Rank Histogram Flatness Check Tool

Audit supplied rank histogram versus uniform bins using descriptive Pearson statistic/end-bin excess; tie randomization and independent cases are caller responsibilities, no automatic significance or calibrated ensemble claim.

Description

An ensemble rank histogram counts where observations fall among sorted ensemble members.

An ensemble rank histogram counts where observations fall among sorted ensemble members. An M-member ensemble has M+1 rank bins, whose uniformity is a descriptive calibration diagnostic.^{[1, 2]}

When to use Rank Histogram Flatness Check Tool

Use this tool to audit supplied rank histogram versus uniform bins using descriptive Pearson statistic/end-bin excess; tie randomization and independent cases are caller responsibilities, no automatic significance or calibrated ensemble claim.

Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.

How to use Rank Histogram Flatness Check Tool and understand its results

Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.
Enter observedRankBinCounts, ensembleMemberCount using the field table and calculation rules, then run the tool.
Read pearsonUniformRankStatistic, uniformRankDegreesOfFreedom, meanRankBinCount, relativeEndBinExcess. 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
observedRankBinCounts	Observed rank bin counts	list of number	Required
ensembleMemberCount	Ensemble member count	integer	Required

Enter M≥1 and exactly M+1 nonnegative integer bin counts, with a positive total. Compare bins with their common mean and return the Pearson statistic, M degrees of freedom and signed relative end-bin excess.

Pearson statistic = Σ(count − mean)²/mean; end excess = (first + last)/(2mean) − 1

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
pearsonUniformRankStatistic	Pearson uniform rank statistic	number
uniformRankDegreesOfFreedom	Uniform rank degrees of freedom	number
meanRankBinCount	Mean rank bin count	number
relativeEndBinExcess	Relative end bin excess	number

json

{
  "input": {
    "observedRankBinCounts": [
      10,
      10,
      10,
      10
    ],
    "ensembleMemberCount": 3
  },
  "output": {
    "pearsonUniformRankStatistic": 0,
    "uniformRankDegreesOfFreedom": 3,
    "meanRankBinCount": 10,
    "relativeEndBinExcess": 0
  }
}

Limitations and assumptions

Ties, observation independence and appropriate bin construction are caller responsibilities. No p-value or automatic reliability verdict is returned.

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 Ensemble Spread Error Consistency Checker: Compare case-wise ensemble-mean RMSE with unbiased member variance under finite-M exchangeability factor sqrt(1+1/M); descriptive comparison, no reliability test/independence claim and perfect zero-error ratio undefined. For a complementary task, use Anomaly Correlation Height Field: Compute uncentered area-weighted anomaly correlation relative to caller climate-normal height field; differs from Pearson centered correlation, matched area exposure required and zero anomaly norms undefined.

Further background: Statistical concepts for probabilistic forecast data.

References

Rank Histogram Flatness Check Tool — tool.io
Statistical concepts for probabilistic forecast data — ECMWF

Similar or alternative tools

Ensemble Spread Error Consistency Checker
Compare case-wise ensemble-mean RMSE with unbiased member variance under finite-M exchangeability factor sqrt(1+1/M); descriptive comparison, no reliability test/independence claim and perfect zero-error ratio undefined.
Anomaly Correlation Height Field
Compute uncentered area-weighted anomaly correlation relative to caller climate-normal height field; differs from Pearson centered correlation, matched area exposure required and zero anomaly norms undefined.