Ultraviolet-B and photosynthetically active radiation environment of inclined leaf surfaces in a maize canopy and implications for modeling

Agricultural and Forest Meteorology 95 (1999) 187±201

Ultraviolet-B and photosynthetically active radiation environment of inclined leaf surfaces in a maize canopy and implications for modeling Richard H. Grant* Department of Agronomy, Purdue University, 1150 Lily Hall, West Lafayette, IN 4707-1150, USA Received 26 October 1997; received in revised form 15 October 1998; accepted 15 November 1998

Abstract The potential increase in ultraviolet-B (UVB) ¯ux density and potential decrease in productivity of agricultural crops due to stratospheric ozone loss requires knowledge of the characteristics of UVB ¯ux density above and within crops. Measurements of the photosynthetically active (PAR) and UVB radiation on inclined surfaces above and within a maize (Zea mays L.) canopy were made in 1990. Sunlit surfaces within the canopy had similar UVB and PAR relative ¯ux density levels to that above the canopy. Shaded surfaces within the canopy had very different relative ¯ux density in the UVB and PAR as a result of differences in sky view, diffuse fraction, and orientation. These differences can be expected to result in canopy transmittance estimation errors of the order of 0.1 in the UVB and 0.05 in the PAR when one assumes an invariant diffuse radiation of leaves with differing aspect. The diffuse fraction of global radiant ¯ux density in¯uenced the radiation regimes present in the canopy. Two distinct radiation regimes were found for surfaces throughout the canopy in the relatively low diffuse fraction PAR waveband; a sunlit regime and a deep shade regime. Three distinct radiation regimes were evident for the relatively high diffuse fraction UVB waveband for surfaces at a height with cumulative leaf area index (LAI) of 1; a sunlit regime, a deep shade regime, and a light shade regime. At greater cumulative LAI, this additional light shade regime in the UVB was absent. Therefore, the bi-modal approach of modeling sunlit or shaded radiation regimes is adequate to estimate the photosynthetically active photon ¯ux density throughout the canopy as well as to estimate the UVB radiant ¯ux density when the cumulative canopy LAI was 2. At lower LAI, the UVB radiant ¯ux density should be modeled using either a threedimensional model or a model partitioning the gap probability into large and small gaps in the canopy. The necessity for two shade sub-models to model the UVB radiation environment apparently depends on the size distribution of gaps in the canopy. # 1999 Elsevier Science B.V. All rights reserved. Keywords: UVB; PAR; Plant canopy; Slopes; Modeling; Radiation measurement

1. Introduction Modeling of photosynthetic production in plant canopies has made great strides since the early attempts in the 1970s. Much of the progress has been *Fax: +1-765-496-2926.

due to the careful evaluation of the thermal infrared, photosynthetically active (PAR; 0.4±0.7 mm), near infrared (NIR; 0.70±1.10 mm), and total short wave radiation environment of plant canopies. These wavebands, however, have primarily the characteristic of having typically low diffuse fraction (Fd). As a result, the development of the theory of diffuse radiation

0168-1923/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 1 9 2 3 ( 9 9 ) 0 0 0 2 3 - 4

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R.H. Grant / Agricultural and Forest Meteorology 95 (1999) 187±201

penetration from the sky into the plant canopy has been largely stagnated. The potential loss of the signi®cant fractions of ozone in the stratosphere has prompted recent efforts in assessing the potential damage to vegetation due to enhanced levels of UVB (0.28±0.32 mm) radiation. Since the Fd in the UVB is much greater than the photosynthetically active radiation (PAR), the view of the sky is a more important factor in radiant ¯ux density in the UVB than of PAR (Grant and Heisler, 1996). Therefore, direct translation of PAR radiation models into simulating the UVB environment may well be fraught with unexpected errors of the estimate. The effect of UVB enhancements varies from crop to crop. Maize (Zea mays L.) seedlings show a decrease in photosynthesis and ultimately aboveground biomass with increased UVB radiant ¯ux density (Mark and Tevini, 1997). Enhanced UVB radiant ¯ux density has been shown to delay the onset of ¯owering and grain ®lling resulting in reduced maize crop yields (Mark et al., 1996). The effects of UVB appear to be in¯uenced by the levels of PAR, although the nature of the in¯uence is still debatable (Berkelaar et al., 1996). Research has shown that UVB damage to plants is mitigated by high PAR photon ¯ux density (PPFD) prior to exposure to enhanced UVB radiant ¯ux density (Warner and Caldwell, 1983; Beggs et al., 1986; Caldwell and Flint, 1994). Cen and Bornman (1990) found that low PPFD made plants more sensitive to UVB radiation. Estimates for photosynthetic production or UVB dose exposures of plants in plant canopies requires a consideration of the distribution of leaves in the canopy. Leaf orientation is commonly considered in estimating the direct beam penetration of canopies, but commonly ignored in estimating diffuse sky penetration in the canopy (Gutschick, 1984; Goudriaan, 1988; Gutschick, 1991; Daudet and Tchamitchian, 1993). For photosynthetic models, this is commonly neglected because the diffuse radiation is readily attenuated near the top of most canopies and the Fd in the PAR is small for cloudless sky conditions. Gutschick (1984) stated that the diffuse radiant ¯ux density at a given depth was almost the same for all leaves at that depth, even though Niilisk et al. (1970) showed a relatively wide range in total radiant ¯ux density in the PAR with changing leaf orientation.

