Simple calculation of extinction coefficient of forest stands

Agricultural Meteorology, 25 (1981) 97--110

97

Elsevier Scientific Publishing Company, Amsterdam - - P r i n t e d in The Netherlands

SIMPLE CALCULATION OF EXTINCTION COEFFICIENT OF FOREST STANDS ANDERS LINDROTH

Jiidra~s Ecological Research Station, S-816 O00ckelbo (Sweden) K U R T H PERTTU

Department of Ecology and Environmental Research, Swedish University of Agricultural Sciences, S-750 07 Uppsala (Sweden) (Received June 6, 1981; accepted July 15, 1981) ABSTRACT Lindroth, A. and Perttu, K., 1981. Simple calculation of extinction coefficient of forest stands. Agric. Meteorol., 25: 97--110. A method to determine the extinction coefficient without extensive radiation measurements is proposed. The crown density, which is a necessary parameter for estimation of sun path length within the canopy, is determined by the use of an instrument similar to the Cajanus cylinder. Sky obscuration factors (SOF) at different solar elevations are estimated from fish-eye photographs. The photographs are also used to determine the relative amount of completely transparent and completely opaque parts of the canopy. Combination of the results from these investigations makes it possible to calculate the extinction coefficient. The calculations are tested against measurements of short-wave radiation above 'and below a Scots pine canopy. For a sparse stand such as this, the calculations are quite sensitive to the determination of SOF. At ground level 35% of the radiation comes through the obstructed part of the canopy when the solar elevation is 45 ° . INTRODUCTION

Short-wave radiation measurements beneath forest canopies are difficult and time-consuming if a reliable mean value is desired. A large number of radiometers is needed if the averaging period chosen is short (less than two hours}, and even if the period is about 12 hours the measurements in a rather sparse stand must be made with about ten radiometers (Reifsnyder et al., 1971/72). The amount of radiation falling upon the forest floor is of the greatest importance for studies of photosynthesis of ground vegetation, snowmelt in the spring-time, thawing of frost in soil, etc. These factors in their turn directly affect the growth and production of the forest by controlling competition, nutrient turnover and water content in the soft. One important parameter frequently used in radiation models (Halldin et al., 1979; Lemeur and Rosenberg, 1979; Perrier, 1979) is the extinction coefficient which, in conjunction with Beers' law, describes how the radiation decreases when passing through the canopy. The aim of this investigation is to introduce a simple field method to determine the extinction coefficient without extensive radiation measurements. Some special stand parameters have to be determined before it is possible to calculate the extinction coefficient. 0002-1571/81/0000---0000/$02.50

© 1981 Elsevier Scientific Publishing Company

98 Various stand parameters relating to radiation exchange in forest stands have been developed. Crown density, defined by the Glossary of Forest Terms (1969) as the ratio of the vertical projection of the crowns to the total area of the stand, can be measured by an instrument called the Cajanus cylinder (Sarvas, 1953). Photographic techniques have also been used to determine sky and stand parameters (e.g. Hill, 1924; Evans and Coombe, 1959; Andersson, 1964; Madgwick and Brumfield, 1969). The sky obscuration factor (SOF) is here defined as the fraction of sky obscured by vegetation at a certain zenith angle, measured from a point and averaged over all azimuths. S O F can be determined from fish-eye photographs as outlined below. The calculation of the extinction coefficient is tested against radiation measurements performed in a Scots pine stand at the J~idra~is Ecological Research Station. MATERIAL AND METHODS The extinction coefficient is defined by the relation I / I o = exp(--kd), where I0 is the short-wave beam radiation intensity above canopy at normal incidence, I is the corresponding intensity after passing through the crowns and d is the distance for the sun rays to pass through the crowns at a specific solar elevation. To determine k it is necessary to know the distance d, no matter which method is used, to find the values of I0 and I. In this paper a method is described to determine the product kd by photographic methods but also to estimate the value of d. The calculations are tested against measurements of short-wave radiation transmissivity by the use of radiometers. Stand description

