Breaks in Linear Trends or Parts of Cycles?
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Pure and Applied Geophysics
Breaks in Linear Trends or Parts of Cycles? RAJESH REKAPALLI1 Abstract—Understanding the trends and periodicities in geophysical processes is imperative for assessing and forecasting their future change. However, it is possible to mistreat parts of cycles as linear trends with sudden breaks when analysing short-term data. We demonstrate this through the analysis of solar irradiance data as well as Northern Hemisphere (NH) and Southern Hemisphere (SH) sea surface temperature (SST) data sets, with emphasis on the (a) analyses of trends in total solar irradiance (TSI) and (b) association of trends in SST with solar activity during the period from 1900 to 2017. The trends estimated using singular spectrum analysis together with linear regression revealed statistically significant long periodic non-linear trends in both TSI and SST data. Our results suggest that the appraisal of linear trends to identify their breaks/sudden changes is a biased approach when analysing data sets of shorter periods, when the data are governed by long periodic dynamical processes. The non-linear trends identified in SST data may be physically associated with the TSI trend change and anthropogenic CO2. A plausible physical mechanism is also discussed with respect to the influence of solar activity on the trend in atmospheric CO2. Finally, our study concludes that (1) breaks in linear trends are pseudo-attribution of parts of cycles, and (2) the statistically significant trends in NH and SH SST are mainly associated with loadings from trend changes in solar irradiance. Keywords: Trend, cycles, solar irradiance, sea surface temperature.
1. Introduction Trend analysis is a robust method used in climate studies for the detection, estimation and prediction of the rate at which data/climate parameters change over time. The trends in climate time series appear as linear or non-linear trends (Tiwari et al. 2015; Rajesh and Tiwari 2018). However, in climate studies, trend is largely synonymous with the slope of the line fit to the data with statistical significance. Nevertheless, most of the earth or climate processes are cyclic in nature. In particular,
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CSIR-National Geophysical Research Institute, Hyderabad, India. E-mail: [email protected]
and R. K. TIWARI1 climate cycles often range from annual to millennial scale oscillations (Tiwari 2005). Starting from annual change in temperature due to a change in solar irradiance, there are periodicities of approximately 2.0 and 1.25 Myr caused by the higher-order eccentricity cycles (Tiwari 1987). Therefore, analyses of data spanning multiple decades to centuries may not give a complete understanding of the trends, as discussed by Pretis and Allen (2013). The linear and non-linear combination of the long periodic cyclic processes (greater than the length of data) may appear as linear or non-linear trends in the geophysical/climate time-series data. Here we analyse (1) a nearly 400-year-long record of total solar irradiance (TSI) and (2) *160-year-long record of northern
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