Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature

Abstract

This study investigates the significance of trends of four temperature time series-Central England Temperature (CET), Stockholm, Faraday-Vernadsky, and Alert. First the robustness and accuracy of various trend detection methods are examined: ordinary least squares, robust and generalized linear model regression, Ensemble Empirical Mode Decomposition (EEMD), and wavelets. It is found in tests with surrogate data that these trend detection methods are robust for nonlinear trends, superposed autocorrelated fluctuations, and non-Gaussian fluctuations. An analysis of the four temperature time series reveals evidence of long-range dependence (LRD) and nonlinear warming trends. The significance of these trends is tested against climate noise. Three different methods are used to generate climate noise: (i) a short-range-dependent autoregressive process of first order [AR(1)], (ii) an LRD model, and (iii) phase scrambling. It is found that the ability to distinguish the observed warming trend from stochastic trends depends on the model representing the background climate variability. Strong evidence is found of a significant warming trend at Faraday-Vernadsky that cannot be explained by any of the three null models. The authors find moderate evidence of warming trends for the Stockholm and CET time series that are significant against AR(1) and phase scrambling but not the LRD model. This suggests that the degree of significance of climate trends depends on the null model used to represent intrinsic climate variability. This study highlights that in statistical trend tests, more than just one simple null model of intrinsic climate variability should be used. This allows one to better gauge the degree of confidence to have in the significance of trends.

On the intrinsic timescales of temporal variability in measurements of the surface solar radiation

“…With respect to the decennial time span of the analysis (10 years), the trend can be thought of as a lowpass approximation of the data (Moghtaderi et al, 2013), but not as an oscillation. Since this work focuses mostly on the characteristic scales of temporal variability, the EMD trends along with their statistical significance and physical meaning do not fall within the scope of the study; for such discussion, see for example Franzke (2012).…”

“…The classical way to solve this when employing the HHT on geophysical signals, such as the SSI, is to presume some model for the background power spectrum, against which the identified features are then compared (Huang and Wu, 2008;Franzke, 2009Franzke, , 2012. Kottek et al (2006).…”

A non-uniqueness problem in the identification of power-law spectral scaling for hydroclimatic time series

“…The results might form the basis for bracketing estimates (cf. Fleming 2007, Vyushin et al 2009, multiple working models (Overland et al 2006, Fleming 2009), or strength-of-evidence assessments (Franzke 2012). 3.…”

On memory and non-memory parts of surface air temperatures over China: can they be simulated by decadal hindcast experiments in CMIP5?

“…During the past years, besides detecting LTM in different climate variables, there are growing efforts focusing on the applications of LTM, such as (1) developing new theories for trend evaluation (Lennartz and Bunde 2009;Franzke 2012;Kumar et al 2013;Ludescher and Bunde 2016;Yuan et al 2017; (2) designing early warning systems for extreme events (Bunde et al 2005;Bogachev and Bunde 2011); as well as (3) evaluating model simulations and reanalysis/proxy datasets using LTM as a test bed (Govindan et al 2002;Vyushin et al 2004;Bunde et al 2013;Zhao et al 2018). However, among all the potential applications of LTM, climate prediction is the most appealing one that has not been studied systematically (Zhu et al 2010).…”