Threshold behaviour in hydrological systems as (human) geo-ecosystems: Manifestations, controls, implications

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.Hydrology and River Basin ManagementCivil Engineering and Geoscience

Effect of spatial heterogeneity of runoff generation mechanisms on the scaling behavior of event runoff responses in a natural river basin

This paper presents a theoretical investigation of the effects of spatial heterogeneity of runoff generation on the scaling behavior of runoff timing responses. A previous modeling study on the Illinois River Basin in Oklahoma had revealed a systematic spatial trend in the relative dominance of different runoff generation mechanisms, attributable to corresponding systematic trends in landscape properties. Considering the differences in the timing of hillslope responses between the different runoff mechanisms, this paper explores their impacts on the catchment?scale runoff routing responses, including how they change with spatial scale. For this purpose we utilize a distributed, physically based hydrological model, with a fully hydraulic stream network routing component. The model is used to generate instantaneous response functions (IRF) for nested catchments of a range of sizes along the river network and quantitative measures of their shape, e.g., peak and time to peak. In order to separate the effects of soil heterogeneity from those due to basin geomorphology, the model simulations are carried out for three hypothetical cases that make assumptions regarding landscape properties (uniform, a systematic trend, and heterogeneity plus the trend), repeating these simulations under wet and dry antecedent conditions. The simulations produced expected and also surprising results. The power law relationship between the peak of the IRF and drainage area is shown to be flatter under wet conditions than under dry conditions, even though the (faster) saturation excess mechanism is more dominant under wet conditions. This result appears to be caused by partial area runoff generation: under wet conditions, the fraction of saturation area is about 30%, while under dry conditions it is less than 10% for the same input of rainfall. This means travel times associated with overland flow (which mostly contributes to the peak and time to peak) are, in fact, longer during wet conditions than during dry conditions. The power law relationship between peak and drainage area also exhibits a scaling break at around 1000 km2, which can be shown to be related to the peculiar geomorphology of the catchment.Water ManagementCivil Engineering and Geoscience

Endogenous technological and population change under increasing water scarcity

The ancient civilization in the Indus Valley civilization dispersed under extreme dry conditions; there are indications that the same holds for many other ancient societies. Even contemporary societies, such as the one in Murrumbidgee river basin in Australia, have started to witness a decline in overall population under increasing water scarcity. Hydroclimatic change may not be the sole predictor of the fate of contemporary societies in water scarce regions and many critics of such (perceived) hydroclimatic determinism have suggested that technological change may ameliorate the effects of increasing water scarcity and as such counter the effects of hydroclimatic changes. To study the role of technological change on the dynamics of coupled human-water systems, we develop a simple overlapping-generations model of endogenous technological and demographic change. We model technological change as an endogenous process that depends on factors such as the investments that are (endogenously) made in a society, the (endogenous) diversification of a society into skilled and unskilled workers, a society’s patience in terms of its present consumption vs. future consumption, production technology and the (endogenous) interaction of all of these factors. In the model the population growth rate is programmed to decline once consumption per capita crosses a “survival” threshold. This means we do not treat technology as an exogenous random sequence of events, but instead assume that it results (endogenously) from societal actions. The model demonstrates that technological change may indeed ameliorate the effects of increasing water scarcity but typically it does so only to a certain extent. It is possible that technological change may allow a society to escape the effect of increasing water scarcity, leading to a (super)-exponential rise in technology and population. However, such cases require the rate of success of investment in technological advancement to be high. In other more realistic cases of technological success, we find that endogenous technology change only helps to delay the peak of population size before it inevitably starts to decline. While the model is a rather simple model of societal development, it is shown to be capable of replicating patterns of technological and population changes. It is capable of replicating the pattern of declining consumption per capita in presence of growth in aggregate production. It is also capable of replicating an exponential population rise, even under increasing water scarcity. The results of the model suggest that societies that declined or are declining in the face of extreme water scarcity may have done so due to slower rate of success of investment in technological advancement. The model suggests that the population decline occurs after a prolonged decline in consumption per capita, which in turn is due to the joint effect of initially increasing population and increasing water scarcity. This is despite technological advancement and increase in aggregate production. We suggest that declining consumption per capita despite technological advancement and increase in aggregate production may serve as a useful predictor of upcoming decline in contemporary societies in water scarce basins.Water ManagementCivil Engineering and Geoscience

