**4. AHP analysis**

The process for the evaluation of a suitable growth simulator is divided into three phases (**Figure 2**). The first phase involves a literature review in which 14 potentially suitable simulators are identified. In a preselection phase, the 14 forest growth simulators are narrowed down to a few. In the second phase, an AHP model is created for the systematic comparison and assessment of the remaining simulators [11, 12]. Using AHP, the four simulators are evaluated in greater depth in terms of their functionality and software structure. Based on the AHP results, a suitable forest growth simulator is selected. In the third phase, the chosen simulator is reparametrised using real data from Switzerland and the simulation results are checked for validity. The simulator is also intended to be incorporated into a decision support system (DSS), used to assist forest planning and management processes. However, phase three

222 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

In an initial literature review, 14 forest growth simulators were identified and their main characteristics were recorded (**Table 1**). The simulators were selected based on the following

**•** Availability/quality of descriptions: Is there written documentation on the simulator and

**•** Area of application: Where was the simulator developed (country/region) and could it be

Ecosystem services Economic + + + + + + + - +

**FBSM SiWaWa MASSIMO ForClim SILVA PrognAus MOSES BWINPro PICUS STAND MOTTI FVS FORECAST TASS** 

+ + - - + + + + - + + + - +


+ + + + + + + ? + + +

+ + + + + + + + +

+ + + + + + + ? + + +

Ecological - + + + + + + + + -

+ - + + + + + + + - - ? ?

+ + + + + + ? + + + +

Note: + = represented in the simulator, - = moderately represented, no sign = not represented, ? = no information available.

**•** Suitability for forest management: Can it simulate treatment strategies?

is not described in this article.

adapted to Switzerland?

key requirements:

Support for forest decision processes

Treatment and thinning methods

Main tree species found in Switzerland

Spatial resolution at individual tree level

Parametrisation using inventory and experimental ‐plot data

Forest types Mixed

stands

Uneven‐ aged stands

**Table 1.** Validation of the simulators during the preselection.

**2. Preselection of simulators**

does it explain its structure and functionality?

The AHP analysis was the central component of the final selection and involved comparing the selected simulators—BWINPro, MOSES, SILVA and PrognAus—with each other and evaluating them. The AHP analysis comprised the following steps:


**•** Performing a sensitivity analysis (4.3).

#### **4.1. Decision criteria and hierarchy**

Based on the widely accepted recommendations concerning the uniform and standardised description of forest growth simulators [35], decision criteria were defined and structured hierarchically using a decision tree (**Figure 3**). On the one hand, the recommendations enable the requirements for the chosen simulator to be defined. On the other hand, they provide a framework for the decisions based on which of the individual simulators can be thoroughly scrutinised, particularly in terms of their model and software structure and functionalities.

The decision tree comprises eight main criteria (model approach, range of application, calibration specification, input, sub‐models for growth, output, environmental influence and

**Figure 3.** Decision‐making hierarchy.

software), which in turn are divided into 28 sub‐criteria. The decision criteria supplement the basic requirements presented in **Table 1**. The simulator that best fulfils all the criteria repre‐ sents the ideal simulator for the purposes of the evaluation. The main criteria are explained below.

#### *4.1.1. Model approach*

**•** Performing a sensitivity analysis (4.3).

Based on the widely accepted recommendations concerning the uniform and standardised description of forest growth simulators [35], decision criteria were defined and structured hierarchically using a decision tree (**Figure 3**). On the one hand, the recommendations enable the requirements for the chosen simulator to be defined. On the other hand, they provide a framework for the decisions based on which of the individual simulators can be thoroughly scrutinised, particularly in terms of their model and software structure and functionalities.

224 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

The decision tree comprises eight main criteria (model approach, range of application, calibration specification, input, sub‐models for growth, output, environmental influence and

**4.1. Decision criteria and hierarchy**

**Figure 3.** Decision‐making hierarchy.


#### *4.1.2. Range of application*


#### *4.1.3. Calibration specification*


**• Available tree species:** The simulator must be able to represent the main tree species in Switzerland, including spruce, fir, pine and larch as well as beech, maple, ash and oak.

#### *4.1.4. Input*


#### *4.1.5. Sub‐models for growth*

The following sub‐models are summarised in this section:


The simulator should include these algorithms so that it can model stand growth in its structural development. The individual growth algorithms can be implemented using a variety of approaches. It is also necessary to record site properties so that different local growing conditions can be taken into account. Aside from the widely used site index (based on top height), there are also approaches that describe the site effects on tree growth with respect to soil properties as well as prevailing temperatures and precipitations. These are often not age dependent and therefore offer a clear advantage over the site index in the case of uneven‐aged stands. The corresponding database, equations and parameters for the individual algorithms must be accessible.

