Carlson's TSI index - how to assess trophic status with a number

Knowledge base · July 27, 2026

A lake’s trophic status can be described in words (oligo-, meso-, eutrophic) or with a number. The latter is what Carlson’s TSI (Trophic State Index) is for, proposed by R.E. Carlson in 1977 (Limnology and Oceanography 22(2): 361-369). A single scale lets you compare water bodies and track change over time.

What it is made of

TSI is calculated from three closely related indicators of fertility:

• transparency (the depth of the Secchi disk, SD),
• chlorophyll-a (Chl) - algal biomass,
• total phosphorus (TP).

Each of them yields a separate TSI value. The scale is anchored on transparency: each halving of Secchi disk visibility raises TSI by 10 points. A doubling of total phosphorus does the same. A doubling of chlorophyll-a raises the index by just under 7 points - each component has its own coefficient, fitted to Carlson’s empirical data.

Values for typical lakes fall roughly in the range 0-100, but that is a practical range, not a mathematical bound - the formulas are logarithmic, so an extremely fertile water body can give a result above 100.

The formulas (after Carlson)

The relationships are logarithmic (SD in metres, Chl and TP in µg/l):

• TSI(SD) = 60 − 14.41 · ln(SD)
• TSI(Chl) = 30.6 + 9.81 · ln(Chl)
• TSI(TP) = 4.15 + 14.42 · ln(TP)

How to read the scale

The higher the TSI, the greater the fertility.

Which indicator matters most

If you have all three, do not average them unthinkingly. In Carlson’s classic treatment the closest to the “truth” about biological production is TSI(Chl) - chlorophyll measures algal biomass directly, while transparency and phosphorus are indirect measures.

The mean of the three components (the calculator shows it only as an auxiliary value, when you supply the full set) is not an assessment of the lake’s state - NALMS states plainly that averaging makes no sense. A mean would combine the best measure of algal biomass (chlorophyll) with two indirect ones. The divergence between components, on the other hand, is information:

• TSI(SD) clearly higher than TSI(Chl) - transparency is limited by something other than algae, most often mineral suspension or humic substances;
• TSI(TP) clearly higher than TSI(Chl) - there is plenty of phosphorus, but fewer algae than it would suggest; production is usually limited by another factor (often nitrogen, algae being grazed by zooplankton, or light).

Reading the divergence between components (in the literature deviation analysis) suggests what limits algae and light in the lake. It is a hypothesis to check, not a diagnosis - and it makes sense only for results from the same date and station, once a sampling or analysis error has been ruled out.

What to watch out for

• Season and single measurements. TSI makes sense computed from the growing season and as a series; a single reading from one day describes the weather, not the state of the water body.
• It is a tool for lakes. TSI was developed for standing waters of the temperate zone. For rivers, reservoirs with short retention times and strongly humic waters it is applied with caution.
• TSI is not a WFD status class. It is a separate, American descriptive index. It neither replaces nor converts into the ecological status classes used in assessing water bodies - it complements them well, but cannot be the basis of a formal assessment.

🧮 Tool: Carlson TSI calculator - enter transparency, chlorophyll-a or total phosphorus and see the result for each component separately, with its class according to the table above. No sign-up.

In practice

For TSI you need consistent series of transparency, chlorophyll-a and total phosphorus - ideally from the same dates and stations, because only then does comparing the components make sense. In LimnoLog you record these three indicators, and the application itself calculates TSI(SD), TSI(Chl) and TSI(TP) for every sample that contains the given component, and plots them side by side on a chart; it calculates the mean (TSI_avg) only when all three are present. All you need to do is add these calculated indicators to the project. Mind the unit: total phosphorus in the app is entered in mg P/l (0.030 mg/l = 30 µg/l) - the conversion to µg/l that Carlson’s formula requires is already built into the indicator formula.