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Height growth patterns of Scots pine and Norway spruce in the coastal areas of western Finland
Forest Ecology and Management 135 (2000) 205±216
Height growth patterns of Scots pine and Norway spruce in the coastal areas of western Finland Kristian Karlsson* The Finnish Forest Research Institute, Kannus Research Station, Box 44, FIN-69101 Kannus, Finland
Abstract Stem analysis data of 46 Scots pine (Pinus sylvestris L.) and 38 Norway spruce (Picea abies (L.) Karst.) trees was used to construct height curves for naturally regenerated and cultivated Scots pine and for naturally regenerated Norway spruce from the coastal areas of western Finland. The curves were compared with each other, with models for 28 naturally regenerated pine trees off the coast and with general site index curves for pine and spruce in southern Finland. The height growth pattern for coastal pine exhibited a strong stagnation over age compared to general site indexes. Spruce height development was dominated by a slow early development followed by an increase in height increment compared to general index curves. There was a large variation in the height growth patterns of coastal spruce and a growth pattern variable was needed in the functions in order to make reliable predictions. Even simple models provided relatively good predictions for coastal pine. It was argued that strong wind, temperature and moisture regimes caused these differences between trees at the western coast and in the inner parts of Finland. The soil provides poor rooting conditions at the coast and this increases trees' susceptibility to the climatic impact. The variation in height growth patterns within the coastal area could partly be explained with location in relation to the sea and stoniness for pine, and humus layer thickness for spruce. The number of years trees had grown to breast height was used as a predictor, which explained the growth patterns very well. This variable did not describe causal relationships, since it depends both on the original status of site and of management intensity. It could be used to improve predictions when such data can is available. The early development speed was correlated with the C/N ratio of the humus in spruce stands. This indicated that the growth patterns of coastal spruce may change along an ecological gradient from dry, stony moraines with thick humus, to moist, dense sorted soils with poor quality humus. The use of soil variables in predicting height development is dif®cult, since they usually are time dependent and affected by stand characteristics and management. # 2000 Elsevier Science B.V. All rights reserved. Keywords: Pinus sylvestris; Picea abies; Height curve; Site index; Ecological site quality; Coast; Wind; Land uplift
1. Introduction The height development of dominant trees has been one of the most used measures of site quality in forest stands (HaÈgglund, 1981). The height of dominant trees at the age of 100 years (H100) has commonly been used in Scandinavia, whereas 50 years (H50) or sometimes * Tel.: 358-6-8743-213; fax: 358-6-8743-201. E-mail address: [email protected] (K. Karlsson)
only 30 years (H30) has been used in North America. Since this kind of site classi®cation is dependent on the forest stand, other methods have been developed for estimations of unforested land, disturbed ecosystems and young plantations. In many of these cases, the functions developed have predicted site index for a certain tree species rather than any absolute value of the site quality. Thus, the height development pattern of these site index functions has had a central role in determining the site quality even though ecological
0378-1127/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 1 1 2 7 ( 0 0 ) 0 0 3 1 1 - X
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K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
information has been used as predictors. Site index curves can be used in young plantations, but the consequences of even small measurement errors would be very large and young trees do not re¯ect actual site quality as well older ones (Varmola, 1996). In Finland site quality estimations have traditionally been based on site types as de®ned by Cajander (1909, 1949) according to the composition of the ground vegetation. This classi®cation was provided with growth and yield data at an early stage (Ilvessalo, 1920a, b), but there was still an obvious need to develop site index curves. Vuokila and VaÈliaho (1980) constructed such functions for cultivated pine and spruce stands and Gustavsen (1980) did the same for naturally regenerated coniferous stands. These have by far been the most used site index curves in practical site classi®cation and forest mensuration in Finland. During the last decade, growth modeling has moved from stand models towards models based on single tree data, but the height development of single, dominant trees has still been used calculating site indexes in the same way as for stand dominant height earlier (Ojansuu et al., 1991). The importance of site index in growth models has even increased (Hynynen, 1995), obviously because they re¯ect the ecological site quality very well. The regional differences in site productivity were partly described by the site types of Cajander (1909), since the land was divided into vegetation zones. Each zone had different site types and subsequently different ®gures of site productivity. This division was a rough one as the areas were very large. Site indexes have been used to describe the regionality of site quality and forest productivity more accurately (Koivisto, 1970; Karlsson, 1996), but these studies have assumed that the height growth patterns remain the same within large areas such as southern and northern Finland. The result of different growth patterns would be that two forest stands having the same height at an early age would end up at different heights later as a result of the growing conditions in the area. This would then result in a serious bias to the estimates of site index based on age and height alone. The problem could be avoided by constructing new models for regions, different ecosites etc. However, the steadily increasing number of area restricted or site speci®c models tells us that there is a need to describe the factors causing
differences in growth patterns more accurately (Wang et al., 1994). The growing conditions are different at the western coast compared to the inner parts of Finland and several factors could cause different growth patterns compared to other regions. The soil has been affected by the uplift (isostatic rebound) from beneath the sea (Perttunen, 1987). Therefore, the surface soil is washed out and very stony and the dense moraine is located close to the surface (Atlas of Finland, 1990). The climate is affected by the water masses in the surroundings. Temperatures remain cooler at the beginning of the vegetation period compared to the inner parts of Finland and the coastal area also receives more radiation (more sunny days) and less precipitation (Heino and Hellsten, 1983). The winds are relatively strong at the coast. Mean wind speed is about 6±7 m sÿ1 at the outer range of the archipelago and goes down to 3±4 m sÿ1 at the coast (Heino and Hellsten, 1983; Tammelin, 1991). The Finnish wind atlas shows that a zone of strong winds extends up to about 30 km from the coast line in western Finland (Tammelin, 1991). The terrain is ¯at in that area, but coastal regions with steeper terrain have a similar windy zone extending up to 10 km from the coastline. The coastal regions of Finland are, thus, as windy as the coastal zones along the North sea, i.e. the southern part of the west coast in Denmark and the east coast in England (Tammelin, 1991). NyyssoÈnen and MielikaÈinen (1978) and Karlsson (1996) have shown that the increment values of forest stands close to the coast are considerably lower than the ones given by yield functions developed for southern Finland. The condition or health of coastal spruce stands, especially old ones, has also been described as poor compared to other regions in Finland (MerilaÈ et al., 1998). This could simply be the result of different, average productivity levels. A marked stagnation at old age, which has been suggested for the coastal area forests (Karlsson, 1996), would again be a sign of different growth patterns. Little effort has been taken neither to adjust the common site index curves for differing conditions nor to describe the effects of varying growth conditions on the height development in Finland. The objectives of this study were to develop tree species speci®c height curves based on stem analysis of trees close to the coast, to compare these curves with curves used for
K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
site index estimation generally and to analyze ecological factors causing the differences found in the growth patterns. Intercept growth and other characteristics of early development were also used to predict different growth patterns. 2. Material and methods The area studied was located between 618 and 648N along the Finnish coast of the Gulf of Bothnia, which separates Finland from Sweden. The material was obtained from different sources. Fifteen spruce stands had been chosen from a network of survey plots established for studying factors affecting forest health in the coastal area. These spruce stands were naturally regenerated. Nineteen pine stands had been located in the oldest known, cultivated pine stands close to the coast. Furthermore, a sample of naturally regenerated pine (eight) and spruce (seven) stands between 80 and 120 years of age had been randomly chosen from the management plan for the forests owned by the Finnish Research Institute along the coast. All coastal stands were located closer than 30 km from the coastline at an altitude of 2±60 m above sea level. Within this research area climatic conditions are very closely related to altitude. An additional group consisting of 14 pine stands on sandy, sorted soils 40±60 km from the coast and 80±120 m above sea level were included in the study. These pine stands were naturally regenerated and the material provided an extension of the material from coast towards the inland serving as a reference material. They were also initially examined as part of a health study. The major differences between groups of forest stands were tree species, location and regeneration regime. The analysis was mainly performed using these groups, with the following descriptions: (1) natural pine, reference; (2) cultivated coastal pine; (3) natural coastal pine and (4) coastal spruce. Homogeneity within groups and possibilities to combine groups were examined using graphics and parameters of the functions calculated. The measurements were exactly the same on all plots. The two largest trees according to diameter at breast height were cut down on each plot. Total height was measured on the felled trees and discs were taken from the relative heights of 2.5, 7.5, 15, 30, 45, 60, 75, 85, 95% and/or at the absolute heights of 1.3 and 6 m.
