Influence of light conditions in canopy gaps on forest regeneration: a new gap light index and its application in a boreal forest in east-central Sweden

Influence of light conditions in canopy gaps on forest regeneration: a new gap light index and its application in a boreal forest in east-central Sweden

Fores~xjology Management ELSEVIER Forest EcologyandManagement84flW61 187-197 Influence of light conditions in canopy gaps on forest regeneration: a ...

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Fores~xjology Management ELSEVIER

Forest EcologyandManagement84flW61 187-197

Influence of light conditions in canopy gaps on forest regeneration: a new gap light index and its application in a boreal forest in east-central Sweden Xiaobing Dai ’ of Ecological







30 January

14, S-752


Uppsala, Sweden


Abstract Forestlight conditionschangedramaticallyafter canopygap formation;other micro-environmental changessuchasair andsoil temperatures, andsoil moisturecanbe relatedto changesin radiation.Light conditionsthereforeplay a key role in gap-phaseregenerationof forests.In this study, a new gap light index, GAF’LI (GAP Light Index) indicatingthe light conditionsat any point in any gap was developed.It is a function of severalparameters,includingsite (latitude and longitude,coordinatesof the point in the gap), vegetation-structural (meanheight and cover of the canopy layer of the forest),geometrical(longand shortaxesandorientationof the gap)andclimatic(meancloudiness of the region).The model was testedin 30 gapswith different sizesand orientationsin a Picea abies forest in Fiby Urskog,Uppsala,east-central Sweden.The resultsshowedthat the meanannualgrowth (in the last5 years)of spruceseedlingswashighly significantly correlatedwith GAPLI (adjustedR* = 0.83, P = 0.0001in 145quadratsin 29 gaps;adjustedR* = 0.47, P < 0.0001in 104 quadratsin a singlegap).The meanannualgrowthof P. abies seedlings coincideswith a rangeof GAPLI valuesfrom 0.9 to 1.7,centredat GAF’LI 1.3; that of Beth pubescens appearedin a narrowerrange(1.3-1.5) but alsocentredat 1.3, while the meangrowthof Pinus syluesh-is seedlings wasrelatedto light conditionswith GAPLI higherthan 1.5. Moreover,most spruceseedlingsappearedin the shadedparts of canopy gaps(i.e. thosewith low GAPLI values).It is concludedthat GAPLI can be usedto predictthe growth anddistributionof seedlingsin forests;with further testing,it may be usefulin othertypesof forest andin other locations. A computerprogram‘Light’ was written for the calculationnot only of GAF’LI, but also sun height and direction (azimuthangle)at any time of the year andat any locationon earth.The programcan be obtainedfrom the author. Keywords:



gap; Fiby


Gap Light


1. Introduction

Canopy gaps play a very important role in forest regeneration (e.g. Denslow, 1987; Hyttebom et al.,

’ Tel.: +46 18 182862; [email protected] 0378-I 127/96/$15.00 Copyright PII SO378-1 127(96)03734-6



18 553419;

0 1996 Elsevier



rate; Picea &es;



Sun height;


1987; Popma and Bongers, 1988; Bongers et al., 1988; Leemans, 1990; Leemans, 1991; Liu and Hyttebom, 199 l>, and have been intensively studied and documented (Pickett and White, 1985; Platt and Strong, 1989). Studies of forest light conditions are available (e.g. Monsi and Oshima, 1955; Anderson, 1966; Evans, 1966; Yoda, 1974; NakashtiLuka, 1985; Canham, 1988), a few of which attempted to de-

