Temporal dynamics of Photosynthetically Active Radiation (PAR) and
Transcript of Temporal dynamics of Photosynthetically Active Radiation (PAR) and
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Temporal dynamics of Photosynthetically Active Radiation (PAR) and
dependence on climatic conditions: seasonal trends, diurnal patterns, and estimation
of ground-based intensity in coastal northern California
Shaokui Ge1,2, Richard G. Smith1*, Marc G. Kramer2 and Raymond I. Carruthers1
1, USDA-Agricultural Research Service, Western Regional Research Center, Exotic and
Invasive Weed Research Unit, 800 Buchanan Street, Albany, CA 94710, USA
2, Department of Earth & Planetary Sciences, University of California, Santa Cruz, CA
95064, USA
Keywords: extraterrestrial solar radiation, Global solar radiation, Clearness index, Energy
efficiency, Energy fraction, Photosynthesis, Biofuel, vegetation production, Photon flux,
Plant growth
Abstract
The seasonal trends and diurnal patterns of Photosynthetically Active Radiation
(PAR) were investigated in the San Francisco Bay Area of Northern California from
March through August in 2007 and 2008. During these periods, the daily values of PAR
flux density (PFD), energy loading with PAR (PARE), and ground broadband solar
radiation (SR) averaged 48.51 mol/m2, 2938.88 watts/m2, and 6208.95 watts/m2,
respectively. PFD and PARE had strong seasonal trends. However, the energy ratio of
PAR to broadband solar radiation (fE) and the conversation efficiency of flux to an
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energy alternative (fFEC) were relatively conserved, but still not constant. Values of both
PFD and PARE were low in March, with monthly averaged daily values of 30.28 mol/m2,
1828.77 watts/m2, respectively. They approached their daily maximums in June at 59.91
mol/m2 and 3638.29 watts/m2, near the summer solstice. They then decreased back to
relatively low levels in August. In parallel, the monthly averaged daily fE and fFEC
changed from 43.60% and 2.01 µmol/J in March to 48.81% and 2.23 µmol/J in June,
respectively. In particular, the lost ratio of PAR loading energy (LPR), was studied for
the firstly time in a study of this type. It had an average daily value of 32.49%. LPR was
highest in March (41.37%) and lowest in June (21.76%). PFD, PARE and LPR all
exhibited clear diurnal patterns, but there existed no significant differences in fE or fFEC
among the morning hours. However, differences between them appeared in the
afternoons. PFD and LPR were highly correlated with selected climatic and astro-
geometric factors, including broadband solar radiation, temperature, relative humanity,
and solar elevation. PFD and LPR were estimated more easily and precisely than either
fE or fFEC. In this study, two models were calibrated and validated to estimate PLR and
PFD from broadband solar radiation and the atmospheric clearness index Kt, and
calculated solar elevation.
Introduction
Photosynthetically Active Radiation (PAR) is often regarded as the spectral range
of global solar radiation at wavebands spanning from approximately 0.4 µm through
0.7µm (McCree, 1972; Alados & Alados-Arboledas, 1999; Jacovides et al. 2004). This
portion of the solar radiation spectrum is extremely important, because it is the sole
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energy source for vegetative photosynthesis to provide us with products such as food and
fiber sources, biofuel carriers and additional material sources that support industrial
process (Mariscal et al. 2000; Tsubo & Walker, 2005; Myers, 2005). In general, plants
use PAR as an energy source to convert CO2 and water through photosynthesis into
organic compounds (typically sugars) that are then used to synthesize structural and
metabolic energy required for plant growth and respiration, as well as stored vegetative
products that result in plant biomass (McCree, 1972; Udo & Aro, 1999; Tsubo & Walker,
2005). Thus, there often exists relationship between intercepted PAR and dry matter
biomass production (Mariscal et al. 2000). Effective and precise estimation of PAR on
the ground is therefore critical to model plant growth and biological production in
different vegetation ecosystems (Alados & Alados-Apboledas, 1999). Such models could
help reasonably integrate various vegetation management practices and optimize solar
energy conversion into biology-formatted energy. This is of importance both for
modification of conversion efficiency of solar energy into biological products and for
better understanding growth patterns of economically important species as well as pest
plants, such as invasive weeds (Spitters et al. 1986; Papaioannou et al. 1993; Alados et
al. 1996; Gueymard, 2000).
The most commonly studied characteristics of PAR are the energy ratio of PAR to
the broadband solar radiation, i.e., fE (Kvifte et al., 1983; Papaioannou et al., 1986; Udo
& Aro, 1999; Tsubo & Walker, 2005), the flux/energy conversion of PAR (fFEC, also
called flux energy efficiency) (Alados et al., 1996; Udo & Aro, 1999; Alados et al. 1996;
Alados & Alados-Arboledas, 1999; Al-Shooshan, 1997; Finch et al., 2004; Jacovides, et
al. 2004, 2007), and the photon flux density (PFD) (McCree, 1969; Papaioannou et al.,
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1993; Alados et al. , 1996; and Jacoivdes, et al. 2004). These quantitative
characteristics described qualities of PAR from different perspectives, but these values
can be readily converted to one another using specific conversion constants (McCree,
1972; McCartney, 1978; Udo & Aro, 1999).
Previous studies have shown that various aspects of PAR exhibit seasonal trends.
For example, PFD was found to be much lower during cool dry seasons, and highest at
the end of hot dry seasons. Additionally, its daily values change significantly during
warm wet seasons, and but less during hot dry seasons (Finch et al, 2004). fE was
measured to be 0.5 during clear and dry summer days, but reduced 0.46 during similar
winter days (Szeicz, 1974). In general, fE was found to range between 0.45 and 0.5
across worldwide areas (Kvifte et al. 1983; Tsudo & Walker, 2005). It was further found
that daily and seasonal patterns of PAR are dependent on local climatic conditions, such
as sky brightness, air clearness, solar elevation (Jacovides, et al. 2004,) and dewpoint
temperature (Alados et al. 1996).
