scholarly journals The high-frequency response correction of eddy covariance fluxes – Part 2: An experimental approach for analysing noisy measurements of small fluxes

2021 ◽  
Vol 14 (7) ◽  
pp. 5089-5106
Author(s):  
Toprak Aslan ◽  
Olli Peltola ◽  
Andreas Ibrom ◽  
Eiko Nemitz ◽  
Üllar Rannik ◽  
...  
Keyword(s):  
Time Series ◽  
Transfer Function ◽  
Frequency Response ◽  
Time Constant ◽  
Experimental Approach ◽  
Power Spectra ◽  
Closed Path ◽  
Time Constants ◽  
Low Pass ◽  
Response Correction

Abstract. Fluxes measured with the eddy covariance (EC) technique are subject to flux losses at high frequencies (low-pass filtering). If not properly corrected for, these result in systematically biased ecosystem–atmosphere gas exchange estimates. This loss is corrected using the system's transfer function which can be estimated with either theoretical or experimental approaches. In the experimental approach, commonly used for closed-path EC systems, the low-pass filter transfer function (H) can be derived from the comparison of either (i) the measured power spectra of sonic temperature and the target gas mixing ratio or (ii) the cospectra of both entities with vertical wind speed. In this study, we compare the power spectral approach (PSA) and cospectral approach (CSA) in the calculation of H for a range of attenuation levels and signal-to-noise ratios (SNRs). For a systematic analysis, we artificially generate a representative dataset from sonic temperature (T) by attenuating it with a first order filter and contaminating it with white noise, resulting in various combinations of time constants and SNRs. For PSA, we use two methods to account for the noise in the spectra: the first is the one introduced by Ibrom et al. (2007a) (PSAI07), in which the noise and H are fitted in different frequency ranges, and the noise is removed before estimating H. The second is a novel approach that uses the full power spectrum to fit both H and noise simultaneously (PSAA21). For CSA, we use a method utilizing the square root of the H with shifted vertical wind velocity time series via cross-covariance maximization (CSAH,sync). PSAI07 tends to overestimate the time constant when low-pass filtering is low, whilst the new PSAA21 and CSAH,sync successfully estimate the expected time constant regardless of the degree of attenuation and SNR. We further examine the effect of the time constant obtained with the different implementations of PSA and CSA on cumulative fluxes using estimated time constants in frequency response correction. For our example time series, the fluxes corrected using time constants derived by PSAI07 show a bias between 0.1 % and 1.4 %. PSAA21 showed almost no bias, while CSAH,sync showed bias of ±0.4 %. The accuracies of both PSA and CSA methods were not significantly affected by SNR level, instilling confidence in EC flux measurements and data processing in set-ups with low SNR. Overall we show that, when using power spectra for the empirical estimation of parameters of H for closed-path EC systems the new PSAA21 outperforms PSAI07, while when using cospectra the CSAH,sync approach provides accurate results. These findings are independent of the SNR value and attenuation level.

scholarly journals The high frequency response correction of eddy covariance fluxes. Part 1: an experimental approach for analysing noisy measurements of small fluxes

2020 ◽  
Author(s):  
Toprak Aslan ◽  
Olli Peltola ◽  
Andreas Ibrom ◽  
Eiko Nemitz ◽  
Üllar Rannik ◽  
...  
Keyword(s):  
Time Series ◽  
Time Constant ◽  
Experimental Approach ◽  
Time Lag ◽  
Power Spectra ◽  
Square Root ◽  
Closed Path ◽  
Time Constants ◽  
Low Pass ◽  
Response Correction