#### *4.1.6. Output*

In addition to analysing different treatment strategies purely from a forest management perspective, the simulator should also enable an assessment of ecological and social aspects. This requires not only common forestry parameters such as individual‐tree data, stand characteristics and economic measures but also outputs relating to stand structure and biomass components.

The simulator should generate results for the following criteria:


#### *4.1.7. Environmental influence*

**• Available tree species:** The simulator must be able to represent the main tree species in Switzerland, including spruce, fir, pine and larch as well as beech, maple, ash and oak.

**• Area shape and size:** It should be able to generate user‐defined polygonal areas as well as

**• Input data requirements:** It should be possible to initialise simulation runs using input data

**• Processing of missing information:** There should be a routine for adding missing input data (e.g. tree positions, tree heights, dbh distributions), so that a simulation can be per‐

The simulator should include these algorithms so that it can model stand growth in its structural development. The individual growth algorithms can be implemented using a variety of approaches. It is also necessary to record site properties so that different local growing conditions can be taken into account. Aside from the widely used site index (based on top height), there are also approaches that describe the site effects on tree growth with respect to soil properties as well as prevailing temperatures and precipitations. These are often not age dependent and therefore offer a clear advantage over the site index in the case of uneven‐aged stands. The corresponding database, equations and parameters for the individual algorithms

In addition to analysing different treatment strategies purely from a forest management perspective, the simulator should also enable an assessment of ecological and social aspects. This requires not only common forestry parameters such as individual‐tree data, stand characteristics and economic measures but also outputs relating to stand structure and biomass

The simulator should generate results for the following criteria:

that is easy to collect in forestry practice (random sampling unit, inventory).

226 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

*4.1.4. Input*

present stands as a standardised square area.

formed even with incomplete information.

The following sub‐models are summarised in this section:

*4.1.5. Sub‐models for growth*

**• Height increment**

**• Crown model**

**• Mortality model**

**• Site properties**

must be accessible.

*4.1.6. Output*

components.

**• Diameter increment**

**• Regeneration/ingrowth model**

Forest ecosystems are open systems, in other words, they are dependent on and can be influenced by external factors. A forest growth simulator should be able to take account of the effect of such factors on tree and stand growth.


#### *4.1.8. Software*


#### **4.2. Results of the pairwise comparisons**

Once the criteria and hierarchy have been established, the individual criteria are compared pairwise with each other. This pairwise comparison method allows the decision maker to extract a highly accurate evaluation from the numerous competing criteria.

The pairwise comparisons were supported by the software 'CelsiEval', which also calculated the normalised weights for the respective criteria. In this case, the criterion software receives the highest weighting (0.306) in relation to the overarching goal of the evaluation. The second‐ level criteria are model approach, range of application, calibration specification, growth and environmental influence (0.121), with the input and output criteria (0.046) coming last (**Table 2**).



Note: The utility values of the alternatives are shown at the end of the table.

**4.2. Results of the pairwise comparisons**

**Sub‐criteria**

/management

and site

**(normalised weights)**

Suitable for research/education

0.121 Specification with regard to region

(**Table 2**).

**Criteria (normalised weights)** 

C1 Model approach

C2 Range of application

C3 Calibration specification

C5 Sub‐models for

growth

Once the criteria and hierarchy have been established, the individual criteria are compared pairwise with each other. This pairwise comparison method allows the decision maker to

The pairwise comparisons were supported by the software 'CelsiEval', which also calculated the normalised weights for the respective criteria. In this case, the criterion software receives the highest weighting (0.306) in relation to the overarching goal of the evaluation. The second‐ level criteria are model approach, range of application, calibration specification, growth and environmental influence (0.121), with the input and output criteria (0.046) coming last

0.121 Spatial resolution 0.800 0.125 0.375 0.375 0.125

0.121 Silvicultural scenario studies 0.429 0.250 0.250 0.250 0.250

Age dependency 0.200 0.125 0.125 0.125 0.625

Updating of forest stands 0.429 0.250 0.250 0.250 0.250

Type of mixtures and stand structure 0.152 0.250 0.250 0.250 0.250 Silvicultural treatment variants 0.390 0.500 0.167 0.167 0.167 Available tree species 0.390 0.375 0.125 0.125 0.375

Input data requirements 0.429 0.250 0.250 0.250 0.250 Processing of missing information 0.429 0.313 0.313 0.313 0.063

Diameter increment 0.143 0.375 0.125 0.125 0.375 Crown model 0.143 0.250 0.250 0.250 0.250 Mortality model 0.143 0.400 0.200 0.200 0.200 Regeneration/ingrowth model 0.143 0.300 0.100 0.300 0.300 Site properties 0.286 0.083 0.417 0.083 0.417

Stand characteristics 0.344 0.250 0.250 0.250 0.250

0.121 Height increment 0.143 0.167 0.167 0.167 0.500

C4 Input data 0.046 Area shape and size 0.143 0.250 0.250 0.250 0.250

C6 Output 0.046 Tree lists 0.344 0.250 0.250 0.250 0.250

**(Relative priorities)**

0.143 0.250 0.250 0.250 0.250

0.068 0.068 0.390 0.390 0.152

**BWINPro SILVA MOSES PrognAus**

extract a highly accurate evaluation from the numerous competing criteria.