207
Site data included ocular estimations (classi®cation) of topographical location, site types (Cajander, 1909), stoniness, paludi®cation and soil texture and mean particle size. Measurements also included thickness of humus and leached out horizons, stoniness according to Viro's (Viro, 1952) method (the average penetration depth of a metal rod into the mineral soil), the average coverage of lichens (mainly Cladonia sp.) and swamp mosses (Spaghnum sp. and Polytrichum sp.) and the area of large rocks or exposed bedrock on the survey plot. A very stony site had a penetration value with the steel rod of 10 cm, whereas a stone free site had a value of 40 cm. The humus thickness varied between 10 and 90 mm, when a soil auger with the diameter 30 mm was used. The data from the health surveys also included some chemical characteristics for the humus layer. The humus samples were compiled from 28 systematically collected subsamples on each plot. Total N and C were determined with a LECO TGA-500 analyzer and organic matter as ignition loss (4858C). Temperature sum was calculated for each plot with a model (Ojansuu and Henttonen, 1983). No other climatic variables were used, because of the close correlation with temperature sum and altitude. Ages for each crosscut section were obtained as all discs were measured for annual radial increment with a stereo microscope measuring system. Annual height growth values were interpolated from crosscut section data using an algorithm by Carmean (1972). There were 9±11 discs per tree in this study resulting in a sampling frequency of about 2 m at an average. The equation for Carmean's algorithm used in this study was from Fabbio et al. (1994) and included modi®cations by Fabbio et al. (1988) and by Newberry (1991). The interpolation provided us with estimates of the actual height at each crosscut age, since the crosscut height in itself often does not include the full measure of the last height growth. A height curve was calculated for each tree using height and age in a model originally presented by Richards (1959): H b1 f1 ÿ exp ÿb2 Agb3
(1)
where H is the tree height (m), A the biological age, exp is the exponential of the base of the natural logarithm and bx are parameters to be estimated for
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K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
each tree. The standard errors of the estimates were very small. The models were used to calculate H at the age of 150, 120, 100, 60 and 30 years, respectively. The interpolated values of H at each crosscut section age were combined with values for H at the age of 100 years. This value for H at the age of 100 years was analogous to site index and will in the following be denoted as SI. The intercept growth (ICEPT), the sum of height growth for 5 years above 2.5 m above ground, was obtained from interpolated yearly height growths and combined with other data in the same way as SI. The height growth pattern was described with the ratio between two points on a height curve (Z), assuming that the form of a height curve can be accurately expressed with only two points as pointed out by Zeide (1978). In order to test the efficiency of different Z ratios, all height curves were described with several Z ratios: H100 /H30, H60 /H30, H120 /H60 and H150 /H100. The number of height±age pairs was the same as the number of crosscuts on the stem analysis trees. Yearly or decadal data were not used, since that approach would have given more weight on slowly growing than on fast growing trees. When calculating height curves observations over 100 years of age were excluded for the same reason, as the old trees at an average had been growing more slowly than the young ones. All single tree height curves were compared to average curves for the group and disturbed trees were excluded. Excluded cases had height curves that were sharply crossed over the group curve or had an asymptotic value of SI (parameter b1) higher than logically could be expected (> 40 m). Five spruce trees and eight pines were excluded. The ®nal data consisted of 1159 observations of height and age from 112 trees in 58 forest stands (Table 1). Height curves were calculated for all the four groups of trees separately. In order to develop ana-
morphic height curves we used the model H b1 SIf1 ÿ exp ÿb2 Agb3
(2)
where H, SI, A and exp are as previously defined and bx parameters to be estimated. With two expressions of SI we could calculate polymorphic height curves according to this model used by, e.g., Ek (1971) H b1 SIb2 f1 ÿ exp ÿb3 Agb4 SI
b5
(3)
Many non-linear functions can be modified into linear ones through transformations (Weisberg, 1985), but these equations were genuine non-linear functions (Draper and Smith, 1981). Therefore, the parameters were calculated with program 3R from the BMDP statistical package, which uses the Gauss±Newton algorithm to calculate least square estimates for non-linear functions (Dixon, 1992). Initial values were chosen by trial-and-error and the results were evaluated with plots of residuals and predicted versus observed values. Eq. (1) was used only to calculate SI values for single trees. Using these individual SI values in Eqs. (3) and (4) provided us with equations describing the height development for the whole range of trees included. The graphical output of Eq. (1) is a single curve, whereas Eqs. (3) and (4) should be visualized with a set of curves. For graphical examinations sets of curves were drawn according to the median values and 25 and 75% quartile values of the SI values in each of the four groups of trees. In other studies Z ratios have been used to stratify height±age data and then calculate separate height curves for each group (Wang et al., 1994). Monserud (1984) used dummy-variables for three identi®ed groups of speci®c height pattern (habitats) and presented them directly into the height equations. A similar approach was used here, when variables such
Table 1 Tree data (minimum±maximum) at the time of measurement. SI's calculated with Eq. (1) for each tree separately Group of trees
n
Age (a)
Height (m)
SI (m)
Natural pine, reference Cultivated coastal pine Natural coastal pine Natural coastal spruce
28 36 10 38
50±137 60±90 100±150 36±147
13±22 15±25 14±26 12±27
12±26 18±28 11±25 13±30
K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
as Z, ICEPT and IAGE (biological age Ð age at breast height) were incorporated as a continuos variable in the polymorphic models instead of SI: H b1 SIb2 f1 ÿ exp ÿb3 Agb4 Z
b5
(4)
The usefulness of Z variables and other similar ones depend entirely on the possibility to measure or predict those variables without stem analysis data. The relationship between Z and site quality variables was studied by means of correlation analysis. The common sheet calculation program, EXCEL 5.0, provided simple regressions, correlation coefficients as well as all graphical output of data and results. 3. Results The height development of coastal pines could be rather well described with an anamorphic function (Eq. (2), Table 2). The residual errors were only slightly smaller using a polymorphic function (Eq. (3), Table 3). The height development in the reference area studied was different. The height curves of the pines there had a polymorphic character because the use of Eq. (4) resulted in smaller residual errors compared to Eq. (3). This indicated that the height growth pattern in the reference area was closer to the one in standard site index curves, since they have a strong polymorphic character as well. The graphical examinations showed that the growth pattern was a steeper one in the reference area compared to the general site index curves (Fig. 1). This was especially clear after the age of 40 years. The coastal pines had a completely different growth pattern than both the standard site index curves and pines in the reference area. There was a marked stagnation over age in the height development of the coastal pines compared to the index curves usually
209
applied. The curves for natural and cultivated pine could be regarded as complementary since the curves mainly were situated on different productivity levels: 14±21 m for natural compared to 21±25 m for cultivated (Fig. 1). The differences in growth patterns between these groups were negligible, with only a slightly stronger stagnation over age for the naturally regenerated trees compared to the cultivated trees. The residual errors were very small for both groups of pines from the coastal area. The SI range was narrow in these groups, but a function calculated for both cultivated and natural pine had a RMSE of only 6% despite a much broader range in SI. The growth patterns were described with Z ratios calculated for each SI class (Table 4). The marked stagnation over age in the height development for coastal pine resulted in Z ratios of 2.1±2.5, whereas the reference area curves had ratios of 2.9±4.8. These ®gures show that the reference area was a slightly exceptional one because of the stone free, sandy soils. The best sites in the reference area had Z ratios close to the general site index curves. The coastal area spruce did not form a homogenous group. The residual error was over 30% using the anamorphic function to predict tree heights (Eq. (2), Table 2). The predictions did not improve much when a polymorphic model was used (Eq. (3), Table 3). The great variation among the spruce stands could not be accounted for by easily recognized abnormal and excludable trees or by a division into a few subclasses like soil types, etc. Using the ratio of H120/H60 as a variable Z in Eq. (4) reduced the residual error to 7.9%. The same kind of function was better predicting height development for pine as well (Table 5). The ratio of H100/H30 was the best growth pattern variable for all pine trees. For spruce the comparison with general site index curves was based on Eq. (4) using Z as a variable
Table 2 Parameters and residual errors for Eq. (2) Group of trees
b1
b2
b3
RMSE (m)
(%)
Natural pine, reference Cultivated coastal pine Natural coastal pine Natural coastal spruce
1.498 1.063 1.051 1.719
0.01471 0.03617 0.03625 0.01206
1.562 2.135 2.175 1.592
2.38 1.29 1.66 6.50
12.6 5.6 9.0 32.3
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K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
Table 3 Parameters and residual errors for Eq. (3) Group of trees
b1
b2
b3
b4
b5
RMSE (m)
(%)
Natural pine, reference Cultivated coastal pine Natural coastal pine Natural coastal spruce
3.921 1.479 1.036 0.2002
0.7282 0.8942 0.9992 1.7764
0.01637 0.03649 0.03882 0.00905
24.31 2.758 10.88 0.2471
ÿ0.8910 ÿ0.07895 ÿ0.5191 0.5817
1.55 1.29 1.36 6.34
8.2 5.6 7.4 31.5
(Fig. 1). The curves were calculated with average values for Z, but the effect of the varying growth patterns is illustrated by inserting a curve calculated with a low value for Z (Fig. 1). When the initial development had been rapid, coastal spruce trees had a development pattern with a stronger stagnation over age than spruce stands in southern Finland generally. The dominating pattern was, however, one with slow initial development followed by an increase in height development that was stronger than in the general site index curves (higher Z ratio). The possibilities to improve the accuracy of tree height development predictions were greatly increased with the use of a variable describing the growth pattern. A ratio like H120/H60 is usually not available when estimating heights for a stand. The growth pattern must be estimated using other variables. Correlation analysis showed a relationship between several soil variables and Z ratios for coastal pines (Table 6). A regression was calculated for the best (smallest RMSE) combination of site and tree variables: Z
H100 17:39 0:076 IAGE 0:018 H30 STONE ÿ 0:014 T-SUM
2
R 0:65; RMSE 10%;
(5)
n 46
All variables included had t-values above four and they were not intercorrelated. According to the function, a stony site had a growth pattern with stronger stagnation over age than a stone free site. Temperature sum worked better than altitude in this combination, but they both described the location in relation to the sea.The Z ratios for spruce were not as clearly dependent on location and soil quality as they were for pine (Table 6). When the best combinations of variables were studied, humus layer thickness still appeared to explain some of the variation in spruce Z ratios. An additional dummy variable receiving the value 1 when soils had been classified as moraines and 0 for sorted soils was included in the function: Z
H120 1:41 0:082 IAGE 0:013 H60 HUMUS ÿ 0:43 DUMMY
R2 0:77; RMSE 20%;
(6)
n 38
All variables had t-values over three. They were not significantly correlated to each other. Including the variables HUMUS and DUMMY reduced the residual error from 26±20%. A thick humus layer had resulted in a growth pattern with stronger stagnation over age than a thin humus layer.
