On the quest for chaotic attractors in hydrological processes

134

Abstract. The absence of a generic modeling framework in hydrology has long been recognized. With our current practice of developing more and more complex models for specific individual situations, there is an increasing emphasis and urgency on this issue. There have been some attempts to provide guidelines for a catchment classification framework, but research in this area is still in a state of infancy. To move forward on this classification framework, identification of an appropriate basis and development of a suitable methodology for its representation are vital. The present study argues that hydrologic system complexity is an appropriate basis for this classification framework and nonlinear dynamic concepts constitute a suitable methodology. The study employs a popular nonlinear dynamic method for identification of the level of complexity of streamflow and for its classification. The correlation dimension method, which has its base on data reconstruction and nearest neighbor concepts, is applied to monthly streamflow time series from a large network of 117 gaging stations across 11 states in the western United States (US). The dimensionality of the time series forms the basis for identification of system complexity and, accordingly, streamflows are classified into four major categories: low-dimensional, medium-dimensional, highdimensional, and unidentifiable. The dimension estimates show some "homogeneity" in flow complexity within certain regions of the western US, but there are also strong exceptions.

Section: Correlation Dimension Methodsmentioning

confidence: 99%

Hydrologic system complexity and nonlinear dynamic concepts for a catchment classification framework

Sivakumar

Singh

2012

134

“…This situation is, of course, complicated by the fact that many hydrological systems exhibit strongly nonlinear behaviour and have unknown boundary and initial conditions. Together, this imposes principal limits on our ability to make (deterministic) predictions (Koutsoyiannis, 2010). So the important question that arises is 2.2 How can we cope with underdetermination and reduce explanatory pluralism in hydrology?…”

Section: Goals and Scope Of This Papermentioning

confidence: 99%

“…The theory of dynamical systems has since its beginnings in the 1950s (Forrester, 1968), developed into a well-established branch of science, that has been proven useful across a wide range of problems and systems (Strogatz, 1994), ranging from weather prediction (Lorenz, 1969), ecology (Hastings et al, 1993;Bossel, 1986) and hydrology (Koutsoyiannis, 2006) to geomorphology (Phillips, 1993) and coupled human-ecological systems (Bossel, 1999(Bossel, , 2007 among many others. The steps of dynamical system analysis (DSA) include identification of the system structure (border, components, and state variables) and of the laws governing its dynamics (i.e.…”

Section: Catchments As Complex Dynamical Systemsmentioning

confidence: 99%

Advancing catchment hydrology to deal with predictions under change

Ehret

Gupta

Sivapalan

et al. 2014

102

Abstract. Throughout its historical development, hydrology as an earth science, but especially as a problem-centred engineering discipline has largely relied (quite successfully) on the assumption of stationarity. This includes assuming time invariance of boundary conditions such as climate, system configurations such as land use, topography and morphology, and dynamics such as flow regimes and flood recurrence at different spatio-temporal aggregation scales. The justification for this assumption was often that when compared with the temporal, spatial, or topical extent of the questions posed to hydrology, such conditions could indeed be considered stationary, and therefore the neglect of certain long-term non-stationarities or feedback effects (even if they were known) would not introduce a large error.However, over time two closely related phenomena emerged that have increasingly reduced the general applicability of the stationarity concept: the first is the rapid and extensive global changes in many parts of the hydrological cycle, changing formerly stationary systems to transient ones. The second is that the questions posed to hydrology have become increasingly more complex, requiring the joint consideration of increasingly more (sub-) systems and their interactions across more and longer timescales, which limits the applicability of stationarity assumptions. Published by Copernicus Publications on behalf of the European Geosciences Union. U. Ehret et al.: Advancing catchment hydrology to deal with predictions under changeTherefore, the applicability of hydrological concepts based on stationarity has diminished at the same rate as the complexity of the hydrological problems we are confronted with and the transient nature of the hydrological systems we are dealing with has increased.The aim of this paper is to present and discuss potentially helpful paradigms and theories that should be considered as we seek to better understand complex hydrological systems under change. For the sake of brevity we focus on catchment hydrology. We begin with a discussion of the general nature of explanation in hydrology and briefly review the history of catchment hydrology. We then propose and discuss several perspectives on catchments: as complex dynamical systems, self-organizing systems, co-evolving systems and open dissipative thermodynamic systems. We discuss the benefits of comparative hydrology and of taking an informationtheoretic view of catchments, including the flow of information from data to models to predictions.In summary, we suggest that these perspectives deserve closer attention and that their synergistic combination can advance catchment hydrology to address questions of change.

“…Others attempted to demonstrate that irregular fluctuations observed in natural processes are au fond manifestations of underlying deterministic dynamics with low dimensionality, thus rendering probabilistic descriptions unnecessary. Some of the above views and recent developments are simply flawed because they make erroneous use of probability and statistics, which, remarkably, provide the tools for such analyses (Koutsoyiannis, 2006).…”

Section: What Is Randomness?mentioning

confidence: 99%

“…The limit of φ m (ε)/(−lnε) as ε tends to zero, which (according to de l'Hôpital's rule) is also equal to the limit of the slope d m (ε):=− φ m (ε)/ lnε, gives the dimension of the subspace of the m-dimensional space where the set of x m i lies. For small ε, d m (ε) cannot exceed m nor d. Application of a standard algorithm that implements this idea for increasing trial values of m (Grassberger and Procaccia, 1983;Koutsoyiannis, 2006) is demonstrated in Fig. 11, where it can be seen that d m does not exceed d=2, thus capturing the system dimensionality, which is 2.…”

Section: The Power Of Datamentioning

confidence: 99%

HESS Opinions "A random walk on water"

Koutsoyiannis

2010

187

130

Abstract. According to the traditional notion of randomness and uncertainty, natural phenomena are separated into two mutually exclusive components, random (or stochastic) and deterministic. Within this dichotomous logic, the deterministic part supposedly represents cause-effect relationships and, thus, is physics and science (the "good"), whereas randomness has little relationship with science and no relationship with understanding (the "evil"). Here I argue that such views should be reconsidered by admitting that uncertainty is an intrinsic property of nature, that causality implies dependence of natural processes in time, thus suggesting predictability, but even the tiniest uncertainty (e.g. in initial conditions) may result in unpredictability after a certain time horizon. On these premises it is possible to shape a consistent stochastic representation of natural processes, in which predictability (suggested by deterministic laws) and unpredictability (randomness) coexist and are not separable or additive components. Deciding which of the two dominates is simply a matter of specifying the time horizon and scale of the prediction. Long horizons of prediction are inevitably associated with high uncertainty, whose quantification relies on the long-term stochastic properties of the processes.