Since light is important for algal growth, its effect is simulated in many water quality models, e.g., WASP model (see Equation 6 in its manual for multiple algae). However, below is what I cannot understand well about this Equation 6:

Why Ia = 0.9*I/f (where Ia is the average incident light intensity during daylight hours; I is incident solar radiation; f is fraction of day that is daylight)? What does this 0.9 come from?

  • 1
    Please ask One question per Question.
    – Vince
    Mar 29, 2020 at 22:24
  • @Vince Sorry, I have deleted one of my question to make it more focused
    – T X
    Mar 29, 2020 at 22:42

2 Answers 2


It seems to be a kind of "average" extinction coefficient which affect the daily amount of light, maybe taking into account some "average foggy effect of the atmosphere" (?) or the amount of directly reflected light by the water surface (?). But as it is said "it is assumed to be...", I wouldn't bother much... it should be some kind of an experimental approximation that best fit some data.

Because when I look at the formula, it's not strictly equivalent to the K parameters defined as the "Vertical extinction coefficient":

A measure of the ability of a particular water sample to exponentially attenuate (decrease) light shining on it. It is the constant k in the famous Beer-(Bouguer)-Lambert Law;
i(z) = i(0) * e(-k*z)
where z is any depth in meters.

Source: https://www.waterontheweb.org/resources/glossary.html#V

This famous equation can be retrieved as part in yours:
Equation 6

Maybe this can also help a little:

From there, I would suggest to read Toro et al. "A Dynamic Model of the Phytoplankton Population in the Sacramento—San Joaquin Delta" (1971);
I unfortunately don't have access to it through my academic subscription.
But I can try to get it (it can take some days) with the help of a PhD friend in water treatment, I'll update my post if I succeed.

I think (and hope) it could be explained there, because for me, it's not 100% sure in the paper of Hernandez et al. "Modeling eutrophication kinetics in reservoir microcosms" (1997) (which is the published version of your document):

I would also suggest to directly contact the authors, via the latter site (sciencedirect).

Good luck.

Further readings

Steele, J. H. (1962). Environmental control of photosynthesis in the sea. Limnology and oceanography, 7(2), 137-150: https://aslopubs.onlinelibrary.wiley.com/doi/pdf/10.4319/lo.1962.7.2.0137

Smith, R. A. (1980). The theoretical basis for estimating phytoplankton production and specific growth rate from chlorophyll, light and temperature data. Ecological Modelling, 10(3-4), 243-264: https://www.researchgate.net/profile/Richard_Smith21/publication/255685721_The_theoretical_basis_for_estimating_phytoplankton_production_and_specific_growth_rate_from_chlorophyll_light_and_temperature_data/links/5b84162e299bf1d5a72b6976/The-theoretical-basis-for-estimating-phytoplankton-production-and-specific-growth-rate-from-chlorophyll-light-and-temperature-data.pdf

  • Thanks so much! I will check these materials you mentioned, and go back here if I have some ideas or something else.
    – T X
    Apr 8, 2020 at 14:45

Just a guess: could be that incident light is related not to the surface but "just below the surface", so the light "just below the surface" might be equivalent to 0.9*incident light (on the surface)?

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