Reply to comment by Xuebin Zhang and Francis W. Zwiers on “Applicability of prewhitening to eliminate the influence of serial correlation on the Mann‐Kendall test”

[1] The main thrust of Zhang and Zwiers [2004] (hereinafter referred to as ZZ) is to try to correct ‘‘some misconceptions of YW’’ (of Yue and Wang [2002], hereinafter referred to as YW). We want to point out that none of these so-called misconceptions exist in our study, which is explained in the forthcoming text. [2] It is known that any scientific conclusion is drawn under certain circumstances. The work of YW intended to show the results of trend analysis for the case where a real trend exists in a time series, by applying prewhitening without considering its limitation in removing serial correlation from a time series, as had been done in previous studies [see Zhang et al., 2000, 2001]. YW suggested, based on empirical simulation results, that when an explicit trend exists in a time series and its sample size is big enough (>80), it might not be wise to blindly prewhiten the series. [3] ZZ introduced their comment on our work based on their misinterpretation of our study. They misinferred that the above suggestion ‘‘requires the user to first judge visually whether trend is present in the data that is to be analyzed.’’ Nowhere in our study [Yue and Wang, 2002] did we impose such a condition on our suggestion. [4] One has to distinguish between simulation and reality. One can manipulate what one wants in simulation. However, in reality, given a sample series, how can one determine that it includes a pure red noise process rather than a real trend, or vice versa, or both? ZZ showed using Figure 1 that a pure red noise process with lag 1 correlation coefficient of 0.4 seemed to be a visual trend and a real negative trend was not visible since a red noise process canceled the trend. However, in reality, no one could provide a proof that there is an apparent negative trend with the slope of 0.02 in the bottom panel of Figure 1 in ZZ, which may potentially mislead the readers. ZZ denied their own trend detection results [Zhang et al., 2000, 2001] by showing these diagrams, which tell the readers that the trends identified in their previous studies may not be real trends but rather red noise processes, and that the series identified without trends may consist of real negative trends and red noise processes but that the two cancel each other out. [5] ZZ’s comment that YW’s suggestion is in contradiction with the advice given by Yue et al. [2002c] is baseless. In the early work of Yue et al. [2002c], which was submitted for review in 2000, we first realized that when both trend and autoregressive process exist in a time series, the presence of trend will contaminate the estimate of serial correlation and blindly prewhitening the time series would cause false assessment of the significance of trend. Hence a modified prewhitening procedure, a trend-free prewhitening procedure, was proposed there to limit the effect of trend on the estimate of serial correlation. It has been applied to assess the significant trend in Canadian streamflows where the sample length of the series is 50 [Yue et al., 2003]. YW’s suggestion does not contradict to the proposed procedure of Yue et al. [2002c]. [6] Simulation conducted by ZZ (section 2) duplicated, in principle, the work of Yue et al. [2002c] that investigated the interactions between serial correlation and trend when both exist within a time series, i.e., how serial correlation affects the accuracy of the estimate of trend and how an existing trend influences the estimate of serial correlation, in which the magnitude of trend is computed by the Sen’s [1968] approach and its accuracy is expressed by its variance. Yue et al. clearly indicated that the existence of positive serial correlation will increase the variance of the estimate of trend, and the existence of trend will affect the estimate of serial correlation, which are further addressed by Yue and Pilon [2003]. We never hint that a ‘‘true’’ trend might be estimated from serially correlated data without considering autocorrelation,’’ as indicated by ZZ. ZZ only duplicated the former part of our work. The difference between YWand ZZ is that in ZZ, besides using Sen’s slope, ZZ also applied the method of maximum likelihood (ML1) and the ordinary least squares (LS1) to estimate the magnitude of trend and used root mean square errors to measure the accuracy of the estimate of trend. [7] ZZ claimed that the modified iterative prewhitening procedure works when both trend and serial correlation Copyright 2004 by the American Geophysical Union. 0043-1397/04/2003WR002547