Table 4 The Z ratios for SI classes and analogous height-age classes for coastal pines. The Z ratios were H100 /H30. SI curves for southern Finland according to Gustavsen (1980) Group of trees
SI/Height-age class 15
18
21
24
27
SI-curve, pine Natural pine, reference Cultivated coastal pine Natural coastal pine
2.9 4.8 ± 2.5
2.7 3.9 2.3 2.3
2.5 3.3 2.3 2.2
2.3 2.9 2.3 2.1
2.2 ± 2.3 ±
K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
211
Fig. 1. Height-age curves for coastal pine and reference area calculated with Eq. (3) and for coastal spruce with Eq. (4) compared with SI curves for southern Finland (Gustavsen, 1980; Vuokila and VaÈliaho, 1980). The curves were calculated for median and quartile SI values in each group. Spruce curves with average Z ratio (1.9) and one with the low quartile (1.4).
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Table 5 Parameters and residual errors for Eq. (4) with ZH100 /H30 for all pine stands and ZH120 /H60 for spruce Group of trees
b1
b2
b3
b4
b5
RMSE (m)
(%)
Natural pine, reference Cultivated coastal pine Natural coastal pine Natural coastal spruce
1.431 1.289 1.074 1.5123
1.022 0.939 0.9894 0.9152
0.02053 0.03735 0.04040 003127
1.1212 0.9105 0.9619 1.8102
1.070 1.094 1.119 1.120
0.42 0.28 0.28 1.59
2.2 1.2 1.5 7.9
Table 6 Correlation coefficients between Z ratios for coastal trees and some other tree and site characteristics. The Z ratios were H100 /H30 for pine and H120 /H60 for spruce
Years to breast height Biological age Leached horizon thicknessa Stoninessb Altitude Temperature sum Lichen coverage Humus layer thickness Swamp moss coverage a b
Pine
Spruce
Abbr.
(n46)
(n38)
in text
0.58 0.31 0.49 0.43 0.34 ÿ0.31 0.11 ÿ0.04 0.03
0.80 0.41 0.07 ÿ0.16 0.07 ÿ0.03 ± ÿ0.23 ÿ0.12
IAGE STONE T-SUM HUMUS
Podsoils. Average penetration depth with steel rod (cm).
The variable IAGE, `years to breast height', was included to describe the initial development speed of the trees. Intercept growth, i.e. the sum of 5 year height growth above 2.5 m height, is another similar variable. The increase in accuracy using these predictors is described with residual errors from equations using IAGE and ICEPT instead of Z (Table 7). Neither IAGE nor ICEPT worked as well as the variable Z, but they increased the accuracy of the prediction signi®cantly compared to a basic polymorphic function with only A and SI as predictors.
An attempt was made to separate the effects of the ecological conditions on the initial development speed with a sub-set of the spruce material were chemical soil characteristics were available. The C/N ratio of the humus layer was correlated with the variable `years to breast height' (R0.64, n27). The C/N ratio could, thus, be related to Z values as well, but the function was not as good as the one including IAGE. The residual error was 30% compared to 20% of the function above. The C/N ratio was also strongly correlated with the biological age of the trees (R0.82,
Table 7 RMSE as % of the dependent variable using Eqs. (3) and (4) with Z, IAGE or ICEPT as variables describing growth patterns. The Z ratios were H100 /H30 for pine and H120 /H60 for spruce Group of trees
Z
IAGE
ICEPT
Eq. (3)
Natural pine, reference Cultivated coastal pine Natural coastal pine Coastal spruce
2.2 1.2 1.5 7.9
3.7 3.8 5.2 17.3
5.1 3.5 3.3 ±
8.2 5.6 7.4 31.5
K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
n27) and this lead to dif®culties in interpreting all relationships between C/N ratios and other variables. 4. Discussion In this study stem analysis data was used to reconstruct the height development of trees. Some procedure was needed to interpolate actual age-related heights from the heights of crosscut sections. A method originally presented by Carmean (1972) was chosen. Dyer and Bailey (1987) compared different algorithms and stated that this algorithm was ef®cient. Fabbio et al. (1994) also concluded that Carmean's (1972) method was the most precise one if the amounts of discs per tree were relatively small. There is also another technical dif®culty using stem analysis data. Some studies have shown that there are differences between stand and tree height development (HaÈgglund, 1972, 1974). This should always be recognized, but these differences are small compared to the differences in height development noted between regions in Finland found in this study. This was especially true for pine. The coastal pines had a very distinct and different development pattern close to the western coast compared to general site curves. The curves used for comparison have been developed with material from southern Finland, but the coastal areas have hardly been represented in that data (Gustavsen, 1980; Vuokila and VaÈliaho, 1980). The height development of pines in the reference area, off the coast, provided some evidence that tree height development can be used analogously with stand dominant height development, since the new curves did not show differences, which cannot be accounted for by actual growing conditions. The special features in the height development of coastal spruce might to some extent be related to the development of single trees rather than to the development of stand dominant height as shown by HaÈgglund (1972, 1974) for spruce in Sweden. This should be studied further, but in that kind of study one needs to have both successive stand measurements over a long period as well as single tree stem analysis data from the same stands (HaÈgglund, 1972). The new height curves for the coastal area had one additional advantage compared to general index curves: they described the early development of trees. This has not been possible with older site index curves,
213
which primarily were based on stands over 30 years of age (Gustavsen, 1980; Vuokila and VaÈliaho, 1980). Therefore, they generally overestimate the height development of stands younger than this (Karlsson, 1996). The differences between growth patterns along the coast compared to the inner parts of Finland are mainly the result of different growing conditions. The high wind loads at the coast cause trees to sway. Swaying generally result in an allocation of growth to the lower parts of the stem of Scots pine, which was shown e.g. by Valinger (1990) in Sweden. He did not ®nd any reduction in height increment, but the results were from one 5-year period only. In a review of wind induced responses in trees, Telewski et al. (1990) lists 40 tree species/studies were mechanical strain had affected height and diameter of trees. In most cases a decrease in height growth had been registered for trees with an increase in diameter growth due to swaying. On the other hand, lack of water also promotes a growth pattern with reduced height and other mechanisms to reduce evapotranspiration (Waring and Schlesinger, 1985). Swaying causes root damage with fungus decay spreading through the rooting system in coastal spruce stands (Hintikka, 1972) and must affect the uptake of water as well. In this sense, the soil component is of great importance, because the dense and stony soils at the coast make a poor media for rooting with increasing susceptibility to root damage. The cool temperatures in coastal spruce stands and accumulation of organic matter have been regarded as factors causing defoliation of spruce in the coastal areas (MerilaÈ et al., 1998). The growth pattern is a result of numerous, intercorrelated ecological factors, which also vary within the coastal area. The effects of the coastal conditions seem to be different for pine than for spruce. The results from this study as well as those cited above suggest that the response of pine mainly is one of mechanistic nature, with changes in the allocation of growth. For spruce the physiological effects are stronger, with defoliation as the clearest sign of the coastal conditions. The functions calculated for spruce had very large residual errors. Obviously, the height growth patterns were too complex to be described with only SI and A as predictors. There was not just a certain pattern for high SI's and one for low SI values. Rather, very
