Mann-Kendall Trend Test and Sen's Slope Estimation

Mann-Kendall trend test and Sen's slope estimation are two widely used non-parametric statistical methods in hydrology, meteorology, environmental science, and other fields, designed to detect trends in time series data and quantify their rates of change. These methods are particularly favored due to their minimal distributional requirements and robustness to outliers. The Mann-Kendall trend test is a non-parametric procedure used to determine whether a time series exhibits a monotonic increasing or decreasing trend. Its core principle relies on data ranking rather than actual values, constructing test statistics by comparing the relative magnitudes of all data pairs. Key advantages include no assumption of specific data distribution and strong resistance to missing values and outliers. The test results are typically presented as significance levels (e.g., p-values), where a p-value below a threshold (such as 0.05) indicates a statistically significant trend. In MATLAB implementation, this involves calculating the test statistic S, its variance, and the standardized test statistic Z through pairwise comparisons. Sen's slope estimation quantifies the magnitude of trends by measuring the rate of change per unit time. This method computes the median of slopes between all data point pairs to estimate the overall trend slope. Its primary benefits include immunity to extreme values and accurate reflection of actual trend rates. A positive Sen's slope indicates an upward trend, while a negative value suggests a downward trend. MATLAB implementation requires iterating through all data pairs to calculate slopes and then determining the median value. When implementing these methods in MATLAB, developers typically create custom functions or utilize components from the statistics toolbox. The Mann-Kendall test implementation involves calculating the S statistic and its variance to derive the normalized Z statistic, while Sen's slope estimation requires comprehensive pairwise slope calculations followed by median extraction. In practical applications, these methods are often combined: first applying the Mann-Kendall test to detect trend existence, then using Sen's slope to quantify trend strength. These methods are particularly suitable for analyzing long-term environmental monitoring data, such as temperature variations, precipitation trends, or pollutant concentration evolution. Their non-parametric nature ensures reliable results even with suboptimal data quality, providing valuable trend information in challenging analytical scenarios.