Articles | Volume 24, issue 3
https://doi.org/10.5194/npg-24-481-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/npg-24-481-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion
NorthWest Research Associates, P.O. Box 3027, Bellevue, WA, USA
Adam M. Sykulski
Data Science Institute, Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
Jeffrey J. Early
NorthWest Research Associates, P.O. Box 3027, Bellevue, WA, USA
Sofia C. Olhede
Department of Statistical Science, University College London, Gower Street, London, UK
Viewed
Total article views: 6,502 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 28 Mar 2017)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 3,611 | 2,574 | 317 | 6,502 | 610 | 277 | 343 |
- HTML: 3,611
- PDF: 2,574
- XML: 317
- Total: 6,502
- Supplement: 610
- BibTeX: 277
- EndNote: 343
Total article views: 5,086 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 21 Aug 2017)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 2,963 | 1,857 | 266 | 5,086 | 365 | 254 | 292 |
- HTML: 2,963
- PDF: 1,857
- XML: 266
- Total: 5,086
- Supplement: 365
- BibTeX: 254
- EndNote: 292
Total article views: 1,416 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 28 Mar 2017)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 648 | 717 | 51 | 1,416 | 245 | 23 | 51 |
- HTML: 648
- PDF: 717
- XML: 51
- Total: 1,416
- Supplement: 245
- BibTeX: 23
- EndNote: 51
Viewed (geographical distribution)
Total article views: 6,502 (including HTML, PDF, and XML)
Thereof 6,185 with geography defined
and 317 with unknown origin.
Total article views: 5,086 (including HTML, PDF, and XML)
Thereof 4,829 with geography defined
and 257 with unknown origin.
Total article views: 1,416 (including HTML, PDF, and XML)
Thereof 1,356 with geography defined
and 60 with unknown origin.
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
Cited
50 citations as recorded by crossref.
- Near-surface dynamic structure in the northern South China Sea and Northwest Pacific revealed using Lagrangian data P. Niu & G. Liao
- The Rational SPDE Approach for Gaussian Random Fields With General Smoothness D. Bolin & K. Kirchner
- Derivative of the expected supremum of fractional Brownian motion at $$H=1$$ K. Bisewski et al.
- The 21st Century Systems: An Updated Vision of Continuous-Time Fractional Models M. Ortigueira & J. Machado
- Impacts of atmospheric turbulence on optic measurements over heterogeneous flat terrain: insights from large eddy simulations G. Kermarrec et al.
- A spatio-temporal random synthetic turbulent velocity field: The underlying Gaussian structure M. Chatelain et al.
- Common-clock GPS single differences: An improved correlation model for GPS phase observations based on turbulence theory G. Kermarrec & S. Schön
- On the impact of correlations on the congruence test: a bootstrap approach K. Gaël et al.
- Persistence and stochastic periodicity in the intensity dynamics of a fiber laser during the transition to optical turbulence L. Carpi & C. Masoller
- Fundamentals of sleep regulation: Model and benchmark values for fractal and oscillatory neurodynamics R. Bódizs et al.
- Integral fractional Ornstein–Uhlenbeck process model for animal movement J. Ramírez González & Y. Sun
- Modeling Spatio‐Temporal Transport: From Rigid Advection to Realistic Dynamics M. Battagliola & S. Olhede
- Eulerian and Lagrangian statistics in an exactly solvable turbulent shear model with a random background mean M. Mohamad & A. Majda
- Pathwise uniqueness for multiplicative young and rough differential equations driven by fractional Brownian motion T. Matsuda & A. Mayorcas
- The debiased Whittle likelihood A. Sykulski et al.
- Smoothing and Interpolating Noisy GPS Data with Smoothing Splines J. Early & A. Sykulski
- Separating Mesoscale and Submesoscale Flows from Clustered Drifter Trajectories S. Oscroft et al.
- Lifespan development of EEG alpha and aperiodic component sources is shaped by the connectome and axonal delays R. Garcia Reyes et al.
- On filtering ionospheric effects in GPS observations using the Matérn covariance family and its impact on orbit determination of Swarm satellites G. Kermarrec et al.
- Regularity of multifractional moving average processes with random Hurst exponent D. Loboda et al.
- On the well-posedness of (nonlinear) rough continuity equations L. Galeati et al.
- Identification of sample path smoothness in soil spatial variability J. Ching et al.