Allen et al. (1975) also assumed uniform diffuse radiant ¯ux density on variously-oriented leaves in a maize canopy to estimate UVB dose. Corresponding measurements of the UVB radiant ¯ux density on variously-oriented surfaces within plant canopies have not been reported in the literature, and consequently the applicability of this assumption to the estimation of UVB exposure of surfaces in plant canopies cannot yet be assessed. Measurements of the UV radiation environment on a horizontal surface have been made at the base of a senescing maize canopy (Grant, 1991), a sorghum canopy (Grant et al., 1995a, b), and forest canopies (Yang et al., 1993; Brown et al., 1994; Grant and Heisler, 1996). In dense canopies, radiant ¯ux density in the UVB and PPFD is typically very low in the under-canopy, with the only exceptions being when sun¯ecks penetrate to the base of the canopy (Grant et al., 1995a, b). In contrast, UVB and PAR radiation levels vary widely across space in low density tree canopies with greater variability in the PPFD than UVB radiant ¯ux density (Brown et al., 1994; Grant and Heisler, 1996). Differences in the UVB and PAR radiation environments in low density plant canopies are due to differences in; (1) the vegetation scattering properties (Grant, 1993), (2) the region of the sky obstructed (Grant, 1997a), (3) the distribution of the sky diffuse radiation (Grant and Heisler, 1996), and (4) the relative proportion of sky diffuse radiation to the total global radiation (Grant, 1997b). Measurements made at the top of a maize canopy showed that the maximum PPFD occurs near the orientation normal to the solar beam while maximum UVB radiant ¯ux density occurs near the orientation parallel to the earth's plane (Grant, 1993). However, maximum UVB radiant ¯ux density depends on the canopy structure (Grant, 1998), indicating canopy scattering and/or biomass orientation and distribution in¯uences the UVB radiant ¯ux density. The UVB radiant ¯ux density for any leaf within the canopy depends in part on leaf orientation and view of the sky and the direct beam. Grant (1991) measured the UV and PAR ¯ux density at the base of a maize canopy and concluded that the canopy re¯ectance of the UV differed substantially from that of PAR while the canopy transmittance was similar. Scattering of the UV radiation appeared anisotropic but no measurements of the leaf transmittance or re¯ectance were

R.H. Grant / Agricultural and Forest Meteorology 95 (1999) 187±201

made in that study. Flux density measurements made at the canopy base indicated a rapid decrease in UV ¯ux density with increasing surface slope. Niilisk et al. (1970) measured the NIR and PAR radiant ¯ux density of variously-oriented planes above and in a sun¯ower canopy. Results showed that angular distribution of NIR radiant ¯ux density was more uniform than that of PAR, with greater attenuation of the PAR than NIR radiant ¯ux density with increasing depth in the canopy. Scattering of the NIR was determined to be the primary cause for the greater penetration of NIR over PAR and the near uniformity of the radiant ¯ux density with change in slope. This study further describes the spatial distribution of UVB and PAR radiation in a maize canopy during the time of silking and evaluates the validity of the common assumptions concerning the modeling of diffuse radiation penetration. 2. Methods UVB radiant ¯ux density and PPFD measurements were made in a maize canopy (Beck's 72) at silking between 26 July through 2 August 1991 at West Lafayette, IN, USA (40.58N Latitude). The maize was planted in east-west rows with a ®nal plant density of 6700/ha. The canopy height (hc) was approximately 3 m. Silks were between 0.5 and 0.6 hc. Canopy leaf area index (LAI) and leaf angle distribution (LAD) was determined directly by dimensional and orientation measurement of leaves from 10 plants. The

189

LAI was 2.0. The canopy had a mean leaf inclination angle of 708, characteristic of an erectophilic canopy. UV radiant ¯ux density and PPFD measurements were made at three levels within the canopy; base of canopy (0.2 hc), mid-canopy (0.6 hc), and above canopy (1.2 hc) (Table 1). The mid-canopy height corresponded to the height of the silks and a cumulative LAI of 1.2. The ¯ux density of surfaces oriented in any plane of the hemisphere facing the sky was determined by the simultaneous measurement of the UV radiation and the plane surface orientation. The sensor mount was designed to provide any view zenith and azimuth orientation (Fig. 1) with the angles recorded using potentiometers. During the 1991 measurement period, the azimuth error increased to 108 due to the hysteresis of the motor and gears installed in 1991. The plane surface of the sensor varied by 0.2 m between the position of the sensor when the view zenith was 08 and 908. This resulted in a 0.07 hc change in the sensor height as the sensor orientation varied between horizontal and vertical to the earth's surface. Therefore, base of canopy measurements varied in height from 0.2 hc to 0.10 hc. The UV sensor was a `solar-blind' vacuum photodiode made by International Light (SED 240/W) with a low-pass ®lter (UVB1,SCS280). The UVB sensor was factory calibrated in 1989. Fifty percent of the relative sensor response lies between 0.274 and 0.310 mm. Using the simulated solar ¯ux density of Schippnick and Green (1982) for a solar zenith angle of 508 and an atmosphere with 3.2 mm ozone, 90% of the UV sensor response lies in the wavelength band of

Table 1 Measurement conditions Run

hc

Date (DOY)

SZAa (deg.)

Qp(0,-0) (mmol mÿ2 ÿ1)

UVB Rs(0,-,0) (Wmÿ2)

 ozoneb (cm-ATM)

PAR Fd

UVB Fd

4 5 2 1 3 7 10 11 9 8

0.2 0.2 0.6 0.6 0.6 0.6 1.2 1.2 1.2 1.2

212 212 207 207 212 213 214 214 214 214

25 22 21 25 36 43 25 29 39 43

178 508 590 455 185 338 1669 1656 1785 1419

0.80 0.82 0.96 1.03 0.33 0.25 2.87 2.71 2.77 2.10

0.323 0.323 0.320 0.320 0.323 0.323 0.324 0.324 0.324 0.324

0.15 0.15 0.15 0.15 0.17 0.18 0.15 0.16 0.17 0.18

0.47 0.46 0.46 0.47 0.51 0.55 0.47 0.48 0.50 0.53

Note: a: Solar zenith angle. b Ozone column thickness.

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Fig. 1. Geometry of the measurement space. S defines the solar disk position in the sky hemisphere while P and D correspond to the perpendicular to the inclined plane and an arbitrary location in the sky respectively. The sky zenith is Z. The plane is oriented with slope  and azimuth . The point in the sky (P) is defined by its zenith d and azimuth d. The solar disk location in the sky is defined by its zenith k and azimuth k. k is the scatter angle between the S and P and d is the scatter angle between the sun and the point in the sky.

