scholarly journals Tune in on 11.57 µHz and listen to primary production

2017 ◽  
Author(s):  
Tom J. S. Cox ◽  
Justus E. E. van Beusekom ◽  
Karline Soetaert
Keyword(s):  
Time Series ◽  
Frequency Domain ◽  
Water Column ◽  
Time Varying ◽  
Carrier Wave ◽  
Theoretical Derivation ◽  
Complex Demodulation ◽  
Tidal Harmonics ◽  
Radio Signals ◽  
Averaging Time

Abstract. In this manuscript we present an an elegant approach to reconstruct slowly varying GPP as a function of time, based on O2 time series. The approach, called complex demodulation, is based on on a direct analogy with amplitude modulated (AM) radio signals. The O2 concentrations oscillating at the diel frequency (or 11.57 μHz) can be seen as a carrier wave, while the time variation in the amplitude of this carrier wave is related to the time varying GPP. The relation follows from an analysis in the frequency domain of the governing equation of O2 dynamics. After the theoretical derivation, we assess the performance of the approach by applying it to 3 artificial O2 time series, generated with models representative for a well mixed vertical water column, a river and an estuary. These models are forced with hourly observed incident irradiance, resulting in a variblity of GPP on scales from hours to months. The dynamic build-up of algal biomass further increases the seasonality. Complex demodulation allows to reconstruct with great precision time varying GPP of the vertical water column and the river model. Surprisingly, it is possible to derive daily averaged GPP – complex demodulation thus reconstructs the amplitude of every single diel cycle. Also in estuaries time varying GPP can be reconstructed to a great extent. But there, the influence of the tides prevent achieving the same temporal resolution. In particular, the combination of horizontal O2 gradients with the O1 and Q1 harmonics in the tides, interferes with the complex demodulation procedure, and introduces spurious amplitude variation that can not be attributed to GPP. But also other tidal harmonics, in casu K1 and P1, introduce diel fluctuations that can not be distinguished from GPP. We demonstrate that these spurious effects also occur in real-world time series (Hörnum Tief, De). The spurious fluctuations introduced by O1 and Q1 can be removed to a large extent by increasing the averaging time to 15 days. As such, we demonstrate that a good estimate of the running 15 day average of GPP can be obtained in tidal systems. Apart from the direct merits to estimating GPP from O2 time series, the analysis in the frequency domain enhances our insights in O2 dynamics in tidal systems in general, and in the performance of O2 methods to estimate GPP in particular.

scholarly journals Tune in on 11.57 µHz and listen to primary production

2017 ◽  
Vol 14 (22) ◽  
pp. 5271-5280
Author(s):  
Tom J. S. Cox ◽  
Justus E. E. van Beusekom ◽  
Karline Soetaert
Keyword(s):  
Time Series ◽  
Primary Production ◽  
Frequency Domain ◽  
Water Column ◽  
Gross Primary Production ◽  
Time Varying ◽  
Carrier Wave ◽  
Theoretical Derivation ◽  
Complex Demodulation ◽  
Averaging Time

Abstract. In this paper we present an elegant approach to reconstruct slowly varying gross primary production (GPP) as a function of time, based on O2 time series. The approach, called complex demodulation, is based on a direct analogy with amplitude-modulated (AM) radio signals. The O2 concentrations oscillating at the diel frequency (or 11.57 µHz) can be seen as a carrier wave, while the time variation in the amplitude of this carrier wave is related to the time-varying GPP. The relation follows from an analysis in the frequency domain of the governing equations of O2 dynamics. After the theoretical derivation, we assess the performance of the approach by applying it to three artificial O2 time series, generated with models representative of a well-mixed vertical water column, a river and an estuary. These models are forced with hourly observed incident irradiance, resulting in a variability of GPP on scales from hours to months. The dynamic build-up of algal biomass further increases the seasonality. Complex demodulation allows for reconstruction, with great precision, of time-varying GPP of the vertical water column and the river model. Surprisingly, it is possible to derive daily averaged GPP – complex demodulation thus reconstructs the amplitude of every single diel cycle. Also, in estuaries time-varying GPP can be reconstructed to a great extent. But there, the influence of the tides prevent achieving the same temporal resolution. In particular, the combination of horizontal O2 gradients with quasi-diurnal harmonics in the tides interferes with the complex demodulation procedure and introduces spurious amplitude variation that can not be attributed to GPP. We demonstrate that these spurious effects also occur in real-world time series (Hörnum Tief, Germany). The spurious effects due to K1 and P1 quasi-diurnals can not be distinguished from GPP. However, the spurious fluctuations introduced by O1 and Q1 can be removed to a large extent by increasing the averaging time to 15 days. As such, we demonstrate that a good estimate of the running 15-day average of GPP can be obtained in tidal systems. Apart from the direct merits of estimating GPP from O2 time series, the analysis in the frequency domain enhances our insights into O2 dynamics in tidal systems in general, and into the performance of O2 methods to estimate GPP in particular.

