Chilean journal of agricultural research
versão ISSN 0718-5839
Chilean J. Agric. Res. vol.71 no.1 Chillán mar. 2011
Chilean Journal of Agricultural Research 71(1):122-131 (January - March 2011)
In Field Assessment on the Relationship between Photosynthetic Active Radiation (PAR) and Global Solar Radiation Transmittance through Discontinuous Canopies.
Determinación en Terreno de la Relación entre la Transmitancia de Radiación Solar Global y Radiación Fotosintéticamente Activa (PAR) a través de Coberturas Vegetales Discontinuas.
Ricardo Oyarzún1, 2*, Claudio Stöckle1, Joan Wu1, and Matthew Whiting3
1Washington State University, Biological Systems Engineering Faculty, Pullman, Washington, 99163, USA.
2Universidad de La Serena, Facultad de Ingeniería, Benavente 980, La Serena, Chile. *Corresponding author (email@example.com)
3Washington State University, Irrigated Agriculture Research and Extension Center, Prosser, Washington, 99350, USA.
In many crop models, the process of radiation transmittance through the canopy is normally described as an exponential attenuation process (Beers Law equation), which is assumed to be valid for canopies covering the ground with a random spatial distribution of leaves. However, for discontinuous canopies, where a distinctive row pattern of plant exists, there is a more complex situation because of the presence of gaps between individual plants. This must be accounted for when characterizing radiation relationships for these kinds of systems, in particular when short time-scales are of interest. Photosynthetically active radiation (PAR) transmittance (τPAR) is more commonly studied and reported than global solar radiation (Sg) transmittance (τSg). However, both PAR and Sg are important in radiative transfer sub-models used in plant growth simulation. In this work simultaneous measurements of τSg and τPAR under discontinuous canopies were performed, and the hourly changes in radiation transmittance for PAR and global solar radiation were characterized. Two methods were assessed to transform between τSg and τPAR. The two methods yielded similar results for low values of transmittance, but disagreement occurred for higher values of transmittance. The method based on a fixed value for the ratio of extinction coefficients for PAR and Sg outperformed the method based on a linear relationship between τPAR and τSg with average relative errors (RE) of 7.97% vs. 13.29% and 2.84% vs. 7.77% for hourly and daily time-scale, respectively.
Key words: radiation interception, extinction coefficient, crop simulation model.
En muchos modelos, la transmisión de radiación a través de la canopia es descrita como un proceso de atenuación exponencial (Ley de Beer), la cual se asume válida para coberturas vegetales completas y con una distribución aleatoria de hojas. Sin embargo, para canopias discontinuas ocurre una situación más compleja debido a la presencia de espacios entre las plantas. Esto debe ser considerado cuando se caracterizan aspectos de radiación en este tipo de sistemas, especialmente cuando es de interés a una escala de tiempo pequeña. La transmisión de radiación fotosintéticamente activa PAR (τPAR) es más típicamente estudiada y mencionada que la transmisión de radiación solar Sg (τSg). Sin embargo, tanto PAR como Sg son importantes en los sub-modelos de radiación que suelen formar parte de los programas usados para simular el crecimiento de cultivos. En este trabajo se realizaron mediciones simultáneas de τSg y τPAR, y se caracterizó la variación horaria en la transmitancia de PAR y Sg. Dos métodos fueron evaluados para realizar la transformación entre τSg y τPAR. Ambos enfoques dieron resultados similares para condiciones de baja transmitancia, pero difieren para valores elevados de ésta. El metodo basado en una razón fija de los coeficientes de extinctión de PAR y Sg se desempeñó mejor que aquel basado en una relación lineal entre τPAR y τSg, con un error relativo promedio de 7.97% vs. 13.29% y 2.84% vs. 7.77%, respectivamente, para escalas de tiempo horarias y diarias.
Palabras clave: interceptación de radiación, coeficiente de extinción, modelo de simulación de cultivos.
