Parameterization of PAR vertical profile within horizontally uniform forest canopies for use in environmental modeling


Corresponding author: B. Lalic, Faculty of Agriculture, Department for Field and Vegetable Crops, University of Novi Sad, Dositej Obradovic Sq. 8, 21000 Novi Sad, Serbia. (


[1] The radiation transfer within the forest canopy plays crucial role in energy balance and turbulent transfer processes. Objective of this study is to suggest a new relation for vertical profile of photosynthetically active radiation (PAR) in case of horizontally uniform forest canopy. It is based on (i) the Lambert-Beer law relationship and (ii) new parameterization of leaf area density (LAD) profile. We have supposed that absorption coefficient μ varies with height and depends on LAD distribution. To check validity of the relation proposed, we have compared calculated values with the observations using data sets assimilated during Anglo-Brazilian Amazonian Climate Observation Study experiment at two observational sites located in Reserva Jaru and Reserva Ducke (Brazil) with different types of forest. Among all available measurements, 615 profiles observed between 08 and 18 local mean time for 72 days at 2 locations were selected. For comparison study, two more profiles based on constant- and variable-LAD approximation were introduced. Obtained results indicate that suggested relation: (i) well reproduces PAR profile within the forest in comparison with observations and (ii) shows better agreement with observations in comparison with two other profiles used in this study.

1 Introduction

[2] Forest is an important element of climate system. Growing demand for better understanding of role of forest in regional and global climate changes leads to more sophisticated parameterization of forest-atmosphere interaction at different scales. Modeling of physical and physiological processes, that describe this interaction, is in the focus of scientific community since 1950s [Monsi and Saeki, 1953]. There has been continuing progress in improving soil-vegetation-atmosphere transfer (SVAT) models for use in global climate models over the last 30 years. Schemes such as those developed by Dickinson et al. [1998], Noilhan and Mahfouf [1996], and Sellers et al. [1996] incorporate more realistic description of energy, mass, and momentum exchange between the plant canopy and the lower atmosphere. In these efforts, a particular attention is devoted to simulation of plant physiological controls of transpiration [Collatz et al., 1991; Jarvis and McNaughton, 1986; Tuzet et al., 2003].

[3] The radiation transfer within the forest canopy plays a crucial role in many aspects of biosphere-atmosphere interaction. First, the shortwave radiation is the governing component of canopy energy balance influencing leaf, soil, and within canopy air temperature. Second, together with friction, it is a driving force of turbulent transfer within the canopy. Finally, intensity of PAR, as a part of shortwave radiation spectrum, affects intensity of photosynthesis which directly influences the exchange of CO2 between the forest canopy and the atmosphere [Ni et al., 1997; Marcado et al., 2007; Wolfe and Thornton, 2011].

[4] Pioneering research of crop-radiation interaction [Allen et al., 1964; Brown and Covey, 1966] were suggesting that distribution of the net radiation with height or with cumulative leaf area index is in an agreement with the Lambert-Beer law relationship [Makar et al., 1999; Falge et al., 2005]. However, in case of forest canopy, this conclusion is valid only for the horizontally uniform forest canopies [Ross, 1981]. Recently, in use is a vast number of techniques in modeling the PAR radiation within the canopies having different levels of sophistication. They vary from very complex 3D radiative transfer models [Kimes et al., 1985] to models based on big-leaf (or sandwich layer) parameterization of canopy structure but without treatment of vertical distribution of radiation within the canopy [see for example, Sellers et al., 1996]. The big-leaf approach is very efficient in parameterization of radiation budget of short and tall grass in SVAT models, while 3D models are designed to be used either in ecological [Botkin, 1993], physiological [Shugart, 2002], or models of forest growth [Running and Gower, 1991; Bartelink et al., 1997]. A comprehensive overview of different concepts in radiation transfer modeling within the canopy can be found in Ni et al. [1997] and Falge et al. [2005].

[5] Parameterization of PAR absorption in SVAT models coupled with atmospheric models of different scales is a challenging issue. Those models should be detailed enough to include most important processes at certain temporal and spatial scales. On the other hand, they should be based on data which are standard input vegetation parameters of atmospheric models (leaf area index (LAI), vegetation height (h), and vegetation covering parameter (σf)). To our knowledge, the main problem and source of uncertainties in above mentioned parameterizations of radiation transfer, i.e., leaf area density (LAD) profile parameterizations, is the choice of empirical parameters in those parameterizations.

