# Probabilistic Wildfire Risk Assessment and Modernization Transitions: The Case of Greece

^{*}

## Abstract

**:**

## 1. Introduction

_{2,}and release of black carbon aerosols show spatiotemporal variations [19,20]; (3) although climate change per se rarely causes fire ignition, it plays a catalytic role in fire events’ severity [21], even of a disastrous character [22], and likely is increasing fire incidences and amplifies damages and risks to humans and infrastructures [23].

## 2. Materials and Methods

#### 2.1. Preliminary Remarks

_{t(i)}. We define φ

_{t(i)}as the ratio of a measure of wildfire activity (e.g., number of events, size of the burned area: nationwide or per administrative jurisdiction or vegetation type) in year t = 1…i over the same measure in the base year t(0) = 2000. Assuming that some power–law function fits the fire occurrence frequency–magnitude distribution, one writes this ratio as:

_{0}) is a hazard function as a function of time of a characteristic event, h(t), calculated after a 2-parameter Weibull distribution, i.e., shape τ and scale γ.

#### 2.2. Descriptors and Data

#### 2.3. Modernization Stressors Trends

#### 2.4. Estimation of Parameters of Wildfire Frequency–Size Distributions Methodology

_{max}), as well as values with very high frequencies (n > 10

^{4}, or s

_{min}→ 0 but always >0 in the global dataset), with a decaying curve linking both extremes. Overall, we focus on estimating the interannual variation of quantities of interest, i.e., the scaling factor γ, the lower limit (smaller size) of burned area s

_{min,}and the upper limit s

_{max}(which is de facto truncated) of the fire frequency–size distribution. Our procedure follows classic demonstrations [67,68,69,70], i.e.,

_{min}. Notice that s

_{min}, the lower limit or threshold of the PLD, is the value that minimizes D, the maximum distance between the data and the fitted model of $F\left(s\right)=\mathit{Pr}\left({s}_{i}\le s\right)$, using a Kolmogorov–Smirnov test approach to calculate it [69]. The calculations are made in R using an adapted version of the power–law package [71].

#### 2.5. Estimation of Parameters of Wildfire Interval Times Distributions Methodology

^{2}were included. Given that the national territory is 132,000 km

^{2}, we consider wildfires >10 km

^{2}a peak event compared with threshold events, which are usually 1 km

^{2}in Greece.

_{0}increases. The Weibull distribution with γ > 1 is the only distribution showing an increasing hazard function with increasing t

_{0}. It is standard practice to test the validity of a Weibull distribution using a Weibull probability plot constructed after plotting interval times data in a 2D plan.

## 3. Results

^{2}of burned areas (forests, afforested areas, shrublands, and agricultural tree plantations) during 2000–2021. Fire events in ‘officially designated forests’ are 9400 and burned surfaces are 2500 km

^{2}. The severity index, i.e., the ratio between surface burned and the number of fire events per year, shows variations of two, even three, orders of magnitude (Figure 4). However, the long-term severity index, i.e., 1955–2021 or the period during which fire statistics data exists, shows a positive but non-significant slope (standardized B = 0.131; p = 0.281). The interesting remark after these general results is that the severity index of forest fires is almost systematically higher than landscape or wooded areas fires.

#### 3.1. Wildfire Frequency–Size Distributions

- In eighteen over twenty-two years, burned areas are distributed as a single power–law, represented by a straight line in log-log scale; in the remaining four, a double power–law fits the actual distributions better;
- since 2000, the frequency of small-sized forest fires has increased;
- the evolution of the γ-scaling factor for forest areas presents a significant negative slope (standardized B = −0.297; p = 0.047), whereas it is non-significant for wooded areas (standardized B = 0.48; p = 0.861).

_{max}for forests is 2.75, whereas for all vegetation types it is 1.63. It suggests that as the number of initial events in forests increases, the probability of large-sized forest fires increases too.

