On the stability of radiometric ratios of photosynthetically active radiation to global solar radiation in Tsukuba, Japan

Agricultural and Forest Meteorology 209–210 (2015) 59–68

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On the stability of radiometric ratios of photosynthetically active radiation to global solar radiation in Tsukuba, Japan Tomoko Akitsu a,∗ , Atsushi Kume b , Yasuo Hirose c , Osamu Ijima d , Kenlo Nishida Nasahara a a

Faculty of Life and Environmental Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8572, Japan Ashoro Research Forest, Department of Forest and Forest Products Sciences, Faculty of Agriculture, Kyushu University, 1-85 Kita-5jo, Ashoro, Hokkaido, 089-3705, Japan c Center for Global Environmental Research, National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba 305-8506, Japan d Aerological Observatory, Japan Meteorological Agency, 1-2 Nagamine, Tsukuba 305-0052, Japan b

a r t i c l e

i n f o

Article history: Received 7 November 2014 Received in revised form 13 April 2015 Accepted 27 April 2015 Available online 21 May 2015 Keywords: PAR Solar radiation Ratio Water vapor pressure Solar zenith angle Clearness index

a b s t r a c t The precise measurement of incident photosynthetically active radiation (PAR) is crucial for the estimation of ecosystem vegetation productivity. However, reliable values of PAR are seldom measured routinely. Instead, it is sometimes estimated based on solar radiation (RS ). One popular estimation method is by use of the conversion ratio PAR/RS . Depending on whether PAR is expressed in energy units (PE , W m−2 ) or photon units (PP , ␮mol m−2 s−1 ), there are two types of conversion ratios: PE /RS (unitless), or PP /RS (␮mol J−1 ). Moreover, to translate PAR expressed in one unit to another, the ratio PP /PE (␮mol J−1 ) is also important. However, past studies have not led to a general understanding of these ratios, mainly due to instrumental errors such as cosine errors. To reduce such errors, we developed a new PAR measurement system using grating spectroradiometers mounted on sun trackers to measure direct and diffuse PAR separately. The present study aims to clarify the characteristics of these three ratios using this new, more precise measurement system and radiative transfer simulation. We carried out measurements for one year in Tsukuba, Japan (36.05◦ N, 140.13◦ E). PE /RS increased with water vapor pressure (e) from 0.40 to 0.47 and increased with decreasing clearness index (kT ), but did not strongly depend on solar zenith angle (). PP /RS also increased with e from 1.9 ␮mol J−1 to 2.2 ␮mol J−1 . Its dependence on climatic factors was similar to that of PE /RS . PP /PE varied by about 3% around the value of 4.57 ␮mol J−1 . © 2015 Elsevier B.V. All rights reserved.

1. Introduction Photosynthetically active radiation (PAR), which is defined as radiation in the 400–700 nm waveband (McCree, 1972), is critical for photosynthesis. However, reliable values of PAR are seldom measured routinely (e.g., Alados et al., 1996; Ge et al., 2011; Ross and Sulev, 2000; Tsubo and Walker, 2005). Quantum sensors commonly used for PAR measurement have problems with their accuracy (e.g., Mizoguchi et al., 2010). In contrast, solar radiation (RS ; W m−2 ) is routinely measured worldwide with high accuracy, for instance, at all sites of the World Climate Research Program’s Baseline Surface Radiation Network (WCRPBSRN). Therefore, models that estimate PAR based on RS are useful and have been reported by many authors. Such models are classi-

∗ Corresponding author. Tel.: +81 298534897; fax: +81 298534897. E-mail address: [email protected] (T. Akitsu). http://dx.doi.org/10.1016/j.agrformet.2015.04.026 0168-1923/© 2015 Elsevier B.V. All rights reserved.

fied into two types. One uses the constant ratio PAR/RS . Depending on whether PAR is expressed in energy units (PE , W m−2 ) or photon units (PP , ␮mol m−2 s−1 ), there are two types of ratios: PE (unitless) RS

 PP  unit : molJ−1 . RS Various values for PE /RS have been reported (e.g., Blackburn and Proctor, 1983; Jacovides et al., 2003; Li et al., 2010; McCree, 1966; Papaioannou et al., 1993; Rao, 1984; Stigter and Musabilha, 1982; Tsubo and Walker, 2005). Furthermore, various values for PP /RS have been reported (e.g., Alados et al., 1996; Britton and Dodd, 1976; Finch et al., 2004; Ge et al., 2011; Howell et al., 1983; Jacovides et al., 2007; Meek et al., 1984; Udo and Aro 1999; Weiss and Norman, 1985). Researchers have indicated that observed ratios depend on the site, season (e.g., dry or wet, summer or

