed in some locations. The increased knowledge of the inherent structure of AMF series and an improved understanding of physical and/or climatic causes of nonstationarity gained from this research should serve as insight for the formulation of a physical-casual based statistical model, incorporating both climatic variations and human impacts, for flood risk over longer planning horizons (e.g., 10-, 50, 100-years) necessary for water resources design, planning, and management.

MODULARITY BASED FUZZY COMMUNITY DETECTION IN SOCIAL NETWORKS

Fuzzy community detection is to identify fuzzy communities in a network, which are groups of vertices in the network such that the membership of a vertex in one community is in [0,1] and that the sum of memberships of vertices in all communities equals to 1. Fuzzy communities are pervasive in social networks, but only a few works have been done for fuzzy community detection. Recently, a one-step forward extension of Newman’s Modularity, the most popular quality function for disjoint community detection, results into the Generalized Modularity (GM) that demonstrates good performance in finding well-known fuzzy communities. Thus, GMis chosen as the quality function in our research. We first propose a generalized fuzzy t-norm modularity to investigate the effect of different fuzzy intersection operators on fuzzy community detection, since the introduction of a fuzzy intersection operation is made feasible by GM. The experimental results show that the Yager operator with a proper parameter value performs better than the product operator in revealing community structure. Then, we focus on how to find optimal fuzzy communities in a network by directly maximizing GM, which we call it Fuzzy Modularity Maximization (FMM) problem. The effort on FMM problem results into the major contribution of this thesis, an efficient and effective GM-based fuzzy community detection method that could automatically discover a fuzzy partition of a network when it is appropriate, which is much better than fuzzy partitions found by existing fuzzy community detection methods, and a crisp partition of a network when appropriate, which is competitive with partitions resulted from the best disjoint community detections up to now. We address FMM problem by iteratively solving a sub-problem called One-Step Modularity Maximization (OSMM). We present two approaches for solving this iterative procedure: a tree-based global optimizer called Find Best Leaf Node (FBLN) and a heuristic-based local optimizer. The OSMM problem is based on a simplified quadratic knapsack problem that can be solved in linear time; thus, a solution of OSMM can be found in linear time. Since the OSMM algorithm is called within FBLN recursively and the structure of the search tree is non-deterministic, we can see that the FMM/FBLN algorithm runs in a time complexity of at least O (n2). So, we also propose several highly efficient and very effective heuristic algorithms namely FMM/H algorithms. We compared our proposed FMM/H algorithms with two state-of-the-art community detection methods, modified MULTICUT Spectral Fuzzy c-Means (MSFCM) and Genetic Algorithm with a Local Search strategy (GALS), on 10 real-world data sets. The experimental results suggest that the H2 variant of FMM/H is the best performing version. The H2 algorithm is very competitive with GALS in producing maximum modularity partitions and performs much better than MSFCM. On all the 10 data sets, H2 is also 2-3 orders of magnitude faster than GALS. Furthermore, by adopting a simply modified version of the H2 algorithm as a mutation operator, we designed a genetic algorithm for fuzzy community detection, namely GAFCD, where elite selection and early termination are applied. The crossover operator is designed to make GAFCD converge fast and to enhance GAFCD’s ability of jumping out of local minimums. Experimental results on all the data sets show that GAFCD uncovers better community structure than GALS.