The mature Scots pine stand (Ih 5) at the J~idra~is Ecological Research Station (Lat. 6 0 ° 4 9 ' N , Long. 16°30'E, Alt. 185 m) was used for the investigations. The area is about 160 ha in size with 400 trees per hectare (Table I). The site is mainly used for research within the fields of micrometeorology, hydrology, soil biology, soil chemistry, and primary production. It is the main field site for the Swedish Coniferous Forest Project. Determination o f average crown diameter and crown density

To estimate the average slant distance for penetration of sun rays (penetration length d) through the canopy it is necessary to know the mean crown diameter (D). This parameter can be calculated from the average crown density (Cd) and the number of trees (N) per hectare by using the following formula D = 2(10,000" Cg/NTr) 1/2

(1)

Crown density values can be estimated by the 'spot' method. The instrument consists of a hand-held brass tube mounted on a universal joint to make

99 TABLE I Short description of the stand and site used for investigations of the short-wave radiation penetration through a Scots pine canopy. The values are slightly modified in relation to Perttu et al. 01980) Stand parameter Age (y) Trees (ha -l ) Mean height (m) Max. height (m) Basal area (m 2 ha -1 ) Crown length (m) Leaf area index (m 2 m -2 ) Stem volume (m 3 ha -1 )

Site description 125 400 15.6 19.0 15.0 7.9 2.6 130

Ground vegetation Soil: profile texture Ground water table

Very dry dwarf-shrub Iron podsol Layered fine to coarse sand 10m

Fig. 1. Instrument for measuring crown density by spot method, consisting of a hand-held tube mounted on a universal joint. it h a n g vertically d u r i n g o p e r a t i o n . A m i r r o r is m o u n t e d at t h e b o t t o m o f the t u b e so t h a t w h e n the o p e r a t o r views it, he sees the p o i n t directly overhead t h r o u g h a 2 × 2 m m square o p e n i n g inside the t u b e (Fig. 1). T h e o p e r a t o r o f the i n s t r u m e n t observes w h e t h e r a n y p a r t o f t h e small o p e n i n g is o b s t r u c t e d b y a n y k i n d o f biomass (needles, branches, etc.) or not. This o b s e r v a t i o n is m a d e at a large n u m b e r o f spots within the stand. C r o w n d e n s i t y is t h e n calculated as t h e q u o t i e n t b e t w e e n t h e n u m b e r o f o b s t r u c t e d a n d the t o t a l n u m b e r o f observations. In the m a t u r e s t a n d t w o estimates o f c r o w n d e n s i t y b y the spot m e t h o d

100 were used with two different sampling schemes. Firstly, the measurements were performed in two fixed coordinate systems. At one location observations were made at 10 m intervals on an area of 200 m 2 and at another at every 1 m on an area of 20 m 2 . In the second scheme, a starting point was randomly chosen in the stand and the observer walked in an arbitrary direction about 100 m in a straight line. Every 5 m an observation was made and after about 100 m the observer moved 5 m aside from the line and walked back in the opposite direction again making observations at every 5 m. This procedure was repeated until observations on an area about 75 m 2 had been performed. Such measurements were made at four locations.

Determination o f penetration length The sun penetrates the canopy at a certain angle, depending on the solar elevation. For high solar elevations, only a few crowns are penetrated before the radiation reaches the ground. To determine how many crowns are penetrated at a certain solar elevation, an investigation using a hypsometer (SUUNTO Oy, Finland) was performed. The observer walked along a straight line in an arbitrary direction in the stand, stopped after each 20 m, aimed with the hypsometer at a certain angle {45 °) and counted how m a n y crowns an imaginary sun ray would have passed. This was done for all azimuths at each spot. It is necessary to know the shape of the crowns to calculate penetration length. The shape is quite characteristic for different species and it is possible to get such information from the literature. However, in this case the stand has been carefully investigated and information of this kind is available. Given the average distribution of the biomass of the crowns in terms of dry weights (Flower-Ellis, personal communication}, the estimated mean crown diameter was used to convert the weight scale to a length scale (Fig. 2). Consider now the conditions when a sun ray penetrates the average tree crown at an angle ~ and a height h (Fig. 2a). The penetration length of this ray equals the distance dl only if the path occurs through the s y m m e t r y line of the crown. The tangential section in the plane of this ray (Fig. 2b) can be regarded approximately as an ellipse, the area of which is given by