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different patterns occurred within different site index classes. Therefore, the use of some kind of growth pattern variable was necessary in order to predict the height development accurately for coastal spruce. Only Eq. (4) using some kind of form factor produced errors small enough to enable models to be used in practical growth predictions. There were several reasons for the large variation in the coastal spruce stands. The varying growth conditions along the coast caused much of that variation. But the effects of earlier forestry practices, mainly heavy cuttings from above, have also been regarded as a major disturbance factor in boreal coniferous forests (Elfving et al., 1996). Cuttings from above would make the estimation of the potential site quality dif®cult using stand or tree data. One would get an underestimation of the potential productivity if dominant trees have been cut down previously. The immediate effect of cuttings from above would be similar to a prolonged phase of natural regeneration, as seedlings and young trees grow suppressed below older trees. Some of the trees in this study had grown for as long as 40 years before reaching breast height. Thus, different measures of early development speed must partly be regarded as measures of silvicultural intensity (methods). The possibility that the height development pattern was affected by silvicultural treatment was very small for the coastal pines as they generally were from very well tended stands. The small residual errors for pine proved that the coastal area pines formed a relatively homogenous group with similar height growth patterns. The picture of large variation in spruce height development was even more complex. The initial development speed could be explained with some ecological factors as well as management practices. There was an intermediate correlation between the time to breast height, the growth pattern and the C/N ratio of the humus layer. However, all old spruce stands had high C/N ratios in the humus layer, whereas all the young stands had low C/N ratios. This imbalance in the material made it impossible to determine whether the C/N ratio had caused a certain growth pattern, or if that growth pattern and/or the stand treatment behind it had resulted in a high C/N ratio. This can only be concluded with a material where a similar range in soil quality, e.g., C/N ratios, exists in both young and old stands. Still, the results indicated that the thick humus layer is characteristical for
relatively dry, moraine soils, where the growth pattern had a slightly pronounced stagnation over age (low Z ratio). Sorted, dense and moist soils may have a humus layer of poor quality (high C/N ratio) even if it is not that thick. The spruces on this kind of soil developed slowly in the beginning, but with an increasing height increment (high Z ratio) once the interception and transpiration caused the site to dry. There was no correlation between humus layer thickness and C/N ratio in the spruce stands studied. Actual exposure and windiness had not been measured directly in this study, but both exposure and windiness increase as one goes to lower locations which are closer to the open sea (Tammelin, 1991). Temperature sum also increases in the same direction (Ojansuu and Henttonen, 1983). Therefore, the variables `altitude' and `temperature sum' re¯ected the degree of exposure and windiness to some extent. Pines close to the sea had lower Z ratios, i.e. a height growth pattern with stronger stagnation over age, than pines further away. The variable `thickness of leached horizon' was also a variable describing location as well as soil character. In this region the podsoils start to develop and show a leached out horizon gradually over time after they have been exposed from the sea and the surface continues to rise. Sites that have clear podsoil pro®les are, therefore, located away from the coast (Starr, 1991). The lack of windiness data is both a measurement and a modeling problem. The terrain is very ¯at along the western coast of Finland, which makes it hard to apply the usual type of topography classi®cation. Windiness in a certain location depends to large degree on the height of the trees in that spot and on the height of the surrounding stands. Static measurements of exposure (e.g. topex, see Miller et al., 1987) do not seem appropriate in this kind of environment. On the other hand, some portion of increasing exposure is automatically incorporated in a model with the variable `age' since exposure usually increases with tree age in a ¯at terrain. Separating that increase in exposure from other age related factors is very dif®cult in models based on ®eld data. 5. Conclusions Coastal area pine and spruce trees have speci®c growth patterns that are different from the ones in
K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
forest stands in the inner parts of Finland. The models presented should be used instead of general site index curves to predict height development and site productivity close to the coast. Information about early development and ecological conditions can be used to make the estimates more accurate and to describe the effects of different conditions and alternative forest management on height development. The effects of ecological and management factors have not yet been explicitly separated from each other.
References Atlas of Finland, 1990. Geology (English text in Appendix 123± 126). National Board of Survey, Geographical Society of Finland, 58 pp. Cajander, A.K., 1909. Ueber waldtypen (in German only). Acta For. Fenn. 1.1, 1±175. Cajander, A.K., 1949. Forest types and their significance. Acta For. Fenn. 56, 1±71. Carmean, W.H., 1972. Site index curve for upland oaks in the Central States. For. Sci. 18, 242±250. Dixon, W.J. (Ed.), 1992. BMDP Statistical Software Manual, Vol. 1 and 2. University of California Press, Berkeley, CA, 1500 pp. Draper, N.R., Smith, H., 1981. Applied Regression Analysis, 2nd edition. Wiley, New York, 83 pp. Dyer, M.E., Bailey, R.L., 1987. A test of six methods for estimating true heights from stem analysis data. For. Sci. 33 (1), 3±13. Ek, A.R., 1971. A formula for white spruce site index curves. For. Res. Note 161, University of Wisconsin, Madison WI, 2 pp. Elfving, B., Tegnhammar, L., Tveite, B., 1996. Studies on growth trends of forests in Sweden and Norway. In: Spiecker, H., MielikaÈinen, K., KoÈhl, M., Skovsgaard, J. (Eds.). Growth Trends In European Forests. Springer, Berlin, pp. 61±70. Fabbio, G., Frattegiani, M., Manetti, M.C., 1988. Il metodo di analisi del fusto. Confroto tra cinque metodi di stima della relazione alterezza-etaÁ, Ann. Ist. Sper. Selv. XIX, 118±153. Fabbio, G., Frattegiani, M., Manetti, M.C., 1994. Height estimation in stem analysis using second differences. For. Sci. 40 (2), 329± 340. Gustavsen, H.G., 1980. Talousmetsien kasvupaikkaluokittelu valtapituuden avulla (Summary: Site index curves for conifer stands in Finland). Folia For. 45 (4), 1±31. HaÈgglund, B., 1972. Om oÈvre hoÈjdens utveckling foÈr gran i norra Sverige (Summary: site index curves for Norway spruce in northern Sweden). Department of Forest Yield Research, Royal College of Forestry, Res. Notes 21, 1±298. È vre hoÈjdens utveckling i tallbestaÊnd HaÈgglund, B., 1974. O (Summary: Site index curves for Scots pine in Sweden). Department of Forest Yield Research, Royal College of Forestry Res. Notes, 31, 1-54. HaÈgglund, B., 1981. Evaluation of forest site productivity. For. Abstr. 42 (11), 515±527.