0.301±0.336 mm. In a previous paper, I described this waveband as the middle UV (MUV) (Grant, 1991). However, subsequent comparisons of the MUV radiant ¯ux density at the canopy top to that computed by integration of a UVB sky radiance distribution (Grant et al., 1997) showed that there was no apparent difference in the computed and measured radiant ¯ux density. Furthermore, the re¯ectance of vegetation canopies has shown that re¯ectances in the UVA and UVB (spanning the MUV waveband) are very similar (Grant, 1993). Therefore, the measured waveband is termed here the UVB. UVB ¯ux density measurements were made using a quartz `wide-eye' lambertian diffuser for cosine response across a 1808 ®eld of view. The cosine response was measured in the laboratory, and determined to be within 10% of true cosine response for all incidence angles (Fig. 2). PPFD was measured using a LI-190SA photodiode sensor (LI-COR, Lincoln, NE, USA). The peak wavelength of sensor response was at 0.660 mm, with a 10% response bandwidth of 0.400±0.702 mm (as reported

Fig. 2. Cosine response of the UVB sensor. Panel A illustrates the relative response of the sensor (filled circles and solid line) and the ideal sensor response (dashed line). Panel B illustrates the relative error of the sensor from the ideal response (filled circles and solid line). The dashed lines indicate the 10% error range. Values represent means of three replicates.

R.H. Grant / Agricultural and Forest Meteorology 95 (1999) 187±201

by the manufacturer). The cosine response error of the PAR sensor were less than 5% for solar zenith angles between 20 and 608 (22). The PAR sensor was last calibrated by the factory in 1987. Measurements of the UVB radiant ¯ux density and PPFD, as well as the view zenith and azimuth angle were recorded at 0.5 Hz on a data logger (Campbell Scienti®c CR21X) as the sensor was rotated through the full hemisphere of zenith and azimuth angles. During the summer of 1990 the sensor mount was hand rotated while during 1991 the sensor mount was rotated using small motors. Scans of the full hemisphere of view orientations were made while the solar zenith angle was less than 508. 2.1. Measurement normalization The ¯ux density measurements for an inclined plane at a given slope () and aspect ( ) were normalized by the maximum ¯ux density on a plane parallel to the earth's surface at the individual j levels. In the UVB waveband, the normalized radiant ¯ux density (Is-UVB) was de®ned by normalizing the measured irradiance at level j (Rs(, ,j)) by the horizontal irradiance under sunlit conditions at that level (Rs (0,±,j)) according to Is …; ; j† ˆ

Rs …; ; j† Rs …0; ÿ; j†

(1a)

where the subscript s refers to a sloped surface. In the PAR waveband, the normalized photon ¯ux density (Is-PAR) was de®ned by normalizing the measured irradiance at level j (Qp(, ,j)) by the horizontal irradiance under sunlit conditions at that level (Qp (0,-,j)) according to: Is …; ; j† ˆ

Qp …; ; j† Qp …0; ÿ; j†

(1b)

Above canopy horizontal conditions are then de®ned as Rs(0,-,0) and Qp(0,-,0). In the measurement normalization represents the sunlit conditions. All Is(, ,j) for a given scan were then gridded using an inverse distance interpolation scheme on averaged values within 58 intervals of  and and plotted using SURFER (Golden Software, Golden, CO). The orientation of the sensor plane surface was de®ned according to Fig. 1. The angle between the zenith (Z) and the sensor plane surface at O was de®ned as the view

191

zenith angle (). The slope aspect angle ( ) was de®ned clockwise relative to magnetic north. The view azimuth represents the difference between the slope aspect and the solar azimuth, with a view azimuth of 0 meaning the slope aspect was equal to the solar azimuth. Measurements with a view azimuth within 908 of the solar azimuth were described as `facing' the sun while those with view azimuth greater than 908 from the solar azimuth were described as `facing away from' the sun. Canopy transmittance  for an inclined plane s at level j in the canopy was de®ned in the UVB waveband as: j;s ˆ j Is …; ; j† ˆ ˆ

Rs …0; ÿ; j† Is …; ; j† Rs …0; ÿ; 0†

Rs …; ; j† Rs …0; ÿ; 0†

(2a)

where  j is the horizontal canopy transmittance at that level. Similarly, the canopy transmittance for an inclined plane in the canopy was de®ned in the PAR waveband as: j;s ˆ j Is …; ; j† ˆ ˆ

Qp …0; ÿ; j† Is …; ; j† Qp …0; ÿ; 0†

Qp …; ; j† Qp …0; ÿ; 0†

(2b)

Since a vegetation canopy is composed of discrete elements of vegetation that obstruct sky and direct beam radiation, the  j is usually described as a time or spatial average condition. 2.2. Model development The measured  j,s values range between a maximum if there is a complete view of the sky and receipt of direct sunlight (max [ j,s]) to a minimum were there is negligible view of the sky and no direct sunlight (mindiffuse[ j,s]). The measured values of canopy transmittance for a given leaf of orientation , in layer j were compared to the expected limits in transmittance estimated by application of a general model to these two extreme conditions. The general model that assumed the total ¯ux density on a leaf within a given leaf angle range was a function of the incidence angle of the leaf to the direct beam and the horizontal ¯ux of diffuse

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R.H. Grant / Agricultural and Forest Meteorology 95 (1999) 187±201

radiation. The diffuse radiation ¯ux was composed of both canopy-scattered (complementary) and sky diffuse radiation in accordance with Gutschick (1991). The relative ¯ux density of the upward facing leaf at depth j in the canopy was then de®ned as: j;s ˆ …1 ÿ Fd †Pj;s cos k ‡ Fd P0j;s ‡ Cj

(3a)

where Fd is the diffuse fraction, Cj is the relative contribution of complementary radiation from the layer j ÿ 1 and layer j ‡ 1, Pj and Pj0 is the probability of penetration of the direct beam and diffuse sky radiation. The view of the sky is de®ned by the inclined plane of the leaf and k is the scattering angle between the slope normal and the sun location (k azimuth and k zenith), de®ned as: cos k ˆ cos  cos k ‡ sin  sin k cos…k ÿ † (3b) The magnitude of  j,s can exceed 1.0 as the surface of interest becomes more normal to the direct beam radiation of the sun. The Pj and P0j equal 1.0 at the canopy top, but within the canopy, P0j can be 1 (in sun¯eck) or less while P0j will always be less than 1.0 since vegetation above the layer of interest will necessarily reduce the view of the sky. The Fd of UVB and PPFD were estimated for cloud-free skies using the Schippnick and Green (1982) and Bird (1984) models, respectively. Ozone column depth, used in the Schippnick and Green (1982) model, was extracted from total ozone mapping spectrometer (TOMS) measurements (Larko and McPeters, 1992). Estimation of the complementary radiation on inclined surfaces greatly increases the model complexity but may be relatively unimportant since complementary radiation is often assumed to be uniformly intense in all directions. The relative importance of complementary radiation to the penetration of radiation to an inclined plane in the canopy in Eq. (3a) was evaluated for SZA between 228 and 458 using a modi®ed Meyers and Paw U (1987) model. The model assumed sky radiance isotropy and spherical leaf angle geometry as originally written, but received inputs of the sky diffuse and direct beam fraction of incident radiation rather than estimating it from empirical relationships. Scattering within the canopy was interatively-calculated for layers with small leaf area using the approach of Norman (1979). Leaf and soil re¯ectance values for maize were set according to