A = (Tradi)/4

(2a)

where d i is the major axis and a the minor axis. The average value of all possible lengths parallel to the major axis of the ellipse equals the area divided by the minor axis. Hence, the average path distance di of the tangential section is di = (~rdi)/4

(2b)

The penetration occurs at any height within the crown, implying that the major axis of the ellipse also will vary. To estimate the mean penetration

i01 (a)

I

8 ~

(b)

I

I

-2

I1

-

i

0

i

I

2

m

Fig. 2. Longitudinal section of the average crown (a) and tangential section in the plane of d i (b). The distance d i will vary depending on angle ~, height h and whether the rays penetrate close to the centre of the crown or at the edge.

distance of a single tree, considering both vertical and horizontal displacement, the following formula is used

where d~ is the maximum distance of penetration for a ~pecific angle and height. The summation is performed for a number (n) of heights from base to top of the crown. The value of n is modified depending on the shape of the crown. In this case, the height increment is chosen to 2 0 c m giving n -- 39. As stated above, the penetration length also depends on the number of trees along the path. From the investigation with hypsorneter the distribution of cases is obtained when one, two, three etc. crowns are penetrated.

102

Hence, the average penetration length (d) of the whole canopy at a specific angle of incidence is calculated by d = d ( l f l + 2f2 + 3f3 + . . . )

(2d)

where fl is the fraction for penetration of one crown, f: is the corresponding value for two crowns etc.

Determination of sky obscuration factor by a photographic method In the photographic method, vertical fish-eye pictures were taken at a number of spots in the mature stand Ih 5. The lens is a Fisheye-Nikkor Auto, 8 mm f/2.8 fitted to a standard Nikon camera. The coverage angle is 180 ° and the lens yields a circular image (23 mm diameter) which, according to the manufacturer, is an exact reproduction on a flat plane of all objects encompassed within the 180 ° hemispherical field. The centre of the image corresponds to the zenith in the angle of view, and the distance of any point in the image from this centre is directly proportional to its angle from zenith. Fourteen different photographs were taken in the mature stand at arbitrary points (Fig. 3). Each picture was examined at 192 different points by means of a transparent grid consisting of 8 concentric circles with 10 ° equidistance and 24 radii equally distributed. At each point of intersection between the radius and the circle, it was decided whether the sky was or was not covered by some part of the tree. In this way sky obscuration factors (SOF) were calculated for different solar elevations (Gemmel and Perttu, 1978). The fish-eye photographs were also used to estimate the relative areas of gaps and stems of the canopy at a certain zenith angle. A grid consisting of

Fig. 3. The mature Scots pine stand at J~'dra~s, central Sweden, depicted with normal lens (left, photo S. Oscarsson) and with fish-eye lens (right, photo H. Grip).

103 one concentric circle corresponding to 45 ° zenith angle was placed over the photographs. Using a microscope (10×) with a built-in scale, the lengths of segments not obstructed by biomass were measured along the circle. A gap is defined as an opening large enough to make the whole solar disc visible (0.5 ° ). The photographs were enlarged about 10 times which gave a minimum gap opening of a b o u t l mm 2 . Corresponding measurements were made for stems, thick branches, etc., i.e. totally opaque parts of the canopy larger than 1 mm 2 . For each photo the gap length and the stem-branch length were divided by the circumference, giving relative areas of gaps (Ag) and stems (As) for the specific zenith angle. The relative area of 'needle-obstructed' canopy (An) was also obtained considering that the sum of all three parts should equal 100%.

Determination of extinction coefficient Introducing a mean light density factor, Dr, for the needle-obstructed part of the canopy it is possible to obtain an expression which corresponds to the SOF estimated by the photographic method. The value of Df is between zero and one depending on h o w dense the crowns are; a density of one corresponds to a completely non-transparent canopy. The SOF for the specific zenith angle can be expressed by the formula

SOF = AnDf + As

(3)

Consider again the expression defining the extinction coefficient k

I/I o = exp(--kd)

(4)

The term on the right hand side gives the fraction of radiation remaining after passage of the crowns, i.e. the expression ( 1 - exp(--kd)) equals the fraction not being transmitted. Following the discussion a b o u t the density factor Df above, it is obvious that the connection between Df and k is given by

Df = 1 - - e x p ( - - k d )

(5)

Combining eqs. 3 and 5 gives k = --lnIAn--SOF+As]/dAn

(6)

Given values of SOF, An and A8 from the photographic method and the value of d by the procedure described earlier, it is possible to calculate the extinction coefficient.