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T. Akitsu et al. / Agricultural and Forest Meteorology 209–210 (2015) 59–68

Fig. 1. Systems for the direct and diffuse separation methods of PAR measurement. (a) Direct spectral irradiance measurement system with a collimation tube, (b) diffuse spectral irradiance measurement system with a shadow ball, (c) the entire system ensemble including (a), (b), and the camera system.

winter), local time (e.g., morning, noon, or late afternoon), and weather conditions (e.g., sunny or cloudy). However, each ratio remains incompletely understood as to how it depends on climatic factors such as solar zenith angle (), water vapor pressure (e), and cloudiness. Therefore, it is difficult to assume reasonable values of these ratios at specific sites and in specific seasons. In addition to the above mentioned ratios, the following conversion ratio has also been used (McCree, 1972; Jacovides et al., 1997; Dye, 2004):





P P /P E unit : ␮molJ−1 . McCree (1972) reported the value of PP /PE as 4.57 ␮mol J−1 . Assuming this value to be constant, many researchers (e.g., Mizoguchi et al., 2014; Tsubo and Walker, 2005) have used it. However, Jacovides et al. (1997) and Dye, (2004) proposed slightly different values—4.53 ␮mol J−1 and 4.56 ␮mol J−1 , respectively. Although these values are quite similar, the dependence of PP /PE on climatic factors is not well documented.

Other PAR estimation models use RS and climate data such as , dew point temperature, e, and the clearness index (kT ). The models are of two types, estimating either PE (e.g., Aguiar et al., 2012) or PP (e.g., Alados et al., 1996; Ge et al., 2011; González and Calbó, 2002; Mizoguchi et al., 2014). However, in practice each model includes inherent systematic errors that propagate from their reference (calibration) data. Therefore, the general models are not well established. The reason that PAR estimation models have not been well established is attributable to PAR measurement. It is well known that quantum sensors commonly used for PAR measurement have problems, such as cosine errors, spectral errors, and the lack of a standard absolute PAR value (Mizoguchi et al., 2010, 2014; Ross and Sulev, 2000). Such errors make it difficult to interpret precise dependencies on climatic factors, particularly on . Some authors have indicated that PAR/RS increases with  (e.g., Meek et al., 1984; Udo and Aro 1999), whereas some have also indicated the opposite (e.g., Ge et al., 2011; González and Calbó, 2002). Moreover, some authors have indicated that the relationship changes based on the

T. Akitsu et al. / Agricultural and Forest Meteorology 209–210 (2015) 59–68

Fig. 2. Dependence of the output on the incident zenith and azimuth angles of the spectroradiometers. Error bars denote the standard deviation (std).

site or season (e.g., Aguiar et al., 2012; Jacovides et al., 2003; Li et al., 2010). The objective of this study is to clarify the values and the dependencies of PE /RS , PP /RS , and PP /PE on important climatic factors: e, , and kT . The understanding will become the basis for the creation of a general PAR estimation model in the future. If a general PAR estimation model cannot be established, we would require a large number of PAR estimation models based on the site. To achieve our objective, accurate measurements of both PAR and RS are needed. We used RS data measured by the direct and diffuse separation method. This system has been recommended for its accurate measurements (WCRP/WMO, 1986). We also developed a system to measure PAR by the direct and diffuse separation method and using spectroradiometers. This separation method contributes to a reduction in cosine errors, and the use of spectroradiometers is helpful to eliminate spectral errors in PAR data. Furthermore, the spectroradiometers were calibrated for accuracy and checked against reliable references. The temporal resolution of our method is high, which enables us to clarify the previously unclear dependencies of the ratios on rapidly changing climatic factors. In principle, each ratio should be understood based on the atmospheric radiative transfer process, because PAR is radiation that reaches the earth’s surface from the sun through the atmosphere. Therefore, these observed ratios were compared with theoretical ratios obtained by the atmospheric radiative transfer code Rstar6b (Nakajima and Tanaka, 1986) using various parameters. These comparisons helped reveal the dependencies of the ratios on climatic factors and verified the accuracy of our data. 2. Materials and methods 2.1. Study site and measurement Measurements were conducted at the Tateno station (36.05◦ N, 140.13◦ E, at 25 m above sea level) of the WCRP-BSRN in Tsukuba, Japan. Measurement instruments were installed on top of the building where the instruments of the WCRP-BSRN have also been installed. Measurements were taken from February 1 to December 28, 2012. In Tsukuba, in 2012, the annual mean air temperature and e were 14.0 ◦ C and 13.7 hPa, respectively.

