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The prediction of wildfire occurrence is an important component of fire management. We have developed probabilistic daily fire prediction models for a Mediterranean region of Europe (Cyprus) at the mesoscale, based on Poisson regression. The models use only readily available spatio-temporal data, which enables their use in an operational setting. Influencing factors included in the models are weather conditions, land cover and human presence. We found that the influence of weather conditions on fire danger in the studied area can be expressed through the FWI component of the Canadian Forest Fire Weather Index System. However, the prediction ability of FWI alone was limited. A model that additionally includes land cover types, population density and road density was found to provide significantly improved predictions. We validated the probabilistic prediction provided by the model with a test data set and illustrate it with maps for selected days.

Predicting the occurrence of wildfire incidents is an important component of fire management. Due to the uncertainties in the influencing factors, as well as to random effects in the fire process, such a prediction must necessarily be probabilistic. Various probabilistic models are proposed in the literature, including Poisson models (

Past probabilistic models of fire occurrence use weather factors, anthropogenic factors or combinations thereof as explanatory variables (

Various studies have looked into the combined effect of weather and anthropogenic factors (

The aim of this paper is the development of a daily probabilistic model for fire occurrences in Mediterranean climates, which includes both natural and anthropogenic factors. Such a daily predictive model with fine spatial resolution can eventually be helpful as a fire management tool. Here, we show that the fire risk prediction at the mesoscale can be improved with readily available data on weather and anthropogenic factors, combined with a sound probabilistic model.

In the proposed model, the potential influence of weather conditions is represented by the Canadian Forest Fire Weather Index System (CFFWIS -

The model is applied to the island of Cyprus, where the model parameters are calibrated from observed fire events. Cyprus is part of the Eastern Mediterranean region, which is drier and warmer than the more commonly studied areas of Spain, Southern France and Northern Italy. The data is separated into a learning set and a validation set, which allows to investigate the predictive power of the proposed model. It is found that the best prediction can be achieved by combining the natural and anthropogenic factors. The main factors describing anthropogenic influences are found to be land cover, population density and road density.

The Canadian Forest Fire Weather Index System (CFFWIS -

The BN in

In the presented study, data is available for all weather variables as well as all yellow variables. All these variables are continuous, with the exception of “land cover”, which has labeled states that are related to fuel type (

The fire occurrence rate

where ^{-1} km^{2}] is the mean occurrence rate and ^{2} is the area of the cell.

Observations of

The response variable is the number of fire occurrences _{1}, …, _{k}] by means of the link function (

where _{0}, …, _{k}] is the vector of regression coefficients. This link function ensures that

Changing one of the explanatory variables from _{i} to _{i}+Δ

In the numerical investigations, several models are examined, which differ in the selection of the explanatory variables _{i} is defined for each of its categories. This variable takes value 1, if the land cover in this area belongs to this category, and value 0 otherwise.

Maximum likelihood estimation (MLE) is applied to determine the coefficients

where _{d} is the number of days with observations and _{a} is the number of spatial units with observations, _{ij} is the number of fires observed on day _{ij} are the values of the explanatory variables on day

The MLE is found as the value of

No analytical solution to this optimization problem exists. Numerical optimization must be applied. For this purpose, it is convenient to express the optimization problem in terms of the log-likelihood instead (

In the numerical investigations, the simplex search method and the quasi-Newton method are used to solve

To compare different models, the Akaike Information Criterion (AIC) is employed (

where ln _{MLE}|_{i} of the model. The first term in the AIC accounts for the likelihood of the model, the second term punishes models with more parameters to avoid overfitting.

An additional comparison between models is performed with a validation data set _{V}, which is not used for estimating _{MLE}. The log-likelihood of _{MLE} calculated with the validation data set _{V}, _{MLE}|_{V}), provides an additional indication of model accuracy.