#### 3.2. Wildfire Time Intervals Distributions

^{2}= 1), leading to a probability distribution with a scale parameter of 235 (ha). In cases of characteristic events of medium (>1000 ha) and large (>5000 ha) size (Figure 7B,C), the number of events recorded during the entire period of observation is much fewer; the probability distribution scale parameter is 2870 and 4600, (ha) respectively. However, the medium size wildfires burned more forest areas (168,671 ha) during the observation period of 2000–2021, the large ones having burned almost half (94,343 ha). Figure 8 presents the conditional probability of a major wildfire event, i.e., s ≥ 5000 ha, in Greece in the next five years, calculated as 1—Weibull reliability function. The probability of such an event is quite remarkable (ca 40%). The message for Civil Protection authorities is that no matter how efficient it might be considered, at an annual scale, with the business-as-usual wildfire suppression plan on the ground, there is a need to reconsider and address the significant social and ecological drivers of the wildfire phenomenon to reduce such a considerable risk.

#### 3.3. Automatic Linear Models of Relationships between Wildfire and Modernization Stressors

^{2}in ALM vocabulary, is 0.464 for Equation (9) and 0.335 for Equation (10). Multiple linear regressions applied to these best subsets of stressors or descriptors, with the addition of the binary variable (0,1) of Political competition (election year vs. non-election year), show significant ANOVAs (p = 0.03 and 0.026, respectively). Given the complexity of the wildfire phenomenon, lying at the intersection of multiple physical, ecological, social, and even human behavior drivers, the obtained R

^{2}values are satisfactory, explaining 46.4% and 33.5% of their overall variance. Descriptors of climate (precipitation anomaly), forest transition (wooded areas that include forests and afforested areas), and modernization (penetration of RES) are indeed automatically selected as the best subsets associated with wildfire metrics.

^{2}= 0.91.

## 4. Discussion

^{2}, especially in touristic real estate value areas. One would legitimately suspect that one cause of such a high frequency of small-sized wildfire events might lie in land-claiming arsons.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

^{2}): land value, real estate transactions, agricultural subventions, and burned areas are expressed per this unit, called stremma. This unit allows for higher resolution in land measurements; for instance, fire records as small as 0.1 or 0.01 stremmas. However, hereafter, all comparisons are based on hectares after binning all records <1 stremma to 0.1 ha.

**Table A1.**Synopsis of variables used in calculating fire frequency vs. size of burned areas and the models’ relationship with material macro-structural aspects of modernization. FS: Forestry Service; (a) HFFC: Hellenic Fire Fighting Corps; (b) EFFIS: European Forest Fire Information System; (c) WB: World Bank; (d) UN: United Nations Population Division; (e) FAO: Food and Agriculture Organization; (f) OECD: Organization for Economic Cooperation and Development; (g) IEA: International Energy Agency; (h) ELSTAT: Hellenic Statistics Authority; (i) MoI: Ministry of the Interior (Greece); (k) meteoblue (m).

Variables | Range | Type of Data | Units | Source | Remarks/Definitions |
---|---|---|---|---|---|

Wildfires | Numeric, count Burned area, ignition time, duration of the event, interval times | Forest.area_x differs according to the institutional regime of ‘forest’ adopted in successive years. Wooded. Areas comprise forests, afforestation areas due to abandonment, plantations and tree cultivations, and shrublands. | |||

Forest.area_1 | 1955–2021 |
10^{3} m^{2}, ha | a | ||

Forest.area_2 | 2000–2021 |
10^{3} m^{2}, ha | b | ||

Wooded.areas_3 | 2000–2021 |
10^{3} m^{2}, ha | c | ||

Number of fire events | 1955–2021 | Numeric, count | # fires | a b c | All fire events recorded |

Modernization | 1960–2021 | Numeric, count Census of population | 10 ^{6} ind#ind/km ^{2} | e, f, h | Population density is midyear rural or urban population divided by the corresponding land area in square kilometers. |

Population | |||||

Urb.pop_dens | |||||

Rur.pop_dens | |||||

RES/Hydro in energy mixture | 1990–2021 | Numeric, count | % | g | % energy produced by Renewable Energy Sources and Hydropower plants |

