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Back to Main Page: Effects of snow on photovoltaic performance


The purpose of this page is to outline current development of radiative transfer modelling and its applications to the prediction and modelling of PV performance

Radiative Transfer Models (RTM)

The following is a breif list of available RTM codes


Computationally heavy simulations package which is consitered to be a reference for these measurements


  Lightweight simulations package capable of simulating cloudy sky information


 Developed my NREL and used to generate ASTM AM1.5 standard spectra. Currently only performs calculations for clear sky phenomena.

-[1]Description and availability of the SMARTS spectral model for phtovoltaic applications, (n.d.).

  • Clear-sky predictions, cloud modifiers fron Nann and Riordan

Line-by line models use quantum properties of radiation, acesssed from the HITRAN database. Band models are simplified LBL models described by Fenn et al. MODTRANS is a band model models based on parmaterizations of transmittance and absorbtin functions are simpler advantages of SMARTS

i) accurate and reg. updated spectral transmitance functions

ii) improved spectral resolution over existing transmittance models

iii) produces spectral irradiances omparable to MODTRAN

iv) predictions can be easily and directly compared to spectroradiometric measurements Anderson et. al. defines LOWTRAN spectra spectra are scaled by air term, RH, average temp Show sensitivity of PV systems to atmospheric consituents.


 Developed by ARM, it is a line-by line radiative transfer model


  Based on the DISTORT code, can handle multiple cloud layers


  Developed by U.S air force, extensively validated spectral modelling code. 


 The rapid radiative transfer model (RRTM) is a validated, correlated k-distribution band model for the calculation of longwave and shortwave atmospheric radiative fluxes and heating rates. The Rapid Radiative Transfer Model for GCMs is an accelerated version of RRTM that provides improved efficiency with minimal loss of accuracy for application to general circulation models.

Modelling and retreiving atmospheric paramters

Aerosol Optical Depth



Ground Based

=Error Analysis

Column Water Vapour



Ground Based

=Error Analysis

Cloud Cover



Ground Based

[1] J.C. Barnard, C.N. Long, A Simple Empirical Equation to Calculate Cloud Optical Thickness Using Shortwave Broadband Measurements, J. Appl. Meteor. 43 (2004) 1057-1066. [2] R. Boers, A. van Lammeren, A. Feijt, Accuracy of Cloud Optical Depth Retrievals from Ground-Based Pyranometers, J. Atmos. Oceanic Technol. 17 (2000) 916-927. [3] E. Leontyeva, K. Stamnes, Estimations of Cloud Optical Thickness from Ground-Based Measurements of Incoming Solar Radiation in the Arctic, J. Climate. 7 (1994) 566-578.

  • Uses broadband measurements (0.3-4um)from an eppley pyranometer.
  • Calculate available solar resource, iterate until finiding correct optical thickness. Good discussion of spectral snow albedo.

[4]A method to account for surface albedo heterogeneity and its application in the retrieval of cloud optical depth from ground-based measurements of irradiance, (n.d.).

  • Addresses the isssues associted with mutliple rebounds of albedo radiation in areas where albedo is non-constant. Not necesarily needed for this project.

[5]Cloud optical thickness retrievals from ground-based pyranometer measurements, (n.d.).

  • Optical thickness from pyranometer readings, incorperating aerosols.

[6]A Simple Empirical Equation to Calculate Cloud Optical Thickness from Shortwave Broadband Measurements, (n.d.).