Grant (1993). For a horizontal surface, complementary radiation contributed approximately 0.01 in the PAR while the penetration of diffuse sky radiation amounted to 0.08±0.10 at 0.6 hc. The corresponding contribution of complementary radiation in the UVB waveband was less than 0.01 compared to a diffuse penetration of sky radiation of 0.24. For a vertical surface at 0.6 hc in a canopy of lambertian re¯ectors, complementary radiation would contribute less than 0.01 to the transmittance in the UVB waveband and approximately 0.02 in the PAR waveband. It was concluded that the complementary radiation contributed a small enough fraction of the total canopy transmittance to be omitted in the models describing the maximum and minimum transmittance. Rather than estimate the mean relative ¯ux density in the maize canopy, as described by Eq. (3a), the relative ¯ux density for sunlit and shaded leaves were considered separately in sub-models. The sub-model describing the shaded surface was separated into two sub-models provide a range in sky view since sky view has been shown to be important in modeling the radiant ¯ux density in the shade (Grant and Heisler, 1996; Grant et al., 1997). 2.2.1. Estimation of maximum canopy transmittance: sunlit surface The maximum limit of canopy transmittance (Eq. (3a)) was de®ned where Pj and P0j ˆ 1:0 and Cj assumed to be negligible, resulting in: max‰j;s Š ˆ …1 ÿ Fd †cos k ‡ Fd

(4a)

The variation in  j due to the slope and aspect of an inclined plane Eq. (2a) at depth j in the canopy was de®ned as max‰Is Š ˆ …1 ÿ Fd †

cos k …; ; 0† cos k …0; 0; 0†

2 ZZ

N…d ; d †sin d cos d dd dd

‡ Fd 0 0

(4b) where k is the scattering angle between the sun position and the slope normal, d is the scattering angle between the location in the sky location (d azimuth and d zenith) and sun position, N is the cloudless sky radiance distribution for the PAR or

R.H. Grant / Agricultural and Forest Meteorology 95 (1999) 187±201

UVB waveband according to Grant et al. (1995a, b, 1997), and z is the limiting horizon angle as de®ned by Gueymard (1987) and also used in Grant (1998). The scattering angle between the location in the sky with  azimuth and  zenith and the sloped surface normal is identical to Eq. (3b) after substituting subscript d for k. 2.2.2. Estimation of maximum canopy transmittance: shaded surface Large gaps in the canopy allow signi®cant penetration of sky diffuse radiation to level j. The maximum  j,s in the shade, corresponding to the surface exposed to the complete sky hemisphere, corresponds to Eq. (3a) with Pj ˆ 0; P0j ˆ 1:0, and Cj assumed to be negligible. The maximum  j,s in the shade is equal to Fd on the horizontal plane. For other orientations of an inclined plane, the maximum shade condition  j,s was de®ned as: maxdiffuse ‰j;s Š ˆ Fd …maxdiffuse ‰Is Š†

(5a)

where maxdiffuse[Is] represents the variation in  j due to the slope and aspect of an inclined plane (Eq. (2a)) at depth j in the canopy according to: Z2 Z maxdiffuse ‰Is Š ˆ

N…d ; d †sind cos d d dd 0

193

where mindiffuse[Is] represents the variation in  j,s due to the slope and aspect of an inclined plane at depth j in the canopy according to: mindiffuse ‰Is Š R 2 R  ˆ

0

0

eÿGj =cos d N…d ; d †sin d cos d d dd maxdiffuse ‰Is Š (6b)

where G is the projection coef®cient of Ross (1981), and  is the fraction of vegetation leaf area from the top of the canopy to the depth of j. In this sub-model, G is invariant (1/2) relative to  and . Comparisons of the predicted and measured Is values provided an indication of the ability of existing canopy radiation models to simulate the radiant ¯ux density on inclined surfaces. If the measured values are well-approximated by a sunlit and shade submodel, then the bi-modal approach to canopy transmission of radiation provides an adequate representation of the radiation environment and it is only a question of the distribution function partitioning the surfaces in the canopy into sunlit and shaded surfaces. If the measured Is values range between the two shade sub-models, then the bi-modal modeling approach is inadequate and a different approach is warranted.

0

(5b) 2.2.3. Estimation of minimum canopy transmittance: shaded surface Small gaps in the canopy allow minimal penetration of sky diffuse radiation to level j. The minimum limit for canopy transmittance occurs when there is negligible sky view and the surface is in the shade. This condition corresponds to Eq. (3a) with Pj ˆ 0 and negligible Cj. In this sub-model, P0j was estimated from the canopy structure and sky radiance distributions. Minimal P0j was estimated assuming a uniform distribution of vegetation elements in accordance with Anisimov and Fukshansky's Anisimov and Fukshansky (1994) conclusion that minimum transmittance occurs for uniformly distributed absorbers. The penetration of light in the portion of canopy entirely shaded was de®ned as the minimum  j,s for diffuse penetration as: mindiffuse ‰j;s Š ˆ Fd P0j;s ˆ Fd …mindiffuse ‰Is Š†

(6a)

3. Results and discussion Earth-parallel measurements of  j for I-UVB showed values close to the maximum possible modeled diffuse value. Since some portion of the sky view must be obstructed, these measurements must be sunlit. The corresponding  j for PPFD showed values higher than the modeled maximum shade condition four of the six measurement periods (Table 2). Direct comparisons between the radiant ¯ux density in the UVB and PPFD is not possible since the measurements are effectively point values separated by a suf®cient distance for sunlit conditions to be present only on one sensor. 3.1. Above canopy conditions There was moderate variability in the above-canopy UVB and PAR ¯ux density for a given slope and a varying azimuth. Typically, the ¯ux density varied (at