Abstract. Fluxes measured with the eddy covariance (EC) technique are subject to flux losses at high frequencies (low-pass filtering). If not properly corrected for, these result in systematically biased ecosystem-atmosphere gas exchange estimates. This loss is corrected using the system's transfer function which can be estimated with either theoretical and experimental approaches. In the experimental approach, commonly used for closed-path EC systems, the low-pass filter transfer function (H) can be derived from the comparison of either (i) the measured power spectra of sonic temperature and the target gas mixing ratio or (ii) the cospectra of both entities with vertical wind speed. In this study, we compare the power spectral approach (PSA) and cospectral approach (CSA) in the calculation of H for a range of attenuation levels and signal-to-noise ratios (SNRs). For a systematic analysis, we artificially generate a representative dataset from sonic temperature (T) by attenuating it with a first order filter and contaminating it with white noise, resulting in various combinations of time constants and SNRs. For PSA, we use two methods to account for the noise in the spectra: the first is the one introduced by Ibrom et al. (2007a) (PSAI07), where the noise and H are fitted in different frequency ranges and the noise is removed before estimating H. The second is a novel approach that uses the full power spectrum to fit both H and noise simultaneously (PSAA20). For CSA, we use three different methods: (1) a plain version of Lorentzian equation describing the H (CSAH), (2) a square-root of the H (CSA√H), and (3) a square-root of the H with shifted vertical wind velocity time series via cross-covariance maximisation (CSA√H,sync). PSAI07 tends to overestimate the time constant when low-pass filtering is low, whilst the new PSAA20 successfully estimates the expected time constant regardless of the degree of attenuation and SNR. CSAH underestimates the time constant with decreasing accuracy as attenuation increases due to the omission of the quadrature spectrum. CSA√H overestimates, but its accuracy increases with time-lag correction in the CSA√H,sync. We further examine the effect of the time constant obtained with the different implementations of PSA and CSA on cumulative fluxes using estimated time constants in frequency response correction. For our example time series, the fluxes corrected using time constants derived by PSAI07 show a bias of ±2 %. PSAA20 showed a similar variation, yet slightly better accuracy. CSAH underestimated fluxes by up to 4 %, while CSA√H overestimated them by up to 3 %, a bias which was mostly eliminated with time-lag correction in the CSA√H,sync (−2 % to 1 % ). The accuracies of both PSA and CSA methods were not affected by SNR level, instilling confidence in EC flux measurements and data processing in setups with low SNR. Overall we show that, when using power spectra for the empirical estimation of parameters of H for closed-path EC systems the new PSAA20 outperforms PSAI07, while when using cospectra the CSA√H,sync approach provides the most accurate results. These findings are independent of the SNR value and attenuation level.

Revising the high frequency response correction of scalar fluxes measured by closed-path eddy covariance systems

2021 ◽  
Author(s):  
Ivan Mammarella ◽  
Olli Peltola ◽  
Toprak Aslan ◽  
Andreas Ibrom ◽  
Eiko Nemitz ◽  
...  
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Eddy Covariance ◽  
High Frequency ◽  
Small Scale ◽  
Systematic Bias ◽  
Closed Path ◽  
Scalar Fluxes ◽  
Wide Range ◽  
Response Correction

<p>Eddy covariance (EC) scalar flux loss at high frequency is due to the incapability of the measurement system to detect small-scale variation of atmospheric turbulent signals. This systematic bias is particularly important for closed-path systems, and it is mainly related to inadequate sensor frequency response, sensor separation and the air sampling trough tubes and filters. Here, we investigate the limitations of current approaches, based on measured power spectra (PSA) or cospectra (CSA), to empirically estimated the spectral transfer function of the EC system needed for the frequency response correction of measured fluxes. We performed a systematic analysis by using EC data from a wetland and forest site for a wide range of attenuation levels and signal-to-noise ratio. We proposed a novel approach for PSA that uses simultaneously the noise and the turbulent signals present in the power spectrum, providing robust estimates of spectral transfer function for all conditions. We further theoretically derived a new transfer function to be used in the CSA approach which specifically accounts for the interaction between the low-pass filtering induced phase shift and the high frequency attenuation. We show that current CSA approaches neglect such effect, giving a non-negligible systematic bias to the estimated scalar fluxes from the studied sites. Based on these findings, we recommend that spectral correction methods, implemented in EC data processing algorithms, are revised accordingly.</p>