- Recovering the Eulerian energy spectrum from noisy Lagrangian tracers M. Mohamad & A. Majda
- How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model: a plane fitting with simulated and real TLS measurements G. Kermarrec & M. Lösler
- Navigating challenges in spatio-temporal modelling of Antarctic krill abundance: Addressing zero-inflated data and misaligned covariates A. Amaral et al.
- Statistical Properties of Small Particle Trajectories in a Fully Developed Turbulent State in He-II W. Kubo & Y. Tsuji
- On a Correlation Model for Laser Scanners: A Large Eddy Simulation Experiment G. Kermarrec
- Analysis of the temporal correlations of TLS range observations from plane fitting residuals G. Kermarrec et al.
- Bayesian comparison of stochastic models of dispersion M. Brolly et al.
- Principles of fractional signal processing M. Ortigueira
- Data-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertainty V. Resseguier et al.
- Fractional interacting particle system: Drift parameter estimation via Malliavin calculus C. Amorino et al.
- Global assessment of linear trend and seasonal variations of GNSS-IR sea level retrievals with nearby tide gauges C. Xu & X. Wang
- Measurement report: Can zenith wet delay from GNSS “see” atmospheric turbulence? Insights from case studies across diverse climate zones G. Kermarrec et al.
- New Trends in Ensemble Forecast Strategy: Uncertainty Quantification for Coarse-Grid Computational Fluid Dynamics V. Resseguier et al.
- The variance inflation factor to account for correlations in likelihood ratio tests: deformation analysis with terrestrial laser scanners G. Kermarrec et al.
- Modeling trends and periodic components in geodetic time series: a unified approach G. Kermarrec et al.
- Fast and Robust Noise Background Modeling and Quasiperiodic Oscillation Detection for Astronomical Time Series C. Xu
- Effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop J. Matulis & H. Bindra
- Meridionally consistent decline in the observed western boundary contribution to the Atlantic Meridional Overturning Circulation Q. Xing et al.
- The Generalized Method of Wavelet Moments with eXogenous inputs: a fast approach for the analysis of GNSS position time series D. Cucci et al.
- The Matérn Model: A Journey Through Statistics, Numerical Analysis and Machine Learning E. Porcu et al.
- Extracting statistically significant eddy signals from large Lagrangian datasets using wavelet ridge analysis, with application to the Gulf of Mexico J. Lilly & P. Pérez-Brunius
- Debiasing Welch’s method for spectral density estimation L. Astfalck et al.
- Long memory estimation for complex-valued time series M. Knight & M. Nunes
- Estimating stable and unstable sets and their role as transport barriers in stochastic flows S. Balasuriya & G. Gottwald
- On the determination of the atmospheric outer scale length of turbulence using GPS phase difference observations: the Seewinkel network G. Kermarrec & S. Schön
- Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space J. Lübke et al.
- A Simple Solution for the General Fractional Ambartsumian Equation M. Ortigueira & G. Bengochea
- Surface Drift and Dispersion in a Multiply Connected Fjord System H. Blanken et al.
50 citations as recorded by crossref.
- Near-surface dynamic structure in the northern South China Sea and Northwest Pacific revealed using Lagrangian data P. Niu & G. Liao
- The Rational SPDE Approach for Gaussian Random Fields With General Smoothness D. Bolin & K. Kirchner
- Derivative of the expected supremum of fractional Brownian motion at $$H=1$$ K. Bisewski et al.
- The 21st Century Systems: An Updated Vision of Continuous-Time Fractional Models M. Ortigueira & J. Machado
- Impacts of atmospheric turbulence on optic measurements over heterogeneous flat terrain: insights from large eddy simulations G. Kermarrec et al.
- A spatio-temporal random synthetic turbulent velocity field: The underlying Gaussian structure M. Chatelain et al.
- Common-clock GPS single differences: An improved correlation model for GPS phase observations based on turbulence theory G. Kermarrec & S. Schön
- On the impact of correlations on the congruence test: a bootstrap approach K. Gaël et al.
- Persistence and stochastic periodicity in the intensity dynamics of a fiber laser during the transition to optical turbulence L. Carpi & C. Masoller
- Fundamentals of sleep regulation: Model and benchmark values for fractal and oscillatory neurodynamics R. Bódizs et al.
- Integral fractional Ornstein–Uhlenbeck process model for animal movement J. Ramírez González & Y. Sun
- Modeling Spatio‐Temporal Transport: From Rigid Advection to Realistic Dynamics M. Battagliola & S. Olhede
- Eulerian and Lagrangian statistics in an exactly solvable turbulent shear model with a random background mean M. Mohamad & A. Majda
- Pathwise uniqueness for multiplicative young and rough differential equations driven by fractional Brownian motion T. Matsuda & A. Mayorcas
- The debiased Whittle likelihood A. Sykulski et al.
