Emergent Spectral Properties Of River Network Topology: An Optimal Channel Network Approach

Characterization of river drainage networks has been a subject of research for many years. However, most previous studies have been limited to quantities which are loosely connected to the topological properties of these networks. In this work, through a graph-theoretic formulation of drainage river networks, we investigate the eigenvalue spectra of their adjacency matrix. First, we introduce a graph theory model for river networks and explore the properties of the network through its adjacency matrix. Next, we show that the eigenvalue spectra of such complex networks follow distinct patterns and exhibit striking features including a spectral gap in which no eigenvalue exists as well as a finite number of zero eigenvalues. We show that such spectral features are closely related to the branching topology of the associated river networks. In this regard, we find an empirical relation for the spectral gap and nullity in terms of the energy dissipation exponent of the drainage networks. In addition, the eigenvalue distribution is found to follow a finite-width probability density function with certain skewness which is related to the drainage pattern. Our results are based on optimal channel network simulations and validated through examples obtained from physical experiments on landscape evolution. These results suggest the potential of the spectral graph techniques in characterizing and modeling river networks

Reorganization Of River Networks Under Changing Spatiotemporal Precipitation Patterns: An Optimal Channel Network Approach

We investigate the impact of changing nonuniform spatial and temporal precipitation patterns on the evolution of river networks. To achieve this, we develop a two-dimensional optimal channel network (OCN) model with a controllable rainfall distribution to simulate the evolution of river networks, governed by the principle of minimum energy expenditure, inside a prescribed boundary. We show that under nonuniform precipitation conditions, river networks reorganize significantly toward new patterns with different geomorphic and hydrologic signatures. This reorganization is mainly observed in the form of migration of channels of different orders, widening or elongation of basins as well as formation and extinction of channels and basins. In particular, when the precipitation gradient is locally increased, the higher-order channels, including the mainstream river, migrate toward regions with higher precipitation intensity. Through pertinent examples, the reorganization of the drainage network is quantified via stream parameters such as Horton-Strahler and Tokunaga measures, order-based channel total length and river long profiles obtained via simulation of three-dimensional basin topography, while the hydrologic response of the evolved network is investigated using metrics such as hydrograph and power spectral density of simulated streamflows at the outlet of the network. In addition, using OCNs, we investigate the effect of orographic precipitation patterns on multicatchment landscapes composed of several interacting basins. Our results show that network-inspired methods can be utilized as insightful and versatile models for directly exploring the effects of climate change on the evolution of river drainage systems

A Heuristic Evolutionary Game Theoretic Methodology For Conjunctive Use Of Surface And Groundwater Resources

In this paper, a methodology based on a new heuristic evolutionary game is developed to determine evolutionary stable equilibrium (ESE) strategies for conjunctive surface and groundwater allocation to water users with conflicting objectives. The methodology provides reasonable and realistic framework to illuminate non-cooperative behaviors of water users in the joint usage of surface and groundwater resources. The developed heuristic evolutionary game theoretic approach can be used for finding equilibrium in asymmetric n-person games with continuous strategies. The penalty function is provided in a way that it can control groundwater table drawdown at monitoring points. It is also shown that applying the proposed penalty function may inhibit the water users’ excessive exploitation and can consequently avoid the tragedy of commons. As the methodology needs to run water allocation optimization and groundwater simulation models for several times, an optimization model based on genetic algorithms is linked with MODFLOW groundwater simulation model. Furthermore, a computational cost reduction method has been used to reduce the computation time caused by several consecutive computational steps in the proposed methodology. A pistachio loss function due to the deficit irrigation is also developed and used for evaluating water users’ objective functions. To illustrate the practical utility of the methodology, it is applied to the Rafsanjan plain in Iran and it is shown that this approach can be used for developing surface and groundwater allocation policies

Emergent spectral properties of river network topology: an optimal channel network approach

Abstract Characterization of river drainage networks has been a subject of research for many years. However, most previous studies have been limited to quantities which are loosely connected to the topological properties of these networks. In this work, through a graph-theoretic formulation of drainage river networks, we investigate the eigenvalue spectra of their adjacency matrix. First, we introduce a graph theory model for river networks and explore the properties of the network through its adjacency matrix. Next, we show that the eigenvalue spectra of such complex networks follow distinct patterns and exhibit striking features including a spectral gap in which no eigenvalue exists as well as a finite number of zero eigenvalues. We show that such spectral features are closely related to the branching topology of the associated river networks. In this regard, we find an empirical relation for the spectral gap and nullity in terms of the energy dissipation exponent of the drainage networks. In addition, the eigenvalue distribution is found to follow a finite-width probability density function with certain skewness which is related to the drainage pattern. Our results are based on optimal channel network simulations and validated through examples obtained from physical experiments on landscape evolution. These results suggest the potential of the spectral graph techniques in characterizing and modeling river networks

Developing Probabilistic Operating Rules for Real-time Conjunctive Use of Surface and Groundwater Resources:Application of Support Vector Machines

Developing optimal operating policies for conjunctive use of surface and groundwater resources when different decision makers and stakeholders with conflicting objectives are involved is usually a challenging task. This problem would be more complex when objectives related to surface and groundwater quality are taken into account. In this paper, a new methodology is developed for real time conjunctive use of surface and groundwater resources. In the proposed methodology, a well-known multi-objective genetic algorithm, namely Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to develop a Pareto front among the objectives. The Young conflict resolution theory is also used for resolving the conflict of interests among decision makers. To develop the real time conjunctive use operating rules, the Probabilistic Support Vector Machines (PSVMs), which are capable of providing probability distribution functions of decision variables, are utilized. The proposed methodology is applied to Tehran Aquifer inTehran metropolitan area,Iran. Stakeholders in the study area have some conflicting interests including supplying water with acceptable quality, reducing pumping costs, improving groundwater quality and controlling the groundwater table fluctuations. In the proposed methodology, MODFLOW and MT3D groundwater quantity and quality simulation models are linked with NSGA-II optimization model to develop Pareto fronts among the objectives. The best solutions on the Pareto fronts are then selected using the Young conflict resolution theory. The selected solution (optimal monthly operating policies) is used to train and verify a PSVM. The results show the significance of applying an integrated conflict resolution approach and the capability of support vector machines for the real time conjunctive use of surface and groundwater resources in the study area. It is also shown that the validation accuracy of the proposed operating rules is higher that 80% and based on these rules, the cumulative groundwater table variation is limited to 80 centimetres during a 15-year planning horizon

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Abstract Developing optimal operating policies for conjunctive use of surface and groundwater resources when different decision makers and stakeholders with conflicting objectives are involved is usually a challenging task. This problem would be more complex when objectives related to surface and groundwater quality are taken into account. In this paper, a new methodology is developed for real time conjunctive use of surface and groundwater resources. In the proposed methodology, a well-known multi-objective genetic algorithm, namely Nondominated Sorting Genetic Algorithm II (NSGA-II) is employed to develop a Pareto front among the objectives. The Young conflict resolution theory is also used for resolving the conflict of interests among decision makers