Dynamics of abducens nucleus neurons in the awake rabbit

1995 ◽  
Vol 73 (4) ◽  
pp. 1383-1395 ◽  
Author(s):  
J. S. Stahl ◽  
J. I. Simpson
Keyword(s):  
Transfer Function ◽  
Firing Rate ◽  
Eye Movement ◽  
Time Constant ◽  
Quantitative Difference ◽  
Stimulus Frequency ◽  
Eye Position ◽  
Abducens Nucleus ◽  
Time Constants ◽  
Position Sensitivity

1. We recorded abducens neurons, identified by electrical stimulation as internuclear neurons or motoneurons, in awake rabbits. The relationship of firing rate to eye movement was determined from responses during stable fixations, sinusoidal rotation in the light (0.05-0.8 Hz), and triangular optokinetic stimulation at 0.1 Hz. 2. All abducens neurons were excited during temporal movement of the ipsilateral eye. Temporal and nasal saccades were associated with bursts or pauses, respectively, in the firing rate. 3. Motoneurons and internuclear neurons are qualitatively indistinguishable. There was no significant quantitative difference between the phase and sensitivity of the two groups for 0.2-Hz sinusoidal rotation in the light. 4. On the basis of the response to stable eye positions, we determined static eye position sensitivity of the abducens neuron pool to be 8.2 +/- 2.5 (SD) spikes.s-1/0, with a static hysteresis of 8.9 spikes/s (1.14 +/- 0.37 degrees). 5. We determined apparent eye position sensitivity (k) and apparent eye velocity sensitivity (r) from the responses to sinusoidal rotation in the light. k increases and r decreases with stimulus frequency, which indicates that the simplest transfer function mediating conversion of abducens nucleus (VI) firing rate to eye position (E) has two poles and one zero. 6. The VI-->E relationship has an "amplitude nonlinearity," manifest as a tendency for k, r, and firing rate phase lead to decrease as eye movement amplitude increases at a fixed frequency. On a percentage basis, phase is less affected than are the sensitivities. The nonlinearity becomes less pronounced for stimulus amplitudes > 2.5 degrees, and consequently a linear model of the VI-->E transformation remains useful, provided that consideration is restricted to the appropriate range of stimulus/response amplitudes. 7. We determined time constants of the linear two-pole, one-zero transfer function from the variation of r/k versus stimulus frequency. The pole time constants were T1 = 3.4 s and T2 = 0.28 s, and the zero time constant (Tz) = 1.6 s. The magnitude of Tz was corroborated by measuring the time constant of the exponential decay in firing rate after step changes in eye position. This transient method yielded a Tz of 1.1 s. 8. The time constants of the VI-->E transfer function are roughly 10 times larger than those reported for the rhesus macaque. The difference is attributable to the reported 10-fold lower stiffness of the rabbit oculomotor plant, which may in turn relate to rabbits postulated lower degree of activation of extraocular muscles at any given position.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Outer hair cell electromotility is low-pass filtered relative to the molecular conformational changes that produce nonlinear capacitance

2019 ◽  
Vol 151 (12) ◽  
pp. 1369-1385 ◽  
Author(s):  
Joseph Santos-Sacchi ◽  
Kuni H. Iwasa ◽  
Winston Tan
Keyword(s):  
Guinea Pig ◽  
Hair Cell ◽  
Frequency Response ◽  
Time Constant ◽  
Outer Hair Cell ◽  
Resting Potential ◽  
Nonlinear Capacitance ◽  
Cochlear Amplification ◽  
Low Pass ◽  
Length Changes

