Mann-Kendall Monotonic Trend Test
Compute ordered Mann–Kendall S, tie-corrected independent-observation null variance and continuity-corrected z; no serial-correlation adjustment or significance claim, at most one million pairs.
Description
The Mann–Kendall statistic assesses whether later values tend to be higher or lower than earlier values.
The Mann–Kendall statistic assesses whether later values tend to be higher or lower than earlier values. Pairwise ordering makes the statistic independent of measurement units, while tied observations require an adjustment to its variance.1
Compute ordered Mann–Kendall S, tie-corrected independent-observation null variance and continuity-corrected z; no serial-correlation adjustment or significance claim, at most one million pairs.
When to use Mann-Kendall Monotonic Trend Test
Use this tool to compute ordered Mann–Kendall S, tie-corrected independent-observation null variance and continuity-corrected z; no serial-correlation adjustment or significance claim, at most one million pairs.
Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.
How to use Mann-Kendall Monotonic Trend Test and understand its results
- Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.
- Enter orderedTimeSeriesValues using the field table and calculation rules, then run the tool.
- Read mannKendallS, tieCorrectedNullVariance, continuityCorrectedZ, kendallTauA. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| orderedTimeSeriesValues | Ordered time series values | list of number | Required |
Enter at least two values in time order; the values themselves need not increase. The tool compares every pair, groups exact numerical ties and applies the displayed tie-adjusted variance. For nonzero variance it reports a continuity-corrected z value using S−1 when S is positive, S+1 when negative, and zero when S is zero. A zero variance also returns z = 0. The pair count may not exceed 1,000,000.
S = Σ sign(y_j − y_i), i < j; Var(S) = [n(n−1)(2n+5) − Σ t(t−1)(2t+5)]/18; τa = S/[n(n−1)/2] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| mannKendallS | Mann kendall s | number |
| tieCorrectedNullVariance | Tie corrected null variance | number |
| continuityCorrectedZ | Continuity corrected z | number |
| kendallTauA | Kendall tau a | number |
{
"input": {
"orderedTimeSeriesValues": [
1,
2,
3
]
},
"output": {
"mannKendallS": 3,
"tieCorrectedNullVariance": 3.6666666666666665,
"continuityCorrectedZ": 1.044465935734187,
"kendallTauA": 1
}
}Limitations and assumptions
The reported Kendall coefficient is tau-a, not tie-normalized tau-b. No p-value, significance verdict, seasonal stratification or serial-correlation correction is returned. Exact ties and the supplied time order control the calculation; autocorrelated observations require additional analysis.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Sen Slope Estimator: Estimate Sen median of all pairwise slopes on actual irregular observation years; distinct from OLS regression and no independence-adjusted interval or extrapolation. For a complementary task, use Lapse Rate Environmental: Fit measured environmental temperature profile and expose extrapolated-height predictions, retaining inversion sign; not a prescribed constant atmosphere or pressure/altitude conversion.
References
-
Mann-Kendall Monotonic Trend Test — tool.io
Similar or alternative tools
- Sen Slope Estimator
Estimate Sen median of all pairwise slopes on actual irregular observation years; distinct from OLS regression and no independence-adjusted interval or extrapolation.
- Lapse Rate Environmental
Fit measured environmental temperature profile and expose extrapolated-height predictions, retaining inversion sign; not a prescribed constant atmosphere or pressure/altitude conversion.