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On the relationship of canopy LAI and photon recollision probability in boreal forests
Remote Sensing of Environment 113 (2009) 458–461
Contents lists available at ScienceDirect
Remote Sensing of Environment j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / r s e
On the relationship of canopy LAI and photon recollision probability in boreal forests Miina Rautiainen a,⁎, Matti Mõttus b, Pauline Stenberg a a b
Department of Forest Resource Management, FI-00014 University of Helsinki, Finland Tartu Observatory, 61602 Tõravere, Tartumaa, Estonia
a r t i c l e
i n f o
Article history: Received 6 September 2008 Received in revised form 14 October 2008 Accepted 18 October 2008 Keywords: Photon recollision probability Spectral invariants Leaf area index Forest reflectance model
a b s t r a c t The theory of spectral invariants, or ‘p-theory’, states that the canopy scattering coefficient at any wavelength can be related to the leaf scattering coefficient at the same wavelength through a spectrally invariant canopy structural parameter — the photon recollision probability p. The p-theory has recently gained interest in the vegetation reflectance modeling community as an efficient tool for characterizing scattering in clumped foliage structures. In this short communication paper, we report empirical data of the relationship of canopy leaf area index (LAI), diffuse non-interceptance and photon recollision probability for 1032 coniferous and broadleaved forest plots measured in Finland. Our results indicate that the relationship of canopy LAI and diffuse non-interceptance is near-universal in boreal stands i.e. it does not depend on stand age, tree species or growth conditions. This allows improving parameterizations used by canopy reflectance models which utilize the photon recollision probability concept. Our results also suggest that establishing species-specific p-LAI functions for northern European forests requires more research on the influence of micro- and macroscale foliage grouping on photon recollision probability. © 2008 Elsevier Inc. All rights reserved.
1. Introduction The theory of spectral invariants, or ‘p-theory’, introduced by Knyazikhin et al. (1998) states that the canopy scattering coefficient at any wavelength can be related to the leaf scattering coefficient at the same wavelength through a spectrally invariant (i.e. wavelength independent) canopy structural parameter p. The parameter can be interpreted as the probability that a photon scattered from a leaf (or a needle) in the canopy will interact within the canopy again — the “recollision probability” (Smolander & Stenberg, 2005). For vegetation reflectance models, the concept of photon recollision probability provides an effective tool to incorporate the effect of the grouping of foliage at different hierarchical levels through the relationship of p with canopy leaf area index (LAI) (e.g., Huang et al., 2007; Manninen & Stenberg, 2008 Mõttus & Stenberg, 2008; Mõttus et al., 2007; Mõttus, 2007; Rautiainen et al., 2007; Stenberg et al., 2008). For example, the relationship of p and LAI has been built into a simple semi-physical forest reflectance model (PARAS) (Rautiainen & Stenberg, 2005) which has successfully been applied to simulate the reflectance of grouped, coniferous canopies. The advantages of the p-theory are its simplicity and intuitiveness, as well as its connection to the radiative transfer theory (i.e. eigenvalues of the radiative transfer equation, Knyazikhin et al., 1998). In addition, photon recollision probability is, by definition, directly linked to canopy albedo, and thus, can be used in versatile remote sensing and ecosystem modeling applications if the theory is further developed. ⁎ Corresponding author. E-mail address: miina.rautiainen@helsinki.fi (M. Rautiainen). 0034-4257/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2008.10.014
Currently, the main weaknesses of the p-theory are that (1) it does not provide information on the directionality of scattering, and (2) the underlying p-LAI relationship has not been quantified with empirical measurements. Recently, Stenberg (2007) proposed a simple analytical formula for calculating canopy average photon recollision probability p from canopy diffuse non-interceptance measurements, and applied the new method in modeled uniform leaf and shoot canopies. Stenberg's theoretical study demonstrated that it is possible to establish quantitative relationships of photon recollision probability p and leaf area index measured using optical devices (e.g. the LAI-2000 Plant Canopy Analyzer). However, the method was not applied to measured data to evaluate the universality of the empirical p–LAI relationships for different forest types. In this short communication paper, we report empirical data of the relationship of canopy leaf area index, diffuse non-interceptance and photon recollision probability for approximately 1000 boreal forest plots. 1.1. Definitions In this paper, we use two concepts and attached abbreviations of leaf area index. According to definition, the true value of LAI (LAItrue) equals the one-sided area for flat leaves and hemisurface needle area for conifers per unit ground area (Chen & Black, 1992; Stenberg, 2006). The optical LAI estimate produced by the LAI-2000 Plant Canopy Analyzer, on the other hand, does not correspond exactly to LAItrue due to clumping of foliage and woody area included in the field-of-view of the instrument. Therefore, we denote the output of the instrument as LAIPCA.