Radiation transmittance through crop canopies is normally described as exponential-type attenuation process as (Thornley and Johnson, 1990; Lizaso et al., 2003):
τ = I(l)/I(o) = e-K LAIo 
where τ is the transmittance in the wavelength of interest, I(l) is the transmitted radiation, I(o) is the incoming radiation (W m-2 for solar radiation, mmol m-2s-1 for photosynthetically active radiation PAR), LAIo is the leaf area index (m2 leaves per m2 of soil), and K is an extinction coefficient. This equation is generally assumed to be valid for full covering canopies with random distribution of leaves. For discontinuous canopies, such as those found in crops with row structure or in fruit tree orchards, a clumping factor (Ω), which varies between 0 and 1, is often included to extend the use of the equation (Campbell and Norman, 1998). Thus, Equation  is re-written as:
t = e-K Ω LAIo 
Although questioned (Sinclair, 2006), it is fairly common to find studies that characterize either diurnal radiation transmittance or interception by crop canopies based only on midday observations (Yunusa et al., 1997; Kiniry, 1999). This practice may seem valid for horticultural and annual crops that tend to develop and reach full soil cover rather quickly. However, a different situation might be expected for discontinuous crop canopies, such as those existing in fruit tree orchards or horticultural crops on early growing stages. In such systems, radiation transmittance processes are affected by both the fraction of the radiation that passes through the canopy, and therefore is attenuated, and the fraction of the radiation that passes unobstructed through and between canopy gaps, which varies greatly through the day. This is of particular significance for radiation transfer on short-time scales, with varying interaction between the crop canopy architecture and the sun position in the sky throughout the day.
Furthermore, radiative transfer sub-models that can be used in plant growth simulations must take into account canopy transmittance or interception of PAR (400 to 700 nm wavelength) as well as global solar radiation (Sg, 300 to 3000 nm). The former is required to calculate photosynthesis, while the latter is used to calculate crop energy balance and crop evapotranspiration and its partitioning into transpiration and soil water evaporation (Weiss and Norman, 1985; Stöckle and Jara, 1998). Moreover, the radiation-use efficiency (RUE) approach that relates dry mass accumulation with the amount of intercepted PAR (Monteith, 1994; Kiniry, 1999), or intercepted Sg (Castellan-Estrada, 2001) is widely used to estimate biomass accumulation in horticultural crops, fruit trees and forest (Landsberg and Hingston, 1996; Kiniry et al., 1998; Mariscal et al., 2000).
Simultaneous direct measurements of PAR transmittance (τPAR) and Sg transmittance (τSg) are rarely done in the field or found in the literature, since instruments need to be placed under leaf canopies and left there for the whole measurement period (Sinclair, 2006). Studies are more commonly performed for PAR than Sg, due to the easiness of its measurement and instrument availability. Thus, the question arises in how to convert between τPAR and τSg. This issue was addressed by Campbell and Van Evert (1994), who proposed a theoretical method based upon the different leaf optical properties of crop leaves regarding different portion of the radiation spectrum, which determines a ratio for the extinction coefficients for Sg and PAR (KSg/KPAR) of 0.7. This is done considering leaf absorptivities for PAR and Sg of 0.8 and 0.4, respectively. From their work, some authors later adopted the same method and value for this ratio on studies reported for horticultural and annual crops (Jovanovic et al., 1999; Jovanovic and Annandale, 2000; Marcos, 2000). In an independent theoretical effort, Kiniry (1999) gave values of KSg and KPAR that determine a figure of 0.75 for the same ratio. However, when considering the conversion of RUE values based on PAR into RUE based on Sg, Bonhomme (2000) argued that the use of a single conversion factor would not be suitable for different situations of LAI and leaf orientations. Nevertheless, a common aspect of these studies is that they relied on theoretical calculations. As pointed out by Yunusa et al. (1993), and later by Sattin et al. (1997), there is a lack of experimental, field-obtained data on this subject.
The purposes of this research were: (i) to study and characterize the diurnal variation of tPAR and tSg, associated with discontinuous canopies; and (ii) to experimentally assess the suitability of reported methods to convert τPAR into τSg for discontinuous canopies.
