Nowadays, a noteworthy temporal alteration of traditional hydrological patterns is being observed, producing a higher variability and more unpredictable extreme events worldwide. This is largely due to global warming, which is generating a growing uncertainty over water system behavior, especially river runoff. Understanding these modifications is a crucial and not trivial challenge that requires new analytical strategies like Causality, addressed by Causal Reasoning. Through Causality over runoff series, the hydrological memory and its logical time-dependency structure have been dynamically/stochastically discovered and characterized. This is done in terms of the runoff dependence strength over time. This has allowed determining and quantifying two opposite temporal-fractions within runoff: Temporally Conditioned/Non-conditioned Runoff (TCR/TNCR). Finally, a successful predictive model is proposed and applied to an unregulated stretch, Mijares river catchment (Jucar river basin, Spain), with a very high time-dependency behavior. This research may have important implications over the knowledge of historical rivers´ behavior and their adaptation. Furthermore, it lays the foundations for reaching an optimum reservoir dimensioning through the building of predictive models of runoff behavior. Regarding reservoir capacity, this research would imply substantial economic/environmental savings. Also, a more sustainable management of river basins through more reliable control reservoirs’ operation is expected to be achieved.

One of the main drawbacks of the traditional methods for computing components in the three-way Tucker model is the complex structure of the final loading matrices preventing an easy interpretation of the obtained results. In this paper, we propose a heuristic algorithm for computing disjoint orthogonal components facilitating the analysis of three-way data and the interpretation of results. We observe in the computational experiments carried out that our novel algorithm ameliorates this drawback, generating final loading matrices with a simple structure and then easier to interpret. Illustrations with real data are provided to show potential applications of the algorithm.

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques, do not guarantee that interpretable loading matrices are obtained in this model. We propose a novel heuristic algorithm that allows simple structure loading matrices to be obtained by calculating disjoint orthogonal components. This algorithm is also an alternative approach for solving the well-known degeneracy problem. We carry out computational experiments by utilizing simulated and real-world data to illustrate the benefits of the proposed algorithm.

The concept of sustainability is assumed for this research from a temporal perspective. Rivers represent natural systems with an inherent internal memory on their runoff and, by extension, to their hydrological behavior, that should be identified, characterized and quantified. This memory is formally called temporal dependence and allows quantifying it for each river system. The ability to capture that temporal signature has been analyzed through different methods and techniques. However, there is a high heterogeneity on those methods’ analytical capacities. It is found in this research that the most advanced ones are those whose output provides a dynamic and quantitative assessment of the temporal dependence for each river system runoff. Since the runoff can be split into temporal conditioned runoff fractions, advanced methods provide an important improvement over classic or alternative ones. Being able to characterize the basin by calculating those fractions is a very important progress for water managers that need predictive tools for orienting their water policies to a certain manner. For instance, rivers with large temporal dependence will need to be controlled and gauged by larger hydraulic infrastructures. The application of this approach may produce huge investment savings on hydraulic infrastructures and an environmental impact minimization due to the achieved optimization of the binomial cost-benefit.