parameterization of par vertical profile within horizontally uniform forest canopies for use in...

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

Branislava Lalic,1 Ana Firanj,2 Dragutin T. Mihailovic,1 and Zorica Podrascanin2

Received 21 November 2012; revised 2 July 2013; accepted 4 July 2013; published 1 August 2013.

[1] The radiation transfer within the forest canopy plays crucial role in energy balance andturbulent transfer processes. Objective of this study is to suggest a new relation for verticalprofile of photosynthetically active radiation (PAR) in case of horizontally uniform forestcanopy. It is based on (i) the Lambert-Beer law relationship and (ii) new parameterization ofleaf area density (LAD) profile. We have supposed that absorption coefficient μ varies withheight and depends on LAD distribution. To check validity of the relation proposed, we havecompared calculated values with the observations using data sets assimilated duringAnglo-Brazilian Amazonian Climate Observation Study experiment at two observationalsites 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 meantime for 72 days at 2 locations were selected. For comparison study, two more profiles basedon constant- and variable-LAD approximation were introduced. Obtained results indicatethat suggested relation: (i) well reproduces PAR profile within the forest in comparison withobservations and (ii) shows better agreement with observations in comparison with twoother profiles used in this study.

Citation: Lalic, B., A. Firanj, D. T. Mihailovic, and Z. Podrascanin (2013), Parameterization of PAR vertical profilewithin horizontally uniform forest canopies for use in environmental modeling, J. Geophys. Res. Atmos., 118, 8156–8165,doi:10.1002/jgrd.50626.

1. Introduction

[2] Forest is an important element of climate system.Growing demand for better understanding of role of forestin regional and global climate changes leads to moresophisticated parameterization of forest-atmosphere inter-action at different scales. Modeling of physical and phys-iological processes, that describe this interaction, is in thefocus of scientific community since 1950s [Monsi andSaeki, 1953]. There has been continuing progress inimproving soil-vegetation-atmosphere transfer (SVAT)models for use in global climate models over the last 30years. Schemes such as those developed by Dickinsonet al. [1998], Noilhan and Mahfouf [1996], and Sellerset al. [1996] incorporate more realistic description ofenergy, mass, and momentum exchange between the plantcanopy and the lower atmosphere. In these efforts, aparticular attention is devoted to simulation of plant phy-siological controls of transpiration [Collatz et al., 1991;Jarvis and McNaughton, 1986; Tuzet et al., 2003].

[3] The radiation transfer within the forest canopy plays acrucial role in many aspects of biosphere-atmosphere interac-tion. First, the shortwave radiation is the governing compo-nent of canopy energy balance influencing leaf, soil, andwithin canopy air temperature. Second, together withfriction, it is a driving force of turbulent transfer within thecanopy. Finally, intensity of PAR, as a part of shortwaveradiation spectrum, affects intensity of photosynthesis whichdirectly influences the exchange of CO2 between the forestcanopy 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 thatdistribution of the net radiation with height or with cumula-tive 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 isvalid only for the horizontally uniform forest canopies[Ross, 1981]. Recently, in use is a vast number of techniquesin modeling the PAR radiation within the canopies havingdifferent levels of sophistication. They vary from verycomplex 3D radiative transfer models [Kimes et al., 1985]to models based on big-leaf (or sandwich layer) parameteri-zation of canopy structure but without treatment of verticaldistribution of radiation within the canopy [see for example,Sellers et al., 1996]. The big-leaf approach is very efficient inparameterization of radiation budget of short and tall grass inSVAT models, while 3D models are designed to be usedeither in ecological [Botkin, 1993], physiological [Shugart,2002], or models of forest growth [Running and Gower,

1Faculty of Agriculture, Department for Field and Vegetable Crops,University of Novi Sad, Novi Sad, Serbia.

2Faculty of Sciences, Department of Physics, University of Novi Sad,Novi Sad, Serbia.

