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.
Description
Anomaly correlation compares departures from a specified climate-normal field.
Anomaly correlation compares departures from a specified climate-normal field. This area-weighted uncentered correlation retains the supplied baseline rather than subtracting each anomaly field's own mean.1
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.
When to use Anomaly Correlation Height Field
Use this tool to 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.
Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.
How to use Anomaly Correlation Height Field 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 forecastHeightFields, observedHeightFields, baselineNormalHeights, representedAreaWeights using the field table and calculation rules, then run the tool.
- Read uncenteredAnomalyCorrelation, forecastAnomalyNorm, observedAnomalyNorm. 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 |
|---|---|---|---|
| forecastHeightFields | Forecast height fields | list of number | Required |
| observedHeightFields | Observed height fields | list of number | Required |
| baselineNormalHeights | Baseline normal heights | list of number | Required |
| representedAreaWeights | Represented area weights | list of number | Required |
Pair forecast, observed and baseline heights with strictly positive area weights. Form baseline anomalies, require both weighted norms positive and compute their normalized dot product, clamped to [−1,1] for floating-point roundoff.
Paired lists must be nonempty and have equal lengths.
correlation = Σweight × forecast anomaly × observed anomaly/(weighted norm forecast × weighted norm observed) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| uncenteredAnomalyCorrelation | Uncentered anomaly correlation | number |
| forecastAnomalyNorm | Forecast anomaly norm | number |
| observedAnomalyNorm | Observed anomaly norm | number |
{
"input": {
"forecastHeightFields": [
101,
202
],
"observedHeightFields": [
102,
204
],
"baselineNormalHeights": [
100,
200
],
"representedAreaWeights": [
1,
2
]
},
"output": {
"uncenteredAnomalyCorrelation": 1,
"forecastAnomalyNorm": 3,
"observedAnomalyNorm": 6
}
}Limitations and assumptions
The baseline and area representation are caller-supplied. Zero anomaly norms are rejected; this is not centered Pearson correlation.
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 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.
References
-
Anomaly Correlation Height Field — tool.io
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.
- 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.