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tribe light conditions in and around canopy gaps Monsi and Oshima, 1955; Nakashizuka, 1985; Canlam, 1988; Poulson, 1989; Clark et al., 1993). The vays canopy gaps function in the regeneration proess are not well studied and understood (Denslow, 987). A project was therefore initiated to study nicro-environmental characters in canopy gaps in boreal forest and their impact on gap-phase regeneraion. The micro-environmental factors included in he study were: air and soil temperature, soil moisure, soil nitrogen availability, physiologically active adiation (PAR), and global radiation. The distribuion of seedlings of canopy species in one gap was napped and their annual growth measured (Dai and lyttebom, 1996). These were dependent variables. )n average, 25.0% of PAR reached the ground in he gap against only 8% in the surrounding forest compared with PAR measured at the top of canopy); global radiation in the stand accounted for only !1.9% of that in the gap. Air and soil temperature, oil moisture, and nitrogen availability varied beween gap and stand, and among different positions n the gap, both diurnally and seasonally. However, he trends were not clear. The highest mean annual growth rate of spruce seedlings was found in the torthem part of the gap where the greatest amount of lirect sunlight was found. Mean growth rate in the :ap was 23.9% higher than in the stand (Dai and lyttebom, 1996). As pointed out previously (e.g. 3hazdon and Fetcher, 1984; Nakashizuka, 1985; Ianham, 1988; Raich and Gong, 19901, light and emperature conditions are the most essential factors, jut each affects the distribution and growth of ,eedlings in different ways. Since air temperature is argely dependent on radiation, it seems that light is he decisive factor. Attempts to quantify the light environment in and around canopy gaps/openings have been based on laily measurements of PAR, gap size (Barton et al., 989; Dirzo et al., 1992) and canopy tree height Welden et al., 19911, or combinations of them Brown and Merritt, 1970a; Brown and Merritt, .970b). However, large diurnal and seasonal changes n the position of the sun produce dramatic changes n the amount of direct sunlight (beam radiation) at a joint in or around a gap. Consequently, instantaieous or even integrated daily measurements of PAR tre of limited use as indices of seasonal total light

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levels. Moreover, there is substantial spatial variation in understory light levels as a result of the.geomeny of the shading by canopy trees adjacent to a gap, so gap size is inadequate as an index of the amount of light received by plants at different locations in or around a gap (Canham, 1988). Nakashizuka (1985) developed a model, based on the studies of Monsi and Oshima (1955), to formulate the diffuse light conditions in canopy gaps. In his model, the relative illuminance of diffuse light was calculated under the assumption that the gap was round, taking into consideration the radius of the gap, height of the canopy, and horizontal distance of the point to the centre of gap. When this method was applied in our gap study, the following disadvantages were encountered. 1. The diffuse light is only a small portion of the total radiation and can hardly represent the totai light conditions. 2. In the model described by Nakashizuka (19851, all points with the same distance to the centre have the same light conditions, which is not realistic. The position in the gap is crucial because the sunlight is not evenly distributed in the gap due to the change of sun height and azimuth with time. 3. The model does not take the geographical location into consideration, so its application is limited. The gap light index (GLI) developed by Canham (1988) is more realistic. Canham considered the location of the site, the geometry of the gap and the climate; hence, the weak points in the model of Nakashizuka (1985) were overcome. However. almost all parameters have to be calculated baaed on real measurements: Tdiffuseand Tbeam were derived from light measurements with quantum sensors, and the coordinates of the target point were calculated from a 180” fisheye photograph (Canham, 1988). The resulting GLI values are precise, but in practice this index is difficult to apply because the coordinates have to be calculated for every gap under~ investigation and the light parameters have to be estimated for every location, i.e. a fisheye photograph must be taken for every gap and direct FAR must be measured for some time in the growing season in every new site. The present study offers an approach for compari-

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son of the light conditions in canopy gaps of different sizes, orientation, in different forest types and in different locations, by developing a unified, easy-touse new gap light index (GAPLI), which involves most important habitat components, including geographical, geometrical, vegetation-structural, climatic and temporal (diurnal and seasonal) factors. This paper discusses the structure of the model, and results of some tests of the model in a boreal forest dominated by Piceu abies.

2. Methods 2.1. GAPLI model

The GAPLI is an index, indicating the light conditions at any specified spot/point in any canopy gap. The model makes the following assumptions: (1) the shape of the gap is an ellipse; (2) the canopy of the forest is flat and the trees are evenly distributed in the forest-with a cover of at least 30%; (3) the forest floor is flat, i.e. this model does not take aspect, slope or elevation into account. The GAPLI index is a function of the following parameters: 1. latitude and longitude of the site; 2. mean annual cloudiness of the region, as duration (in hours) of direct sunlight measured over the duration of sun above 5” in the year, expressed as a percentage; 3. mean canopy height of the forest; 4. mean cover of the canopy and sub-canopy layers of the forest; 5. orientation of the long axis of the gap; 6. length of the long and short axes of the gap; 7. coordinates of the point in the gap. The model equation can be summarized as THBEAM x ( 1 - CLOUDY) kx