[6] The main goal of this paper is to offer a simple parameterization of vertical profile of PAR in horizontally uniform forest canopies based on the Lambert-Beer law relationship and LAD profile for forest canopy given by Lalic and Mihailovic [2004]. The main advantage of this profile is its nondemanding nature for empirical parameters. Namely, forest canopy is described only by the forest height, LAI, and height of maximum LAD, which are commonly used characteristics in describing the forest. In order to access features of the proposed parameterization of PAR, we have compared this profile with the following profiles: (i) the constant LAD approach and (ii) LAD profile suggested by Teske and Thistle [2004].

[7] The suggested parameterizations are elaborated in section 2. Data for comparison are assimilated from Anglo-Brazilian Amazonian Climate Observation Study (ABRACOS) experiment for two locations, Reserva Jaru (RJ) and Reserva Ducke (RD) [Cabral et al., 1996]. They are described in section 3, while results and discussion are given in section 4. Section 5 includes conclusions with short elaboration of further plans.

2 Methodology

[8] Radiation transfer within the forest canopy is affected primarily by incident radiation distribution (proportion of direct and diffuse radiation in incident beam) and the canopy structure. Because of high absorption by plants in the visible spectrum, radiation interception approaches the absorption, and multiple scattering can be ignored [Roujean, 1996]. The basic approach used in this study is that incident PAR is partitioned into radiation absorbed by leaves and transmitted one [Makar et al., 1999; Wolfe and Thornton, 2011].

[9] The effect of distribution of vegetative elements is incorporated into the Lambert-Beer law relationship through the LAD distribution. The level of complexity of the LAD parameterization is closely related to the complexity of the vegetation parameterization in the SVAT models. In big-leaf or single vegetation layer models, the constant-LAD is a commonly used approach. However, in multilayer vegetation models, a more detailed parameterization of LAD is required. In Table 1 are given the modeling approaches for the LAD and radiation transfer in the SVAT models. A comprehensive overview of SVAT models and radiation transfer parameterizations used can be found in Falge et al. [2005].

Table 1. Approaches for the LAD and Radiation Transfer in Different SVAT Models
ModelRadiation ParameterizationLAD ParameterizationVegetation ModelReferences
PLATINSurface energy balance partitioning: direct, diffuse, LW by layer, latent, sensible, and soil heat fluxconstant LADBig leaf

Grünhage and Haenel [1997]

MixFor-SVATModified two-stream approximationLAD profile, leaf angle distributionMultilayerDickinson [1983]; Oltchev et al. [1997, 2002]

Solar elevation, direct and diffuse PAR, NIR, and LW energy balance, and radiation regime in

each canopy layer

constant LAD, leaf angleMultilayer (up to 30 layers);Caldwell et al. [1986]; Harley and Tenhunen [1991]; Tenhunen et al. [1995]
PnET-N-DNDC and DNDCBeers-Lambert exponential decayfine root, leaf, bole mass50 layersAber and Federer [1992]; Aber et al. [1996]; Li et al. [1992, 1994, 2000]; Li [2000]
HIRVACBeers-Lambert exponential decayLAD profileMultilayerMix et al. [1994]; Ziemann [1998]; Goldberg and Bernhofer [2001]
CAFEModified Beers-Lambert lawLAD profile (according to modified Weibull distribution)Vertically resolved canopy structureMakar et al. [1999]; Teske and Thistle [2004]; Wolfe and Thornton [2011]

2.1 Parameterization of the Forest Canopy Structure

[10] The forest canopy structure in different environmental models is often quantified by the amount of leaves and stems, and their spatial distribution represented by leaf area index, LAI and LAD, respectively. Following the definitions of these two quantities, the relation between them can be written in the form

display math(1)

where h is the forest height.

[11] The simplest parameterization of the LAD includes the assumption about vertically uniform forest structure. Correspondingly, the LAD can be calculated by simple averaging LAI over the canopy height, i.e.,

display math(2)

[12] In further text, this assumption will be denoted with CL.