Corresponding author: B. Lalic, Faculty of Agriculture, Department forField and Vegetable Crops, University of Novi Sad, Dositej Obradovic Sq.8, 21000 Novi Sad, Serbia. ([email protected])

©2013. American Geophysical Union. All Rights Reserved.2169-897X/13/10.1002/jgrd.50626

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JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, 8156–8165, doi:10.1002/jgrd.50626, 2013

1991; Bartelink et al., 1997]. A comprehensive overview ofdifferent concepts in radiation transfer modeling within thecanopy can be found in Ni et al. [1997] and Falgeet al. [2005].[5] Parameterization of PAR absorption in SVAT models

coupled with atmospheric models of different scales is achallenging issue. Those models should be detailed enoughto include most important processes at certain temporal andspatial scales. On the other hand, they should be based ondata which are standard input vegetation parameters of atmo-spheric 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 men-tioned parameterizations of radiation transfer, i.e., leaf areadensity (LAD) profile parameterizations, is the choice ofempirical parameters in those parameterizations.[6] The main goal of this paper is to offer a simple param-

eterization of vertical profile of PAR in horizontally uniformforest canopies based on the Lambert-Beer law relationshipand LAD profile for forest canopy given by Lalic andMihailovic [2004]. The main advantage of this profile is itsnondemanding nature for empirical parameters. Namely,forest canopy is described only by the forest height, LAI,and height of maximum LAD, which are commonly usedcharacteristics in describing the forest. In order to accessfeatures of the proposed parameterization of PAR, we havecompared this profile with the following profiles: (i) theconstant LAD approach and (ii) LAD profile suggested byTeske and Thistle [2004].

[7] The suggested parameterizations are elaborated in section2. Data for comparison are assimilated from Anglo-BrazilianAmazonian Climate Observation Study (ABRACOS)experiment for two locations, Reserva Jaru (RJ) andReserva Ducke (RD) [Cabral et al., 1996]. They aredescribed in section 3, while results and discussion aregiven in section 4. Section 5 includes conclusions withshort elaboration of further plans.

2. Methodology

[8] Radiation transfer within the forest canopy is affectedprimarily by incident radiation distribution (proportion of di-rect and diffuse radiation in incident beam) and the canopystructure. Because of high absorption by plants in the visiblespectrum, radiation interception approaches the absorption,and multiple scattering can be ignored [Roujean, 1996].The basic approach used in this study is that incident PARis partitioned into radiation absorbed by leaves and transmit-ted 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 throughthe LAD distribution. The level of complexity of the LADparameterization is closely related to the complexity of thevegetation parameterization in the SVAT models. In big-leafor single vegetation layer models, the constant-LAD is acommonly used approach. However, in multilayer vegetationmodels, a more detailed parameterization of LAD is required.In Table 1 are given the modeling approaches for the LAD

Table 1. Approaches for the LAD and Radiation Transfer in Different SVAT Models

Model Radiation Parameterization LAD Parameterization Vegetation Model References

PLATIN Surface energy balance partitioning:direct, diffuse, LW by layer, latent, sensible,

and soil heat flux

constant LAD Big leaf Grünhage and Haenel [1997]

MixFor-SVAT Modified two-stream approximation LAD profile, leaf angledistribution

Multilayer Dickinson [1983]; Oltchev et al.[1997, 2002]

SVAT-CN Solar elevation, direct and diffuse PAR,NIR, and LW energy balance, and radiation

regime ineach canopy layer

constant LAD, leaf angle Multilayer(up to 30 layers);

Caldwell et al. [1986]; Harley andTenhunen [1991]; Tenhunen et al.

[1995]PnET-N-DNDCand DNDC

Beers-Lambert exponential decay fine root, leaf, bole mass 50 layers Aber and Federer [1992]; Aber et al.[1996]; Li et al. [1992, 1994,

2000]; Li [2000]HIRVAC Beers-Lambert exponential decay LAD profile Multilayer Mix et al. [1994]; Ziemann [1998];

Goldberg and Bernhofer [2001]CAFE Modified Beers-Lambert law LAD profile (according to

modified Weibull distribution)Vertically resolvedcanopy structure

Makar et al. [1999];Teske and Thistle [2004];Wolfe and Thornton [2011]

0 0.1 0.2 0.3 0.4

LAD(z)

0

0.2

0.4

0.6

0.8

1

1 -

z/h

RJRD

40 1 2 3 5 6

LAD(z)

0

0.2

0.4

0.6

0.8

1

RJRD

LM TT

Figure 1. Calculated leaf area density profiles LAD(z) using LM and TT approaches for RJ and RD sites.