PAR was also found to vary with the time scale (Udo & Aro, 1999) and
geographical region of assessment (Stigter & Musabilha, 1982; Udo & Aro, 1999), which
makes local evaluation important for many applications. After comparing differences of
fE it was demonstrated that fE in the tropics could not to be extrapolated from values
assessed in higher latitudes (Udo & Aro, 1999). The monthly average hourly fFEC values
had notable diurnal patterns, but the daily and seasonal fFEC varied only slightly during
dry months, compared with those values within wet season months (Udo & Aro, 1999).
The daily average values of fE were not significantly affected by atmospheric and sky
conditions, but day-to day differences were related to cloud cover (McCree, 1966; Szeicz,
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1974; Britton & Dodd, 1976; Papaioannou et al., 1993), because the effect of cloud
events plays out at a longer scale than hourly ones (Udo & Aro, 1999). Therefore, it was
concluded that although fE is not a constant, it is relatively conservative in daily or
monthly averaged values, however, within-day patterns are extremely important and
affect overall plant growth. These diurnal patterns of PAR were considered to be
dominating factors in controlling diurnal variation of important ecophysiological
processes of plants, e.g. photosynthesis, photoinhibition, and net ecosystem energy
exchange (Mohotti & Lawlor, 2002; Mission et al., 2005).
PAR plays very important roles in plant growth, and it is the principal factor in
regulating the rate of solar energy conversion into biological mediated energy. Therefore,
it is a required parameter that must be estimated to predict the production of plant
products and biomass (Goudriaan & van Laar, 1994; Asner & Wessman, 1997; and
Mariscal et al., 2000). Even though PAR is of extreme importance to human endeavors
such as agriculture and bioenergy production, a routine network for its measurement is
not available. Thus, PAR either must be locally measured or estimated from existing
measures of solar radiation. A very rough estimation of PAR that has long been used is
that PAR is approximately half of incident global solar radiation, but it is clear that this
estimate is sub-optional for many uses and that more precise models to estimate PAR are
needed. This need to estimate PAR with more accuracy and efficiency has resulted in a
number of studies focusing on two of critical PAR related values and thus two respective
predictive models, i.e. fE (e.g. Tsubo & Walker, 2005) and fEFC (e.g. Jacovides et al.
2004). These existing PAR estimation models included astro-geometric parameters such
as solar elevation, and climatic factors such as temperature and relative humidity.
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Usually, these models employ an indirect deriving factor, i.e. the clearness index Kt,
which is calculated with two levels of solar radiation, one on the ground and the other
from the extra-terrestrial system, respectively. These models commonly assume that the
ground gaining part of PAR flux from the extra-terrestrial system varies with short wave
scattering and long wave absorption caused by cloudiness, water vapor, ozone, dust and
aerosols (Misson et al. 2005; Jacovides et al. 2007). In practice, when PAR is transmitted
from the top of atmosphere to earth, the ratio of PAR energy lost (LPR) to its initial
energy in the extra terrestrial system, is more directly related to these atmospheric
conditions than the gaining part of PAR on the ground. However, no attention is paid to
this missing portion of PAR that is lost in the atmosphere (LPR).
This study is the first step of a larger research effort to assess canopy-level PAR
dynamics under natural field condition as an incident value. This is being conducted to
estimate the absorbed PAR, which is being used to predict plant growth for an important
invasive weed, yellow starthistle (YST), Centaurea solstitialis. YST is an exotic species
from Eurasia that has invaded many areas in the western United States, where it is
considered one of the most noxious weeds in the states of California, Idaho, Oregon and
Washington (Roche and Thill, 2001). Such information is extremely important for efforts
aimed at the development of biological and other integrated management programs for
various plants. Beyond this project, estimation of PAR will also be used to explore
similar plant growth topics, e.g., crop and biofuel production and other plant-based
growth studies. In this study, our immediately objectives are (1), to investigate trends of
PAR related values, i.e. PFD, its alternative value as an energy term (PARE), fE, fFEC,
and the ratio of lost PAR (LPR) to total extra terrestrial PAR, including diurnal patterns
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during the primary plant growing season from March through August in Northern
California; (2), to find relationships between these PAR relevant parameters and climatic
factors commonly measured in local weather stations and calculable solar predictions
(e.g. solar elevation, day length, etc.) that can be used in predictive physical models, and
(3) to develop models to precisely estimate hourly values of PAR in Northern California
field sites.
Methods
Study site
The primary field study site was a grass dominated hill slope infested with
moderate densities of YST. This site is adjacent to Chabot Regional Park located near the
City of Moraga, California in the San Francisco Bay region of the state. This area is
characterized by a typical Mediterranean climate, with warm dry summers and cool wet
winters. The rainy season typically begins in October and runs through the following
March, while the dry season runs from April through September. During the dry season,
however, there is periodic fog due to an emergent marine layer that inundates the land at
night but often dissipates during a mid-day. The study periods from March through
August represent YST's main growing season in this area. Thus, the field aspects of our
study focused on the dry season months ranging from March to August, as this is the time
period most critical for YST population development and spread.
Data collection and processing
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This study was conducted in two sequential plant-growing seasons during the
spring and summer of 2007 and 2008. In the first year of the study, PAR data were
collected within a whole day from sunrise to sunset every two weeks from June through
August 2007. In the second year of the study, PAR data were collected within two days
from sunrise to sunset every week from March through August 2008. PFD data were
measured using an AccuPAR LP-80 Ceptometer (Decagon Devices, Pullman, WA). The
ceptometer was set to automatically collect PAR data every 15 minutes. Commonly
collected climatic data were download from the website of California Irrigation
Management Information System (CIMIS), a state agency in California, and included
hourly ground solar radiation, vapor pressure, air temperature, precipitation, relative
humidity, and dew point temperature. In addition, in order to control errors of cosine
effect of solar elevation angels, this study only focused on hourly data when the averaged
solar elevation was greater than 0.21 radians during the observational hour, thus early
morning and evening results were not included in these assessments (sampling times
varied as the seasons changed).