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Fig. 3. Output of the spectroradiometers relative to the spectral radiance reference. The spectral radiance reference was two integrating spheres: a 12-inch-diameter integrating sphere (inner-coated by PTFE), which was used for wavelength shorter than 600 nm, and a 1-m-diameter integrating sphere (inner-coated by BaSO4 ) for wavelength above 530 nm.

Direct and diffuse solar radiation (Rdir and Rdif ) were measured and recorded as a part of WCRP-BSRN activities. They were separately measured using a pyrheliometer (CHP1, Kipp & Zonen B. V., Delft, Netherlands; first class) and a pyranometer (CM22, Kipp & Zonen B. V.; secondary standard). The pyranometer equipped with a fan was fixed on the horizontal stage on a sun tracker, and a shadow ball was mounted on the tracker. The pyrheliometer was mounted on the same sun tracker. The measurements were taken at 1-s intervals. Air temperature (t) and relative humidity (rh) were measured at the same site by the Japan Meteorological Agency (JMA). Direct and diffuse PAR (Pdir and Pdif ) were measured separately using two grating spectroradiometers (MS-700, EKO Instruments Co., Ltd., Tokyo, Japan; the serial numbers are S10125.02 and S10125.03). Each spectroradiometer was fixed to a sun tracker (STR-22G-S, EKO Instruments Co. Ltd.). One was equipped with a collimation tube with a 5◦ field of view for Pdir measurement (Fig. 1a), and the other was equipped with a shadow ball for Pdif measurement (Fig. 1b). Measurements were taken at 1-min intervals during the daytime. In case of rain, we stopped measurements and covered the collimation tube. The glass domes of the spectroradiometers were cleaned at least once a month. An automatic digital fisheye-lens camera (Nishida, 2007) was set in place to record the sky conditions at 5-min intervals. The spectroradiometers and the camera were installed close to each other (Fig. 1c), and these systems were positioned about 10 m from the WCRP-BSRN radiation instruments. To eliminate errors caused by surrounding structures, only data with  from 0◦ to 78◦ were used. Data were also eliminated when Rdir , Rdif , PE dir , and PE dif were below 5 W m−2 , because of the detection threshold. Some periods of data were missing because of maintenance and the avoidance of bad weather. 2.2. Spectroradiometers The specifications of the grating spectroradiometers were as follows: spectral range of 350–1050 nm, spectral interval of 3.3 nm, half bandwidth of 10 nm, and field of view of 180◦ . Errors in the

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Table 1 Comparison of peak wavelengths between a mercury lamp and spectroradiometers. Peak wavelength (nm)

Difference from Hg peak (nm)

Hg

MS-700 1

MS-700 2

MS-700 1

MS-700 2

365.015 404.656 435.833 546.074 763.511

365.005 405.039 435.730 546.206 764.123

365.065 405.066 435.821 546.075 764.136

0.010 −0.383 0.103 −0.132 −0.612

−0.050 −0.410 0.012 −0.001 −0.625

directional responses of the spectroradiometers were checked by an inspection system (PREDE, Tokyo, Japan) at the Meteorological Instruments Center of the JMA. The system was designed to test the incident angle characteristics. As seen in Fig. 2, the error in response to the zenith angle is at most 6.6% when the light source was at an 80◦ zenith angle, and the error in response to the azimuth angle is ±2.2% when the light source was at a 60◦ zenith angle. Before and after our field measurement, the absolute values of the spectroradiometers were calibrated by the manufacturer against an OL-FEL 1000 W standard lamp, traceable to the National Institute of Standards and Technology (NIST). The maximum difference of the spectral irradiance I() was less than 2%, and the average difference of I() was less than 0.7%. Furthermore, we performed additional calibration at the Japan Aerospace Exploration Agency (JAXA). The spectral irradiance of each spectroradiometer with attached collimation tube was compared with that of two types of integrating spheres traceable to a Japanese national standard fixed-point blackbody furnace by the Japan Calibration Service System (Yamamoto et al., 2002). The maximum difference within the PAR waveband was 1.8% at  = 400 nm, and the average difference was 0.95% (Fig. 3). The accuracy of the wavelength was confirmed by a low-pressure mercury lamp (L937-03 by Hamamatsu Photonics, Hamamatsu, Japan). The maximum difference of the wavelength within the PAR waveband was 0.41 nm (Table 1).

