Detection of chaos: New approach to atmospheric pollen time-series analysis

Bianchi, Martha S.; Arizmendi, C. M.; Sánchez, J. R.

doi:10.1007/bf01224822

Cited by 10 publications

(12 citation statements)

References 16 publications

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“…This validates the results of our first report on short-range pollen forecasting (Delaunay et al 2004) and contradicts a study by Bianchi et al (1992) claiming lowdimensional chaotic behavior for their pollen series. In the latter study, evidence of chaos in the pollen series was obtained from estimating the correlation dimension, an approximate value for the dimension of the strange attractor of a low-dimensional chaotic series.…”

Section: Resultssupporting

confidence: 88%

“…In this respect, time series analysis of measured pollen concentration may provide a means to improve short-range prediction and/or to better understand the underlying dynamics of pollen series. Bianchi et al (1992) and Arizmendi et al (1993) used nonlinear time series techniques to analyze 2-h pollen series and concluded that their series exhibited low-dimensional chaotic behavior. Examining cedar pollen series with the correlation integral method (Grassberger and Procaccia 1983), the largest Lyapunov exponent method (Wolf et al 1985), and Casdagli's test (1991), we found no convincing evidence of low-dimensional chaotic behavior though the pollen series were found to have some degree of determinism as revealed by Casdagli's test.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of cedar pollen time series: no evidence of low-dimensional chaotic behavior

2005

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Much of the current interest in pollen time series analysis is motivated by the possibility that pollen series arise from low-dimensional chaotic systems. If this is the case, short-range prediction using nonlinear modeling is justified and would produce high-quality forecasts that could be useful in providing pollen alerts to allergy sufferers. To date, contradictory reports about the characterization of the dynamics of pollen series can be found in the literature. Pollen series have been alternatively described as featuring and not featuring deterministic chaotic behavior. We showed that the choice of test for detection of deterministic chaos in pollen series is difficult because pollen series exhibit [see text] power spectra. This is a characteristic that is also produced by colored noise series, which mimic deterministic chaos in most tests. We proposed to apply the Ikeguchi-Aihara test to properly detect the presence of deterministic chaos in pollen series. We examined the dynamics of cedar (Cryptomeria japonica) hourly pollen series by means of the Ikeguchi-Aihara test and concluded that these pollen series cannot be described as low-dimensional deterministic chaos. Therefore, the application of low-dimensional chaotic deterministic models to the prediction of short-range pollen concentration will not result in high-accuracy pollen forecasts even though these models may provide useful forecasts for certain applications. We believe that our conclusion can be generalized to pollen series from other wind-pollinated plant species, as wind speed, the forcing parameter of the pollen emission and transport, is best described as a nondeterministic series that originates in the high dimensionality of the atmosphere.

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Section: Resultssupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Analysis of cedar pollen time series: no evidence of low-dimensional chaotic behavior

2005

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“…Reports by Bianchi et al [6] and Arizmendi et al [7,8] conclude that pollen time series feature low-dimensional chaotic dynamics with an attractor dimension of 0.66, as estimated by the correlation integral and further confirmed by wavelet analysis. It was also reported that the neural network forecast technique with an embedding dimension of 6 provides accurate forecasts for 1-and 12-h lead times with-out any significant degradation in forecast performance for the extremely large lead time of 12 h. In light of our study, we should like to comment on these results.…”

Section: Discussionmentioning

confidence: 74%

“…3 shows an almost continuous shape that could indicate chaotic dynamics underlying the pollen variations or colored noise. The nonlinearity of the equations of motion of the atmosphere permits chaotic solutions, so finding chaos in the variation of the pollen series could be a possibility, as previously reported [6][7][8][9].…”

Section: Pollen Time-series Analysismentioning

confidence: 98%

“…A different approach to forecasting short-range pollen variations near a pollen observation station could come from time-series forecasting techniques. It has been reported that pollen series dynamics can be described as low-dimensional deterministic chaos [6][7][8][9], thus opening the way for short-range forecasts using nonlinear forecasting techniques such as artificial neural network models.…”

Section: Introductionmentioning

confidence: 99%

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Investigation of short-range cedar pollen forecasting

Delaunay

Seymour²,

Fouillet³

2004

Phys. Rev. E

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Pollen forecasting is of increasing interest as a way to help the general public avoid contact with allergyinducing pollen. It was recently reported that the dynamics underlying pollen concentration series is very similar to that of low-dimensional deterministic chaos, thus opening up new avenues of development in local pollen forecasting. Our analysis of hourly cedar pollen series for two seasons showed evidence of a small degree of determinism underlying the pollen time-series dynamics. However, we could not confirm that our pollen series was generated by a low-dimensional chaotic system. The nearest-neighbor method using local constant prediction applied to hourly pollen forecasting with a 1-h lead time was effective for small to medium pollen variations, but failed to reproduce large and intermittent pollen bursts. The performance of the nearestneighbor model was significantly improved by applying a nonlinear filter to the source dataset. Standard time-series techniques such as neural networks did not improve upon these results. The difficulty in fully characterizing and accurately forecasting the pollen series was thought to originate in the nonstationarity of the series and in the large and intermittent pollen bursts that were found to have no apparent time structure. Thus the dynamics of hourly pollen series is probably not strongly tied to a low-dimensional chaotic system.

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