Modelling bark beetle disturbances in a large scale forest scenario model to assess climate change impacts and evaluate adaptive management strategies

Abstract

To study potential consequences of climate-induced changes in the biotic disturbance regime at regional to national scale we integrated a model of Ips typographus (L. Scol. Col.) damages into the large-scale forest scenario model EFISCEN. A two-stage multivariate statistical meta-model was used to upscale stand level damages by bark beetles as simulated in the hybrid forest patch model PICUS v1.41. Comparing EFISCEN simulations including the new bark beetle disturbance module against a 15-year damage time series for Austria showed good agreement at province level (R² between 0.496 and 0.802). A scenario analysis of climate change impacts on bark beetle-induced damages in Austria’s Norway spruce [Picea abies (L.) Karst.] forests resulted in a strong increase in damages (from 1.33 Mm³ a⁻¹, period 1990–2004, to 4.46 Mm³ a⁻¹, period 2095–2099). Studying two adaptive management strategies (species change) revealed a considerable time-lag between the start of adaptation measures and a decrease in simulated damages by bark beetles.

Appendices

Appendix 1: A meta-model of infestation probability

Both the statistical models of infestation probability (Eq. 4, Table 4) and of soil moisture index (Eq  5, Appendix 2) represent meta-models (cf. Urban et al. 1999) designed to capture the main model behaviour of the stand level model PICUS. It has to be noted that the reported statistics describe the fit of the meta-models to the PICUS simulations rather than to independent observed data. Whereas the stand level model PICUS uses detailed climate information on quasi-daily to monthly time steps aggregated climate parameters (annual integration) were used as explanatory variables in the meta-modelling to assure compatibility with widely available data sets of large spatial coverage. Thus the interannual climate variation is fixed in the meta-model.

Table 4 Parameters for the multivariate logit model of bark beetle infestation probability (Eq. 4)

The statistical pBB model (Eq. 4) showed sensible model behaviour in line with expectations and PICUS model logic. Simulated pBB increased with increasing temperature and decreasing precipitation. Furthermore, older stands showed higher probability of bark beetle damage than young stands and the susceptibility to bark beetle increased with increasing host tree share. Decreasing stand densities resulted in slightly increasing probabilities of bark beetle damage in the model, related to increasing light levels in the forest and subsequently increasing bark temperatures. The R² for the logit-model was calculated as:

$$ R^{2} = \frac{{1 - \left( {\hat{L}_{0} /L} \right)^{2/n} }}{{1 - \hat{L}_{0}^{2/n} }} $$

where n is the number of binary observations and $\hat{L}_{0}$ is the maximised likelihood under the null (R² = 0.923; see Faraway 2006). Average model bias (E) was calculated as an average of errors for all predictions by

$$ E = \frac{1}{n}\sum {(y_{i} - \hat{y}_{i} )} $$

where y _i is the observed and $\hat{y}_{i}$ is the predicted value. The resulting average model bias for the pBB model was small (E = −1.792 × 10⁻¹⁵) and not significantly different from zero (α = 0.05). Also the mean absolute error of pBB, |E|,

$$ \left| E \right| = \frac{1}{n}\sum {\left| {y_{i} - \hat{y}_{i} } \right|} $$

was found to be satisfactorily low with 0.0389. Analysing model residuals over the range of estimation showed no evidence for non-constant residual variation.

Appendix 2: A meta-model of soil moisture index

Generalised linear model behaviour was generally in line with the definition of SMI (see Eq. 3), showing a directly proportional relationship between SMI and temperature and an indirectly proportional relationship between SMI and precipitation. However, SMI response to precipitation was found to be widely insensitive to precipitation levels of more than 1,100 mm per year in the PICUS simulations with a strong increase in SMI at lower precipitation levels. Thus, a transformation of the corresponding predictor variable was applied (Eq. 5, Table 5). Nevertheless, the residual distribution showed a slight trend towards an underestimation of low and an overestimation of high SMI values but was, however, not significantly different to the normal distribution around zero. The GLM explained a high proportion of variance in SMI estimates (R ² = 0.945) and average model bias E (2.885 × 10⁻¹⁹) was not significantly different from zero at α = 0.05. Also the mean absolute error of the GLM was small (|E| = 0.0234).