M. Rautiainen et al. / Remote Sensing of Environment 113 (2009) 458–461
2. Materials The empirical data set for our study was collected from five coniferous dominated test sites in central and northern Finland. The data set comprised 1032 forest plots measured during summers 2001– 2006 in Puumala, Saarinen, Hirsikangas, Rovaniemi and Tähtelä (Table 1). The plots were divided into five categories: pure Scots pine plots (n = 552), pure Norway spruce plots (n = 204), mixed coniferous (i.e. Scots pine and Norway spruce) plots (n = 110), mixed broadleaved-coniferous plots (n = 131) and pure broadleaved (i.e. Silver birch and Downy birch) plots (n = 35). A plot was defined as ‘pure’ when 75% of the trees (by stem count) belonged to the given tree species. Leaf area index measurements were carried out at all plots with the LAI-2000 Plant Canopy Analyzer (Li-Cor Inc.). The LAI-2000 instrument's optical sensor consists of five detectors arranged in concentric rings measuring radiation between 320 and 490 nm i.e. in the range where scattering from leaves is minimal. Canopy gap fraction in each of the five different zenith angle bands (centered at zenith angles: 7°, 23°, 38°, 53° and 68°) is calculated as the ratio of below- and above canopy readings by the corresponding detector rings. For our study plots, the below-canopy measuring height was 1 m above the ground, so that only trees were included in the field of view. Above canopy measurements were collected by automatic logging every 15 to 30 s in an open area located adjacent to or in the middle of the study sites. LAIPCA is obtained (by inversion of the Beer–Lambert law) as a hemispherically weighted average of the logarithm of canopy gap fractions in different view directions: Zπ=2 LAIPCA = −2 lnðcgf ðθÞÞ sinðθÞ cosðθÞdθ
ð1Þ
0
where cgf(θ) is the canopy gap fraction at zenith angle θ (averaged over azimuth angle). Notice that, in the (usual) case of several (LAI) measurement points per plot, ln(cgf) in Eq. (1) represents the mean of the logarithms of the gap fraction values (and not the logarithm of the mean gap fraction). The measurement schemes used at the study sites differed slightly. For the Puumala, Saarinen and Tähtelä sites, the LAI of the plots was calculated from canopy gap fraction values averaged over 15 measurements, comprising three readings taken at each of the five different points within the plot: the plot center point, and at 6 m distance from the center point in each of the four cardinal directions (North, South, East and West). For the Rovaniemi and Hirsikangas sites, LAI measurements were made according to the VALERI network (Validation of Land European Remote Sensing Instruments Network. Online at: http://www.avignon.inra.fr/valeri/) standards: a cross at the plot center point with measurement points placed at 4 m intervals on a North–South transect (6 points) and on a East–West transect (6 points), totaling to 12 measurement readings per plot. In both measurement schemes, a 90° view restrictor was used on the optical sensors to remove possible sun flecks and to exclude the operator from the field of view. Although few measurements were made under
459
clear skies, the view restrictor was used permanently to make measurements under variable sky conditions comparable. The orientation of the above- and below-canopy sensors was similar with respect to the field-of-view. An estimate of photon recollision probability p for a canopy can be calculated from the LAI-2000 measurements. According to Stenberg (2007), an average p for a canopy can be estimated with a simple analytical method from uncollided canopy transmittances in different viewing angles (i.e. canopy gap fractions) and leaf area index
p = 1−
1−DIFN LAItrue
ð2Þ
and Zπ=2 DIFN = 2 cgf ðθÞsinðθÞcosðθÞdθ
ð3Þ
0
