Description
Return largestPopulation/rank^exponent, observed/reference ratio, and observed minus reference.
Spatial models compare distances, travel intervals, activity areas, or supplied interaction functions. Coordinates and model parameters must share a compatible basis, and a local term does not establish observed behavior.
Return largestPopulation/rank^exponent, observed/reference ratio, and observed minus reference.
When to use this tool
Use Settlement Rank Size Reference Term when you need one explicit spatial or travel-model component.
How to use the tool and how it works
- Enter largestPopulation, rank, exponent, observedPopulation. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read referencePopulation, observedReferenceRatio, residual. Use the output convention below.
Require positive largestPopulation and rank and nonnegative observedPopulation. Return largestPopulation/rank^exponent, observed/reference ratio, and observed minus reference.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| largestPopulation | Largest Population | Required. Finite number; strictly above 0. |
| rank | Rank | Required. Safe integer; minimum 1. |
| exponent | Exponent | Required. Finite number. |
| observedPopulation | Observed Population | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| referencePopulation | Reference Population | Required. Finite number. |
| observedReferenceRatio | Observed Reference Ratio | Required. Finite number. |
| residual | Residual | Required. Finite number. |
{
"input": {
"largestPopulation": 1000000,
"rank": 2,
"exponent": 1,
"observedPopulation": 600000
},
"output": {
"referencePopulation": 500000,
"observedReferenceRatio": 1.2,
"residual": 100000
}
}Limitations and assumptions
- Rank is one-based and exponent is supplied; this rank-size reference is not a fitted settlement law or a population forecast.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Check projection, route definitions, calibration, and the complete model before interpreting access or predicted flows.
References
Similar or alternative tools
- Population Cell Density Factor
Divide nonnegative integer population by positive cellArea for density.
- Location Quotient One Employment Cell
Divide localSector by positive localTotal and positive referenceSector by referenceTotal, validating sector counts within totals.