Amaro A., Reed D., Soares P. (editors) Modelling Forest Systems

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03Amaro Forests - Chap 02 25/7/03 11:04 am Page 16

16 R.A. Monserud and S. Huang

Table 2.1. Summary statistics for the lodgepole pine stem analysis data.

No. of

HT (m)

SI (m)

Subregion

trees Mean Min. Max. SD Mean Min. Max. SD

Central Mixedwood 20 20.42 8.92 27.71 5.36 17.09 13.71 22.77 3.10

Dry Mixedwood 17 17.18 5.50 27.15 8.92 18.02 14.66 21.03 1.98

Wetland Mixedwood 14 15.33 11.28 20.78 2.74 11.49 8.77 16.21 2.42

Peace River Lowlands 3 21.53 19.90 23.08 1.59 14.64 12.72 16.75 2.02

Boreal Highlands 3 16.55 14.21 18.76 2.28 14.50 12.05 16.50 2.26

Alpine 2 17.75 17.70 17.80 0.07 7.74 7.30 8.18 0.63

Subalpine 305 15.65 8.45 25.00 3.29 11.38 4.30 18.29 3.05

Montane 47 15.01 9.90 18.41 1.71 13.74 8.14 19.12 2.90

Lower Foothills 1327 18.74 5.99 31.78 4.41 14.07 5.41 24.41 3.43

Upper Foothills 883 21.46 6.10 36.80 4.47 15.90 7.90 26.46 3.13

Central Parkland 3 15.93 14.87 17.02 1.08 12.25 10.56 13.47 1.51

Grand total 2624 19.21 5.50 36.80 4.73 14.39 4.30 26.46 3.56

Site index (m)

0 20 40 60 80 100 120 140 160 180 200 220

Breast height age (years)

SI, site index, which refers to tree height at 50 years breast height age.

Methods

tude, latitude, elevation and SI for each of the stem analysis stands. Elevation was

SI at each sample location (n

Fig. 2.3. Consistency of site index estimates vs. age. Each line represents repeated site index estimates for

one stem analysis tree (this graph was based on 10% of the stem analysis trees).

Subregions of Alberta are deﬁned in Alberta Environmental Protection (1994).

HT, total tree height (m).

Our goal was to produce a map of SI isoclines within and bordering the natural

range of lodgepole pine in Alberta. We began by assembling a database of longi-

obtained from a digital elevation model (DEM) using a 100 m grid for the province.

= 995) was estimated directly using felled-tree stem

analysis data (see previous paragraph). We then used a thin-plate smoothing spline

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17 Mapping Lodgepole Pine Site Index in Alberta

program (ANUSPLIN; see Hutchinson, 2002) to ﬁt this SI surface as a function of the

three topographic variables: longitude, latitude and elevation. Finally, we combined

this ﬁtted surface with a province-wide DEM to predict isoclines of SI for the entire

range of lodgepole pine in Alberta. Maps were produced using the ArcView geo-

graphical information system.

ANUSPLIN

The aim of the ANUSPLIN package (acronym: Australian National University

SPLINe) is to provide a facility for transparent analysis and interpolation of noisy

multivariate data using thin-plate smoothing splines (Hutchinson, 2002). The sur-

face-ﬁtting procedure was primarily developed for ﬁtting climate surfaces such

as temperature and precipitation. Thus, there are normally at least two indepen-

dent spline variables, longitude and latitude (in decimal degrees). A third in-

dependent variable, elevation above sea level, is normally included as a third

independent spline variable (in kilometre units). Our problem is directly akin to the

standard problem of ﬁtting a temperature surface using a network of weather

stations, except that our weather stations are actually stem analysis locations and

temperature is replaced by SI.

The original thin-plate (formerly Laplacian) smoothing spline surface-ﬁtting

technique was described by W

ahba (1979), with modiﬁcations for larger data sets

due to Hutchinson and de Hoog (1985). Thin-plate smoothing splines can be viewed

as a generalization of standard multivariate linear regression, in which the paramet-

ric model is replaced by a suitably smooth non-parametric function (Hutchinson,

2002). The degree of smoothness (or complexity) of the ﬁtted function is determined

by minimizing a measure of predictive error of the ﬁtted surface given by the gener-

alized cross-validation (Craven and Wahba, 1979; Wahba, 1983).

