Models are the mathematical functions or algorithms designed to generate a desired solar radiation component from a set of inputs that can include other solar radiation related components, time and site information.
The need for models arose in order to conduct measurement each time a particular solar radiation component was needed in a particular location. Models is generally linked to a simple, easily available, solar radiation or related parameters to a more complex component that is not available.
The first models were developed to predict global irradiance from more commonly available quantities such as cloud cover and/or sunshine duration (Angstorm, 1924, Kimball, 1919).
In the 1940s and 1950s, ‘component to component’ models came into play with the work of Liu and Jordan (1960). Recently the interest has been growing for models capable of predicting solar radiation from remote sensing (satellite-based) observations.
The Liu and Jordan (1960) model was developed to related monthly averaged values of global and diffuse irradiance. Recently, however, most models have been developed to address hourly,
instantaneous, time scales. Hourly time scale is quasi-instantaneous, with a few exceptions; hourly, instantaneous, models are one and the same.
We placed the focus on the hour or less because:
1) From the physical standpoint, relationships between components lend themselves to a sound physical understanding with a known solar geometry – the solar geometry integration process a longer time scales ‘dilutes’ physical interpretation.
2) From the physical standpoint, this is the type of information that is in greatest demand.
We grouped the models into four categories:
a) Transposition models that relate one or more solar radiation components to another.
b) Meteorological models that convert standard meteorological data into solar radiation parameters.
c) Satellite models that convert satellite images into solar radiation parameters.
d) Stochastic models that can generate streams of synthetic solar radiation data from a limited number of parameters.
5.1 Input - Output and Parameterisation
When introducing or validating model, the first task is to specify its input and output parameters.
Input to a model consists of:
Review of the State of the Art: Solar Radiation Measurement and Modeling
1) Deterministic parameters, which including solar geometry or the means to derive it, i.e. time of day, time of year and site geometric coordinates, i.e. site elevation.
2) Information parameters, which are available from monitoring the programmes, such as cloud cover, global and direct irradiance.
These inputs can then be processed inside the model, for instance to parameterize insolation conditions, prior to producing the model output. As accurate as the model can be, its operational accuracy depends on the precision of its input. There should be encouragement to perform
sensitivity analysis to link input uncertainty to output accuracy. The validation and intercomparison of the models require precise input information, as well as precise output verification
measurements. IEA Task IX-B model evaluation, Hay and McKay, 1988, have shown the evaluation results are considerably influenced by the quality and precision of input-output data.
Information parameters should allow a model to adjust to these major influences, Since cloud cover and sunshine duration have been measured by numerous stations, they have been the first quantities that used to parameterize insolation conditions in global irradiation models. The relationship
between cloudiness and sunshine duration is far from linear relationship. Sunshine duration has the advantage over he cloud clover of being based on the measurement of the actual direct solar irradiance. However, because of its only reported as exceeding or not the threshold, sunshine duration can not be used to characterize the turbidity of the site
5.2 Component to component Model
5.2.1 Sunshine duration models (V.Estrada-Cajigal) fall under the empirical models consisted of simple regression approximating the real radiative transfer. Angstrom (1924) model used the mathematical expression for relationship with an empirical coefficient. Angstrom equation has been extensively used and applied to large number
of location.
H H /
0= a + bn / N
Where H is monthly averaged daily global radiation H0
is daily extraterrestrial irradiation n is monthly average sunshine hours N is day time length
Figure 6: Distribution of 4931 hourly diffuse fractions observed under solar radiation, h and clearness index, k, at Bergen, Norway
Review of the State of the Art: Solar Radiation Measurement and Modeling
5.3 Spectral model
Spectral irradiance data and models are needed in a variety of application spread over different disciplines. Spectral irradiance data are most useful to analyse the energetic response of
photovoltaic system, high performance glazing, selective coatings and daylighting applications.
Nann and Bakenfelder (1993) describe twelve possible uses of Spectral radiation models for solar energy system and buildings applications.
Figure 7: Beam spectral irradiance predicted by SMARTS2 and BRITE for a standard air mass 1.5 atmosphere with rural aerosol, as defined in ASTM (1987a) or ISO (1992).
5.4 Meteorological Model
Meteorological Model attempts to estimate solar radiation from information provided by weather stations. This approach is attractive because weather measurement sites vastly outnumber solar radiation measurement sites. Frequency distribution: most system responds non-linearly to weather parameters, average, frequency and normal distribution.
Figure 8: (1965-79) and AAS (1968-79)
at 60º N, based on observation at 7, 13, 19 CET
Review of the State of the Art: Solar Radiation Measurement and Modeling
distribution at Bergen
Figure 9: Pobability density function P of hourly (left) and daily (right) normalized clearness index
5.5 Auto correlation structure model
Most buildings and solar systems possess a dependent memory that response to
hourly irradiances, spectrum of time scale occur, which yields a positive autocorrelation for most of the weather parameters. Spectrum of time scale occur, which yields a positive autocorrelation for most of the weather parameters.
Figure 10: Percentile curves of daily and ten days global irradiation at Bergen (left) and AAS (right)
Review of the State of the Art: Solar Radiation Measurement and Modeling
Figure 11: Autocorrelation hourly function (average, variance, quadratic deviation) of the periodical alternating beam and diffuse irradiance
Figure 12: Autocorrelation weekly
function (average, variance, quadratic deviation) of the periodical alternating beam and diffuse irradiance (summer 1999-2002)
Figure 13: Autocorrelation monthly function (average, variance,
quadratic deviation) of the periodical alternating beam and diffuse irradiance ( 1955-2001)
Review of the State of the Art: Solar Radiation Measurement and Modeling
5.6 Cross correlation structure model
Solar systems response to any single weather parameters depends on the simultaneously and past values of other parameters.
Figure 14: Average monthly of air temperature vs global radiation at Bergen and AAS
5.7 Satellite Data
An important function of meteorological satellites is detecting cloud fields and monitoring their evolution in time over extended regions of the world
Figure 15: Compare in the north-eastern U.S.A. from satellite image (A) and U.S.
National Solar Radiation Database (B). NSRDB is based on combination of ground irradiance measurements and irradiances derived from meteorological observations
Review of the State of the Art: Solar Radiation Measurement and Modeling
∆
σ
2∑
= m iPki
1
P
Stochastic of daily and hourly time series of global irradiation and sunshine fraction were explored in the late 1970s. These models become the useful tool for im
be made from observed data. Substitute missing and spurious values, ex observation series, and data compression. The followings are the suggested m
5.8.1 Auto Regressive Moving Average (ARMA) Model
X (t + t) = x(t) + r(t)
Where r(t) is a random uncorrelated variables
x and r have zero mean and normally distributed Variance of r is (r) = 1-
5.8.2 Markov Transition Matrix Model (MTM).Equation:
u(t)
Where probability of transition from state i to j are computed for all case
φ
1φ
1ij
Figure 16: Hourly globala irradiance extrapolation RMSE error as a function of distance from station compared to observed satellite prediction error
5.8 Stochastic and Multi correlation
proving the use that can tending the length of an
odels:
i, j = 1,…., N, yielding the MTM matrix, starting from x(t) to a state k, the next state m is determined with the aid of a random uncorrelated variable u, uniformly distributed.
2
≥