Detecting trends in hydrometerological data through the commonly used Mann-Kendall test is misleading in the presence of data autocorrelation. Autocorrelation seriously interferes with type I errors and power of trend detection. To mitigate this effect, the authors introduce a variance correction prewhitening method. It addresses two important issues that lacked appropriate attention in the past application of trend-free prewhitening method: inflationary variance of slope estimator and deflationary serial variance. After serial and slope variances correction, the new method keeps a better balance between maintaining a low type I error and a relatively strong power of trend detection. In comparison, other methods for the same purpose only address one of these two characteristics. The new method bears some resemblance to the block-bootstrap method; however, it is superior in its simplicity for implementation. Case studies reveal that uncertainties arising from autocorrelation are substantial. Applying more than one test is helpful to interpret results with uncertainties information. The new method provides a robust choice to this strategy.

Hydrometeorological data are commonly serially dependent and thereby deviate from the assumption of independence that underlies the Spearman rho trend test. The presence of autocorrelation will influence the significance of observed trends. Specifically, the positive autocorrelation inflates Type І errors, while it deflates the power of trend detection in some cases. To address this issue, we derive a theoretical formula and recommend an appropriate empirical formula to calculate the rho variance of dependent series. The proposed procedure of the variance correction for the Spearman rho method is capable of mitigating the effect of autocorrelation on both, Type І error and power of the test. Similar to the Block Bootstrap method, it has the advantage that it does not require an initial knowledge of the autocorrelation structure or modification of the series. In comparison, the capability of the Pre-Whitening method is sensitive to model misspecification if the series are whitened by a parametric autocorrelation model. The Trend-Free Pre-Whitening method tends to lead to an overestimation of the statistical significance of trends, similar to the original Spearman rho test. The results of the study emphasize the importance of selecting a reliable method for trend detection in serially dependent data.

The heterogeneous hydraulic conductivity of a subsurface medium is vital to the groundwater flow and solute transport. Probability is efficient for characterizing and quantifying the field characterization of hydraulic conductivity. Compared with sandy mediums, silty clay is paid less attention to due to its low hydraulic conductivity. For long-term solute transport and seawater intrusion, the low-permeable medium is considered as a remarkably permeable medium. This study reports on a comprehensive investigation on the hydraulic conductivity field of the Ningchegu site, located east of Tianjin City of China. Four layers recognized by 52 boreholes, plain fill, continental silty clay, mud–silt clay and marine silty clay, were deposited from the top to the bottom. The hydraulic conductivities measured via permeameter tests ranged from 2 × 10⁻⁶ m/d to 1.6 × 10⁻¹ m/d, which corresponded to the lithology of silty clay. The magnitude and the range of the hydraulic conductivity increased with the depth. Five probability distribution models were tested with the experimental probability, indicating that a Levy stable distribution was more matched than the log-normal, normal, Weibull or gamma distributions. A simple analytical model and a Monte Carlo technique were used to inspect the effect of the silty clay hydraulic conductivity field on the statistical behavior of the solute transport. The Levy stable distribution likely generates higher peak concentrations and lower peak times compared with the widely-used log-normal distribution. This consequently guides us in describing the transport of contaminations in subsurface mediums.