Solis Clear Sky Scheme: Extension to High Turbidity, Development and Validation Dr Pierre Ineichen University of Geneva – Institute of Environmental Sciences

Clear sky models clear turbid clear turbid In the field of solar radiation modeling, the first step is a precise knowledge of the highest possible radiation reaching the ground. It depends on the atmospheric turbidity. For worldwide online satellite irradiance evaluation, it should use as low as possible calculation time. Clear sky models: CPCR2, input: b, w (aod700 < 0.65 rural aerosols) REST2, input: b, w (aod700 < 1.7 rural aerosols) Bird, input: aod, w (aod700 < 0.27) ESRA, input: Linke turbidity TL2 (aod700 < 0.44) Solis 2008, input: aod , w (aod700 < 0.45, w > 0.2 cm) Data sets 10% with aod700 > 0.45 (aod550 > 0.6, rural aerosols) 9% with water vapor column w < 0.2 cm

Simplified Solis model Basics of Solis model Lambert-Beer attenuation equation LibRadTran RTM spectral calculations use of modified L-B equation due to band calculations, where to is the vertical optical depth and n evaluated at air mass M = 2) at high aod, Io has to be enhanced and is used for the 3 components final broadband simplified model derived from RTM calculations at 2 solar elevations Solis 2008 limitations: aod700 0 -> 0.45 w 0.2 -> 8cm altitude 0 -> 7000m

Zhang extension of Solis 2008 Solis 2008 presents an unrealistic behavior for high aod and low water vapor w column. Taiping Zhang made a modification for aod values up to 7 two additional constant terms in the extinction equation for aod > 0.45 and w < 0.2 null derivative at these limits validation against LibRadTran calculations better behavior with an aod dependent correction limitation: only valid for the beam component © Zhang

Solis 2017 derivation For fixed O3 (340 DU), US standard atmosphere four aerosol types (rural, urban, maritime and tropospheric): 2450 LibRadTran RTM spectral calculations altitude from sea level to 7000m aod550 from 0.01 to 7 water column w from 0.01 to 10cm results: I’o, tb, b , tg, g , td, d function of aod and w analytic formulation of these coefficients tn dependence with aod Io dependence with aod third degree polynomial = a  aod3 + b  aod2 + c  aod + d

Solis 2017 derivation analytic formulation of a, b, c and d coefficients coefficients dependence with w power and logarithm n = n1  w 0.5 + n2  ln(w) + n3 same behavior for the for coefficients altitude dependence ni = ni1  p/po + ni2

Parameters validation visual validation: scatter plots RTM calculations versus analytical model average, mean bias, standard deviation and correlation coefficient (same weight for all validation couple of values -> difficult to interpret the standard deviations)

Model/RTM irradiance validation visual validation: scatter plots RTM calculations versus analytical model average, mean bias, standard deviation and correlation coefficient (same weight for all validation couple of values -> difficult to interpret the standard deviations) diffuse: graphs made at h = 60°. Slightly better for the closure equation, but becomes negative at very low solar elevations Igh Idh Ibn Igh – Ibh   aerosol type Igh Ibn Idh rural 0.5% 0.9% 3.3% urban 1.0% 0.6% 4.1% tropo 1.2% 2.9% maritime 2.2% 3.4% 4.0%

Validation against ground data Comparison with data from Geneva, relatively low turbidity, slightly better than Solis 2008 Comparison with data from Jaipur, aod550 up to 2 Jaipur, same data, but McClear model