Reply to “Which chaos in the rainfall-runoff process?” (original) (raw)
Related papers
Water Resources Research, 2002
1] The reliability of the correlation dimension estimation in short hydrological time series is investigated using an inverse approach. According to this approach, first predictions are made using the phase-space reconstruction technique and the artificial neural networks. The correlation dimension is estimated next independently and is compared with the prediction results. A short hydrological series, monthly runoff series of 48 years (with a total of only 576 values) observed at the Coaracy Nunes/Araguari River watershed in northern Brazil, is studied. The correlation dimension results are in reasonably good agreement with the optimal embedding dimension obtained from the phase-space method and the optimal number of inputs from the neural networks. No underestimation of the correlation dimension is observed due to the small data size, rather there seems to be a slight overestimation due to the presence of noise in the data. The results indicate that the accuracy of the correlation dimension may not be judged on the basis of the length of the time series but on whether the time series is long enough to reasonably represent the dynamical changes in the system. Such an observation suggests that the correlation dimension could indeed be a reliable indicator of low-dimensional chaos even in short hydrological time series, which is certainly encouraging news for hydrologists who often have to deal with short time series.
Evidence of chaos in the rainfall-runoff process
Hydrological Sciences Journal, 2001
The transformation of rainfall into runoff is one of the most important processes in hydrology. In the past few decades, a wide variety of automated or computer-based approaches have been applied to model this process. However, many such approaches have an important limitation in that they treat the rainfall-runoff process as a realization of only a few parameters of linear relationships rather than the process as a whole. What is required, therefore, is an approach that can capture not only the overall appearance but also the intricate details of the nonlinear behaviour of the process. The purpose of this study is to investigate the possibility of understanding the dynamics of the rainfall-runoff process from a new perspective, as a chaotic process. The possible existence of chaotic behaviour in the rainfall-runoff process is studied by investigating the rainfall and runoff time series: (a) separately; and (b) jointly (using the runoff coefficient). Monthly rainfall and runoff observed over a period of 131 years (January 1807-December 1937) at the Gôta River basin in the south of Sweden are analysed. The correlation dimension method is employed to identify the presence of chaos. The correlation dimensions obtained for the rainfall and runoff time series are 6.4 and 5.5, respectively. The finite dimensions obtained for the rainfall and runoff time series indicate the possible existence of chaos in these processes, implying that the joint rainfall-runoff process might also exhibit chaotic behaviour. The correlation dimension of about 7.8 obtained for the runoff coefficient also indicates the possible presence of chaos and supports the above results.
Journal of Hydrology, 2006
Are point rainfall time series resulting from stochastic or low-dimensional deterministic chaotic processes? This issue is still controversial, but important for the choice of the best suited rainfall simulation approach to generate realistic synthetic series. It is firstly shown, through a simple theoretical example (the logistic model), that the efficiency of the nonlinear analysis tools dedicated to the identification of chaotic behavior, especially the correlation dimension method (CDM), is drastically reduced if the data are contaminated by noise. The results of a CDM based analysis of a eight year point rainfall record with a time resolution of five minutes are then presented. More precisely, the series of rainfall disaggregation weights between the 10-minute and 5-minute time steps is studied. The discrete nature of tipping bucket data appears as a limiting factor at this time resolution for the analysis. To overcome this problem, optical raingage data are also studied. The results obtained in both -tipping bucket and optical raingage -cases show actually no clear evidence of a low-dimensional chaotic behavior. Furthermore, the results obtained suggest that the CDM is an effective tool for exploring data also in other contexts in addition to chaos analysis. The CDM analysis reveals in the present case study that the time series are neither chaotic nor composed of independent and identically distributed random variables. This is also verified on the basis of standard statistical tests.
Temporal scaling comparison of real hydrological data and model runoff records
Journal of Hydrology, 2007
We show that the scaling properties of river runoff records represent a useful tool for evaluating precipitation-runoff models that are widely used in hydrology for assessment of the water balance in a given river catchment. In this respect, it is important that the model maps the processes that control the water balance. The main field of application is therefore water management in a given area over a long time scale (at least several years). Here, we compare the temporal scaling properties of the runoff of three Bavarian rivers (Naab, Regnitz, and Vils) with the corresponding ASGi model records. In the evaluation, we use: (i) detrended fluctuation analysis (DFA); (ii) multifractal analysis; (iii) periodic volatility analysis; and (iv) long-term volatility analysis. Our study generally shows close similarity between real and simulated data for the main statistical parameters (e.g., correlation and multifractal exponents). Therefore, the ASGi model output seems to adequately describe real basin processes and might be useful for hydrological purposes, such as a posteriori estimation of water balance in a river catchment.
