Background information for talk to be held by Lars Wichmann (lars@wichmann.dk) at the workshop on image analysis and spatial statistics in forestry on November 2, 1999 at KVL, Frederiksberg, Denmark.

Competition models for forest stands
Analysis of data from an unthinned sitka spruce stand


Fig 1. Wood disc #9 from tree #12

            The following text contains a summary of some ideas for the PhD project "Models for the analysis and management of uneven-aged mixed stands" by phd student Lars Wichmann. Readers must keep in mind that the project started 1st of September 1999.

Project outline (abstract)
            There is an increasing political awareness of the need for sustainable management of forests (Larsen 1997) and a demand in society for a range of new products from the forest, e.g. biodiversity and recreation, which makes uneven-aged mixed stands preferable to present silvicultural systems (Vanclay 1994). Further, there is increasing evidence that uneven-aged mixed stands are more stable, ecologically and economically, than even-aged monocultures (Larsen 1997, Thorsen 1999).
            The majority of the existing applications of planning in Danish forstry are based on yield models for even-aged monocultures. This aggregation is valid because the distribution of species and tree sizes in even-aged monocultures is relatively homogeneous within stands. As the use of the forests become more diverse, the spatial and temporal heterogeneity increases, and at some point it is no longer possible to divide the forests into stands of equal age or size.
            Modelling, statistical analysis of data and multi-purpose planning for mixed forests are therefore becoming increasingly important. The objectives of this project are 1) to develop stand simulation models based on the growth of individual trees, and hereby enable 2) analysis of different silvicultural practices, growth and yield of managed uneven-aged mixed forests in Denmark.
            To obtain these objectives the main project is divided into smaller sub-projects:

  1. Datacollection.
  2. Develop an image analysis program that can measure the width of growth rings, based on digital images of wood discs (i.e. fig 1)
  3. Examine and develop competition index/models to be used in aggregated stand simulation / growth models
  4. Estimate or "guesstimate" reasonable single tree growth models for the main tree species
  5. Develop simulation tools based on the results from sub-project 2 and 3

Sub-project 1.
Datacollection
            Data was collected from an app. 0.5 ha sitka spruce stand (intermixed with a few Scotch pine, Norway spruce and Larch) planted in the forest of Marbæk Plantage in 1942. The stand was left largely untouched until it was felled in July 1999. All the trees (in total 573) are positioned. The temporal height development is registered for each tree, measuring the distance between breast height and each branch whorl (branch whorls are determined by visual inspection of the stem and by occational counts of shoot numbers). The longitudinal development (shoot length) and direction of all branches in the 5th and 10th whorl is registered along with crown depth. 13 wood discs are sampled from each stem (10 discs at equally spaced intervals at and above breast-height and 3 discs below breast-height). North is marked on each disc, which is then sanded and scanned on a standard flatbed scanner (fig 1). The annual diameter-growth in an arbitrary direction from the pith may then be measured manually or by digital image analysis. The combination of all these data gives an almost complete record of the temporal diameter, height and taper-curve development for the entire stand. Among other options, the data offer an excellent opportunity to examine and validate competition indices.

Sub-project 2.
Develop digital image analysis program.
            Development of a computer program that can measure the width of growth rings along several radii, based on grey-scaled digital images of sanded/planed wood discs. This computer program is currently under construction, but so far the following ideas seem promising. There is a sharp border between the dark latewood and the brighter early wood. The growth rings may therefore be identified by analysing the colour gradient in the pictures. The corresponding local maximums and minimums in the gradient function may be further enhanced by averaging. The location of the pith may be determined by a Hough transformation applied in a smaller area around an estimate of the location of the pith, i.e. the "centre of gravity" or by successive Hough transformations.

Fig 2. The location of Marbæk plantage Sub-project 3.
Examine and develop competition index/models for stand simulation / growth models
            A way to develop a stand growth model is to interpret the stand as the sum of individual trees. The growth of single trees may be modelled by species and site characteristic single tree models. But in order to incorporate between-tree competition in aggregated stand models some measure of competition needs to be developed. Several existing single tree growth models, i.e. FOREST (Ek & Monserud 1984), MOSES (Hasenauer, Moser & Eckmüller 1995), PROGNAUS (Sterba & Monserud 1997), SILVA (Kahn & Pretzsch 1997), Prognosis (Internet 1999a), PrognosisBC (Internet 1999b), include such measures of competition (e.g. Martin-Ek, Hegyi, Bella, Crown Cross Sectional Area).
            Which competition measure is the best suited to describe between-tree competition has been investigated earlier. Pukkala (1989) based the investigations on estimates of historical growth. Biging and Dobbertin (1992) sampled the growth of individual trees for a large number of species and sites, but with maximum plot size = 0.08 ha.
            The main goal of sub-project 2 is to determine which index is best suited to describe between-tree competition for sitka spruce and Scotch pine, based on data from a much larger plot (0.5 ha). Hopefully the results for these species may somehow be elaborated to cover other species as well.

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