where cgf is the canopy gap fraction at zenith angle θ (averaged over azimuth angle and horizontal area). DIFN can also be called canopy diffuse non-interceptance i.e. the fraction of radiation that penetrates a canopy of optically ‘black’ (totally absorbing) leaves under isotropic illumination condition. As Eq. (3) shows, it can be calculated from LAI2000 measurements. For the coniferous plots (i.e. highly grouped structures and mutual shading within the shoots), the LAI-2000 estimate (LAIPCA) must be converted to true LAI (LAItrue) before calculating p (Eq. (2)). This was done simply by dividing LAIPCA by a shoot scale grouping correction factor which is directly related to STAR (spherically averaged shoot silhouette to total area ratio) and, based on previous extensive measurements, is approximately 0.56 (=4 ⁎ STAR) for the coniferous species examined in this study (Oker-Blom & Smolander, 1988; Palmroth et al., 2002; Stenberg, 1996). For pure broadleaved and mixed plots, the LAI provided by the LAI-2000 instrument was used without any clumping correction. 3. Results and discussion Photon recollision probability can be derived from measurements of canopy diffuse non-interceptance (Stenberg, 2007, Eq. (2)), and therefore, we begin by assessing the relationship of diffuse noninterceptance (DIFN) and LAIPCA for the measured canopies. The logarithm of DIFN of natural (measured) canopies decreases linearly with LAIPCA (Fig. 1). Based on our results, we propose the following approximation formula for natural canopies: DIFNnatural = expð−kCAN LAIPCA Þ
ð4Þ
The empirical value of kCAN (a canopy extinction coefficient) was obtained by fitting a linear relationship (which passes through the origin) to the measured relationship of ln(DIFN) and LAIPCA (Fig. 1). For all the study plots, kCAN = 0.77 (r2 = 0.99), for pure coniferous plots kCAN = 0.77 (r2 = 0.98), and for pure broadleaved plots kCAN = 0.81
Table 1 A summary of the study sites Study site
Coordinates
Number of plots
LAIPCA
Tree species
Puumala Saarinen Hirsikangas Rovaniemi Tähtelä
61.32 N, 28.42 E 62.41 N, 27.29 E 62.38 N, 27.00 E 66.47 N, 25.32 E 67.37 N, 26.63 E
347 370 30 24 261
0.04–3.84 0.04–4.26 0.27–4.52 0.03–2.67 0.06–2.35
Pinus silvestris, Picea abies, Picea abies, Pinus silvestris, Pinus silvestris, Picea abies, Picea abies, Pinus silvestris, Pinus silvestris
LAIPCA denotes effective LAI i.e. the LAI measured with the LAI-2000 instrument.
Field campaign year Betula Betula Betula Betula
sp. sp. sp. sp.
2001 2001 2003 2004 2006
460
M. Rautiainen et al. / Remote Sensing of Environment 113 (2009) 458–461
(Fig. 2B). Another important result obtained in this study is the nearuniversal validity of the relationship of canopy LAI and diffuse noninterceptance (Eq. (4)); in the studied data set, it did not depend on stand age, tree species or growth conditions. This allows improving parameterizations used by canopy reflectance models which utilize the photon recollision probability concept (e.g. Rautiainen & Stenberg, 2005). Additionally, the quantitative relationship of canopy LAI and diffuse non-interceptance allows quickly relating canopy transmittance to LAI in boreal forests. Such ‘universal’ constants or relationships of canopy LAI and diffuse non-interceptance, and their connection to photon recollision probability may become useful also in the flux and albedo modeling community in medium-spatial resolution applications.
Fig. 1. The relationship of leaf area index (LAIPCA) and canopy diffuse non-interceptance (DIFN). for measured coniferous, broadleaved and mixed stands.
(r2 = 0.98). For comparison, in a horizontally homogeneous canopy with horizontal leaves kCAN would equal one. Next, we will examine the relationships of leaf area index and photon recollision probability which is calculated from DIFN using Eq. (2) and, for the coniferous stands, applying the shoot scale correction factor to convert LAIPCA to LAItrue. The p–LAIPCA relationships of coniferous and broadleaved plots were clearly different (Fig. 2A): the p-values for broadleaved stands were smaller and increased slower as LAIPCA grew than in coniferous stands. Assuming the variation of STAR in the studied coniferous species the same, there seems to be no difference in the p–LAIPCA relationship of Scots pine and Norway spruce stands i.e. species-specific equations cannot be