A preferential flow leaching index

The experimental evidence suggests that for many chemicals surface runoff and rapid preferential flow through the shallow unsaturated zone are significant pathways for transport to streams and groundwater. The signature of this is the episodic and pulsed leaching of these chemicals. The driver for this transport is the timing and magnitude of rainfall events which trigger rapid flow and the release of solute from a source zone, located near the soil surface. Based on these considerations we develop a conceptual model capable of reproducing many of the signatures of this rapid transport. This driver-source-trigger-signature framework forms the basis of the development of a new leaching index which describes the potential for rapid solute transport by preferential flow or surface runoff. This preferential flow (PF) index is based upon soil and chemical parameters as well as the timing and magnitude of rainfall and preferential flow events. The PF index suggests that a chemical's potential to experience rapid transport increases as sorption strength increases, however, when an approximation to account for sorption kinetics is considered the PF index peaks at moderate sorption values. The model is sensitive to the timing and magnitude of rapid flow events, which may require existing data or infiltration models for their estimation.Water ManagementCivil Engineering and Geoscience

Intra-annual rainfall variability control on interannual variability of catchment water balance: A stochastic analysis

We evaluate the extent to which within-year rainfall variability controls interannual variability of catchment water balance. To this end, we analytically derive the probability density function of the annual Budyko evaporation index, B (i.e., the ratio of annual actual evapotranspiration to annual precipitation), by accounting for the stochastic nature of intra-annual rainfall fluctuation and neglecting all other sources of variability. We apply our analytical model to 424 catchments located in different climatic regions across the conterminous United States to perform this assessment. In general, we found that the model is capable of explaining mean B but is less accurate in predicting its coefficient of variation. Nonetheless, in a significant number of catchments the model can provide adequate predictions of the probability density function of B. Clear geographic patterns can be distinguished in the residuals between observed and predicted statistics of B. Interannual variability is thus not always associated with random intra-annual rainfall fluctuations. In some regions, other controls, such as seasonality and vegetation adaptations, are possibly more important. A sensitivity analysis of model parameters helped characterize the dominant controls on the distribution of B in terms of three dimensionless ratios that include climatic and soil characteristics. This study represents the first step in a diagnostic, data-driven analysis of the climatic controls on the interannual variability of catchment water balance.Water ManagementCivil Engineering and Geoscience

HESS Opinions: Hydrologic predictions in a changing environment: behavioral modeling

Civil Engineering and Geoscience

Catchment classification: Empirical analysis of hydrologic similarity based on catchment function in the eastern USA

Hydrologic similarity between catchments, derived from similarity in how catchments respond to precipitation input, is the basis for catchment classification, for transferability of information, for generalization of our hydrologic understanding and also for understanding the potential impacts of environmental change. An important question in this context is, how far can widely available hydrologic information (precipitation-temperature-streamflow data and generally available physical descriptors) be used to create a first order grouping of hydrologically similar catchments? We utilize a heterogeneous dataset of 280 catchments located in the Eastern US to understand hydrologic similarity in a 6-dimensional signature space across a region with strong environmental gradients. Signatures are defined as hydrologic response characteristics that provide insight into the hydrologic function of catchments. A Bayesian clustering scheme is used to separate the catchments into 9 homogeneous classes, which enable us to interpret hydrologic similarity with respect to similarity in climatic and landscape attributes across this region. We finally derive several hypotheses regarding controls on individual signatures from the analysis performed here.Civil Engineering and Geoscience

Socio-hydrologic modeling to understand and mediate the competition for water between agriculture development and environmental health: Murrumbidgee River Basin, Australia

