Analysis and prediction of chaos in rainfall and stream flow time series

Jayawardena, A. W.; Lai, Fachun

doi:10.1016/0022-1694(94)90185-6

Cited by 205 publications

(149 citation statements)

References 28 publications

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“…A variety of techniques developed in the context of nonlinear and chaotic dynamics have been employed to runoff observed in various geographical regions to identify and/or predict their dynamics (e.g. Jayawardena & Lai, 1994;Porporato & Ridolfi, 1996, 1997Liu et al, 1998;Wang & Gan, 1998;Krasovskaia et al, 1999;Stehlik, 1999;Jayawardena & Gurung, 2000). The results obtained from such studies are encouraging, as they reveal the possible presence of lowdimensional deterministic components in the runoff dynamics, suggesting the possibility of (nearly) accurate short-term predictions.…”

Section: Introductionmentioning

confidence: 99%

Monthly runoff prediction using phase space reconstruction

Sivakumar

Berndtsson

Persson

2001

Hydrological Sciences Journal

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A nonlinear prediction method, developed based on the ideas gained from deterministic chaos theory, is employed: (a) to predict monthly runoff; and (b) to detect the possible presence of chaos in runoff dynamics. The method first reconstructs the single-dimensional (or variable) runoff series in a multi-dimensional phase space to represent its dynamics, and then uses a local polynomial approach to make predictions. Monthly runoff series observed at the Coaracy Nunes/Araguari River basin in northern Brazil is studied. The predictions are found to be in close agreement with the observed runoff, with high correlation coefficient and coefficient of efficiency values, indicating the suitability of the nonlinear prediction method for predicting the runoff dynamics. The results also reveal the presence of lowdimensional chaos in the runoff dynamics, when an inverse approach is adopted for identification, as: (a) an optimal embedding dimension exists, and (b) the prediction accuracy decreases with an increase in prediction lead time.Key words runoff; prediction; chaotic dynamics; phase space reconstruction; local approximation; Coaracy Nunes/Araguari River basin, Brazil Prévision du débit mensuel par reconstruction dans l'espace des phases Résumé Une méthode de prévision non-linéaire, développée à partir d'idées tirées de la théorie du chaos déterministe, a été utilisée: (a) pour prévoir le débit mensuel; et (b) pour détecter l'éventuelle présence de chaos dans la dynamique de l'écoulement. Tout d'abord la méthode reconstruit la série mono-dimensionnelle (ou variable) du débit dans un espace des phases multi-dimensionnel pour représenter sa dynamique, puis s'appuie sur une approche polynomiale locale pour réaliser des prévisions. Nous avons étudié la série des débits mensuels observés sur le bassin versant de la rivière Coaracy Nunes/Araguari, dans le Nord du Brésil. Les prévisions s'avèrent être très proches des observations de débit avec de bons coefficients de corrélation et d'efficacité, ce qui montre la pertinence de la méthode non-linéaire pour prévoir la dynamique de l'écoulement. Les résultats révèlent également la présence de chaos de petite dimension dans la dynamique de l'écoulement, lorsqu'une méthode inverse est utilisée pour l'identification, dans la mesure où (a) il existe une dimension englobante optimale et (b) la précision de la prévision diminue avec l'augmentation de son l'horizon.

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Section: Introductionmentioning

confidence: 99%

Monthly runoff prediction using phase space reconstruction

Sivakumar

Berndtsson

Persson

2001

Hydrological Sciences Journal

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“…Rodriguez-Iturbe et al, 1989;Tsonis et al, 1993;Berndtsson et al, 1994;Jayawardena and Lai, 1994;Koutsoyiannis and Pachakis, 1996;Puente and Obregon, 1996;Porporato and Ridolfi, 1997;Krasovskaia et al, 1999;Sivakumar et al, 1999a;Stehlik, 1999). That such applications have resulted in noticeable progress in the areas of identification and prediction of hydrological processes is encouraging news for hydrologists.…”

Section: Introductionmentioning

confidence: 99%

“…Berndtsson et al, 1994;Jayawardena and Lai, 1994;Sivakumar et al, 1999a) or of different scales observed in different geographical locations (e.g. Rodriguez-Iturbe et al, 1989).…”

Section: Introductionmentioning

confidence: 99%

Rainfall dynamics at different temporal scales: A chaotic perspective

Sivakumar

2001

Hydrol. Earth Syst. Sci.