Radiation measurements The short-wave radiation ( 3 0 0 - - 3 0 0 0 n m ) below and above canopy was measured by using Kipp and Zonen solarimeters. One sensor situated at 27 m

104

on the mast (Perttu et al., 1977) recorded the incoming global radiation above canopy (G O) while 10 sensors, placed at 0.5 m above ground in a square pattern with 10 m distance, measured the radiation below the canopy. During the period July 23--August 2 2 , 1 9 7 8 the sensors were moved 4 times to different places within the stand to minimize possible effects of inhomogeneity of the mature stand. The sensors were calibrated in the spring of 1978 shortly before the measurements started (Lindroth, 1978). Considering calibration accuracy, levelling, etc., the absolute accuracy of each sensor was estimated to -+10% for solar elevations above 10 ° (Perttu et al., 1977). The incoming radiation below canopy (G) was calculated as the average value of the 10 different sensors. Assuming non-systematic errors between the sensors, the accuracy of the mean value is within about + 3%. RESULTS

The various measurements were taken, in part, over several years. The mature stand (approximately 125 years old) is at a stage where the variation in crown shape is negligible. The leaf area index is, however, not constant throughout the year which implies that the canopy density will change slightly.

Stand parameters and sky obscuration factor The spot method, which was applied in two different ways, gave the result that the average crown density value for the mature stand Ih 5 was 0.41 +0.025 (Table II). This means that the horizontal projection of branches, twigs and needles covers 41% of the total area. This figure includes the basal area, which amounts to 0.15% (see Table I). As can be seen from Table II, there are rather small variations in the crown density values, which lie between 0.37 and 0.43. Given that there are 400 trees ha -1 , that the projected area of the crowns covers 41% of the total area, T A B L E II Crown density

Location

(CD) at d i f f e r e n t l o c a t i o n s in the Scots pine stand Crown density

deviation

No. o f observations

1 2 3 4 5 6

0.37 0.44 0.42 0.40 0.42 0.43

0.036 0.038 0.028 0.028 0.027 0.029

176 169 310 298 330 300

M e a n value Std. dev.

0.41 0.025

Standard

105 TABLE III Average sky obscuration factor (SOF), canopy opening factor (C o) and weights (w), for different solar elevations (SEL) evaluated from 14 fish,eye photographs taken in the mature Scots pine stand

SEL (o)

SOF

Std. dev. SOF

Co

w

Cow

5 15 25 35 45 55 65 75 85

1.00" 0.86 0.71 0.61 0.52 0.48 0.41 0.37 0.33

-0.08 0.05 0.08 0.10 0.10 0.14 0.16 0.33

0.00 0.14 0.29 0.39 0.48 0.52 0.59 0.63 0.67

0.210 0.185 0.160 0.136 0.111 0.086 0.062 0.037 0.012

0.000 0.026 0.046 0.053 0.053 0.045 0.037 0.023 0.008

Co = ~,Cow = 0.291 * By definition. a n d a s s u m i n g t h a t t h e h o r i z o n t a l p r o j e c t i o n s o f t h e c r o w n s are a p p r o x i m a t e l y circular, t h e average c r o w n d i a m e t e r was c a l c u l a t e d f r o m eq. 1 t o be 3.6 m. T h e investigation w i t h t h e h y p s o m e t e r gave t h e result t h a t 88% o f t h e p e n e t r a t i o n s o c c u r r e d t h r o u g h o n e c r o w n a n d 12% t h r o u g h t w o c r o w n s w h e n the e l e v a t i o n angle was 45 °. F r o m t h e s e d a t a a n d using eq. 2 t h e pene t r a t i o n length d was c a l c u l a t e d to be 2.3 m f o r t h a t specific solar elevation. T h e s k y o b s c u r a t i o n f a c t o r , o b t a i n e d b y t h e p h o t o g r a p h i c m e t h o d , increased f r o m a b o u t 0.30 at zenith t o 1.00 at h o r i z o n (Table III). T h e SOF can be e x p r e s s e d as a f u n c t i o n o f solar angle (SEL, in degrees) b y

SOF = 1 . 0 2 6 4 " e x p ( - - 0 . 0 1 3 8 " SEL)

(7)

T h e c u r v e is well f i t t e d to t h e values w i t h a m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t o f 0.991 (Fig. 4).