228 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

**Table 2.** AHP‐calculated normalised weights for the criteria and sub‐criteria as well as the relative priorities of the different alternatives in respect to the sub‐criteria.

The next step was to compare the model alternatives with each other in pairs. Therefore, the information in the appendix (**Tables 4**–**7**) was used as a basis for the decision‐making process. The pairwise comparisons were performed in group discussions by three scientists from the Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), who have a sound knowledge of forestry science and management.

Afterwards, the relative priorities of the model alternatives in relation to the sub‐criteria and the utility value for the different alternatives were calculated (**Table 2**). In the AHP analysis performed here, BWINPro achieves the highest utility value of 0.319. In other words, it is likely

**Figure 4.** AHP performance graph.

to be the most suitable simulator for the goals specified in the AHP. The AHP performance graph shows how the individual simulators perform in relation to the main criteria (**Fig‐ ure 4**). It can be seen that BWINPro is not the best‐performing simulator in all criteria. The contents of the performance graph are explained in the following sections.

*Model approach:* SILVA and MOSES use a distance‐dependent approach based on individual‐ tree coordinates, which the decision makers consider important for the simulation of a continuous cover forestry system. They, therefore, receive the highest priority on the first criterion. PrognAus is rated higher than BWINPro because its approach is not age dependent. However, because the 'age‐dependency' criterion has a lower weighting than 'spatial resolu‐ tion', this rating has less of an impact on the ranking (**Table 2**).

*Range of application:* The simulators scored equally in the three sub‐criteria 'silvicultural scenario studies', 'updating of forest stands' and 'suitable for research/education/manage‐ ment'.

*Calibration specification:* Although MOSES and SILVA (site performance model) have been partially parametrised with Swiss data from long‐term forest experimental plots, BWINPro receives a higher priority than the other models on this criterion. This is partly attributable to the 'silvicultural treatment variants' criterion: BWINPro offers treatment concepts geared towards nature conservation and promoting biodiversity, such as protecting trees with a dbh above a certain value or the possibility of selecting habitat trees. In addition, the model has been parametrised for a whole range of tree species. Only the PrognAus model offers a similarly extensive selection of tree species.

*Input:* The four simulators scored equally on the 'area shape and size' and 'input data require‐ ments' sub‐criteria. However, PrognAus receives a lower priority than the other simulators due to its lack of a structure/stand generator.

*Sub‐models for growth:* PrognAus receives the highest priority in this criterion, mainly owing to its potential‐independent approach for describing height and diameter increment. The decision makers rated this higher than a potential‐dependent approach. Furthermore, Prog‐ nAus describes the site potential in terms of multiple site factors. On the 'crown model' sub‐ criterion, the four simulators were ranked equally as no direct conclusion can be made without comparing model results with real data. The decision makers feel that this aspect is not so important in the context of the AHP comparison because the selected simulator is to be adapted to Swiss conditions in phase 3. In the 'mortality' sub‐criterion, BWINPro receives a higher priority than the other simulators as it considers age‐related as well as simply density‐related mortality. In the 'regeneration/ingrowth' criterion, SILVA was rated lower due to its lack of a corresponding sub‐model (cf. [10]).

*Output:* SILVA receives the highest priority in this area as it provides a variety of economic and ecological indicators needed for the planning and management of forest stands. BWINPro and MOSES receive the second‐highest priority. In BWINPro's case, this is due to its inability to calculate timber‐harvesting expenses, while for MOSES the lower ranking is owing to its limited output on stand structure. PrognAus receives the lowest priority of all the simulators as it delivers limited output on economic indicators and stand structure and none at all on biomass.

*Environmental influence:* PrognAus features a calamity model to simulate random harvesting as a result of windthrow/wind breakage, snow breakage and beetle infestation. The height and basal area increment model has also been expanded to include climatic variables. As a result, this simulator receives the highest priority, followed by SILVA in second place. SILVA does not consider disturbances but is able to simulate climatic influences, which are covered by the empirical database. MOSES comes third. It is not climate sensitive, but does enable an estimate of windthrow and snow breakage based on slenderness. BWINPro receives the lowest priority as it cannot currently simulate either disturbances or climatic influence.