Agricultural.land% Wooded.land% | 1961–2018 1990–2020 | Numeric, count Agricultural statistics | % Territory | d, g | Agricultural land is the share of arable land under permanent crops and pastures. Forest area is land under natural or planted trees of at least 5 m in situ. |

GDP/cap_PPP | 1990–2021 | Numeric, count Economic statistics | Current $ | d, h | Per capita values for the gross domestic product in current international $ converted by purchasing power parity (PPP) conversion factor. |

Energy.consumption/cap | 1960–2014 | Numeric, count Energy statistics | kWh/cap | d, i | Production of power plants and combined heat and power plants less transmission, distribution, and transformation losses and use by heat and power plants. |

Automobile fleet | 1985–2020 | Numeric, count | Number | h | Total of cars, trucks, motorbikes |

Political risk | 1955–2021 | Nominal | Y/N | i | General elections for the Parliament |

Climate change anomalies | 1979–2021 | Numeric, count | dimensionless | k | Deviations of Temperature and Precipitation from the 30-year average. |

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**Figure 1.**A triangular representation of the relationships between three determinants of wildfire occurrence under modernization transitions. The basal side of the triangle refers to the functional relationship between some metrics of wildfires and a series of endogenous and exogenous modernization and other administrative and political predictor variables of the social-ecological system (SES). The right side of the triangle refers to the basic form of the SOC statistics component. The left side of the triangle refers to the statistics of recurrence or interval times between wildfire events. Reference is made to Greece as it is our model case for the period of 2000–2021. Details of the mathematical formulations are given in the Methods section.

**Figure 2.**A diagrammatic transformation of the triangular representation of the determinants of wildfire occurrence under modernization transitions. The definitions of the poles and the corresponding mathematical formulations are explained in detail in the text.

**Figure 3.**Three hypothetical forms of the relationship between the best subset of modernization stressors and a metric of pyric activity, e.g., burned areas in Greece, 2000–2021.

**Figure 4.**Evolution of wildfire statistics in Greece, 2000–2021; blue dots: all vegetation types summed, orange dots: forests. (

**a**) Total burned areas; (

**b**) Severity index (ratio surface burned/number of events). Dotted lines: moving average, lag period = 2.

**Figure 5.**(

**a**) Absolute frequency cumulative distributions of burned areas of size s′ > s. (

**b**) Empirical probability densities of frequency n of wildfire events (size s′ > s). In both panels, annual distributions are color-coded: green lines: forests; orange lines: wooded areas (including forests). Bold red and purple lines are the respective average distribution, as a simile aggregation, derived from the corresponding vegetation type global dataset.

**Figure 6.**Indicative examples of the wildfire frequency–size power–law relationship and the corresponding value of the γ scaling factor. (

**a**) Log-log PLD relationships in wooded areas and (

**b**) forest areas in 2005, a year of low wildfire severity index value. The overall relationship is modeled as a broken PLD (two power–laws combined). The linear log-log relationships are very close for wooded and forest areas burned. The threshold value is identical. (

**c**,

**d**) Log-log PLD relationships between wildfire frequency–size in forest areas during 2007 and 2021, the highest wildfire severity index value in the 21st century. Notice the range of sizes (x-axis) and the similarity of the respective γ-scaling factors.

**Figure 7.**(

**Upper row**): Indicative cumulative distribution function p(t) of recurrence times t for small (

**A**), medium (

**B**), and large-sized (

**C**) limits of wildfires in Greece. Dots represent the distribution of observed recurrence times in various conditions. The continuous red line is the best-fit Weibull distribution with shape α and scale β parameter values per case. (

**Lower row**): Weibull probability plot of the cumulative distribution of recurrence times for the data given in the corresponding panels of the upper row. The solid line corresponds to the Weibull distribution with shape γ and scaled τ parameter values per case.

**Figure 8.**Conditional probability (%) (red line) of a major wildfire event in Greece, i.e., s ≥ 5000 ha, in the next five years. The dotted lines present boundaries of sensitivity analysis of the Weibull reliability function, with a ± 10% variation in the values of the shape α and scale β parameters of the distribution.