Extinction coefficient T h e investigation to find t h e relative area o f gap a n d n e e d l e - o b s t r u c t e d p a r t s o f t h e c a n o p y gave t h e result t h a t , f o r a solar elevation o f 45 °, 9% was t o t a l l y o b s t r u c t e d (stems, t h i c k b r a n c h e s , etc.) while 26% was c o m p l e t e l y uno b s t r u c t e d (gaps). This m e a n s t h a t 65% o f direct r a d i a t i o n was t r a n s m i t t e d t h r o u g h a layer o f needles, smaller twigs, etc. (Table IV). T h e sun r a y pene t r a t i o n length f o r t h e c o r r e s p o n d i n g solar e l e v a t i o n was e s t i m a t e d to 2.3 m. Using eq. 7 t o derive an a p p r o p r i a t e value o f SOF, t h e e x t i n c t i o n c o e f f i c i e n t a c c o r d i n g to eq. 6 was e s t i m a t e d t o be 0 . 5 2 9 m -~ . This m e a n s , f o r e x a m p l e , t h a t o n l y 10% o f t h e r a d i a t i o n i n t e n s i t y r e m a i n s a f t e r passage o f a 4.4 m

106

1.0

0.8

o c o

0.6

o

5

0.4

o cD

0.2

I

/

0

20

i

I

I

40

6O

80

Solor elev0tion {degrees)

Fig. 4. Sky o b s c u r a t i o n f a c t o r as a f u n c t i o n o f solar e l e v a t i o n in t h e m a t u r e stand. Vertical bars c o r r e s p o n d to s t a n d a r d deviations. T h e curve was f i t t e d b y a least-squares fit. T A B L E IV

Relative area o f gap, s t e m a n d n e e d l e p a r t s of t h e c a n o p y in t h e m a t u r e s t a n d for a z e n i t h angle o f 4 5 ° Relative area Gap Mean Std. dev.

(As)

0.259 0.061

S t e m (As)

Needle

0.085 0.012

0.656 0.057

(An)

thick canopy layer. To reduce the intensity by 50% only 1.3 m of canopy must be passed. The accuracy of the estimated extinction coefficient could only be tested indirectly by means of measured values of global radiation above and below canopy. Assuming that during clear sky conditions and for relatively high solar elevations, the diffuse part of the global radiation above canopy is 15% (Lunelund, 1940, Liu and Jordan, 1960}, it is possible to prepare the following formula which gives the ratio of global radiation below the canopy (G) to global radiation above the canopy (G O) G / G o = 0.85(A e + ( 1 - - ~ ) A n exp(--kmd)) + 0.15Co

(8)

where A s and An are the relative areas of gap and needle parts of the canopy

107

0.8 :>, ~n

0.6

E o 2

/

0.4

o

0 Solar e l e v a t i o n

(degrees)

Fig. 5. Canopy transmissivity of global radiation for different solar elevations in the mature Scots pine stand. The dots represent values measured by radiation sensors during completely clear sky conditions. The curve is estimated from sky obscuration factors by the photographic technique. at a certain solar elevation, ~ is the albedo of the stand and km is the extinction coefficient to be estimated from radiation measurements. Co is a weighted mean canopy opening factor calculated from the SOF-values. SOF is, by definition, the obscured part of the sky for a certain solar elevation and Co --- 1 -- SOF (Table III) is then the non-obscured part for that specific elevation, i.e. the part of the sky that contributes to the diffuse radiation below canopy. Now, because each Co is only the relative opening area at each elevation, weights w (Table III) have to be given to each value with respect to how much of the hemisphere they really represent. The grid used to calculate SOF was constructed in such a way that the pictures were divided into 9 circular segments with a constant angular increase of 10 °. This means that if the area of the zenith segment is A, then the various areas of the segments will be 3A, 5A, 7A . . . . . 17A. Thus, Co at the periphery should have a weight of 17 compared to Co at zenith. It should be pointed out that the average canopy opening factor Co, is not the arithmetic mean of the Co values, but rather the sum of Co times weights for all elevations. This is on the assumption that the sum of the weights equals unity. The reflected part of the global radiation below the canopy is assumed to be negligible. Solving eq. 8 for km gives

