Time-series analysis in monitoring - trends, seasonality, anomalies

Knowledge base · July 15, 2026

In environmental monitoring a single reading means little - real knowledge is born when the measurements form a time series. Only a series shows whether something is rising, falling, returning each year, or has suddenly “shot up”. It is worth knowing what to look for in such a chart.

Three things we read from a series

• Trend - the long-term direction (e.g. a slowly rising phosphorus concentration over the years). It answers the question “are things getting better or worse”.
• Seasonality - a repeating annual or daily rhythm (e.g. summer minima of oxygen, night-time drops, spring blooms). It has to be recognised so as not to confuse it with a trend.
• Anomalies - single, unusual deviations (e.g. a spike in turbidity after heavy rain). Some are real events, some are measurement errors.

Interpretation tools - with names and conditions of use

The limits of an I-MR chart are not computed from the standard deviation of the whole series but from the moving range: σ̂ = MR̄ / 1.128 (the d₂ constant for a two-element window), and the limits are the mean ± 3σ (warning limits ± 2σ). This detail matters: a standard deviation taken from the whole series contains the trend and the season, so the limits would become so wide that they would detect nothing.

⚠️ A trap few people write about: environmental data are correlated in time. A probe measuring every 15 minutes does not give 96 independent observations per day - the next reading largely repeats the previous one. Significance tests assume independence, so on densely sampled data they return inflated significance: p = 0.002 can become p = 0.064 - a non-significant result - after correcting for autocorrelation (e.g. the Hamed-Rao correction for Mann-Kendall, or an effective sample size n_eff). A month of 15-minute measurements can be worth n_eff ≈ 5, not 2880.

The most common mistakes

• Confusing seasonality with a trend - “rising” in July does not mean “rising year on year”.
• Uneven intervals / gaps - they affect averages and charts; it is worth marking them, not hiding them.
• Reacting to a single point - an anomaly is only confirmed by the next measurement or by context.
• A “categorical” time axis - dates must be treated as time (proportionally), not as labels.
• Mixing stations in one series - data from several sites glued together describe a spatial gradient, not a process in time; it can even reverse the sign of a relationship.
• Treating dense sampling as a larger sample - see above: the number of rows is not the number of independent pieces of information.

Sources

• Mann-Kendall test: Mann H.B. (1945), Nonparametric tests against trend, “Econometrica” 13(3): 245-259, doi:10.2307/1907187; Kendall M.G. (1975), Rank Correlation Methods.
• Sen’s slope: Sen P.K. (1968), Estimates of the regression coefficient based on Kendall’s tau, “Journal of the American Statistical Association” 63(324): 1379-1389, doi:10.1080/01621459.1968.10480934.
• Correction for autocorrelation: Hamed K.H., Rao A.R. (1998), A modified Mann-Kendall trend test for autocorrelated data, “Journal of Hydrology” 204(1-4): 182-196, doi:10.1016/S0022-1694(97)00125-X.
• Control charts and the d₂ constant: classic SPC methodology (Shewhart); the constant 1.128 applies to a moving range with a window of 2.

In practice

Good analysis starts with an orderly, continuous series at fixed points. In LimnoLog measurements immediately form charts over time (with an option to compare seasons), and the full dataset you can export to Excel or prepare for statistical analysis when you need deeper methods.