Eiji Tokunaga

Bio: Eiji Tokunaga is an academic researcher. The author has contributed to research in topics: Drainage. The author has an hindex of 1, co-authored 1 publications receiving 117 citations.

A coupled channel network growth and hillslope evolution model: 1. Theory

Abstract: This paper presents a model of the long-term evolution of catchments, the growth of their drainage networks, and the changes in elevations within both the channels and the hillslopes. Elevation changes are determined from continuity equations for flow and sediment transport, with sediment transport being related to discharge and slope. The central feature of the model is that it explicitly differentiates between the sediment transport behavior of the channels and the hillslopes on the basis of observed physics, and the channel network extension results solely from physically based flow interactions on the hillslopes. The difference in behavior of channels and hillslopes is one of the most important properties of a catchment. The flow and sediment transport continuity equations in the channel and the hillslope are coupled and account for the long-term interactions of the elevations in the hillslope and in the channels. Sediment transport can be due to fluvial processes, creep, and rockslides. Tectonic uplift may increase overall catchment elevations. The dynamics of channel head advance, and thus network growth, are modeled using a physically based mechanism for channel initiation and growth where a channel head advances when a channel initiation function, nonlinearly dependent on discharge and slope, exceeds a threshold. This threshold controls the drainage density of the basin. A computer implementation of the model is introduced, some simple simulations presented, and the numerics of the solution technique described.

Scaling, Universality, and Geomorphology

Abstract: Theories of scaling apply wherever similarity exists across many scales. This similarity may be found in geometry and in dynamical processes. Universality arises when the qualitative character of a system is sufficient to quantitatively predict its essential features, such as the exponents that characterize scaling laws. Within geomorphology, two areas where the concepts of scaling and universality have found application are the geometry of river networks and the statistical structure of topography. We begin this review with a pedagogical presentation of scaling and universality. We then describe recent progress made in applying these ideas to networks and topography. This overview leads to a synthesis that attempts a classification of surface and network properties based on generic mechanisms and geometric constraints. We also briefly review how scaling and universality have been applied to related problems in sedimentology—specifically, the origin of stromatolites and the relation of the statistical pro...

New Results for Self-Similar Trees with Applications to River Networks

Abstract: In a little-known series of papers beginning in 1966, Tokunaga introduced an infinite class of tree graphs based on the Strahler ordering scheme. As recognized by Tokunaga (1984), these trees are characterized by a self-similarity property, so we will refer to them as self-similar trees, or SSTs. SSTs are defined in terms of a generator matrix which acts as a “blueprint” for constructing different trees. Many familiar tree constructions are absorbed as special cases. However, in Tokunaga's work an additional assumption is imposed which restricts from SSTs to a much smaller class. We will refer to this subclass as Tokunaga's trees. This paper presents several new and unifying results for SSTs. In particular, the conditions under which SSTs have well-defined Horton-Strahler stream ratios are given, as well as a general method for computing these ratios. It is also shown that the diameters of SSTs grow like mβ, where m is the number of leaves. In contrast to many other tree constructions, here β need not equal 1/2; thus SSTs offer an explanation for Hack's law. Finally, it is demonstrated that large discrepancies exist between the predictions of Shreve's well-known model and detailed measurements for large river networks, while other SSTs fit the data quite well. Other potential applications of the SST framework include diffusion-limited aggregation (DLA), lightning, bronchial passages, neural networks, and botanical trees.

Coupled numerical–analytical approach to landscape evolution modeling

Abstract: The Earth's topography is shaped by surface processes that operate on various scales. In particular, river processes control landscape dynamics over large length scales, whereas hillslope processes control the dynamics over smaller length scales. This scale separation challenges numerical treatments of landscape evolution that use space discretization. Large grid spacing cannot account for the dynamics of water divides that control drainage area competition, and erosion rate and slope distribution. Small grid spacing that properly accounts for divide dynamics is computationally inefficient when studying large domains. Here we propose a new approach for landscape evolution modeling that couples irregular grid-based numerical solutions for the large-scale fluvial dynamics and continuum-based analytical solutions for the small-scale fluvial and hillslope dynamics. The new approach is implemented in the landscape evolution model DAC (divide and capture). The geometrical and topological characteristics of DAC's landscapes show compatibility with those of natural landscapes. A comparative study shows that, even with large grid spacing, DAC predictions fit well an analytical solution for divide migration in the presence of horizontal advection of topography. In addition, DAC is used to study some outstanding problems in landscape evolution. (i) The time to steady-state is investigated and simulations show that steady-state requires much more time to achieve than predicted by fixed area calculations, due to divides migration and persistent reorganization of low-order streams. (ii) Large-scale stream captures in a strike-slip environment are studied and show a distinct pattern of erosion rates that can be used to identify recent capture events. (iii) Three tectono-climatic mechanisms that can lead to asymmetric mountains are studied. Each of the mechanisms produces a distinct morphology and erosion rate distribution. Application to the Southern Alps of New Zealand suggests that tectonic advection, precipitation gradients and non-uniform tectonic uplift act together to shape the first-order topography of this mountain range. Copyright © 2014 John Wiley & Sons, Ltd.