Wahba (1990) provides a comprehensive introduction to the technique of thin-

plate smoothing splines.

A brief overview of the basic theory and applications to

spatial interpolation of monthly mean climate is given in Hutchinson (1991). A com-

prehensive discussion of the algorithms and associated statistical analyses, and

comparisons with kriging, are given in Hutchinson (1993) and Hutchinson and

Gessler (1994).

Results

The network of SI observations (995 locations) had a standard deviation of 3.32 m.

This collection of observations was then ﬁtted with a thin-plate smoothing spline

using

ANUSPLIN. Residuals between the resulting surface and the observations had

a root mean squared error of 1.16 m. Analysis of residuals revealed no bias in the

predictions. Furthermore, residuals were homogeneous and had no apparent pat-

tern. Using this

ANUSPLIN surface of lodgepole pine SI, predictions of SI were made

on a 1-km grid across Alberta. This grid of predictions was then mapped using

ArcView.

The ﬁrst problem we encountered was somewhat expected: the negative corre-

lation between elevation and SI (Fig. 2.4) r

esulted in some negative SI predictions in

the high Rockies. This is an instance of using an interpolation tool for unintended

extrapolation. The Canadian Rockies contain a seemingly endless chain of dramatic

3000+ m peaks, all well above the timberline and above the elevational limits of

lodgepole pine. The elevation limit for lodgepole in our data set is 2200 m, with an

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18 R.A. Monserud and S. Huang

Site index (m)

0 400 800 1200 1600 2000 2400

Elevation (m)

able for the mountains (Figs 2.5 and 2.6).

ANUSPLIN

distribution of lodgepole pine (Fig. 2.7).

Discussion

<10 m), again conforming to ﬁeld

and elevation exhibited in the data (Fig. 2.4).

Fig. 2.4. The relationship between elevation and plot site index for lodgepole pine.

observed minimum SI near 4 m. Our solution was simply to impose a linear con-

straint setting SI = 0 if elevation exceeds 2400 m. The revised map appeared reason-

Next, we used ArcView to overlay a block-out map of the agricultural lands

and Wood Buffalo National Park (Fig. 2.2) on top of the predictions of SI

(Fig. 2.6). We intentionally left Jasper and Banff National Parks in the map to illus-

trate the predictions in the high Rocky Mountains (Fig. 2.6), even though we have

no data there. Finally, we overlaid the predictions of SI with the natural

We have a very large sample of SIs from the most important regions for lodgepole

pine (Table 2.1): 2210 observations from the Foothills Natural Region (Upper

Foothills and Lower Foothills subregions) and 352 observations from the Rocky

Mountain Natural Region (Montane and Subalpine subregions). These subregions

are all in southwestern and western Alberta. Sample size is relatively small (57

observations) in the largely roadless Boreal Forest Natural Region (mostly the

Central Mixedwood, Dry Mixedwood and Wetland Mixedwood subregions), which

includes much of northern Alberta.

Although map patterns are complex, predicted SI decreases regularly and con-

tinuously as elevation increases from the parklands, through the foothills, to the

mountains, conforming to ﬁeld observations and a shorter growing season. In the

high mountains, SI predictions are the lowest (

observations. Thus, the map correctly represents the inverse relationship between SI

Predictions on agricultural land warrant closer examination. Because we have

no observations in agricultural land, these predictions are clearly extrapolations and

should be viewed with caution. Generally, they fall into two categories. First, the

Grassland Natural Region (the prairies of southeastern Alberta) is clearly too dry to

support the establishment and growth of forest trees. Moisture stress would also

limit lodgepole pine establishment and growth in sections of the Montane subregion

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19 Mapping Lodgepole Pine Site Index in Alberta

Fig. 2.5. Unblocked site index predictions from ANUSPLIN. These maps are mostly extrapolations beyond the

range of the data (compare Fig. 2.2), and are intended only to examine the limitations of the predictions.

