The Linear Index of Tree Appraisal (LITA) Model for Economic Valuation of Large Urban Trees in Sweden

Circumference or Cross-Sectional Area

Regarding the relationship between tree price and tree circumference, for the data obtained from the nurseries, a linear and a second order polynomial both proved to be good fits to the Tilia data (R² = 0.970 and 0.994, respectively) (Figure 1). A noteworthy feature of the linear fit was the large constant offset. It was also found that the three most common species of trees were very similar in their price behavior, and therefore, for reasons of clarity, only the Tilia data are shown in Figure 1 and Figure 2. Quercus robur deviated as expected by being consistently more expensive, but the general shape of the curve was similar.

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Figure 1.

Tree price as a function of stem circumference at 1 m stem height (in accordance with tree nursery standards) for Acer platanoides, Betula pendula, Quercus robur, and Tilia × europaea. The linear and second order polynomial functions for Tilia × europaea are also shown.

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Figure 2.

Tree price as a function of cross-sectional diameter at 1 m stem height (in accordance with tree nursery standards) for Acer platanoides, Betula pendula, Quercus robur, and Tilia × europaea. The linear and second order polynomial functions for Tilia × europaea are also shown.

Similarly, a second order polynomial and a linear function of the cross-sectional area gave a good fit to the data for all individual species (R² = 0. 990 and 0. 997, respectively) (Figure 2). The three common species were very similar in this case too, while Quercus robur again deviated by being more expensive. It is important to note that the constant factor in the linear case was comparatively small, which was a general feature for all tree species studied. The LITA model is therefore based on the approximation that this constant factor can be neglected.

The reason for choosing tree cross-sectional area, as opposed to tree circumference, as the basis for linear extrapolation is perhaps not immediately clear, especially since a linear function was a very good fit in both cases (Figure 1; Figure 2). The choice stemmed from a desire for simplicity and for the ability to extrapolate from a single or a few data point(s). If the constant factor in the linear extrapolation function is zero, then the extrapolation is determined only by the gradient, which greatly simplifies calculation. Perhaps the most important feature is that it simplifies without significant loss of accuracy. In fact, forcing the fitted cross-sectional function to have a zero constant term changed the goodness-of-fit only slightly (Figure 2), while in the case of tree circumference it decreased it substantially (Figure 1).

Another possible parameter instead of circumference and cross-sectional area could be tree volume or mass, but these are more complicated to compute due to the need for data on factors such as tree height and density. Such a model would have to rely on estimated data and would thus be more complicated to explain in a court situation than data based on cross-sectional area. However, the best argument against using higher-order parameters is that it is clear from the data that this will never yield a substantially more accurate description.

The final price calculated by the LITA approach depends on the choice of size, or more correctly, on the price per cm² of that size, which is used as the starting point of the extrapolation. This is the primary parameter in the LITA approach and has a much larger impact than the ‘zero constant’ assumption. There are naturally some variations in price per cm² for the tree sizes available in commercial nurseries. In the case of Tilia × europaea, the lowest price per cm² can be found for size 12–14 (measured according to European tree nursery standards as stem circumference at 1 m height), and the highest for size 45–50 (stem circumference at 1 m height). Trees of size 12–14 are almost always available in nurseries and, for all species, have the lowest, or among the lowest, price per cm². In line with the goal that calculated tree price should be based on the lower base limit of the value produced by the method, the cost per cm² should therefore be based on that of size 12–14. On applying the LITA model and comparing the results against existing data, it emerged that only in rare cases did the proposed LITA base price exceed the nursery price. For Tilia × europaea the price was never overestimated but rather underestimated, by 33% on average, for all tree sizes available in the tree nursery catalogs studied here. In the vast majority of cases, the price for other species was also underestimated (Table 1).

As stated, the LITA model uses only one tree size (12–14) from which to extrapolate. This makes the model simple to update, owing to the large number of tree nurseries that have this plant size in stock, and it is very easy to work with. A possible alternative to the one-point approach would be to use the mean value of all data points or of some carefully selected subset of points. However, this would make the LITA model difficult to update and could make it dependent on the verdict of committees or steering groups, and thereby not in compliance with the three goals initially set for the tree appraisal model.

