Nonlinear analysis of rainfall dynamics in California's Sacramento Valley

Sivakumar, Bellie; Wallender, W. W.; Horwáth, William R.; Mitchell, Jeffrey P.; Prentice, Samuel E.; Joyce, Brian

doi:10.1002/hyp.5952

Cited by 25 publications

(14 citation statements)

References 44 publications

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“…Similar results on the effects of scale on hydrologic process complexity (i.e. increase in complexity or change from determinism to stochasticity with increasing time scale) were also observed by a few other studies as well (e.g., Sivakumar et al 2004Sivakumar et al , 2006Salas et al 2005;Sivakumar and Chen 2007), albeit in different contexts and employing different methodologies to different systems and processes (including rainfall, river flow and sediment load). There may indeed be exceptions to this situation with no trend possibly observed in the 'scale versus complexity' relationship [see Sivakumar et al (2001b) for details], since this relationship essentially depends on, for example, rainfall characteristics (e.g.…”

Section: Scale and Scale-invariancesupporting

confidence: 73%

Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward

Sivakumar

2008

Stoch Environ Res Risk Assess

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During the last two decades or so, studies on the applications of the concepts of nonlinear dynamics and chaos to hydrologic systems and processes have been on the rise. Earlier studies on this topic focused mainly on the investigation and prediction of chaos in rainfall and river flow, and further advances were made during the subsequent years through applications of the concepts to other problems (e.g. data disaggregation, missing data estimation, and reconstruction of system equations) and other processes (e.g. rainfall-runoff and sediment transport). The outcomes of these studies are certainly encouraging, especially considering the exploratory stage of the concepts in hydrologic sciences. This paper discusses some of the latest developments on the applications of these concepts to hydrologic systems and the challenges that lie ahead on the way to further progress. As for their applications, studies in the important areas of scaling, groundwater contamination, parameter estimation and optimization, and catchment classification are reviewed and the inroads made thus far are reported. In regards to the challenges that lie ahead, particular focus is given to improving our understanding of these largely less-understood concepts and also finding ways to integrate these concepts with the others. With the recognition that none of the existing one-sided 'extremeview' modeling approaches is capable of solving the hydrologic problems that we are faced with, the need for finding a balanced 'middle-ground' approach that can integrate different methods is stressed. To this end, the viability of bringing together the stochastic concepts and the deterministic concepts as a starting point is also highlighted.

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Section: Scale and Scale-invariancesupporting

confidence: 73%

Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward

Sivakumar

2008

Stoch Environ Res Risk Assess

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“…These τ -values do not seem to indicate any consistent relevance to seasonality or other catchment dynamics; for instance, τ = 40 indicates a delay time of over three years (τ = 3 is obtained in a few cases). Similar problems have also been encountered in dealing with other hydrologic data, whether at the monthly scale or at other temporal scales; see Sivakumar et al (2006) for some details in regards to rainfall data from California. Considering these issues and associated complications, in the present study, τ is chosen equal to the sampling (i.e.…”

Section: Discussionmentioning

confidence: 84%

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

Sivakumar

Singh

2012

Hydrol. Earth Syst. Sci.

134

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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.

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“…As some rainfall series seem to support the presence of chaotic-deterministic behavior (e.g., Sivakumar et al, 1999;Dhanya and Nagesh Kumar, 2010), and some do not (e.g., Koutsoyiannis and Pachakis, 1996;Sivakumar et al, 2006), the analysis of continuous rainfall records has not yielded conclusive answers yet. The detection of chaotic behavior is usually performed by analyzing the correlation dimension D 2 computed via the Grassberger-Procaccia algorithm (e.g., Takens, 1981;Grassberger and Procaccia, 1983), based on the phase space reconstruction theorem (Takens, 1981).…”

Section: A Look At Nonlinear Dynamicsmentioning

confidence: 99%

Multifractality, imperfect scaling and hydrological properties of rainfall time series simulated by continuous universal multifractal and discrete random cascade models

Serinaldi

2010

Nonlin. Processes Geophys.

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Abstract. Discrete multiplicative random cascade (MRC) models were extensively studied and applied to disaggregate rainfall data, thanks to their formal simplicity and the small number of involved parameters. Focusing on temporal disaggregation, the rationale of these models is based on multiplying the value assumed by a physical attribute (e.g., rainfall intensity) at a given time scale L, by a suitable number b of random weights, to obtain b attribute values corresponding to statistically plausible observations at a smaller L/b time resolution. In the original formulation of the MRC models, the random weights were assumed to be independent and identically distributed. However, for several studies this hypothesis did not appear to be realistic for the observed rainfall series as the distribution of the weights was shown to depend on the space-time scale and rainfall intensity. Since these findings contrast with the scale invariance assumption behind the MRC models and impact on the applicability of these models, it is worth studying their nature. This study explores the possible presence of dependence of the parameters of two discrete MRC models on rainfall intensity and time scale, by analyzing point rainfall series with 5-min time resolution. Taking into account a discrete microcanonical (MC) model based on beta distribution and a discrete canonical beta-logstable (BLS), the analysis points out that the relations between the parameters and rainfall intensity across the time scales are detectable and can be modeled by a set of simple functions accounting for the parameterrainfall intensity relationship, and another set describing the link between the parameters and the time scale. Therefore, MC and BLS models were modified to explicitly account for these relationships and compared with the continuous in Correspondence to: F. Serinaldi (f.serinaldi@unitus.it) scale universal multifractal (CUM) model, which is used as a physically based benchmark model. Monte Carlo simulations point out that the dependence of MC and BLS parameters on rainfall intensity and cascade scales can be recognized also in CUM series, meaning that these relations cannot be considered as a definitive sign of departure from multifractality. Even though the modified MC model is not properly a scaling model (parameters depend on rainfall intensity and scale), it reproduces the empirical traces of the moments and moment exponent function as effective as the CUM model. Moreover, the MC model is able to reproduce some rainfall properties of hydrological interest, such as the distribution of event rainfall amount, wet/dry spell length, and the autocorrelation function, better than its competitors owing to its strong, albeit unrealistic, conservative nature. Therefore, even though the CUM model represents the most parsimonious and the only physically/theoretically consistent model, results provided by MC model motivate, to some extent, the interest recognized in the literature for this type of discrete models.

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Nonlinear analysis of rainfall dynamics in California's Sacramento Valley

Cited by 25 publications

References 44 publications

Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward

Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward

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

Multifractality, imperfect scaling and hydrological properties of rainfall time series simulated by continuous universal multifractal and discrete random cascade models

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