Chaos and scaling in daily river flow
2010
Adequate knowledge of the nature of river flow process is crucial for proper planning and management of our water resources and environment. This study attempts to detect the salient characteristics of flow dynamics of the Karoon River in Iran. Daily discharge series observed over a period of six years (1999-2004) is analyzed to examine the chaotic and scaling characteristics of the flow dynamics. The presence of chaos is investigated through the correlation dimension and Lyapunov exponent methods, while the Hurst exponent and R\'enyi dimension analyses are performed to explore the scaling characteristics. The low correlation dimension ($2.60 \pm 0.07$) and the positive largest Lyapunov exponent ($0.014 \pm 0.001$) suggest the presence of low-dimensional chaos; they also imply that the flow dynamics are dominantly governed by three variables and can be reliably predicted up to 48 days (i.e. prediction horizon). Results from the Hurst exponent and R\'enyi dimension analyses reveal the multifractal character of the flow dynamics, with persistent and anti-persistent behaviors observed at different time scales.
Does the river run wild? Assessing chaos in hydrological systems
Advances in Water Resources, 1999
The standing debate over whether hydrological systems are deterministic or stochastic has been taken to a new level by controversial applications of chaos mathematics. This paper reviews the procedure, constraints, and past usage of a popular chaos time series analysis method, correlation integral analysis, in hydrology and adds a new analysis of daily stream¯ow from a pristine watershed. Signi®cant problems with the use of correlation integral analysis (CIA) were found to include a continued reliance on the original algorithm even though it was corrected subsequently and failure to consider the physics underlying mathematical results. The new analysis of daily stream¯ow reported here found no attractor with D T 5. Phase randomization of the Fourier Transform of stream¯ow was used to provide a better stochastic surrogate than an Autoregressive Moving Average (ARMA) model or gaussian noise for distinguishing between chaotic and stochastic dynamics. Ó : S 0 3 0 9 -1 7 0 8 ( 9 9 ) 0 0 0 0 8 -1
A chaotic approach to rainfall disaggregation
Water Resources Research, 2001
The importance of high-resolution rainfall data to understanding the intricacies of the dynamics of hydrological processes and describing them in a sophisticated and accurate way has been increasingly realized. The last decade has witnessed a number of studies and numerous approaches to the possibility of transformation of rainfall data from one scale to another, nearly unanimously pointing to such a possibility. However, an important limitation of such approaches is that they treat the rainfall process as a realization of a stochastic process, and therefore there seems to be a lack of connection between the structure of the models and the underlying physics of the rainfall process. The present study introduces a new framework based on the notion of deterministic chaos to investigate the behavior of the dynamics of rainfall transformation between different temporal scales aimed toward establishing this connection. Rainfall data of successively doubled resolutions (i.e., 6, 12, 24, 48, 96, and 192 hours) observed at Leaf River basin, in the state of Mississippi, United States of America, are studied. The correlation dimension method is employed to investigate the presence of chaos in the rainfall transformation. The finite and low correlation dimensions obtained for the distributions of weights between rainfall data of different scales indicate the existence of chaos in the rainfall transformation, suggesting the applicability of a chaotic model. The formulation of a simple chaotic disaggregation model and its application to the Leaf River rainfall data provides encouraging results with practical potential. The disaggregation model results themselves indicate the presence of chaos in the dynamics of rainfall transformation, providing support for the results obtained using the correlation dimension method. 1. Introduction The lack of high-resolution temporal and spatial rainfall data has been one of the most prominent limiting factors in hydrological, meteorological, and agricultural calculations. The recent shift of our focus to deal with complex problems, such as pollution transport, rainfall-related pollution effects on treatment plants, runoff-induced washoff from impermeable surfaces, soil water infiltration movement, and water erosion, only indicates the added uncertainties on the outcomes if the required quality of data is not available. One possible way to solve this problem is to collect high-resolution data relevant for the problem in question. However, this is costly and timeconsuming and therefore hardly a competitive alternative in practice. As a result, the only alternative seems to be to try to transform the available data from one time and space scale to another. The last decade has witnessed a number of studies investigating the possibility of transformation of rainfall data from one scale to another [e.g., Hershenhorn and Woolhiser, 1987;