LALIC ET AL.: PARAMETERIZATION OF PAR VERTICAL PROFILE

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and radiation transfer in the SVATmodels. A comprehensiveoverview of SVAT models and radiation transfer para-meterizations used can be found in Falge et al. [2005].

2.1. Parameterization of the Forest Canopy Structure

[10] The forest canopy structure in different environmentalmodels 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 thesetwo quantities, the relation between them can be written inthe form

LAI ¼ ∫h

0LAD zð Þdz; (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 simpleaveraging LAI over the canopy height, i.e.,

LAD zð Þ ¼ LAI

h: (2)

[12] In further text, this assumption will be denotedwith CL.[13] In the high-resolution atmospheric, environmental,

and chemical models, vegetation parameterization has to beas 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 twoLAD profiles (Figure 1). The first one was derived usingthe LAD measurements from 16 Eastern hardwoods with10 sets of measurements made for each forest type [Yanget al., 1999]. Observed data were subsequently fit to amodified Weibull cumulative distribution function[Weibull, 1951] to obtain the LAD profile in the form[Teske and Thistle, 2004]

LAD zð Þ=LAIc ¼ 1� exp � 1� z=hð Þ=bð Þ½ �cf g= 1� exp � 1=bð Þc½ �f g (3)

where LAIc is the cumulative LAI on the canopy floor(z = 0m), while b and c are curve fitting constants. In furthertext, results that come from this LAD profile will be denotedwith TT.[14] The second profile was the empirical formula for LAD

suggested by Lalic and Mihailovic [2004] based on observedspatial distribution of leaves and stems. Taking into accounttree height, h, maximum value of LAD, Lm, and correspond-ing height (LAD(zm) =Lm), zm, as key parameters of the forestcanopy characteristics [Kolic, 1978; Mix et al., 1994; Lawet al., 2001], they set the expression in the form

LAD zð Þ ¼ Lm h� zmð Þ= h� zð Þ½ �nexp n 1� h� zmð Þ= h� zð Þ½ �f g

where n ¼6 0 ≤ z < zm

1=2 zm ≤ z ≤ h

(

(4)[15] Parameter n was found from analysis of minimum

root-mean square error (RMSE) for different observed LADdistribution data sets. Results of these analyses pointed outthat 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 pa-rameters [Kolic, 1978], all forest canopies can be divided intothe 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 isshown in parentheses. Following this classification, empiri-cal relation for the LAD described by equation (4) can be ap-plied 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 onRadiation Profile

[16] The Lambert-Beer’s law in optics relates absorptionof light to the properties of material through which thelight propagates. Let us consider absorbing sample of for-est canopy volume with unit base surface and height fromthe ground to the forest top. Divide the sample into thinlayers, of thickness dz. Suppose that angle between z axisand direction of incident radiation (s) is θ (also calledzenith angle). According to the Lambert-Beer’s law, theradiation, that emerges from a layer dz at height z, afterpassing the path length ds, is reduced for

dG zð Þ ¼ �μ zð ÞG zð Þds; (5)

where μ is the attenuation coefficient which depends only oncharacteristics of absorbing material [Liou, 2004]. Pathlength ds can be calculated using layer thickness, dz and ze-nith angle, θ as

ds ¼ dz= cosθ: (6)

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

dG zð Þ ¼ �μ zð ÞG zð Þdz= cosθ; (7)

where coefficient μ describes dependence of vegetationtype and its structure on amount of radiation which is

Table 2. Morphological Characteristics of Forest Canopies (h, LAI,zm) and Empirical Parameters (b and c) Used in Calculation ofPAR Profiles