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R.H. Grant / Agricultural and Forest Meteorology 95 (1999) 187±201

Table 2 Measured and modeled canopy transmittances hc

 jPAR Measured

0.2 0.2 0.6 0.6 0.6 0.6 1.2 1.2 1.2 1.2

0.10 0.29 0.87 0.26 0.13 0.26 1.00 1.00 1.00 1.00

 jUVB Predicted

Measured

maxdiffuse

mindiffuse

0.15 0.15 0.15 0.15 0.17 0.18 0.15 0.16 0.17 0.18

0.04 0.04 0.08 0.09 0.09 0.09 0.15 0.16 0.17 0.18

458) by 0.73 for the PAR and 0.6 in the UVB, with the greatest ¯ux density for surfaces perpendicular to (facing) the sun and least facing away from the sun (slope aspect 1808 from that of the solar beam). The above canopy Is in the PAR (designated Is -PAR) was more strongly in¯uenced by the slope of the measurement plane than Is in the UVB (designated Is-UVB) (Fig. 3). This was largely due to the greater cloud-free diffuse fractions in the UVB than in the PAR. Surfaces

Fig. 3. Top-of-canopy Is-UVB and Is-PAR along the principal plane of the sun. Panels A and B illustrate the variability in Is at SZA of 248 and 438, respectively. The Is-UVB and Is-PAR are indicated by the solid and open circles, respectively. The  for surfaces facing the sun are positive while those facing away from the sun are negative.

0.30 0.29 0.44 0.46 0.15 0.13 1.00 1.00 1.00 1.00

Predicted maxdiffuse

maxdiffuse

0.47 0.46 0.46 0.47 0.51 0.55 0.47 0.48 0.50 0.53

0.08 0.08 0.23 0.24 0.22 0.24 0.47 0.48 0.50 0.53

facing away from the sun (greater than 908 relative azimuth) had higher Is-UVB than Is-PAR as the sensor plane slope exceeded approximately 458 (Fig. 3). The difference between Is-PAR and Is-UVB increased as the solar zenith angle increased for any given slope. In general, Is-UVB was greater than Is-PAR when the plane normal was away from the sun while Is-PAR was greater than Is-UVB when the plane normal faced the sun (Fig. 3). Is-PAR values are comparable to those reported by Niilisk et al. (1970) (Fig. 4a). Is-PAR exceeded Is-UVB when the plane faced the sun was probably largely due to: (1) the smaller PAR diffuse fraction than UVB, (2) the greater fraction of the diffuse sky radiation in the semi-hemisphere of the sun (especially in the solar aureole) in the PAR than UVB (Grant, 1997a, b), and (3) the greater re¯ectance of the leaf surfaces in the PAR than the UVB (Grant, 1993). When facing the sun, Niilisk et al. (1970) values for Is-NIR were generally higher than the corresponding values of Is-PAR as well as the measured values of Is-UVB at high slopes. Hence, when a surface faces the sun, results indicate that Is increases with increasing wavelength of waveband, from UVB to PAR to NIR (Fig. 4). The greater Is in the UVB than PAR when the plane faced away from the sun was probably largely due to the greater UVB diffuse fraction than PAR and the greater fraction of that sky radiation coming from the semi-hemisphere away from the sun. Niilisk et al. (1970) found that Is-NIR was greater than Is-PAR when the surface faced away from the sun (Fig. 4(a)).

R.H. Grant / Agricultural and Forest Meteorology 95 (1999) 187±201

Fig. 4. Influence of waveband on Is along the principal plane of the sun. Panel A illustrates the above-canopy angular variability in IsUVB and Is-PAR at SZA of 298 in comparison to values of Is-PAR (solid line) and Is-NIR (dashed line) over a sunflower canopy for a SZA of 308 from Niilisk et al. (1970). The Is-UVB and Is-PAR over the maize canopy are indicated by triangles and circles respectively. The  for surfaces facing the sun are positive while those facing away from the sun are negative. Panel B compares the angular variability in Is-UVB and Is-PAR of sunlit surfaces in a maize canopy at a height with cumulative LAI of 1.2 and SZA of 258 with Is-PAR (solid line) and Is -NIR (dashed line) in a LAI 1 sunflower canopy for SZA of 308 from Niilisk et al. (1970).

Since in general we expect a greater PAR diffuse fraction than NIR (Grant et al., 1997), these results indicate that the sky radiance distribution of NIR must be more evenly distributed than the PAR, resulting in greater relative radiance from the sky semi-hemisphere opposite the sun. Unfortunately, the author was unable to ®nd NIR sky radiance distributions in the literature to substantiate this conclusion. Combining the results from this study and that reported by Niilisk et al. (1970), it appears that when a surface faces away from the sun, Is varies by waveband as UVB > NIR > PAR (Fig. 4(a)). Given the diurnal path of the sun, surfaces facing north away from the sun would be expected to have greater UVB/PAR ratios than those facing south towards the sun. The juxtaposition of the NIR Is between the UVB and PAR Is cannot be explained based on atmospheric scattering principles. 3.2. Within canopy conditions At low slopes, Is-UVB was typically greater than IsPAR when shaded, since most large gaps in the canopy occur near the zenith (Hutchison et al. (1980) and the

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Fig. 5. Is-UVB and Is-PAR along the principal plane of the sun for 0.6 hc. The Is-UVB and Is-PAR for run 1 are indicated by the solid and open circles, respectively. Predicted values for the maximum sunlit condition (max), maximum shaded condition (maxdiffuse), and minimum shaded condition (mindiffuse) are labeled for Is-UVB (solid lines). Corresponding predicted values for Is-PAR are indicated by the dashed lines. The location of a leaf over the sensors and the solar zenith angle of the sun are indicated. The  for surfaces facing the sun are positive while those facing away from the sun are negative.