*Software:* In the 'software' criterion, which has the heaviest weighting of all the main criteria, BWINPro receives the highest priority by some distance. This simulator has the advantage of being freely available online. It was programmed in the Java programming language as part of the TreeGrOSS (Tree Growth Open Source Software) project, using open‐source software packages. The advantage of this is that the software is free of charge, the program code is clearly identifiable and users can easily adapt the program to their specific needs. Another advantage of BWINPro is its object‐oriented software structure consisting of multiple Java packages. SILVA and MOSES also feature sub‐modules and components, but because less information was available about these, they were both rated below BWINPro. SILVA receives a slightly lower priority than MOSES because it did not have a user manual, although in other respects this simulator is well documented. PrognAus receives the lowest priority as it performed badly in all three sub‐criteria, although the main reason was its patchy documentation.

#### **4.3. Sensitivity analysis**

to be the most suitable simulator for the goals specified in the AHP. The AHP performance graph shows how the individual simulators perform in relation to the main criteria (**Fig‐ ure 4**). It can be seen that BWINPro is not the best‐performing simulator in all criteria. The

*Model approach:* SILVA and MOSES use a distance‐dependent approach based on individual‐ tree coordinates, which the decision makers consider important for the simulation of a continuous cover forestry system. They, therefore, receive the highest priority on the first criterion. PrognAus is rated higher than BWINPro because its approach is not age dependent. However, because the 'age‐dependency' criterion has a lower weighting than 'spatial resolu‐

*Range of application:* The simulators scored equally in the three sub‐criteria 'silvicultural scenario studies', 'updating of forest stands' and 'suitable for research/education/manage‐

*Calibration specification:* Although MOSES and SILVA (site performance model) have been partially parametrised with Swiss data from long‐term forest experimental plots, BWINPro receives a higher priority than the other models on this criterion. This is partly attributable to the 'silvicultural treatment variants' criterion: BWINPro offers treatment concepts geared towards nature conservation and promoting biodiversity, such as protecting trees with a dbh above a certain value or the possibility of selecting habitat trees. In addition, the model has been parametrised for a whole range of tree species. Only the PrognAus model offers a

*Input:* The four simulators scored equally on the 'area shape and size' and 'input data require‐ ments' sub‐criteria. However, PrognAus receives a lower priority than the other simulators

*Sub‐models for growth:* PrognAus receives the highest priority in this criterion, mainly owing to its potential‐independent approach for describing height and diameter increment. The decision makers rated this higher than a potential‐dependent approach. Furthermore, Prog‐ nAus describes the site potential in terms of multiple site factors. On the 'crown model' sub‐ criterion, the four simulators were ranked equally as no direct conclusion can be made without comparing model results with real data. The decision makers feel that this aspect is not so important in the context of the AHP comparison because the selected simulator is to be adapted to Swiss conditions in phase 3. In the 'mortality' sub‐criterion, BWINPro receives a higher priority than the other simulators as it considers age‐related as well as simply density‐related mortality. In the 'regeneration/ingrowth' criterion, SILVA was rated lower due to its lack of a

*Output:* SILVA receives the highest priority in this area as it provides a variety of economic and ecological indicators needed for the planning and management of forest stands. BWINPro and MOSES receive the second‐highest priority. In BWINPro's case, this is due to its inability to calculate timber‐harvesting expenses, while for MOSES the lower ranking is owing to its limited output on stand structure. PrognAus receives the lowest priority of all the simulators

contents of the performance graph are explained in the following sections.

230 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

tion', this rating has less of an impact on the ranking (**Table 2**).

similarly extensive selection of tree species.

due to its lack of a structure/stand generator.

corresponding sub‐model (cf. [10]).

ment'.

The utility values of the simulator alternatives are heavily dependent on the normalised weights of the main criteria. Consequently, small changes in the weights could alter the ranking of the alternatives. Because the weightings are based on subjective decisions, the stability of the alternative ranking must be verified using different normalised weights. A sensitivity analysis was therefore conducted to determine how stable the utility values would remain if the criteria weightings were to be subsequently changed. Should the change in weightings cause a variation in the utility value ranking, a review/revision would be needed. To this end, nine additional scenarios were simulated with different normalised weights for the main criteria:


The results are presented in **Table 3**. By comparing the total number of position points it can be seen that BWINPro, SILVA and PrognAus come very close together in the various sensitivity scenarios. However, BWINPro is still the best simulator in five of the nine scenarios, slightly outperforming SILVA in terms of the total number of position points.


Note: Calculated utility values if the normalised criteria weights are changed, (i) same weighting of each criteria (0.125), (ii) with one criterion in each case being considered as very important (0.500) and the rest as equally 'unimportant' (0.071). The last row contains the sum of the position points.

**Table 3.** Results of the sensitivity analysis.