 

E E Phor = Pdir × cos  ,

(6)

P P Phor = Pdir × cos  .

(7)

 

The energy-based incident global PAR (PE glb ) is the sum of PE hor and PE dif . The photon-based global PAR (PP glb ) is the sum of PP hor and PP dif . To mitigate the error caused by the different measurement time intervals for RS and PAR, the observed PE /RS and PP /RS were calculated every 10 min by



PE (obs.) = RS

E Pglb

10-min



,

(8)

.

(9)

Rglb

10-min



PP (obs.) = RS

PP (obs.) = PE

(1)

P Pglb

10-min



Rglb

P Pglb

10-min



.

(10)

E Pglb

10-min

2.4. Calculation of clearness index (kT ) and water vapor pressure (e) Clearness index kT is the ratio of Rglb to the extraterrestrial solar radiation R0 (W m−2 ) (Tsubo and Walker, 2005; Li et al., 2010; Aguiar et al., 2012). R0 is calculated with the equation of Kondo (1994) as



R0 =RSC cos  × (1.00011+0.034221 cos () +0.00128 sin () +0.000719 cos (2)) ,

0.7␮m

E = Pdir

Idir ()d,

(2)

Idif ()d,

(3)

(11)

0.4␮m



0.7␮m

E = Pdif 0.4␮m

where d is the wavelength interval. PE and PP are linked to each other through the Planck relation E = hc/, where h is the Planck constant (6.626 × 10−34 J s), c is the speed of light (3.00 × 108 m s−1 ), and  is the wavelength. PP dir and PP dif are calculated by

 P Pdir

0.7m

= 0.4m

(5)

where NA is the Avogadro constant (6.023 × 1023 mol−1 ). The horizontal component of the incident direct PAR (PE hor and P P hor ) is defined as



where  was calculated at 1-s intervals. Rhor and Rdif were averaged every 1 min. The incident global solar radiation (Rglb ) was the sum of the 1-min mean Rhor and Rdif . The incident direct and diffuse spectral irradiance Idir () and Idif () were measured simultaneously at 1-min intervals. PE dir and PE dif were calculated based on the integral of I() (W m−2 ␮m−1 ) within the PAR waveband (for wavelengths from 0.4 ␮m to 0.7 ␮m) as follows:



0.4m

Idif () ×  d, h × c × NA

The observed PP /PE was calculated by

The horizontal component of the incident direct solar radiation (Rhor ) is defined as Rhor = Rdir × cos  ,

0.7m

=

10-min

2.3. Calculation of solar radiation (RS ) and photosynthetically active radiation (PAR)

 

 P Pdif

Idir () ×  d, h × c × NA

(4)

=

 2  365

× d,

(12)

where RSC is the solar constant (1367 W m−2 ) and d is the day of the year. Water vapor pressure e (hPa) was calculated using the saturation water vapor pressure (es ; hPa) and rh (%). The saturation water vapor pressure es was calculated using t (◦ C) from the following equation of Tetens (1930):



es = 6.1078 × 10

7.5t t+237.3



.

(13)

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Fig. 4. The monthly mean in 2012 of (a) air temperature, (b) relative humidity, (c) water vapor pressure, (d) PE /RS , (e) PP /PE , and (f) PP /RS . Error bars denote the std.

2.5. Atmospheric radiative transfer code Rstar6b Rstar6b (http://157.82.240.167/∼clastr), which was developed by the Center for Climate System Research at the University of Tokyo, is a general radiative transfer code for simulating radiation with wavelength between 0.17 ␮m and 1000 ␮m. The model describes the atmosphere between the earth’s surface and an altitude of 120 km as a plane-parallel layer divided into 50 horizontal sub-layers. It includes six atmospheric models, including midlatitude summer, mid-latitude winter, tropical, and US standard. In this study, we adopted the mid-latitude summer and winter as the atmospheric models. Each atmospheric model simulates temperature, pressure, and gaseous concentration profiles. The seven major gases (H2 O, CO2 , O3 , N2 O, CO, CH4 , and O2 ) are treated. Gaseous absorption is taken into account using the nonlinear-fitting, kdistribution method of Nakajima et al. (2000) and Sekiguchi and