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20 R.A. Monserud and S. Huang

Fig. 2.6. Site index predictions from ANUSPLIN, excluding agricultural lands and Wood Buffalo National Park.

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21 Mapping Lodgepole Pine Site Index in Alberta

Fig. 2.7. Site index predictions within the natural distribution of lodgepole pine (see Fig. 2.1).

03Amaro Forests - Chap 02 25/7/03 11:04 am Page 22

22 R.A. Monserud and S. Huang

and Parkland Natural Region (e.g. parkland areas between Grande Prairie and

Peace River). These parklands are both too dry and probably have soils with a hard-

pan, both of which would limit the establishment of trees. Our solution is simply to

refrain from making predictions in the agricultural land (Figs 2.6 and 2.7).

The second type of agricultural land is not too dry for forests, however. Both

the Peace River V

alley and the agricultural area west of Edmonton belong to the Dry

Mixedwood or Central Mixedwood subregions. Because these cultivated areas also

support pure deciduous and mixed white spruce and aspen forests, it is likely that

interspeciﬁc competition (and cultivation) rather than moisture stress is the prime

factor limiting lodgepole pine.

ANUSPLIN predicts high SI levels (16–20 m) in the

Peace River Valley and the agricultural area west of Edmonton (Fig. 2.5), an extrapo-

lation that cannot be conﬁrmed by the data.

When we applied the

ANUSPLIN predictions to the entire 1-km grid of Alberta

(Fig. 2.5), we were forced to use vast extrapolations (compare the lodgepole distrib-

ution map in Fig. 2.1). This was intentional, so as to examine the geographical limits

of the predictions. We succeeded in ﬁnding two limits: all elevations >2400 m, and

most predictions into agricultural land. Note that the model extrapolates quite well

into the mountains of Banff and Jasper National Parks (Figs 2.6 and 2.7), where we

have no data. The elevation effect is correctly captured by

ANUSPLIN, provided that SI

predictions are set to zero above 2400 m.

Northern Alberta (55–60° N, 110–120° W) presents another interesting case. It is

sparsely r

epresented in the data, so predictions there should be viewed with cau-

tion. We do have 26 plots in the area, but the vastness of the mostly unroaded land-

scape makes this a relatively small sample for inference. Because lodgepole pine

occurs in isolated hilltops to the north and east of its present continuous range, it

probably had a broader distribution in the immediate period following the retreat of

the Laurentide ice mass, and later retreated, leaving scattered outliers on favourable

sites (Rudolph and Yeatman, 1982). L. Barnhardt (Edmonton, 2002, personal com-

munication) points out that the persistent pockets of lodgepole on the hilltops in the

north (as in the Cypress Hills in the southeast) are the only evidence of its suitability

in this region, but that he expects that it would grow better lower down the slopes.

It probably does not occur there because it is out-competed in early succession by

aspen. Interspeciﬁc (density-dependent) competition becomes the limiting factor,

rather than climate (Rehfeldt et al., 1999). The predictive world of

ANUSPLIN is one-

dimensional (lodgepole pine SI, with no competing species to complicate things.

ANUSPLIN predicts intermediate lodgepole SI for most of northern Alberta (Fig. 2.6),

even though most of this boreal forest/wetland is outside the species’ distribution

(Fig. 2.1; Little, 1971). Clearly, this is an extrapolation, except for the isolated hill sys-

tems inside the species’ range (Fig. 2.7).

Northeastern Alberta is actually in the natural range of jack pine, a closely

elated serotinous species. Lodgepole and jack pine hybridize extensively in north-

central Alberta, where the two species’ ranges overlap (Little, 1971; Wheeler, 1981;

Rudolph and Yeatman, 1982). Although our predictions of lodgepole pine SI could

possibly be viewed as jack pine predictions in the northeast, we do not have data

from jack pine in this analysis, so such predictions thus remain extrapolations.

