Sheng Yue

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

Abstract In many hydrological studies, two non-parametric rank-based statistical tests, namely the Mann–Kendall test and Spearmans rho test are used for detecting monotonic trends in time series data. However, the power of these tests has not been well documented. This study investigates the power of the tests by Monte Carlo simulation. Simulation results indicate that their power depends on the pre-assigned significance level, magnitude of trend, sample size, and the amount of variation within a time series. That is, the bigger the absolute magnitude of trend, the more powerful are the tests; as the sample size increases, the tests become more powerful; and as the amount of variation increases within a time series, the power of the tests decrease. When a trend is present, the power is also dependent on the distribution type and skewness of the time series. The simulation results also demonstrate that these two tests have similar power in detecting a trend, to the point of being indistinguishable in practice. The two tests are implemented to assess the significance of trends in annual maximum daily streamflow data of 20 pristine basins in Ontario, Canada. Results indicate that the P -values computed by these different tests are almost identical. By the binomial distribution, the field significant downward trend was assessed at the significance level of 0.05. Results indicate that a higher number of sites show evidence of decreasing trends than one might expect due to chance alone.

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

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.

A review of bivariate gamma distributions for hydrological application

A univariate gamma distribution is one of the most commonly adopted statistical distributions in hydrological frequency analysis. A bivariate gamma distribution constructed from specified gamma marginals may be useful for representing joint probabilistic properties of multivariate hydrological events such as floods and storms. This article presents a review of various bivariate gamma distribution models that are constructed from gamma marginals. Advantages and limitations of each of these models are pointed out. Applicability of a few bigamma distributions whose gamma marginal distributions have different scale and shape parameters is investigated. The dependence of these models is directly or indirectly measured via the Pearsons product-moment correlation coefficient. The scale and shape parameters of the models are estimated from their marginal distributions by the method of moments. Results indicate that these bigamma distribution models will be useful for describing the joint probability distribution of two correlated random variables with gamma marginals.

The bivariate lognormal distribution to model a multivariate flood episode

Complex hydrological events such as floods always appear to be multivariate events that are characterized by a few correlated variables. A complete understanding of these events needs to investigate joint probabilistic behaviours of these correlated variables. The lognormal distribution is one of frequently selected candidates for flood-frequency analysis. The multivariate lognormal distribution will serve as an important tool for analysing a multivariate flood episode. This article presents a procedure for using the bivariate lognormal distribution to describe the joint distributions of correlated flood peaks and volumes, and correlated flood volumes and durations. Joint distributions, conditional distributions, and the associated return periods of these random variables can be readily derived from their marginal distributions. The approach is verified using observed streamflow data from the Nord river basin, located in the Province of Quebec, Canada. The theoretical distributions show a good fit to observed ones. Copyright

Probability distribution type of Canadian annual minimum streamflow / Type de distribution de probabilité du débit minimum annuel au Canada

Abstract The method of L-moment ratio diagrams along with the averaged weighted distance (AWD) is applied to identify a probability distribution of annual minimum streamflow, namely annual minimum daily streamflow in 11 climatic regions of Canada. Across the entire country, the Pearson type III probability distribution is an acceptable distribution for describing annual minimum streamflow with the 3-parameter lognormal and log Pearson type III distributions as potential candidates. Some minor differences in the probability distribution type among different climatic regions are also observed, which may be taken into account in the selection of the distribution type of annual minimum streamflow.