Networks of Historical Contingency in Earth Surface Systems

Abstract

Earth surface systems (ESS) are characterized by various degrees of historical contingency, which complicates efforts to relate observed features and phenomena to environmental controls. This article provides a conceptual framework for understanding and assessing historical contingency in ESS that is based on algebraic graph theory. ESS are conceptualized as consisting of components (e.g., climate, topography, and lithology) observed or inferred at time periods. Each component at each time period represents a node of a network or graph, and interactions among components constitute the links or edges. Four indexes are applied: the S-metric, which indicates the extent to which observations of part of the network (e.g., topographic changes between two time periods) are likely to represent the dynamics of the network as a whole; spectral radius, which measures coherence and potential amplification of changes or disturbances; Laplacian spectral radius, an index of the relationship between network stability and time steps and an indication of path dependence; and algebraic connectivity, which measures the inferential synchronizability. For each of these, an index on a 0–1 scale is developed, which represents high and minimum levels of historical contingency for a given n, q. These are applied to several archetypal graph structures that represent various forms of historical contingency in the geosciences and to two specific case studies involving Quaternary evolution of fluvial systems in Texas and Kentucky.