We employ data from the Republic of Cyprus, which is selected due to its representative Eastern Mediterranean climate (short cool winters followed by long hot and dry summers), vegetation and fire history and data availability. The study area and the five weather stations used in the analysis are indicated in

Both spatial and temporal explicit data are used in this study. Data are managed in a geodatabase processed with ArcGIS^{®} 10.1 (ESRI, Redlands, CA, USA) and Python^{®} 2.6.8 (Python Software Foundation, Wilmington, DE, USA) and are attached to a 1 km2 grid covering the whole area of the case study (6447 grid cells). The population density in each grid cell (people km-2) is determined from the municipality census data (

Daily weather observations (extracted from 3 hr and 6 hr observations) are interpolated using Inverse Distance Weighting (IDW -

Temperature is additionally adjusted to the altitude based on the normal lapse rate (0.65 °C/100m - _{i} as _{0,i}=_{i} +0.0065·_{i}, where _{i} is the altitude of the weather station in m. The IDW interpolation is performed using the _{0,i} values, resulting in a temperature value at sea level _{0,c} for each cell _{c} is then computed as _{c} =_{0,c}-0.0065·_{c}. Here, _{c} is the altitude at the center of cell

After the weather observations are interpolated, the daily FWI is calculated for each cell based on the formulation given in

After the data pre-processing, weather interpolation and FWI calculation, each of the 6447 grid cells is described by spatial information, noon daily weather conditions and FWI, and recorded fire events for the period 2006-2010 (11.772.222 records). Only the records of the period 2006-2009 (9.419.067 records) are used for parameter estimation.

Poisson regression with MLE is employed as described above. Various candidate models for the fire occurrence rate

Preliminary analysis of the time series 2006-2010 is shown in ^{-5} fires d^{-1} km^{-2}.

The results of

The investigated alternative candidate models included the components BUI, ISI and FWI of the CFFWIS. Maximum likelihood estimation (with respect to the learning set 2006-2009) results in the parameter values, which best explains the data for a given model. To compare the different models, the AIC is applied, which corresponds to the maximum log likelihood value and combined with a term that punishes the use of additional model parameters to avoid overfitting (see

In

In models M2, M3 and M5, road density as well as (road density)^{2} are included as explanatory variables, to represent the non-linear effect of road density on the fire occurrence rate observed from Fig. S4c (in Supplementary Material). It is important to stress that road and population density are highly positively correlated, and are also dependent on land cover type.

Based on the learning data set, model M5 performs best, as it exhibits the lowest AIC, followed by M3 and M4. The estimated parameters of the explanatory variables FWI, road density and population density in all models M1-M5 are consistent. In models M4 and M5, the estimated parameters of the land cover types take slightly different values. They are higher in M4 due to the fact that in M5 the additional terms in the link function describing road and population density on average take a value slightly above zero.

It is also worthwhile noting that the variables describing road and population density in Model M5 are not independent of the land use type. Pearson’s correlation coefficient _{11} alone. Because of this dependence, there is also a significant correlation (

Eqn. 4 is used to compare the sensitivity of the studied models to changes in the explanatory variables.

Fire observations of the study area in 2010 are used to verify the predictive ability of the proposed models. The best model is the one that best discriminates the actual locations with fire occurrences from those without. This is described by the sum of the likelihood values for all cells and all days of the prediction data set. Model M5 predicts the highest log-likelihood for the entire data of 2010 (

Two days in 2010 with the highest number of fires are selected to investigate and demonstrate the prediction of the fire occurrence rate with the model (whose parameters were learnt by data for 2006-2009).