The hourly and daily astro-geometric parameters were calculated as shown in
Appendix I. Using these procedures, the longitude and latitude (-122.12W, 37.84N) of
the study site were required for calculation of extra-terrestrial solar radiation, sunrise
time, sunset time, length of daytime, and day angle, which were all estimated daily. The
declination angle, the solar angle, and the solar elevation were calculated at the middle of
the local solar hour and used to relate the calculated and corresponding observed values
during each hourly sampling period. Accordingly, the clearness index (Kt) was defined
as the ratio of ground based broadband solar radiation energy measured at the local
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weather station to the corresponding solar radiation calculated for the extraterrestrial
system for all the daylight sample periods. For the extraterrestrial system, fE was
assumed to be 40% of broadband solar radiation (Monteith & Unsworth, 1990).
PFD was obtained using the following formula:
where, is an instantaneous reading of PFD from the LP-80 ceptometer during a short
time interval (typically every 15 minutes). This sampling interval accounted for the
time required to obtain one reading and thus n is the number of intervals in an hour. The
default unit of an instantaneous measure of PFD is µmol/m2/s. When PFD was presented
as an hourly value, the unit was mol/m2/hour (1 mol=106µmol), and similarly, the daily
PDF was accumulated as mol/m2/day.
Conversion of PAR from a photon flux to an energy unit requires expensive
detailed spectral and solar radiation data. To simplify such conversions, hourly PAR
quantum flux is often converted into its energy counterpart (PARE) using the constant
conversion factor of 4.6 µmol/Joule (J) (McCree, 1972; Jones et al., 2003). This
conversion was of a conservative quantity (McCartney, 1978) and thus adequate for our
experimental and modeling purposes. After transforming PFD into its energy alternative,
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fE was calculated as the ratio of PAR loading energy relative to the overall energy of
broadband SR measured at the local weather station in the City of Moraga.
When light was transmitted from the extra-terrestrial system through the sky to
the ground, LPR in the trace of transmission was calculated as followed:
where, LPR is the percentage of energy of extra-terrestrial PAR lost in the atmosphere;
is the broadband solar radiation from the extra-terrestrial system; PARE is the
energy alternative of PFD; and 0.4 is a constant which stands for the energy part of PAR
in broad band solar radiation from the extra terrestrial system (Monteith & Unsworth,
1990).
Also, fFEC was represented as PFD per energy unit (Joule) of broadband solar
radiation at the study time period, (e.g. an hour or a day). Hourly PFD was accumulated
within the day when hourly solar elevation was higher than 0.21 radians to estimate a
daily PFD. Daily fE, was estimated as the ratio of the energy alternative of daily PAR
flux, to the energy of broadband solar radiation commonly measured as an energy unit at
local weather stations, but typically not as the average of hourly fE. Similarly, the daily
fFEC was calculated as the daily sum of PAR flux divided by daily energy-termed
broadband solar radiation. These values were then averaged across each month to get a
monthly averaged daily PFD, fE and fEFC. PAR values from the same hourly period
were then averaged within each month to get monthly-averaged hourly values. For
example, the monthly averaged hourly PAR value at 12:00 pm was calculated as the
mean of all the corresponding PAR values measured at 12:00 pm during each day across
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the entire month. Thus, in this analysis, we assessed the seasonal trends of monthly
averaged PAR values at two time scales, using data averaged daily and data averaged
hourly for each given month. Then, using Tukey’s Honestly significant differences
(HSD) test, the seasonal trends and diurnal patterns of PAR parameters (PFD, fE, fFEC,
and PLR) were evaluated based on the comparisons of the monthly averaged hourly
values. The seasonal trends were determined by comparisons of monthly averaged hourly
values of PAR among the same hourly periods, spanning from the sunrise to sunset. In
March, the PAR collected time was between 8:00 and 17:00. From April through August,
they were set between 7:00 and 18:00, respectively. The seasonal trends were assessed by
significance of differences of monthly averaged hourly values among different months
from March through August. The diurnal patterns of PAR relevant values were judged
by the differences of monthly averaged hourly values within the same seasons.
Correlation analysis was used to examine associations between these PAR-related
values and important climatic factors as well as astro-geometric parameters, including
ground based broadband solar radiation, air temperature, relative humidity, vapor
pressure, dew point temperature, solar elevation (transformed to its sine function), and
the clearness index (Kt). From the associated variables, two different assembles of
independent variables were selected on the basis of their adjusted R2 with the dependent
PAR values. These selected variables were then used to develop multiple linear models to
estimate hourly PAR. About three-forths of these hourly values (n=375) were randomly
selected for model calibration, while the remaining one-forth (n=126) was used to
validate these two models.
Results
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Astro-geometric characteristics
Across the entire year, the calculated geometric characteristics showed the
expected trends in solar occurrence patterns (Figure 1). The daytime lengths in our study
site were between 14.63 hours around the summer solstice and 9.37 hours around the
winter solstice. Their sunrise local times are 4:50am, 7:26am, respectively. During our
experimental days, the minimum day length was cut off at 11.13 hours on the first day of
March with sunrise at 6:47am. Extrapolating for the whole year, the maximum and
minimum daily extra-terrestrial solar radiations are 12027.72 watt/m2 in summer and
3991.43 watt/m2 in winter. The hourly solar radiation from the extraterrestrial system is
extremely high at about 1330 watt/m2 at 12:00 pm at peak times near summer solstice in
June. The monthly averages of solar elevation at local noon hours from January across
the whole year to December were radians of 0.54, 0.67, 0.86, 1.07,1.24, 1.31, 1.27, 1.14,
0.94, 0.74, 0.58, and 0.51, respectively. The corresponding averages of hourly solar
radiation from the extra terrestrial system were 780.31 watt/m2, 875.80 watt/m2, 1071.93
watt/m2, 1238.68 watt/m2, 1318.48 watt/m2, 1325.27 watt/m2, 1291.32 watt/m2, 1209.88
watt/m2, 1069.81 watt/m2, 892.87 watt/m2, 731.65 watt/m2, and 661.68 watt/m2,
respectively. In addition to these seasonal trends, the geometrics also showed strong
diurnal patterns driven by solar elevation angles, with low values at the time of sunrise,
approaching the maximum values around noon, and returning to low values at sunset.
