*Article* **Probability-Based Wildfire Risk Measure for Decision-Making**

#### **Adán Rodríguez-Martínez \* and Begoña Vitoriano**

Interdisciplinary Mathematics Institute, Complutense University of Madrid (UCM), 28040 Madrid, Spain; bvitoriano@mat.ucm.es

**\*** Correspondence: adanro01@ucm.es

Received: 6 March 2020; Accepted: 5 April 2020; Published: 10 April 2020

**Abstract:** Wildfire is a natural element of many ecosystems as well as a natural disaster to be prevented. Climate and land usage changes have increased the number and size of wildfires in the last few decades. In this situation, governments must be able to manage wildfire, and a risk measure can be crucial to evaluate any preventive action and to support decision-making. In this paper, a risk measure based on ignition and spread probabilities is developed modeling a forest landscape as an interconnected system of homogeneous sectors. The measure is defined as the expected value of losses due to fire, based on the probabilities of each sector burning. An efficient method based on Bayesian networks to compute the probability of fire in each sector is provided. The risk measure is suitable to support decision-making to compare preventive actions and to choose the best alternatives reducing the risk of a network. The paper is divided into three parts. First, we present the theoretical framework on which the risk measure is based, outlining some necessary properties of the fire probabilistic model as well as discussing the definition of the event 'fire'. In the second part, we show how to avoid topological restrictions in the network and produce a computable and comprehensible wildfire risk measure. Finally, an illustrative case example is included.

**Keywords:** wildfire management; risk measure; probability; Bayesian networks; decision-making; prescribed burns; firebreak location
