# A Bayesian Belief Network Approach to Predict Damages Caused by Disturbance Agents

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Conceptual Framework for BBN Development

#### 2.1. Structural Development

#### 2.2. Parameter Estimation

_{c}).

_{jo}

_{int}(2) and (3) represents an assignment where all parent nodes pa(X

_{c}) are in a state so as to maximize the positive and negative influences, respectively. An individual influence factor i

_{k}underlines the positive or negative influence of each parent node with respect to the joint influence factor i

_{jo}

_{int}.

_{low}) experts had to identify the assignment where “stand age” and “dry period” were in their most positive values (“stand age” is in the state “>100 years” and “dry period” in its state “2 periods”).

#### 2.3. Model Evaluation

## 3. Case Study Application

## 4. Discussion

#### 4.1. Model Development

#### 4.2. Model Evaluation

#### 4.3. Model Justification

#### 4.4. Limitations of BBN Development

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Influence diagram for the damaged trees network relating wind and bark beetle disturbance agents to predict quantity of damaged tress.

**Figure 2.**Influence diagram for the bark beetle disturbance network (“+” and “−“ indicate a positive or negative relation of a pair of nodes, respectively).

**Figure 3.**Conditional probability table (CPT) approximation graphs of two nodes of the bark beetle damage submodel (stand stability and stand vitality).

**Figure 4.**Sensitivity of each node of the bark beetle damage submodel. “Share of Norway spruce” shows the highest sensitivities (Min = −0.058; Max = 0.131).

**Figure 5.**Sensitivities for the storm damage submodel. “Fire damages” and “bark beetle damages” share the highest sensitivities (Min = −0.085; Max = 0.1).

**Figure 6.**Sensitivities for the damaged trees network. “Wind damage intensity” shows the highest negative sensitivity (Min = −0.078) while “bark beetle damage intensity” shows the highest positive sensitivity (Max = 0.108).

**Figure 7.**(

**a**) Probabilities (y-axis) for bark beetle predisposition categories (x-axis) over five stand types; (

**b**) Probabilities (y-axis) for storm damage predisposition categories (x-axis) over five stand types.

**Figure 8.**Probabilities (y-axis) for the damage intensity classes (x-axis) of the overall node “quantity of damage” for the five stand types. Intensities are defined with damage class on stand level scale (where “horst” defines damages > a “group of trees” in a scale not more than 0.5 ha in size and “group of trees” defines damages to more than five trees within a radius of tree length).

Input Parameter | Stand Type A | Stand Type B | Stand Type C | Worst Case | Best Case |
---|---|---|---|---|---|

stand age | 60–79 years | 90–100 years | >100 years | >100 years | <60 years |

share of Norway spruce | 25–49% | 50–70% | >70% | >70% | <10% |

canopy closure | moderately low | moderately high | moderately high | low | high |

number of seasonal dry periods | 0 | 1 | >2 | >2 | 0 |

H/D value | >80 | >85 | >100 | >100 | <80 |

proportion of hardwood | ≥30% | <30% | <30% | <30% | ≥30% |

canopy roughness | homogeneous | single dominant trees | rough, irregular | rough, irregular | even |

soil water saturation | well drained | well drained | well drained | excessively drained | wet |

soil type | Cambisol | Cambisol | Cambisol | Gley | Cambisol |

wind intensity | strong wind (>60 km/h) | storm (>75 km/h) | orcane (>120 km/h) | orcane (>120 km/h) | breeze (>10 km/h) |

bark beetle population density | <1 generation | 1 generation | ≥2 generations | ≥2 generations | <1 generation |

previous disturbances | low | moderately low | moderately high | high | low |

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**MDPI and ACS Style**

Radl, A.; Lexer, M.J.; Vacik, H.
A Bayesian Belief Network Approach to Predict Damages Caused by Disturbance Agents. *Forests* **2018**, *9*, 15.
https://doi.org/10.3390/f9010015

**AMA Style**

Radl A, Lexer MJ, Vacik H.
A Bayesian Belief Network Approach to Predict Damages Caused by Disturbance Agents. *Forests*. 2018; 9(1):15.
https://doi.org/10.3390/f9010015

**Chicago/Turabian Style**

Radl, Alfred, Manfred J. Lexer, and Harald Vacik.
2018. "A Bayesian Belief Network Approach to Predict Damages Caused by Disturbance Agents" *Forests* 9, no. 1: 15.
https://doi.org/10.3390/f9010015