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 - and 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). It is convenient, because it lets you compare water bodies and track change over time on one consistent scale.

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 - that is not an inconsistency but the effect of each component having 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 (which is how our calculator computes it when you supply the full set) is a convenient shortcut and works well for typical lakes, but the divergence between components is often more valuable than their mean:

• 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 algae are not using it; production is then limited by another factor (often nitrogen or light).

This way of reading divergence (in the literature: deviation analysis) is usually more useful for assessing the causes of eutrophication than the value of the index itself.

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 index and trophic status according to the table above at once. No sign-up.

In practice

For TSI you need consistent series of transparency, chlorophyll and phosphorus - ideally from the same dates and the same station, because only then does comparing the components make sense. In LimnoLog you record these indicators in a single project and track their trend; the TSI value itself you can keep as a custom indicator and watch it change season after season.