[13] In the high-resolution atmospheric, environmental, and chemical models, vegetation parameterization has to be as much as physically realistic expression for LAD [Witcosky et al., 1998; Law et al., 2001; Karlik and McKay, 2002; Teske and Thistle, 2004; Lalic and Mihailovic, 2004]. For the purpose of this study, we have chosen two LAD profiles (Figure 1). The first one was derived using the LAD measurements from 16 Eastern hardwoods with 10 sets of measurements made for each forest type [Yang et al., 1999]. Observed data were subsequently fit to a modified Weibull cumulative distribution function [Weibull, 1951] to obtain the LAD profile in the form [Teske and Thistle, 2004]

display math(3)

where LAIc is the cumulative LAI on the canopy floor (z = 0 m), while b and c are curve fitting constants. In further text, results that come from this LAD profile will be denoted with TT.

Figure 1.

Calculated leaf area density profiles LAD(z) using LM and TT approaches for RJ and RD sites.

[14] The second profile was the empirical formula for LAD suggested by Lalic and Mihailovic [2004] based on observed spatial distribution of leaves and stems. Taking into account tree height, h, maximum value of LAD, Lm, and corresponding height (LAD(zm) = Lm), zm, as key parameters of the forest canopy characteristics [Kolic, 1978; Mix et al., 1994; Law et al., 2001], they set the expression in the form

display math(4)

[15] Parameter n was found from analysis of minimum root-mean square error (RMSE) for different observed LAD distribution data sets. Results of these analyses pointed out that the best choice is n = 0.5 for z ≥ zm and n = 6 for z < zm. According to the forest classification based on zm and h parameters [Kolic, 1978], all forest canopies can be divided into the three groups: (1) zm = 0.2 h (oak and silver birch), (2) 0.2 h < zm < 0.4 h (common maple), and (3) zm = 0.4 h (pine); a typical species representative of each classification is shown in parentheses. Following this classification, empirical relation for the LAD described by equation (4) can be applied for the broad range of forest canopies. In further text, results obtained using LAD profile described by equation (4) will be denoted with LM.

2.2 Impact of Forest Canopy Structure on Radiation Profile

[16] The Lambert-Beer's law in optics relates absorption of light to the properties of material through which the light propagates. Let us consider absorbing sample of forest canopy volume with unit base surface and height from the ground to the forest top. Divide the sample into thin layers, of thickness dz. Suppose that angle between z axis and direction of incident radiation (s) is θ (also called zenith angle). According to the Lambert-Beer's law, the radiation, that emerges from a layer dz at height z, after passing the path length ds, is reduced for

display math(5)

where μ is the attenuation coefficient which depends only on characteristics of absorbing material [Liou, 2004]. Path length ds can be calculated using layer thickness, dz and zenith angle, θ as

display math(6)

[17] Replacing ds from equation (6) in equation (5), then reduction of radiation dG(z) is expressed in the form

display math(7)

where coefficient μ describes dependence of vegetation type and its structure on amount of radiation which is absorbed. For forest, μ varies with height and depends on the surface area of vegetative elements in layer dz at height z what is exact definition of LAD(z). According to this physical description of problem, reduction of radiation dG(z) can be written in the form

display math(8)

where k is the extinction coefficient depending on forest type, which is determined from measurements. Integrating equation (8) from z to h in respect to height and denoting radiation at canopy top with G0, vertical profile of radiation within the canopy has following form

display math(9)

[18] The same relation for radiation profile within the canopy was obtained by Makar et al. [1999], where inline image is defined as a cumulative LAI down the ith layer. For extinction coefficient, k from measurements at the site, they have obtained values 0.42 and 0.38 for solar radiation and PAR, respectively.

[19] Replacing equations (2)-(4) into equation (9), we obtained vertical radiation profile for vertically uniform (CL) and nonuniform (TT and LM) forest canopies

2.3 Description of the Experimental Sites

[20] Field observations conducted under ABRACOS project represent detailed studies of surface climatology, micrometeorology, plant physiology, and soil hydrology carried out from late 1990 to December 1993 at three pairs of forested and deforested areas in the Amazon River basin [Shuttleworth et al., 1991; Gash et al., 1996]. The radiation profile measurements were established on two forest sites, RD and RJ, as a part of the study reported by Cabral et al. [1996].

