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

TLDR

The Mann‑Kendall test is widely used to detect trends in hydrological series, but serial correlation at sites and cross‑correlation among sites can bias its significance assessment. This study introduces a trend‑free pre‑whitening procedure to eliminate serial correlation from streamflow series and a bootstrap test that preserves cross‑correlation to evaluate field‑level trend significance separately for upward and downward trends. Using the pre‑whitened Mann‑Kendall test (TFPW‑MK) at α = 0.05, the authors assessed site‑level trends in Canadian annual minimum, mean, and maximum daily streamflows over 30‑, 40‑, and 50‑year records, and applied the bootstrap method to test field significance across the network. Spatial analysis revealed significant decreases in 30‑year minimum and mean flows in southern British Columbia, central Prairie Provinces, and Atlantic Provinces, increases in northern BC and Yukon, and a nationwide decrease in maximum flows, yet none of the flow regimes reached field‑significant change at the 5 % level.

Abstract

Abstract 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 assessed by the MK test with the TFPW procedure (TFPW-MK). The spatial illustration of the significant trends at sites indicates that: (a) the 30-year annual minimum and mean daily flows significantly decreased in the regions of southern British Columbia (BC), around the centre of Prairie Provinces, and in Atlantic Provinces, and significantly increased in the region of northern BC and Yukon Territory; and (b) the annual maximum daily flow significantly decreased across southern Canada. The field significance of trends over the whole country was evaluated by the bootstrap test at the significance level of 0.05 and none of the three flow regimes experienced field-significant changes.