A Frequency-Domain Filtering Technique for Triple Decomposition of Unsteady Turbulent Flow

1992 ◽  
Vol 114 (1) ◽  
pp. 45-51 ◽  
Author(s):  
G. J. Brereton ◽  
A. Kodal
Keyword(s):  
Time Series ◽  
Turbulent Flow ◽  
Frequency Domain ◽  
Measurement Data ◽  
Averaging Technique ◽  
Phase Averaging ◽  
Spectral Estimates ◽  
Improved Performance ◽  
A New Technique ◽  
Flow Variables

A new technique is presented for decomposing unsteady turbulent flow variables into their organized unsteady and turbulent components, which appears to offer some significant advantages over existing ones. The technique uses power-spectral estimates of data to deduce the optimal frequency-domain filter for determining the organized and turbulent components of a time series of data. When contrasted with the phase-averaging technique, this method can be thought of as replacing the assumption that the organized motion is identically reproduced in successive cycles of known periodicity by a more general condition: the cross-correlation of the organized and turbulent components is minimized for a time series of measurement data, given the expected shape of the turbulence power spectrum. The method is significantly more general than the phase average in its applicability and makes more efficient use of available data. Performance evaluations for time series of unsteady turbulent velocity measurements attest to the accuracy of the technique and illustrate the improved performance of this method over the phase-averaging technique when cycle-to-cycle variations in organized motion are present.

Selective Linear Segmentation for Detecting Relevant Parameter Changes*

2020 ◽  
Author(s):  
Arnaud Dufays ◽  
Elysee Aristide Houndetoungan ◽  
Alain Coën
Keyword(s):  
Time Series ◽  
Hedge Fund ◽  
Expectation Maximization Algorithm ◽  
Model Parameters ◽  
Relevant Parameter ◽  
Time Varying ◽  
Long Time ◽  
Model Selection Uncertainty ◽  
Penalized Likelihood Approach ◽  
Changes Over Time

Abstract Change-point (CP) processes are one flexible approach to model long time series. We propose a method to uncover which model parameters truly vary when a CP is detected. Given a set of breakpoints, we use a penalized likelihood approach to select the best set of parameters that changes over time and we prove that the penalty function leads to a consistent selection of the true model. Estimation is carried out via the deterministic annealing expectation-maximization algorithm. Our method accounts for model selection uncertainty and associates a probability to all the possible time-varying parameter specifications. Monte Carlo simulations highlight that the method works well for many time series models including heteroskedastic processes. For a sample of fourteen hedge fund (HF) strategies, using an asset-based style pricing model, we shed light on the promising ability of our method to detect the time-varying dynamics of risk exposures as well as to forecast HF returns.

A Novel Solution to Compute Stress Time Series in Nonlinear Hydro-Structure Simulations

2015 ◽  
Author(s):  
Fabien Bigot ◽  
François-Xavier Sireta ◽  
Eric Baudin ◽  
Quentin Derbanne ◽  
Etienne Tiphine ◽  
...  
Keyword(s):  
Time Series ◽  
Frequency Domain ◽  
Time Domain ◽  
Hot Spot ◽  
Structural Response ◽  
Container Ship ◽  
Time Step ◽  
Computation Cost ◽  
Hull Girder ◽  
Non Linear

Ship transport is growing up rapidly, leading to ships size increase, and particularly for container ships. The last generation of Container Ship is now called Ultra Large Container Ship (ULCS). Due to their increasing sizes they are more flexible and more prone to wave induced vibrations of their hull girder: springing and whipping. The subsequent increase of the structure fatigue damage needs to be evaluated at the design stage, thus pushing the development of hydro-elastic simulation models. Spectral fatigue analysis including the first order springing can be done at a reasonable computational cost since the coupling between the sea-keeping and the Finite Element Method (FEM) structural analysis is performed in frequency domain. On the opposite, the simulation of non-linear phenomena (Non linear springing, whipping) has to be done in time domain, which dramatically increases the computation cost. In the context of ULCS, because of hull girder torsion and structural discontinuities, the hot spot stress time series that are required for fatigue analysis cannot be simply obtained from the hull girder loads in way of the detail. On the other hand, the computation cost to perform a FEM analysis at each time step is too high, so alternative solutions are necessary. In this paper a new solution is proposed, that is derived from a method for the efficient conversion of full scale strain measurements into internal loads. In this context, the process is reversed so that the stresses in the structural details are derived from the internal loads computed by the sea-keeping program. First, a base of distortion modes is built using a structural model of the ship. An original method to build this base using the structural response to wave loading is proposed. Then a conversion matrix is used to project the computed internal loads values on the distortion modes base, and the hot spot stresses are obtained by recombination of their modal values. The Moore-Penrose pseudo-inverse is used to minimize the error. In a first step, the conversion procedure is established and validated using the frequency domain hydro-structure model of a ULCS. Then the method is applied to a non-linear time domain simulation for which the structural response has actually been computed at each time step in order to have a reference stress signal, in order to prove its efficiency.

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