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.
Research article
| 
21 Aug 2017
Research article |
| 21 Aug 2017
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: 4,218 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 28 Mar 2017)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 2,480 | 1,493 | 245 | 4,218 | 524 | 185 | 198 |
- HTML: 2,480
- PDF: 1,493
- XML: 245
- Total: 4,218
- Supplement: 524
- BibTeX: 185
- EndNote: 198
Total article views: 3,203 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 21 Aug 2017)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 1,890 | 1,116 | 197 | 3,203 | 324 | 165 | 152 |
- HTML: 1,890
- PDF: 1,116
- XML: 197
- Total: 3,203
- Supplement: 324
- BibTeX: 165
- EndNote: 152
Total article views: 1,015 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 28 Mar 2017)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 590 | 377 | 48 | 1,015 | 200 | 20 | 46 |
- HTML: 590
- PDF: 377
- XML: 48
- Total: 1,015
- Supplement: 200
- BibTeX: 20
- EndNote: 46
Viewed (geographical distribution)
Total article views: 4,218 (including HTML, PDF, and XML)
Thereof 3,998 with geography defined
and 220 with unknown origin.
Total article views: 3,203 (including HTML, PDF, and XML)
Thereof 3,028 with geography defined
and 175 with unknown origin.
Total article views: 1,015 (including HTML, PDF, and XML)
Thereof 970 with geography defined
and 45 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
34 citations as recorded by crossref.
- The debiased Whittle likelihood A. Sykulski et al. 10.1093/biomet/asy071
- Smoothing and Interpolating Noisy GPS Data with Smoothing Splines J. Early & A. Sykulski 10.1175/JTECH-D-19-0087.1
- Separating Mesoscale and Submesoscale Flows from Clustered Drifter Trajectories S. Oscroft et al. 10.3390/fluids6010014
- Near-surface dynamic structure in the northern South China Sea and Northwest Pacific revealed using Lagrangian data P. Niu & G. Liao 10.1007/s10872-023-00687-4
- 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. 10.1007/s10291-018-0733-y
- Regularity of multifractional moving average processes with random Hurst exponent D. Loboda et al. 10.1016/j.spa.2021.05.008
- Identification of sample path smoothness in soil spatial variability J. Ching et al. 10.1016/j.strusafe.2019.101870
- The Rational SPDE Approach for Gaussian Random Fields With General Smoothness D. Bolin & K. Kirchner 10.1080/10618600.2019.1665537
- Recovering the Eulerian energy spectrum from noisy Lagrangian tracers M. Mohamad & A. Majda 10.1016/j.physd.2020.132374
- 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 10.1007/s00190-020-01456-7
- Derivative of the expected supremum of fractional Brownian motion at $$H=1$$ K. Bisewski et al. 10.1007/s11134-022-09859-3
- The 21st Century Systems: An Updated Vision of Continuous-Time Fractional Models M. Ortigueira & J. Machado 10.1109/MCAS.2022.3160905
- Statistical Properties of Small Particle Trajectories in a Fully Developed Turbulent State in He-II W. Kubo & Y. Tsuji 10.1007/s10909-019-02192-9
- Analysis of the temporal correlations of TLS range observations from plane fitting residuals G. Kermarrec et al. 10.1016/j.isprsjprs.2020.10.012
- Bayesian comparison of stochastic models of dispersion M. Brolly et al. 10.1017/jfm.2022.472
- Principles of fractional signal processing M. Ortigueira 10.1016/j.dsp.2024.104490
- Data-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertainty V. Resseguier et al. 10.5194/npg-27-209-2020
- Common-clock GPS single differences: An improved correlation model for GPS phase observations based on turbulence theory G. Kermarrec & S. Schön 10.1016/j.asr.2023.05.042
- On the impact of correlations on the congruence test: a bootstrap approach K. Gaël et al. 10.1007/s40328-020-00302-8
- New Trends in Ensemble Forecast Strategy: Uncertainty Quantification for Coarse-Grid Computational Fluid Dynamics V. Resseguier et al. 10.1007/s11831-020-09437-x
- Persistence and stochastic periodicity in the intensity dynamics of a fiber laser during the transition to optical turbulence L. Carpi & C. Masoller 10.1103/PhysRevA.97.023842
- The variance inflation factor to account for correlations in likelihood ratio tests: deformation analysis with terrestrial laser scanners G. Kermarrec et al. 10.1007/s00190-022-01654-5
- Modeling trends and periodic components in geodetic time series: a unified approach G. Kermarrec et al. 10.1007/s00190-024-01826-5
- The Generalized Method of Wavelet Moments with eXogenous inputs: a fast approach for the analysis of GNSS position time series D. Cucci et al. 10.1007/s00190-023-01702-8
- Fundamentals of sleep regulation: Model and benchmark values for fractal and oscillatory neurodynamics R. Bódizs et al. 10.1016/j.pneurobio.2024.102589
- 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 10.5194/npg-28-181-2021
- Long memory estimation for complex-valued time series M. Knight & M. Nunes 10.1007/s11222-018-9820-8
- Estimating stable and unstable sets and their role as transport barriers in stochastic flows S. Balasuriya & G. Gottwald 10.1103/PhysRevE.98.013106
- On the determination of the atmospheric outer scale length of turbulence using GPS phase difference observations: the Seewinkel network G. Kermarrec & S. Schön 10.1186/s40623-020-01308-w
- Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space J. Lübke et al. 10.1088/2632-072X/acb128
- Eulerian and Lagrangian statistics in an exactly solvable turbulent shear model with a random background mean M. Mohamad & A. Majda 10.1063/1.5121705
- A Simple Solution for the General Fractional Ambartsumian Equation M. Ortigueira & G. Bengochea 10.3390/app13020871
- Surface Drift and Dispersion in a Multiply Connected Fjord System H. Blanken et al. 10.1029/2019JC015425
- Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals A. Sykulski et al. 10.1109/TSP.2017.2686334
33 citations as recorded by crossref.