Such diurnal features are fundamental driving factors in determining the diurnal patterns
of PAR at the hourly scale.
PAR seasonal trends
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During the field sampling days in 2007 and 2008, the averaged hourly values of
directly measured PFD and broadband solar radiation were 4.25mol/m2 and
543.61watts/m2, respectively, while, the means of the converted fEs, fFEC, and LPR
were 0.46, 2.17µmol/J, and 32.49%. At a daily scale, the averaged values of PFD,
broadband solar radiation, fE, fFEC, and LPR were 48.51mol/m2, 6208.95watts/ m2, 0.47,
2.16 µmol/J, and 29.32%, respectively. These PAR relevant values also showed strong
seasonal trends (Figure 2). In March, the averaged daily value of PFD was 30.28 mol /m2.
It increased from April through June to a peak value of 59.91 mol/m2 at the summer
solstice and then started to decrease in July. Ground based daily solar radiation and PARE
displayed patterns similar to PFD. Monthly averaged daily PARE in March was 1828.77
watts/m2, which increased to 3638.29 watts/ m2 in June. The monthly averaged daily
fFEC ranged from 2.01 µmol/J in March to 2.23 µmol/J in June. The corresponding fEs
were 0.44, 0.49 in March and June, respectively. LPRs were 41.37% and 21.76% in these
two months.
Individual averaged hourly PAR values also revealed strong seasonal patterns
(Tukey’s HSD test, P<=0.05; Tables 1-5). Values of hourly PFD at different hours across
a day was very low in March, when compared with the corresponding hourly values in
any month ranging from April to August (Table 1).
Insert Tables 1 &2
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Regardless of the hours, PFD in March never exceeded than 5.0 mol/m2/hour.
However, during the late spring and early summer months from May through July,
averaged hourly PFD was greater than 5 mol/m2/hour from about 10:00 am to 15:00 pm.
Only during the early mornings and late afternoons, was hourly PFD lower than 5
mol/m2. PARE also displayed a seasonal trend (Table 2). The Maximum of hourly PARE
was 301.45 watt/m2/hour in March. The hourly PARE from April through August
generally exceeded 300 watt/m2/hour from 10:00am to 15:00pm, and was even greater
than 400 watt/m2/hour during noon hours in the summer months. However, compared
with PFD and PARE, fFEC and fE were less variable (Table 3 & 4). The values of fE
and fFEC were relatively low in both Match and April, with hourly fE only exceeding 0.5
at 12:00 pm in April. From May to August, fE mostly exceeded 0.5 from 10:00 am to
14:00 pm. However, when comparing values of fE at the same morning hour intervals
(sunrise to 12:00pm) for different months, the monthly averaged hourly values of fE was
not found to differ substantially. To some extent, differences of hourly values of fE were
observed in the afternoon hours. Similarly, fFECs for the morning hours were quite
similar across different months. The only exception appeared after sunrise at 7:00 am in
both July and August, which was likely caused by the long wave absorption due to moist
air from the early morning fog. Similar to fEs, fFECs were also different during the same
hours in the afternoon. On the other hand, more PAR lost (LPR) was observed early in
the season from March to April, especially during early mornings and late afternoons.
Therefore, based on comparisons of monthly averaged hourly values of PFD, PARE, fE,
fFEC and LPR, these PAR relevant parameters were broken down into four different
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seasonal periods: the early spring (March), the late spring (April), the summer (May,
June, and July), and the late summer (August).
Insert tables 3, 4 & 5.
PAR diurnal patterns
During the experimental periods in 2007 and 2008, we observed clear diurnal
patterns in the monthly averaged hourly PAR relevant values (i.e. PFD, PARE, fE, fFEC,
and PLR) within the above four seasonal periods. When we confined the averaged hourly
values at an individual given hour from sunrise to sunset, the hourly PFD changed
between 0.22 mol/m2 and 8.22 mol/m2, the hourly PARE between 13.56 J/m2 and 496.08
J/m2, hourly fFEC between 1.05 µmol/J to 3.35 µmol/J, and fE between 0.32 and 0.72.
These hourly-scale changes are responsible for the observed diurnal patterns.
During the early mornings in March, the averaged hourly PFD was much smaller
due to the low solar elevation angles. Hourly PFD was found to be between 0.47 mol/m2
and 1.19 mol/m2 with an average of 0.85 mol/m2/h at 8:00am in March. Around solar
noons from 12:00 to 13:00, on average it approached nearly 5.00 mol/m2, with the range
of 2.44 ~ 6.07 mol/m2. After 15:00, the flux returned to a low level once again. At this
time of the year, the averaged hourly fFEC and fE were 1.36~2.26 mol/J and 0.29~0.49,
respectively.
After comparing the differences of these PAR relevant values among individual
averaged hourly estimates in March, the diurnal patterns of PAR were separated into
three periods to cover similar response levels within days for March, (i.e. time periods
between 8:00~9:00, 10:00~15:00, and 16:00~18:00 were not significantly different
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(P<=0.05, using Tukey’s HSD test)). Among these periods, differences of PFD and
PARE were clearly significant, while fE and fFEC did not differ (Tukey’s HSD test,
P>0.05), indicating that fE and fFEC are highly conserved.
In April, the PFD increased significantly, thus PARE also become higher. In
particular, during the noon hours the PFD was more than 6.00 mol/m2, and PARE was
nearly 400 watt/m2. However, the fE, fFEC, and LPR again remained similar to those
values calculated in March. The fE did not exceed 0.50, with a single exception of fE
being 0.54 at 12:00. Valuses for fFEC were generally between 1.45 µmol/J and 2.49
µmol/J. During solar noon hours in April, the LPR was approximately 20%, which was
less than that estimated in March. Five distinct diurnal periods showing similar patterns
of PAR were identified for the month of April using the Tukey’ HSD test (i.e., time
periods between 7:00~8:00, 9:00, 10:00~15:00, 16:00, and 17:00~18:00, (P<=0.05)).