4500 COVER


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reaches a maximum value of 4 for a point in the gap receiving up to four times more global radiation than other points under the canopy-according to a previous study (Dai and Hyttebom, 1996; THBEAM is the total number of hours in a year that direct sunlight (beam radiation) reaches that point; CLOUDY is the mean value of cloudiness (%) in the study area, as duration (in hours) of direct sunlight measured over the duration of the sun above 5” in the year; it can be obtained from a nearby meteorological observatory. 4500 is the maximal amount of THBEAM; COVER is the mean cover value of the canopy and sub-canopy layers of the forest. For deciduous forests, this is the mean cover of the forest in the middle of the growing season. Cover must be greater or equal to 0.3-this is a pragmatic definition of ‘forest’. GAPLI is computed with the help of a program named Light. For all plots and quadrats, the coordinates of the centre were used and the index applies to all seedlings in the plot/quadrat (50 cm X 50 cm or 1 m X 1 m). The main task of the program is to compute the parameter THBEAM (Total Hours of BEAM radiation, to two decimal places) on the specified point. To calculate THBEAM, it is first necessary to calculate the sun height (H) and azimuth angle (AZ). The following formulae were used to calculate H and AZ (Anonymous, 19921, giving the local time (LT), latitude and longitude (LAT and LONG, in degrees), and day of the year (DAY, Julian day) TD = LONG/

15 .O

where TD is the time difference (h), east longitude being positive, and west negative UT= LT-


where UT is universal time or Greenwich time cp=LAT


n = - 2557.5 + DAY + fraction of day from Oh UT

GI = k x THBEAM x ( 1 - CLOUDY) 4500 x COVER where: k is a constant; it takes the value 1 when the target point is under a canopy of 100% cover, and

where n is the number of days from Julian year 2000.0 0, = 6h.6444987 + Oh.0657098243 DAY + lh.00273791 UT

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84 (19961187-197

where 8, is Greenwich mean sidereal time; this Formula holds for 1993, but for our purpose, the difference among years is very small, so this is used for all years (1950-2050) 6, = 8, + TD

where 8, is local sidereal time L = 280”.460 + OO.9856474 n

where L is mean longitude aberration

of sun, corrected for

g = 357O.528 + 0”.9856003 n

where g is the mean anomaly (put L and g in the range O-360” by adding multiple of 360”) X = L + 1”.915sin g +0”.020sin2g B

where A is ecliptic longitude (ecliptic latitude is 0’)


E = 23O.439 - 0”.OOOOOO4n

where E is obliquity of ecliptic

Fig. 1. A sketch showing

a canopy

gap under consideratiou.

r=tan-‘(COSEtanA) where a is right ascension (in same quadrant as X> S= sin-‘(sin

c sin A)

where 6 is declination t=()L--.(y zos(90 - H) = cos(90 - 6) - cos(90 - ‘p)

+ sin(90 - 6)sin(90 - cp)cost sin(360-AZ)

= (sin(90-


$0 H and AZ are calculated. In general, both H and AZ are functions of latitude, longitude, day of the year, and time of the day. To calculate the number of hours that direct sunlight reaches the point, the length of line AD is zompared with line AC (the length of the shadow of he tree in the direction of AB (the same as SC> (Fig. 1). As sun height (H, i.e. angle SCA) and azimuth mgle (AZ, angle between sun and the north) change with time, all variables, including position of A (x,, rr), length of line AC (LAC) and AD CL,,,), are a Function of time, when canopy height h, the long md short axes and the orientation of the long axis of he gap, and the position point D (co-ordinates of D :o point 0 as the origin) are constant. Given the long axis of the gap 2a (X axis in Fig.

l), short 4, (angle north, in (x,, y,>,

axis 2b (Y axis), the orientation of the gap between the long axis (X axis) and the the range O-l&O’), co-ordinates of point D we have

Lc = h/&C H) 0=9O”+AZ-


The co-ordinates of point A (x2, yz) can be obtained as one of the solutions of following system of equations: u2





L there are two solutions to this system of equations, i.e. they are the co-ordinates of the two intercept points, A and B, respectively. The values of + and AZ together will determine which point to take. Therefore L AD



( Y, -

Y 1)’

+ ( x2 - XI ,‘I

when L,, > L,,, then point D receives direct sunlight. If we set t, as the first local time (LD)_when the point starts to receive direct sunlight, t, as the last moment in a day when the point stops receiving

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direct sunlight, HBEAM as the number of hours in a day that point has received direct sunlight (beam radiation), and THBEAM as the total number of hours in a year that point has received direct sunlight, we have

well as the amount of beam radiation (in hours) a point can receive during any specified time period (any day, week, month, etc.). The program is written and compiled in Turbo Pascal 7.0.