Nakajima (2008). Rstar6b accounts for multiple scattering in the atmosphere by molecules and aerosol particles and bidirectional surface reflection (Nakajima and Tanaka, 1986, 1988). Aerosol particle models such as water, ice, soot, volcanic ash, yellow sand, rural, urban, and tropo (a tropospheric aerosol model) are defined by Rstar6b. The models of urban, rural, and tropo were used for our sunny analysis; we set 0.2 as the aerosol optical thickness (), which is the mean aerosol  at Tsukuba (Sasano, 1996). The particle models of ice and water were used for our cloudy analysis; we set the cloud  to 9.0, which is the zonal-mean cloud  around 35◦ latitude (Tselioudis et al., 1992). We then reset the cloud  to 1.0 to examine the effect of cloudiness. Theoretical values for PE /RS , PP /RS , and PP /PE were calculated using I() obtained by Rstar6b for wavelengths from 0.3 ␮m to 4.0 ␮m (at 0.01-␮m intervals below 1 ␮m and 0.05-␮m intervals above 1 ␮m) for each aerosol particle type in each atmospheric

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Fig. 5. Comparison between PE /RS and climatic factors ((a) water vapor pressure e, (b) solar zenith angle , (c) clearness index kT ). Small dots denote observed data, while symbol marks denote mean value of simulation output (Rstar). Error bars denote the std. (For interpretation of the references to color in this figure text, the reader is referred to the web version of this article.)

model with changes in both  (from 10◦ to 80◦ ) and rh (from 10% to 98%) as follows: PE (Rstar) = RS PP (Rstar) = RS PP (Rstar) = PE

 0.7␮m 0.4␮m

 4.0␮m 0.3␮m

I () d ,

(14)

I () d

 0.7␮m

I()× d 0.4␮m h×c×NA , 4.0␮m



0.3␮m

(15)

I () d

 0.7␮m

I()× d 0.4␮m h×c×NA . 0.7␮m



0.4␮m

winter: 0.465 and 0.420, respectively (Fig. 4d). In fact, the monthly mean PE /RS was similar to a seasonal variation of e (Fig. 4c). However, some researchers indicated that PE /RS can be estimated using kT without using e (Tsubo and Walker, 2005; Aguiar et al., 2012). Therefore, we investigated the dependence of PE /RS on e. PE /RS positively correlated with e (r = 0.844, Table 2), and it increased from 0.40 to 0.47 as e increased from 2 to 30 hPa (see

(16)

Table 2 Correlation coefficients (r), partial correlation coefficients and standard errors of PE /RS , PP /RS , and PP /PE for climatic factors (e: water vapor pressure, : solar zenith angle, kT : clearness index).

I () d

Sample size: 6384 e

kT is calculated by kT (Rstar) =

RS (Rstar) . RSC × cos()



kT

E

(17)

3. Results and discussion 3.1. PE /RS 3.1.1. Dependence of PE /RS on water vapor pressure (e) The dependence of PE /RS on e has been roughly described in seasonal variations such as the higher values in summer and lower in winter (e.g., Papaioannou et al., 1996; Rao, 1984). We also observed that the monthly mean PE /RS is higher in summer and lower in

P /RS Correlation coefficient (r) Partial correlation coefficient Standard error

0.844*** 0.808*** 0.0117

−0.323*** −0.288*** 0.0210

−0.376*** −0.446*** 0.0206

PP /RS Correlation coefficient (r) Partial correlation coefficient Standard error (␮mol J−1 )

0.847*** 0.814*** 0.0510

−0.298*** −0.234*** 0.0940

−0.380*** −0.434*** 0.0911

PP /PE Correlation coefficient (r) Partial correlation coefficient Standard error (␮mol J−1 )

−0.404*** −0.174*** 0.0121

0.606*** 0.611*** 0.0105

0.120*** 0.318*** 0.0130

***

p < 0.001.

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Fig. 6. Diurnal variations of solar radiation and PE /RS for (a) sunny in winter, (b) cloudy in winter, (c) sunny in summer, and (d) cloudy in summer. In each plot, solar radiation is shown by the left vertical axis and PE /RS by the right vertical axis.