The production methods used in nurseries and their influence on price vary, and therefore basing economic valuations on tree nursery prices is reported to be problematic because of the effects of production method on total price of the tree (Hegedüs et al. 2011). One of the examples cited in that study concerns tree species that are propagated only by grafting, which have a higher price because of the increased use of manpower in their propagation. The LITA model will be affected by this, but it is how the commercial tree market works, and it is difficult to find a market that would better describe tree replacement cost. This was also recognized by Hegedüs et al. (2011), who noted that it is difficult to avoid the use of nursery prices. However, the final differences in tree prices in the current study were not very large, either in the tree nursery catalogs or the calculated replacement cost (Table 1). Thus, although the problems arising from using tree nursery figures seem serious, they will only have a limited effect on the model and calculated replacement cost.

Adjustment Factors

The base cost calculated in the LITA model is for a tree without damage and without loss of vitality, since this is the state in which trees are bought from nurseries. However, the tree being replaced may very well have damage and loss of vitality, and the valuation will not be credible unless this is accounted for. This is why a depreciation factor is included in the LITA model to adjust the base cost of the tree. Use of depreciation parameters, based on damage and loss of vitality, is common in existing evaluation models (CTLA 2000; Helliwell 2000; CAVAT 2010), but the actual parameters used vary between models.

The adjustment factor in the LITA model is based on the Koch method (Bulíř 2009) and is in line with Swedish tree inventory standards (Östberg et al. 2012). It consists of three parts: tree crown, trunk, and root system. Depending on how much damage has occurred to these individual parts of the tree being replaced, a reduction in the total value of the tree is calculated according to set percentages (Table 2).

The Koch method was chosen due to the rather clear recommendations on percentages and the subdivision of the tree into zones (roots, stem, and crown), which are easy to understand and already accepted by Swedish tree officials. Inclusion of existing and accepted parameters means that the model is likely to be accepted more readily and does not require additional tree inventories if a city chooses to calculate the overall replacement cost of its urban tree stock.

In some models for the economic evaluation of trees (Randrup 2005; Bulíř 2009), estimated age or expected lifetime of the tree is included as a parameter. These parameters are intended to reflect a natural progression where a tree with only a few years to live is given a reduced value, while a tree that has a long time left is given an unreduced or even increased economic value. It could also be argued that the age factor is a way of acknowledging the future benefits and contributions of the tree rather than the actual appearance it has today or the significance it has. As Cullen writes, “This notion of anticipation or expectation is important. The past is gone. It is only the future benefits that have remaining utility” (Cullen 2007, pp. 30). There are several problems with adopting this notion of urban trees. The first is that focusing on future contributions implies that a younger tree has a higher value than an older tree, as it will probably have a longer time to contribute future benefits than an older tree. The second problem rests in identifying how old the tree is and predicting how long it will keep contributing and thereby giving these future benefits. Different tree species have different life expectancies, but life expectancy is a blunt instrument to use because of the large variation even among individuals of the same species. In extreme cases, the difference between individuals can be more than 100 years. Tree age is therefore problematic to introduce into some type of economic depreciation, which is really only intended to comply with any other objective change that the courts are accustomed to value, such as material goods or similar, comparatively short-lived objects. Tree age is important, of course, but in the LITA model it is instead reflected in the damage and vitality parameters. When a tree is reaching the end of its life, it is likely to have damage, or at least diminishing vitality, thus reducing its value. Conversely, if the tree does not have damage or loss of vitality, there is nothing to show that it is nearing the end of its life. For this reason, there is no estimate of tree age in the LITA model, and by omitting a specific tree age factor, the model remains simple.

