Investigating bias in the application of curve fitting programs to atmospheric time series

Abstract

Abstract. The decomposition of an atmospheric time series into its constituent parts is an essential tool for identifying and isolating variations of interest from a data set, and is widely used to obtain information about sources, sinks and trends in climatically important gases. Such procedures involve fitting appropriate mathematical functions to the data. However, it has been demonstrated that the application of such curve fitting procedures can introduce bias, and thus influence the scientific interpretation of the data sets. We investigate the potential for bias associated with the application of three curve fitting programs, known as HPspline, CCGCRV and STL, using multi-year records of CO 2 , CH 4 and O 3 data from three atmospheric monitoring field stations. These three curve fitting programs are widely used within the greenhouse gas measurement community to analyse atmospheric time series, but have not previously been compared extensively.The programs were rigorously tested for their ability to accurately represent the salient features of atmospheric time series, their ability to cope with outliers and gaps in the data, and for sensitivity to the values used for the input parameters needed for each program. We find that the programs can produce significantly different curve fits, and these curve fits can be dependent on the input parameters selected. There are notable differences between the results produced by the three programs for many of the decomposed components of the time series, such as the representation of seasonal cycle characteristics and the long-term (multi-year) growth rate. The programs also vary significantly in their response to gaps and outliers in the time series. Overall, we found that none of the three programs were superior, and that each program had its strengths and weaknesses. Thus, we provide a list of recommendations on the appropriate use of these three curve fitting programs for certain types of data sets, and for certain types of analyses and applications. In addition, we recommend that sensitivity tests are performed in any study using curve fitting programs, to ensure that results are not unduly influenced by the input smoothing parameters chosen.Our findings also have implications for previous studies that have relied on a single curve fitting program to interpret atmospheric time series measurements. This is demonstrated by using two other curve fitting programs to replicate work in Piao et al. (2008) on zero-crossing analyses of atmospheric CO 2 seasonal cycles to investigate terrestrial biosphere changes. We highlight the importance of using more than one program, to ensure results are consistent, reproducible, and free from bias.

Adaptive Baseline Finder, a statistical data selection strategy to identify atmospheric CO<sub>2</sub> baseline levels and its application to European elevated mountain stations

“…STL has been widely used on atmospheric CO 2 and other trace gases measurements (Cleveland et al, 1983;Carslaw, 2005;Brailsford et al, 2012;Hernández-Paniagua et al, 2015;Pickers and Manning, 2015). It decomposes a time series of interest into a trend component , a seasonal component and a remainder 25 component , which allows separately detailed analyses and comparisons of trend and seasonality.…”

Trend Assessment for a CO2 and CH4 Data Series in Northern Spain

“…Small changes in the trends of greenhouse gases can have a major impact on the Earth, and thus may be of great significance for climate change [2].…”

“…Due to the periodic and irregular variations on both long and short timescales, analysis of atmospheric time series is a complex process. The long-term is mainly derived from fossil fuel burning processes and from land-use change emissions, overlapped to a large interannual variability related to climate-driven changes in source and sinks [2,3]. Studying the data trend requires subtracting the seasonal component from the complete time series by a deseasonalization process.…”

“…Studying the data trend requires subtracting the seasonal component from the complete time series by a deseasonalization process. This procedure involves fitting appropriate mathematical functions to the data [2].pollution analysis. Cleveland [7] suggested local regression methods to obtain visual information from scatterplots [8].…”

Comparison of the regional CO<sub>2</sub> mole fraction filtering approaches at a WMO/GAW regional station in China

“…Sometimes it further considers the diurnal CO 2 variation as it can be closely linked to the above parameters (Zhou et al, 2005). (3) Statistical methods is an approach that generally uses the variations (e.g., a low standard deviation) of observed data in certain time windows as a threshold to select the regional values (Cunnold et al, 2002;Morimoto et al, 2003;Pickers and Manning, 2015;Zhang et al, 2007). (4) Numerical transport methods use atmospheric dispersion modeling (e.g., air mass back trajectories) to study the advection regimes with subsequent distinction in periods with potential influence of local or regional source/sink and uninfluenced conditions (Cape et al, 2000;Manning et al, 2011;Ryall et al, 2001).…”