Dynamics of hourly sea level at Hillarys Boat Harbour, Western Australia: a chaos theory perspective

Abstract

Water level forecasting using recorded time series can provide a local modelling capability to facilitate local proactive management practices. To this end, hourly sea water level time series are investigated. The records collected at the Hillarys Boat Harbour, Western Australia, are investigated over the period of 2000 and 2002. Two modelling techniques are employed: low-dimensional dynamic model, known as the deterministic chaos theory, and genetic programming, GP. The phase space, which describes the evolution of the behaviour of a nonlinear system in time, was reconstructed using the delayembedding theorem suggested by Takens. The presence of chaotic signals in the data was identified by the phase space reconstruction and correlation dimension methods, and also the predictability into the future was calculated by the largest Lyapunov exponent to be 437 h or 18 days into the future. The intercomparison of results of the local prediction and GP models shows that for this site-specific dataset, the local prediction model has a slight edge over GP. However, rather than recommending one technique over another, the paper promotes a pluralistic modelling culture, whereby different techniques should be tested to gain a specific insight from each of the models. This would enable a consensus to be drawn from a set of results rather than ignoring the individual insights provided by each model.

River flow simulation using a multilayer perceptron-firefly algorithm model

“…This is due to the influence of correlated lag times to the model accuracies. Thus, mutual information function was performed to specify the numbers of lags (Khatibi et al 2011).The AMI shows well-defined first minima at time lag 3 months ( Fig. 3).…”

Application of Wavelet Decomposition and Phase Space Reconstruction in Urban Water Consumption Forecasting: Chaotic Approach (Case Study)

“…where X t is a vector of the observed data of {x t } t =1 , …,N, N is the total number of observed data, τ is the lag time, and m is embedding dimension. The embedding dimension (m)i s typically in the range of 1-10 [53,54]. The lag-embedding method is sensitive to both embedding parameters of τ and m. Average mutual information (AMI) and autocorrelation function (ACF) are the two well-known methods for estimating the lag time [71,72].…”

“…In a deterministic system, C e increases by increasing m until eventually remaining unchanged. The correlation dimension of time series is defined as the specific value of m after which C e remains unchanged [54,59].…”

Nonlinear Dynamic Modeling of Urban Water Consumption Using Chaotic Approach (Case Study: City of Kelowna)

“…By aggregating data at increasing temporal scales, the effects of scaling time series on deterministic chaos can be found [54,55] and any missing data can be generated [56,57]. This approach has been used in solving problems in various fields of study such as river discharge [58][59][60], sedimentation [61][62][63], climate [64], lake level variability [65,66], rainfall [67][68][69][70], traffic speed [71], finance [72], image processing [73] and ship motion prediction [74]. However, there is a paucity of study on the application of chaos theory on water consumption forecasting methods.…”

“…Evolutionary techniques became popular in modeling and optimizing fields. Genetic programming (GP) and gene expression programming (GEP) place on heuristic algorithms that are found in Darwin's evolution theory [66]. Evolutionary techniques adjust the population of a specific solution.…”