Models M4 and M5 generally predict higher occurrence rates than model M1, which includes only the influence of FWI (

Since the likelihood is only a relative measure of prediction performance, additionally receiver operating characteristic (ROC) curves are computed for the dataset of 2010 and each model M1-M5 (

This study is a step towards an improved prediction of fire occurrence in the Mediterranean for fire management purposes. The selected probabilistic modeling approach provides a quantitative metric of the ability of different explanatory variables to predict daily fire occurrence. Of particular interest is the ability of the FWI, which was developed for Canada, to predict fire danger in the Mediterranean. As we found in this study, the FWI is a good indicator for fire danger also in the Eastern Mediterranean, even if its prediction ability is lower than in Canada and similar climates. In previous empirical studies, the components of the CFFWIS (FFMC, expressing fine fuel moisture; ISI, representing relative fire spread expected immediately after ignition; and BUI, expressing moisture content of heavier fuels) were found to be relevant indicators for predicting people-caused fire occurrence in Canada (

In agreement with previous studies (

Further explanatory variables describing anthropogenic factors may be included in the analysis (see also

Due to the randomness of fire occurrence, there is a limitation to any prediction. This is evident in the results presented in this paper. Consider the predicted fire occurrence rate at locations and days where fires occurred, shown in ^{-5} day^{-1} km^{-2}). Therefore, while the developed models are able to identify days and locations with higher fire risks, they are not - and of course will not - be able to deterministically predict fire occurrences in advance. Nevertheless, the predictions can support the planning of preventive and mitigating measures. Importantly, they also improve the understanding of influential factors.

A probabilistic model was developed for predicting fire occurrences in the Mediterranean based on readily available data on weather conditions, human presence and land cover at the mesoscale. The model was learned with data from Cyprus. In agreement with existing forecasting systems, components of the CFFWIS are included to represent daily weather conditions. Among these components, FWI proved to express best the conditions favoring relevant fires. The final model including environmental and social factors was shown to provide improved predictions compared to a forecast based solely on FWI.

We gratefully acknowledge the support of Stefan Peters in data preprocessing and of Florian Klein in weather interpolation. We thank Areti Christodoulou from the Department of Forests of Cyprus for supplying the fire data and the comments of Dr. Gavriil Xanthopoulos on the literature review. The comments of five anonymous reviewers to an earlier version are highly appreciated.

^{rd}ACM National Conference”. Las Vegas (NV, USA) 27-29 Aug 1968. ACM, New York, USA, pp. 517-524.

Bayesian Network for fire occurrence prediction. Blue nodes represent weather conditions; orange nodes are the components of the CFFWIS, which result in a FWI value; the variables in yellow represent the anthropogenic influence and the vegetation type; the variables in white are the predicted fire occurrence rate and the actual number of fires. The yellow variables change over space but are constant in time, whereas all other variables change both in time and space. Dashed arrows indicate a dependence on the value of the previous day.

(a) ASTER Digital Elevation Model (m) showing the highest peak of the Troodos massiv in white (1956 m a.s.l.) and the included five weather stations on Cyprus; (b) Municipality borders of the area of the numerical investigations and registered fire events during 2006-2010 (616 events); (c) population density; (d) road density; (e) land cover.

Histograms of (a) FFMC, (b) ISI, (c) BUI and (d) FWI (2006-2010) conditional on fire occurrence. CV=σμ is the coefficient of variation.

Expected occurrence rates of fires predicted by different regression models on (a) 8th October 2010 (day with maximum number of fires in 2010) and (b) on 26th June 2010 (day with second maximum number of fires and largest resulted burnt area (3.4 km2 = 340 ha) in 2010). Black dots represent the registered fires on this day (a - e). The predictions are estimated by the models M1, M2, M3, M4, M5. Occurrence rate results are in the order of 1e-5.

ROC curves and AUC values (in brackets) for models M1-M5.

Selected models with explanatory variables and estimated parameters (2006-2009). (*): Permanent crops include olives, vineyards and fruits; (**): Urban-Wet-Past variable includes Urban areas, Wetlands and Pastures.