The outer hair cell (OHC) of the organ of Corti underlies a process that enhances hearing, termed cochlear amplification. The cell possesses a unique voltage-sensing protein, prestin, that changes conformation to cause cell length changes, a process termed electromotility (eM). The prestin voltage sensor generates a capacitance that is both voltage- and frequency-dependent, peaking at a characteristic membrane voltage (Vh), which can be greater than the linear capacitance of the OHC. Accordingly, the OHC membrane time constant depends upon resting potential and the frequency of AC stimulation. The confounding influence of this multifarious time constant on eM frequency response has never been addressed. After correcting for this influence on the whole-cell voltage clamp time constant, we find that both guinea pig and mouse OHC eM is low pass, substantially attenuating in magnitude within the frequency bandwidth of human speech. The frequency response is slowest at Vh, with a cut-off, approximated by single Lorentzian fits within that bandwidth, near 1.5 kHz for the guinea pig OHC and near 4.3 kHz for the mouse OHC, each increasing in a U-shaped manner as holding voltage deviates from Vh. Nonlinear capacitance (NLC) measurements follow this pattern, with cut-offs about double that for eM. Macro-patch experiments on OHC lateral membranes, where voltage delivery has high fidelity, confirms low pass roll-off for NLC. The U-shaped voltage dependence of the eM roll-off frequency is consistent with prestin’s voltage-dependent transition rates. Modeling indicates that the disparity in frequency cut-offs between eM and NLC may be attributed to viscoelastic coupling between prestin’s molecular conformations and nanoscale movements of the cell, possibly via the cytoskeleton, indicating that eM is limited by the OHC’s internal environment, as well as the external environment. Our data suggest that the influence of OHC eM on cochlear amplification at higher frequencies needs reassessment.

scholarly journals The high-frequency response correction of eddy covariance fluxes – Part 1: An experimental approach and its interdependence with the time-lag estimation

2021 ◽  
Vol 14 (7) ◽  
pp. 5071-5088 ◽  
Author(s):  
Olli Peltola ◽  
Toprak Aslan ◽  
Andreas Ibrom ◽  
Eiko Nemitz ◽  
Üllar Rannik ◽  
...  
Keyword(s):  
Time Series ◽  
Phase Shift ◽  
Data Processing ◽  
Frequency Response ◽  
High Frequency ◽  
Time Lag ◽  
Cross Covariance ◽  
Low Pass ◽  
Processing Algorithms ◽  
Data Processing Algorithms

Abstract. The eddy covariance (EC) technique has emerged as the prevailing method to observe the ecosystem–atmosphere exchange of gases, heat and momentum. EC measurements require rigorous data processing to derive the fluxes that can be used to analyse exchange processes at the ecosystem–atmosphere interface. Here we show that two common post-processing steps (time-lag estimation via cross-covariance maximisation and correction for limited frequency response of the EC measurement system) are interrelated, and this should be accounted for when processing EC gas flux data. These findings are applicable to EC systems employing closed- or enclosed-path gas analysers which can be approximated to be linear first-order sensors. These EC measurement systems act as low-pass filters on the time series of the scalar χ (e.g. CO2, H2O), and this induces a time lag (tlpf) between vertical wind speed (w) and scalar χ time series which is additional to the travel time of the gas signal in the sampling line (tube, filters). Time-lag estimation via cross-covariance maximisation inadvertently accounts also for tlpf and hence overestimates the travel time in the sampling line. This results in a phase shift between the time series of w and χ, which distorts the measured cospectra between w and χ and hence has an effect on the correction for the dampening of the EC flux signal at high frequencies. This distortion can be described with a transfer function related to the phase shift (Hp) which is typically neglected when processing EC flux data. Based on analyses using EC data from two contrasting measurement sites, we show that the low-pass-filtering-induced time lag increases approximately linearly with the time constant of the low-pass filter, and hence the importance of Hp in describing the high-frequency flux loss increases as well. Incomplete description of these processes in EC data processing algorithms results in flux biases of up to 10 %, with the largest biases observed for short towers due to the prevalence of small-scale turbulence. Based on these findings, it is suggested that spectral correction methods implemented in EC data processing algorithms are revised to account for the influence of low-pass-filtering-induced time lag.

scholarly journals Improving Efficiency of NPP Software Based I&C

2016 ◽  
pp. 71-76
Author(s):  
H. Ukhina ◽  
A. Bilenko ◽  
V. Sytnikov
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Digital Filters ◽  
First Order ◽  
Response Characteristics ◽  
Function Coefficient ◽  
Low Pass ◽  
Frequency Response Characteristics ◽  
Digital Components ◽  
High Pass