2.2. Test forest


= t, - ri =

365 c (HBEAM) day= 1

The model was tested in Fiby Urskog, a natural Picea abies forest, 20 km west of Uppsala, in cen-

tral-east Sweden (57”53’30”N, 17”21’4O”E). The forest has many gaps, varying from 9 to 360 m2 (except for one big gap of 2900 m’), and the total area of gaps accounted for 31% of the forest. The mean height of the canopy trees was 21.6 m and the mean

The program can calculate the GAPLI for any point given in a gap, and compute the sun height and direction (azimuth angle) at any time (any hour, day, month, year) and location (anywhere on earth), as

Table 1 Gaps investigated Gap no.

4 5 6

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

in a Picea abies forest in Fiby Urskog,



Orientation (deg.)

Long axis

Short axis





27.0 0.0 0.0 0.0 7.0 0.0 155.0 125.0 120.0 55.0 5.0 0.0 80.0 45.0 45.0 90.0 164.0 154.0 60.0 0.0 140.0 70.0 40.0 0.0 160.0 140.0 0.0 0.0 40.0 0.0

23.0 20.5 3.2 21.6 17.0 10.4 15.0 7.5 17.0 7.0 32.0 7.5 16.8 12.0 15.0 10.5 7.5 12.5 32.0 98.0 18.0 20.5 6.0 9.0 10.0 10.2 22.0 31.5 20.0 18.0

8.0 11.5 10.4 8.4 5.5 6.4 5.2 4.7 10.0 6.0 9.0 3.5 7.3 9.5 5.0 10.5 3.5 6.5 7.0 60.0 16.0 7.5 5.0 4.5 3.4 5.4 7.0 23.5 10.1 13.6

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 16 4 4


No. quadrat 104 5 5 5 4 4 3 5 4 7 4 5 5 5 5 5 5 6 8 5 5 5 5 5 5 5 9 6 5


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:over of the forest 55% (Liu and Hyttebom, 199 1). Details of the forest are described in Dai and Hyttemm (1996). Potentially, the area could receive direct sunlight ‘or 4492.16 h year- ’ (calculated using a timetable of jaily sunrise and sunset for Stockholm, about 80 km coutheast of Fiby), but the mean amount of direct Gunlight received in the meteorological station in LJltuna, Uppsala (about 19.5 km east of the study site), was 1601 .I h (average over 1983-19931, thus he annual mean cloudiness of the region was 54.36%. Z.3. Data collection

Data on the distribution and growth of spruce seedlings (defined as all individuals below 50 cm Ieight) were collected in August 1991. In a gap of nedium size (Gap 1, 196 m2; for size distribution of he gaps in the forest see Liu and Hyttebom, 19911, he positions of all spruce seedlings were mapped md their annual growth for the last 5 years (when mssible) measured in millimetres. In this gap, the )hoton flux density of photosynthetically active radiition (PAR) was measured in the centre of each Juadrat in a 2 m X 2 m grid system, using a LICOR juantameter, during 12:00-l 2:40 h on a clear day, 5 luly 1991 (Dai and Hyttebom, 1996). Distribution md growth rate data were also collected from 29 zaps in the same forest. The long and short axes of be gaps, and orientations of the long axes were -ecorded. One hundred and forty-five quadrats (2 n X 2 m in most gaps, 1 m X 1 m in five small gaps md 4 m X 4 m in the largest gap of 2900 m2) were laid out in the centre of the gap, in four directions Ihalf way from the centre to the border, oi two quadrats in the same direction at one-third and twobirds of the distance between the centre and the >order), five to nine quadrats per gap according to he gap size (Table 1). Seedlings of all species (from most to least frequent species: Picea abies, Populus pt-em&z, Bet&a pubescense, Pinus sylvestk, Ulmus plabra, Corylus avellanan Tilia cordata, Salix zaprea, Quercus robur) in each quadrat were counted

md their annual growth during the last 5 years measured. Only the first four species were used in the analyses, the remainder accounted for fewer than ten individuals.