UVB diffuse fraction is larger than the PAR under clear skies. Penetration of the radiation through the canopy depended on the semi-hemisphere of the plane normal, with greater penetration of both wavebands when the plane normal was oriented towards the sun. Within the canopy, the maximum values of Is in PAR exceeded that for the UVB when the surface faced the sun and the solar zenith angle was less than the surface slope. This is in contrast to the relationship between IsPAR and Is-UVB above the canopy (Fig. 3). When the surface faced away from the sun in the canopy, the maximum values of Is-PAR equaled or exceeded IsUVB (Fig. 5). This also was the opposite that observed for Is above the canopy (Fig. 3). For sunlit conditions (maximum values), Is-PAR corresponded closely to values reported by Niilisk et al. (1970) for a similar cumulative LAI above the measurement location in a sun¯ower canopy (Fig. 4(b)). The corresponding NIR values from Niilisk et al. (1970) indicated greater Is than for the PAR and UVB when the surface was facing away from the sun (but still sunlit). This was likely due to the typically greater scattering by the canopy in the NIR than in the PAR or UVB.

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Fig. 6. Is-UVB and Is-PAR along the principal plane of the sun for 0.2 hc. The Is-UVB and Is-PAR for run 4 are indicated by the solid symbols and open symbols, respectively. Predicted values for the maximum sunlit condition (max), maximum shaded condition (maxdiffuse), and minimum shaded condition (mindiffuse) are labeled for the Is-UVB (solid lines). Corresponding predicted values for Is-PAR are indicated by the dashed lines. The location of a gap over the sensors and the solar zenith angle of the sun are indicated. The (for surfaces facing the sun are positive while those facing away from the sun are negative.

Is within the canopy was highly variable, with many values that cannot be clearly ascribed to sunlit or shaded conditions (Figs. 5 and 6). Gaps resulting in sunlit surfaces had equal Is-UVB and Is-PAR for orientations affected by the gap. At 0.6 hc, the range in slopes of gap-in¯uenced Is was essentially the same for both PAR and UVB wavebands (Figs. 5 and 7(a)Fig. 7(b)). At 0.2 hc, the range in slopes with gap-in¯uenced Is was greater for the UVB than the PAR (Fig. 7(c±d)). Brown et al. (1994) found UVB attenuated less than PAR in `disturbed' canopies and gaps in dense canopies. Typically Is-UVB varied to a lesser extent between sunlit and shaded leaves than the Is-PAR. This is a direct result of the relative importance of the diffuse sky radiation, with increasing sky view in canopy gaps resulting in less increase in ¯ux density in the PAR than in the UVB waveband. Increased obstruction of the sky view was evident by the reduction in Is (presumably in shade) with increasing depth in the canopy (Fig. 5, Fig. 6). At 0.2 hc, the minimum measured Is in the UVB exceeded that in the PAR by a 5±1 ratio at small slopes to nearly equal values at high slopes (Fig. 6). The greater penetration of UVB over PAR at small surface slopes

Fig. 7. Comparative influence of canopy gaps on Is-UVB and IsPAR. Panels A and B illustrate the Is for 0.6 hc at one location (SZA 228) while panels C and D illustrate the Is for 0.6 hc at a second location (SZA 258). Is-UVB is illustrated in panels B and D. Is-PAR is illustrated in panels A and C. Contour interval is 0.1 with greater relative penetration is indicated by lighter contours.

was probably a result of gap penetration of diffuse sky radiation on the shaded surface. The relative impacts of obstructions to sky view depend on the presence or absence of direct beam radiation. When the view of the sun is blocked, the decrease in Is corresponds to the greater relative decrease in global radiation for the PAR than the UVB. When the sky is obstructed and the location is in shade at 0.6 hc, the minimum measured Is levels for a given obstruction were greater in the UVB than PAR (Figs. 5 and 6). At the canopy top where direct radiation was present, Is-UVB was reduced more by obstructions of sky view than the Is-PAR. This was likely due to the greater importance of the diffuse sky radiation to the Is-UVB than the Is-PAR, and illustrates the effect of diffuse fraction on the distribution of radiation in crop canopies. 3.3. Comparisons between modeled and measured relative flux density The sub-models de®ning the bounds for  j,s of sunlit and shaded surfaces in the maize canopy were described by Eqs. (3a) and (3b) through Fig. 6. The

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variation in modeled and measured Is values at 0.6 hc and 0.2 hc were evaluated for varying orientations of the surface. Table 2 indicates the horizontal measured and modeled  j values. The predicted maximum values of Is-PAR overestimated the measured values at both 0.6 hc and 0.2 hc when the surface faced the sun (Figs. 5 and 6). The predicted values of Is-UVB approximated the measured values at 0.6 hc and 0.2 hc when the surface faced the sun (Figs. 5 and 6). Similar predictions of Is on surfaces facing away from the sun tended to approximate the measured Is-PAR well but over-estimated Is-UVB (Figs. 5 and 6). Errors in the sub-model for maxdiffuse[Is] were at least partly a result of the in¯uence of location and size of canopy gaps on sky view and partly due to differences between the estimated and actual diffuse fraction. The prediction errors did not appear to be due to the assumption of negligible complementary radiation, since the omission of complementary radiation from the sub-models should result in greater prediction errors for planes facing away from the sun than facing the sun. This would be expected since due to leaf scatterance in the PAR is twice that in the UVB waveband (Grant, 1993) and radiation scattered off vegetation would be less for surfaces facing the sun than for surfaces facing away from the sun. Comparisons between modeled and measured shaded surfaces are dif®cult, since the presence and location of gaps in the canopy strongly in¯uenced the measured transmittance. The sub-model describing the deep shade minimum Is correctly de®ned the minimum PAR levels for both 0.6H for planes with small slopes and 0.2 hc for all inclined planes (Figs. 5 and 6). The sub-model describing the deep shade minimum Is correctly de®ned the minimum UVB level for 0.2 hc (Fig. 6) but under-estimated the minimum UVB for all planes with slopes less than 608 (Fig. 5). The modeled mindiffuse[Is] appeared to match the measured value when there were no distinct canopy gaps' conditions associated with the one-dimensional requirements (canopy homogeneity) of the model approach. A gap in the canopy dramatically changed the Is-PAR levels from maximal levels when the sun was in view to minimal levels when the sun was blocked from view (and sun view in Fig. 6). As a result, Is in the PAR was typically either equal to the max[Is] or mindiffuse[Is] sub-models. The under-prediction of the minimum Is levels in the