Parameter Profile RJ RD

TTb 0.7 0.7c 2 2LAIc (m

2m�2) 4.7 5.7k 0.8 0.7H (m) 33 35

CLLAI (m2m�2) 4.7 5.7H (m) 33 35

LMLAI (m2m�2) 4.7 5.7zm (m) 0.86 · h 0.40 · hk 0.8 0.7H (m) 33 35


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absorbed. For forest, μ varies with height and depends onthe surface area of vegetative elements in layer dz atheight z what is exact definition of LAD(z). According tothis physical description of problem, reduction of radiationdG(z) can be written in the form

dG zð Þ ¼ �k LAD zð ÞG zð Þdz= cos θ (8)

where k is the extinction coefficient depending on foresttype, which is determined from measurements. Integratingequation (8) from z to h in respect to height and denoting

radiation at canopy top with G0, vertical profile of radiationwithin the canopy has following form

G zð Þ ¼ G0 exp �k= cos θ�∫z

hLAD zð Þdz

� �: (9)

[18] The same relation for radiation profile within thecanopy was obtained by Makar et al. [1999], where

∫z

hLAD zð Þdz is defined as a cumulative LAI down the ith layer.

For extinction coefficient, k from measurements at the site,

0 50 100 150 2000

10

20

30

40

Fore

st h

eigh

t (m

)

LMCLTTObserved

08

0 200 400 600 800

10

0 500 1000 1500 2000

12

0 500 1000 15000

10

20

30

40

Fore

st h

eigh

t (m

)

14

0 500 1000

PAR (μmol / m2 s)

PAR (μmol / m2 s)

16

(a)

0 10 20 30 40 500

10

20

30

40

Fore

st h

eigh

t (m

)

LMCLTTObserved

08

0 100 200 300 400

10

0 100 200 300 400 500

12

0 200 400 6000

10

20

30

40

Fore

st h

eigh

t (m

)

14

0 100 200 300

16

(b)

Figure 2. Calculated (CL, TT, and LM) and observed vertical profiles of the PAR within the forest in theRJ on (a) 13 September (257 DOY) and (b) 14 September 1992 (258 DOY). Time of measurement is indi-cated on the top of panels.


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they have obtained values 0.42 and 0.38 for solar radiationand 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 projectrepresent detailed studies of surface climatology, micrometeo-rology, plant physiology, and soil hydrology carried out fromlate 1990 to December 1993 at three pairs of forested anddeforested areas in the Amazon River basin [Shuttleworth

et al., 1991; Gash et al., 1996]. The radiation profile measure-ments were established on two forest sites, RD and RJ, as a partof the study reported by Cabral et al. [1996].[21] The RD site (02°57′S, 59°57′W, altitude 80m) is

located about 25 km from Manaus, Amazonas in the cen-tral Amazonia, in area of protected primary forest wherethere is only limited forest clearing. The forest is madeup of a large variety of tree species with the mean canopyheight of 35m, with some trees of 40m height. The tallestspecies in the area around the tower are Piptadeniasuaveolens Miq. (39.3m), Licania micrantha Miq.(31.3 m), Bocoa viridiflora (Ducke) Cowan (26.2 m), and

0 100 200 300 400 5000

10

20

30

40

Fore

st h

eigh

t (m

)

LMCLTTObserved

08

0 500 1000

10

0 500 1000 1500 2000

12

0 500 10000

10

20

30

40

Fore

st h

eigh

t (m

)

14

0 200 400 600 800

PAR (μmol / m2 s)

16

(a)

0 50 100 150 2000

10

20

30

40

Fore

st h

eigh

t (m

)

LMCLTTObserved

08

0 50 100 150 200

10

0 50 100 150

12

0 200 400 600 8000

10

20

30

40

Fore

st h

eigh

t (m

)

14

0 50 100 150 200 250

PAR (μmol / m2 s)

16

(b)

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 ofpanels.


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Naucleopsis glabra Spruce ex Baill (21.9 m) undisturbedfor 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

120m) is located 80 km northeast of Ji-Paraná, Rondônianear the south-western edge of the Amazon forest. In thisregion, the forest has been progressively cleared over thelast two decades in an organized way, resulting in a“fishbone” pattern of clearings [Gash et al., 1996]. Thetallest tree species in the area immediately surroundingthe tower are Cedrella odorata (36m), Inga sp. (35.1m),Protium polybotrium (22.1m), and Leonia glycicarpaRuiz (16.6m) with the average tree height of 33m, andmaximum height reached 44m [McWilliam et al., 1996].

