Examining optimum prediction time of rainfall dynamics based on chaotic perspective at different temporal scales: a case study in Bojonegoro, Indonesia

Abstract As the driving force of the hydrological system, rain has severe impact when dealing with petroleum mining activities, especially in protecting assets and safety. Rainfall has high variability, both spatial and temporal (chaotic data). Due to this reason, ones can only create long-range prediction using the stochastic method. Here we use the Lyapunov exponent to analyze the nonlinear pattern of rainfall dynamics. This method is useful for identifying chaotic deportment in rainfall data. This study uses rainfall data for six years obtained from one of the largest petroleum mining sites in Bojonegoro, Indonesia. Rainfall dynamics have been analyzed on three different time scales, namely daily data, 5-day, and 10-day. The time delay (τ) was obtained by using the Average Mutual Information (AMI) method for the three-rainfall series (3, 2, 3, respectively). The observed rainfall data in Bojonegoro show signs of chaos as the finite correlation dimensions (m) attain values about 4 for all time scales. The maximum Lyapunov exponent λmax for each of three-rainfall series in Bojonegoro is 0.111, 0.057, 0.062, respectively. These values were analyzed to find the optimum prediction time of rainfall occurrence to perform better forecasting. The result shows that the optimum range of prediction time for daily, 5-day, and 10-day have 9, 18, and 16 times longer than their temporal scale.

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Development of IDF-curves for tropical india by random cascade modeling

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-10-4709-2013 ◽

2013 ◽

Vol 10 (4) ◽

pp. 4709-4738 ◽

Cited By ~ 4

Author(s):

A. Rana ◽

L. Bengtsson ◽

J. Olsson ◽

V. Jothiprakash

Keyword(s):

Time Scales ◽

Time Scale ◽

Daily Rainfall ◽

Rainfall Data ◽

Efficient Design ◽

Daily Data ◽

Current Design ◽

Idf Curves ◽

Intensity Duration Frequency ◽

Fine Time

Abstract. Efficient design of urban drainage systems is based on statistical analysis of past rainfall events at fine time scales. However, fine time scale rainfall data are usually lacking in many parts of the world. A possible way forward is to develop methods to derive fine time scale rain intensities from daily observations. This paper applied cascade-based disaggregation modeling for generation of fine time scale rainfall data for Mumbai, India from daily rainfall data. These data were disaggregated to 10-min values. The model was used to disaggregate daily data for the period 1951–2004 and develop intensity-duration-frequency (IDF) relationships. This disaggregation technique is commonly used assuming scale-invariance using constant parameters. For the Mumbai rains it was found better to use parameters dependent on time scale and rain volume. Very good agreement between modeled and observed disaggregation series was found for the time scales larger than 1/2 h for the 1/2-yr period when short term data were available. Although the parameters were allowed to change with time scale, the rain intensities of duration shorter than 1/2 h were overestimated. When IDF-curves had been established, they showed that the current design standard for Mumbai city, 25 mm h−1, has a return period of less than one year. Thus, annual recurring flooding problems in Mumbai appear evident.

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Non-Linearity and Chaotic Behaviour in Cyprus Stock Market

International Journal of Financial Management ◽

10.21863/ijfm/2015.5.4.018 ◽

2015 ◽

Vol 5 (4) ◽

Author(s):

Athina Bougioukou

Keyword(s):

Lyapunov Exponent ◽

Stock Market ◽

Chaos Theory ◽

Linear Dependence ◽

Chaotic Behavior ◽

Efficient Market Hypothesis ◽

Chaotic Behaviour ◽

Maximum Lyapunov Exponent ◽

Efficient Market ◽

General Index

The intention of this research is to investigate the aspect of non-linearity and chaotic behavior of the Cyprus stock market. For this purpose, we use non-linearity and chaos theory. We perform BDS, Hinich-Bispectral tests and compute Lyapunov exponent of the Cyprus General index. The results show that existence of non-linear dependence and chaotic features as the maximum Lyapunov exponent was found to be positive. This study is important because chaos and efficient market hypothesis are mutually exclusive aspects. The efficient market hypothesis which requires returns to be independent and identically distributed (i.i.d.) cannot be accepted.

