Carlson Trophic State Index Calculators

0 calculators tagged with “Carlson Trophic State Index”

The Carlson Trophic State Index (TSI) is a quantitative measure of lake eutrophication — the enrichment of water bodies with nutrients leading to increased algal productivity. Developed by Robert Carlson in 1977, the TSI integrates three measurements: Secchi depth (SD), total phosphorus (TP), and chlorophyll a (chl a). Each measurement independently produces a TSI value ranging from 0 (ultra-oligotrophic) to 100+ (hypereutrophic). Higher TSI = more eutrophic = more algae, less water clarity, more potential for oxygen depletion. The TSI is the most widely used lake water quality index in North America.

All Calculators

No calculators found for this topic.

Carlson TSI Formulas

TSI(SD) = 60 − 14.41 × ln(SD) (SD in meters)

TSI(TP) = 14.42 × ln(TP) + 4.15 (TP in μg/L)

TSI(CHL) = 9.81 × ln(CHL) + 30.6 (chlorophyll a in μg/L)

Average: TSI = mean(TSI(SD) + TSI(TP) + TSI(CHL)) / 3. Or use individual values to diagnose limiting factors.

TSI Classification

  • TSI < 40: Oligotrophic — clear water; low productivity; high DO throughout; deep blue; salmonid fish
  • TSI 40–50: Mesotrophic — moderate clarity; some algal growth; good fishery
  • TSI 50–70: Eutrophic — reduced clarity; algal blooms possible; periodic oxygen depletion
  • TSI > 70: Hypereutrophic — very low clarity; dense algal blooms; frequent oxygen depletion; poor fish habitat; cyanobacteria blooms

Interpreting Discrepancies Between TSI Values

If TSI(CHL) > TSI(TP): non-algal turbidity present (clay, color). TSI(TP) > TSI(CHL): algal growth is nutrient-limited despite available P (light or N limitation). TSI(SD) > TSI(CHL): non-algal turbidity reducing clarity beyond algae.

Secchi Depth

A Secchi disk (20 cm diameter, white) is lowered until it disappears from view; the average depth of disappearance = Secchi depth. Simple, inexpensive, easily understood by the public.

Glossary

Carlson TSI
A lake eutrophication index ranging 0–100+; calculated from Secchi depth, total phosphorus, and chlorophyll a; < 40 = oligotrophic; 40–50 = mesotrophic; 50–70 = eutrophic; > 70 = hypereutrophic.
Secchi Depth
The depth at which a 20 cm black-and-white disk disappears from view; a simple measure of water clarity; low Secchi depth = turbid, algae-rich water; TSI(SD) = 60 − 14.41 × ln(depth in m).
Trophic State
The classification of a water body's biological productivity level based on nutrient content and algal biomass: oligotrophic (low) → mesotrophic → eutrophic → hypereutrophic (high).

Frequently Asked Questions

The Carlson TSI quantifies lake eutrophication on a continuous 0–100+ scale using three measurements: TSI(SD) = 60 − 14.41 × ln(Secchi depth in m); TSI(TP) = 14.42 × ln(total phosphorus in μg/L) + 4.15; TSI(Chl a) = 9.81 × ln(chlorophyll a in μg/L) + 30.6. Example: Secchi depth = 1.5 m: TSI(SD) = 60 − 14.41 × ln(1.5) = 60 − 14.41 × 0.405 = 60 − 5.84 = 54.2 → eutrophic. TSI values are most meaningful when averaged across multiple measurements within the summer growing season.

TSI interpretation: TSI < 40 (oligotrophic): clear, deep, well-oxygenated, low productivity; Secchi depth > 4 m; TP < 12 μg/L; chl a < 2 μg/L; supports cold-water fish (trout, cisco); few algal blooms. TSI 40–50 (mesotrophic): moderate clarity; Secchi depth 2–4 m; TP 12–24 μg/L; warm-water and cold-water fish; some algal growth in late summer. TSI 50–70 (eutrophic): reduced clarity; Secchi depth 0.5–2 m; TP 24–96 μg/L; warm-water fish dominant; algal blooms likely; oxygen depletion in hypolimnion. TSI > 70 (hypereutrophic): turbid; Secchi depth < 0.5 m; dense algal blooms; cyanobacteria; dissolved oxygen < 2 mg/L in deep water; limited fish habitat.

A Secchi disk is a 20 cm diameter circular plate divided into alternating black and white quadrants. Measurement: lower the disk on a calibrated line until it just disappears from view; record the depth (disappearance depth); lower further until just below vision; slowly raise until it just reappears; record the depth (reappearance depth); Secchi depth = average of these two depths. Measure from the shaded side of the boat to avoid glare. Best measured around solar noon on a clear day. Secchi depth reflects water clarity, which is influenced by: algal biomass (primary influence in productive lakes); suspended sediments (turbidity); water color (dissolved organic matter in dystrophic lakes). Typical values: oligotrophic mountain lakes 10–40 m; hypereutrophic lakes < 0.5 m.

Comparing TSI values from the three measurements diagnoses what is controlling lake productivity: TSI(Chl a) ≈ TSI(TP) ≈ TSI(SD): the lake behaves as expected; phosphorus controls algal biomass; algae control clarity. TSI(Chl a) << TSI(TP): phosphorus is available but algae are not growing proportionally → nitrogen or light limitation; algal grazers (zooplankton) suppressing algae; non-algal turbidity. TSI(SD) << TSI(Chl a): clarity is better than expected from algal biomass → large-celled algae that sink; low-scattering algae. TSI(SD) >> TSI(Chl a): clarity worse than algal biomass predicts → non-algal turbidity (clay, humic color, fine sediment). These diagnostics guide management: P limitation → target P reduction; N co-limitation → reduce both; non-algal turbidity → address erosion or watershed color.