Abstract
Abstract. The MLB parameterisation (Modified Lambert-Beer, Mueller et al., 2004) describes the change in SSI with sun zenith angle (SZA) in clear-sky conditions. It applies to the direct and global SSI as well as their spectral distribution. We assess its performances by comparing its results to the outputs of the radiative transfer model libRadtran and standard interpolation procedures. The standard two-point fitting MLB function performs very well at SZA between 0° and 60° and fairly bad from 60° to 89.9°. A parameterisation made of four MLBs for four intervals (0°, 60°), (60°, 75°), (75°, 85°) and (85°, 89.9°) is also tested. This piecewise MLB parameterisation exhibits satisfactory performances at any SZA and outperforms standard linear interpolation techniques. 95 % of errors in global SSI are less than 1 W m−2 for each band and less than 5 W m−2 for total irradiance.
Highlights
A new direct method, Heliosat-4, is currently developed by the MINES ParisTech and the German Aerospace Center (DLR), aiming at estimating surface downwelling solar irradiance (SSI)
It depicts the error in the total global SSI as a function of the sun zenith angles (SZA)
In low SZA conditions, errors in SSI are generally small for Piecewise Modified Lambert-Beer function (MLB) (P95 < 5 W m−2) as what we showed in the Fig. 3
Summary
A new direct method, Heliosat-4, is currently developed by the MINES ParisTech and the German Aerospace Center (DLR), aiming at estimating surface downwelling solar irradiance (SSI). The clear-sky module, an important part of this method, is based on the radiative transfer model (RTM) libRadtran (Mayer et al, 2010) and benefits from advanced products derived from recent Earth Observation missions (Oumbe et al, 2009). Mueller et al (2004, 2009) suggest the use of parameterisations, among which the Modified Lambert-Beer function (MLB) to reduce the number of runs of RTM for the different sun zenith angles (SZA). Instead of calculating SSI values for each SZA with RTM runs, we use the MLB to interpolate SSI at any SZA by using SSI calculated by RTM at only two SZAs. The novelty of this article is twofold: firstly to establish the performances of the MLB function by comparing its outcomes to those from libRadtran, and secondly, to propose an extended-MLB parameterisation to overcome the errors observed for large SZA. It is assumed that libRadtran is delivering the actual values that should be reproduced
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