Chapman-Richards Site Index Height Age

Normalize supplied dominant height/age to a reference-age Chapman–Richards site index with explicit growth/shape calibration; no generic height/age ratio or universal regional site table.

Description

Site index expresses dominant height at a reference age under a fitted growth curve.

Site index expresses dominant height at a reference age under a fitted growth curve. Chapman–Richards calibration differs from a simple height/age ratio.^[1]

Normalize supplied dominant height/age to a reference-age Chapman–Richards site index with explicit growth/shape calibration; no generic height/age ratio or universal regional site table.

When to use Chapman-Richards Site Index Height Age

Use this tool to normalize supplied dominant height/age to a reference-age Chapman–Richards site index with explicit growth/shape calibration; no generic height/age ratio or universal regional site table.

Gather the tree inventory, plot measurements or model parameters. Check diameter, area, time and moisture conventions; keep paired observations aligned.

How to use Chapman-Richards Site Index Height Age and understand its results

Gather the tree inventory, plot measurements or model parameters. Check diameter, area, time and moisture conventions; keep paired observations aligned.
Enter observedDominantHeightM, observedStandAgeYears, referenceSiteAgeYears, chapmanGrowthRatePerYear, chapmanShapeExponent using the field table and calculation rules, then run the tool.
Read calibratedAsymptoticHeightM, referenceAgeSiteIndexM. 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
observedDominantHeightM	Observed dominant height m	number	Required
observedStandAgeYears	Observed stand age years	number	Required
referenceSiteAgeYears	Reference site age years	number	Required
chapmanGrowthRatePerYear	Chapman growth rate per year	number	Required
chapmanShapeExponent	Chapman shape exponent	number	Required

Use positive observed height/age, reference age, rate k and shape exponent. Evaluate growth with −expm1(−kt), infer the asymptotic height and return predicted reference-age height in meters.

h(t)=A[1−exp(−kt)]^shape; infer A from observed height/age

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

Output field	Meaning	Value type
calibratedAsymptoticHeightM	Calibrated asymptotic height m	number
referenceAgeSiteIndexM	Reference age site index m	number

json

{
  "input": {
    "observedDominantHeightM": 10,
    "observedStandAgeYears": 10,
    "referenceSiteAgeYears": 20,
    "chapmanGrowthRatePerYear": 0.06931471805599453,
    "chapmanShapeExponent": 1
  },
  "output": {
    "calibratedAsymptoticHeightM": 20,
    "referenceAgeSiteIndexM": 15
  }
}

Limitations and assumptions

Curve parameters are supplied. Species, region and extrapolation suitability are not automatically validated.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Näslund Height Curve: Evaluate caller calibrated Näslund h=breast height+(d/(a+b d))² with explicit cm/metre calibration convention; no universal species curve or measured height lookup. For a complementary task, use Site Productivity Index: Compare accounted standing+removed+mortality production to a caller age/area-compatible reference; unlike standing-volume MAI, removals and mortality are included, with no universal yield class.

References

Chapman-Richards Site Index Height Age — tool.io

Similar or alternative tools

Näslund Height Curve
Evaluate caller calibrated Näslund h=breast height+(d/(a+b d))² with explicit cm/metre calibration convention; no universal species curve or measured height lookup.
Site Productivity Index
Compare accounted standing+removed+mortality production to a caller age/area-compatible reference; unlike standing-volume MAI, removals and mortality are included, with no universal yield class.