MATERIALS AND METHODS
Field measurements were carried out in selected clear days from May to July in the summer of 2004 at the Roza experimental orchards of Washington State University-Irrigated Agriculture Research and Extension Center (WSU-IAREC) near Prosser (46.2o N, 119.7o W, 380 m.a.s.l.), Washinton, USA. They were performed on a mature sweet cherry (Prunus avium L.) orchard, and on a corn (Zea mays L.) crop during early stages of development, under variable experimental conditions in terms of both sun position through the day (cherry dataset) and canopy cover (corn dataset), as shown in Table 1.
Table 1. Days and experimental conditions of field measurements, in terms of sun position (zenith and azimuth angles, in degrees) at three different hours (standard time), leaf area index (LAIo), and incoming global radiation (Sg, MJ m-2 d-1).
Measurements were made on 9 yr-old Bing/Gisela 5® sweet cherry trees spaced at 2.5 m by 4.5 m within and between rows, respectively, in North-South oriented rows, trained to a free standing, standard multiple-leader open-center architecture, forming a nearly continuous hedgerow of 3.2 m tall and 2.8 m width. Leaf area of the trees (Lt) was estimated non-destructively along the season as the sum of spur leaf area (Lp) and shoot leaf area (Ls) following the technique outlined in Whiting (2001).
Simultaneous τPAR and τSg measurements were carried out on May 9 (DOY 130), June 1 (DOY 153), and July 10 (DOY 192), 2004, at two locations in the orchard (Figure 1). PAR transmittance was measured hourly from 07:00 to 17:00 h (standard time), using a 0.8 m linear quantum sensor (AccuPAR probe, Decagon Devices, Pullman, Washington, USA). At each hour, incoming PAR (PARh) was determined on an open area near the trees. This was done twice on each measurement period, i.e. immediately before and after the below-canopy measurements, the average value was calculated and a mean time was assigned. Hourly below-canopy PAR measurements (PARh¯) were taken at 30 cm above the orchard floor on seven positions parallels to the tree row and separated by 65 cm, with the fourth measurement at the tree row center, by hand-moving the probe from one position to another, following Cohen et al. (1997). Individual and average readings (PARh¯ and PARh,avg¯, respectively) were recorded. The fractional PAR transmittance on each hour (τPAR,h) and the PAR extinction coefficient (KPAR,h) were determined as:
Figure 1. Schematic representation of the disposition of the solarimeters on the two locations on the orchard in (A) plan view and in (B) cross-section view, as well as the location of the reference solarimeter measuring incoming solar radiation (R), and the datalogger unit (shadowed rectangle). The photosynthetically active radiation (PAR) sensor was hand-moved through the same positions for measurements. The same procedure was used for the corn field.
τPAR,h = PARh,avg¯/PARh 
KPAR,h = (-ln τPAR,h)/LAIo 
it should be noted that KPAR,h is an effective extinction coefficient, and it already includes the effect of gaps between canopies, since it is obtained from field measured τPAR,h and LAIo. Thus, it corresponds to the product of K and Ω showed in Equation .
Daily weighted average PAR transmittance (τPAR,D) and extinction coefficient (KPAR,D) were obtained as:
Global solar radiation transmittance was assessed on the same positions as described above for tPAR, but using seven 0.9 m long solarimeter tubes (Marcos, 2000) per location, permanently installed throughout each day. An additional solarimeter tube was placed in an open area next to the orchard and was used to register the incoming solar radiation (Sgh). All the solarimeters used were calibrated against a Precision Eppley thermopile pyranometer (The Eppley Laboratory, Newport, Rhode Island, USA).
The solarimeters were connected to a CR10 datalogger (Campbel Scientific, Logan, Utah, USA). A scan rate of 30 s was used and signals were averaged every 5 min, and data were recorded every 60 min coincidental with PAR measurements were considered for the analysis. Similar to PAR measurements, the global radiation transmittance (τSg,h) and the extinction coefficient (KSg,h) were obtained for each hour as:
τSg,h = Sgh,avg¯/Sghr 
KSg,hr = (-ln tSg,h)/LAIo 
where Sgh,avg¯ is the average value obtained from the below-canopy solarimeter tubes. Similarly, KSg represents the effective extinction coefficient. The respective daily averages were obtained as:
Finally, the hourly and daily values for the ratio between the PAR and Sg extinction coefficients (βh and βD respectively) were obtained as:
βh = KPAR,h/KSg,h 
βD = KPAR,D/KSg,D 
The corn crop used in this study was grown near the cherry trees, with a planting distance of 0.10 m by 0.75 m, within and between rows respectively, in near North-South oriented rows. Measurements were made during early stages of development. The average leaf area per plant was estimated non-destructively several times during the experimental period using a laser area meter (CI-203 CID, Vancouver, Washington, USA), measuring all the leaves on 16 to 20 plants from the tip toward the base. The leaf area index was determined as well.
