SDI (Stream Disturbance Index) Calculators
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Reineke SDI Formula
SDI = TPA × (QMD / 10)^1.605
TPA = trees per acre; QMD = quadratic mean diameter (inches). QMD = √(Σ DBH²/N). The exponent 1.605 is Reineke's empirically derived constant (the slope of log TPA vs. log DBH at maximum density for many species).
Metric version: SDI = trees/ha × (QMD_cm / 25)^1.605
Example: stand with 180 TPA and QMD = 12 inches: SDI = 180 × (12/10)^1.605 = 180 × 1.2^1.605 = 180 × 1.334 = 240 SDI.
SDI_max and Stocking Levels
SDI_max = the maximum SDI at which competition mortality begins. Species-specific values: ponderosa pine ≈ 365–420; Douglas-fir ≈ 595; Pacific silver fir ≈ 440; loblolly pine ≈ 450. Stocking zones relative to SDI_max: < 25%: understocked; 25–35%: lower management zone; 35–60%: active management zone (optimal for growth); > 60%: imminent competition mortality zone; > 80–100%: at or above SDI_max (heavy mortality occurring).
Density Management Diagrams
DMDs plot log(TPA) vs. log(QMD) showing: self-thinning line (SDI_max); thinning prescription zones; volume per acre lines. Used to plan thinning entries, target residual densities, and predict future stand development.
Why SDI Over Basal Area?
Basal area alone doesn't account for tree size distribution; SDI integrates both tree count and average size — a more stable index across stand ages and site qualities for expressing competition status.
Glossary
Frequently Asked Questions
SDI measures forest stocking relative to maximum density, integrating tree count and average diameter. Reineke formula: SDI = TPA × (QMD/10)^1.605, where TPA = trees per acre and QMD = quadratic mean diameter in inches. QMD = √(Σ(DBH²)/N). Example: 250 TPA with QMD = 8 inches: SDI = 250 × (8/10)^1.605 = 250 × 0.8^1.605 = 250 × 0.729 = 182. Compare to SDI_max for the species to assess competition status.
SDI_max is the maximum SDI at which competition-induced mortality begins — the carrying capacity of the site for that species. It is species-specific (Douglas-fir SDI_max ≈ 595; ponderosa pine ≈ 365–420). Thinning management: aim to maintain SDI between 25–60% of SDI_max for optimal growth; thin before SDI exceeds 60% of SDI_max. Above 60%: trees begin competing strongly (suppression and mortality risk). Above 80–100%: self-thinning mortality is occurring and the stand is overstocked. Thinning should reduce SDI to the lower management zone (35% of SDI_max) then allow recovery before the next entry.
Basal area (BA, m²/ha or ft²/acre): sum of cross-sectional areas of all trees; easy to measure (prism sampling); widely used in forestry. Limitation: same BA can represent many small or few large trees — different competition levels. SDI integrates both tree count and average size into one index that is more stable across stand ages. A 20-year-old thinned stand and a 60-year-old stand at the same BA may have very different competition status, but SDI better reflects the actual crowding relative to carrying capacity. For forest planning and density management diagrams, SDI is preferred; for quick field assessment and yield estimation, BA is simpler and equally useful.
A density management diagram (DMD) is a graphical tool for planning and tracking forest stand development. It plots log(TPA) on the y-axis vs. log(QMD) on the x-axis and includes: the maximum density line (self-thinning line, corresponding to SDI_max) — no stand can plot above this; management zones showing optimal SDI ranges; lines of constant relative density (%SDI_max); production isocurves (volume per acre lines). Forest managers use DMDs to: identify current stand position (using measured TPA and QMD); plan thinning entries (move stand to target density zone); predict future development (stands track upward along the maximum density line as trees grow); compare alternative management intensities.