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Hintikka, V., 1972. Wind-induced root movements in forest trees. Comm. Inst. For. Fenn. 76 (2), 1±56. Hynynen, J., 1995. Modeling tree growth for managed stands Thesis. Finn. For. Res. Inst. Res. Pap. 579, 1±59. Ilvessalo, Y., 1920a. Tutkimuksia metsaÈtyyppien taksatoorisesta merkityksestaÈ (Studies of the mensurational significance of forest site types. In Finnish with German summary). Acta For. Fenn. 15, 1±157. Ilvessalo, Y., 1920b. kuusi- ja koivumetsille. (Growth and yield tables for pine, spruce and birch stands in the southern part of Finland. In Finnish with German summary). Acta For. Fenn. 15, 1±94. Karlsson, K., 1996. Kasvupaikkojen puuntuotoskyvyn ja puuston kasvun alueellinen vaihtelu Pohjanmaan rannikolta sisaÈmaahan (In Finnish only: Regional variation in site quality and forest increment from the western coast to the inner parts of Finland). Folia For. 2, 113±132. Koivisto, P., 1970. Regionality of forest growth in Finland. Comm. Inst. For. Fenn. 71 (2), 1±76. MerilaÈ, P., Lindgren, M., Raitio, H., Salemaa, M., 1998. Relationships between crown condition, tree nutrition and soil porperties in the coastal Picea abies forests (western Finland). Scand. J. For. Res. 13 (4), 414±421. Miller, K.F., Quine, C.P., Hunt, J., 1987. The assessment of wind exposure for forestry in upland Britain. Forestry 60 (2), 179±192. Monserud, R.A., 1984. Height growth and site index curves for inland Douglas-fir based on stem analysis data and forest habitat type. For. Sci. 30, 943±965. Newberry, J.D., 1991. A note on Carmean's estimate of height from stem analysis data. For. Sci. 37 (1), 368±369. NyyssoÈnen, A., MielikaÈinen, K., 1978. MetsikoÈn kasvun arviointi (Summary: Estimation of stand increment). Acta For. Fenn. 163, 1±40. Ojansuu, R., Henttonen, H., 1983. laÈmpoÈsumman ja sademaÈaÈraÈn johtaminen Ilmatieteen laitoksen mittaustiedoista (Summary: Estimation of the local values of monthly mean temperature). Silva Fenn. 17.2, 143±160. Ojansuu, R., Hynynen, J., Koivunen, J., Luoma, P., 1991. Luonnonprosessit metsaÈlaskelmassa (Mela) ± MetsaÈ 200versio. (In Finnish only: Natural processes in forest management calculations). Finn. For. Res. Inst. Res. Pap., 385, 1±59. Perttunen, M., 1987. Fennoscandian land uplift. In: Proceedings Of A Symposium At TvaÈrminne, 10±11 April, 1986. Geological Survey of Finland, Spec. Pap. 2, 1±61. Richards, F.J., 1959. A flexible growth function for empirical use. J. Exp. Bot. 10, 290±300. Starr, M.R., 1991. Soil formation and fertility along a 5000 year chronosequence. In: Pulkkinen, E. (Ed.) Environmental Geochemistry In Northern Europe. Geological Survey of Finland, Special Paper 9, pp. 99±104. Telewski, F.W., 1990. Wind-induced physiological and developmental responses in trees. In: Coutts, M.P., Grace, J. (Eds.), Wind and Trees. Cambrigde University Press, Cambridge, MA, pp 237±263. Varmola, M., 1996. Nuorten viljelymaÈnnikoÈiden tuotos ja laatu, Dissertation. Abstract: Yield and quality of young Scots pine cultivations. Finn. For. Res. Inst. Res. Pap. 585, 1±70.
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Valinger, E., 1990. Inverkan av gallring, goÈdsling, vind och traÈdstorlek paÊ tallars utveckling (Summary: Influence of thinning, fertilization, wind and tree size on the development of Scots pine trees), Dissertation. Swedish University of Agricultural Sciences, Department of Silviculture, Umea, Sweden. 27 pp. Viro, P.J., 1952. Kivisyyden maÈaÈrittaÈmisestaÈ (Summary: On the determination of stoniness). Comm. Inst. For. Fenn. 39 (4), 1±54. Vuokila, Y., VaÈliaho, H., 1980. Viljeltyjen havumetsikoÈiden kasvatusmallit (Summary: Growth and yield models for conifer cultures in Finland). Comm. Inst. For. Fenn. 99 (2), 1±271.
Wang, G.G., Marshall, P.L., Klinka, K., 1994. Height growth pattern of white spruce in relation to site quality. For. Ecol. Manage. 68, 137±147. Waring, R.H., Schlesinger, W.H., 1985. Forest Ecosystems, Concepts And Managment. Academic Press, New York, 340 pp. Weisberg, S., 1985. Applied Linear Regression, 2nd edition. Wiley, NewYork, 324 pp. Zeide, B., 1978. Standardization of growth curves. J. For. 76, 289± 292.
Height growth patterns of Scots pine and Norway spruce in the coastal areas of western Finland Kristian Karlsson* The Finnish Forest Research Institute, Kannus Research Station, Box 44, FIN-69101 Kannus, Finland
Abstract Stem analysis data of 46 Scots pine (Pinus sylvestris L.) and 38 Norway spruce (Picea abies (L.) Karst.) trees was used to construct height curves for naturally regenerated and cultivated Scots pine and for naturally regenerated Norway spruce from the coastal areas of western Finland. The curves were compared with each other, with models for 28 naturally regenerated pine trees off the coast and with general site index curves for pine and spruce in southern Finland. The height growth pattern for coastal pine exhibited a strong stagnation over age compared to general site indexes. Spruce height development was dominated by a slow early development followed by an increase in height increment compared to general index curves. There was a large variation in the height growth patterns of coastal spruce and a growth pattern variable was needed in the functions in order to make reliable predictions. Even simple models provided relatively good predictions for coastal pine. It was argued that strong wind, temperature and moisture regimes caused these differences between trees at the western coast and in the inner parts of Finland. The soil provides poor rooting conditions at the coast and this increases trees' susceptibility to the climatic impact. The variation in height growth patterns within the coastal area could partly be explained with location in relation to the sea and stoniness for pine, and humus layer thickness for spruce. The number of years trees had grown to breast height was used as a predictor, which explained the growth patterns very well. This variable did not describe causal relationships, since it depends both on the original status of site and of management intensity. It could be used to improve predictions when such data can is available. The early development speed was correlated with the C/N ratio of the humus in spruce stands. This indicated that the growth patterns of coastal spruce may change along an ecological gradient from dry, stony moraines with thick humus, to moist, dense sorted soils with poor quality humus. The use of soil variables in predicting height development is dif®cult, since they usually are time dependent and affected by stand characteristics and management. # 2000 Elsevier Science B.V. All rights reserved. Keywords: Pinus sylvestris; Picea abies; Height curve; Site index; Ecological site quality; Coast; Wind; Land uplift
1. Introduction The height development of dominant trees has been one of the most used measures of site quality in forest stands (HaÈgglund, 1981). The height of dominant trees at the age of 100 years (H100) has commonly been used in Scandinavia, whereas 50 years (H50) or sometimes * Tel.: 358-6-8743-213; fax: 358-6-8743-201. E-mail address: [email protected] (K. Karlsson)
only 30 years (H30) has been used in North America. Since this kind of site classi®cation is dependent on the forest stand, other methods have been developed for estimations of unforested land, disturbed ecosystems and young plantations. In many of these cases, the functions developed have predicted site index for a certain tree species rather than any absolute value of the site quality. Thus, the height development pattern of these site index functions has had a central role in determining the site quality even though ecological
0378-1127/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 1 1 2 7 ( 0 0 ) 0 0 3 1 1 - X
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information has been used as predictors. Site index curves can be used in young plantations, but the consequences of even small measurement errors would be very large and young trees do not re¯ect actual site quality as well older ones (Varmola, 1996). In Finland site quality estimations have traditionally been based on site types as de®ned by Cajander (1909, 1949) according to the composition of the ground vegetation. This classi®cation was provided with growth and yield data at an early stage (Ilvessalo, 1920a, b), but there was still an obvious need to develop site index curves. Vuokila and VaÈliaho (1980) constructed such functions for cultivated pine and spruce stands and Gustavsen (1980) did the same for naturally regenerated coniferous stands. These have by far been the most used site index curves in practical site classi®cation and forest mensuration in Finland. During the last decade, growth modeling has moved from stand models towards models based on single tree data, but the height development of single, dominant trees has still been used calculating site indexes in the same way as for stand dominant height earlier (Ojansuu et al., 1991). The importance of site index in growth models has even increased (Hynynen, 1995), obviously because they re¯ect the ecological site quality very well. The regional differences in site productivity were partly described by the site types of Cajander (1909), since the land was divided into vegetation zones. Each zone had different site types and subsequently different ®gures of site productivity. This division was a rough one as the areas were very large. Site indexes have been used to describe the regionality of site quality and forest productivity more accurately (Koivisto, 1970; Karlsson, 1996), but these studies have assumed that the height growth patterns remain the same within large areas such as southern and northern Finland. The result of different growth patterns would be that two forest stands having the same height at an early age would end up at different heights later as a result of the growing conditions in the area. This would then result in a serious bias to the estimates of site index based on age and height alone. The problem could be avoided by constructing new models for regions, different ecosites etc. However, the steadily increasing number of area restricted or site speci®c models tells us that there is a need to describe the factors causing