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3. Remits


and discus&m

To test the model, the GAPLI values for all 2 m X 2 m quadrats in a grid laid out in’.Gap 1 were computed. The results were used to create the picture shown in Fig. 2(a) (104 quadrats used). The data were compared with those of the photon flux density of PAR (Fig. 2(b)). The (Pearson) correlation between the two data sets was 0.5 14 (P = O.OOUI 1. The overlap was not very large, since the PAR values were measured during a short period of time (12:00-12:4O h), when the sunlight came almost exactly from the south. GAPLI was calculated for each seedling found in Gap 1. A significant correlation between the mean annual growth of each spruce seedling and the GAPLI for its position was found CR2 = 0.47, r?= 17 1. P = 0.0001) (Fig. 3). On the other hand, most spruce seedlings (165 out of 171) appeared in the part of the gap which was shaded by the surroundings. This echoes the statement made in our previous study (Dai and Hytt eb om, 19961, that low radiation may be



PAR< 100








Fig. 2. Distribution of PAR (pmol m-l) and GAPLI in a quadrat with a 22 m grid system. The plot is 28 mX38 m (only 104 of 226 quadrats were used here). A canopy gap (Gap 1) with long axis of 23.0 m, short axis of 8.0 m and orientation of 27” was encompassed in the plot. The Pearson corretation coefficient between PAR and GAPLI was 0.5 14 with P = O.OOO1. (a) Distribution of GAPLI. (b) Distribution of PAR in the plot. The value of GAPLI of each quadrat was computed taking the coordinates of the centre of the quadrat.

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MeanGrowth = 1.57 +7.47 GAPLI


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n=171 Adj R2= 0.47 P = 0.0001




i 4,00 +

l 4




3,00 i ’



2,so P I



1,50 1,oo


/ 0,50 t 0,oo

I 0,oo







I 0,40


GAPLI Fig. 3. Scattergram

of the mean annual growth

rate (mm year-

essential for germinated spruce seedlings to survive and establish, while high radiation could accelerate the growth of established seedlings.

‘) of Picea a&es seedlings

For the other 29 gaps, GAPLI was calculated for each quadrat using the coordinates of the centre of the quadrat. Number of species, seedling density of

MeanGrowth = 1.56 + 10.92 GAPLI + 4.15 GAPLI*





in Gap 1 against GAPLI.





Adj R* = 0.83



P = 0.0001



GAPLI Fig. 4. Scattergram GAPLI.

of the mean annual growth

rate (mm


‘1 of P.rcea abies


in 145 quadrats

taken from

29 gaps against


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1 .oo





GAPLI of seedling Fig. 5. Distribution quadrats from 29 gaps.




of Picea

each species (no. of seedlings mW2) and the annual mean growth of each species were also calculated for each quadrat. The results show that GAPLI is highly significantly correlated with the annual mean growth of Picea abies (adjusted R2 = 0.83, n = 145, P = 0.0001; Fig. 4), and the highest annual growth rate of spruce seedling appeared within a range of 0.9- 1.7 of GAF’LI, centred at about 1.3. Again, in the 24 quadrats with spruce seedling density higher than 5, only three quadrats had a GAPLI greater than 0.1, and all eight quadrats with seedling density higher




axis. Seedling


were calculated

145 quadrats in miilimetres




MAG of seedlings of all species P icea seedling density MAG of Picea seedlings Berth seedling density MAG of Betula seedlings Pinus seedling density MAG of Pinus seedlings Populus seedling density MAG of Populus see$lings

0.50 0.09 0.91 0.07 0.87 0.35 0.89 0.25 0.69

145 141 141 19 19 24 24 28 28

O.OOOi NS 00001 NS O.#l NS o.oW NS O.ooal

B. pubescens;


Pinus syluestris;


in 29 gaps in a Picea nbies forest in Fiby per quadrat. Values of seedling density.&


Picea abies; Betula,


than 10 were situated in the shaded parts of the gaps (Fig. 5). Different species respond to light conditions in different ways. In general, the growth ofthe seedlings of the species investigated in this forest- responded positively to increased light conditions (Table 2). The highest mean annual growth of [email protected]~~ appeared in a range of 1.3- 1.5 of GAPLI, narrower than the range for Piceu a&es, but centred at 1.3, the same as spruce seedlings (Fig. 6, when taking only the quadrats receiving direct sunlight). For Pinus

Table 2 Correlation coeffkients between GAPLI and seedling densities and growth from Urskog, east-central Sweden. Values of mean annual growth (MAC) are expressed numbers m-*






NS, not significant.

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MeanGr.= 11.04 -94.68 GAPLI +182.95 GAPLI* -70.07 GAPLI’ n= 19 adj. R*=O.74



+ !