  • Empircial curve fit, very simple, only valid to albedos of 0.3
  • optical thickness is a function of broadband iradiation
  • To construct the cloud optical thickness, either the Min algorithm or SBDART (Barnard et. al derived in 2001) are used.
  • Hu and Stammes, 1993 found that optical thickness is relatively constant over visible wavelengths.
  • Min and SBDART produce same result except for optical thikness<10
  • Error of ~1 for t=2, and decreases to 0 around 10
  • Min chosen becasue of computational efficiecny
  • t related to T (transmission) which is downwelling diffuse irradiance D/at the top of the atmosphere, Io. Io is solar constant times u0, min error of D is ~5w/m^2
  • Can measure C instead of I0, giving a modified transmission of D/C, C is clear-sky total irradiance, measured with the same device. (Lonk and Long and Ackerman. Using this method reduces seasonal dependance on aerosols.
  • r is of the form (D/Cu^alpha), with alpha chosen experimentally to be .25
  • D is corrected for IR loss according to Dutton, 2001 and Long,2003
  • Multi-Filter Rotating Shadowband Radiometer (MFRSR; Harrison et al. 1994)
  • cloud fraction (Long algorithm, Long 2001)
  • Sensitivity analysis using SBDART, Errors due to water vapour fraction are lowered by using C, because it takes this into account from the previous day's water content.
  • t e 5 exp[2.15 1 A 1 1.91 arctanh(1 2 1.74r)],

[7]Development and Evaluation of a Simple Algorithm to Find Cloud Optical Depth with Emphasis on Thin Ice Clouds, (n.d.).

=Error Analysis

Application to RTM modelling

Geographic Distribution of spectra

Effects of spectrum on PV technologies

Spectral effects on amorphous PV cells

--Effect of atmospheric parameters on the silicon solar cells performance, M. Chegaar, P. Mialhe Spectral effects simulated for Algeirs

effects in short-circuit current due to turbidity, decrease of: 4.41%, 4.7%, 7.34% for mono multi and amorphous. Turbidity decreases UV radiaiton

Increasing water vapour leads to decrease of 4.57%,4.4%, o.2% for same

Efficiency increase with air mass for crystalline, decrease for amorphous

-- [1. Rüther R, Kleiss G, Reiche K. Spectral effects on amorphous silicon solar module fill factors. Solar Energy Materials and Solar Cells 2002 Feb;71(3):375-385.]

amorphous silicon is more efficient in the summer

crystalline more efficient in winter

A:Si matches very well with indoor illumination spectra, they are more efficient indoors

Spectral mismatch factor: ratio between Isc rated and Isc extrapolated to 1000W/m2

Does not neccesarily hold true for a:Si cells: "However, in amorphous silicon solar cells, the proposition of the non-dependence of sðlÞ on the operating voltage does not hold. It is known that in p-i-n structures a typical blue-dispersion of the spectral response occurs for higher bias voltages [14]. Since the field-driven transport is the dominant mechanism with respect to diffusion, and since the electrical field is extended over practically the whole cell, the generation profile inside the cell produces a feedback on the internal quantum efficiency. In a-Si cell modelling, one takes advantage of this effect by application of the DICE method [12,15,16] to yield for a spatially resolved description of the field distribution inside the cell."

FF is the ratio between Imp and Isc

Used a filtered pyranometer to find "Red" and "Blue" spectra

Plots of FF vs Isc,shows much scatter in the central area of Isc.

Attrubited to the spectral effect, blue increasing FF, red to decrease it

Shows curves of spectral senstivity as a function of irradiation

--1. Rüther R, Livingstone J. Seasonal variations in amorphous silicon solar module outputs and thin film characteristics. Solar Energy Materials and Solar Cells 1995 Jan;36(1):29-43.

Outdoors testing of A:Si generally leads to better efficiency in summer, worse in winter

Attributed to thermal annealing and seasonal spectral variations

Conclusion of this paper is that spectral effects are dominating

first cells utilized indoors in calculators

power efficiency from 71% in winter to 83% in summer

bandgap from 360-780

Crystal silicon is better in the winter

therefore, the seasonal variatoin is likely due to the seasonal changes in spectrum, not annealing. Does not really support this with numbers

--R. Gottschalg, Experimental study of variations of the solar spectrum of relevance to thin film solar cells, Solar Energy Materials and Solar Cells. 79 (n.d.) 527-537.

useful fraction can very in the range of +6 to -9% from annual average

spectral mismatch factor: Fabero and Chenlo [7] and Merten [8] model the spectral mismatch with a spectral mismatch factor for the short circuit current of crystalline and amorphous silicon

Hirata and Tani [9], who used a pyranometer and 6 filters up to a maximum wavelength of 1200 nm and investigated the effect of the spectral changes on a-Si and c-Si devices.

