Statistics in monitoring - detecting trends and correlations
“It looks like it’s rising” is not enough - in monitoring it is worth checking numerically whether a trend is real and whether the indicators are actually linked. This does not require advanced statistics; a few proven methods and an awareness of common pitfalls suffice.
Is there a trend
- The Mann-Kendall test - a popular, non-parametric trend test, coping well with environmental data (it does not require a normal distribution and handles outliers).
- Sen’s slope - an outlier-robust measure of the rate of change.
Together they answer the questions “is it rising/falling” and “how fast”.
Are the indicators linked
- Pearson correlation - a linear relationship,
- Spearman correlation - a monotonic (rank) relationship, more robust to extreme values.
They help, for example, to confirm that oxygen falls as temperature rises, or that turbidity rises after rainfall (see combining with public data).
Question → method → limitation
The method follows the question, not what the software happens to compute. Each answers something different and each has a limit of applicability:
| Question | Method | What it returns | Limitation |
|---|---|---|---|
| Is there a trend at all? | Mann-Kendall | direction of change + significance | autocorrelation inflates significance; dense series need a correction (e.g. Hamed-Rao) |
| How fast is it rising or falling? | Sen’s slope | rate of change per unit of time | describes a monotonic change - a step after an event blurs into a slow trend |
| Do two parameters move together linearly? | Pearson correlation (r) | strength and sign of the linear relation | sensitive to extreme values; a curved relation lowers r |
| And if the relation is not linear? | Spearman correlation (ρ) | strength of the monotonic (rank) relation | says nothing about the shape or the cause |
| Does a single reading fall outside ordinary variability? | I-MR control chart | limits computed from the moving range | assumes independence of consecutive points - with a 15-minute probe the limits come out too narrow |
⚠️ A correlation computed on stations pooled together can reverse its sign. On our own data the pH × temperature pair gave −0.54 once the stations were pooled, and +0.30 and +0.44 within each of them separately. The reason: pooling stations mixes the question about the process in the water with the question about differences in level between places. Compute correlations within a station first, and only then ask whether the stations may be pooled at all.
The most common pitfalls
- Seasonality posing as a trend - first remove or account for the annual rhythm (see time series).
- Autocorrelation - successive measurements can depend on the previous ones; it inflates the “significance”.
- Correlation ≠ cause - a link between two indicators does not prove that one causes the other.
- Gaps and values below the threshold - they affect the results; they must be treated consciously.
What to compute it with
Simple analyses you can do in Excel, fuller ones in R or STATISTICA - the key is well-prepared data.
📊 See it live: Global Rivers & Lakes Watch - a public dashboard from three stations in three countries: the Maumee River (Ohio, USA), the river Main in Frankfurt and the LéXPLORE research platform on Lake Geneva. Water temperature, dissolved oxygen, pH, conductivity, turbidity and chlorophyll-a are fetched automatically (USGS Water Services, WSV Pegelonline, Eawag Datalakes), with correlation tiles and a station map. No login.
Sources
- Mann-Kendall trend test: Mann H.B. (1945), Nonparametric tests against trend, Econometrica 13(3), 245-259 - DOI.
- Sen’s slope (a robust estimate of the rate of change): 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.
- Correction for autocorrelation - why a series “with memory” overstates the significance of a trend: 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.
(Addresses checked on 18 August 2026.)
In practice
The starting point is an orderly, continuous series. In LimnoLog measurements immediately form charts (with a comparison of seasons), which lets you make a preliminary judgement of the trend and relationships, and for heavier statistics you can export the data ready for processing.
See it in the LimnoLog app
Explore LimnoLog features