Study of General Effects of River Runoff Variations
Russian Meteorology and Hydrology
Time series of monthly mean water discharges from some rivers of Europe and the European part of the former USSR are analyzed. The aim of the analysis is to study the effects of general variability of the monthly mean river runoff which arise simultaneously in joint processing of the time series. A river system over large areas coupled with the atmospheric circulation, which affects the river runoff regime, can be considered as a large distributed nonlinear dynamic system. Therefore, it is interesting to study probable effects of interactions within this system. The effects of general variability (coherence) are determined using two procedures: by estimating the evolution of the Hurst constant for different rivers and by estimating the change in the spectral measure of coherence of variations in the specified frequency range. The spectral measure is calculated as a product of component-wise canonical coherences of a multivariate spectral matrix. As a result of analysis, low-frequency effects of general variability are found. Based on the comparison with spectral characteristics of the reconstructed winter mean temperatures for the last 1500 years, a hypothesis of the climatic origin of these variations is proposed.
On the quest for chaotic attractors in hydrological processes
Hydrological Sciences Journal, 2006
In the last two decades, several researchers have claimed to have discovered low-dimensional determinism in hydrological processes, such as rainfall and runoff, using methods of chaotic analysis. However, such results have been criticized by others. In an attempt to offer additional insights into this discussion, it is shown here that, in some cases, merely the careful application of concepts of dynamical systems, without doing any calculation, provides strong indications that hydrological processes cannot be (low-dimensional) deterministic chaotic. Furthermore, it is shown that specific peculiarities of hydrological processes on fine time scales, such as asymmetric, J-shaped distribution functions, intermittency, and high autocorrelations, are synergistic factors that can lead to misleading conclusions regarding the presence of (low-dimensional) deterministic chaos. In addition, the recovery of a hypothetical attractor from a time series is put as a statistical estimation problem whose study allows, among others, quantification of the required sample size; this appears to be so huge that it prohibits any accurate estimation, even with the largest available hydrological records. All these arguments are demonstrated using appropriately synthesized theoretical examples. Finally, in light of the theoretical analyses and arguments, typical real-world hydrometeorological time series, such as relative humidity, rainfall, and runoff, are explored and none of them is found to indicate the presence of chaos.
Hydrological Sciences Journal, 2002
In the 1980s, there were numerous claims, based on estimates of the correlation dimension, that the variability of various geophysical processes, in particular rainfall, is generated by a low-dimensional deterministic chaos. Due to a recent attempt (Sivakumar et al., 2001) to revive the same approach and with claims of an analogous result for the rainfall-runoff process, we think it is necessary to clarify why this approach can be easily misleading. At the same time, we ask which chaos is involved in the rainfall-runoff process and what are the prospects for its modelling? Key words rainfall-runoff models; (multi-) fractals; chaotic dynamics; stochastic processes; nonlinear analysis; time series analysis; correlation dimension Quel chaos dans le processus pluie-débit? Résumé Au cours des années 1980, il a été souvent annoncé, à partir d'estimations de la dimension de corrélation, que la variabilité de différents processus géophysiques, en particulier la pluie, était générée par un chaos déterministe de faible dimension. Du fait d'une récente tentative (Sivakumar et al., 2001) de ressusciter cette approche et l'annonce d'un résultat similaire sur le processus pluie-débit, nous pensons qu'il est nécessaire de clarifier pourquoi cette approche peut être facilement trompeuse. En même temps, nous indiquons quel chaos est en jeu dans le processus pluie-débit et quelles sont les perspectives pour sa modélisation. Mots clefs modèles pluie-débit; (multi-) fractals; dynamique chaotique; processus stochastiques; analyse nonlinéaire; analyse de séries temporelles; dimension de corrélation