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Fatigue damage evaluation of metallic components based on the maximum Lyapunov exponent of modified Duffing system

Results in Physics ◽

10.1016/j.rinp.2021.104252 ◽

2021 ◽

pp. 104252

Author(s):

Yuhua Zhang ◽

Silong Quan ◽

Guoquan Liu

Keyword(s):

Lyapunov Exponent ◽

Fatigue Damage ◽

Maximum Lyapunov Exponent ◽

Damage Evaluation ◽

Duffing System

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Study on State Recognition of ASCE Benchmark Based on Lyapunov Exponent Spectrum Entropy

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.243-249.5435 ◽

2011 ◽

Vol 243-249 ◽

pp. 5435-5439 ◽

Cited By ~ 1

Author(s):

Jian Xi Yang ◽

Jian Ting Zhou ◽

Yue Chen

Keyword(s):

Lyapunov Exponent ◽

Time Sequence ◽

Maximum Lyapunov Exponent ◽

Entropy Analysis ◽

Structural System ◽

Time Duration ◽

State Recognition ◽

Chaotic Characteristic ◽

Lyapunov Exponent Spectrum ◽

Maximum Lyapunov Exponents

The paper has made a maximum Lyapunov exponent and Lyapunov exponent spectrum entropy analysis of ASCE Benchmark using non-linear theory and chaos time sequence. The maximum Lyapunov exponents in the two kinds of structural monitored data are both over zero, indicating that in the structural system chaos phenomenon has appeared. And, experiments have shown that the maximum Lyapunov exponent is sensitive of the amount of samples and the time delay. So, to compute the chaos index, the amount of samples and the time duration are of importance. Meanwhile, the Lyapunov exponent spectrum entropy is effective to measure the chaotic characteristic of the system, but ,the entropy is less sensitive to state recognition more than the max Lyapunov exponent.

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Point process models of rainfall: developments for fine-scale structure

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2007.1889 ◽

2007 ◽

Vol 463 (2086) ◽

pp. 2569-2587 ◽

Cited By ~ 62

Author(s):

Paul Cowpertwait ◽

Valerie Isham ◽

Christian Onof

Keyword(s):

Poisson Process ◽

Time Scales ◽

Rain Gauge ◽

Historical Record ◽

Rainfall Data ◽

Process Models ◽

Third Order ◽

Time Intervals ◽

Historical Series ◽

Derived Properties

A conceptual stochastic model of rainfall is proposed in which storm origins occur in a Poisson process, where each storm has a random lifetime during which rain cell origins occur in a secondary Poisson process. In addition, each cell has a random lifetime during which instantaneous random depths (or ‘pulses’) of rain occur in a further Poisson process. A key motivation behind the model formulation is to account for the variability in rainfall data over small (e.g. 5 min) and larger time intervals. Time-series properties are derived to enable the model to be fitted to aggregated rain gauge data. These properties include moments up to third order, the probability that an interval is dry, and the autocovariance function. To allow for distinct storm types (e.g. convective and stratiform), several processes may be superposed. Using the derived properties, a model consisting of two storm types is fitted to 60 years of 5 min rainfall data taken from a site near Wellington, New Zealand, using sample estimates taken at 5 min, 1 hour, 6 hours and daily levels of aggregation. The model is found to fit moments of the depth distribution up to third order very well at these time scales. Using the fitted model, 5 min series are simulated, and annual maxima are extracted and compared with equivalent values taken from the historical record. A good fit in the extremes is found at both 1 and 24 hour levels of aggregation, although at the 5 min level there is some underestimation of the historical values. Proportions of time intervals with depths below various low thresholds are extracted from the simulated and historical series and compared. A tendency for underestimation of the historical values is evident at some time scales, with a close fit being obtained as the threshold is increased.

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Inhomogeneity detection in the rainfall series for the Mae Klong River Basin, Thailand

Applied Water Science ◽

10.1007/s13201-021-01474-6 ◽

2021 ◽

Vol 11 (9) ◽

Author(s):

Alamgir Khalil

Keyword(s):

River Basin ◽

Curve Analysis ◽

Rainfall Series ◽

Rainfall Data ◽

Homogeneity Test ◽

Significance Level ◽

Von Neumann ◽

Standard Normal Homogeneity Test ◽

Double Mass ◽

Climate Studies

AbstractAn accurate and complete rainfall record is prerequisite for climate studies. The purpose of this research study was to evaluate the homogeneity of the rainfall series for the Mae Klong River Basin in Thailand. Monthly rainfall data of eight stations in the Mae Klong River Basin for the period 1971–2015 were used. The double mass curve analysis was used to check the consistency of rainfall data, whereas the absolute homogeneity was assessed using the Pettitt test, standard normal homogeneity test, Buishand test, and von Neumann test at a 5% significance level. The results of these tests were qualitatively classified as ‘useful’, ‘doubtful’, and ‘suspect’ according to the null hypothesis. Results of the monthly time series indicated the rainfall data as ‘useful’ for 75% of the stations, while two stations’ data were classified as ‘doubtful’ (Stn130221) and ‘suspect’ (Stn376401). On an annual scale, seven out of eight stations data were classified as ‘useful,’ while one station (Stn376401) data were classified as ‘suspect’. Double mass curve analysis technique was used for the adjustment of inhomogeneous data. The results of this study can help provide reliable rainfall data for climate studies in the basin.

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