differences in growth patterns more accurately (Wang et al., 1994). The growing conditions are different at the western coast compared to the inner parts of Finland and several factors could cause different growth patterns compared to other regions. The soil has been affected by the uplift (isostatic rebound) from beneath the sea (Perttunen, 1987). Therefore, the surface soil is washed out and very stony and the dense moraine is located close to the surface (Atlas of Finland, 1990). The climate is affected by the water masses in the surroundings. Temperatures remain cooler at the beginning of the vegetation period compared to the inner parts of Finland and the coastal area also receives more radiation (more sunny days) and less precipitation (Heino and Hellsten, 1983). The winds are relatively strong at the coast. Mean wind speed is about 6±7 m sÿ1 at the outer range of the archipelago and goes down to 3±4 m sÿ1 at the coast (Heino and Hellsten, 1983; Tammelin, 1991). The Finnish wind atlas shows that a zone of strong winds extends up to about 30 km from the coast line in western Finland (Tammelin, 1991). The terrain is ¯at in that area, but coastal regions with steeper terrain have a similar windy zone extending up to 10 km from the coastline. The coastal regions of Finland are, thus, as windy as the coastal zones along the North sea, i.e. the southern part of the west coast in Denmark and the east coast in England (Tammelin, 1991). NyyssoÈnen and MielikaÈinen (1978) and Karlsson (1996) have shown that the increment values of forest stands close to the coast are considerably lower than the ones given by yield functions developed for southern Finland. The condition or health of coastal spruce stands, especially old ones, has also been described as poor compared to other regions in Finland (MerilaÈ et al., 1998). This could simply be the result of different, average productivity levels. A marked stagnation at old age, which has been suggested for the coastal area forests (Karlsson, 1996), would again be a sign of different growth patterns. Little effort has been taken neither to adjust the common site index curves for differing conditions nor to describe the effects of varying growth conditions on the height development in Finland. The objectives of this study were to develop tree species speci®c height curves based on stem analysis of trees close to the coast, to compare these curves with curves used for
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site index estimation generally and to analyze ecological factors causing the differences found in the growth patterns. Intercept growth and other characteristics of early development were also used to predict different growth patterns. 2. Material and methods The area studied was located between 618 and 648N along the Finnish coast of the Gulf of Bothnia, which separates Finland from Sweden. The material was obtained from different sources. Fifteen spruce stands had been chosen from a network of survey plots established for studying factors affecting forest health in the coastal area. These spruce stands were naturally regenerated. Nineteen pine stands had been located in the oldest known, cultivated pine stands close to the coast. Furthermore, a sample of naturally regenerated pine (eight) and spruce (seven) stands between 80 and 120 years of age had been randomly chosen from the management plan for the forests owned by the Finnish Research Institute along the coast. All coastal stands were located closer than 30 km from the coastline at an altitude of 2±60 m above sea level. Within this research area climatic conditions are very closely related to altitude. An additional group consisting of 14 pine stands on sandy, sorted soils 40±60 km from the coast and 80±120 m above sea level were included in the study. These pine stands were naturally regenerated and the material provided an extension of the material from coast towards the inland serving as a reference material. They were also initially examined as part of a health study. The major differences between groups of forest stands were tree species, location and regeneration regime. The analysis was mainly performed using these groups, with the following descriptions: (1) natural pine, reference; (2) cultivated coastal pine; (3) natural coastal pine and (4) coastal spruce. Homogeneity within groups and possibilities to combine groups were examined using graphics and parameters of the functions calculated. The measurements were exactly the same on all plots. The two largest trees according to diameter at breast height were cut down on each plot. Total height was measured on the felled trees and discs were taken from the relative heights of 2.5, 7.5, 15, 30, 45, 60, 75, 85, 95% and/or at the absolute heights of 1.3 and 6 m.
207
Site data included ocular estimations (classi®cation) of topographical location, site types (Cajander, 1909), stoniness, paludi®cation and soil texture and mean particle size. Measurements also included thickness of humus and leached out horizons, stoniness according to Viro's (Viro, 1952) method (the average penetration depth of a metal rod into the mineral soil), the average coverage of lichens (mainly Cladonia sp.) and swamp mosses (Spaghnum sp. and Polytrichum sp.) and the area of large rocks or exposed bedrock on the survey plot. A very stony site had a penetration value with the steel rod of 10 cm, whereas a stone free site had a value of 40 cm. The humus thickness varied between 10 and 90 mm, when a soil auger with the diameter 30 mm was used. The data from the health surveys also included some chemical characteristics for the humus layer. The humus samples were compiled from 28 systematically collected subsamples on each plot. Total N and C were determined with a LECO TGA-500 analyzer and organic matter as ignition loss (4858C). Temperature sum was calculated for each plot with a model (Ojansuu and Henttonen, 1983). No other climatic variables were used, because of the close correlation with temperature sum and altitude. Ages for each crosscut section were obtained as all discs were measured for annual radial increment with a stereo microscope measuring system. Annual height growth values were interpolated from crosscut section data using an algorithm by Carmean (1972). There were 9±11 discs per tree in this study resulting in a sampling frequency of about 2 m at an average. The equation for Carmean's algorithm used in this study was from Fabbio et al. (1994) and included modi®cations by Fabbio et al. (1988) and by Newberry (1991). The interpolation provided us with estimates of the actual height at each crosscut age, since the crosscut height in itself often does not include the full measure of the last height growth. A height curve was calculated for each tree using height and age in a model originally presented by Richards (1959): H b1 f1 ÿ exp ÿb2 Agb3
(1)
where H is the tree height (m), A the biological age, exp is the exponential of the base of the natural logarithm and bx are parameters to be estimated for
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K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
each tree. The standard errors of the estimates were very small. The models were used to calculate H at the age of 150, 120, 100, 60 and 30 years, respectively. The interpolated values of H at each crosscut section age were combined with values for H at the age of 100 years. This value for H at the age of 100 years was analogous to site index and will in the following be denoted as SI. The intercept growth (ICEPT), the sum of height growth for 5 years above 2.5 m above ground, was obtained from interpolated yearly height growths and combined with other data in the same way as SI. The height growth pattern was described with the ratio between two points on a height curve (Z), assuming that the form of a height curve can be accurately expressed with only two points as pointed out by Zeide (1978). In order to test the efficiency of different Z ratios, all height curves were described with several Z ratios: H100 /H30, H60 /H30, H120 /H60 and H150 /H100. The number of height±age pairs was the same as the number of crosscuts on the stem analysis trees. Yearly or decadal data were not used, since that approach would have given more weight on slowly growing than on fast growing trees. When calculating height curves observations over 100 years of age were excluded for the same reason, as the old trees at an average had been growing more slowly than the young ones. All single tree height curves were compared to average curves for the group and disturbed trees were excluded. Excluded cases had height curves that were sharply crossed over the group curve or had an asymptotic value of SI (parameter b1) higher than logically could be expected (> 40 m). Five spruce trees and eight pines were excluded. The ®nal data consisted of 1159 observations of height and age from 112 trees in 58 forest stands (Table 1). Height curves were calculated for all the four groups of trees separately. In order to develop ana-
morphic height curves we used the model H b1 SIf1 ÿ exp ÿb2 Agb3
(2)
where H, SI, A and exp are as previously defined and bx parameters to be estimated. With two expressions of SI we could calculate polymorphic height curves according to this model used by, e.g., Ek (1971) H b1 SIb2 f1 ÿ exp ÿb3 Agb4 SI
b5
(3)
