Trophic State Index (TSI) Calculators

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The Trophic State Index (TSI) is a numerical system for classifying lake water quality based on nutrient loading and biological productivity. The most widely used version is Carlson's TSI (1977), which calculates three sub-indices from Secchi disk transparency, chlorophyll-a concentration, and total phosphorus, then averages them into a single 0–100 score. TSI provides a standardized framework for comparing lakes, tracking eutrophication trends, and communicating lake health to managers and the public.

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Carlson's TSI Formulas

Each sub-index is calculated independently then averaged:

TSI(SD) — Secchi Depth

TSI(SD) = 60 − 14.41 × ln(SD)
Where SD = Secchi depth in meters.

TSI(Chl) — Chlorophyll-a

TSI(Chl) = 9.81 × ln(Chl) + 30.6
Where Chl = chlorophyll-a in μg/L.

TSI(TP) — Total Phosphorus

TSI(TP) = 14.42 × ln(TP) + 4.15
Where TP = total phosphorus in μg/L. Overall TSI = average of the three sub-indices.

TSI Classification

  • TSI < 30: Oligotrophic — ultra-clear, cold lakes; very low nutrients; high dissolved oxygen to depth
  • TSI 30–50: Mesotrophic — moderate clarity; moderate algae; good fisheries
  • TSI 50–70: Eutrophic — algal blooms likely; low summer DO in hypolimnion
  • TSI > 70: Hypereutrophic — dense algal blooms; frequent anoxia; fish kills

Key Parameters

  • Secchi depth: Depth at which a white disk disappears — measures clarity. Deep = low TSI.
  • Chlorophyll-a: Primary phytoplankton pigment — directly measures algal biomass
  • Total phosphorus: Key limiting nutrient in most freshwater lakes

Sub-Index Deviations

TSI(Chl) > TSI(TP): non-algal turbidity reducing light despite low nutrients.
TSI(SD) > TSI(Chl): algae dominate turbidity — classic eutrophic pattern.
TSI(Chl) < TSI(TP): nutrients present but algal growth limited by light or grazing.

Glossary

Trophic State Index (TSI)
Carlson's numerical scale (0–100) classifying lake eutrophication from Secchi depth, chlorophyll-a, and total phosphorus. TSI < 30 = oligotrophic; 30–50 = mesotrophic; 50–70 = eutrophic; > 70 = hypereutrophic.
Secchi Depth
The depth at which a white Secchi disk disappears from view — measures water transparency. Used in TSI(SD) = 60 − 14.41 × ln(SD). Deeper = clearer = lower trophic state.
Eutrophication
The process by which excessive nutrient loading (primarily phosphorus and nitrogen) stimulates algal growth, depletes dissolved oxygen, and degrades water quality. A leading cause of lake and coastal ecosystem degradation worldwide.

Frequently Asked Questions

Carlson's TSI is a 0–100 scale classifying lake eutrophication from three parameters: Secchi depth, chlorophyll-a, and total phosphorus. TSI < 30 = oligotrophic (pristine); 30–50 = mesotrophic; 50–70 = eutrophic (algal blooms); > 70 = hypereutrophic (dense blooms, fish kills). Each sub-index is calculated separately then averaged for the overall TSI score.

TSI(SD) = 60 − 14.41 × ln(SD), where SD = Secchi disk depth in meters. Deeper Secchi depth = clearer water = lower TSI = better trophic status. Example: SD = 4 m → TSI(SD) = 60 − 14.41 × ln(4) = 60 − 19.97 = 40 (mesotrophic). Secchi depth is measured by lowering a white disk until it disappears from view and recording the depth.

Oligotrophic lakes have very low nutrients, high clarity, deep Secchi depths, high dissolved oxygen throughout, and low algal biomass (TSI < 30). They support cold-water fish (trout, salmon). Eutrophic lakes have high nutrients, poor clarity, frequent algal blooms, low dissolved oxygen in deep water in summer, and often support warm-water fish. TSI 50–70. Hypereutrophic lakes (TSI > 70) experience dense blooms and recurrent fish kills.

Phosphorus is the primary limiting nutrient for algal growth in most freshwater lakes. Unlike nitrogen, which can be fixed from the atmosphere by cyanobacteria, phosphorus has no atmospheric source — it enters lakes from agricultural runoff, septic systems, and stormwater. Controlling phosphorus loading is therefore the most effective management strategy for reducing eutrophication, which is why Carlson's TSI uses total phosphorus as one of its three sub-indices.