Explanatoryvariables | Param | Selected Models | ||||
---|---|---|---|---|---|---|

M1 | M2 | M3 | M4 | M5 | ||

Intercept | _{0} |
-10.61 | -10.95 | -10.92 | -10.90 | -10.90 |

FWI | _{1} |
0.0278 | 0.0282 | 0.0302 | 0.0327 | 0.0329 |

Road density [km km-2] | _{2} |
- | 0.3236 | 0.3198 | - | 0.3217 |

(Road density)2 [km km-2] | _{3} |
- | -0.0324 | -0.0276 | - | -0.0234 |

Population dens. [people km-2] | _{4} |
- | - | -0.0018 | - | -0.0010 |

Arable | _{5} |
- | - | - | -0.6501 | -0.9681 |

Permanent* | _{6} |
- | - | - | 0.8383 | 0.3235 |

Heterogeneous | _{7} |
- | - | - | 0.4098 | -0.0760 |

Forest | _{8} |
- | - | - | 0.3497 | 0.1057 |

Shrub/Herbaceous | _{9} |
- | - | - | 0.3279 | 0.0486 |

Open spaces | _{10} |
- | - | - | -0.1310 | -0.1882 |

Urban-Wet-Past** | _{11} |
- | - | - | -0.9556 | -1.1863 |

log-likelihood (2006-2009) | - | -5198.4 | -5166.1 | -5151.2 | -5147.3 | -5111.9 |

AIC (2006-2009) | - | 10400.8 | 10340.2 | 10312.4 | 10312.6 | 10247.8 |

Relative change of occurrence rate Δ_{i}=exp[Δ_{2 }+ 2 _{3 }μ_{RD }+ _{3}Δ_{RD}=2.09 being the mean value of road density.

Explanatory variables | Δx | (Δ_{i} eqn. 4 |
---|---|---|

FWI | 0.791 | |

Population density | -0.271 | |

Road density | 0.614 * | |

(Road density)2 | ||

Arable | 1 | -0.620 |

Permanent | 1 | 0.382 |

Heterogeneous | 1 | -0.073 |

Forest | 1 | 0.111 |

Shrub/Herbaceous | 1 | 0.050 |

Open spaces | 1 | -0.172 |

Urban-Wet-Past | 1 | -0.695 |

Predicted fire occurrence rate at the locations of fires shown in

Day in 2010 | Fire locations | Fire occurrence rate (× 10^{-5} d^{-1} km^{-2}) |
||||
---|---|---|---|---|---|---|

M1 | M2 | M3 | M4 | M5 | ||

Oct 8 | a | 7.2 | 7.1 | 7.8 | 9.1 | 9.4 |

b | 6.4 | 4.6 | 5.1 | 8.1 | 6.4 | |

c | 6.0 | 4.3 | 4.8 | 7.5 | 5.9 | |

d | 5.7 | 6.3 | 7.0 | 7.0 | 8.8 | |

e | 5.4 | 4.0 | 4.4 | 6.6 | 5.3 | |

Jun 26 | a | 3.9 | 5.3 | 5.8 | 4.7 | 5.9 |

b | 6.2 | 8.4 | 8.6 | 7.6 | 10.9 | |

c | 5.1 | 8.0 | 8.0 | 6.0 | 10.7 | |

2010 | log-likelihood in study area | -1388.6 | -1383.2 | -1388.7 | -1380.6 | -1377.1 |

Fig. S1 - Interpolated weather parameters on 8th October 2010. (a) wind speed (km h-1), (b) temperature (°C), (c) relative humidity (%).

Fig. S2 - Estimated components of the Canadian Forest Fire Weather Index system on 8th October 2010. (a) Fine Fuel Moisture Code (FFMC), (b) Duff Moisture Code (DMC), (c) Drought Code (DC), (d) Initial Spread Index (ISI), (e) Buildup Index (BUI), (f) Fire Weather Index (FWI).

Fig. S3 - Daily values of Fire Weather Index (FWI), precipitation (mm) and noon dry-bulb temperature (°C) at Paphos weather station, and daily number of fire occurrences in the investigated area in 2006.

Fig. S4 - Observed mean occurrence rate (Nr.Fires day-1 km2) conditional on (a) FWI, (b) Population density, (c) Road density and (d) Land cover types for 2006-2010.

Tab. S1 - Data types, resolution and sources.

Tab. S2 - Alternative models with explanatory variables and estimated parameters (2006-2009).