derived. On the other hand, if we assume that coniferous canopies exhibit shootscale clumping then establishing separate p–LAIPCA functions for pure broadleaved and coniferous stands is reasonable (Fig. 2A). However, one must note that since the DIFN–LAIPCA relationships were similar for all the tree species, the differences in the p–LAIPCA relationships arise from the shoot grouping correction factor (4STAR) applied in the coniferous plots (Eq. (2)). If mean STAR varies significantly between species, then it is possible to establish separate p–LAI functions for each tree species. However, accounting for species–specific variation in STAR when establishing p–LAI relationships still remains a challenge: in coniferous species, sun shoots typically have small STAR values due to dense packing of needle area in the shoot, whereas shade shoots are flatter (i.e. their needles are located mainly at the sides) and have larger STAR values. Typical STAR ranges displayed by our study species are from 0.10 to 0.19 for Norway spruce (Stenberg et al., 1999) and from 0.10 to 0.22 for Scots pine (Stenberg et al., 2001). Due to the large range of STAR values displayed by our study species, an average value (i.e. across species- and vertical light gradients) needs to be used. The use of a mean value is also supported by an observation made by Thérézien et al. (2007): the average, species–specific STAR value does not necessarily vary significantly between different coniferous species. For applying forest reflectance parameterizations based on the photon recollision probability, it is useful to have simple functions for predicting p from easily measurable canopy variables. Using the empirical data presented in this study (resulting in Eq. (4)), we can reformulate Eq. (2) to produce separate functions for the relationship of LAI and canopy average p for broadleaved and coniferous stands
Fig. 2. A. The relationship of leaf area index (LAIPCA) and photon recollision probability. B. An example of functions for predicting photon recollision probability p from measured LAI-2000 data (LAIPCA) (fitted to data presented in A). The fitted functions are: for broadleaved stands: p = 1 − (1/LAIPCA) ⁎ (1 − exp(−kCAN ⁎ LAIPCA), where kCAN = 0.81. For coniferous stands: p = 1 − (1/LAIPCA ⁎ κ) ⁎ (1 − exp(−kCAN ⁎ LAIPCA), where kCAN = 0.77 and κ = 4 STAR = 0.56.
M. Rautiainen et al. / Remote Sensing of Environment 113 (2009) 458–461
4. Conclusions Our results indicated that the relationship of canopy LAI and diffuse non-interceptance is nearly universal in boreal stands — it did not depend on tree species, stand age or growth conditions. Our results also suggest that establishing species-specific p–LAI functions for northern European forests requires more research on the influence of micro- and macroscale foliage grouping (STAR) on photon recollision probability. Acknowledgements Our study was supported by the Academy of Finland (COOLFUTURE and SPRINTER projects) and the Estonian Science Foundation (grant 6812). We thank Mr. Pekka Voipio for his dedication and innovative solutions during the LAI field campaigns. References Chen, J. M., & Black, T. A. (1992). Defining leaf area index for non-flat leaves. Plant, Cell and Environment, 15, 421−429. Huang, D., Knyazikhin, Y., Dickinson, R., Rautiainen, M., Stenberg, P., Disney, M., et al. (2007). Canopy spectral invariants for remote sensing and model applications. Remote Sensing of Environment, 106, 106−122. Knyazikhin, Y., Martonchik, J., Myneni, R., Diner, D., & Running, S. (1998). Synergistic algorithm for estimating vegetation canopy leaf area index and fraction of absorbed photosynthetically active radiation from MODIS and MISR data. Journal of Geophysical Research, D103(32), 257−32 276. Manninen, T., & Stenberg, P. (2008). Simulation of the effect of snow covered forest floor on the total forest albedo. Agricultural and Forest Meteorology, doi:10.1016/j. agrformet.2008.08.016. Mõttus, M. (2007). Photon recollision probability in discrete crown canopies. Remote Sensing of Environment, 110(2), 176−185.
