Throughout the course of a forest fire, it is of the utmost importance to constantly track and evaluate firefighting activity, because the rate of fire advance normally progresses geometrically in line with costs and potential damage (

As individual fires usually differ greatly, the study of a sample of actual forest fires from a Mediterranean area of central Chile was undertaken. Data obtained from these fires corresponds to the area, burnt perimeter, size category and average rate of fire advance. Using these records, it was possible to construct efficiency functions for combat costs based on the criteria of economic efficiency.

In the field of fire economics,

In Chile, this analysis is imperative due to the fact that practically all decisions concerning the allocation of methods for fire extinction are based on personal experience (

The research considered a geographical area of approximately 112,000 hectares (

In geographical and environmental terms, the study area was situated in an area of high forest fire occurrence with a Mediterranean climate. Similar climates are found in Spain, Portugal, Greece, France and Italy. Human influence has a high impact on initiation and spread of forest fires (

The first stage in data analysis was to define supply criteria for efficiency model inputs. This was undertaken by considering the economic value of forestry resources, deriving results from the simulation of forest fires in free advance and the extinction costs of actual firefighting activity. Studies with similar characteristics were carried out by

The resources involved in efficiency were consolidated in commercial plantations of radiata pine (the main commercial forestry species in Chile): Parameter

Here,

The function determining the burnt area

As shown in the previous chart, more than 77% of the sample focuses on fires of small surface area. In this respect it is clear that small fires can affect vegetation of the highest commercial value and are responsible for practically 85% of total damage. The values indicated in

In order to represent the result from efficiency analysis inputs, it was necessary to determine the expression or effect of the computational simulation of damage using the Chilean KITRAL system, by measuring fires geometrically. For this purpose, a coefficient indicator that measures the relationship between fires in free advance (without containment of extinction activities and simulated in this computer system) and their relationship to fire spread in the presence of firefighting work was defined.

This information was compared in turn with information from the fire simulator, which resulted in the definition of a cost and loss function that depends on affected area and duration of fire spread. This was defined in the following expression:

In the expression above,

By incorporating

The point of equilibrium must now be found by developing the

In the expressions above, the critical value to be determined is the average cost identified for each progressive unit of affected area, to facilitate classification into the appropriate category.

Using the data in

The next step was the application of expressions [1] of value for economic losses and the function of costs and losses developed in expressions [2] to [5] to represent mathematically the relationship between inputs (costs and combination of extinction methods) and the combination of these expressed in the area and perimeter affected (

Affected area (

Considering values

Affected area (in hectares):

Direct losses (in US$):

Extinction costs (in US$):

As validation for these parameters for the 5,876 fires, an actual occurrence that took place in the study area was used and simulated with KITRAL to calculate the

These results varied considerably for the characteristics of each fire, especially for the

The efficiency analysis may also be addressed in terms of the proportion of vegetation affected by fire. In the past, direct and indirect losses were estimated according to size categories. Generally the highest amount of damage tended to be concentrated in a reduced number of fires. However it is now appropriate to analyze the impacts in terms of fire size categories. In this analysis, data was separated into five groups in order to minimize the mathematical effect of standard deviation of results for de burnt areas from all data considered. Thus the criteria are applied as follows: Example of a fire of size category 1.01 – 5 ha:

In each of the cases mentioned in

Surface intervals were considered for economic analysis allow an approximation of the degree of combat efficiency to be established, through the inclusion of the following criteria: extinction (combat) costs, value of unaffected resources and economic value of affected resources. This information may be used to determine technical efficiency which is based on the timely control of the fire advance perimeter and which in turn defines the FCS under local conditions where containment activities are carried out.

Here, technical efficiency

It has been particularly difficult to establish a precise approximation of

The comparative analysis of fire spread for fires where there were defense barriers contrasted with the spread of fire in free advance, provides useful references for determining the degree of efficiency in containment works, as well as the potential projection of losses. Thus the application of the superficial contraction factor (

The economic analysis of input variables and fire combat product for the study area and the subsequent results demonstrate that it is possible to establish links between burnt area, extinction costs and economic losses. Therefore in order for the application of the mathematical models proposed here to have a practical benefit, it is necessary to have a very varied and statistically reliable database, which registers information about as many situations as possible regarding the variables used in the construction of these models. Finally, it should be noted that these first results obtained for the study area allow more precise records to be used in further research by broadening the sample base of fires of a greater size, in order to corroborate the technical coefficients associated with the productivity equations proposed here and to maintain its degree of reliability.