Estimating hourly incoming solar radiation from limited
meteorological data
Kurt Spokas
Corresponding Author. U.S. Department
... [Show More] of
Agriculture—Agricultural Research Service (USDAARS) North Central Soil Conservation Research
Laboratory, 803 Iowa Avenue, Morris, MN 56267;
[email protected]
Frank Forcella
USDA-ARS North Central Soil Conservation
Research Laboratory, 803 Iowa Avenue, Morris, MN
56267
Two major properties that determine weed seed germination are soil temperature
and moisture content. Incident radiation is the primary variable controlling energy
input to the soil system and thereby influences both moisture and temperature profiles. However, many agricultural field sites lack proper instrumentation to measure
solar radiation directly. To overcome this shortcoming, an empirical model was developed to estimate total incident solar radiation (beam and diffuse) with hourly
time steps. Input parameters for the model are latitude, longitude, and elevation of
the field site, along with daily precipitation with daily minimum and maximum air
temperatures. Field validation of this model was conducted at a total of 18 sites,
where sufficient meteorological data were available for validation, allowing a total of
42 individual yearly comparisons. The model performed well, with an average Pearson correlation of 0.92, modeling index of 0.95, modeling efficiency of 0.80, root
mean square error of 111 W m22, and a mean absolute error of 56 W m22. These
results compare favorably to other developed empirical solar radiation models but
with the advantage of predicting hourly solar radiation for the entire year based on
limited climatic data and no site-specific calibration requirement. This solar radiation
prediction tool can be integrated into dormancy, germination, and growth models
to improve microclimate-based simulation of development of weeds and other plants.
Key words: Energy balance, germination modeling, light, microclimate, weed development.
The quantity of solar radiation reaching the earth’s surface
varies dramatically as a function of changing atmospheric
conditions as well as the changing position of the sun
through the day. Solar radiation controls both thermal and
moisture balances of the soil system, and accordingly it is a
major variable in soil physic models (Flerchinger and Saxton
1989). Additionally, the amount of radiation is a primary
factor for plant growth (Steckel et al. 2003; van Dijk et al.
2005), is a component in crop–weed interactions (Lindquist
2001), and influences weed seed germination rates (Miles et
al. 2002). Thus, solar radiation is a deterministic quantity
that can be used for improving current efforts on weed seed
germination and growth modeling.
Previous modeling efforts of total incoming solar radiation (Rs
) have been conducted. The simplest assumption is
that solar radiation varies as a sine function through the day
(Liu 1996; Monteith 1965):
t R 5 S sin , [1] s noon 1 2 Lday
where Rs is the solar radiation at time t, Snoon is the solar
radiation at solar noon, and Lday is day length. The major
limitation is that the Snoon value is still needed.
Bristow and Campbell (1984) developed an empirical algorithm for estimating Rs using daily maximum and minimum air temperatures. Their model reduces the total daily
solar radiation incident at the top of the atmosphere (Ra)
by a correction factor calculated from the temperature extremes and is given by:
R 5 R C [A[1 2 exp(2B(DT ) )] s a [2]
where A, B, and C are empirical coefficients unique to each
location and DT is the difference between Tmax and Tmin.
Because of the empirical constants, the Bristow and Campbell model requires calibration, which involves a large
amount of meteorological data (including solar radiation)
and is numerically complex (McVicar and Jupp 1999). Despite these factors, the Bristow and Campbell model has
been the basis for a large variety of derivative models (e.g.,
Ball et al. 2004; Donatelli et al. 2003; Goodwin et al. 1999;
Wong and Chow 2001) and some that have tried to reduce
the amount of site-specific calibration (Antonic´ 1998).
Another model that estimates daily total radiation was
formulated by Hargreaves and Samani (1985). They observed that total solar radiation was related directly to the
square root of the differences between daily temperature extremes (Tmax 2 Tmin) as well as geographical information.
This relationship is given by:
R 5 R (k )Ï(T 2 T ) , [3] s aR max min
where Ra is the extraterrestrial radiation (W m22), which is
calculated from geometric relationships; Tmax is maximum
air temperature (C); Tmin is minimum air temperature (C);
and kR is an adjustment coefficient (0.16–0.19 C20.5). The
correction factor is empirical and is determined by the (kR )
s
geographical location with recommended values of 0.16 for
sites away from water bodies (interior) and 0.19 for locations near water bodies (coastal) (Hargreaves and Samani
1985). Gautier et al. (1980) have developed algorithms for
estimating daily solar radiation from satellite imagery. However, satellite data are expensive and not typically available
for the field-scale predictions.
More complex equations to estimate solar radiation also
exist but require extensive amounts of detailed meteorological data, such as wind speed, relative humidity, dew point
temperature, and cloud cover (e.g., Monteith 1965; Nikolov
Spokas and Forcella: Solar model • 183
TABLE 1. Decision matrix used to assign value for atmospheric
transmitivity (t).