Table 5 Parameters for the multivariate regression model of soil moisture index (Eq. 5)

Appendix 3: Aggregation of annual damage events to periodic area transitions

To demonstrate the approach of scaling annual damage probabilities to EFISCEN periods we use data of the Burgenland region (bgl) for the period 2001–2005 (baseline climate scenario), 100% host tree share, age class five (80–100 years) and volume class seven (280–394 m³ ha⁻¹), see Table 6.

Table 6 Example meta-model output for annual damage probability (pBB) and damage intensity (iBB) for the years y of a 5-year simulation period in EFISCEN

We apply probability theory to account for multiple damages per area unit in aggregating annual meta-model estimates. The joint probability of all independent annual events contained in a subset Y _n , i.e., the area share in the matrix cell damaged |Y _n | times in the years y ∈ Y _n , is represented by $\prod\limits_{{y \in Y_{n} }} {p{\text{BB}}_{y} }$ (Eq. 6, first term). Since we are interested in the area damaged only in the years y ∈ Y _n (and not also in other years of the period), this estimate needs to be corrected for all Y ⊆ I of higher cardinality than |Y _n | containing the elements of Y _n . (Eq. 6, second term, $\prod\limits_{{z \in I\backslash Y_{n} }} {q{\text{BB}}_{z} }$). Overall n = 31 subsets of Y _n exist for Y ⊆ I in a 5-year period $\left( {n = \sum\limits_{i = 1}^{5} {\left( {\begin{array}{*{20}c} 5 \\ i \\ \end{array} } \right)} } \right).$ For Y ₁  = I = {1, 2, 3, 4, 5}, the subset with the maximum cardinality, $s{\text{BB}}_{{Y_{1} }}$ represents the area in the EFISCEN matrix cell damaged by bark beetle in all 5 years of the period. In this case the second term in Eq. 6 is an empty set and $s{\text{BB}}_{{Y_{1} }}$ is computed as the joint probability of the five damage probabilities, resulting in 4.36 × 10⁻³ in our example. This area share in the EFISCEN matrix cell is subject to stand replacing disturbance and moved to the bare forest land class. For subset Y ₂  = {1, 2, 3, 4} the joint probability of 12.34 × 10⁻³ (Eq. 6, first term) contains also the joint probability for subset Y ₁ (Y ₂ ⊂ Y ₁) and the corrected $s{\text{BB}}_{{Y_{2} }}$ is $s{\text{BB}}_{{Y_{2} }} = \prod\limits_{y = 1}^{4} {p{\text{BB}}_{y} - \prod\limits_{y = 1}^{5} {p{\text{BB}}_{y} = \prod\limits_{{y \in Y_{2} }} {p{\text{BB}}_{y} \cdot \prod\limits_{{z \in I\backslash Y_{2} }} {q{\text{BB}}_{z} } } } }$ (confer the general formulation in Eq. 6), i.e., a value of 7.98 × 10⁻³ in our example. Applying Eq. 7 the corresponding cumulative damage intensity $i{\text{BB}}_{{Y_{2} }}$ is 0.128 and will be treated as non-stand replacing disturbance in the EFISCEN framework $\left( {iBB_{{Y_{n} }} \le 0.5} \right).$ Following this sequence for all n subsets of I and applying Eq. 8 results in a volume damage percentage vBB of 5.60% (non-stand replacing) for the 5-year period in our example matrix cell. This percentage is subsequently converted to area transitions to a lower volume class in the EFISCEN matrix framework.

Appendix 4: Species change management regimes based on the current potential natural vegetation composition (PNV)

For the two species change strategies the potential natural species composition for every ecoregion was defined in three elevation belts according to Kilian et al. (1994). Additionally assumptions on the average species composition of the respective natural forest types were made (see Table 7). Aggregated with the respective share of the elevation belts on the ecoregion the target species composition (i.e., natural species composition under current conditions) was derived and implemented in the conversion rules (see Table 8). In both PNV strategies Norway spruce forests with a share of less than 30% (category Pa.s, Table 8) were only subject to conversion in areas where Norway spruce is not a dominant species of the potential natural tree species composition (Kilian et al. 1994). If two main forest types had been classified for one elevation belt and ecozone in Kilian et al. (1994) we assumed an equal share of both forest types.

Table 7 Distribution of the simulated forest area (i.e., current Norway spruce forest area) to elevation belts and the associated potential natural vegetation^a for the ecoregions as applied for the calculation of conversion area in the PNV scenarios

Table 8 Species change in the PNV conversion strategies