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This study of the behaviour of rainfall dynamics at different temporal scales identifies the type of approach most suitable for transformation of rainfall data from one scale to another. Rainfall data of four different temporal scales, i.e. daily, 2-day, 4-day and 8-day, observed over a period of about 25 years at the Leaf River basin, Mississippi, USA, are analysed. The correlation dimension method is employed to identify the behaviour of rainfall dynamics. The finite correlation dimensions obtained for the four rainfall series (4.82, 5.26, 6.42 and 8.87, respectively) indicate the possible existence of chaotic behaviour in the rainfall observed at the four scales. A possible implication of this might be that the rainfall processes at these scales are related through a chaotic (scale-invariant) behaviour. However, a comparison of the correlation dimension and coefficient of variation of each of the time series reveals an inverse relationship between the two (higher dimension for lower coefficient of variation and vice versa). The presence of a large number of zeros in the higher resolution time series (that could result in an underestimation of the dimension) and the possible presence of a higher level of noise in the lower resolution time series (that could result in an overestimation of the dimension) might account for such results. In view of these problems, it is concluded that the results must be verified using other chaos identification methods and the existence of chaos must be substantiated with additional evidence.

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“…The theory of nonlinear dynamic systems associated with the concept of strange attractors for the determination of deterministic chaos has drawn the attention of a number of researchers over the recent decades. This concept also provides a new technique for time series analysis, because in many instances, the time series can be viewed as a dynamic system with a low-dimensional attractor, which can be reconstructed using the time delay embedding method [27].…”

Section: Decriptive and Chaotic Analysismentioning

confidence: 99%

Dynamic Analysis of Meteorological Parameters in Košice Climatic Station in Slovakia

Zeleňáková

Jothiprakash

Arjun

et al. 2018

Water

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Evaporation and precipitation are often considered the most important processes in the water cycle. Recent studies have turned to chaotic analysis and short-term prediction for analyzing and forecasting the time series of such phenomena. However, even with chaos theory, the accurate forecasting of pan evaporation is not a straightforward business, as it involves a number of variables whose changes directly and/or indirectly affect the scale and amount of pan evaporation. In this study, the use of the false nearest neighbour method for the chaotic analysis of pan evaporation and related metrological parameters is discussed. A literature review is presented on chaos theory and its applications in modelling physical systems. Also, a review of the literature on multivariate analysis and the presence of chaos in meteorology are presented. A detailed procedure for finding the presence of chaos in a time series using false nearest neighbour (FNN) is discussed. The possible lag time to be considered in the FNN analysis is estimated using the autocorrelation function (ACF) and average mutual information (AMI) apart from the time-step of the measurement. Thus, FNN is studied with three different lag times of the time series. Six meteorological parameters: average temperature, relative humidity, wind speed, sunshine hours, dew point temperature, and pan evaporation are measured at the observation station Kosice in Slovakia for a period of 20 years. Thus, the available time series are analysed using ACF, AMI, and FNN methods, and the results obtained are analysed in the study. Nonlinear behaviour is seen in all of the observed parameters. Pan evaporation, average temperature, and dew point temperature are found to exhibit clear chaotic behaviour, while relative humidity, sunshine hours, and wind speed show stochastic behaviour.

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Analysis and prediction of chaos in rainfall and stream flow time series

Cited by 205 publications

References 28 publications

Monthly runoff prediction using phase space reconstruction

Monthly runoff prediction using phase space reconstruction

Rainfall dynamics at different temporal scales: A chaotic perspective

Dynamic Analysis of Meteorological Parameters in Košice Climatic Station in Slovakia

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