the small dots in Fig. 5a). The numerical model showed a similar relationship. For instance, PE /RS (Rstar, sunny) in summer (the open squares in Fig. 5a) and in winter (the open triangles in Fig. 5a) increased continuously with e, throughout all seasons. Although the values of PE /RS are different in cloudy and sunny conditions (e.g., see the three types of triangles in Fig. 5a), PE /RS in each sky condition increased continuously with e, throughout all seasons (e.g., see the solid triangles and solid squares in Fig. 5a). In principle, the increase in PE /RS with e is attributable to the absorption of near-infrared radiation (NIR) by water vapor. Meanwhile, the effect of cloud type on PE /RS was small. For instance, PE /RS (Rstar, cloudy:  = 9.0) in summer (the solid squares in Fig. 5a) had small error bars, which are standard deviations (stds) caused by changing cloud types (ice and water) and changing  (from 10◦ to 80◦ ). The effect of aerosol types was also limited. PE /RS (Rstar, sunny) in summer (the open squares in Fig. 5a) also had small error bars, which are stds caused by changing aerosol types (urban, rural, and tropo) and changing  (from 10◦ to 80◦ ). 3.1.2. Dependence of PE /RS on solar zenith angle () Although many authors (e.g., Aguiar et al., 2012; Jacovides et al., 2003; Li et al., 2010) reported dependence on site or season, the reasons for any dependence of PE /RS on  have been unclear. Because this dependence is often described implicitly in diurnal variations, we first show the diurnal variations of PE /RS . We saw very little diurnal variation in PE /RS in both sunny (dotted lines in Figs. 6a and c) and cloudy conditions (dotted lines in Figs. 6b and d). The figures show that the dependence of PE /RS on  is small. If PE /RS depended on , it should have clear diurnal variations, such as higher values in the morning and late afternoon, and lower values at noon. Next, we show the direct relationship between PE /RS and  in Fig. 5b. The dependence of PE /RS on  was minimal, because PE /RS (the small dots) widely spread in the range from 0.40 to 0.50. Fur-

thermore, a closer look reveals that PE /RS values in each season (the red, blue, or gray dots) lined up horizontally and did not depend on . The numerical model also showed minimal dependence. PE /RS in cloudy conditions (e.g., solid squares) lined up horizontally, and PE /RS in sunny conditions (e.g., open triangles) almost lined up horizontally, except at large  (larger than 70◦ ). Thus, we found no clear relationship between PE /RS and . However, it appears that PE /RS was negatively correlated with  (r = −0.323, Table 2). We must interpret this correlation carefully, because the vacancy of the data shown in the left-lower part of Fig. 5b is the cause for the negative correlation. The vacancy exists because the sun does not come to small  (namely high solar elevation) in winter. The previously reported dependencies may be attributed to this apparent (but false) correlation or to some artifacts, such as instrumental cosine errors. We note a slight decrease in PE /RS when the sky is sunny at large . For instance, PE /RS (Rstar, sunny) in summer (open triangles in Fig. 5b) showed a little decrease at large . Therefore, when estimating PE at a high latitude, we should account for a small decrease at large , because the sun exhibits a large  for a long time in those regions. 3.1.3. Dependence of PE /RS on clearness index (kT ) Tsubo and Walker (2005) related PE /RS to kT in a simple function in which PE /RS increases with decreasing kT . We also observed the negative correlation between PE /RS and kT (the correlation coefficient and the partial correlation coefficient were −0.376 and −0.446, respectively, as seen in Table 2). Next, in order to illustrate the dependence of PE /RS on kT by eliminating the influence of e, which varies seasonally, observation data for PE /RS were classified according to season. It follows that the negative correlation between PE /RS and kT is obvious in each season (red and blue dots in Fig. 5c). In fact, PE /RS increased from 0.47 to 0.50 (in summer)

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Fig. 7. Comparison between PP /RS and climatic factors ((a) water vapor pressure e, (b) solar zenith angle , (c) clearness index kT ). Small dots denote observed data, while symbol marks denote mean value of simulation output (Rstar). Error bars denote the std. (For interpretation of the references to color in this figure text, the reader is referred to the web version of this article.)

and from 0.40 to 0.45 (in winter) with decreasing kT from 0.8 to 0.3 (see the red and blue dots in Fig. 5c, respectively). Furthermore, the numerical model reproduced this negative correlation, as shown by the open diamonds and the open inverted triangles in Fig. 5c. These simulation outputs were produced by changing cloud . In other words, PE /RS increases with cloud . This is attributable to the absorption of NIR radiation by cloud particles. In principle, the cloud particles absorb NIR more strongly than PAR, hence transmittance of PAR through clouds is larger than NIR. Therefore, PE /RS increases with cloud . Meanwhile, the factor inducing a change in kT is not only cloud  but also . As seen in Fig. 5c, the simulation output plotted by changing  showed positive correlation between PE /RS and kT . These opposite dependencies of PE /RS on kT (the negative correlation caused by  and the positive correlation caused by ) may have caused the dispersion of the observed data in Fig. 5c. Note that these simulations for kT were performed under constant e, which means both kT and e are controlling factors of PE /RS independent from each other. 3.2. PP /RS 3.2.1. Dependence of PP /RS on climatic factors The findings related to dependence of PP /RS on climatic factors were similar to the findings for PE /RS . 1.

