The main objective of this paper is to implement different methods to assess the salient
features of the data trend for a CO2 and CH4 data series. Said series was obtained at the Low
Atmosphere Research Centre (41°48′49″ N, 4°55′59″ W) using a Picarro analyser (G1301). Different functions were employed to determine and quantify the data trend. The first was a harmonic function based on a third-degree polynomial. An increasing trend, below 2.30 ppm year−1 for CO2 and below 11.90 ppb year−1 for CH4, was reported. Epanechnikov, Gaussian, biweight, tricubic, rectangular and triangle kernels, were applied with a 500-day bandwidth for the trend. The best fit was obtained by the biweight kernel (r > 0.20), with an increasing trend around 1.80 ppm year−1 for CO2 and around 7.15 ppb year−1 for CH4. The final analysis, which included local linear regression functions also applying a 500-day bandwidth, revealed increasing trends for both CO2, around 1.98 ppm year−1, and CH4, around 10.85 ppb year−1. Trend values were far more accelerated in the latter years of the series, regardless of the chosen function. This paper demonstrated the usefulness of the mathematical functions, allowing for an accurate determination of the data trend.