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UVB were probably due to gaps in the canopy providing sky view (and sun view in Fig. 6). As a result, the region of near maximum Is in the vicinity of a gap differed between the PAR and UVB wavebands because high Is-PAR was associated with view of the sun and high Is-UVB was associated with view of the sun and sky. Revisiting the leaf obstruction evident in Figs. 5 and 7, the obstruction of the direct beam radiation reduced the measured Is to levels to the modeled deep shade minimum Is for some inclined planes and to within 0.1±0.05 of the maximum shade Is (maxdiffuse[Is]) for other planes (Fig. 5). The cause for the under-estimate of maxdiffuse[Is] is probably due to an underestimate in the diffuse fraction, which varies within cloud-free conditions as a result of differing amounts of atmospheric aerosol. The difference between the Is at the `Leaf' location to that nearer zenith in Fig. 5 is probably a result of the location of the sky view blockage by the leaf. Values of Is-UVB and Is-PAR between maxdiffuse[Is] and mindiffuse[Is] (Figs. 5 and 6) were probably a result of the passage of short duration sun¯ecks across the sensors resulting from wind moving the plant leaves in the canopy. The greater number of Is-UVB than IsPAR values between these two theoretical values were likely due to the larger diameter of the UVB sensor diffuser (25 mm) than the PAR sensor diffuser (8 mm). 3.4. Evaluation of the bi-modal flux density modeling assumption Evidence for the bi-modality of the ¯ux density on sloped surfaces and the relative importance of the transitional values between sunlit and shade Is was assessed using probability analyses of the instantaneous measurements of Is for the PAR and UVB wavebands. At 0.6H (mid-canopy) radiation in both wavebands had characteristic peaks associated with shaded surfaces (leaves) and sunlit surfaces (leaves). At 0.2 hc, the PAR and UVB had two peaks in the probability distribution of Is. These were associated with sunlit and shaded surfaces as noted by Niilisk et al. (1970) and many others. At 0.6 hc, there were waveband differences in the distribution of Is. There were two distinct Is-PAR probability peaks, designated `A' and `D' in Fig. 8(A). There were three and at some slopes four distinct Is-UVB probability peaks at 0.6 hc.

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Fig. 8. Probability distributions of Is-UVB and Is-PAR at mid-canopy. Part A illustrates the probability distributions for Is-UVB and Is -PAR at 0.6H at intervals of 108 slope (slopes indicated at right of panel). The solid and dashed lines correspond to the distributions of Is -UVB and IsPAR, respectively. Labeled vectors correspond to tendencies in peak Is regions with increasing surface slope. Part B illustrates the conceptual explanation of the peaks noted in Part A. Predicted values for max[Is] from Eqs. (4a) and (4b), maxdiffuse[Is] from Eqs. (5a) and (5b), mindiffuse[Is] from Eqs. (6a) and (6b) are indicated for Is-UVB. The magnitude of each peak identified in part A is indicated with the appropriate label.

The probability peaks at the high (D peak) and low end (A peak) of Is were evident in the analysis for both wavebands. The Is at the A probability peak corresponded with a surface in deep shade (mindiffuse[Is]) and little view of the sky (Fig. 8). The Is of the D probability peak corresponded with the sunlit surface (max[Is]) either facing the sun or at small slope (Fig. 8). A peak in the probability distribution of Is appeared to transition from the sunlit (D) peak to the deep shade (A) peak as the slope of the plane increased (Fig. 8). The Is of this peak, designated `C' in Fig. 8, corresponded with planes facing away from the sun (Fig. 8(B)). In general, the C and D peaks corresponded to the sunlit surface described by the max[Is] sub-model (Fig. 8), with the sub-model over-predicting Is on planes with small slopes. This over-prediction was likely due to partial obscuration of the sky radiation in this run, and probably does not represent a general problem with the modeling approach. These three peaks (A, C, and D) would be expected from a bimodal distribution of light in the canopy.

An additional dominant peak was found in the probability analysis of the Is-UVB at 0.6H (Fig. 8(A)). This peak (designated `B' in Fig. 8) ranged in value between the deep shade and sunlit peaks, and appeared to be transitional between these two relative ¯ux density extremes. The Is at the B probability peak (Fig. 8(A)) appeared to be associated with the Is at the A probability peak since the two Is peaks converge at high surface slopes. The magnitude of the difference in Is between the B and A probability peaks differed between the PAR and UVB wavebands. The Is-UVB at the B probability peak ranged from 0.55±0.4; 0.3±0.2 greater than the shaded (A) probability peak value. The corresponding Is-PAR of the B probability peak ranged from 0.25±0.2 and was between 0.2 and 0.1 greater than the A probability peak value. The magnitude of Is at the B probability peak (Fig. 8(A)) was similar to the diffuse fraction of the respective waveband (Table 1). In general, Is at the `B' probability peak corresponded with the expected values of the maxdiffuse[Is] submodel (Fig. 8(B)) and, therefore, likely represented

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penetration of diffuse sky radiation through large gaps in the canopy and is, hereafter, termed the `light shade' peak. Differences between Is at the light shade and deep shade probability peaks generally corresponded to the expected difference associated with maxdiffuse[Is] and mindiffuse[Is], and was likely associated with the relative contribution of sky diffuse radiation to the global irradiance of sloped surfaces in the canopy. Decreasing sky view, expected with increasing slope, may account for the transition of Is from values near the light shade to the deep shade probability peak (Fig. 8). Remembering that the maxdiffuse[Is] sub-model (Eq. (5b)) describes relative ¯ux density in the shade with maximal view of the sky, the magnitude of the probability and difference in Is between the light shade and deep shade probability peaks may be expected to be a function of the frequency of occurrence of relatively large gaps in the canopy (Fig. 7). Although the light shade probability peak was evident in the distribution of Is-PAR at 0.6 hc, the difference between the Is of the light shade and deep shade probability peaks in the PAR was 0.1 or less. As a result, the assumption of a bi-modal probability distribution for PPFD would likely be adequate for most applications even when the plant response was decidedly non-linear. The difference in Is-UVB of the light shade and deep shade probability peak was 0.4 or less and nearly centered between the sunlit and shaded conditions. Since the difference between the probability peaks is relatively large and the probability of the light shade peak is relatively high at 0.6 hc, a bimodal probability distribution of Is-UVB would misrepresent the distribution of UVB radiant ¯ux density in the maize canopy. This misrepresentation of the canopy radiation ®eld may translate into errors in estimating non-linear plant responses to the radiation. In this study, the higher cumulative LAI at 0.2 hc had smaller gaps in the canopy (Fig. 7) and a negligible light shade probability peak in both the UVB and PAR distributions (Fig. 8). Under these conditions, a bimodal distribution would represent the radiation environment reasonably well. The presence of large gaps in the canopy is identical to characterizing the canopy vegetation as clumped. The clumping of vegetation elements in the canopy can be dealt with in one-dimensional radiation models by addition of a clumping factor in the gap probability