During the months of May through July, PFD approached a high level. During
solar noon hours, hourly PFD was 6.99 mol/m2. Thus, the resulting fE and fFEC were
higher than the corresponding values found in March and April. The averaged hourly
fFEC at noon was between 2.18 and 2.43 µmol/J, and fE values were higher than 0.50.
Significant testing, revealed almost continuous changes in the diurnal hourly patterns
with significant differences found in 10 of the 13 hour groups examined (i.e. time period
between 7:00, 8:00, 9:00, 10:00, 11:00-14:00, 15:00, 16:00, 17:00, 18:00, and 19:00
(Tukey’s HSD test, P<=0.05). Apparently, during these three months, PAR values
frequently change more in magnitude on an hour by hour base, especially during the early
mornings and late afternoon hours. Essentially, PAR is highest in value and stable
primarily in the middle of the day from 11:00 to 14:00.
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In August, values of PFD and PARE had similar levels to that in April. PFD
started with 0.75 mol/m2/h at 7:00, approached a maximum of 6.47 mol/m2/h at noon, and
then decreased to 0.69 mol/m2/h at 18:00. It was noted that fE and fFEC were both high
in the early mornings in August. When investigating the associated climatic conditions, it
was found that such high values were associated with high atmospheric moisture caused
by seasonal fog. Using Tukey’s HSD test, the diurnal patterns were again determined to
be significant during the following five periods: 7:00, 8:00~9:00, 10:00~15:00, 16:00,
and 17:00~18:00 (P<0.05). These significant diurnal patterns in the magnitude of PAR
within days and across months suggest that the variability in PAR should to be taken into
account when estimating photosynthetic activity in plants. It is thought that hourly
estimation of photosynthesis would be more accurate and reliable in capturing detailed
photosynthetic changes than a daily estimation, that may cause large errors in estimation,
particular, during summer months, when these differences are the largest.
Association of PAR values with climatic conditions and astro-geometrics
We investigated relationships between PAR-relevant values and several climatic
and astro-geometric variables (Table 6). Results revealed that the selected variables had
high correlations with PFD and LPR. Variation in hourly PFD and LPR was highly
dependent on solar elevation angle (and its sine function), Kt, and ground based solar
radiation (SR). Of the measured climatic factors, temperature and relative humidity were
the most highly correlated with PFD. Similarly, LPR was also closely correlated with the
same five factors as discussed previously (see Table 6). In addition, vapor pressure was
found to relate highly to LPR.
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Insert table 6
As a routinely measured climatic factor, broadband solar radiation demonstrated
strong correlations with PFD and LPR, but not with fE and fFEC. Their correlation
coefficients were 0.97, 0-0.85, 0.44 and 0.44 on an hourly scale (n=501, p<0.00). These
relations made PFD and LPR to be easily estimated on an hourly scale. It was clearly
noted that LPR and PFD were more highly associated with Kt than with other factors.
This analysis documented that PAR was conserved best within clear days. Therefore, it
was concluded that the primary effect of Kt was to affect the atmospheric degradation of
PAR as the sunlight transits the atmosphere.
Estimation models of PAR-deriving values
Based on Mallow’s Cp values, R2 and adjusted R2 from the calibration subset
(n=375), SR was chosen as the main effect variable and integrated its interaction with
solar elevation and the clearness index to develop the following estimation model.
(1)
(n=375, R2=0.96, p<0.01)
where, PFD is the hourly flux density *PAR (mol/m2/hour), SR is ground based
broadband solar radiation (watt/m2), se is the solar elevation, and Kt is the atmospheric
clearness index.
Using an independent subset (n=126) of the original observed data, the fitted
model and parameters of hourly PFD were successfully validated (Figure 3). These
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analyses demonstrated outstanding model performance based on a strong positive
correlation coefficient and a highly significant probability (R2=0.95, n=126, p=0.00). It
was found that the estimated flux closed the predicted actual flux (Figure 3), with an
offset of only 0.18 mol/m2/hour. The slope of 0.93 (not different than 1.0) was
approximately was unity, which implied that the estimated values followed the same
pattern as the measured values across the entire ranges of the independent variables.
Therefore, it was concluded that the hourly PFD could be precisely estimated from the
ground solar radiation (SR) measurements together with field measurements of relative
humidity and calculated actual solar elevation angles on the hourly-scale.
An estimation model was also constructed to assess LPR from Kt and solar
elevation. The optimal model treated Kt as a main effect and involved the interaction of
Kt with relative humidity and solar elevation angles as follows.
(2)
(n=375, R2=0.84, p=0.00, Figure 4.)
where, LPR is the ratio of lost energy of PAR in the atmosphere and extraterrestrial
radiation; Kt is the clearness index (a ratio of SR on the ground to the original solar
radiation from the extraterrestrial system); and se is the combined daily and hourly solar
elevation.
When this model and its estimated parameters were validated using the reserved
set of 126 independent observations, it was found that LPR could also be adequately
estimated for our research site. When comparing estimated values with actual values
20
calculated directly from field measured values, it was found they were highly correlated
and statistically significant (R2=0.82, n=126, p=0.00, Figure 4). However, a small offset
of 0.0721was noted in this assessment. This offset implies that the resulting model
overestimated LPR by 7.21%. On the other hand, the slope of the validation function
revealed that the relationship between the estimated and measured values was close
(slope = 0.86), thus the model seemed to accurately follow the routine course of LPR
calculated from our measured environmental parameters.