Measurements of simultaneous τSg and τPAR were carried out on July 1 (DOY 183), July 7 (DOY 189), and July 16 (DOY 198) 2004, at two locations in the field. The first measurement set was obtained on a crop sowed on April 23, while the second and third set (July 7 and 16) corresponded to a second crop sowed on June 7. On those days, τPAR was determined hourly from 08:00 to 16:00 h (standard time), using the AccuPAR probe. At each hour, PARh and PARh¯ were determined as previously described for the cherry trees (now with a separation of 10.5 cm between positions). The same spacing applies for the solarimeter tubes used for τSg determinations. An additional solarimeter was placed above the canopies to register Sgh. The solarimeters were connected to a datalogger, using a scan rate of 30 s averaged every 15 min. Only data for each hour, coincidental with PAR measurements, were used for analysis. Thus, τPAR,h, τPAR,D, KPAR,h, KPAR,D, τSg,h, τSg,D, KSg,h, KSg,D, bh, and bD were computed as described earlier (Equations  to , only now the daily aggregation was obtained from h = 1 to 9).
The following methodologies apply for the conversion between τPAR and τSg. For the sake of space, mainly τPAR®τSg is discussed, although the performance of the methods in each conversion was evaluated.
Calculation procedures for transmittance conversion: fixed-ratio of extinction coefficients
Campbell and Van Evert (1994) related values of fraction of interception (one minus transmission) of global solar radiation (fSg) to fraction of interception of PAR (fPAR) for a plant canopy. In a follow-up analysis, and based on a Beers law equation-type, Campbell (2004) proposed that the ratio τSg/τPAR can be obtained as:
Assuming a fixed ratio (β) KSg/KPAR = 0.7 (Campbell and Van Evert, 1994), Equation  can be rewritten as:
The use of Equation  requires knowing both KPAR and LAIo. However, from Equation :
KPAR Ω = -ln(tPAR)/LAIo 
KSg Ω = -ln(tSg)/LAIo 
KSg/KPAR = ln(τSg)/ln(τPAR) 
Therefore, solving for τSg and assuming that b = 0.7, the expression becomes
Although Equation  is mathematically similar to Equation , it has the advantage of not requiring the knowledge of LAI. Thus, this method was selected and evaluated in this work, and is herein referred to as the fixed-ratio method.
Calculation procedures for transmittances conversion: Kiniry´s method
Kiniry (1999) briefly discusses two methods to convert fraction of interception of Sg (fSg), measured using a tube solarimeter, to fraction of interception of PAR (fPAR), measured using a PAR sensor, that produced nearly identical results. The first one was based on reported K values by Monteith and Unsworth (1990) for PAR and Sg (-0.485 and -0.65 respectively). He calculated, over a range of LAI from 0.1 to 3.0, a weighted mean value of 1.184 for the ratio fPAR/fSg. The second method, based on Gates (1965) which relates radiation transmitted through a leaf as a function of wavelength, yields a value of 1.190 for the referred ratio. Thus, assuming an average value of 1.187, and given the fact that the interception fraction is the complement (to one) of the transmittance, we have:
τSg = 0.842 τPAR + 0.158 
This will be referred to as the Kinirys method, and as the fixed-ratio method, it does not require information of LAIo.