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Mõttus, M., & Stenberg, P. (2008). A simple parameterization of canopy reflectance using photon recollision probability. Remote Sensing of Environment, 112, 1545−1551. Mõttus, M., Stenberg, P., & Rautiainen, M. (2007). Photon recollision probability in heterogeneous forest canopies: Compatibility with a hybrid GO-model. Journal of Geophysical Research, 112, D03104. Oker-Blom, P., & Smolander, H. (1988). The ratio of shoot silhouette area to total needle area in Scots pine. Forest Science, 34, 894−906. Palmroth, S., Stenberg, P., Smolander, S., Voipio, P., & Smolander, H. (2002). Fertilization has little effect on light interception efficiency of Picea abies shoots. Tree Physiology, 22, 1185−1192. Rautiainen, M., & Stenberg, P. (2005). Application of photon recollision probability in simulating coniferous canopy reflectance. Remote Sensing of Environment, 96, 98−107. Rautiainen, M., Suomalainen, J., Mõttus, M., Stenberg, P., Voipio, P., Peltoniemi, J., et al. (2007). Coupling forest canopy and understory reflectance in the Arctic latitudes of Finland. Remote Sensing of Environment, 110, 332−343. Smolander, S., & Stenberg, P. (2005). Simple parameterizations for the radiation budget of uniform broadleaved and coniferous canopies. Remote Sensing of Environment, 94, 355−363. Stenberg, P. (1996). Correcting LAI-2000 estimates for the clumping of needles in shoots of conifers. Agricultural and Forest Meteorology, 79, 1−8. Stenberg, P. (2006). A note on the G-function for needle leaf canopies. Agricultural and Forest Meteorology, 136, 76−79. Stenberg, P. (2007). Simple analytical formula for calculating average photon recollision probability in vegetation canopies. Remote Sensing of Environment, 109(2), 221−224. Stenberg, P., Kangas, T., Smolander, H., & Linder, S. (1999). Shoot structure, canopy openness, and light interception in Norway spruce. Plant, Cell and Environment, 22, 1133−1142. Stenberg, P., Palmroth, S., Bond, B., Sprugel, D., & Smolander, H. (2001). Shoot structure and photosynthetic efficiency along the light gradient in a Scots pine canopy. Tree Physiology, 21, 805−814. Stenberg, P., Rautiainen, M., Manninen, T., Voipio, P., & Mõttus, M. (2008). Boreal forest leaf area index from optical satellite images: Model simulations and empirical analyses using data from central Finland. Boreal Environment Research, 13, 433−443. Thérézien, M., Palmroth, S., Brady, R., & Oren, R. (2007). Estimation of light interception properties of conifer shoots by an improved photographic method and a 3D model of shoot structure. Tree Physiology, 27, 1375−1387.
Contents lists available at ScienceDirect
Remote Sensing of Environment j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / r s e
On the relationship of canopy LAI and photon recollision probability in boreal forests Miina Rautiainen a,⁎, Matti Mõttus b, Pauline Stenberg a a b
Department of Forest Resource Management, FI-00014 University of Helsinki, Finland Tartu Observatory, 61602 Tõravere, Tartumaa, Estonia
a r t i c l e
i n f o
Article history: Received 6 September 2008 Received in revised form 14 October 2008 Accepted 18 October 2008 Keywords: Photon recollision probability Spectral invariants Leaf area index Forest reflectance model
a b s t r a c t The theory of spectral invariants, or ‘p-theory’, states that the canopy scattering coefficient at any wavelength can be related to the leaf scattering coefficient at the same wavelength through a spectrally invariant canopy structural parameter — the photon recollision probability p. The p-theory has recently gained interest in the vegetation reflectance modeling community as an efficient tool for characterizing scattering in clumped foliage structures. In this short communication paper, we report empirical data of the relationship of canopy leaf area index (LAI), diffuse non-interceptance and photon recollision probability for 1032 coniferous and broadleaved forest plots measured in Finland. Our results indicate that the relationship of canopy LAI and diffuse non-interceptance is near-universal in boreal stands i.e. it does not depend on stand age, tree species or growth conditions. This allows improving parameterizations used by canopy reflectance models which utilize the photon recollision probability concept. Our results also suggest that establishing species-specific p-LAI functions for northern European forests requires more research on the influence of micro- and macroscale foliage grouping on photon recollision probability. © 2008 Elsevier Inc. All rights reserved.
