Pierre Ineichen

Modeling daylight availability and irradiance components from direct and global irradiance

This paper presents the latest versions of several models developed by the authors to predict short time-step solar energy and daylight availability quantities needed by energy system modelers or building designers. The modeled quantities are global, direct and diffuse daylight illuminance, diffuse irradiance and illuminance impinging on tilted surfaces of arbitrary orientation, sky zenith luminance and sky luminance angular distribution. All models are original except for the last one which is extrapolated from current standards. All models share a common operating structure and a common set of input data: Hourly (or higher frequency) direct (or diffuse) and global irradiance plus surface dew point temperature. Key experimental observations leading to model development are briefly reviewed. Comprehensive validation results are presented. Model accuracy, assessed in terms of root-mean-square and mean bias errors, is analyzed both as a function of insolation conditions and site climatic environment.

A NEW SIMPLIFIED VERSION OF THE PEREZ DIFFUSE IRRADIANCE MODEL FOR TILTED SURFACES

A new, more accurate and considerably simpler version of the Perez[1] diffuse irradiance model is presented. This model is one of those used currently to estimate short time step (hourly or less) irradiance on tilted planes based on global and direct (or diffuse) irradiance. It has been shown to perform more accurately than other models for a large number of locations worldwide. The key assumptions defining the model remain basically unchanged. These include (1) a description of the sky dome featuring a circumsolar zone and horizon zone superimposed over an isotropic background, and (2) a parameterization of insolation conditions (based on available inputs to the model), determining the value of the radiant power originating from these two zones. Operational modifications performed on the model are presented in a step by step approach. Each change is justified on the basis of increased ease of use and/or overall accuracy. Two years of hourly data on tilted planes from two climatically distinct sites in France are used to verify performance accuracy. The isotropic, Hay and Klucher models are used as reference. Major changes include (1) the simplification of the governing equation by use of reduced brightness coefficients; (2) the allowance for negative coefficients; (3) reduction of the horizon band to an arc-of-great-circle; (4) optimization of the circumsolar region width; and (5) optimization of insolation conditions parameterization.

A new operational model for satellite-derived irradiances: description and validation

We present a new simple model capable of exploiting geostationary satellite visible images for the production of site/time-specific global and direct irradiances The new model features new clear sky global and direct irradiance functions, a new cloud-index-to-irradiance index function, and a new global-to-direct-irradiance conversion model. The model can also exploit operationally available snow cover resource data, while deriving local ground specular reflectance characteristics from the stream of incoming satellite data. Validation against 10 US locations representing a wide range of climatic environments indicates that model performance is systematically improved, compared to current visible-channel-based modeling practice.

A new airmass independent formulation for the Linke turbidity coefficient

We propose a new formulation for the Linke turbidity coefficient with the objective of removing its dependence upon solar geometry. In the process, we also develop two new simple clear sky models for global and direct normal irradiance.

Making full use of the clearness index for parameterizing hourly insolation conditions

An enhanced parameterization of insolation conditions based only on the knowledge of global irradiance is presented. Two limitations associated with the current approach using the clearness index are pointed out: its dependence on solar elevation and its inability to differentiate between different conditions that produce the same global irradiance. Suggestions are provided which could overcome part of these limitations. Arguments are substantiated with solid experimental evidence. It is further shown that noticeable gains in accuracy for the decomposition of global into direct and diffuse irradiance are possible if one makes optimum use of the information available within a global irradiance time series.

Climatic evaluation of models that predict hourly direct irradiance from hourly global irradiance: Prospects for performance improvements

This paper presents a comprehensive evaluation of recent models designed to predict direct from global irradiance on a short time step basis. Three models are selected for the present evaluation. These were proposed by Erbs et al., Skartveit and Olseth, and Maxwell. Model validation is performed against a large array of experimental data: A total of over 60,000 global and direct data points from 14 sites in Europe and the United States. Environments range from humid oceanic to desertic, including humid continental, high altitude, subtropical, and polluted. It is found that specific models are better adapted to certain climatic types than others. However, each model is found to have a “generic” insolation-dependent error pattern across all climates. This error pattern may be deterministically corrected and yield substantial performance improvement without additional input data.

Direct luminous efficacy and atmospheric turbidity—Improving model performance

Of all the atmospheric constituents, aerosol content is shown to be responsible for the greatest variations in direct luminous efficacy. Some clarity is brought to the comparison between Linkes and Angstroms turbidity coefficients, respectively TL and β. Greniers recent formulation of the optical thickness of a water and aerosol free atmosphere is presented here in a simplified expression. Based on these results and Dogniauxs illuminance turbidity factor, Til, two direct luminous efficacy models are derived, one of which is tuned to our experimental data. The input parameters are optical air mass, β, and water vapour content in the tuned version. These models perform significantly better than any of twelve other models found in the literature when compared to 1 yrs measurements from each of two sites in the U.S. and Switzerland. In both sites, β was derived from horizontal visibility estimated in a nearby airport.

Equivalence of pyrheliometric and monochromatic aerosol optical depths at a single key wavelength

The atmospheric aerosol optical depth (AOD) weighted over the solar spectrum is equal to the monochromatic AOD at a certain wavelength. This key wavelength is ~0.7 mum, which is only slightly influenced by air mass and aerosol content. On the basis of this result, simple relations are proposed to predict monochromatic AOD from pyrheliometric data and vice versa. The accuracy achieved is close to ?0.01 units of AOD at ~0.7 mum, estimated from simultaneous sunphotometer data. The precision required for the estimation of the precipitable water-vapor content is approximately ?0.5 cm.

Ground-reflected radiation and albedo

The diffuse radiation incident on an inclined plane is composed of both the ground-reflected radiation and the sky diffuse radiation. The evaluation of the sky diffuse radiation has already been described in many references. In this paper we focus on the ground-reflected radiation, its relation to insolation conditions and its evaluation by means of models. We used six data banks from the following four countries: Switzerland, France, The Netherlands, and the U.S.A. We investigated how the albedo depends on the amount and the composition of the incident radiation, on geometrical parameters such as the height and/or the azimuth of the sun and on meteorological parameters such as the humidity. We did not find any notable dependence. We also tested different models evaluating the ground-reflected radiation on tilted planes with corresponding measurements on an inverse horizontal plane (facing the ground) and on inclined planes. We came to the conservative conclusion that the best results are obtained when using a constant averaged measured albedo, for transposition to tilted surfaces, when assuming the ground-reflected radiation to be isotropic.

The importance of correct albedo determination for adequately modeling energy received by tilted surfaces

The aim of this work is to demonstrate the importance of correct estimation of the radiation reflected by the ground and perceived on a tilted surface. A good evaluation of the reflected radiation is an essential complement to any diffuse radiation and daylight transposition model.