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function based on a Markov model (Nilson, 1971) or using a negative binomial function to describe the gap probability (Nilson, 1971). These methods however still only can produce a bi-modal distribution of the radiant ¯ux density in the canopy where there is only deep shade and sunlit conditions. These approaches to dealing with clumping in the canopy cannot describe light and deep shade conditions associated with diffuse sky penetration through both large and small gaps. It is proposed that an analysis of the distribution of gap sizes in the canopy be used to partition the gap probability function into a component for small, random gaps and a component for the dominant large gap size. It is important to remember that this analysis is for cloud-free sky conditions under a narrow range of diffuse fractions for both PAR and UVB. Different sky conditions may result in different conclusions concerning the applicability of bi-modal distributions of radiant ¯ux density for plant response estimation. Greater UVB due to reduced atmospheric ozone results in less diffuse sky radiation and consequently a more bi-modal probability distribution of Is. Greater aerosol concentrations in the atmosphere increases diffuse fraction for both wavebands and, consequently, tends to shift the probability distribution of Is in the PAR to the conditions reported here for the UVB. 3.5. Evaluation of the diffuse radiant flux density invariance modeling assumption Most canopy radiation models assume that the incident diffuse radiation is not dependent on leaf orientation and, consequently, assume a horizontal leaf to estimate the penetration of sky diffuse radiant ¯ux density (Norman, 1979; Daudet and Tchamitchian, 1993). While it may be reasonable to assume this for complementary radiation by assuming Lambertian scattering of the leaves, it is not obvious that this can be assumed for the penetrating sky diffuse radiation. Variability in measured and modeled Is levels with changing surface slope (Figs. 5±8) of approximately 0.1±0.2 indicate that the assumption of ¯ux density uniformity with respect to surface orientation results in prediction errors for both the PAR and UVB wavebands. The impact of this source of error in the modeled radiant ¯ux density (or canopy transmittance) for sloped surfaces depends on Fd. Since Fd

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for clear sky PPFD is typically less than 0.2 during most of the day, the error in modeled  j,s is expected to be less than 0.05 regardless of sky view fraction. Assuming a horizontal leaf to estimate the diffuse sky penetration at high leaf angles will likely overestimate the radiant ¯ux density of the mean leaf by 0.05 in the UVB and 0.02 in the PAR waveband for a canopy with LAI of 1. For the UVB waveband, Fd for clear skies is approximately 0.5 for much of the day. If the UVB sky diffuse radiant ¯ux density is assumed independent of surface orientation, the expected error in modeled  j,s is approximately 0.05±0.10 depending on the sky view fraction. Ultimately, a three-dimensional model may be needed to estimate the UVB radiant ¯ux density in some low LAI canopies to account both for the distribution of gaps of various sizes and the variation in sky radiance with azimuth and zenith. 4. Summary and conclusions The mean penetration of PAR was predicted to exceed that of UVB when horizontal locations in the canopy are sunlit and to be less than that of UVB when the horizontal locations in the canopy were shaded. The measured UVB penetration exceeded that of PAR since leaf surfaces are not entirely sunlit in the canopy. Typically, the extinction of radiation in the same semi-hemisphere of the sky as the location of the sun was greater in the UVB than the PAR, with greater penetration of PAR than UVB ¯ux density. Conversely, for planes facing away from the sun the extinction of PAR ¯ux density was greater than the UVB ¯ux density, with the result of greater penetration of UVB than PAR ¯ux density. Therefore, leaves facing away from the sun may be expected to receive relatively more UVB than PAR ¯ux density while leaves facing the sun may be expected to receive more PAR than UVB ¯ux density. The sky diffuse radiation component of the global ¯ux density on inclined planes varied by 0.1±0.2 for low cumulative leaf areas. However,  j,s in sunlit locations at a given depth could be approximated by Is measured (or modeled) above the canopy times the predicted horizontal  j for the same orientation. Three radiation regimes were evident for Is within the canopy; a sunlit regime with some view of the sky,

a light shade regime with signi®cant view of the sky through large gaps, and a deep shade regime with little sky view through small gaps. The difference between the latter two regimes was smaller for the PAR than the UVB, indicating that a bi-modal probability distribution for Is is likely to adequately describe the PPFD environment but not the UVB radiant ¯ux density environment. Models that assume a bi-modal distribution of radiation received by plant surfaces in the canopy appear to be appropriate for both wavebands at cumulative LAI of two or more, but only for PAR when the cumulative LAI was one. Prediction of nonhorizontal UVB radiant ¯ux density in open canopies such as the mid-canopy height in this study will require the prediction of three levels of radiant ¯ux density, with the additional level associated sky view. As a result, one-dimensional models of UVB radiation need to account for different probabilities of large and small gap sizes. Most canopy radiation models assume that the incident diffuse radiation is not dependent on leaf orientation; assuming a planar leaf to estimate diffuse radiant ¯ux density (Norman, 1979; Daudet and Tchamitchian, 1993). This assumption resulted in an underestimate of the relative ¯ux density in the maize canopy when the leaf faces the sun and an overestimate of the relative ¯ux density when the leaf faces away from the sun. Acknowledgements Thanks go to Michelle Paterson for aiding in the ®eld hemispherical measurements. This study was supported by the Purdue University Agricultural Experiment Station, and is Journal Paper Number 15,571. References Allen Jr., L.H., Gausman, H.W., Allen, W.A., 1975. Solar ultraviolet radiation in terrestrial plant communities. J. Environ. Qual. 4, 285±294. Anisimov, O., Fukshansky, L., 1994. Light-vegetation interaction: a new stochastic approach for description and classification. Agric. For. Meteorol. 66, 93±110. Beggs, C.J., Schneider-Ziebert, U., Wellmann, E., 1986. UVB radiation and adaptive mechanisms in plants. In: Worrest, R.C., Caldwell, M.M. (Eds.), Stratospheric Ozone Reduction, Ultra-

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