temporal dynamics of photosynthetically active radiation (par) and

1

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

2

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

3

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.

6

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

13

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

15

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

16

(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

19

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).


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



34

Table 3. Comparison of the monthly averaged hourly fEs (n=86~96).


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



35

Table 4. Comparison of the monthly averaged hourly fFECs (n=86~96).


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



36

Table 5. Comparison of the monthly averaged hourly LPRs (n=86~69).


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


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


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.

temporal dynamics of photosynthetically active radiation (par) and

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