Discussion
Variability of PAR values
Both fE and fFEC are two very important characteristics of PAR, because they are
closely related to light use efficiency in plant growth (McCree 1972; Papaioannou et al.,
1993; Alados et al. 1996), and also are important for global climate change and related
issues (Hanan et al. 2002). Therefore, many studies have focused on these two
characteristics of PAR, where it has been concluded that fE and fFEC are conserved but
slightly variable, rather than constant (Udo & Aro, 1999; Tsubo & Walker, 2005). Across
the worldwide range of latitudes, the mean of fEs is known to vary between 0.43 and 0.49
with individual values only ranging from 0.41 to 0.52, when PAR was defined as sunlight
wavebands between 0.4 and 0.7 µm (Kvifte et al. 1983; Tsubo & Walker,
2005).Variability increases, however, with changes in timescale from long (seasonal
means) to short (hourly means). While, within a season, the daily ratios did not vary
much from day to day, or even from month to month (Udo & Aro, 1999). In most studies,
daily fE was assumed to not vary significantly with latitude, daytime, or dates (Williams
21
1976). Jacovides et al. (2004) similarly demonstrated that fFEC changed seasonally from
only 2.006 in the winter to 1.989 in the summer, with an annual mean of 1.995. Although
variable, this variation was less than the measurement uncertainty and thus might be
ignored. The corresponding daily and hourly values of fFEC changed from 1.865 to 2.01
µmol/J and from 1.878 to 2.197 µmol/J, respectively. In this study, the monthly averaged
daily fE and fFEC changed from 0.44 to 0.49 and from 2.01 µmol/J to 2.23 µmol/J,
respectively. These values were very similar to values mentioned above. It was also
found that the seasonal differences of fE and fFEC at a daily scale were not as large as
those values recorded at the hourly scale. These results further confirmed that the effect
of the timescale has important consequences for the conversion of PAR flux to its energy
load and PAR fraction of broadband solar radiation. The hourly values can capture more
detailed changes of PAR values than those daily values.
Due to the conservative nature of fE and fFEC, the effect of sky conditions on
their values was limited, to some extent. As a comprehensive indicator, the clearness
index (Kt), has been regarded as a key factor correlated with variation found in fE and
fFEC. Within different ranges of Kt, fEs was usually presented as mean values cross a
region of Kt, and then linearly regressed with Kt, (e. g. Tsubo & Walker, 2005) to build
estimation model of fEs. Such studies broke Kt values down to three common intervals,
using the midpoint of an interval of kt vs. means of fE to develop a linear model to
estimate fE. Although this method was used to estimate fE with a certain accuracy, it
induced additional errors into the estimation process. In reality, using the midpoints of
the Kt intervals and means of fE corresponding to these segments for model calibration,
was actually a procedure that caused data smoothing. Such an approach easily found
22
general trends between Kt and fE or fFEC, but this approach also lost useful information
that has the potential to capture more subtle changes in these relationships. For example,
when Kt is on the boundaries of these intervals, the resulting estimation typically over- or
under-estimated the expected values. In our study, no close relationship was found
between Kt and fE nor fFEC. However, using the hourly PAR data, it was found that
PFD and LPR very closely correlated with the clearness index (Kt). In fact, LPR had a
correlation coefficient (R) of -0.85 (n=501, p=0.00) with Kt. Therefore, it was
demonstrated that PFD and LPR could be estimated more accurately than fE and /or
fFEC, given their underlying their high correlations with atmospheric and astro-
geometric conditions.
We also found that PFD and LPR significantly changed with both season and
diurnal time, but fE and fFEC were nearly constant, especially within a day. During the
study period, PFD was low in March while LPR was high. Both of these variables were
measured at moderate levels in April and August. PFD, while highest from May through
June to July. During this same time period, LPR was low. Both fE and fFEC revealed
only subtle differences during the six months of our primary growing season of our
Northern California study area. It was further found that fE and fFEC were very similar
in the mornings across the entire study season, increasing only a little around solar noon.
Such dampened diurnal patterns of fE and fFEC were different from a reported diurnal
pattern (Jacovides et al. 2004, 2007), which had high ratios in early mornings and late
afternoons but were low around mid-day. This is presumably due to differences in local
climate conditions. We therefore assume that the short-wave scattering of light dominated
changes of solar radiation in our case, resulting in more PAR lost than the long wave
23
portion of the spectrum. Such loss is correlated with the transit path of sunlight in air
before becoming incident on the ground and/or vegetation canopies. Therefore, values of
fE and fFEC were low in the early mornings and late afternoons, and high around solar
noon hours, following a trend opposite of solar elevation. Another possible reason for this
reduction in PAR was that effect of urban aerosols on the shortwave portion of PAR,
which may have been stronger than that of the long-wave solar radiation (Jacovides et al.
1997). Urban aerosols were also thought to be highest during early mornings and late
afternoons, associated with heavy traffic patterns in the adjacent San Francisco
metropolitan area.
Predictability of PAR values
PAR exert important affects on the ecophysiological characteristics of plants, thus
various models have been developed to estimate values of PAR as necessary to aid in
applications of plant physiology, biomass production and natural illumination in
greenhouses (Alados et al., 1996). These models ranged from physics-based radiation
transfer models, to more descriptive empirical models. The physics-based models have a
reasonable and reliable scientific underpinning, but are often complex making it difficult
to obtain all of the required parameters. Thus, their detailed requirements make them
difficult and costly to use, especially if they are fully developed. Thus, empirical models
have proven to be both reasonable and useful in practice (Al-Shooshan, 1997). These
empirical models are often based on different ground-based climatic factors and/or astro-
geometric parameters, that generally are in the form of multiple linear regression models.
A more reliable and accurate method is to incorporate important correlated factors into
more complex models for more accurate estimations (Udo & Aro, 1999). Some of these
24
models force the intercept to be zero thus requiring the models go through the origin
(Udo & Aro, 1999; Jacovides et al., 2004). Such models although simple and direct to
obtain, may induce large errors, especially when estimating values at an hourly time
scale. At an hourly scale the diurnal variations in these PAR relevant values clearly. [In
these situations, the model intercepts might be treated as an offset, which sourced from
the trends at longer terms than at the study timescale. Therefore, when forcing the
estimation models to going through the origin, the result could remove the long-term
trends and overweight variables at a fine scale, such as hourly data. Accordingly, in this
study, multiple linear models with offsets were used to estimate PAR values. In addition,
prior to this study, the models published to date only considered the main effects of the
weather and astro-geometric variables, while their interactions have never been taken into
consideration or incorporated into predictive models (Alados et al., 1999; Tsubo &
Walker, 2005)). In this study, it was clearly revealed that these interaction terms played a
very important role in improving model estimation. After developing the fitted models of
LPR, they were extended to estimate PARE in 2008 at our study site, which allowed the
dynamic prediction of the hourly values of PAR (figure 5). In our research, this is the first
step in the process of applying a plant growth model to assess YST growth and
development, which we hope will aid in establishing new management strategy to
effectively control this invasive weed and further prevent its spread. The application of
these models to predict PAR and PAR related values at different time scales, may also be
useful for other activities such as the affect of changing climate conditions on plant
growth, or for biofuel production and thus should be of interest to others.
