flux_uncertainties.flux_uncertainties

flux_uncertainties.flux_uncertainties(ini, w_prime, c_prime)

Computes different forms of turbulent flux uncertainties.

This function implements various methods to estimate flux uncertainties and detection limits in eddy covariance measurements, including methods from Spirig et al. (2005), Finkelstein and Sims (2001), and others.

Parameters:

• ini (dict) –

  Initialization dictionary containing:

  • param.SAMPLING_RATE_FINALfloat

    Final sampling rate in Hz

  • param.WINDOW_LENGTHfloat

    Length of the averaging window in seconds

• w_prime (numpy.ndarray) – 1D array of high-frequency fluctuations of vertical wind component (W) Units: m s⁻¹

• c_prime (numpy.ndarray) – 1D array of high-frequency fluctuations of scalar atmospheric variable (e.g., CO₂, CH₄, or VOCs) Units: Dependent on the scalar (e.g., ppb for VOCs)

Returns:

• flux_noise_mean (float) – Flux detection limit using mean of covariance between ±160-180s. Method from Spirig et al. (2005)

• flux_noise_std (float) – Flux detection limit using standard deviation of covariance between ±160-180s. Method from Spirig et al. (2005)

• flux_noise_rmse (float) – Flux detection limit using RMSE of covariance between ±160-180s

• random_error_FS (float) – Random error calculated using the Finkelstein and Sims (2001) method

• random_flux (float) – Flux detection limit using random shuffle method from Billesbach (2011)

• random_error_noise (float) – Random error from white noise using autocovariance methods from Lenschow (2000), Mauder (2013), and Langford (2015)

Notes

The white noise computation uses sqrt(difference) instead of difference(sqrt) as described in Langford (2015) pp. 4200-4201. This differs from the MATLAB InnFLUX implementation where interpolated variance at zero lag could be negative, leading to imaginary numbers in the MATLAB sqrt function.

References

[1]

Spirig, C., et al. (2005). Eddy covariance flux measurements of biogenic VOCs during ECHO 2003 using proton transfer reaction mass spectrometry. Atmospheric Chemistry and Physics, 5(2), 465-481.

[2]

Finkelstein, P. L., & Sims, P. F. (2001). Sampling error in eddy correlation flux measurements. Journal of Geophysical Research: Atmospheres, 106(D4), 3503-3509.

[3]

Billesbach, D. P. (2011). Estimating uncertainties in individual eddy covariance flux measurements: A comparison of methods and a proposed new method. Agricultural and Forest Meteorology, 151(3), 394-405.

[4]

Langford, B., et al. (2015). Eddy-covariance data with low signal-to-noise ratio: time-lag determination, uncertainties and limit of detection. Atmospheric Measurement Techniques, 8(10), 4197-4213.

See also

xcov

Cross-covariance calculation

cospectrum

Co-spectrum analysis

Examples

>>> import numpy as np
>>> # Setup example data (30 minutes at 10 Hz)
>>> ini = {'param': {'SAMPLING_RATE_FINAL': 10, 'WINDOW_LENGTH': 1800}}
>>> w = np.random.randn(18000)  # Vertical wind fluctuations
>>> c = np.random.randn(18000)  # Scalar concentration fluctuations
>>> results = flux_uncertainties(ini, w, c)
>>> print(f'Random error (FS method): {results[3]:.2e}')

Author

Written by Bernard Heinesch University of Liege, Gembloux Agro-Bio Tech