Fig. 6. Scattergram of the mean annual growth (mm year-‘) of Betula pubescens in the 145 quadrats sampled from the 29 gaps, against GAPLI. Because the distribution of Betula is not even in this spruce forest, the quadrats without Betula seedling were left out in this analysis.

MeanGr. = 2.57 - 0.82 GAPLI + 8.19 GAPLI* n = 24 adj. R* = 0.79 P = 0.0001




0,oo 0,oo











Fig. 7. Scattergram of the mean annual growth (mm year-‘) of Pinus syluesrris in the 145 quadrats sampled from tbe 29 gaps, against GAPLI. Because the distribution of Pinus is not even in this spruce forest, the quadrats without Pinus seedling were left out in this analysis.


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(Fig. 71, no peak was found in the growth-GAPLI curve, reflecting the fact that it is a light demanding species, or at least its growth could be promoted by light conditions with GAPLI higher than 1.5. The radiation which penetrates the forest canopy is changed quantitatively (e.g. amount of PAR) and qualitatively (e.g. spectral composition), depending upon the canopy cover, leaf type (needle-leafed, broad-leaved), and leaf characteristics (shape, thickness, etc.) (Anderson, 1966). However, the beam radiation, as considered in the model, varies with the geographical location of the site (latitude and longitude), the size and the shape of the gap, the cloudiness of the region, the cover and canopy height, which were considered in the model so the difference is minimised. Therefore, not only will the GAPLIs from gaps in the same forest with different sizes and orientations be comparable, but also GAPLI obtained for points in gaps in different forest types and locations. When significant correlations are found between the GAPLI and other variables, for instance growth rate and distribution pattern (seedling densities in different locations in a gap), GAPLI can be used to select a location for specific purposes, for example, planting of seedlings/saplings of the species concerned. In plant population studies, when a species appears in two or more types of forest/locations with different characters (distribution, succession, dynamics, etc.), GAPLI could be helpful in finding the difference in light conditions among the forest types/locations for the species, and to check whether light conditions affect the behaviour of the species in these forests/locations. The weak point of the model is that slope is not taken into consideration. This affects the results, particularly on sites with steep slopes. However, it is very complicated to include the slope in the model. If we wish to consider slope, we must take the aspect (facing direction) of the slope, the elevation of the site and elevation of the mountain where the site is located, into account. To date, no model has succeeded in this, but further developments of the model will make it possible. Furthermore, the constant k in the model might vary and the relationship between forest cover and the amount of beam radiation (COVER and THBEAM in the model) should be investigated more quantitatively. syluestris


84 (1996)


In conclusion, GAPLI may be practically useful in determining the general light conditions in and around canopy gaps, and the values of GAPLI from different forest types and locations could be used for comparison since most spatial and temporal differences are considered and reflected in the model. The model needs to be tested in other forest types on more locations, so any data which can be used to test the model are welcome. The program Light is available from the author free of charge, but US$lO would be appreciated to cover the disk and postal cost.


The project was funded by a World Wildlife Fund grant to H&an Hyttebom and a Swedish Institute scholarship to the author. H&an Hytteborn, Ulf Grandin, Chung-Yi Hu and Liu Qinghorrg~helped to collect part of the data. I thank H&an Hytteborn for the opportunity to do the project and his kind supervision. Dr. Chen Yuanji from the Department of Mathematics and Dot. Claes-Ingvar Lagerkvist from the Astronomical Observatory, both Uppsala University, provided much help in their respective fields of expertise. Prof. Eddy van der Maarel helped to improve the manuscript linguistically and scientifically. Last but not least, I thank two anonymous referees for useful suggestions and detailed linguistic corrections.

References Anderson, M.C., 1966. Stand structure and light penetration. J. Ekol., 3: 41-54. Anonymous, 1992. The Astronomical Almanac for the year 1993. Science and Engineering Council, WashingtQn. Barton, A.M., Fetcher, N. and Redhead, S., 1989. The relationship between treefall gap size and light flux in a neotrqical rain forest in Costa Rica. J. Trop. Ecol., 5: 437-439. Bongers, F., Popma, J. and Iriarte-Vivar, S., 1988. Response of Cordia megulantha saplings to gap environments in tropical rain forest. Funct. Ekol., 2: Ill- 124. Brown, K.M. and Merritt, C., [email protected], A shadow pattern simulation model for forest openings Pu* University Bxperimedxt Station Bull. No. 868. Brown, K.M. and Merritt, C., 1970. SimuIated sunlight duration maps of forest openings. Proc. Ind. Acad. Sci., 80: 220-224.

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