[23] The measurements were carried out with leveled quan-tum radiation sensors, model SKP 215 (sky Instruments Ltd,Powys, UK), placed on the 52m height tower in RJ, and45m high tower in RD together with micrometeorological ob-servations. Sensors were typically 1.5m – 2.5m from the in-struments tower appointed on both the east- and west-facingsides of the tower above the canopy at 35m and at five heightswithin it (RD: 25, 20, 15, 10, 5m and RJ: 21.3, 15.7, 11.6, 6.1,2.3m) [Marcado et al., 2007].

2.4. Simulations and Analyses

[24] Impact of the LAD parameterization on calculation ofPAR profile within the forest was tested through the CL, TT,and LM profiles, which are calculated by replacing equations

800 900 1000 1100 1200 1300 1400 1500 1600 1700 18000

50

100

150

200

250

300

ν (μ

mol

/ m

2 s)ν

(μm

ol /

m2 s)

σ o(μ

mol

/ m

2 s)σ o

(μm

ol /

m2 s)

LMCLTT

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

LMT (hours)

0

50

100

150

200

250

300

ObservedEast

West

Figure 4. RMSE (ν) of the simulated (CL, TT, and LM) and standard deviation (σο) of the observed PARprofiles for the RJ site for E (East) and W (West) orientations.

800 900 1000 1100 1200 1300 1400 1500 1600 1700 18000

50

100

150

200

250

300

ν (μ

mol

/ m

2 s)ν

(μm

ol /

m2 s)

σ o (μ

mol

/ m

2 s)σ o

(μm

ol /

m2 s)

LMCLTT

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

LMT (hours)

0

50

100

150

200

250

300

ObservedEast

West

Figure 5. RMSE (ν) of the simulated (CL, TT, and LM) and standard deviation (σο) of the observed PARprofiles for the RD site for E (East) and W (West) orientations.


8161

(2–4) into equation (9). Morphological characteristicsof forest canopies (LAI and zm) and empirical parameters(b and c) used in calculations are given in Table 2. Fromthe RD site, we have assimilated data collected from 27July to 12 August 1991 (209 to 224 DOY), while fromthe RJ site, we have used observations from 2 April to22 April (92 to 112 DOY), 25 May to 12 June 1992(146 to 163 DOY), and 30 August to 14 September (242to 258 DOY), as 10 min averages of PAR in μmol/m2 s1.Vertical profiles of radiation were calculated for 437 and178 cases for the RJ and RD, respectively. For a morereliable comparison of the PAR profiles, we have testedimpact 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 consideredthe temporal variation of the PAR within the forest canopyemploying profiles measured in the interval from 08 to 18local mean time (LMT). The reason why this interval ischosen comes from the fact that after 18 LMT, theintensity of radiation is negligible. For example, underclear sky, the PAR intensity at canopy top varies from600 – 800 μmol/m2 s1 at 16 LMT to 1 – 25 μmol/m2 s1 at18 LMT.[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 methodemployed by Pielke [1984], Mahfouf [1990], and

800 900 1000 1100 1200 1300 1400 1500 1600 1700 18000

50

100

150

200

σ (μ

mol

/ m

2 s)σ

(μm

ol /

m2 s)

LMCLTTObserved

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

LMT (hours)

0

50

100

150

200

East

West

Figure 6. Standard deviation (σο) of the simulated (CL, TT, and LM) and observed PAR profiles for theRJ site for the E (East) and W (West) orientations.

800 900 1000 1100 1200 1300 1400 1500 1600 1700 18000

50

100

150

200

250

300

σ (μ

mol

/ m

2 s)σ

(μm

ol /

m2 s)

LMCLTTObserved

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

LMT (hours)

0

50

100

150

200

250

300

East

West

Figure 7. Standard deviation (σο) of the simulated (CL, TT, and LM) and observed PAR profiles for theRD site for E (East) and W (West) orientations.