Conditions Value of t
No precipitation at DT . 10C (assumed clear sky
conditions)
No precipitation today, but precipitation fell the
previous day
Precipitation occurring on present day
Precipitation today and also the previous day
t 5 0.70
t 5 0.60
t 5 0.40
t 5 0.30
a DT is defined as (Tairmax 2 Tairmin).
and Zeller 1992). However, application of these complex
relationships for an agricultural weed model is limited since
detailed meteorological data (e.g., cloud cover and dew
point temperatures) are not typically available. An example
of this limited availability is illustrated in Texas, where there
is only one weather station for every 40,000 ha of irrigated
farmland (Henggeler et al. 1996). Globally, it has been estimated that the ratio of the weather stations monitoring
solar radiation compared to those that do not is around 1:
500 (Thornton and Running 1999).
Empirical models for the prediction of total solar radiation have been used successfully in water balance models
(ASCE-EWRI 2004) but to date have not been implemented for weed seed germination modeling. Another drawback is that a majority of the developed empirical models
have used daily time steps, which do not lend themselves to
model the soil microclimate conditions that do change drastically diurnally and to which the seeds of many species
respond (Lang 1996). The goal of this paper is to present a
revised model that will extend the empirical-mechanistic relationships to include precipitation events as well as predictions of total solar radiation on an hourly basis for the ultimate purpose of improving weed development models.
Materials and Methods
Total radiation energy from the sun can be separated into
two basic components: direct beam radiation (Sb) and diffuse solar radiation (Sd). The sum of these two results in the
total incident solar radiation (Rs
) and is represented by
Rsbd 5 S 1 S [4]
The local intensity of solar beam radiation is determined by
the angle between the direction of the sun’s rays and the
earth’s surface. The location of the sun is given by the angle
between the sun location and the normal to the surface,
referred to as the zenith angle (C). Zenith angles vary temporally and geographically but are a function of the time of
day, latitude, and time of year by the following relationship
(Campbell and Norman 1998):
cos C 5 sin(F)sin(d ) SD
1 cos(F)cos(d )cos[0.0833p*(t 2 t )] SD sn [5]
where C is the zenith angle (radians), F is the latitude of
the site (radians), t is the time (standard time), tsn is the
time of the solar noon, and dSD is the solar declination angle
(radians; Equation 6). Zenith angle will change during the
day and is a function of latitude as well as seasonal differences as captured by the solar declination angle. Solar declination ranges from 10.130p to 20.130p radians, with
the extremes occurring on summer and winter solstices, respectively. Solar declination angle can be found by the following formula (Campbell and Norman 1998):
sin(d ) SD
5 0.39785 sin[4.869 1 0.0172J
1 0.03345 sin(6.2238 1 0.0172J )], [6]
where J is the calendar day with J 5 1 on January 1 and J
5 365 on December 31 (or 366 during leap years).
The model chosen for the beam radiation is from Liu
and Jordan (1960), where the beam radiation (Sp) is given
by:
m Sp 5 Spot [7]
where Spo is the solar constant (1,360 W m22), t is the
atmospheric transmittance, and m is the optical air mass
number. The optical mass number (m) is found from the
following relationship (Campbell and Norman 1998):
Pa m 5 , [8] 101.3(cos C)
with Pa being the atmospheric pressure (kPa) at the site and
C the zenith angle from Equation 5. Average barometric
pressure was estimated from the relationship (Campbell and
Norman 1998):
2(a/8,200) P 5 101.3e , [9] a
where a is the elevation of the site (m).
Atmospheric transmittance (t) is the percentage of the beam
(direct) radiation that will penetrate the atmosphere without
being scattered. Gates (1980) suggested values of 0.6 to 0.7
for clear sky conditions. Additional values for atmospheric
transmittance for a variety of conditions and topographic
slopes can be found in Sellers (1965) and Nikolov and Zeller
(1992). For this model, 0.70 was used for clear skies and was
the same value used for all sites. Clouds are the primary variable that determines the amount of direct beam solar radiation
reaching the surface of the earth. Consequently, regions with
higher cloud density (e.g., humid regions) receive less solar
radiation than the cloud-free climates (e.g., deserts). For any
given location, solar radiation reaching the earth’s surface decreases with increasing cloud cover. The range in daily temperature extremes was assumed to be an important factor in
determining the presence or absence of clouds (Mahmood and
Hubbard 2002), along with precipitation. Table 1 presents the
decision matrix that was established to determine the atmospheric transmittance for the modeled day. This matrix is based
on the concept that wet and dry days affect solar radiation
through influences on cloud cover, which is in agreement with
other models (Acock and Pachepsky 2000; Bristow and Campbell 1984; W [Show Less]