J.T. Hack

Bio: J.T. Hack is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 1257 citations.

The Fractal Geometry of Nature

Abstract: "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

A hierarchical framework for stream habitat classification: Viewing streams in a watershed context

Abstract: Classification of streams and stream habitats is useful for research involving establishment of monitoring stations, determination of local impacts of land-use practices, generalization from site-specific data, and assessment of basin-wide, cumulative impacts of human activities on streams and their biota. This article presents a frame-work for a hierarchical classification system, entailing an organized view of spatial and temporal variation among and within stream systems. Stream habitat systems, defined and classified on several spatiotemporal scales, are associated with watershed geomorphic features and events. Variables selected for classification define relative long-term capacities of systems, not simply short-term states. Streams and their watershed environments are classified within the context of a regional biogeoclimatic landscape classification. The framework is a perspective that should allow more systematic interpretation and description of watershed-stream relationships.

Dynamics of the stream‐power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs

Abstract: The longitudinal profiles of bedrock channels are a major component of the relief structure of mountainous drainage basins and therefore limit the elevation of peaks and ridges. Further, bedrock channels communicate tectonic and climatic signals across the landscape, thus dictating, to first order, the dynamic response of mountainous landscapes to external forcings. We review and explore the stream-power erosion model in an effort to (1) elucidate its consequences in terms of large-scale topographic (fluvial) relief and its sensitivity to tectonic and climatic forcing, (2) derive a relationship for system response time to tectonic perturbations, (3) determine the sensitivity of model behavior to various model parameters, and (4) integrate the above to suggest useful guidelines for further study of bedrock channel systems and for future refinement of the streampower erosion law. Dimensional analysis reveals that the dynamic behavior of the stream-power erosion model is governed by a single nondimensional group that we term the uplift-erosion number, greatly reducing the number of variables that need to be considered in the sensitivity analysis. The degree of nonlinearity in the relationship between stream incision rate and channel gradient (slope exponent n) emerges as a fundamental unknown. The physics of the active erosion processes directly influence this nonlinearity, which is shown to dictate the relationship between the uplift-erosion number, the equilibrium stream channel gradient, and the total fluvial relief of mountain ranges. Similarly, the predicted response time to changes in rock uplift rate is shown to depend on climate, rock strength, and the magnitude of tectonic perturbation, with the slope exponent n controlling the degree of dependence on these various factors. For typical drainage basin geometries the response time is relatively insensitive to the size of the system. Work on the physics of bedrock erosion processes, their sensitivity to extreme floods, their transient responses to sudden changes in climate or uplift rate, and the scaling of local rock erosion studies to reach-scale modeling studies are most sorely needed.

A detachment-limited model of drainage basin evolution

Abstract: A drainage basin simulation model introduced here incorporates creep and threshold slumping and both detachment- and transport-limited fluvial processes. Fluvial erosion of natural slopes and headwater channels is argued to be dominantly detachment-limited. Such slopes undergo nearly parallel retreat and replacement with alluvial surfaces under fixed base level, in contrast with gradual slope decline for transport-limited conditions. The arrangement of divides and valleys is sensitive to initial conditions, although average morphology is insensitive. Dissected, initially flat surfaces in which downstream concavity is slight exhibit nearly parallel drainage, compared to very wandering main valleys when concavity is great. Steady state is reached after a cumulative base level drop approximately 3 times the final relief. Simulated valley systems are similar to those predicted by a previous model of optimal drainage basins. A critical value of slope divergence normalized by average slope gradient is a useful criterion for defining the valley network.

Tectonics from topography: Procedures, promise, and pitfalls

Abstract: Empirical observations from fl uvial systems across the globe reveal a consistent power-law scaling between channel slope and contributing drainage area. Theoretical arguments for both detachmentand transport-limited erosion regimes suggest that rock uplift rate should exert fi rst-order control on this scaling. Here we describe in detail a method for exploiting this relationship, in which topographic indices of longitudinal profi le shape and character are derived from digital topographic data. The stream profi le data can then be used to delineate breaks in scaling that may be associated with tectonic boundaries. The description of the method is followed by three case studies from varied tectonic settings. The case studies illustrate the power of stream profi le analysis in delineating spatial patterns of, and in some cases, temporal changes in, rock uplift rate. Owing to an incomplete understanding of river response to rock uplift, the method remains primarily a qualitative tool for neotectonic investigations; we conclude with a discussion of research needs that must be met before we can extract quantitative information about tectonics directly from topography.