[21] The RD site (02°57′S, 59°57′W, altitude 80 m) is located about 25 km from Manaus, Amazonas in the central Amazonia, in area of protected primary forest where there is only limited forest clearing. The forest is made up of a large variety of tree species with the mean canopy height of 35 m, with some trees of 40 m height. The tallest species in the area around the tower are Piptadenia suaveolens Miq. (39.3 m), Licania micrantha Miq. (31.3 m), Bocoa viridiflora (Ducke) Cowan (26.2 m), and Naucleopsis glabra Spruce ex Baill (21.9 m) undisturbed for at least 5 km with on distinct layering in canopy [Roberts et al., 1990].

[22] The RJ forest site (10°5′ S, 61°55′ W, altitude 120 m) is located 80 km northeast of Ji-Paraná, Rondônia near the south-western edge of the Amazon forest. In this region, the forest has been progressively cleared over the last two decades in an organized way, resulting in a “fishbone” pattern of clearings [Gash et al., 1996]. The tallest tree species in the area immediately surrounding the tower are Cedrella odorata (36 m), Inga sp. (35.1 m), Protium polybotrium (22.1 m), and Leonia glycicarpa Ruiz (16.6 m) with the average tree height of 33 m, and maximum height reached 44 m [McWilliam et al., 1996].

[23] The measurements were carried out with leveled quantum radiation sensors, model SKP 215 (sky Instruments Ltd, Powys, UK), placed on the 52 m height tower in RJ, and 45 m high tower in RD together with micrometeorological observations. Sensors were typically 1.5 m – 2.5 m from the instruments tower appointed on both the east- and west-facing sides of the tower above the canopy at 35 m and at five heights within it (RD: 25, 20, 15, 10, 5 m and RJ: 21.3, 15.7, 11.6, 6.1, 2.3 m) [Marcado et al., 2007].

2.4 Simulations and Analyses

[24] Impact of the LAD parameterization on calculation of PAR profile within the forest was tested through the CL, TT, and LM profiles, which are calculated by replacing equations (2)-(4) into equation (9). Morphological characteristics of forest canopies (LAI and zm) and empirical parameters (b and c) used in calculations are given in Table 2. From the RD site, we have assimilated data collected from 27 July to 12 August 1991 (209 to 224 DOY), while from the RJ site, we have used observations from 2 April to 22 April (92 to 112 DOY), 25 May to 12 June 1992 (146 to 163 DOY), and 30 August to 14 September (242 to 258 DOY), as 10 min averages of PAR in µmol/m2 s1. Vertical profiles of radiation were calculated for 437 and 178 cases for the RJ and RD, respectively. For a more reliable comparison of the PAR profiles, we have tested impact of the instrument orientation on those profiles. Therefore, we have used data measured with radiation sensors mounted in Eastern and Western directions (E and W in further text). In addition, we have considered the temporal variation of the PAR within the forest canopy employing profiles measured in the interval from 08 to 18 local mean time (LMT). The reason why this interval is chosen comes from the fact that after 18 LMT, the intensity of radiation is negligible. For example, under clear sky, the PAR intensity at canopy top varies from 600 – 800 µmol/m2 s1 at 16 LMT to 1 – 25 µmol/m2 s1 at 18 LMT.

Table 2. Morphological Characteristics of Forest Canopies (h, LAI, zm) and Empirical Parameters (b and c) Used in Calculation of PAR Profiles
b 0.70.7
c 22
LAIc (m2 m−2) 4.75.7
k 0.80.7
H (m) 3335
LAI (m2 m−2) 4.75.7
H (m) 3335
LAI (m2 m−2) 4.75.7
zm (m) 0.86 · h0.40 · h
k 0.80.7
H (m) 3335

[25] In order to quantify the validity of the PAR profiles and differences between the CL, TT, and LM approaches, we have performed an error analysis based on the method employed by Pielke [1984], Mahfouf [1990], and Mihailovic et al. [2000]. Following them, (i) we have calculated RMSE (ν) for CL (νCL), TT (νTT), and LM (νLM) profiles of PAR, and (ii) we have compared standard deviations of observed (σo) and simulated (σCL, σTT, and σLM) radiation profiles. RMSE (ν) is widely used since it gives a good overview of a data set, with large errors weighted more than many small errors [Mahfouf, 1990].