25
Acknowledgements
This project is funded by a grant from NASA for a joint cooperation invasive species
control program between NASA and USDA. We thank MS. Marie Franc for the project
coordination and Ms. Skye Harper for the field assistance. We also appreciate California
Department of Water Sources for providing the online weather data through the
California Irrigation Management Information System (CIMIS).
Appendix
Day angle (DA):
(a)
Where JD is Julian day, starting on January 1, ending December 31. In the leap
years, 365 in (1) is replaced by 366.
Corrected solar constant (CSC) (watt/m2 or KJ/m2/hour)
(b)
Where Isc= 4921 watt/m2 or 1367 KJ/m2/hour.
E0 often is simply approximated as (Beckman, 1980):
(c)
So at any instant the intensity of solar radiation at the extraterrestrial system
(SRex) can be calculated as:
(d)
Where is the zenith angle, and is calculated from the following
equation:
26
(e)
where is latitude of the study site, is solar declination, and is the hour angle
from noon, at 15°C per hour.
Solar declination is converted from its sine function as follows:
(f)
The hourly and daily solar radiation on the top of atmosphere from the
extraterrestrial system may be integrated from the equation (d) during a time period of an
hour and a day, respectively (modified from Elminir (2007) and Whillier ()).
For hourly values,
(g)
Where is the sunrise hour angle, the value of .
For daily values, .
27
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32
Table 1. Comparisons of monthly averaged hourly PAR flux (PDF, mol/m2/ hour,
n=68~96) in 2007 and 2008 in Moraga, California.
Time March April May June July August
7:00 0.75a 1.06ab 1.61b 1.04ab 0.75a
8:00 0.85a 1.92b 2.29bc 3.10bc 2.09bc 1.81b
9:00 2.00a 3.49ab 3.86b 4.64b 3.49b 3.00ab
10:00 3.31a 4.81ab 5.37ab 5.99b 5.30ab 4.73ab
11:00 4.36a 5.64ab 6.45ab 6.99b 6.67b 5.59ab
12:00 4.99a 6.41ab 6.99b 7.49b 7.46b 6.47ab
13:00 4.44a 6.31b 6.99b 7.34b 7.52b 6.70b
14:00 3.94a 5.28b 6.57bc 7.12bc 6.98bc 6.07b
15:00 3.30a 4.71ab 5.72b 6.06b 5.96b 5.34ab
16:00 2.15a 3.43bc 4.24d 4.70d 4.54d 3.81bc
17:00 1.17a 1.82bc 2.55d 3.11d 2.97d 2.05ab
18:00 0.68a 1.09ab 1.64b 1.45b 0.69ab
Note: For a given hour interval, values sharing the same letter are not significantly
different at the P<0.05 level (Tukey’s HSD test).
33
Table 2. Comparison of the monthly averaged hourly PARE (watts/m2, n=68~96).
Time March April May June July August
7:00 45.25 a 64.17ab 96.92 b 62.5 ab 45.36 a
8:00 51.62 a 115.83 ab 138.32 ab 187.41 b 126.16 ab 109.42 ab
9:00 120.91 a 210.98 ab 233.13 b 280.40 b 210.46 ab 180.92 ab
10:00 200.16 a 290.69 ab 324.5 ab 361.69 b 320.05 ab 285.53 ab
11:00 263.33 a 340.67 ab 389.5 ab 422.04 b 402.77 b 337.75 ab
12:00 301.45 a 387.23 ab 422.31 b 452.11 b 450.28 b 391.00 ab
13:00 268.05 a 380.87 b 421.89 b 443.1 b 454.40 b 404.61b
14:00 237.83 a 362.08 ab 396.57 b 429.83 b 421.76 b 366.43b
15:00 199.49 a 284.63 ab 345.63 b 366.14 b 360.13 b 322.29 ab
16:00 129.97 a 207.38 b 255.92 bc 283.83 c 274.33 c 229.88 bc
17:00 70.72 a 109.6 b 154.23 bc 187.83 c 179.11 c 123.7 b
18:00 92.85 a 65.68 a 99.1 a 87.7 a 41.68 a
Note: For a given hour interval, values sharing the same letter are not significantly
different at the P<0.05 level (Tukey’s HSD test).
34
Table 3. Comparison of the monthly averaged hourly fEs (n=86~96).
Time March April May June July August
7:00 0.32a 0.36a 0.42ab 0.45b 0.43b
8:00 0.38a 0.44b 0.41b 0.46b 0.44b 0.45b
9:00 0.41a 0.45a 0.45 a 0.49 a 0.48a 0.49 a
10:00 0.47 a 0.48a 0.51 a 0.50 a 0.53a 0.49 a
11:00 0.48 a 0.49a 0.52 a 0.51 a 0.53a 0.53 a
12:00 0.49 a 0.54a 0.51 a 0.51 a 0.52a 0.53 a
13:00 0.44 a 0.49ab 0.50 ab 0.51 b 0.52b 0.50 ab
14:00 0.42 a 0.49ab 0.47 ab 0.51 b 0.5 b 0.47 ab
15:00 0.45 a 0.46 a 0.47 a 0.49 a 0.48a 0.48 a
16:00 0.37 a 0.44ab 0.44 ab 0.46 b 0.46b 0.43 ab
17:00 0.29 a 0.38ab 0.38 ab 0.42 b 0.4 b 0.36 ab
18:00 0.31 a 0.31 a 0.36 a 0.33a
Note: For a given hour interval, values sharing the same letter are not significantly
different at the P<0.05 level (Tukey’s HSD test).