PP /RS

positively correlated with e (r = 0.847, Table 2). It increases with e regardless of sky condition (Fig. 7a). In fact, PP /RS increased

from 1.9 to 2.2 ␮mol J−1 as e increased from 2 to 30 hPa (see the small dots in Fig. 7a). 2. Dependence of PP /RS on  is minimal. The correlation between PP /RS and  was negative (r = –0.298, Table 2). However, we consider that the correlation is false. The negative correlation is caused by the lower solar elevation in winter (see the vacancy of data in the lower left of Fig. 7b). Previously reported dependencies on  (e.g., Meek et al., 1984; Udo and Aro, 1999; Ge et al., 2011) may be attributed to this false correlation or to artifacts (such as cosine and spectral errors) in the quantum sensor and the pyranometer. 3. PP /RS increases with kT (in response to changes in cloud ) (Fig. 7c). In other words, kT is another essential factor to control PP /RS independently from e. In fact, PP /RS increased from 2.1 to 2.3 ␮mol J−1 (in summer) and from 1.9 to 2.1 ␮mol J−1 (in winter) with decreasing kT from 0.8 to 0.3 (see the red and blue dots in Fig. 7c, respectively). The correlation coefficient (r) and partial correlation coefficient between PP /RS and kT were −0.380 and −0.434, respectively (Table 2). 4. PP /RS varies with season. The monthly mean PP /RS was higher in summer (a wet season) and lower in winter (a dry season), at 2.12 and 1.92 ␮mol J−1 , respectively (Fig. 4f). 3.3. PP /PE PP /PE is generally assumed to be constant. As seen in Fig. 4e, the monthly mean PP /PE was constant, with a slightly lower value in summer and a higher value in winter: 4.56 and 4.58 ␮mol J−1 ,

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Fig. 8. Comparison between PP /PE and climatic factors ((a) water vapor pressure e, (b) solar zenith angle , (c) clearness index kT ). Small dots denote observed data, while symbol marks denote mean value of simulation output (Rstar). Error bars denote the std.

respectively. The values are similar to the value (4.57 ␮mol J−1 ; McCree, 1972) that is generally used. However, the error bars of the monthly mean PP /PE in Fig. 4e are somewhat large. Therefore, we clarified how PP /PE is constant, and which factors influence PP /PE . 3.3.1. Dependence of PP /PE on water vapor pressure (e) The dependence of PP /PE on e had been unclear. As seen in Fig. 8a, we found that the percent change of PP /PE in response to changes in e is approximately 0.7%. However, with a closer look, we observed the negative correlation between PP /PE and e (r = −0.404, Table 2), in which PP /PE decreased from 4.58 to 4.55 ␮mol J−1 with increasing e from 2 to 30 hPa (see the small dots in Fig. 8a). Moreover, the numerical model reproduced this negative correlation. For instance, PP /PE (Rstar, sunny) in summer (open squares in Fig. 8a) and in winter (open triangles in Fig. 8a) decreased continuously with increasing e, throughout all seasons. In principle, the small decrease in PP /PE with increasing e is caused by the water absorption bands at 660 nm and 605 nm wavelengths within the PAR waveband. 3.3.2. Dependence of PP /PE on solar zenith angle () As seen in Fig. 8b, we found that the change of PP /PE in response to changes in  is approximately 1%. However, with a closer look, we observed the positive correlation between PP /PE and  (r = 0.606, Table 2), in which PP /PE increased from 4.55 to 4.60 ␮mol J−1 with increasing  from 12◦ to 78◦ (see the small dots in Fig. 8b). This happened in both sunny and cloudy conditions, but the numerical model reproduced it in sunny conditions only (see the open squares in Fig. 8b). In principle, at large , Rayleigh scattering selectively reduces the transmitted radiation in shorter wavelengths and