**Scheme 1.**A synthesis of the data describing the trajectories of climatic anomalies (upper panel), modernization stressors (middle stressors), wildfire severity index (lower panel), and political competition events (National elections) in Greece during 1990–2021. Color code: Upper panel: blue line: total annual precipitation anomaly (mm); yellow line: mean temperature anomaly (°C). Middle panel: yellow line: RES penetration; grey line: GDP/cap; blue line: forest area; orange line: wooded area (forest, afforested land, shrublands); green line: rural population. For comparison reasons, the middle and lower panel’s actual data per measure are weighted by the corresponding value of 1990 and are log-transformed.

**Scheme 2.**A synthesis of the predictions of SOC theory for the fire frequency–magnitude PL relationship and the corresponding wildfire management policies.

**Table 1.**Synopsis of metadata and methodology of the study of the relationships between the three determinants (modernization, fire frequency–magnitude relationship, interval times) of wildfire occurrences under modernization transitions in Greece, 2000–2021.

Methodology | Metadata | Remarks |
---|---|---|

Case study | Country: Greece | Although wildfire data are recorded at the Department level (51), country-wide sums are used here. |

Range | 2000–2021 | More extensive periods were used when data were available, e.g., 1990–2021 or 1955–2021. |

Relationships | ||

Power-law distribution | PDF, CDF, cCDF | Probability Density Function, Cumulative Density Function, Complementary Cumulative Density Function |

Models | Linear, Hyperbolic, Parabolic | Detection of the best-fit model |

Dependent variables | Burned area, number of wildfires, interval times/year | Calculations of scaling factor γ, the lower size of burned area s_{min}, upper size s_{max} |

Independent variables | ||

Modernization variable | Penetration RES (%), (GDP_PPP $) | RES: Renewable Energy Sources, PPP: Purchasing Power Parity |

Complementary variables | Population change, wooded areas%, agricultural land%, rural population density, automobile fleet, energy consumption/cap, political risk, climate anomalies | Collinear variables excluded |

Regressions | Automatic Linear Modeling procedure | Definition of one subset from the pool of candidate predictors that gives adequate prediction accuracy as an alternative to various regression methods |

**Table 2.**Synopsis of independent variables (stressors) used in calculating wildfire metrics’ (response) relationship with material macro-structural aspects of modernization. Meteorological and political events are also listed as potential moderators of these variables.

Modernization Stressors | Remarks/Definitions |
---|---|

Population size Urban population density Rural population density | Total number of individuals residing during a census period Population density is midyear rural or urban population divided by the corresponding land area in square kilometers. |

Agricultural land % Wooded land % | Agricultural land is the share of arable land under permanent crops and pastures. A forest (wooded) area is land under natural or planted trees of at least 5 m in situ. |

GDP/cap_PPP $US | Per capita values for the gross domestic product in current international $ converted by purchasing power parity (PPP) conversion factor. |

Energy consumption/cap | Production of power plants and combined heat and power plants less transmission, distribution, and transformation losses and use by heat and power plants. |

RES/Hydro in energy mixture | % of the energy produced by Renewable Energy Sources and Hydropower plants |

Automobile fleet | Total of cars, trucks, motorbikes |

Political competition | General elections for the Parliament |

Climate anomalies | Annual deviations (positive or negative) of mean temperature and precipitations from the 30-year average trend |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Troumbis, A.Y.; Gaganis, C.M.; Sideropoulos, H.
Probabilistic Wildfire Risk Assessment and Modernization Transitions: The Case of Greece. *Fire* **2023**, *6*, 158.
https://doi.org/10.3390/fire6040158

**AMA Style**

Troumbis AY, Gaganis CM, Sideropoulos H.
Probabilistic Wildfire Risk Assessment and Modernization Transitions: The Case of Greece. *Fire*. 2023; 6(4):158.
https://doi.org/10.3390/fire6040158

**Chicago/Turabian Style**

Troumbis, Andreas Y., Cleo Maria Gaganis, and Haralambos Sideropoulos.
2023. "Probabilistic Wildfire Risk Assessment and Modernization Transitions: The Case of Greece" *Fire* 6, no. 4: 158.
https://doi.org/10.3390/fire6040158