Many non-linear functions can be modified into linear ones through transformations (Weisberg, 1985), but these equations were genuine non-linear functions (Draper and Smith, 1981). Therefore, the parameters were calculated with program 3R from the BMDP statistical package, which uses the Gauss±Newton algorithm to calculate least square estimates for non-linear functions (Dixon, 1992). Initial values were chosen by trial-and-error and the results were evaluated with plots of residuals and predicted versus observed values. Eq. (1) was used only to calculate SI values for single trees. Using these individual SI values in Eqs. (3) and (4) provided us with equations describing the height development for the whole range of trees included. The graphical output of Eq. (1) is a single curve, whereas Eqs. (3) and (4) should be visualized with a set of curves. For graphical examinations sets of curves were drawn according to the median values and 25 and 75% quartile values of the SI values in each of the four groups of trees. In other studies Z ratios have been used to stratify height±age data and then calculate separate height curves for each group (Wang et al., 1994). Monserud (1984) used dummy-variables for three identi®ed groups of speci®c height pattern (habitats) and presented them directly into the height equations. A similar approach was used here, when variables such
Table 1 Tree data (minimum±maximum) at the time of measurement. SI's calculated with Eq. (1) for each tree separately Group of trees
n
Age (a)
Height (m)
SI (m)
Natural pine, reference Cultivated coastal pine Natural coastal pine Natural coastal spruce
28 36 10 38
50±137 60±90 100±150 36±147
13±22 15±25 14±26 12±27
12±26 18±28 11±25 13±30
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as Z, ICEPT and IAGE (biological age Ð age at breast height) were incorporated as a continuos variable in the polymorphic models instead of SI: H b1 SIb2 f1 ÿ exp ÿb3 Agb4 Z
b5
(4)
The usefulness of Z variables and other similar ones depend entirely on the possibility to measure or predict those variables without stem analysis data. The relationship between Z and site quality variables was studied by means of correlation analysis. The common sheet calculation program, EXCEL 5.0, provided simple regressions, correlation coefficients as well as all graphical output of data and results. 3. Results The height development of coastal pines could be rather well described with an anamorphic function (Eq. (2), Table 2). The residual errors were only slightly smaller using a polymorphic function (Eq. (3), Table 3). The height development in the reference area studied was different. The height curves of the pines there had a polymorphic character because the use of Eq. (4) resulted in smaller residual errors compared to Eq. (3). This indicated that the height growth pattern in the reference area was closer to the one in standard site index curves, since they have a strong polymorphic character as well. The graphical examinations showed that the growth pattern was a steeper one in the reference area compared to the general site index curves (Fig. 1). This was especially clear after the age of 40 years. The coastal pines had a completely different growth pattern than both the standard site index curves and pines in the reference area. There was a marked stagnation over age in the height development of the coastal pines compared to the index curves usually
209
applied. The curves for natural and cultivated pine could be regarded as complementary since the curves mainly were situated on different productivity levels: 14±21 m for natural compared to 21±25 m for cultivated (Fig. 1). The differences in growth patterns between these groups were negligible, with only a slightly stronger stagnation over age for the naturally regenerated trees compared to the cultivated trees. The residual errors were very small for both groups of pines from the coastal area. The SI range was narrow in these groups, but a function calculated for both cultivated and natural pine had a RMSE of only 6% despite a much broader range in SI. The growth patterns were described with Z ratios calculated for each SI class (Table 4). The marked stagnation over age in the height development for coastal pine resulted in Z ratios of 2.1±2.5, whereas the reference area curves had ratios of 2.9±4.8. These ®gures show that the reference area was a slightly exceptional one because of the stone free, sandy soils. The best sites in the reference area had Z ratios close to the general site index curves. The coastal area spruce did not form a homogenous group. The residual error was over 30% using the anamorphic function to predict tree heights (Eq. (2), Table 2). The predictions did not improve much when a polymorphic model was used (Eq. (3), Table 3). The great variation among the spruce stands could not be accounted for by easily recognized abnormal and excludable trees or by a division into a few subclasses like soil types, etc. Using the ratio of H120/H60 as a variable Z in Eq. (4) reduced the residual error to 7.9%. The same kind of function was better predicting height development for pine as well (Table 5). The ratio of H100/H30 was the best growth pattern variable for all pine trees. For spruce the comparison with general site index curves was based on Eq. (4) using Z as a variable
Table 2 Parameters and residual errors for Eq. (2) Group of trees
b1
b2
b3
RMSE (m)
(%)
Natural pine, reference Cultivated coastal pine Natural coastal pine Natural coastal spruce
1.498 1.063 1.051 1.719
0.01471 0.03617 0.03625 0.01206
1.562 2.135 2.175 1.592
2.38 1.29 1.66 6.50
12.6 5.6 9.0 32.3
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Table 3 Parameters and residual errors for Eq. (3) Group of trees
b1
b2
b3
b4
b5
RMSE (m)
(%)
Natural pine, reference Cultivated coastal pine Natural coastal pine Natural coastal spruce
3.921 1.479 1.036 0.2002
0.7282 0.8942 0.9992 1.7764
0.01637 0.03649 0.03882 0.00905
24.31 2.758 10.88 0.2471
ÿ0.8910 ÿ0.07895 ÿ0.5191 0.5817
1.55 1.29 1.36 6.34
8.2 5.6 7.4 31.5
(Fig. 1). The curves were calculated with average values for Z, but the effect of the varying growth patterns is illustrated by inserting a curve calculated with a low value for Z (Fig. 1). When the initial development had been rapid, coastal spruce trees had a development pattern with a stronger stagnation over age than spruce stands in southern Finland generally. The dominating pattern was, however, one with slow initial development followed by an increase in height development that was stronger than in the general site index curves (higher Z ratio). The possibilities to improve the accuracy of tree height development predictions were greatly increased with the use of a variable describing the growth pattern. A ratio like H120/H60 is usually not available when estimating heights for a stand. The growth pattern must be estimated using other variables. Correlation analysis showed a relationship between several soil variables and Z ratios for coastal pines (Table 6). A regression was calculated for the best (smallest RMSE) combination of site and tree variables: Z
H100 17:39 0:076 IAGE 0:018 H30 STONE ÿ 0:014 T-SUM
2
R 0:65; RMSE 10%;
(5)
n 46
All variables included had t-values above four and they were not intercorrelated. According to the function, a stony site had a growth pattern with stronger stagnation over age than a stone free site. Temperature sum worked better than altitude in this combination, but they both described the location in relation to the sea.The Z ratios for spruce were not as clearly dependent on location and soil quality as they were for pine (Table 6). When the best combinations of variables were studied, humus layer thickness still appeared to explain some of the variation in spruce Z ratios. An additional dummy variable receiving the value 1 when soils had been classified as moraines and 0 for sorted soils was included in the function: Z
H120 1:41 0:082 IAGE 0:013 H60 HUMUS ÿ 0:43 DUMMY
R2 0:77; RMSE 20%;
(6)
n 38
All variables had t-values over three. They were not significantly correlated to each other. Including the variables HUMUS and DUMMY reduced the residual error from 26±20%. A thick humus layer had resulted in a growth pattern with stronger stagnation over age than a thin humus layer.
Table 4 The Z ratios for SI classes and analogous height-age classes for coastal pines. The Z ratios were H100 /H30. SI curves for southern Finland according to Gustavsen (1980) Group of trees
SI/Height-age class 15
18
21
24
27
SI-curve, pine Natural pine, reference Cultivated coastal pine Natural coastal pine
2.9 4.8 ± 2.5
2.7 3.9 2.3 2.3
2.5 3.3 2.3 2.2
2.3 2.9 2.3 2.1
2.2 ± 2.3 ±
K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
211
Fig. 1. Height-age curves for coastal pine and reference area calculated with Eq. (3) and for coastal spruce with Eq. (4) compared with SI curves for southern Finland (Gustavsen, 1980; Vuokila and VaÈliaho, 1980). The curves were calculated for median and quartile SI values in each group. Spruce curves with average Z ratio (1.9) and one with the low quartile (1.4).
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K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
Table 5 Parameters and residual errors for Eq. (4) with ZH100 /H30 for all pine stands and ZH120 /H60 for spruce Group of trees
b1
b2
b3
b4
b5
RMSE (m)
(%)
Natural pine, reference Cultivated coastal pine Natural coastal pine Natural coastal spruce
1.431 1.289 1.074 1.5123
1.022 0.939 0.9894 0.9152
0.02053 0.03735 0.04040 003127
1.1212 0.9105 0.9619 1.8102
1.070 1.094 1.119 1.120
0.42 0.28 0.28 1.59
2.2 1.2 1.5 7.9
Table 6 Correlation coefficients between Z ratios for coastal trees and some other tree and site characteristics. The Z ratios were H100 /H30 for pine and H120 /H60 for spruce
Years to breast height Biological age Leached horizon thicknessa Stoninessb Altitude Temperature sum Lichen coverage Humus layer thickness Swamp moss coverage a b
Pine
Spruce
Abbr.
(n46)
(n38)
in text
0.58 0.31 0.49 0.43 0.34 ÿ0.31 0.11 ÿ0.04 0.03
0.80 0.41 0.07 ÿ0.16 0.07 ÿ0.03 ± ÿ0.23 ÿ0.12
IAGE STONE T-SUM HUMUS
Podsoils. Average penetration depth with steel rod (cm).
The variable IAGE, `years to breast height', was included to describe the initial development speed of the trees. Intercept growth, i.e. the sum of 5 year height growth above 2.5 m height, is another similar variable. The increase in accuracy using these predictors is described with residual errors from equations using IAGE and ICEPT instead of Z (Table 7). Neither IAGE nor ICEPT worked as well as the variable Z, but they increased the accuracy of the prediction signi®cantly compared to a basic polymorphic function with only A and SI as predictors.
