Parametric Assessment of Trend Test Power in a Changing Environment

Abstract

In the context of climate and environmental change assessment, the use of probabilistic models in which the parameters of a given distribution may vary in accordance with time has reinforced the need for appropriate procedures to recognize the “statistical significance” of trends in data series arising from stochastic processes. This paper introduces a parametric methodology, which exploits a measure based on the Akaike Information Criterion (AICΔ), and a Rescaled version of the Generalized Extreme Value distribution, in which a linear deterministic trend in the position parameter is accounted for. A Monte Carlo experiment was set up with the generation of nonstationary synthetic series characterized by different sample lengths and covering a wide range of the shape and scale parameters. The performances of statistical tests based on the parametric AICΔ and the non-parametric Mann-Kendall measures were evaluated and compared with reference to observed ranges of annual maxima of precipitation, peak flow, and wind speed. Results allow for sensitivity analysis of the test power and show a strong dependence on the trend coefficient and the L-Coefficient of Variation of the parent distribution from the upper-bounded to the heavy-tailed special cases. An analysis of the sample variability of the position parameter is also presented, based on the same generation sets.

Estimation of Peak Discharges under Different Rainfall Depth–Duration–Frequency Formulations

“…A wide number of procedures is currently available for this type of modelling. At the same time, a growing number of papers criticized the traditional tools for assessing nonstationarity, both with parametric and non-parametric tests [14][15][16][17], in particular with respect to their statistical power. This is not a trivial issue because of, as recognized by Vogel et al [18], when moving in the field of infrastructure decision committing a type II error means incurring in under-preparedness.…”

“…However, concerns about past changes and possible evolutions of climate on the phenomenology of rainfall raised questioning about the opportunity of retaining the still valid adoption of stationary hypothesis during the IDF/DDF deriving procedure [7][8][9][10]. Implications arising from the adoption of nonstationary probability distributions for modelling changes in extremes and applications of related statistical tests for trend detection were discussed in several studies (e.g., [11][12][13][14][15][16][17][18]).…”

“…However, it should be noted that databases of rainfall time series in short durations (5, 15 and 30 min) are generally less extensive than hourly data. In this sense, short-duration rainfall data constitute a precious source of information for investigating if remodulation in the extreme rainfall regime is happening, and their use in the context of a test for trend detection (and the consequent adoption of a nonstationary probabilistic model) may deserve particular attention, because the low magnitude of the trend and the reduced sample size of recorded data may lead to low power statistical tests [14,15].…”

Tropical Convection in the Caribbean and Surrounding Region during a Regional, Warming Sea-Surface Temperature Period, 1982–2020

“…Additionally, this test is not dependent on the magnitude of the data, assumptions of distribution, missing data, or the regularity of monitoring periods. Although the MK test is used in many studies for detection of trends in hydrological time series, there are some caveats regarding the power of the test based on the pre-assigned significance level, magnitude of the trend, sample size, and the amount of variation in the time series [45][46][47][48][49][50].…”

Estimating the Occurrence Rate for Alpha-Series Process in Rayleigh Distribution

“…The parameters (, and are important parameters for the ASP, given that knowing these parameters leads to knowledge of both the process's mean and variance and the process's general trend and power [10]. The statistical inference results of ASP were recently presented with the assumption that the random variable follows specific distributions [11], [12].…”