km = --lnIG/G°--O'15C°--O'85Ag]/d j

{9)

From the measurements of global radiation, G/G o was estimated as 0.40 (Fig. 5) for a solar elevation of 45 °. The albedo of the mature stand is about 8% (Perttu et al., 1980). This gives k m = 0.577 m -1 which is about 7% larger than the extinction coefficient estimated by eq. 6 above. The limitation of this way of testing the accuracy of the calculated extinction coefficient lies

108

in the fact that both methods depend on results from the investigation by the photographic method. However, examining eq. 9 it is clear that Ag ~ ( G / G o -- 0.15Co)/0.85

(10)

otherwise the equation is undefined. Inserting appropriate values yields AK ~ 0.42 for a solar elevation of 45 °. The estimated value was 0.26, which

seems to be quite reasonable (Table IV). Another sensitive point concerning the calculation of k is the estimation of S O F . Again, the S O F values can only be tested indirectly by comparisons with measured global radiation above and below the canopy. From the definition of the sky obscuration factor, it can be assumed that there should be a close relation between the relative amount of direct radiation reaching the ground and S O F . This implies that the relative amount of global radiation below the canopy can be calculated from GIG o = 0 . 8 5 ( 1 - - S O F ) + 0.15Co

(11)

Substituting S O F with eq. 7 gives G / G o = 0.85(1 -- 1.0264 exp(--0.0138 " S E L ) ) + 0.15 "0.291

(12)

The rather good agreement between measured and estimated values of GIG o (Fig. 5) indicates that the obtained S O F values are quite acceptable, at

least for lower solar elevation. However, at high elevations the estimated value of G/Go is too large, which indicates that the sky obscuration factor is somewhat underestimated (see eq. 11). This also explains why the estimated extinction coefficient is slightly too small. The calculations are fairly sensitive to the determination of S O F . A 10% change of S O F gives 20% change in extinction coefficient. It is also interesting that 35% of the radiation reaching the ground in the Scots pine stand has passed through the obscured part of the canopy when the solar elevation is 45 ° . Equations 8 and 11 are not especially sensitive to the distribution of global radiation between direct and diffuse components. Increasing the fraction of direct radiation by 10% (from 0.85 to 0.935) only increases G/G o by 3%. CONCLUSIONS

Using eq. 6, the extinction coefficient of a forest canopy can be easily determined by a m e t h o d involving measurements of crown density and slant ray penetration length by simple field techniques, and the sky obscuration factor from fish-eye canopy photographs. Radiation measurements above and below the canopy of the stand were used to test the calculations. The agreement between the two methods was good (7%), but it should be pointed out that the methods were n o t completely independent of each other in the sense that both relied on determinations of the relative areas of openings and of needle obstruction of the canopy.

109

The main feature of the method is that the field work can usually be carried out within one or two days, in contrast to the extensive measurements that are necessary when radiation sensors are used. This also implies that a large number of stands can be investigated during a growing season. The manual evaluation of the pictures demands a work effort of a b o u t the same magnitude as the field work. The fraction of short-wave radiation reaching the ground during clear sky conditions can be accurately estimated from sky obscuration factors determined from the fish-eye photographs {Fig. 5). Agreement between measured and calculated values was good, in spite of the large spread of the SOF values at high solar elevations (Fig. 4). It should also be possible to improve eq. 11 to be valid for mixed weather conditions also. There are now possibilities to evaluate fish-eye photographs by an automatic method, developed at the Royal Institute of Technology, Stockholm (Olsson et al., 1981). The pictures should preferably be exposed in homogeneous conditions in order to facilitate the evaluation and to improve the results. ACKNOWLEDGEMENTS

This paper was prepared as part of the abiotic research within the Swedish Coniferous Forest Project, Swedish University of Agricultural Sciences. Measurements of crown densities were performed by forestry students under the guidance of the authors. Thanks are due to Mr. P. Gemmel who t o o k part in the fish-eye photography and to Mrs. L. LSthman for careful recording of the radiation measurements. Mr. H. Grip and Prof. W. E. Reifsnyder contributed with valuable information and ideas during many discussions.