An attempt was made to separate the effects of the ecological conditions on the initial development speed with a sub-set of the spruce material were chemical soil characteristics were available. The C/N ratio of the humus layer was correlated with the variable `years to breast height' (R0.64, n27). The C/N ratio could, thus, be related to Z values as well, but the function was not as good as the one including IAGE. The residual error was 30% compared to 20% of the function above. The C/N ratio was also strongly correlated with the biological age of the trees (R0.82,
Table 7 RMSE as % of the dependent variable using Eqs. (3) and (4) with Z, IAGE or ICEPT as variables describing growth patterns. The Z ratios were H100 /H30 for pine and H120 /H60 for spruce Group of trees
Z
IAGE
ICEPT
Eq. (3)
Natural pine, reference Cultivated coastal pine Natural coastal pine Coastal spruce
2.2 1.2 1.5 7.9
3.7 3.8 5.2 17.3
5.1 3.5 3.3 ±
8.2 5.6 7.4 31.5
K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
n27) and this lead to dif®culties in interpreting all relationships between C/N ratios and other variables. 4. Discussion In this study stem analysis data was used to reconstruct the height development of trees. Some procedure was needed to interpolate actual age-related heights from the heights of crosscut sections. A method originally presented by Carmean (1972) was chosen. Dyer and Bailey (1987) compared different algorithms and stated that this algorithm was ef®cient. Fabbio et al. (1994) also concluded that Carmean's (1972) method was the most precise one if the amounts of discs per tree were relatively small. There is also another technical dif®culty using stem analysis data. Some studies have shown that there are differences between stand and tree height development (HaÈgglund, 1972, 1974). This should always be recognized, but these differences are small compared to the differences in height development noted between regions in Finland found in this study. This was especially true for pine. The coastal pines had a very distinct and different development pattern close to the western coast compared to general site curves. The curves used for comparison have been developed with material from southern Finland, but the coastal areas have hardly been represented in that data (Gustavsen, 1980; Vuokila and VaÈliaho, 1980). The height development of pines in the reference area, off the coast, provided some evidence that tree height development can be used analogously with stand dominant height development, since the new curves did not show differences, which cannot be accounted for by actual growing conditions. The special features in the height development of coastal spruce might to some extent be related to the development of single trees rather than to the development of stand dominant height as shown by HaÈgglund (1972, 1974) for spruce in Sweden. This should be studied further, but in that kind of study one needs to have both successive stand measurements over a long period as well as single tree stem analysis data from the same stands (HaÈgglund, 1972). The new height curves for the coastal area had one additional advantage compared to general index curves: they described the early development of trees. This has not been possible with older site index curves,
213
which primarily were based on stands over 30 years of age (Gustavsen, 1980; Vuokila and VaÈliaho, 1980). Therefore, they generally overestimate the height development of stands younger than this (Karlsson, 1996). The differences between growth patterns along the coast compared to the inner parts of Finland are mainly the result of different growing conditions. The high wind loads at the coast cause trees to sway. Swaying generally result in an allocation of growth to the lower parts of the stem of Scots pine, which was shown e.g. by Valinger (1990) in Sweden. He did not ®nd any reduction in height increment, but the results were from one 5-year period only. In a review of wind induced responses in trees, Telewski et al. (1990) lists 40 tree species/studies were mechanical strain had affected height and diameter of trees. In most cases a decrease in height growth had been registered for trees with an increase in diameter growth due to swaying. On the other hand, lack of water also promotes a growth pattern with reduced height and other mechanisms to reduce evapotranspiration (Waring and Schlesinger, 1985). Swaying causes root damage with fungus decay spreading through the rooting system in coastal spruce stands (Hintikka, 1972) and must affect the uptake of water as well. In this sense, the soil component is of great importance, because the dense and stony soils at the coast make a poor media for rooting with increasing susceptibility to root damage. The cool temperatures in coastal spruce stands and accumulation of organic matter have been regarded as factors causing defoliation of spruce in the coastal areas (MerilaÈ et al., 1998). The growth pattern is a result of numerous, intercorrelated ecological factors, which also vary within the coastal area. The effects of the coastal conditions seem to be different for pine than for spruce. The results from this study as well as those cited above suggest that the response of pine mainly is one of mechanistic nature, with changes in the allocation of growth. For spruce the physiological effects are stronger, with defoliation as the clearest sign of the coastal conditions. The functions calculated for spruce had very large residual errors. Obviously, the height growth patterns were too complex to be described with only SI and A as predictors. There was not just a certain pattern for high SI's and one for low SI values. Rather, very
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K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
different patterns occurred within different site index classes. Therefore, the use of some kind of growth pattern variable was necessary in order to predict the height development accurately for coastal spruce. Only Eq. (4) using some kind of form factor produced errors small enough to enable models to be used in practical growth predictions. There were several reasons for the large variation in the coastal spruce stands. The varying growth conditions along the coast caused much of that variation. But the effects of earlier forestry practices, mainly heavy cuttings from above, have also been regarded as a major disturbance factor in boreal coniferous forests (Elfving et al., 1996). Cuttings from above would make the estimation of the potential site quality dif®cult using stand or tree data. One would get an underestimation of the potential productivity if dominant trees have been cut down previously. The immediate effect of cuttings from above would be similar to a prolonged phase of natural regeneration, as seedlings and young trees grow suppressed below older trees. Some of the trees in this study had grown for as long as 40 years before reaching breast height. Thus, different measures of early development speed must partly be regarded as measures of silvicultural intensity (methods). The possibility that the height development pattern was affected by silvicultural treatment was very small for the coastal pines as they generally were from very well tended stands. The small residual errors for pine proved that the coastal area pines formed a relatively homogenous group with similar height growth patterns. The picture of large variation in spruce height development was even more complex. The initial development speed could be explained with some ecological factors as well as management practices. There was an intermediate correlation between the time to breast height, the growth pattern and the C/N ratio of the humus layer. However, all old spruce stands had high C/N ratios in the humus layer, whereas all the young stands had low C/N ratios. This imbalance in the material made it impossible to determine whether the C/N ratio had caused a certain growth pattern, or if that growth pattern and/or the stand treatment behind it had resulted in a high C/N ratio. This can only be concluded with a material where a similar range in soil quality, e.g., C/N ratios, exists in both young and old stands. Still, the results indicated that the thick humus layer is characteristical for
relatively dry, moraine soils, where the growth pattern had a slightly pronounced stagnation over age (low Z ratio). Sorted, dense and moist soils may have a humus layer of poor quality (high C/N ratio) even if it is not that thick. The spruces on this kind of soil developed slowly in the beginning, but with an increasing height increment (high Z ratio) once the interception and transpiration caused the site to dry. There was no correlation between humus layer thickness and C/N ratio in the spruce stands studied. Actual exposure and windiness had not been measured directly in this study, but both exposure and windiness increase as one goes to lower locations which are closer to the open sea (Tammelin, 1991). Temperature sum also increases in the same direction (Ojansuu and Henttonen, 1983). Therefore, the variables `altitude' and `temperature sum' re¯ected the degree of exposure and windiness to some extent. Pines close to the sea had lower Z ratios, i.e. a height growth pattern with stronger stagnation over age, than pines further away. The variable `thickness of leached horizon' was also a variable describing location as well as soil character. In this region the podsoils start to develop and show a leached out horizon gradually over time after they have been exposed from the sea and the surface continues to rise. Sites that have clear podsoil pro®les are, therefore, located away from the coast (Starr, 1991). The lack of windiness data is both a measurement and a modeling problem. The terrain is very ¯at along the western coast of Finland, which makes it hard to apply the usual type of topography classi®cation. Windiness in a certain location depends to large degree on the height of the trees in that spot and on the height of the surrounding stands. Static measurements of exposure (e.g. topex, see Miller et al., 1987) do not seem appropriate in this kind of environment. On the other hand, some portion of increasing exposure is automatically incorporated in a model with the variable `age' since exposure usually increases with tree age in a ¯at terrain. Separating that increase in exposure from other age related factors is very dif®cult in models based on ®eld data. 5. Conclusions Coastal area pine and spruce trees have speci®c growth patterns that are different from the ones in
K. Karlsson / Forest Ecology and Management 135 (2000) 205±216
forest stands in the inner parts of Finland. The models presented should be used instead of general site index curves to predict height development and site productivity close to the coast. Information about early development and ecological conditions can be used to make the estimates more accurate and to describe the effects of different conditions and alternative forest management on height development. The effects of ecological and management factors have not yet been explicitly separated from each other.
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