Nordebo Sven, Naeem Muhammad Farhan, Tans Pieter
Department of Physics and Electrical Engineering, Linnæus University, 351 95, Växjö, Sweden.
NOAA Global Monitoring Laboratory, Boulder, CO, 80305, USA.
Sci Rep. 2020 Dec 4;10(1):21222. doi: 10.1038/s41598-020-77921-2.
What exactly is the short-time rate of change (growth rate) in the trend of [Formula: see text] data such as the Keeling curve? The answer to this question will obviously depend very much on the duration in time over which the trend has been defined, as well as the smoothing technique that has been used. As an estimate of the short-time rate of change we propose to employ a very simple and robust definition of the trend based on a centered 1-year sliding data window for averaging and a corresponding centered 1-year difference (2-year data window) to estimate its rate of change. In this paper, we show that this simple strategy applied to weekly data of the Keeling curve (1974-2020) gives an estimated rate of change which is perfectly consistent with a more sophisticated regression analysis technique based on Taylor and Fourier series expansions. From a statistical analysis of the regression model and by using the Cramér-Rao lower bound, it is demonstrated that the relative error in the estimated rate of change is less than 5 [Formula: see text]. As an illustration, the estimates are finally compared to some other publicly available data regarding anthropogenic [Formula: see text] emissions and natural phenomena such as the El Niño.
像基林曲线这样的[公式：见原文]数据趋势中的短期变化率（增长率）究竟是什么？这个问题的答案显然在很大程度上取决于定义该趋势所依据的时间跨度，以及所使用的平滑技术。作为短期变化率的一种估计，我们建议采用一种基于以一年为中心的滑动数据窗口进行平均的非常简单且稳健的趋势定义，以及相应的以一年为中心的差值（两年数据窗口）来估计其变化率。在本文中，我们表明，将这种简单策略应用于基林曲线（1974 - 2020年）的每周数据时，所得到的变化率估计值与基于泰勒和傅里叶级数展开的更复杂的回归分析技术完全一致。通过对回归模型的统计分析并使用克拉美 - 罗下界，证明了估计变化率中的相对误差小于5[公式：见原文]。作为一个示例，最后将这些估计值与其他一些关于人为[公式：见原文]排放以及诸如厄尔尼诺等自然现象的公开可用数据进行了比较。
