Effects of the prewhitening method, the time granularity and the time segmentation on the Mann-Kendall trend detection and the associated Sen's slope

Abstract

Abstract. The most widely used non-parametric method for trend analysis is the Mann-Kendall test associated with the Sen's slope. The Mann-Kendall test requires serially uncorrelated time series, whereas most of the atmospheric processes exhibit positive autocorrelation. Several prewhitening methods have been designed to overcome the presence of lag-1 autocorrelation. These include a prewhitening, a detrending and/or a correction for the detrended slope and the original variance of the time series. The choice of which prewhitening method and temporal segmentation to apply has consequences for the statistical significance, the value of the slope and of the confidence limits. Here, the effects of various prewhitening methods are analyzed for seven time series comprising in-situ aerosol measurements (scattering coefficient, absorption coefficient, number concentration and aerosol optical depth), Raman Lidar water vapor mixing ratio and the tropopause and zero degree levels measured by radio-sounding. These time series are characterized by a broad variety of distributions, ranges and lag-1 autocorrelation values and vary in length between 10 and 60 years. A common way to work around the autocorrelation problem is to decrease it by averaging the data over longer time intervals than in the original time series. Thus, the second focus of this study is evaluation of the effect of time granularity on long-term trend analysis. Finally, a new algorithm involving three prewhitening methods is proposed in order to maximize the power of the test, to minimize the amount of erroneous detected trends in the absence of a real trend and to ensure the best slope estimate for the considered length of the time series.

Deep learning shows declining groundwater levels in Germany until 2100 due to climate change

“…In doing so, we are able to capture both the range and the individual development of all considered future climate projections. Even though considering yearly values, we applied the 3PW prewhitening method 56 development for individual years (also historically), which can cause a bias between the end of historical data records and the start of our simulations. We, therefore, investigated the trend of the aforementioned quantities between the start of the simulation and the end in 2100 and did not directly consider the end of the historical records.…”

A global analysis of climate-relevant aerosol properties retrieved from the network of GAW near-surface observatories

“…For scattering, the parallel development is 56 sites with 1 year, 45 sites with 5 years, and 30 sites with 10 years of data. It is worth noting that, besides Antarctic stations, no stations were located outside North America and continental Europe in Collaud Coen et al (2013) and Asmi et al (2013), while nine stations outside those regions are now contributing to Collaud Coen et al (2020b). Overall, the total number of measurement years increased substantially, which will contribute to a more robust vision of the state of the atmosphere.…”

“…The analysis of trends in aerosol properties needs to be regularly revisited as longer homogeneous time series become available at more sites, providing better spatial and temporal coverage. The non-parametric seasonal Mann-Kendall (MK) statistical test associated with several prewhitening methods and with Sen's slope was used as main trend analysis method (Collaud Coen et al, 2020b). Comparisons with General Least Mean Square associated with Autoregressive Bootstrap (GLS/ARB) and with standard Least Mean Square analysis (LMS) (Asmi et al, 2013;Collaud Coen et al, 2013) enabled confirmation of the detected MK statistically significant trends and the assessment of advantages and limitations of each method.…”

“…Location of sites contributing to the present study. In blue, sites which provided information for the reference year 2017 and in red, sites that in addition, provided > 10-year time series for optical properties used in CollaudCoen et al (2020b).…”

Response of atmospheric composition to COVID-19 lockdown measures during spring in the Paris region (France)

“…To that end, a seasonal Mann-Kendall (MK) test was performed on each variable for the January 2012-February 2020 period. The Mann-Kendall R package was used (Bigi and Vogt, 2020;Collaud Coen et al, 2020), which includes three pre-whitening approaches in order to reduce the weight of autocorrelation. Results are summarized in Table 1.…”