REFERENCES Andersson, M.C., 1964. Studies o f the woodland light climate. I. The photographic computation of light conditions. J. Ecol., 52: 537--542. Evans, G.C. and Coombe, D.E., 1959. Hemispherical and woodland canopy photography and the light climate. J. Ecol., 47: 103--113. Gemmel, P. and Perttu, K., 1978. Short-wave radiation within a pine stand. Comparison between measured radiation and radiation calculated from fish-eye photographs. Swedish Coniferous Forest Project, IR 76, Swedish University of Agricultural Sciences, 18 pp. (in Swedish, English abstr.). Halldin, S., Grip, H. and Perttu, K., 1979. Model for energy exchange of a pine forest canopy. In: S. Halldin (Editor), Comparison of Forest Water and Energy Exchange Models. International Society for Ecological Modelling, Copenhagen, pp. 59--75. Hill, R., 1924. A lens for whole sky photographs. Q.J.R. Meteorol. Soc., 50: 227--235. Lemeur, R. and Rosenberg, N.J., 1979. Simulating the quality and quantity of short-wave radiation within and above canopies. In: S. Halldin (Editor), Comparison of Forest Water and Energy Exchange Models. International Society for Ecological Modelling, Copenhagen, pp. 77--100. Lindroth, A., 1978. Calibration of radiation meters. Swedish Coniferous Forest Project, IR 81, Swedish University of Agricultural Sciences, 17 pp. (in Swedish, English abstr.).

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Liu, B.Y.H. and Jordan, R.C., 1960. The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Sol. Energy, 4: 1--19. Lunelund, H., 1940. Bestrahlung verschieden oreintierten Fl~/chen in Finnland dutch Sonne und Himmel. Soc. Sci. Fenn., Comm. Phys. Math. X, 13: 1--28. Madgwick, H.A.I. and Brumfield, G.L., 1969. The use of hemispherical photographs to assess light climate in the forest. J. Ecol., 57: 537--542. Olsson, L., Carlsson, K., Grip, H. and Perttu, K., 1981. Evaluation of forest canopy photographs with diode-array scanner OSIRIS. Submitted to Can. J. For. Res. Perrier, A., 1979. Physical model to simulate energy exchange of plant canopies. In: S. Halldin (Editor), Comparison of Forest Water and Energy Exchange Models. International Society for Ecological Modelling, Copenhagen, pp. 101--113. Perttu, K., Lindgren, ~., Lindroth, A. and Nor~n, B., 1977. Micro- and Biometeorological Measurements at J~dra~s. Instrumentation and Measurement Techniques. Swedish Coniferous Forest Project, TR 7, Swedish University of Agricultural Sciences, 67 pp. Perttu, K., Bischof, W., Grip, H., Jansson, P.-E., Lindgren, ~., Lindroth, A. and Nor~n, B., 1980. Micrometeorology and hydrology of pine forest ecosystems. I. Field studies. In : T. Persson (Editor), Structure and function of northern coniferous forests -- an ecosystem study. Ecol. Bull., 32: 75--121. Reifsnyder, W.E., Furnival, G.M. and Horowitz, J.L., 1971/1972. Spatial and temporal distribution of solar radiation beneath forest canopies. Agric. Meteorol., 9 : 21--37. Sarvas, R., 1953. Measurement of the crown closure of a stand. Commun. Inst. For. Fenn., 41: 1--13. Swedish Centre of Technical Terminology, 1969. Glossary of Forest Terms. Swedish Centre of Technical Terminology, Stockholm TNC 4 3 , 4 7 7 pp.