Case Study #3 Oslo - Urban Tree Valuation Modelling (example google maps)

By: David N. Barton
WWW: Martin Karlsen & Anders L Madsen

The tree valuation Bayesian network model by [Randrup, 2005] adjusted to the Oslo case study #3 (click image to enlarge)

City trees constitute perhaps the single most important green structure in addition to open green space in cities. City trees potentially provide a bundle of ecosystem services. Oslo Municipality has a strategy to replace every municipal tree felled within the built zone with at least one new one. Damage to trees on municipal land is subject to a fine and a compensation claim using an established liability assessment model for city trees.


This liability or compensation value for city trees is calculated using the VAT03 assessment model developed by [Randrup, 2005] and adapted to a BBN by [Barton et al, 2015]. The VAT03 assessment model is based on the replacement cost of a city tree, including purchase and planting costs. This base value is then adjusted for the tree.s structural health and for its qualities in a neighbourhood context, including adaptation and contribution to its local environmental. Environmental qualities include aesthetics, noise and pollution reduction, in other words several regulating ecosystem services. An overview of the VAT03 model structure is provided in Figure 1.

The tree valuation model is based on [Randrup, 2005] adjusted to the Oslo case study #3.


[Barton et al, 2015] used the VAT03-BBN to calculate the aggregate expected compensation value of all city trees taller than 5 meters in Oslo.s built zone.

Property rights (work in progress)

There is currently no environmental liability on trees on private land from a legal point of view. However, there is no reason to believe that trees have less regulating functions just because they are located on private land. Private land might be correlated with other spatial factors that differentiate demand for a tree.s regulating services. As a precautionary principle one could argue that also trees on private land should have environmental liability because a number of the regulating and cultural ecosystem services are public goods. With this in mind the VAT03-BBN may be used to answer the question, what would be the liability value of any city tree in the built zone - whether on public or private land - if it were assessed according to VAT03?

Tree density (work in progress)

Another limitation of VAT03 to be addressed in further model development concerns the value of individual trees in forest stands within or bordering the city built zone. The liability values calculated by the municipality using VAT03 for individual trees have been challenged in cases were trees are in stands. As a demo we show how the VAT03 could scale between individual trees valued at full VAT03 liability value and trees in forest stands assessed only for timber value. In the demo the model scales tree compensation value according to the tree density in the neighbourhood of the tree in question.

Map Interpretation

Each blue element (polygon) on the map represents a tree. When the left mouse button is pressed on a blue element, the value of the selected tree is computed and added to a layer on top of the blue placemarks. This layer has a polygon for the selected element with color green. The intensity of the green color is determined by the expected tree compensation value.

That is, the intensity of the chloropleth color is determined by the expected tree compentation value (normalized using division by 70000). An expected value of zero produce a transparent placemark where as the value one (or above) produce a placemark with color green at full intensity.

Full compatibility of the maps can be viewed with IE11 or Firefox 33.

Model Usage

Below are some HUGIN widgets for interacting with the model shown on the right (click on the probability bar to instantiate a node or remove evidence). Notice that Dashboard contains a lot of variables that can be instantiated.

Associated with each tree is information on properties of the tree. The tree compensation value is computed by propagating this information in the Bayesian network shown in the figure above. The intensity of the green color is determined by expected tree compensation value. The more intense the color is, the higher the expected value of the tree is.

The Compute button computes the sum of the expected values of the selected trees on the map, i.e., the trees selected so far. The set of selected trees can be reset (and all evidence removed from the models) by presseing Reset.

The Save data button allows the user to download a file with the information entered using the widgets for a single tree.

Assessment mode

Tree species

Age phase

Circumference damaged (cm)

Tree compensation value adjusted (NOK)

Expected values

E(basis value (NOK))

E(Location factor)

E(Health factor)

E(Tree compensation value adjusted (NOK))


Chlorpleth value scale

Details of the model for a single tree

Tree compensation value (NOK)

Tree compensation value adjusted (NOK)

Basis value (NOK)

Circumference new (cm)

Price new tree (NOK)

Establishment cost (NOK)

Health factor



Scaffold branches

Small branches

Foliage & buds

Location factor

Environmental factors

Natural / Ecological adaptation




Details of the model related to spillover effects for a single tree

Wood volumne (m3/tree)

Wood price (NOK/m3)

Forestry value (NOK/tree)

Public concern

Distance to public space (m)

Public Good factor

Neighboring trees

Tree height (m)

Density factor

Total expected tree compensation value of selected trees: (select a set of trees and press the button)

Selected tree:


Useful references for those interested in BBN include:

[Kjærulff, U. B. and Madsen, A. L. (2013)] Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis. Springer, Second Edition.

[Randrup, T.B. (2005)] Development of a Danish Model for Plant Appraisal. Journal of Arboriculture 31(3): May 2005.

[Barton, D.N. (2015)] Barton, D.N., Stange,E., Blumentrath, S., and Traaholt, N.V. (2015) Economic valuation of ecosystem services for policy. A pilot study on green infrastructure in Oslo. NINA Report 1114. 77 pp.

Contact information

For further details contact: David Barton (David(dot)Barton(at)nina(dot)no)