Uncertainty analysis in the detection of trends, cycles, and shifts in water resources time series

Scientists and water resources managers are increasingly worried about issues related to uncertainty. Although uncertainty analysis has been required in the decision-making processes, there is still a lack of knowledge on how to do it. The application of statistical methods for water resources research requires time series to be compliant with the hypotheses of randomness, homogeneity, independence, and stationarity (RHIS). Noncompliance may occur when trends, cycles, and/or shifts are present. However, the uncertainties and associated subjectivity in assessment and expression may make it difficult to detect these patterns of variability. In this research, synthetic time series (STS) were generated from the uncertainties in flow rates and a water quality parameter, and tested for RHIS by the Single-Sample Runs, Mann-Whitney, Wald and Wolfowitz, and Mann-Kendall tests, respectively. The tests were applied with an increasing number of elements (N). Three uncertainty scenarios were defined, the low level (LL: 10–30%), mid level (ML: 30–50%) and high level (HL: 50–70%). The Monte Carlo Method (MCM) was applied with uniform, normal and lognormal probability distributions. In each scenario, averages and standard deviations (std) were calculated as a measure of the p-values uncertainty. Although the complete series were compliant with the hypotheses, the p-values and std ranges varied from one extreme to the other (0.0–1.0) as N increased. The std ranges had an impact on the decisions when the p-value was close to the rejection limit. The randomness p-value for the flows in the uniform case was 0.04, while the STS p-values were ≈ 0.05 ± 0.04, 0.09 ± 0.10, and 0.18 ± 0.20 in the LL, ML and HL scenario respectively. However, the decision on significance should not be based only on p-values, since the actual existence and continuity of patterns of variability depends more on representativity-related issues. The results lead to the conclusion that efforts to reduce uncertainties should be directed towards the development of appropriate monitoring and data analysis/interpretation strategies.