makes the direct sunlight more abundant in longer wavelengths. Hence, the average energy of a photon is reduced. This results in more photon density per unit energy of radiation and larger value of PP /PE . This is one possible reason for larger PP /PE in winter than summer (Fig. 4e). However, the failure of simulation in cloudy conditions cannot be explained from the available data. 3.3.3. Dependence of PP /PE on clearness index (kT ) Dye (2004) indicated that PP /PE is nearly constant with changes of Pdif /Pglb , which is a similar factor to kT . We found that the correlation between PP /PE and kT is weak (r = 0.12, Table 2). In fact, as seen in Fig. 8c, we cannot identify a single simple relationship between PP /PE and kT (see the small dots). The simulation output plotted by changing cloud  produced a positive correlation between PP /PE and kT (see the open diamonds and open inverted triangles). In contrast, the simulation output plotted by changing  produced a negative correlation (see the open squares and open triangles). These contrasting dependencies of PP /PE on kT (in response to changes in cloud  and ) may have led to disparate understandings of the relationship between PP /PE and kT in previous studies. The change of PP /PE in response to changes in kT was approximately 2%. 4. Conclusions 4.1. Conclusion of dependence of PE /RS on climatic factors PE /RS changes, in the range of 0.40–0.50, in response to changes in climatic factors. The controlling factors of PE /RS are both e and kT : PE /RS increases with increasing e, and it increases with decreasing kT . The range of PE /RS in response to changes in e and kT was within

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approximately 15% and 7% of the maximum PE /RS , respectively. On the other hand, the dependence of PE /RS on  is minimal. 4.2. Conclusion of dependence of PP /RS on climatic factors PP /RS changes in the range from 1.8 ␮mol J−1 to 2.3 ␮mol J−1 in response to changes in climatic factors. The range of PP /RS in response to changes in e and kT was within approximately 14% and 9% of the maximum PP /RS , respectively. The controlling factors of PP /RS , which are similar to those of PE /RS , are both e and kT . The dependence of PP /RS on  is minimal. 4.3. Conclusion of dependence of PP /PE on climatic factors PP /PE may change within 3% around McCree’s constant value (4.57 ␮mol J−1 ) in response to changes in e, , and kT . Therefore, for most purposes, the use of McCree’s value is probably acceptable, though the ratio is not strictly constant. To make clear the dependencies of PE /RS , PP /RS , and PP /PE on each climatic factor, accurate measurements were essential. For highest accuracy, measurements or estimates of e and kT should be used when it is necessary to estimate PAR from measurements of global solar radiation. Furthermore, the location of Tsukuba was appropriate. Because, in Tsukuba, each climatic factor varies dramatically throughout the year. If a study site was located in a place where e and kT mainly vary in synchronized timing or where any one climatic factor varies little, the dependencies of these ratios on climatic factors would not be made clear. Acknowledgments The authors thank the staff members of the Ozone and Radiation Division, Aerological Observatory, JMA. We appreciate the solar radiation data provided by BSRN and the climate data provided by JMA at Tateno. We are grateful to OpenCLASTR project for using the Rstar6b package in this research. We also thank Dr. Masahiro Hori (JAXA) and Mr. Takeshi Sakai (JMA) for support of our experiments. This work was supported by the JAXA GCOM-C project under contract 102: “Development of integrative information of the terrestrial ecosystem” (PI: Kenlo Nishida Nasahara). References Aguiar, L.J.G., Fischer, G.R., Ladle, R.J., Malhado, A.C.M., Justino, F.B., Aguiar, R.G., Costa, J.M.N., 2012. Modeling the photosynthetically active radiation in South West Amazonia under all sky conditions. Theor. Appl. Climatol. 108, 631–640. Alados, I., Foyo-Moreno, I., Alados-Arboledas, L., 1996. Photosynthetically active radiation: measurements and modeling. Agric. For. Meteorol. 78, 121–131. Blackburn, W.J., Proctor, J.T.A., 1983. Estimating photosynthetically active radiation from measured solar irradiance. Sol. Energy 31, 233–234. Britton, C.M., Dodd, J.D., 1976. Relationships of photosynthetically active radiation and shortwave irradiance. Agric. Meteorol. 17, 1–7. Dye, D.G., 2004. Spectral composition and quanta-to-energy ratio of diffuse photosynthetically active radiation under diverse cloud conditions. J. Geophys. Res. 109 (D10), 1–12. Finch, D.A., Bailey, W.G., McArthur, L.J.B., Nasitwitwi, M., 2004. Photosynthetically active radiation regimes in a southern African savanna environment. Agric. For. Meteorol. 122, 229–238. Ge, S., Smith, R.G., Jacovides, C.P., Kramer, M.G., Carruthers, R.I., 2011. Dynamics of photosynthetic photon flux density (PPFD) and estimates in coastal northern California. Theor. Appl. Climatol. 105, 107–118. González, J., Calbó, J., 2002. Modelled and measured ratio of PAR to global radiation under cloudless skies. Agric. For. Meteorol. 110, 319–325. Howell, T.A., Meek, D.W., Hatfield, J.L., 1983. Relationship of photosynthetically active radiation to shortwave in the San Joaquin Valley. Agric. Meteorol. 28, 157–175.

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