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Mihailovic et al. [2000]. Following them, (i) we have calcu-lated RMSE (ν) for CL (νCL), TT (νTT), and LM (νLM) profilesof PAR, and (ii) we have compared standard deviations ofobserved (σo) and simulated (σCL, σTT, and σLM) radiationprofiles. RMSE (ν) is widely used since it gives a good over-view of a data set, with large errors weighted more than manysmall errors [Mahfouf, 1990].[26] According to Pielke [1984], the simulation is

performed more realistic if: (a) RMSE ν is less than standarddeviation of observed values, σo, and (b) standard deviationof calculated profile, σc, is close to standard deviation ofobserved values, σo.

3. Results and Discussion

[27] The results of comparison between the calculated andobserved values of the PAR profile within the forest canopyare presented on Figure 2 for RJ and Figure 3 for RD.Among 72 days of simulations, we have decided to presenttwo, for each site, representing days with highest (RJ - 257DOY and RD - 210 DOY) and lowest (RJ - 258 DOY andRD - 216 DOY) intensity of the PAR radiation at the canopytop. Since these intensities differ for the order of magnitudedue to cloudiness, it seems that in Figures 2a and 3a domi-nates direct, while in Figures 2b and 3b diffuse radiation inthe incident beam. Profiles obtained for 18 LMT are notpresented because of very low intensities of radiation.[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 thestrong attenuation of radiation what is particularly

enhanced for the RJ site; (ii) comparison for the RD siteshows (a) that slightly better results are obtained for theTT profile at 08 LMT and 16 LMT and (b) that for the in-terval 10 LMT – 12 LMT, the LM profile is much closerto the observations than the TT and CL profiles; (iii) devi-ation of the CL profile from the observations is largestcomparing to others for both selected days; (iv) for theempirically obtained coefficient k given in Table 2, forall 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 andstandard deviation for all calculated profiles. Each bar onthese figures represents calculated ν and σ for each profile.Summarizing the inspection of these figures, we can enhancethe following comments:[30] 1. for all locations in the interval 11 LMT–15 LMT,

the values of σo take high values (Figures 6 and 7). Furtheranalysis of the observations leads to insights that such valuesof standard deviation are the consequence of irregularities ofmeasuring procedure. Namely, in some cases on the first twoor three measurement levels within crown, the intensity of ra-diation is the same as at the canopy top. Below these levels, itis reduced to 20 times less value. For example, on the RD siteat 223 DOY for 14 LMT, at the canopy top (35m) and 20mlevel, the PAR intensity was 690μmol/m2 s1, while on 15m,it was 33μmol/m2 s1;[31] 2. RMSE of the LM profile (νLM) is less then νCL and

νTT for both E and W orientations for all profiles for the RJsite (Figure 4);[32] 3. for the RD site (Figure 5), the RMSE of the LM pro-

file (νLM) is less then νCL for all profiles (except for the E

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

Hour ν σ

CL TT LM CL TT LM OBS.

Reserva Jaru (East)8 6 6 6 0 0 0 39 11 8 16 4 7 0 1110 15 20 19 19 24 2 1711 47 63 31 39 51 6 3212 98 116 40 65 79 12 4213 71 80 38 48 57 9 3914 62 68 55 49 58 9 5815 49 53 46 38 46 6 4416 28 32 26 28 34 3 2417 12 12 19 9 12 1 1318 12 12 12 0 1 0 7Average 37 43 28 27 34 4 26

Reserva Jaru (West)8 7 7 7 0 0 0 39 5 5 11 5 6 0 610 32 39 15 27 33 1 1211 56 61 41 40 47 5 3412 107 121 34 63 75 8 2713 113 126 49 69 80 11 4514 91 100 69 66 77 10 7215 66 77 27 46 55 6 2316 32 39 14 27 33 2 1217 9 10 17 8 10 0 1018 10 10 10 0 1 2 6Average 48 54 27 32 38 4 23

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

Hour ν σ

CL TT LM CL TT LM OBS.