1. Introduction The theory of spectral invariants, or ‘p-theory’, introduced by Knyazikhin et al. (1998) states that the canopy scattering coefficient at any wavelength can be related to the leaf scattering coefficient at the same wavelength through a spectrally invariant (i.e. wavelength independent) canopy structural parameter p. The parameter can be interpreted as the probability that a photon scattered from a leaf (or a needle) in the canopy will interact within the canopy again — the “recollision probability” (Smolander & Stenberg, 2005). For vegetation reflectance models, the concept of photon recollision probability provides an effective tool to incorporate the effect of the grouping of foliage at different hierarchical levels through the relationship of p with canopy leaf area index (LAI) (e.g., Huang et al., 2007; Manninen & Stenberg, 2008 Mõttus & Stenberg, 2008; Mõttus et al., 2007; Mõttus, 2007; Rautiainen et al., 2007; Stenberg et al., 2008). For example, the relationship of p and LAI has been built into a simple semi-physical forest reflectance model (PARAS) (Rautiainen & Stenberg, 2005) which has successfully been applied to simulate the reflectance of grouped, coniferous canopies. The advantages of the p-theory are its simplicity and intuitiveness, as well as its connection to the radiative transfer theory (i.e. eigenvalues of the radiative transfer equation, Knyazikhin et al., 1998). In addition, photon recollision probability is, by definition, directly linked to canopy albedo, and thus, can be used in versatile remote sensing and ecosystem modeling applications if the theory is further developed. ⁎ Corresponding author. E-mail address: miina.rautiainen@helsinki.fi (M. Rautiainen). 0034-4257/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2008.10.014
Currently, the main weaknesses of the p-theory are that (1) it does not provide information on the directionality of scattering, and (2) the underlying p-LAI relationship has not been quantified with empirical measurements. Recently, Stenberg (2007) proposed a simple analytical formula for calculating canopy average photon recollision probability p from canopy diffuse non-interceptance measurements, and applied the new method in modeled uniform leaf and shoot canopies. Stenberg's theoretical study demonstrated that it is possible to establish quantitative relationships of photon recollision probability p and leaf area index measured using optical devices (e.g. the LAI-2000 Plant Canopy Analyzer). However, the method was not applied to measured data to evaluate the universality of the empirical p–LAI relationships for different forest types. In this short communication paper, we report empirical data of the relationship of canopy leaf area index, diffuse non-interceptance and photon recollision probability for approximately 1000 boreal forest plots. 1.1. Definitions In this paper, we use two concepts and attached abbreviations of leaf area index. According to definition, the true value of LAI (LAItrue) equals the one-sided area for flat leaves and hemisurface needle area for conifers per unit ground area (Chen & Black, 1992; Stenberg, 2006). The optical LAI estimate produced by the LAI-2000 Plant Canopy Analyzer, on the other hand, does not correspond exactly to LAItrue due to clumping of foliage and woody area included in the field-of-view of the instrument. Therefore, we denote the output of the instrument as LAIPCA.
M. Rautiainen et al. / Remote Sensing of Environment 113 (2009) 458–461
2. Materials The empirical data set for our study was collected from five coniferous dominated test sites in central and northern Finland. The data set comprised 1032 forest plots measured during summers 2001– 2006 in Puumala, Saarinen, Hirsikangas, Rovaniemi and Tähtelä (Table 1). The plots were divided into five categories: pure Scots pine plots (n = 552), pure Norway spruce plots (n = 204), mixed coniferous (i.e. Scots pine and Norway spruce) plots (n = 110), mixed broadleaved-coniferous plots (n = 131) and pure broadleaved (i.e. Silver birch and Downy birch) plots (n = 35). A plot was defined as ‘pure’ when 75% of the trees (by stem count) belonged to the given tree species. Leaf area index measurements were carried out at all plots with the LAI-2000 Plant Canopy Analyzer (Li-Cor Inc.). The LAI-2000 instrument's optical sensor consists of five detectors arranged in concentric rings measuring radiation between 320 and 490 nm i.e. in the range where scattering from leaves is minimal. Canopy gap fraction in each of the five different zenith angle bands (centered at zenith angles: 7°, 23°, 38°, 53° and 68°) is calculated as the ratio of below- and above canopy readings by the corresponding detector rings. For our study plots, the below-canopy measuring height was 1 m above the ground, so that only trees were included in the field of view. Above canopy measurements were collected by automatic logging every 15 to 30 s in an open area located adjacent to or in the middle of the study sites. LAIPCA is obtained (by inversion of the Beer–Lambert law) as a hemispherically weighted average of the logarithm of canopy gap fractions in different view directions: Zπ=2 LAIPCA = −2 lnðcgf ðθÞÞ sinðθÞ cosðθÞdθ
ð1Þ
0