- Smoothing and Interpolating Noisy GPS Data with Smoothing Splines J. Early & A. Sykulski
- Separating Mesoscale and Submesoscale Flows from Clustered Drifter Trajectories S. Oscroft et al.
- Lifespan development of EEG alpha and aperiodic component sources is shaped by the connectome and axonal delays R. Garcia Reyes et al.
- On filtering ionospheric effects in GPS observations using the Matérn covariance family and its impact on orbit determination of Swarm satellites G. Kermarrec et al.
- Regularity of multifractional moving average processes with random Hurst exponent D. Loboda et al.
- On the well-posedness of (nonlinear) rough continuity equations L. Galeati et al.
- Identification of sample path smoothness in soil spatial variability J. Ching et al.
- Recovering the Eulerian energy spectrum from noisy Lagrangian tracers M. Mohamad & A. Majda
- How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model: a plane fitting with simulated and real TLS measurements G. Kermarrec & M. Lösler
- Navigating challenges in spatio-temporal modelling of Antarctic krill abundance: Addressing zero-inflated data and misaligned covariates A. Amaral et al.
- Statistical Properties of Small Particle Trajectories in a Fully Developed Turbulent State in He-II W. Kubo & Y. Tsuji
- On a Correlation Model for Laser Scanners: A Large Eddy Simulation Experiment G. Kermarrec
- Analysis of the temporal correlations of TLS range observations from plane fitting residuals G. Kermarrec et al.
- Bayesian comparison of stochastic models of dispersion M. Brolly et al.
- Principles of fractional signal processing M. Ortigueira
- Data-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertainty V. Resseguier et al.
- Fractional interacting particle system: Drift parameter estimation via Malliavin calculus C. Amorino et al.
- Global assessment of linear trend and seasonal variations of GNSS-IR sea level retrievals with nearby tide gauges C. Xu & X. Wang
- Measurement report: Can zenith wet delay from GNSS “see” atmospheric turbulence? Insights from case studies across diverse climate zones G. Kermarrec et al.
- New Trends in Ensemble Forecast Strategy: Uncertainty Quantification for Coarse-Grid Computational Fluid Dynamics V. Resseguier et al.
- The variance inflation factor to account for correlations in likelihood ratio tests: deformation analysis with terrestrial laser scanners G. Kermarrec et al.
- Modeling trends and periodic components in geodetic time series: a unified approach G. Kermarrec et al.
- Fast and Robust Noise Background Modeling and Quasiperiodic Oscillation Detection for Astronomical Time Series C. Xu
- Effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop J. Matulis & H. Bindra
- Meridionally consistent decline in the observed western boundary contribution to the Atlantic Meridional Overturning Circulation Q. Xing et al.
- The Generalized Method of Wavelet Moments with eXogenous inputs: a fast approach for the analysis of GNSS position time series D. Cucci et al.
- The Matérn Model: A Journey Through Statistics, Numerical Analysis and Machine Learning E. Porcu et al.
- Extracting statistically significant eddy signals from large Lagrangian datasets using wavelet ridge analysis, with application to the Gulf of Mexico J. Lilly & P. Pérez-Brunius
- Debiasing Welch’s method for spectral density estimation L. Astfalck et al.
- Long memory estimation for complex-valued time series M. Knight & M. Nunes
- Estimating stable and unstable sets and their role as transport barriers in stochastic flows S. Balasuriya & G. Gottwald
- On the determination of the atmospheric outer scale length of turbulence using GPS phase difference observations: the Seewinkel network G. Kermarrec & S. Schön
- Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space J. Lübke et al.
- A Simple Solution for the General Fractional Ambartsumian Equation M. Ortigueira & G. Bengochea
- Surface Drift and Dispersion in a Multiply Connected Fjord System H. Blanken et al.
Saved (final revised paper)
Latest update: 11 May 2026
Short summary
This work arose from a desire to understand the nature of particle motions in turbulence. We sought a simple conceptual model that could describe such motions, then realized that this model could be applicable to an array of other problems. The basic idea is to create a string of random numbers, called a stochastic process, that mimics the properties of particle trajectories. This model could be useful in making best use of data from freely drifting instruments tracking the ocean currents.
This work arose from a desire to understand the nature of particle motions in turbulence. We...