Reserva Ducke (East)8 23 21 23 0 2 0 139 52 23 50 10 29 14 3610 30 72 40 20 42 29 4411 86 120 68 60 107 85 12712 59 106 40 62 102 88 10613 24 36 18 28 45 40 5014 50 51 42 40 65 57 9415 107 57 100 47 81 67 12616 93 41 91 27 54 39 7317 96 60 93 13 32 18 5818 42 36 42 1 7 2 30Average 56 52 51 26 47 37 63

Reserva Ducke (West)8 23 21 22 0 2 0 179 46 24 43 8 23 11 4210 26 16 22 13 27 18 3811 43 49 33 29 53 42 6812 36 61 23 31 52 44 6113 42 82 26 38 60 54 6614 70 89 54 42 69 61 10315 83 103 64 50 87 72 12316 37 44 27 28 54 40 6017 43 20 38 13 33 19 4818 35 26 34 2 9 3 29Average 44 49 35 23 43 33 59


8163

orientation at 10 LMT), while in comparing to νTT, νLM is lessin the intervals 10 LMT–13 LMT (the E orientation) and 11LMT–16 LMT (the W orientation);[33] 4. 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);[34] 5. 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 RDsite (Figure 7);[35] 6. for the RJ site and for the E orientation (Figure 4,

top panel), the RMSE of the LM profile (νLM) is less thanσo in the interval 11 LMT–14 LMT, νTT is significantlyhigher than νLM, while νCL takes different values. After16 LMT, for all profiles, ν values are close to each other.On the other side, for the W orientation (Figure 4, bottompanel), νLM and σo have the same order of magnitude forall profiles. For the interval 10 LMT – 16 LMT (with ex-ception for 11 LMT), νCL and νTT are significantly higherthan σo;[36] 7. for the RD site and for the E orientation (Figure 5,

top panel), the RMSE of the LM profile (νLM) is less thanσo for the interval 10 LMT–15 LMT. On the other side, forthe W orientation (Figure 5, bottom panel), νLM is less thanσo for the interval 10 LMT–17 LMT giving better results incomparison to other profiles.[37] In order to reinforce the above quantitative analysis,

we have calculated average values of the RMSE and standarddeviation for all analyzed PAR profiles (Tables 3 and 4).Presented results can be summarized on the following way:[38] 1. for the RJ and RD sites, the average ν for the LM

profile is lowest;[39] 2. lowest values of average σ on the RJ site have the

LM profile. In contrast to that, on the RD site, the CL profilehas slightly lower value than the LM profile;[40] 3. for all calculated profiles (the RD site), ν is less then

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

then σo, but the LM profile has lowest value.

4. Conclusions

[42] The main goal of this study is to improve parameteri-zation of the PAR radiation transfer within the forest canopy.To achieve this goal: (1) we have proposed a new relation forthe PAR vertical profile (LM) within the horizontally uni-form forest; (2) we have calculated vertical profiles of thePAR using: (i) the proposed relation LM (LAD varies withheight), (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 observa-tions obtained from the campaigns in the RJ and RD forests(Brazil) from the ABRACOS project. After statistical analy-sis, we can enhance the following conclusions:[43] 1. The LM relation gives PAR profiles with lowest

RMSE comparing to observation. Its characteristics are morepronounced for the period with the high intensity of radiation(10 LMT – 16 LMT) and both sites (RJ and RD);[44] 2. All relations for calculating the PAR show similar

behavior outside of the period with the high intensity of radi-ation (10 LMT – 16 LMT) for the site RJ;

[45] 3. For the radiation sensors oriented towards the easton the RD site, both relations, with LAD varying with height,give good results. In the case of the west orientation, the LMrelation 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 de-scribes the radiation changes with height inside the forestcanopy. Let us note that such agreement between the calcu-lated and observed values is achieved for whole day and fordifferent types of forest communities. The important featuresof the proposed relation for the PAR profile are: (i) absenceof empirical parameters and (ii) morphological characteris-tics of vegetation, included in the relation, which are easy ac-cessible from the broadly available vegetation maps makingthis relation suitable for use in different atmospheric, ecolog-ical, or chemical models.

[47] Acknowledgments. The research work described in this paperwas realized as a part of the project “Studying climate change and its influ-ence on the environment: impacts, adaptation, and mitigation” (43007) fi-nanced by the Ministry of Education and Science of the Republic of Serbiawithin the framework of integrated and interdisciplinary research for the pe-riod 2011–2014.

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parameterization of par vertical profile within horizontally uniform forest canopies for use in...

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