where cgf(θ) is the canopy gap fraction at zenith angle θ (averaged over azimuth angle). Notice that, in the (usual) case of several (LAI) measurement points per plot, ln(cgf) in Eq. (1) represents the mean of the logarithms of the gap fraction values (and not the logarithm of the mean gap fraction). The measurement schemes used at the study sites differed slightly. For the Puumala, Saarinen and Tähtelä sites, the LAI of the plots was calculated from canopy gap fraction values averaged over 15 measurements, comprising three readings taken at each of the five different points within the plot: the plot center point, and at 6 m distance from the center point in each of the four cardinal directions (North, South, East and West). For the Rovaniemi and Hirsikangas sites, LAI measurements were made according to the VALERI network (Validation of Land European Remote Sensing Instruments Network. Online at: http://www.avignon.inra.fr/valeri/) standards: a cross at the plot center point with measurement points placed at 4 m intervals on a North–South transect (6 points) and on a East–West transect (6 points), totaling to 12 measurement readings per plot. In both measurement schemes, a 90° view restrictor was used on the optical sensors to remove possible sun flecks and to exclude the operator from the field of view. Although few measurements were made under
459
clear skies, the view restrictor was used permanently to make measurements under variable sky conditions comparable. The orientation of the above- and below-canopy sensors was similar with respect to the field-of-view. An estimate of photon recollision probability p for a canopy can be calculated from the LAI-2000 measurements. According to Stenberg (2007), an average p for a canopy can be estimated with a simple analytical method from uncollided canopy transmittances in different viewing angles (i.e. canopy gap fractions) and leaf area index
p = 1−
1−DIFN LAItrue
ð2Þ
and Zπ=2 DIFN = 2 cgf ðθÞsinðθÞcosðθÞdθ
ð3Þ
0
where cgf is the canopy gap fraction at zenith angle θ (averaged over azimuth angle and horizontal area). DIFN can also be called canopy diffuse non-interceptance i.e. the fraction of radiation that penetrates a canopy of optically ‘black’ (totally absorbing) leaves under isotropic illumination condition. As Eq. (3) shows, it can be calculated from LAI2000 measurements. For the coniferous plots (i.e. highly grouped structures and mutual shading within the shoots), the LAI-2000 estimate (LAIPCA) must be converted to true LAI (LAItrue) before calculating p (Eq. (2)). This was done simply by dividing LAIPCA by a shoot scale grouping correction factor which is directly related to STAR (spherically averaged shoot silhouette to total area ratio) and, based on previous extensive measurements, is approximately 0.56 (=4 ⁎ STAR) for the coniferous species examined in this study (Oker-Blom & Smolander, 1988; Palmroth et al., 2002; Stenberg, 1996). For pure broadleaved and mixed plots, the LAI provided by the LAI-2000 instrument was used without any clumping correction. 3. Results and discussion Photon recollision probability can be derived from measurements of canopy diffuse non-interceptance (Stenberg, 2007, Eq. (2)), and therefore, we begin by assessing the relationship of diffuse noninterceptance (DIFN) and LAIPCA for the measured canopies. The logarithm of DIFN of natural (measured) canopies decreases linearly with LAIPCA (Fig. 1). Based on our results, we propose the following approximation formula for natural canopies: DIFNnatural = expð−kCAN LAIPCA Þ
ð4Þ
The empirical value of kCAN (a canopy extinction coefficient) was obtained by fitting a linear relationship (which passes through the origin) to the measured relationship of ln(DIFN) and LAIPCA (Fig. 1). For all the study plots, kCAN = 0.77 (r2 = 0.99), for pure coniferous plots kCAN = 0.77 (r2 = 0.98), and for pure broadleaved plots kCAN = 0.81
Table 1 A summary of the study sites Study site
Coordinates
Number of plots
LAIPCA
Tree species
Puumala Saarinen Hirsikangas Rovaniemi Tähtelä
61.32 N, 28.42 E 62.41 N, 27.29 E 62.38 N, 27.00 E 66.47 N, 25.32 E 67.37 N, 26.63 E
347 370 30 24 261
0.04–3.84 0.04–4.26 0.27–4.52 0.03–2.67 0.06–2.35
Pinus silvestris, Picea abies, Picea abies, Pinus silvestris, Pinus silvestris, Picea abies, Picea abies, Pinus silvestris, Pinus silvestris
LAIPCA denotes effective LAI i.e. the LAI measured with the LAI-2000 instrument.
Field campaign year Betula Betula Betula Betula
sp. sp. sp. sp.
2001 2001 2003 2004 2006
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(Fig. 2B). Another important result obtained in this study is the nearuniversal validity of the relationship of canopy LAI and diffuse noninterceptance (Eq. (4)); in the studied data set, it did not depend on stand age, tree species or growth conditions. This allows improving parameterizations used by canopy reflectance models which utilize the photon recollision probability concept (e.g. Rautiainen & Stenberg, 2005). Additionally, the quantitative relationship of canopy LAI and diffuse non-interceptance allows quickly relating canopy transmittance to LAI in boreal forests. Such ‘universal’ constants or relationships of canopy LAI and diffuse non-interceptance, and their connection to photon recollision probability may become useful also in the flux and albedo modeling community in medium-spatial resolution applications.
Fig. 1. The relationship of leaf area index (LAIPCA) and canopy diffuse non-interceptance (DIFN). for measured coniferous, broadleaved and mixed stands.
