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.
Description
Sen's slope is a robust trend estimate based on the median of all slopes between observation pairs.
Sen's slope is a robust trend estimate based on the median of all slopes between observation pairs. Actual observation years allow irregular spacing without pretending each sample is one year apart.1
Estimate Sen median of all pairwise slopes on actual irregular observation years; distinct from OLS regression and no independence-adjusted interval or extrapolation.
When to use Sen Slope Estimator
Use this tool to estimate Sen median of all pairwise slopes on actual irregular observation years; distinct from OLS regression and no independence-adjusted interval or extrapolation.
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 Sen Slope Estimator 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 observationYears, observedValues using the field table and calculation rules, then run the tool.
- Read senSlopePerYear, senSlopePerDecade, pairwiseSlopeCount. 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 |
|---|---|---|---|
| observationYears | Observation years | list of number | Required |
| observedValues | Observed values | list of number | Required |
Enter at least two strictly increasing observation years and aligned finite values. The tool forms every pairwise slope, sorts them and takes their median, averaging the central two for an even count. It returns annual and decadal slopes plus the number of pairs. The pair count n(n−1)/2 may not exceed 1,000,000.
Paired lists must be nonempty and have equal lengths. Each sequence checked for increasing order must contain at least two strictly increasing values.
s_ij = (y_j − y_i)/(year_j − year_i); slope = median(s_ij), i < j; decadal slope = 10 × annual slope Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| senSlopePerYear | Sen slope per year | number |
| senSlopePerDecade | Sen slope per decade | number |
| pairwiseSlopeCount | Pairwise slope count | number |
{
"input": {
"observationYears": [
2000,
2001,
2002
],
"observedValues": [
1,
3,
6
]
},
"output": {
"senSlopePerYear": 2.5,
"senSlopePerDecade": 25,
"pairwiseSlopeCount": 3
}
}Limitations and assumptions
The calculation supplies a point estimate without a confidence interval, significance test or correction for serial correlation. Outliers can still affect a small dataset, and the measurement unit of the values carries through into the slope.
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 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. 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
-
Sen Slope Estimator — tool.io
Similar or alternative tools
- 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.
- 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.