The performance of the described methodologies was evaluated using graphical and statistical methods. The statistical indices (goodness of fit criteria) included the root mean square error (RMSE) and the relative RMSE or relative error (RE), the mean absolute error (MAE; Annandale et al., 2004); the Willmott index of agreement (D; Willmott, 1982); and the coefficient of residual mass (CRM; Loague and Green, 1991). These relationships have the following expressions:
RE (%) = (100 RMSE)/Oavg 
where Pi and Oi are the simulated and measured transmittances; n is the number of pairs of data (both observed and predicted values), and O is the mean of the measured values. The optimal values of RMSE, RE, MAE and CRM criteria are zero. For D, a value of one expresses perfect agreement between Oi and Pi whereas zero describes complete disagreement. The RMSE is dimensionless, and RE and MAE are in percentage. Positive values of CRM indicate that the model underestimates the measurements, whereas negative values indicate overestimates. All the analyses were made in Excel (Microsoft Inc.).
RESULTS AND DISCUSSION
Radiation transmittance relations
Hourly transmittance values were at their maximum around noon, when a relative higher proportion of the incoming radiation passes unobstructed through inter-canopy gaps, and at their minimum in early morning and late afternoon (Figure 2). Thus, when comparing the daily average of transmittance, either PAR or Sg, with hourly-instantaneous measurements, differences are found. Therefore, it is possible to argue that instantaneous, around-noon measurements of radiation transmittance, as is rather commonly reported in crop light capture- or RUE-related studies (e.g. Gallo et al., 1993; Yunusa et al., 1993; Lizaso et al., 2003) may not be a good practice when these studies are done on discontinuous canopies such as fruit trees or horticultural crops in their early stages of development, confirming the theoretical results of Sinclair (2006). In fact, τPAR and τSg measurements performed around noon tended to be higher than the daily weighted average, potentially introducing errors if the former are taken as representative of the overall daily situation. This is especially true for clear days with a high beam fraction in the incoming radiation that is able to penetrate through canopy (or inter-rows) gaps and reach the orchard floor during the central hours of the day. These ideas had been suggested before (Flenet et al., 1996; Sinclair and Muchow, 1999), but they tend to be, in general, overlooked (Yunusa et al., 1997; Kiniry et al., 1998; Kiniry, 1999).
Figure 2. Hourly global solar radiation transmittance (tSg) (open circles) and photosynthetically active radiation (PAR) transmittance (tPAR) (filled circles) and daily averaged tSg (segmented line) and tPAR (solid line) as determined from field measurements on the cherry orchard (panels A, B, and C) and corn (panels D, E, and F).
The general pattern was similar for all the measurement dates, with minor differences being detected for two situations: cherries on June 1 and corn on July 7. The former (Figure 2B) is a consequence of the particular cloudiness dynamic of that day. Although all measurement days can be classified as clear sky based on the daily total amount of incoming radiation (Table 1), June 1 presented intermittent episodes of clouds passing through the day. The presence of clouds enhances solar radiation scattering and reduces the relative importance of the beam fraction of the incoming radiation. Under such conditions, radiation comes from several directions from the sky and not a single source, as is the case under clear-sky conditions. Thus, the presence of gaps has a lesser effect on the transmittance of radiation reaching the orchard floor. In the case of corn on July 7 (Figure 2E), the high transmittance values obtained were likely a consequence of early stage of the crop development with low leaf area index (LAI), allowing a large amount of incoming radiation to penetrate and reach the soil surface, not only at solar noon but for an extended period through the day.
Transmittance was higher for global radiation than for PAR, a natural consequence of the different optical properties of leaves for PAR and Sg (Szeicz, 1974; Yunusa et al., 1993). Thus, the ratio τSg/τPAR was always higher than one. Moreover, this ratio is not constant, being generally higher early and late on the day and lower around noon. The differences in transmittance are highly dependant on the differential leaf optical properties, especially early or late in a day, since beam radiation is forced to pass through the canopies given the large zenith angle. Around noon, the proportion of incoming radiation (either Sg or PAR) that passes unobstructed through canopy gaps (either within or inter rows) is higher, reducing the effect of different optical properties of leaves for the different wavelengths and tending to make τSg and τPAR more similar.