Within the observed range of lodgepole pine, the

ANUSPLIN predictions conform

generally to expectations (L. Barnhardt, Edmonton, 2002, personal communication)

and to ﬁeld data (Table 2.1). Lodgepole does not grow well at higher elevations,

where it is the most prevalent. At the upper elevation limits of its distribution, cli-

matic factors and poor soil determine its range. At the lower elevational extremes,

density-dependent competition (primarily from aspen) rather than climatic factors is

limiting. The largest lodgepole trees are often in mixed stands (or adjacent to them)

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23 Mapping Lodgepole Pine Site Index in Alberta

in the foothills. In early succession, aspen frequently outcompetes lodgepole pine on

these low-elevation, mesic sites in the foothills and lowlands (L. Barnhardt,

Edmonton, 2002, personal communication). Stand history (e.g. frequency and inten-

sity of burning) sometimes tips the balance toward persistence of lodgepole,

although it cannot outcompete white spruce in later successional stages. The model

predicts lodgepole pine SI to be high in the Foothills subregions.

Finally, Barnhardt expects that the best sites for lodgepole may very well be

bor

dering or outside its present range and be occupied by aspen in early succession

and white spruce as succession proceeds. This is supported by genetic results for

British Columbia by Rehfeldt et al. (1999). For example, they found that populations

in the northern portion of its range were occupying sites 5–6°C cooler (mean annual

temperature) than is optimal for those populations.

To our knowledge, this is the ﬁrst application of thin-plate smoothing splines

to continuous mapping of for

est SI. This methodology was developed for model-

ling climatic surfaces (e.g. Tchebakova et al., 1994; Monserud and Tchebakova,

1996), but it generalizes quite well to other ecological surfaces such as SI. The

result is a map that continuously predicts lodgepole pine SI across all possible

areas in the Province. Judgement must be used to limit the predictions to the cur-

rent distribution limits or perhaps to the immediate vicinity. Predictions appear

reasonable, primarily because of the locally adaptive nature of the spline-ﬁtting

methods. These are strongest where the data are strongest. Caution should be

exercised in areas where data are sparse, such as the northern half of the Province.

Predictions outside the range of the data, especially into agricultural land, should

not be used.

This application is largely possible because of the availability of a very large

sample of destr

uctively sampled trees. Stem analysis is quite labour-intensive and

expensive. It is rare that an organization will go to such great expense to obtain

comprehensive productivity data on a regional scale. Although we might appear

to be highlighting the interpolation and mapping technology (

ANUSPLIN and

ArcView), the real star is the enormous and comprehensive database on produc-

tivity and growth that the Province of Alberta has amassed over several decades.

This study is a pilot of sorts. Future work will expand this to all commercial

species in

Alberta. We will then replace SI with m

/ha/year, which is more directly

related to net primary production. The thin-plate smoothing splines methodology

can also be applied to many other variables. We plan to incorporate climate into our

analyses, including climate-change scenarios, to assess the impact of climate change

on site productivity and forest growth and yield in general.

Acknowledgements

We are very grateful to the many people and organizations that supported this project.

In particular, we thank Yuqing Yang, Tammy Kobliuk, Leonard Barnhardt, Narinder

Dhir, Christine Hansen, Thomas Braun, Bob Held, Greg Behuniak, Dave Morgan,

Grady Ung, Barb Osterhout, Frank Liu, Olenka Bakowsky, Yanguo Qin and Daryl

Gilday for their tremendous help on data management, data analysis and data map-

ping. We thank Leonard Barnhardt and Andy Hudak for their excellent review com-

ments. Because of his vast experience in the forests of Alberta, Leonard Barnhardt

served ably as our Jedi Knight. We greatly appreciate the contributions of

Weyerhaeuser Canada, Sunpine Forest Products, The Forestry Corp. and, particularly,

Weldwood of Canada, for providing the data and/or supporting the data collection

and analyses. We are also grateful to Alberta Departments of Environment and

03Amaro Forests - Chap 02 25/7/03 11:04 am Page 24

24 R.A. Monserud and S. Huang

Sustainable Resource Development for providing part of the funding necessary to

carry out the work described here. Robert Monserud was supported by the Rocky

Mountain Research Station (USDA Forest Service) for his contribution to this research.

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