35
Table 4. Comparison of the monthly averaged hourly fFECs (n=86~96).
Time March April May June July August
7:00 1.47 a 1.67 ab 1.91 ab 2.05 b 2.28 b
8:00 1.74 a 2.03 a 1.90 a 2.11 a 2.02 a 2.16 a
9:00 1.91 a 2.09 a 2.08 a 2.23 a 2.21 a 2.08 a
10:00 2.18 a 2.23 a 2.33 a 2.32 a 2.43 a 2.27 a
11:00 2.23 a 2.24 a 2.40 a 2.36 a 2.43 a 2.25 a
12:00 2.26 a 2.49 a 2.33 a 2.37 a 2.4 a 2.45 a
13:00 2.03 a 2.26 ab 2.32 ab 2.34 b 2.37 b 2.31 ab
14:00 2.05 a 2.25 ab 2.18 ab 2.35 b 2.31 b 2.14 ab
15:00 1.91 a 2.10 a 2.17 a 2.25 a 2.22 a 2.20 a
16:00 1.70 a 2.04 ab 2.00 ab 2.14 b 2.06 b 1.96 ab
17:00 1.36 a 1.73 ab 1.74 ab 1.91 b 1.83 b 1.64 ab
18:00 1.45 a 1.36 a 1.65 a 1.51 a 1.10 a
Note: For a given hour interval, values sharing the same letter are not significantly
different at the P<0.05 level (Tukey’s HSD test).
36
Table 5. Comparison of the monthly averaged hourly LPRs (n=86~69).
Time March April May June July August
7:00 0.60 a 0.57 a 0.43 a 0.59 a 0.52 a
8:00 0.61 a 0.46 a 0.46 a 0.31 a 0.50 a 0.45 a
9:00 0.46 a 0.33 0.34 a 0.22 a 0.39 a 0.39 a
10:00 0.36 a 0.27 a 0.25 a 0.17 a 0.24 a 0.24 a
11:00 0.31 a 0.25 a 0.20 a 0.14 a 0.16 a 0.22 a
12:00 0.28 a 0.21 a 0.19 a 0.14 a 0.12 a 0.16 a
13:00 0.38 a 0.20 ab 0.19 ab 0.16 b 0.12 b 0.13 b
14:00 0.42 a 0.22 ab 0.20 ab 0.15 b 0.15 b 0.17 b
15:00 0.45 a 0.31 ab 0.22 ab 0.20 b 0.20 b 0.17 b
16:00 0.54 a 0.38 ab 0.31 b 0.26 b 0.28 b 0.27 b
17:00 0.62 a 0.55 ab 0.44 b 0.37 b 0.39 b 0.46 ab
18:00 0.42 a 0.62 b 0.50 ab 0.55 ab 0.69 b
For a given hour interval, values sharing the same letter are not significantly different at
the P<0.05 level (Tukey’s HSD test).
37
Table 6. Significant correlation coefficients (r) of four PAR-relevant values with climatic
variables and astro-atmospheric parameters (n=501, r>=0.11, p<=0.01).
PFD LPR fE or fFEC Sin(solar elevation)/solar elevation
0.93/0.92 -0.72/-0.73 0.61/0.62
Ground solar radiation 0.97 -0.87 0.53 Kt
0.70 -0.85 0.13
Vapor pressure
-0.15 0.21
Air temperature
0.45 -0.40 0.18
Relative humidity
-0.42 0.35
Dew point temperature 0.19
Note: r is the correlation coefficients between PAR values and the selected associated
independent variables.
38
Figure legends
Figure 1, The periodic patterns of the calculated geometric values of (a), day lengths; (b),
local times of sunrise and sunset; and (c), daily solar radiation from the extra terrestrial
system.
Figure 2, The seasonal trends of monthly averaged daily values of PAR and PAR related values. (a), Measured daily PAR flux density, PFD; (b), Measured daily ground based broadband solar radiation, SR (watts/m2); (c), Measured daily Photosynthetically Active Radiation (PAR) loading energy; (d), Measured daily energy ratio, fE (PAR/SR); (e),Daily fFEC; and (f) Calculated daily ratio of lost PAR to PAR from extraterrestrial radiation.
Figure3, Comparison of model predictions and measured field observations for estimation of hourly PAR flux density (PFD). Figure 4, Comparison of model predictions and measured field observations for estimation of hourly PAR loading energy (LPR). Figure 5, Accumulated energy of hourly PAR estimated from the fitted model of LPR.
39
0 100 200 300
Julian days in a year
9
10
11
12
13
14
Day
leng
th in
hou
rs
0 100 200 300
Julian days in a year
5.0
5.5
6.0
6.5
7.0
7.5
Sunr
ise
loca
l tim
e in
hou
rs
16.5
17.0
17.5
18.0
18.5
19.0
19.5
Suns
et lo
cal t
ime
in h
ours
Sunrise timeSunset time
40
0 100 200 300
Julian days in a year
4000
6000
8000
10000
12000
Dai
ly e
xtra
-terr
estr
ial s
olar
radi
atio
n (J
oule
s)
Figure 1.
41
(a), Measured daily PAR flux density, PFD.
(b), Measured daily ground based broadband solar radiation, SR (watts/m2).
42
(c), Measured daily Photosynthetically Active Radiation (PAR) loading energy.
(d), Measured daily energy ratio, fE (PAR/SR).
43
(e), Daily fFEC
(f) Calculated daily ratio of lost PAR to PAR from extraterrestrial radiation.
Figure 2.
44
0 2 4 6 8
Hourly PFD from field measured data (mol/m2/hour)
0
2
4
6
8
Hou
rly P
FD e
stim
ated
from
the
mod
el(m
ol/m
2/h
our)
Figure 3.
0.0 0.2 0.4 0.6 0.8
LPR calculated from PAR the measured on the ground
0.0
0.2
0.4
0.6
0.8
Estim
ated
LPR
from
Ass
ocia
ted
clim
atic
fact
ors
Figure 4.
45
Figure 5.