Trend detection in observations helps one to identify anthropogenic forces on natural hydrological and climatic systems. Hydrometeorological data are often persistent over time that deviates from the assumption of independence used by many statistical methods. A recently proposed Sen’s trend test claimed to be free of this problem and thereby received widespread attention. However, both theoretical derivation and stochastic simulation of the current study implies that persistence inflates the trend significance, leading to false trends. To tackle this problem, we incorporate the feature of persistence into the variance of the trend test statistic, whereby an innovative variance-corrected Sen’s trend test is developed. Two theoretical variances of the trend test statistic are newly derived to account for short-term and long-term persistent behavior. The original variance for independent data is also corrected because of its negative bias. A stepwise procedure, including steps to specify the underlying persistent behavior and to test trend with new statistic, is outlined for performing the new test on factual data. Variance-corrected Sen’s trend test can effectively restore the inflated trend significance back to its nominal state. This study may call for the reassessment of published results of the original Sen’s trend test on data with persistence.
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