[26] According to Pielke [1984], the simulation is performed more realistic if: (a) RMSE ν is less than standard deviation of observed values, σo, and (b) standard deviation of calculated profile, σc, is close to standard deviation of observed values, σo.

3 Results and Discussion

[27] The results of comparison between the calculated and observed values of the PAR profile within the forest canopy are presented on Figure 2 for RJ and Figure 3 for RD. Among 72 days of simulations, we have decided to present two, for each site, representing days with highest (RJ - 257 DOY and RD - 210 DOY) and lowest (RJ - 258 DOY and RD - 216 DOY) intensity of the PAR radiation at the canopy top. Since these intensities differ for the order of magnitude due to cloudiness, it seems that in Figures 2a and 3a dominates direct, while in Figures 2b and 3b diffuse radiation in the incident beam. Profiles obtained for 18 LMT are not presented because of very low intensities of radiation.

Figure 2.

Calculated (CL, TT, and LM) and observed vertical profiles of the PAR within the forest in the RJ on (a) 13 September (257 DOY) and (b) 14 September 1992 (258 DOY). Time of measurement is indicated on the top of panels.

Figure 3.

Calculated (CL, TT, and LM) and observed vertical profiles of PAR within the forest in RD on (a) 29 July (210 DOY) and (b) 4 August 1992 (216 DOY). Time of measurement is indicated on the top of panels.

[28] Simple inspection of Figures 2 and 3 can be commented and summarized on the following way: (i) the LM profile is evidently better in reproducing the strong attenuation of radiation what is particularly enhanced for the RJ site; (ii) comparison for the RD site shows (a) that slightly better results are obtained for the TT profile at 08 LMT and 16 LMT and (b) that for the interval 10 LMT – 12 LMT, the LM profile is much closer to the observations than the TT and CL profiles; (iii) deviation of the CL profile from the observations is largest comparing to others for both selected days; (iv) for the empirically obtained coefficient k given in Table 2, for all profiles are obtained satisfactory results.

[29] The error analysis of calculated profiles is given in Figures 4-7, where are presented results of the RMSE and standard deviation for all calculated profiles. Each bar on these figures represents calculated ν and σ for each profile. Summarizing the inspection of these figures, we can enhance the following comments:

  1. [30] for all locations in the interval 11 LMT–15 LMT, the values of σo take high values (Figures 6 and 7). Further analysis of the observations leads to insights that such values of standard deviation are the consequence of irregularities of measuring procedure. Namely, in some cases on the first two or three measurement levels within crown, the intensity of radiation is the same as at the canopy top. Below these levels, it is reduced to 20 times less value. For example, on the RD site at 223 DOY for 14 LMT, at the canopy top (35 m) and 20 m level, the PAR intensity was 690 µmol/m2 s1, while on 15 m, it was 33 µmol/m2 s1;

  2. [31] RMSE of the LM profile (νLM) is less then νCL and νTT for both E and W orientations for all profiles for the RJ site (Figure 4);

  3. [32] for the RD site (Figure 5), the RMSE of the LM profile (νLM) is less then νCL for all profiles (except for the E orientation at 10 LMT), while in comparing to νTT, νLM is less in the intervals 10 LMT–13 LMT (the E orientation) and 11 LMT–16 LMT (the W orientation);

  4. [33] standard deviation of the LM profile (σLM) is less than σo, but it is less than σCL and σTT, as well. For all profiles, σCL is less than σTT for the RJ site (Figure 6);

  5. [34] standard deviation of the LM profile (σLM) is less than σo and σTT (except for the E orientation at 10 LMT), while σCL has lowest value for all profiles for the RD site (Figure 7);

  6. [35] for the RJ site and for the E orientation (Figure 4, top panel), the RMSE of the LM profile (νLM) is less than σo in the interval 11 LMT–14 LMT, νTT is significantly higher than νLM, while νCL takes different values. After 16 LMT, for all profiles, ν values are close to each other. On the other side, for the W orientation (Figure 4, bottom panel), νLM and σo have the same order of magnitude for all profiles. For the interval 10 LMT – 16 LMT (with exception for 11 LMT), νCL and νTT are significantly higher than σo;

  7. [36] for the RD site and for the E orientation (Figure 5, top panel), the RMSE of the LM profile (νLM) is less than σo for the interval 10 LMT–15 LMT. On the other side, for the W orientation (Figure 5, bottom panel), νLM is less than σo for the interval 10 LMT–17 LMT giving better results in comparison to other profiles.

