## 1. Introduction

[2] Recently, a great interest has been addressed to the study of CO_{2} Earth degassing. There are many objectives to such studies, for example, the definition of the relations between the flux and the tectonic structures [*Etiope*, 1999; *Etiope et al.*, 1999; *Lewicki and Brantley*, 2000], the quantification of deeply derived CO_{2} release to the atmosphere in the framework of the carbon global budget [*Allard et al.*, 1991; *Brantley and Koepenick*, 1995; *Seward and Kerrick*, 1996; *Kerrick et al.*, 1995; *Marty and Tolstikhin*, 1998; *Williams et al.*, 1992], and the study of volcanic degassing. In particular, numerous studies have been focused on the CO_{2} soil diffuse degassing from quiescent active volcanoes [*Brombach et al.*, 2001; *Chiodini et al.*, 2001, 1996, 1998; *Hernandez et al.*, 1998; *Gerlach et al.*, 2001; *Salazar et al.*, 2001; *Farrar et al.*, 1995]. Most of these studies showed that gas is not released uniformly from the whole volcanic apparatus, but rather from relatively restricted regions, which were named diffuse degassing structures (DDS) [*Chiodini et al.*, 2001]. Moreover, quantitative estimates of hydrothermal-volcanic gas released from DDS highlighted the importance of gas and thermal energy released by DDS in the mass and energetic balance of quiescent volcanic systems [*Chiodini et al.*, 2001]. Independently from the specific aims of investigations, the mapping of DDS and the quantification of the amount of released CO_{2} can be considered common objectives of all these studies.

[3] Mapping of CO_{2} fluxes from soil was mainly performed by use of interpolation algorithms, generally kriging [e.g., *Bergfeld et al.*, 2001; *Chiodini et al.*, 1996, 1998, 2001; *Rogie et al.*, 2001; *Gerlach et al.*, 2001]. The kriging algorithm is focused in providing the “best,” defined in a minimized least squares sense, hence unique, local estimate of a variable without specific regard to the resulting spatial statistics of the all estimates taken together [*Deutsch and Journel*, 1998], producing a set of estimated values at the unsampled locations whose variogram does not match that of the original data. Moreover, kriging smoothes out the extreme extrapolated values, with small values being overestimated while large values are underestimated, hiding the pattern of high values, which is important in our applications to define degassing structures.

[4] Total CO_{2} releases were usually calculated either by multiplying the arithmetic mean value of CO_{2} fluxes by the surveyed areas, or by applying volume and area integration algorithms to the grids produced to contour the CO_{2} flux, or by a graphical statistical approach (GSA) independent from any interpolation technique (described by *Chiodini et al.* [1998]). Together with the quantification of total CO_{2} release, the definition of the related uncertainty is essential, especially in volcanic surveillance for the recognition of anomalous states. Kriging provides only an incomplete measure of local accuracy, except if a Gaussian model for errors is assumed, and no indication of the accuracy if several points are considered together [*Deutsch and Journel*, 1998]. On the contrary GSA approach allows the definition of a confidence interval for the estimation, but this calculation does not take into account the spatial correlation between the data, resulting generally in an overestimation of the uncertainty. This overestimation of the uncertainty is particularly unsuitable for monitoring purposes, since smaller uncertainty makes it possible to detect smaller variations.

[5] The aim of this work is the application of stochastic simulation algorithms to soil gas flux data. This approach is becoming common and preferred to traditional interpolation algorithms in the soil science, where the spatial variability of the measured attributes has to be preserved [*Goovaerts*, 2000], for example, in the definition and characterization of contaminated soils and groundwater [*Goovaerts*, 1997, 1999b, 2001, and references therein; *Lin and Chang*, 2000; *Lin et al.*, 2001; *Istok and Rautman*, 1996] and for assessment of corn yield risks connected to soil strength/compaction [*Lapen et al.*, 2001].

[6] The basic idea of stochastic simulation is to generate a set of equiprobable representations (realizations) of the spatial distribution of the attribute, all reproducing reasonably the global statistic and spatial features of data samples (i.e., sample histogram and semivariogram model), instead of producing a single representation that yields the minimum error variance at each location. The ensemble of these realizations is thus an explicit representation of the uncertainty associated with our conceptual understanding of the single, but unknown reality [*Rautman and Istok*, 1996]. According to *Goovaerts* [2001], differences among many simulated maps have been used as a measure of the uncertainty.

[7] In this paper a stochastic simulation algorithm is applied to 5 data set of soil CO_{2} fluxes measured in different volcanic and nonvolcanic degassing areas, with the objective of mapping the degassing areas, i.e., defining the diffuse degassing structures, and evaluating the total emitted CO_{2} with the associated uncertainty. Moreover, we try to define a reasonable criterion for the definition of an “opportune” sampling design.