Difficult to quantify the effects on multijunction units because it will cause a mismatch in the series connectes cells, leading to non-linear effects [13]

spectral effects though air mass and cloud cover(clearness index)

Annual fluctiations in useful fractions ~10%

--Y. Hirata, T. Tani, Output variation of photovoltaic modules with environmental factors--I. The effect of spectral solar radiation on photovoltaic module output, Solar Energy. 55 (1995) 463-468.

Panels set at 35.5 degrees due south

Calculated output based upon global irradiaiton

Compared this to actual output: 20% variation in A:Si, derived a 3.7% increase in output over predicted

--J. Merten, J. Andreu, Clear separation of seasonal effects on the performance of amorphous silicon solar modules by outdoor I/V-measurements, Solar Energy Materials and Solar Cells. 52 (1998) 11-25.

clearness index: H/H0/Hmax/Ho

I-V Curve at 10 min intervals

Use silver paste to T/C measurements

Spectral effect is ~16% increase in summer

--R. Gottschalg, T.R. Betts, D.G. Infield, M.J. Kearney, On the importance of considering the incident spectrum when measuring the outdoor performance of amorphous silicon photovoltaic devices, Meas. Sci. Technol. 15 (2004) 460-466.

The fraction of the specturm falling into spectrally useful ranges is 10% to -15%

Previous studies utilize clear sky models of irradiance for spectral disribution

< 10W/m2 ignored

Use a custom detector with spectral range 300-1700nm

Useful fraction is defined as ratio of irradiaion within useful range to total irradiaiton (300-780 nm)

UF for 300-1700nm is 60.4%

--[http://www.stefankrauter.com/info/23rd_EU_PVSEC_Krauter_Preiss_et%20al.pdf S. Krauter,, PV YIELD PREDICTION FOR THIN FILM TECHNOLOGIES AND THE EFFECT OF INPUT PARAMETERS INACCURACIES, (n.d.).] Outlines the errors in measurement for various PV technologies. Quantifies error due to albedo byt hrouwing out a number

Has created a computer program to simulate the performance of an a:Si PV module, however up to 20% inaccuracy due to innacuracy of inputs.

Good list of inputs for PV simulation

--R.P. Kenny, A. Ioannides, H. Müllejans, W. Zaaiman, E.D. Dunlop, Performance of thin film PV modules, Thin Solid Films. 511-512 (2006) 663-672.

Outdoors measurement of amorphous, crystalline and CIS modules

Using eppley spectroradiometer, 5 min scans up to 2500nm with integrating sphere

Air pressure utilized to measure pressure corrected air mass

Uses an ESTI reference cell, divided in two sections, one shorted with a shunt resistor and one open circuit. Cell temperature derived from open circuit voltage

Temperatuer coefficient for Voc

Contains equations for translating the Isc, Impp and Vmpp to STC, omitting curve correction factor

Shows mismatch factor for measurement of c-si, a-si and CIS with pyran and reference cell as reference. graphs show high mismatch factors for a-si when using both techniques. shows that using a pyranometer with MMF correction can remove spectral effects

spectral mismatch factor, calculations included

Tests performed on days with <20% diffuse fraction therefore spectram mismatch was largely dependant upon AM

Very comprehensive spectral evaluation resource

Spectral effects on c Si cells

--M. Simon, E.L. Meyer, The effects of spectral evaluation of c-Si modules, Prog. Photovolt: Res. Appl. 19 (2011) 1-10.

  • Defines Weighted Useful fractoin

Spectral modelling and prediction

Atmospheric turbidity


Atmospheric modelling