Some models use soft values (e.g., aesthetic, architectonic, and recreational values) that increase or decrease the value of the tree (Randrup 2005). Studies have also shown that citizens’ willingness-to-pay and their attachment to urban trees are connected with the aesthetic attributes of these trees (Zhang and Zheng 2011). It might therefore seem surprising that no adjustment is made for these soft values in the LITA model. These values are important to take into consideration when a city council is choosing (e.g., which trees should be saved in a development context) and when promoting urban trees to the public. However, inclusion of aesthetic and architectural parameters in all economic models raises two questions that are difficult to answer, namely: 1) To whom is the tree aesthetically and architecturally beautiful? and 2) Who should judge whether this is the right opinion? These two questions are crucial in aesthetic and architectural valuation, which can cause problems. Courts can perceive these values differently, even in the same case in different instances, as seen in court cases in Sweden [e.g., Bergin v Geisel (2009) and Bergin v Geisel (2010)], where the District Court and Court of Appeals reached different conclusions on the aesthetic values of the same trees). Sometimes the path chosen is to disregard these values because of the problems in judging them neutrally [e.g., Pohland v Värnamo municipality (2012)], where the court chose to disregard the aesthetic value). However, the aesthetic, cultural, and location characteristics of a tree are important in the sense that the courts use these to demonstrate that the trees are not commercial forest and to determine the compensation to be paid [e.g., Pohland v Värnamo municipality (2012), where the aesthetic value was used to determine whether the trees were commercial forest or not].

Planting Costs

When it comes to calculating the costs of planting a tree, there are many factors to consider:

• the number of trees to be planted or managed

• the specific requirements of the planting site (e.g., the size of the planting bed, the number of layers in the structure, and the paving type, such as concrete or asphalt)

• odd and difficult placements, which can radically affect, for example, the costs of construction and transportation to the site

• the cost of caring for replacement trees during the initial years of their life

The list of special conditions is almost limitless, but the general assumption was that it is not reasonable to create a model that calculates an exact cost for the planting and maintenance of replacement trees for every conceivable scenario. Obtaining a standard planting cost per cm² for a tree requires a simplified model, which in turn leads to a classic dilemma—the model should reflect reality in a reasonable way, but should not be linked too precisely to tree replacement in the individual case. The LITA model is therefore a compromise that allows the planting costs to be included when calculating a replacement cost for urban trees. If a value is required for particularly demanding planting sites, or for sites regarded as more labor demanding, then a case-specific estimate must be made.

For common planting conditions, the cost per tree increases step-wise (Figure 3). This is especially noticeable for large trees. Nonetheless, a linear function captures most of the behavior in the costs for street planting and park planting (R² = 0.804 and 0.810, respectively). These two cases are very similar, however, so the combined mean is used in the LITA model.

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Figure 3.

Tree planting costs, based on the mean planting costs for trees in street and park environments.

The Final Formula

Having specified the replacement cost of the tree based on the cross-sectional area, the adjustment factors, and the planting costs as described in this article, the proposed formula for calculating the value is:

1

where Vr is the total replacement cost; Pt is the nursery catalog price per cm² for a tree of size 12–14 and of the same tree species as the tree being replaced; A is the cross-sectional area of the tree being replaced (cm²); D is the reduction due to damage to the tree being replaced; Pp is the planting cost per cm²; and B is the base planting cost.

The LITA approach is a solid way of calculating a replacement value, is easy to update and explain, and has a clear link to the marketplace for trees (i.e., tree nurseries). The model also produces an economic replacement cost for specific trees, although replacement cost is not necessarily equal to value (CTLA 2000). A replacement tree, although of the same size, species, and condition, will not have the same value as the tree being replaced (i.e., it will not have the same history or architectural features that the lost tree might have had). Hence, the economic valuation made by the LITA model and the adjustment factors proposed in the model will never fully replace the lost value of the original tree.

The LITA model is designed to evaluate large trees and to err on the side of underestimation. As a result, the calculated replacement cost will not be the best option for smaller trees that are available from nurseries. Such smaller trees, in most cases, will be allocated a lower replacement cost than the nursery price, due to the decision to base the model on the lowest price per cm². In short, calculated costs are not meant to replace nursery prices when such exist, as with the LITA model this will most likely result in a lower replacement cost. In fact, it may also underestimate the cost for sizes just slightly above those available from nurseries.

The model is designed to estimate the replacement value of trees in an urban environment. For most urban situations, the costs of planting and establishing the trees are small in relation to the LITA value, so excluding these costs is not a major issue, but the planting costs in common urban environments are nonetheless included. This is the correct approach unless the location involves major problems for tree planting (e.g., if specialist and expensive equipment is needed). The cost of such work is not included in the model and must be added separately for each such case.