Multicriteria Optimization Model to Generate on-DEM Optimal Channel Networks

Abstract

The theory of optimal channel networks (OCNs) explains the existence of self-similarities in river networks by multiple optimality principles, namely, (i) the minimum energy expenditure in any link, (ii) the equal energy expenditure per unit area of channel anywhere, and (iii) the minimum total energy expenditure (TEE). These principles have been used to generate OCNs from 2-D networks. The existing notion of OCN considers the concavity of river longitudinal profiles as a priori condition. Attempts to generate OCNs starting from a random 3-D digital elevation model (DEM) and minimizing solely TEE have failed to reproduce concave profiles. Yet alternative approaches can be devised from the three optimality principles, for instance, focusing on the local energy expenditure (LEE). In this paper, we propose a Multiobjective modeling framework for Riverscape Exploration (MoRE) via simultaneous optimization of multiple OCN criteria. MoRE adopts a multiobjective evolutionary algorithm and radial basis functions to efficiently guide DEM elevation variations required to shape 3-D OCNs. By minimizing both TEE and the variance in LEE, MoRE successfully reproduces realistic on-DEM, OCN-based riverscapes, for the first time. Simulated networks possess scaling laws of upstream area and length and river longitudinal profile resembling those of real river networks. The profile concavity of generated on-DEM OCNs emerges as a consequence of the minimization of TEE constrained to the equalization of LEE. Minimizing TEE under this condition generates networks that possess specific patterns of LEE, where the scaling of slope with basin area resembles the patterns observed in real river networks. Plain Language Summary In nature, river networks self-organize their branches so that the energy spent by the water flow to reach the outlet is kept to a minimum. This physical process can be expressed mathematically with diverse formulations, which inspired a theory called Optimal Channel Network. Several studies applied Optimal Channel Network theory to reproduce two-dimensional features of channel networks, that is, how river branches develop and organize within the network. Yet these studies were not able to reproduce realistic river networks in three dimensions, for instance, starting from a random digital elevation model. In this paper, we propose the first modeling framework able to generate artificial river networks from random digital elevation model that resemble those observed in nature for their 3-D characteristics, in terms of 2-D organization of the river network branches, as well as longitudinal profile of the river elevations. This work contributes to enrich our understanding about the mechanisms guiding the development and evolution of river networks in nature and provides a software tool that can be used for future research on real-world 3-D river landscapes.