## How to detect clear sky instants |

... in time series of solar radiation values. The method described here and exploited by the SoDa team is the one of **Lefèvre et al. (2013)**, which has originally been suited for 1 min BSRN stations. For other data sets or other time steps, please take the greatest care in adapting this algorithm.

## Recipe of Lefèvre et al. (2013)

### Ingredients:

- DHI: Diffuse Horizontal Irradiation
- GHI: Global Horizontal Irradiation
- TOA: Irradiation over a horizontal plane at the Top of Atmosphere

### Assumptions

1 min GHI and DHI data, like the one available via BSRN stations

### Preparation

- Filter 1: for each 1 min BSRN data, only keep instants when DHI / GHI < 0.3
- Filter 2:
- Step 1: take a temporal window of [t - 90 min; t + 90 min], and only keep instants when at least 30% of the 1 min data pass Filter 1
- Step 2: take a temporal window of [t - 90 min; t + 90 min], and compute Kt' as:

*KT′ = KT / [1.031 exp( −1.4/(0.9 + 9.4/m)) + 0.1]*

with*m*the air mass computed using the following expression (Kasten and Young (1989)):

*m(Θ*_{S}) = (p/p0)/ [cos(Θ) + 0.50572 (Θ_{S}+ 6.07995) − 1.6364]_{S}

with*Θ*the solar zenithal angle expressed in degrees._{S}

and only keep Kt' when standard deviation of Kt' in this temporal window is below**0.02**

## Extract from Lefèvre et al. 2013, pp 2408-2409

[...*Two filters have been applied on the remaining BSRN data in order to retain reliable clear-sky instants: The first one was a constraint on the amount of diffuse irradiance with respect to the global irradiance since the direct irradiance is prominent in the case of clear sky. Only those minutes for which E ^{diff} / E^{glo} < 0.3, i.e. when the diffuse component is much less than the direct one, have been retained. *

*The second filter dealt with the temporal variability of the irradiance. If there is no cloud, the sky should be clear for a long period. Checking this would avoid cases of broken clouds or noticeable spatial heterogeneity around the site if ergodicity is assumed. The first step of this filter was to retain only periods with enough measurements that have passed the first filter. A given instant t , expressed in min, was kept only if at least 30 % of the 1 min observations in both intervals [ t − 90, t ] and [ t , t + 90] have been retained after the first filter. A corrected clearness index, KT ′ (Ineichen and Perez, 1999) is computed for this instant: *

*KT′ = KT / [1.031 exp (− 1.4/(0.9 + 9.4/m)) + 0.1 ] (10)*

*... where m is the air mass defined by Kasten and Young (1989): *

*m(Θ_{S}) = (p/p0)/ [cos(Θ_{S}) + 0.50572 (Θ_{S} + 6.07995) − 1.6364] (11) *

*... where Θ_{S} is expressed in degree, and p and p0 are respectively the pressure at the site under consideration and that at sea level. *

*An instant was considered clear if the standard deviation of KT′ in the interval [ t − 90, t + 90] was less than a threshold, set empirically to 0.02. Only these 1 min clear-sky instants were retained for the validation. Figure 3 displays a time series of E ^{glo} for the selected clear-sky instants in the year 2005 in Payerne, in black circles. Payerne experiences a large number of clear skies during the year and many instants are selected. In this graph are also drawn the clear-sky instants selected by the algorithm of Long and Ackerman (2000), in light-grey crosses. One may see that they are differences between the results. The proposed algorithm presents less low values of E^{glo} than that of Long and Ackerman and offers more confidence in the fact that the instant is clear.*..]

## Bibliography about clear-sky instant detection

Kasten and Young 1989 | Kasten, F. and Young, A. T.: Revised optical air mass tables and approximation formula, Appl. Optics, 28, 4735–4738, 1989 | Air mass |

**Content: **Compute air mass necessary for instance to detect clear sky instants in the method proposed by Lefèvre *et al.* 2013 about McClear validation

Lefèvre et al. 2013 | Lefèvre M., A. Oumbe, P. Blanc, B. Espinar, B. Gschwind, Z. Qu, L. Wald, M. Schroedter-Homscheidt, C. Hoyer-Klick, A. Arola, A. Benedetti, J. W. Kaiser, and J.-J. Morcrette, 2013. "McClear: a new model estimating downwelling solar radiation at ground level in clear-sky conditions", Atmos. Meas. Tech., 6, 2403-2418, doi:10.5194/amt-6-2403-2013. | McClear |

Long and Ackerman 2000 | Long, C. N. and Ackerman, T. P., 2000. "Identification of clear skies from broadband pyranometer measurements and calculation of down- welling shortwave cloud effects", J. Geophys. Res., 105, 15609, doi: 10.1029/2000JD900077. | Detection of clear sky instants |