The Carbon Cycle Group (CCG) of the Climate Monitoring and Diagnostics Laboratory (CMDL) of the National Oceanic and Atmospheric Administration (NOAA) has been making measurements of atmopheric carbon dioxide (CO2) mixing ratios since 1967. There are currently four continuous in-situ monitoring stations and more than 40 flask sampling sites worldwide monitoring not only CO2 but also methane (CH4), carbon monoxide (CO), Hydrogen (H2), Nitrous Oxide (N2O) and Sulpher Hexaflouride (SF6).
The resulting time series from these measurements are examined in order to try and understand the global cycles and budgets of these species so that better information can be provided for predicting associated climate changes. The objective of analysis of time series data at CMDL is to decompose the signals into separate long term trends, annual cycles and short term variations. This is normally accomplished by fitting a curve to the data and mathematically manipulating this curve to obtain the desired signal parameters.
Early uses of curve fitting involved knotted cubic splines (Komhyr et al., 1985). The disadvantages of this type of curve fitting were that the resulting curve depended highly on the placement of the knots, which could be arbitrarily adjusted until the desired fit was obtained. Problems with possible phase shifts were also found (Enting, 1986). Cubic splines with knots every 12 months for determining the long term trend were subject to large end effects.
An improvement on spline fits was used by Conway et al. (1988) in examining flask data for 1981 through 1984. This spline was a modification of the smoothing spline presented by De Boor (1978). The modification (M. Manning, personal communication) involved using a statistical criterion, the runs test, for determining the stiffnes of the spline. This resulted in an objective method for fitting a curve to the data. However, this type of curve had difficulty in following data which showed a large seasonal cycle, such as the far norhtern hemisphere sites, so that determinations of the annual cycle amplitude may have been underestimated. In addition, this spline was too flexible for large amounts of closeley spaced data such as daily averaged data from the in-situ stations since the stiffness criterion was not easily changed.
A different type of curve fit was used by Thoning et al. (1989) for examining the in-situ CO2 data from the Mauna Loa Observatory (MLO) in Hawaii. This method used the Fast Fourier Transform (FFT) to convert the data from the time domain into the frequency domain, applied a low-pass filter in the frequency domain to separate the CO2 signal into its separate components, then performed an invers FFT to convert the filtered data back into the time domain. This method had the advantage of explicitlydefining the frequency response of the filter, as well as computationally being faster than a spline fit. In addition, the statistical uncertainty of the filter could be determined, so that estimates of the uncertainties of the decomposed signals was possible. The main disadvantage of this technique was that large end effects could occur, requiring padding of the data at each end of the record.
A curve fit which was a combination of a trend function and a series of annual harmonics with FFT filtering of the residuals showd the best results of a comparison of several curve fitting methods (Tans et al., 1989). Current curve fitting methods at CMDL are based on this type of filter. The inclusion of a trend plus yearly harmonic functions reduces the problem of end effects, as well as providing seasonal cycle parameters that are useful in carbon cycle models. The determination of uncertainties has been extended to include a variance estimate for all of the parameters derived for the signal, which is very important when trying to determine small changes in a large, noisy signal.
Conway, T.J., P. Tans, L.S. Waterman, K.W. Thoning, K.A. Masarie, and R.H. Gammon, Atmospheric carbon dioxide measurements in the remote global troposphere, 1981-1984, Tellus, 40B, 81-115, 1988.
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Enting, I.G., Potential problems with the use of least squares spline fits to filter CO2 data. J. Geophys. Res. 91, 6668-6670. 1986,
Komhyr, W.D., R.H. Gammon, T.B. Harris, L.S. Waterman, T.J. Conway, W.R. Taylor, and K.W. Thoning, Global atmospheric CO2 distributions and variations from 1968-1982 NOAA/GMCC CO2 flask-sample data, J. Geophys. Res., 90, 5567-5596, 1985.
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Tans, P.P., Thoning, K.W., Elliot, W.P., and Conway, T.J., Background atmospheric CO2 patterns from weekly flask samples at Barrow, Alaska: Optimal signal recovery and error estimates, NOAA Tech. Memo. (ERL-ARL-173). Environ. Res. Lab., Boulder, Colo., 131 pp. 1989,
Thoning, K.W., P.P. Tans, and W.D. Komhyr, Atmospheric carbon dioxide at Mauna Loa Observatory 2. Analysis of the NOAA GMCC data, 1974-1985, J. Geophys. Res., 94, 8549-8565, 1989.