(r2 = 0.98). For comparison, in a horizontally homogeneous canopy with horizontal leaves kCAN would equal one. Next, we will examine the relationships of leaf area index and photon recollision probability which is calculated from DIFN using Eq. (2) and, for the coniferous stands, applying the shoot scale correction factor to convert LAIPCA to LAItrue. The p–LAIPCA relationships of coniferous and broadleaved plots were clearly different (Fig. 2A): the p-values for broadleaved stands were smaller and increased slower as LAIPCA grew than in coniferous stands. Assuming the variation of STAR in the studied coniferous species the same, there seems to be no difference in the p–LAIPCA relationship of Scots pine and Norway spruce stands i.e. species-specific equations cannot be derived. On the other hand, if we assume that coniferous canopies exhibit shootscale clumping then establishing separate p–LAIPCA functions for pure broadleaved and coniferous stands is reasonable (Fig. 2A). However, one must note that since the DIFN–LAIPCA relationships were similar for all the tree species, the differences in the p–LAIPCA relationships arise from the shoot grouping correction factor (4STAR) applied in the coniferous plots (Eq. (2)). If mean STAR varies significantly between species, then it is possible to establish separate p–LAI functions for each tree species. However, accounting for species–specific variation in STAR when establishing p–LAI relationships still remains a challenge: in coniferous species, sun shoots typically have small STAR values due to dense packing of needle area in the shoot, whereas shade shoots are flatter (i.e. their needles are located mainly at the sides) and have larger STAR values. Typical STAR ranges displayed by our study species are from 0.10 to 0.19 for Norway spruce (Stenberg et al., 1999) and from 0.10 to 0.22 for Scots pine (Stenberg et al., 2001). Due to the large range of STAR values displayed by our study species, an average value (i.e. across species- and vertical light gradients) needs to be used. The use of a mean value is also supported by an observation made by Thérézien et al. (2007): the average, species–specific STAR value does not necessarily vary significantly between different coniferous species. For applying forest reflectance parameterizations based on the photon recollision probability, it is useful to have simple functions for predicting p from easily measurable canopy variables. Using the empirical data presented in this study (resulting in Eq. (4)), we can reformulate Eq. (2) to produce separate functions for the relationship of LAI and canopy average p for broadleaved and coniferous stands
Fig. 2. A. The relationship of leaf area index (LAIPCA) and photon recollision probability. B. An example of functions for predicting photon recollision probability p from measured LAI-2000 data (LAIPCA) (fitted to data presented in A). The fitted functions are: for broadleaved stands: p = 1 − (1/LAIPCA) ⁎ (1 − exp(−kCAN ⁎ LAIPCA), where kCAN = 0.81. For coniferous stands: p = 1 − (1/LAIPCA ⁎ κ) ⁎ (1 − exp(−kCAN ⁎ LAIPCA), where kCAN = 0.77 and κ = 4 STAR = 0.56.
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4. Conclusions Our results indicated that the relationship of canopy LAI and diffuse non-interceptance is nearly universal in boreal stands — it did not depend on tree species, stand age or growth conditions. Our results also suggest that establishing species-specific p–LAI functions for northern European forests requires more research on the influence of micro- and macroscale foliage grouping (STAR) on photon recollision probability. Acknowledgements Our study was supported by the Academy of Finland (COOLFUTURE and SPRINTER projects) and the Estonian Science Foundation (grant 6812). We thank Mr. Pekka Voipio for his dedication and innovative solutions during the LAI field campaigns. References Chen, J. M., & Black, T. A. (1992). Defining leaf area index for non-flat leaves. Plant, Cell and Environment, 15, 421−429. Huang, D., Knyazikhin, Y., Dickinson, R., Rautiainen, M., Stenberg, P., Disney, M., et al. (2007). Canopy spectral invariants for remote sensing and model applications. Remote Sensing of Environment, 106, 106−122. Knyazikhin, Y., Martonchik, J., Myneni, R., Diner, D., & Running, S. (1998). Synergistic algorithm for estimating vegetation canopy leaf area index and fraction of absorbed photosynthetically active radiation from MODIS and MISR data. Journal of Geophysical Research, D103(32), 257−32 276. Manninen, T., & Stenberg, P. (2008). Simulation of the effect of snow covered forest floor on the total forest albedo. Agricultural and Forest Meteorology, doi:10.1016/j. agrformet.2008.08.016. Mõttus, M. (2007). Photon recollision probability in discrete crown canopies. Remote Sensing of Environment, 110(2), 176−185.
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