Forest Growth Rate Calculator

Forest growth is expressed in two incompatible ways, and confusing them is the commonest error. Mean annual increment divides total accumulated stock by stand age and therefore describes average performance over the whole life of the stand. Periodic annual increment divides the change between two measurements by the interval and describes current performance. The relationship between them fixes rotation length in classical silviculture: periodic increment rises to a peak in youth then declines, mean increment lags behind it, and the age at which the falling periodic curve crosses the mean curve is the point of maximum sustained volume production, the biological rotation age. A compound annual growth rate, borrowed from finance, expresses the same change as a constant proportional rate, which suits the exponential phase of young stands but misleads badly in mature forest where increment is closer to linear and eventually flat. Typical values anchor the interpretation. Intensively managed tropical eucalypt plantations can sustain 20 to 40 cubic metres per hectare per year, temperate conifer plantations commonly reach 5 to 15, and undisturbed boreal or natural tropical forest often adds only 1 to 5 tonnes of biomass per hectare per year. Gross growth adds back the biomass lost to mortality, which is why an old-growth stand can show vigorous gross increment alongside a net change near zero. Caveats: a two-point measurement blends real growth with measurement error and with ingrowth, meaning trees newly crossing the minimum diameter threshold, and extrapolating any compound rate forward will overstate future stock because growth is sigmoid rather than exponential.

Growth and yield measurement is the oldest quantitative branch of forestry, driven by the need to regulate harvests. Hans Carl von Carlowitz articulated the principle of sustained yield in Sylvicultura Oeconomica in 1713, arguing that no more timber should be cut than the forest reproduces. Turning that principle into numbers required tables of expected stock by age and site quality. Johann Christian Paulsen produced what is generally treated as the first yield table in 1795, and Heinrich Cotta published influential auxiliary tables in 1821 that tabulated volume and increment for German stands. Martin Faustmann added the economic layer in 1849 with his formula for the value of forest land, which made the choice of rotation age an explicit optimisation rather than a custom. The mathematics of the growth curve arrived from outside forestry. Benjamin Gompertz described his sigmoid mortality function in 1825 and Pierre-Francois Verhulst published the logistic equation in 1838. Ludwig von Bertalanffy proposed a general growth equation in 1938 grounded in the balance between anabolism and catabolism, which F. J. Richards generalised in 1959 into the flexible form now known in forestry as the Chapman-Richards function and still fitted to height, diameter, and volume series. Site index curves developed in the early twentieth century to separate site quality from age. Computerised stand projection followed once Albert Stage built the PROGNOSIS model for the United States Forest Service in 1973, the ancestor of the Forest Vegetation Simulator.