Abstract
Trend detection is model-dependent. We analyze this for auto-correlated temperature time series. By the comparison of two different models which both describe the same stochastic process, we can introduce the distinction between the observed trend and the intrinsic trend. We transform a model with correlated noise into the lagged dependent variable (LDV) model with white noise. Although the commonly used climate dynamical model usually contains the LDV, existing trend studies barely consider it. For the LDV model, the auto-correlation effect on trend detection not only induces the stochastic trend, but also leads to an additional trend by accumulating the intrinsic trend. The intrinsic trend exclusive of the auto-correlation effect should be more likely related to the external forcing like anthropogenic factors, which is actually the trend of main interest. By applying the LDV model to the monthly mean anomalies at the Potsdam, Hamburg, and Frankfurt stations, it is found that 87%, 78%, and 75%, respectively, of the observed trends are the intrinsic trend, which may be more relevant to anthropogenic factors; and the rest should be due to auto-correlation. Analysis of two additional Chinese stations, namely the Guangzhou and Turpan stations, demonstrates the general applicability of the LDV model for different climate zones. Our study refreshes the current understanding of the observed trend and the auto-correlation effect, which is expected to be beneficial in the exploration of the underlying mechanism of global warming.
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Data availability
The German temperature records are extracted from the historical daily station observations (temperature, pressure, precipitation, wind, sunshine duration, etc.) for Germany, version v004, 2016: Data set description. The complete meteorological data sets of the stations were downloaded from the Climate Data Center of the German Weather Service DWD via ftp://ftp-cdc.dwd.de/pub/CDC/observations_germany/climate/daily/kl/historical/. The temperature records at two Chinese stations can be downloaded from China Meteorological Data Service Centre via http://data.cma.cn/ (registration required).
Code availability
In this study, only the estimation method, namely ordinary least squares (OLS), was used. The codes to implement OLS can be found in all programming languages, such as R, Python, or Matlab.
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Acknowledgements
This work was supported by the General Research Fund Grant (CUHK14653316) of the Hong Kong Research Grant Council. The authors would like to thank the reviewer for the valuable comments and suggestions. YZ would like to thank Ming Luo for inspired discussions.
Funding
This work was supported by the General Research Fund Grant (CUHK14653316) of the Hong Kong Research Grant Council.
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Tung Fung, Yee Leung, Changlin Mei, and Yu Zhou conceived and designed the analysis. Feng Chen and Yu Zhou performed the numerical simulations and real-life data analysis. Philipp G. Meyer, Holger Kantz, and Yu Zhou contributed to the interpretation of the results. Philipp G. Meyer, Holger Kantz, Yee Leung, and Yu Zhou wrote the manuscript.
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Chen, F., Meyer, P.G., Kantz, H. et al. Trends in auto-correlated temperature series. Theor Appl Climatol 147, 1577–1588 (2022). https://doi.org/10.1007/s00704-021-03893-6
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DOI: https://doi.org/10.1007/s00704-021-03893-6