Performance of transmittance conversion methods
The first step was to verify the validity of the 0.7 value for b, the ratio of extinction coefficients for Sg and PAR, as an expression of the effect of leaves optical properties. Thus, b was initially calculated considering for each hour only the below-canopy measurements positions, both for Sg and PAR that were completely shaded by the plants. Since on July 7 (DOY 189) the corn foliage coverage was extremely low, this day was initially excluded from this analysis as it was impossible to characterize any measurement position as completely shaded at any time of the day. Despite some variability at certain hours, the general trend of the hourly values was normally around 0.55-0.75 (Figure 3). Daily averages were around 0.65 (Table 2). It should be noted that all these values include, to some extent, the effect of plant parts other than leaves such as branches, fruit (for cherry trees) and dead leaves, all of them affecting radiation transmittance conditions. However, these particular effects are highly difficult to separate and quantify in actual field situations. Therefore, although we included different canopies such as cherry and corn, a value around 0.65 for b, such as the 0.7 figure proposed by Campbell and Van Evert (1994) seems to be accurate enough for its use in general applications and on a daily basis. Moreover, when considered all the below-canopy positions in the calculations (i.e. not only the shaded ones), there were no major differences in the extinction coefficients ratio despite of the variable relative importance of gaps between canopies at different times, even when there were differences in transmittance throughout the days (data not shown). Indeed, the variability in radiation transmittance for PAR and Sg through the day (Figure 2) does not extend in the same magnitude to the ratio of their extinction coefficients. Thus, the value of 0.70 for KSg/KPAR may be extended to general situations, including discontinuous canopies.
Figure 3. Hourly variation in the ratio of extinction coefficients for global solar radiation (Sg) and photosynthetically active radiation (PAR) KSg/KPAR for cherry trees (panel A) and corn (panel B) for the different days of measurements, considering only shadowed below-canopy positions.
Finally, Table 3 presents the results obtained when using the two reported methods for the conversion of transmittances. In general, the methods behave similarly when used for either tPAR®tSg or tSg®tPAR. Also, for low values of transmittance, e.g., less than 0.45, both methods tend to perform rather similarly (Figure 4A). However, differences were evident for transmittance values higher than 0.45. This is likely to be due to the fact that the Kinirys method is not flexible, in terms of the relation between τPAR and τSg. While the coefficients used in Kinirys linear relationship may be good enough for low values of τPAR, as the transmittance gets higher, τSg should be more similar to τPAR, where the extreme case is when all radiation is transmitted, and therefore, τSg approaches τPAR. This situation is not accounted for in the approach derived from Kinirys analysis. The fixed-ratio method therefore outperformed Kinirys method. The same behavior was observed on a daily time scale (Figure 4B). We found that it does not make an important difference to use 0.65 or 0.7 for b when using the fixed-ratio method (result not shown). Thus, unless there are field determinations of leaf optical properties for a given crop, the general use of 0.7 and the fixed ratio approach are adequate.
Figure 4. Comparison of global solar radiation transmittance (τSg) measured and simulated using the fixed-ratio method (FR) and Kinirys method (KM) for hourly (panel A) and daily (panel B) time scale.
Transmittance of both global solar radiation and PAR through discontinuous canopies proved to be affected by the optical properties of the leaves of the crop (cherry trees, corn) to the corresponding wavelength, by the existence of gaps between canopies, and the relative importance of the beam fraction of the incoming radiation. Nonetheless, the use of a value of 0.7 for the ratio of extinction coefficients appeared valid for both shadowed situations and non-complete covering canopies.
Regarding the conversion of transmittances for different wavelengths, the methods proposed generally performed properly for the different experimental conditions considered. The method based on a fixed value for the ratio of extinction coefficients outperformed Kinirys method both hourly (average RE = 7.97% and 13.29% respectively) and daily (average RE = 2.84% and 7.77% respectively). The former is a simple and suitable method to convert transmittance values of PAR and Sg at different time-scales and canopy-coverage conditions.
This research was partially funded through the project FONDEF D021-1146. The technical assistance of A. Milla in the field data acquisition is greatly appreciated as well as special collaboration given by E. Quiroz, C. Kremer and A. Kemanian during the installation and set-up process of the solarimeters. The paper benefited from the comments of anonymous reviewers and the editor.
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Received: 03 January 2010.
Accepted: 11 September 2010.