The paper considers improving efficiency of NPP software based I&C during adjustment and readjustment of its characteristics. The research analyzes impact of transfer function coefficient of digital components on features of frequency-response characteristics, which shall be considered during design of software based I&C. The paper objective was to determine the numerator and denominator dependencies of transfer function of first order high-pass and low-pass digital filters of cut-off frequency, and also to determine dependencies on pulsation coefficient.

scholarly journals The high frequency response correction of eddy covariance fluxes. Part 2: the empirical approach and its interdependence with the time-lag estimation

2021 ◽  
Author(s):  
Olli Peltola ◽  
Toprak Aslan ◽  
Andreas Ibrom ◽  
Eiko Nemitz ◽  
Üllar Rannik ◽  
...  
Keyword(s):  
Time Series ◽  
Phase Shift ◽  
Data Processing ◽  
Frequency Response ◽  
High Frequency ◽  
Time Lag ◽  
Cross Covariance ◽  
Low Pass ◽  
Processing Algorithms ◽  
Data Processing Algorithms

Abstract. The eddy covariance (EC) technique has emerged as the prevailing method to observe ecosystem - atmosphere exchange of gases, heat and momentum. EC measurements require rigorous data processing to derive the fluxes that can be used to analyse exchange processes at the ecosystem - atmosphere interface. Here we show that two common post-processing steps (time-lag estimation via cross-covariance maximisation, and correction for limited frequency response of the EC measurement system) are interrelated and this should be accounted for when processing EC gas flux data. These findings are applicable to EC systems employing closed- or enclosed-path gas analysers which can be approximated to be linear first-order sensors. These EC measurement systems act as a low-pass filters on the time-series of the scalar χ (e.g. CO2, H2O) and this induces a time-lag (tlpf) between vertical wind speed (w) and scalar χ time series which is additional to the travel time of the gas signal in the sampling line (tube, filters). Time-lag estimation via cross-covariance maximisation inadvertently accounts also for tlpf and hence overestimates the travel time in the sampling line. This results in a phase shift between the time-series of w and χ, which distorts the measured cospectra between w and χ and hence has an effect on the correction for dampening of EC flux signal at high frequencies. This distortion can be described with a transfer function related to the phase shift (Hp) which is typically neglected when processing EC flux data. Based on analyses using EC data from two contrasting measurement sites, we show that the low-pass filtering induced time-lag increases approximately linearly with the time constant of the low-pass filter, and hence the importance of Hp in describing the high frequency flux loss increases as well. Incomplete description of these processes in EC data processing algorithms results in flux biases of up to 10 %, with the largest biases observed for short towers due to prevalence of small scale turbulence. Based on these findings, it is suggested that spectral correction methods implemented in EC data processing algorithms are revised to account for the influence of low-pass filtering induced time-lag.

Stop-go temperature logging for precision applications

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. E119-E123 ◽  
Author(s):  
Robert N. Harris ◽  
David S. Chapman
Keyword(s):  
Time Series ◽  
Time Constant ◽  
Diffusion Theory ◽  
Wait Time ◽  
Fixed Time ◽  
Heat Diffusion ◽  
Time Constants ◽  
Precision Temperature ◽  
Long Cylinder

We describe a new field procedure for stop-go temperature logging of boreholes that attains millikelvin precision. Temperature is recorded continuously throughout the entire log, but the logging probe is held stationary for a fixed time at discrete depth intervals. Equilibrium temperatures at the discrete depths are based on extrapolations of time series using the heat-diffusion theory for an infinitely long cylinder. For a Fenwahl K212E thermistor probe having a time constant of about [Formula: see text], temperatures are still [Formula: see text] away from equilibrium after a wait time of [Formula: see text]; but temperatures extrapolated from the time series are within [Formula: see text] of equilibrium. A time series over a duration of seven time constants of the probe allows the user to reproduce temperature estimates within millikelvins. The technique was applied at GC-1, a borehole in northwestern Utah.

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