Culmination Age MAI PAI

Audit sampled cumulative production through MAI and interval PAI, returning first age of sampled MAI maximum; distinct from existing one-interval increment formulas and no continuous unsampled peak inferred.

Description

Mean annual increment divides cumulative production by age, while periodic annual increment uses change between surveys.

Mean annual increment divides cumulative production by age, while periodic annual increment uses change between surveys. Their sampled maxima need not locate an unsampled continuous peak.^[1]

When to use Culmination Age MAI PAI

Use this tool to audit sampled cumulative production through MAI and interval PAI, returning first age of sampled MAI maximum; distinct from existing one-interval increment formulas and no continuous unsampled peak inferred.

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

How to use Culmination Age MAI PAI 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 surveyAgesYears, cumulativeProductionM3PerHa using the field table and calculation rules, then run the tool.
Read observedMaiM3PerHaYear, intervalPaiM3PerHaYear, sampledMaiCulminationAgeYears. 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
surveyAgesYears	Survey ages years	list of number	Required
cumulativeProductionM3PerHa	Cumulative production m3 per ha	list of number	Required

Use increasing positive ages and aligned nonnegative nondecreasing cumulative m³/ha. Return sampled MAIs, interval PAIs and the first survey age attaining maximum MAI.

Paired lists must be nonempty and have equal lengths. Each sequence checked for increasing order must contain at least two strictly increasing values.

MAI=production/age; interval PAI=production change/age change

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

Output field	Meaning	Value type
observedMaiM3PerHaYear	Observed mai m3 per ha year	list of number
intervalPaiM3PerHaYear	Interval pai m3 per ha year	list of number
sampledMaiCulminationAgeYears	Sampled mai culmination age years	number

json

{
  "input": {
    "surveyAgesYears": [
      10,
      20,
      30
    ],
    "cumulativeProductionM3PerHa": [
      50,
      160,
      210
    ]
  },
  "output": {
    "observedMaiM3PerHaYear": [
      5,
      8,
      7
    ],
    "intervalPaiM3PerHaYear": [
      11,
      5
    ],
    "sampledMaiCulminationAgeYears": 20
  }
}

Limitations and assumptions

Only observed ages are searched. A continuous growth culmination or economic rotation optimum is not inferred.

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 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. For a complementary task, use Optimal Rotation Length: Select the best supplied rotation by perpetual equal-cycle land expectation value with establishment and year-end annual holding cost; fixed real discount/price/productivity assumptions, not a continuous biological optimum.

References

Culmination Age MAI PAI — tool.io

Similar or alternative tools

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.
Optimal Rotation Length
Select the best supplied rotation by perpetual equal-cycle land expectation value with establishment and year-end annual holding cost; fixed real discount/price/productivity assumptions, not a continuous biological optimum.