Figure 4.

RMSE (ν) of the simulated (CL, TT, and LM) and standard deviation (σο) of the observed PAR profiles for the RJ site for E (East) and W (West) orientations.

Figure 5.

RMSE (ν) of the simulated (CL, TT, and LM) and standard deviation (σο) of the observed PAR profiles for the RD site for E (East) and W (West) orientations.

Figure 6.

Standard deviation (σο) of the simulated (CL, TT, and LM) and observed PAR profiles for the RJ site for the E (East) and W (West) orientations.

Figure 7.

Standard deviation (σο) of the simulated (CL, TT, and LM) and observed PAR profiles for the RD site for E (East) and W (West) orientations.

[37] In order to reinforce the above quantitative analysis, we have calculated average values of the RMSE and standard deviation for all analyzed PAR profiles (Tables 3 and 4). Presented results can be summarized on the following way:

  1. [38] for the RJ and RD sites, the average ν for the LM profile is lowest;

  2. [39] lowest values of average σ on the RJ site have the LM profile. In contrast to that, on the RD site, the CL profile has slightly lower value than the LM profile;

  3. [40] for all calculated profiles (the RD site), ν is less then σo, but the LM profile has lowest value;

  4. [41] for all calculated profiles (the RD site), ν is greater then σo, but the LM profile has lowest value.

Table 3. Average Values of RMSE (ν) and Standard Deviation (σ) of Simulated (CL, TT, and LM) and Observed (σο) PAR Profiles for the RJ Site for E (East) and W (West) Orientations
Reserva Jaru (East)
Reserva Jaru (West)
Table 4. Average Values of RMSE (ν) and Standard Deviation (σ) of Simulated (CL, TT, and LM) and Observed (σο) PAR Profiles for the RD Site for E (East) and W (West) Orientations
Reserva Ducke (East)
Reserva Ducke (West)

4 Conclusions

[42] The main goal of this study is to improve parameterization of the PAR radiation transfer within the forest canopy. To achieve this goal: (1) we have proposed a new relation for the PAR vertical profile (LM) within the horizontally uniform forest; (2) we have calculated vertical profiles of the PAR using: (i) the proposed relation LM (LAD varies with height), (ii) a relation with the constant LAD (CL), and (iii) a relation with the LAD, which varies with height (TT), and (3) we have compared these PAR profiles with the observations obtained from the campaigns in the RJ and RD forests (Brazil) from the ABRACOS project. After statistical analysis, we can enhance the following conclusions:

  1. [43] The LM relation gives PAR profiles with lowest RMSE comparing to observation. Its characteristics are more pronounced for the period with the high intensity of radiation (10 LMT – 16 LMT) and both sites (RJ and RD);

  2. [44] All relations for calculating the PAR show similar behavior outside of the period with the high intensity of radiation (10 LMT – 16 LMT) for the site RJ;

  3. [45] For the radiation sensors oriented towards the east on the RD site, both relations, with LAD varying with height, give good results. In the case of the west orientation, the LM relation is much better in comparison with the TT one.

[46] On the basis of presented results, it can be concluded that suggested relation for the PAR quite realistically describes the radiation changes with height inside the forest canopy. Let us note that such agreement between the calculated and observed values is achieved for whole day and for different types of forest communities. The important features of the proposed relation for the PAR profile are: (i) absence of empirical parameters and (ii) morphological characteristics of vegetation, included in the relation, which are easy accessible from the broadly available vegetation maps making this relation suitable for use in different atmospheric, ecological, or chemical models.


[47] The research work described in this paper was realized as a part of the project “Studying climate change and its influence on the environment: impacts, adaptation, and mitigation” (43007) financed by the Ministry of Education and Science of the Republic of Serbia within the framework of integrated and interdisciplinary research for the period 2011–2014.