Agricultural and Forest Meteorology 106 2001 41–59
Estimation of solar radiation in Australia from rainfall and temperature observations
D.L. Liu
∗
, B.J. Scott
NSW Agriculture, Wagga Wagga Agricultural Institute, PMB, Wagga Wagga, NSW 2650, Australia Received 1 May 2000; received in revised form 9 June 2000; accepted 21 June 2000
Abstract
This study evaluated the accuracy of several models for estimating daily solar radiation Q across Australia. Data from 39 sites were taken from MetAccess. The sites were grouped into four climatic zones. Coefficients of nine models, including
two newly developed formulae, were fitted for the 39 sites. Correlation coefficients R
2
between estimated Q and measured Q and root mean squared error RMSE associated with the estimates were calculated. It was concluded that models which
expressed rainfall as a binary quantity 1 for rainfall 0; 0 for rainfall = 0 performed better than those using amount of rainfall precipitation in mm. The best performed models, one using temperature data only, one using rainfall data only and
one using rainfall and temperature were further evaluated. A newly developed model that included temperatures minimum and maximum and rain-day information proved the best method. Using the coefficients for estimates of Q at the same sites,
averaged R
2
was 0.68, 0.74 and 0.79 and RMSE was 3.24, 3.05 and 2.89 MJ m
− 2
, for the model using rainfall only, temperature only and both rainfall and temperature, respectively. When Q was estimated using the coefficients from other sites, estimation
of Q within eastern and southern zones were more reliable than in northern and central zones. In general, the model using both temperature and rainfall was the best model for either estimated Q for the site where
coefficients of the model were developed at the site or imported from other sites. However, in some tropical coastal sites of Australia, such as Broome and Darwin, estimates of Q based on rainfall only can be more reliable when the coefficients were
imported from other sites. It was concluded that radiation within a similar climatic region could be well estimated with no local recording, regardless of distance between sites. © 2001 Elsevier Science B.V. All rights reserved.
Keywords: Solar radiation; Precipitation; Overcast conditions; Air temperature; Atmospheric transmittance
1. Introduction
Daily radiation is required by most models that sim- ulate crop growth because growth is primarily based
on the photosynthetic processes which involve the utilisation of radiation and its conversion to chemi-
cal energy. However, solar radiation is an infrequently measured meteorological variable, compared to tem-
perature and rainfall. In Australia, the meteorological
∗
Corresponding author. E-mail address: de.li.liuagric.nsw.gov.au D.L. Liu.
database MetAccess Donnelly et al., 1997 contains 16,000 weather stations, nearly all of which have daily
rainfall records while 1,400 stations have records of temperature. Only 50 stations have records of solar ra-
diation. Lack of solar radiation data is also common in other countries, such as USA Richardson, 1985;
Hook and McClendon, 1992 and Canada De Jong and Stewart, 1993, and can be a major limitation to
the use of crop growth simulation models.
In order to use crop simulation models, techniques are required to estimate radiation based on other com-
monly measured meteorological variables for the days
0168-192301 – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 1 9 2 3 0 0 0 0 1 7 3 - 8
42 D.L. Liu, B.J. Scott Agricultural and Forest Meteorology 106 2001 41–59
or years when the data are missing, or for the sites when the data are not measured. Two methods used
to generate radiation data are stochastic generation Nicks and Harp, 1980; Richardson, 1981; Richard-
son and Wright, 1984 and empirical relationships Bristow and Campbell, 1984; McCaskill, 1990a,b;
Hook and McClendon, 1992; De Jong and Stewart, 1993; Hunt et al., 1998.
An example of stochastic weather generation is the method using a continuous multivariate stochastic
process to generate weather data including radiation Richardson, 1981; Richardson and Wright, 1984.
Sharpley and Williams 1990a,b adopted this ap- proach to generate radiation data using only the
monthly means of daily radiation as inputs.
Stochastic generated data may be useful to explore possible model scenarios for an average theoretical
situation of long term simulation. However, the data generated by this approach cannot be used for model
validation and simulation analysis for a particular period of time as the method may not generate the
data to match the actual weather at a particular time of interest. It fails to generate weather extremes reli-
ably, such as frost that can damage crops Wallis and Griffiths, 1995.
Using empirical relationships requires the devel- opment of a set of equations to estimate solar radia-
tion from the commonly measured meteorological variables. A number of formulae and methods have
been reported using this approach Fitzpatrick and Nix, 1970; Bristow and Campbell, 1984; Richardson,
1985; Hook and McClendon, 1992; De Jong and Stewart, 1993. Daily total extraterrestrial radiation
Q
o
is often included in the relationships. The under- lying approach is to express solar radiation reaching
the earth surface Q as a fraction of Q
o
. This is based on the attenuation of incoming radiation through
the atmosphere. The physics involved in the interac- tion between radiation and atmospheric constituents
are complex, but the relationship between the atmo- spheric transmittance and some weather variables can
be empirically described. Parameters used as inputs in the relationships include sunshine duration Hux-
ley, 1973; Schulze, 1976; Boisvert et al., 1990, mean humidity Fitzpatrick and Nix, 1970, temperature
Richardson, 1985, rainfall McCaskill, 1990a,b, or in combination Hook and McClendon, 1992.
Hayhoe 1998 recently evaluated the empirical ap- proaches for estimating solar radiation and compared
them to stochastic weather generation Sharpley and Williams, 1990a,b. He found that an empirical model
based on temperature and rainfall provided better estimates than the stochastic model.
Availability of weather data at locations varies from only one variable to several variables, so models de-
veloped should suit the varying availability of data. The aim of this study was to evaluate the accuracy and
applicability of several models for estimating daily value of solar radiation Q across Australia for differ-
ent situations: only rainfall available, only temperature available, or both rainfall and temperature available at
a site with or without some radiation recordings.
2. Materials and methods
