Power of the Mann–Kendall and Spearman's rho tests for detecting monotonic trends in hydrological series

Climate strongly influences global wildfire activity, and recent wildfire surges may signal fire weather-induced pyrogeographic shifts. Here we use three daily global climate data sets and three fire danger indices to develop a simple annual metric of fire weather season length, and map spatio-temporal trends from 1979 to 2013. We show that fire weather seasons have lengthened across 29.6 million km 2 (25.3%) of the Earth’s vegetated surface, resulting in an 18.7% increase in global mean fire weather season length. We also show a doubling (108.1% increase) of global burnable area affected by long fire weather seasons (41.0 s above the historical mean) and an increased global frequency of long fire weather seasons across 62.4 million km 2 (53.4%) during the second half of the study period. If these fire weather changes are coupled with ignition sources and available fuel, they could markedly impact global ecosystems, societies, economies and climate.

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Climate-induced variations in global wildfire danger from 1979 to 2013

Analysis of changes in meteorological variables using Mann-Kendall and Sen's slope estimator statistical tests in Serbia

Trend detection in hydrologic data: The Mann–Kendall trend test under the scaling hypothesis

The non-parametric Mann-Kendall (MK) statistical test has been popularly used to assess the significance of trend in hydrological time series The test requires sample data to be serially independent When sample data are serially correlated, the presence of serial correlation in time series will affect the ability of the test to correctly assess the significance of trend To eliminate the effect of serial correlation on the MK test, effective sample size (ESS) has been proposed to modify the MK statistic This study investigates the ability of ESS to eliminate the influence of serial correlation on the MK test by Monte Carlo simulation Simulation demonstrates that when no trend exists within time series, ESS can effectively limit the effect of serial correlation on the MK test When trend exists within time series, the existence of trend will contaminate the estimate of the magnitude of sample serial correlation, and ESS computed from the contaminated serial correlation cannot properly eliminate the effect of serial correlation on the MK test However, if ESS is computed from the sample serial correlation that is estimated from the detrended series, ESS can still effectively reduce the influence of serial correlation on the MK test

The Mann-Kendall test modified by effective sample size to detect trend in serially correlated hydrological series

This study investigated using Monte Carlo simulation the interaction between a linear trend and a lag-one autoregressive (AR(1)) process when both exist in a time series. Simulation experiments demonstrated that the existence of serial correlation alters the variance of the estimate of the Mann–Kendall (MK) statistic; and the presence of a trend alters the estimate of the magnitude of serial correlation. Furthermore, it was shown that removal of a positive serial correlation component from time series by pre-whitening resulted in a reduction in the magnitude of the existing trend; and the removal of a trend component from a time series as a first step prior to pre-whitening eliminates the influence of the trend on the serial correlation and does not seriously affect the estimate of the true AR(1). These results indicate that the commonly used pre-whitening procedure for eliminating the effect of serial correlation on the MK test leads to potentially inaccurate assessments of the significance of a trend; and certain procedures will be more appropriate for eliminating the impact of serial correlation on the MK test. In essence, it was advocated that a trend first be removed in a series prior to ascertaining the magnitude of serial correlation. This alternative approach and the previously existing approaches were employed to assess the significance of a trend in serially correlated annual mean and annual minimum streamflow data of some pristine river basins in Ontario, Canada. Results indicate that, with the previously existing procedures, researchers and practitioners may have incorrectly identified the possibility of significant trends. Copyright  2002 Environment Canada. Published by John Wiley & Sons, Ltd.

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The influence of autocorrelation on the ability to detect trend in hydrological series

The nonparametric Mann-Kendall (MK) statistical test has been widely applied to assess the significance of trends in hydrological time series. It is known that the existence of serial correlation in a time series will affect the ability of the test to assess the site significance of a trend; and the presence of cross-correlation among sites in a network will influence the ability of the test to evaluate the field significance of trends over the network. This study proposes to use a trend-free pre-whitening (TFPW) procedure to remove serial correlation from time series, and hence to eliminate the effect of serial correlation on the MK test. An additional bootstrap test with preserving the cross-correlation structure of a network is proposed to assess the field significance of upward and downward trends over the network separately. At the significance level of 0.05, the site significance of trends in Canadian annual minimum, mean, and maximum daily streamflows with 30-, 40- and 50-year records was ...

https://www.tandfonline.com/doi/pdf/10.1623/hysj.48.1.51.43478

Canadian streamflow trend detection: impacts of serial and cross-correlation

Numerous studies have investigated spatial patterns of trend in streamflow. However, there is no consensus on the best methods to detect streamflow trends and the spatial extent or field significance of those trends. This paper looks at two of the contentious issues in trend analysis and assessment of field significance: serial correlation and cross-correlation. Both serial and crosscorrelation are known to reduce the accuracy of trend detection. The Trend-Free Pre-Whitening method was found to effectively remove the influence of serial correlation from a time series, enabling a more accurate assessment of site significance. An additional bootstrap test was developed to preserve the existing cross-correlation and to allow for a more reliable assessment of field significance. These methods and several others were applied to the annual mean, maximum and minimum streamflow data for 213 stations in the Canadian Reference Hydrometric Basin Network. These analyses revealed relatively consistent results for upward and downward trends for the three streamflow regimes. Mapping the results of these trend analyses revealed several interesting patterns, including three wide bands of trend that stretch across the country. A three band of downward trend stretches from Pacific to Atlantic at latitudes between approximately 50° and 58°; this band is particularly noticeable for the mean and maximum flows. A band of upward trend lies to the north of the downward band and stretches from northern B.C. and the Yukon through the Northwest Territories and into Nunavut; this band is noticeable for mean, maximum and minimum flows. A second band of upward trend lies to the south of the downward band, at latitudes between 44° and 50°; this band is noticeable for the same three flow variables.

Bob Phinney

Papers

The influence of autocorrelation on the ability to detect trend in hydrological series

Canadian streamflow trend detection: impacts of serial and cross-correlation

Patterns of Trend in Canadian Streamflow