Daily gross assimilation

After the calculation of total instantaneous gross assimilation for the entire canopy (see topic Instantaneous gross assimilation), an integration over the day should be executed. For doing this, some preparatory calculations are needed.

Three points in time are selected at which the photosynthetically active radiation is calculated. It is assumed that radiation is homogeneously distributed over the day according to the sine of the solar elevation (see topic Astronomic equations) The weighted average CO2 assimilation rate can therefore be calculated for half a day only.

Firstly, the three points in time are selected from noon to sunset (this explains the use of the constants 0.5 and 12.00).

where Hour is the hour of the day (h), Dl is day length (hours, see topic Astronomic equations) and Gausspt  is the Gaussian integration points.

The three values for Hour are introduced in the following equation:

where SinB is the sin of solar elevation (unitless), Sinld is seasonal offset of sine of solar height at a certain day (unitless), Cosld is amplitude of sine of solar height at a certain day  (unitless), and Hour is the hour of the day (h). (see topic Astronomic equations for details).

Next step, with the values of SinB calculated in the three moments of the day, the photosynthetically active radiation in the three points of time can be calculated with the equation:

where Pardir is photosynthetically active radiation for each of the three moments of the day (W m-2),  Radshort is shortwave net radiation  (W m-2), SinB is the sin of solar elevation (unitless) and Solarheff is effective solar height (s).

After this calculation, the diffused photosynthetically active radiation and the direct photosynthetically active diffused radiation for each of the three moments of the day can be calculated:

where PARdiff,h is diffused photosynthetically active radiation at the moment h (W m-2), Pardir is  photosynthetically active radiation at the same point of time (W m-2), SinB is the sin of solar elevation (unitless) and Radperp is diffuse irradiation perpendicular to the direction of light (W m-2).

where Pardir,h is direct photosynthetically active radiation at the moment h (W m-2), Pardir is  photosynthetically active radiation at the same point of time (W m-2) and PARdiff,h is diffused photosynthetically active radiation at the moment h (W m-2).

Once the photosynthetically active radiation fluxes have been established for each value of Hour, and the instantaneous gross assimilation for each layer and for the entire canopy is calculated (see topic Instantaneous gross assimilation)  daily gross CO2 assimilation rate can be established as the weighted average of the three selected hours of the day (i.e. integration over time, see topic Gaussian integration).

Multiplying daily gross CO2 assimilation rate by day length results in the total daily gross rate of CO2 assimilation:

where Asstot is daily total gross CO2 assimilation rate (kg ha-1 d-1), AssHour is total gross CO2 assimilation rate derived from Gaussian integration of the three canopy layers and of the three points of time in a day (kg ha-1 d-1), and Dl is day length (hours).

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