Threshold behaviour in hydrological systems as (human) geo-ecosystems: manifestations, controls, implications
Authors: Zehe E. , Sivapalan M. 
Published: April 2010

Abstract. In this paper we review threshold behaviour in environmental systems, which are often associated with the onset of floods, contamination and erosion events, and other degenerative processes. Key objectives of this review are to a) suggest indicators for detecting threshold behavior, b) discuss their implications for predictability, c) distinguish different forms of threshold behavior and their underlying controls, and d) hypothesise on possible reasons for why threshold behaviour might occur. Threshold behaviour involves a fast qualitative change of either a single process or the response of a system. For elementary phenomena this switch occurs when boundary conditions (e.g., energy inputs) or system states as expressed by dimensionless quantities (e.g. the Reynolds number) exceed threshold values. Mixing, water movement or depletion of thermodynamic gradients becomes much more efficient as a result. Intermittency is a very good indicator for detecting event scale threshold behavior in hydrological systems. Predictability of intermittent processes/system responses is inherently low for combinations of systems states and/or boundary conditions that push the system close to a threshold. Post hoc identification of "cause-effect relations" to explain when the system became critical is inherently difficult because of our limited ability to perform observations under controlled identical experimental conditions. In this review, we distinguish three forms of threshold behavior. The first one is threshold behavior at the process level that is controlled by the interplay of local soil characteristics and states, vegetation and the rainfall forcing. Overland flow formation, particle detachment and preferential flow are examples of this. The second form of threshold behaviour is the response of systems of intermediate complexity – e.g., catchment runoff response and sediment yield – governed by the redistribution of water and sediments in space and time. These are controlled by the topological architecture of the catchments that interacts with system states and the boundary conditions. Crossing the response thresholds means to establish connectedness of surface or subsurface flow paths to the catchment outlet. Subsurface stormflow in humid areas, overland flow and erosion in semi-arid and arid areas are examples, and explain that crossing local process thresholds is necessary but not sufficient to trigger a system response threshold. The third form of threshold behaviour involves changes in the "architecture" of human geo-ecosystems, which experience various disturbances. As a result substantial change in hydrological functioning of a system is induced, when the disturbances exceed the resilience of the geo-ecosystem. We present examples from savannah ecosystems, humid agricultural systems, mining activities affecting rainfall runoff in forested areas, badlands formation in Spain, and the restoration of the Upper Rhine river basin as examples of this phenomenon. This functional threshold behaviour is most difficult to predict, since it requires extrapolations far away from our usual experience and the accounting of bidirectional feedbacks. However, it does not require the development of more complicated model, but on the contrary, only models with the right level of simplification, which we illustrate with an instructive example. Following Prigogine, who studied structure formation in open thermodynamic systems, we hypothesise that topological structures which control response thresholds in the landscape might be seen as dissipative structures, and the onset of threshold processes/response as a switch to more efficient ways of depleting strong gradients that develop in the case of extreme boundary conditions.