The

Photosynthetically active radiation, abbreviated in PAR, is the solar
radiation in the range [400, 700] nm that can be used by organisms via the
process of photosynthesis. PAR is defined as the incident power per unit
surface for this spectral interval and may be expressed in W m

In situ measurements of PAR are rare in space and time. This scarcity leads
researchers and practitioners to calculate PAR from the global broadband
solar irradiance by empirical means. For example, Udo and Aro (1999)
proposed a ratio of 2.079 between the daily mean of

KB covering and close to PAR spectral interval, selected
sub-intervals

Other approaches to PAR assessment and more generally to assessment of the
solar radiation in any spectral interval are atmospheric radiative transfer
models (RTM). Besides the difficulty in knowing all inputs requested by
RTMs, their main disadvantage is the computational load because many
spectral calculations must be performed. Several methods have been proposed
to reduce the number of calculations. Among them, are the

The global PAR irradiance

The direct normal irradiance is the irradiance received on a plane always
facing the sun rays with a normal incidence. Let note respectively

The integral may be replaced by a Riemann sum using very narrow spectral
intervals or bands, hereafter abbreviated NB. Here, we chose

The PAR spectral band [400, 700] nm is covered by 11 KB, from #6 [363, 408] nm
to #16 [684, 704] nm (Table 1). Wandji Nyamsi et al. (2014)
demonstrated that as a whole the approach of Kato et al. (1999) offer
accurate estimates of the spectral irradiance in most of the 32 KB when
compared to detailed spectral calculations in clear sky and cloudy
conditions, and especially for the KB #6 to 16. It follows that the PAR
may be computed by a Riemann sum based on 11 KB instead of 300 NBs. KB #6
and #16 are partly outside the PAR range. One solution is a weighted sum
based on the overlap between KB

Actually, the bandwidth in several KB is larger than 30 nm and may be considered large for estimating PAR in an accurate manner. The concept underlying the proposed technique is to determine several narrower spectral bands NB whose transmissivities are correlated to those of the KB and then use these transmissivities in a linear interpolation process to compute the PAR. This technique is elaborated and validated by the means of the RTM libRadtran (Mayer and Kylling, 2005).

Ranges and distributions of values taken by the solar zenith angle, the ground albedo and the 7 variables describing the clear atmosphere.

The clearness index KT

Several plots were made superimposing KT

In each selected NB, an affine function is determined by least-square
fitting technique:

A comparison of the results of the proposed technique against the results
from the detailed spectral calculations made by libRadtran considered as a
reference is performed to assess the performances of the proposed technique
for

Synthesis of the performance of the proposed technique.

Deviations: estimates minus reference, are computed for each state of the
validation sample for

Figure 2 exhibits the statistical indicators for

There are two causes for this similarity. The first cause is that all KB
contain one

Performance of different methods: Jacovides et al. (2004); Udo and Aro (1999), weighted sum and the proposed technique.

The

The proposed technique is very useful for the operational estimation of PAR
when computational load and great accuracy in PAR are major issues. In addition,
this technique may be extended to be able to accurately estimate other spectral
quantities taking into account spectral absorption of photosynthetic pigments
found in plants and algae such as chlorophyll, carotenoids. The authors are
aware of the heuristic way used for selecting the specific NBs for each KB
in their work. Other ways are possible. For example, one may think of using
the variance between KT

The research leading to these results has received funding from the ADEME, research grant No. 1105C0028. Edited by: S.-E. Gryning Reviewed by: two anonymous referees