- The debiased Whittle likelihood A. Sykulski et al. 10.1093/biomet/asy071
- Smoothing and Interpolating Noisy GPS Data with Smoothing Splines J. Early & A. Sykulski 10.1175/JTECH-D-19-0087.1
- Separating Mesoscale and Submesoscale Flows from Clustered Drifter Trajectories S. Oscroft et al. 10.3390/fluids6010014
- Near-surface dynamic structure in the northern South China Sea and Northwest Pacific revealed using Lagrangian data P. Niu & G. Liao 10.1007/s10872-023-00687-4
- 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. 10.1007/s10291-018-0733-y
- Regularity of multifractional moving average processes with random Hurst exponent D. Loboda et al. 10.1016/j.spa.2021.05.008
- Identification of sample path smoothness in soil spatial variability J. Ching et al. 10.1016/j.strusafe.2019.101870
- The Rational SPDE Approach for Gaussian Random Fields With General Smoothness D. Bolin & K. Kirchner 10.1080/10618600.2019.1665537
- Recovering the Eulerian energy spectrum from noisy Lagrangian tracers M. Mohamad & A. Majda 10.1016/j.physd.2020.132374
- 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 10.1007/s00190-020-01456-7
- Derivative of the expected supremum of fractional Brownian motion at $$H=1$$ K. Bisewski et al. 10.1007/s11134-022-09859-3
- The 21st Century Systems: An Updated Vision of Continuous-Time Fractional Models M. Ortigueira & J. Machado 10.1109/MCAS.2022.3160905
- Statistical Properties of Small Particle Trajectories in a Fully Developed Turbulent State in He-II W. Kubo & Y. Tsuji 10.1007/s10909-019-02192-9
- Analysis of the temporal correlations of TLS range observations from plane fitting residuals G. Kermarrec et al. 10.1016/j.isprsjprs.2020.10.012
- Bayesian comparison of stochastic models of dispersion M. Brolly et al. 10.1017/jfm.2022.472
- Principles of fractional signal processing M. Ortigueira 10.1016/j.dsp.2024.104490
- Data-driven versus self-similar parameterizations for stochastic advection by Lie transport and location uncertainty V. Resseguier et al. 10.5194/npg-27-209-2020
- Common-clock GPS single differences: An improved correlation model for GPS phase observations based on turbulence theory G. Kermarrec & S. Schön 10.1016/j.asr.2023.05.042
- On the impact of correlations on the congruence test: a bootstrap approach K. Gaël et al. 10.1007/s40328-020-00302-8
- New Trends in Ensemble Forecast Strategy: Uncertainty Quantification for Coarse-Grid Computational Fluid Dynamics V. Resseguier et al. 10.1007/s11831-020-09437-x
- Persistence and stochastic periodicity in the intensity dynamics of a fiber laser during the transition to optical turbulence L. Carpi & C. Masoller 10.1103/PhysRevA.97.023842
- The variance inflation factor to account for correlations in likelihood ratio tests: deformation analysis with terrestrial laser scanners G. Kermarrec et al. 10.1007/s00190-022-01654-5
- Modeling trends and periodic components in geodetic time series: a unified approach G. Kermarrec et al. 10.1007/s00190-024-01826-5
- The Generalized Method of Wavelet Moments with eXogenous inputs: a fast approach for the analysis of GNSS position time series D. Cucci et al. 10.1007/s00190-023-01702-8
- Fundamentals of sleep regulation: Model and benchmark values for fractal and oscillatory neurodynamics R. Bódizs et al. 10.1016/j.pneurobio.2024.102589
- 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 10.5194/npg-28-181-2021
- Long memory estimation for complex-valued time series M. Knight & M. Nunes 10.1007/s11222-018-9820-8
- Estimating stable and unstable sets and their role as transport barriers in stochastic flows S. Balasuriya & G. Gottwald 10.1103/PhysRevE.98.013106
- On the determination of the atmospheric outer scale length of turbulence using GPS phase difference observations: the Seewinkel network G. Kermarrec & S. Schön 10.1186/s40623-020-01308-w
- Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space J. Lübke et al. 10.1088/2632-072X/acb128
- Eulerian and Lagrangian statistics in an exactly solvable turbulent shear model with a random background mean M. Mohamad & A. Majda 10.1063/1.5121705
- A Simple Solution for the General Fractional Ambartsumian Equation M. Ortigueira & G. Bengochea 10.3390/app13020871
- Surface Drift and Dispersion in a Multiply Connected Fjord System H. Blanken et al. 10.1029/2019JC015425
1 citations as recorded by crossref.
Latest update: 24 Apr 2024
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...