Competition for water between humans and ecosystems is set to become a flash point in the coming decades in many parts of the world. An entirely new and comprehensive quantitative framework is needed to establish a holistic understanding of that competition, thereby enabling the development of effective mediation strategies. This paper presents a modeling study centered on the Murrumbidgee River basin (MRB). The MRB has witnessed a unique system dynamics over the last 100 years as a result of interactions between patterns of water management and climate driven hydrological variability. Data analysis has revealed a pendulum swing between agricultural development and restoration of environmental health and ecosystem services over different stages of basin-scale water resource development. A parsimonious, stylized, quasi-distributed coupled socio-hydrologic system model that simulates the twoway coupling between human and hydrological systems of the MRB is used to mimic and explain dominant features of the pendulum swing. The model consists of coupled nonlinear ordinary differential equations that describe the interaction between five state variables that govern the co-evolution: reservoir storage, irrigated area, human population, ecosystem health, and environmental awareness. The model simulations track the propagation of the external climatic and socio-economic drivers through this coupled, complex system to the emergence of the pendulum swing. The model results point to a competition between human “productive” and environmental “restorative” forces that underpin the pendulum swing. Both the forces are endogenous, i.e., generated by the system dynamics in response to external drivers and mediated by humans through technology change and environmental awareness, respectively. Sensitivity analysis carried out with the model further reveals that socio-hydrologic modeling can be used as a tool to explain or gain insight into observed co-evolutionary dynamics of diverse human–water coupled systems. This paper therefore contributes to the ultimate development of a generic modeling framework that can be applied to human–water coupled systems in different climatic and socio-economic settings.Water ManagementCivil Engineering and Geoscience

Socio-hydrologic modeling to understand and mediate the competition for water between agriculture development and environmental health: Murrumbidgee River Basin, Australia (discussion paper)

Competition for water between humans and ecosystems is set to become a flash point in the coming decades in many parts of the world. An entirely new and comprehensive quantitative framework is needed to establish a holistic understanding of that competition, thereby enabling the development of effective mediation strategies. This paper presents a modeling study centered on the Murrumbidgee River Basin (MRB). The MRB has witnessed a unique system dynamics over the last 100 years as a result of interactions between patterns of water management and climate driven hydrological variability. Data analysis has revealed a pendulum swing between agricultural development and restoration of environmental health and ecosystem services over different stages of basin scale water resource development. A parsimonious, stylized, quasidistributed coupled socio-hydrologic system model that simulates the two-way coupling between human and hydrological systems of the MRB is used to mimic dominant features of the pendulum swing. The model consists of coupled nonlinear ordinary differential equations that describe the interaction between five state variables that govern the co-evolution: reservoir storage, irrigated area, human population, ecosystem health, and a measure of environmental awareness. The model simulations track the propagation of the external climatic and socio-economic drivers through this coupled, complex system to the emergence of the pendulum swing. The model results point to a competition between human “productive” and environmental “restorative” forces that underpin the pendulum swing. Both the forces are endogenous, i.e., generated by the system dynamics in response to external drivers and mediated by humans through technology change and environmental awareness, respectively. We propose this as a generalizable modeling framework for coupled human hydrological systems that is potentially transferable to systems in different climatic and socio-economic settings.Water ManagementCivil Engineering and Geoscience

Nutrient loads exported from managed catchments reveal emergent biogeochemical stationarity

Complexity of heterogeneous catchments poses challenges in predicting biogeochemical responses to human alterations and stochastic hydro?climatic drivers. Human interferences and climate change may have contributed to the demise of hydrologic stationarity, but our synthesis of a large body of observational data suggests that anthropogenic impacts have also resulted in the emergence of effective biogeochemical stationarity in managed catchments. Long?term monitoring data from the Mississippi?Atchafalaya River Basin (MARB) and the Baltic Sea Drainage Basin (BSDB) reveal that inter?annual variations in loads (LT) for total?N (TN) and total?P (TP), exported from a catchment are dominantly controlled by discharge (QT) leading inevitably to temporal invariance of the annual, flow?weighted concentration, Cf = (LT/QT). Emergence of this consistent pattern across diverse managed catchments is attributed to the anthropogenic legacy of accumulated nutrient sources generating memory, similar to ubiquitously present sources for geogenic constituents that also exhibit a linear LT?QT relationship. These responses are characteristic of transport?limited systems. In contrast, in the absence of legacy sources in less?managed catchments, Cf values were highly variable and supply limited. We offer a theoretical explanation for the observed patterns at the event scale, and extend it to consider the stochastic nature of rainfall/flow patterns at annual scales. Our analysis suggests that: (1) expected inter?annual variations in LT can be robustly predicted given discharge variations arising from hydro?climatic or anthropogenic forcing, and (2) water?quality problems in receiving inland and coastal waters would persist until the accumulated storages of nutrients have been substantially depleted. The finding has notable implications on catchment management to mitigate adverse water?quality impacts, and on acceleration of global biogeochemical cycles.Water ManagementCivil Engineering and Geoscience