Progress in Prediction Using Geomorphic Transport Laws

Abstract:

Predictions by landscape evolution models are an expression of the rules or laws used to drive erosion and deposition. These equations quantify our understanding of how landscapes work. Twenty years ago, we proposed the term “geomorphic transport law” to be “a mathematical statement derived from a physical principle or mechanism, which expresses the mass flux or erosion caused by one or more processes in a manner that: 1) can be parameterized from field measurements, 2) can be tested in physical models, and 3) can be applied over geomorphically-significant spatial and temporal scales.” Such laws capture what we termed an “essential realism”, a compromise between the “detailed realism” of physically-explicit models applied at small scales and the “apparent realism” of rules-based models that reproduce patterns observed at large scales without incorporating physical mechanisms. Geomorphic transport laws thus reproduce essential landscape form and dynamics without the details of individual storms, local material properties, or the specific actions of biota. Since then, we have seen advances in accounting for biotic processes on hillslope soil production and transport, and the physical mechanisms governing downslope transport. Models for landslide rates and size have been developed. But we have also seen an over-reliance on the stream power equation for bedrock incision, which creates realistic slope-area scaling at large scales despite failing to explain variations in bedrock erosion rates measured in laboratory experiments and channel-scale field studies, or debris flow incision. Do landscape evolution models using this equation get the “right answer” for the wrong reason, or perhaps lead to erroneous interpretations because essential controls and potential feedbacks are absent? More mechanistic bedrock incision models have been derived, for example by accounting for sediment size and its dependence on climate and lithology. More mechanistic models require more information, but this is our challenge: we use models to test and discover how the world works and our model outcomes are only reliable if the laws used represent real and relevant processes. We have much still to learn. Frontier research areas, for which geomorphic transport laws now are needed, include: bedrock landscapes and the critical zone.