Comparative soil CO₂ flux measurements and geostatistical estimation methods on Masaya volcano, Nicaragua

Abstract

We present a comparative study of soil CO₂ flux ($F_{{\rm CO}_2 }$) measured by five groups (Groups 1–5) at the IAVCEI-CCVG Eighth Workshop on Volcanic Gases on Masaya volcano, Nicaragua. Groups 1–5 measured $F_{{\rm CO}_2 }$ using the accumulation chamber method at 5-m spacing within a 900 m² grid during a morning (AM) period. These measurements were repeated by Groups 1–3 during an afternoon (PM) period. Measured $F_{{\rm CO}_2 }$ ranged from 218 to 14,719 g m⁻² day⁻¹. The variability of the five measurements made at each grid point ranged from ±5 to 167%. However, the arithmetic means of fluxes measured over the entire grid and associated total CO₂ emission rate estimates varied between groups by only ±22%. All three groups that made PM measurements reported an 8–19% increase in total emissions over the AM results. Based on a comparison of measurements made during AM and PM times, we argue that this change is due in large part to natural temporal variability of gas flow, rather than to measurement error. In order to estimate the mean and associated CO₂ emission rate of one data set and to map the spatial $F_{{\rm CO}_2 }$ distribution, we compared six geostatistical methods: arithmetic and minimum variance unbiased estimator means of uninterpolated data, and arithmetic means of data interpolated by the multiquadric radial basis function, ordinary kriging, multi-Gaussian kriging, and sequential Gaussian simulation methods. While the total CO₂ emission rates estimated using the different techniques only varied by ±4.4%, the $F_{{\rm CO}_2 }$ maps showed important differences. We suggest that the sequential Gaussian simulation method yields the most realistic representation of the spatial distribution of $F_{{\rm CO}_2 }$, but a variety of geostatistical methods are appropriate to estimate the total CO₂ emission rate from a study area, which is a primary goal in volcano monitoring research.

Appendices

Appendix I: Data Analyses

MVU Estimators

The mean of the lognormal distribution was estimated using the MVU estimator $\hat \mu$ according to

$$\hat \mu = \exp \left( {\bar y + \frac{{s_y^2 }}{2}} \right),$$

(2)

where $\bar y$ is the arithmetic mean of the n log-transformed values y _i , calculated according to

$$\bar y = \frac{1}{n}\sum\limits_{i = 1}^n {y_i },$$

(3)

and $s_y^2$ is the variance of the n transformed values, calculated according to

$$s_y^2 = \frac{1}{{n - 1}}\sum\limits_{i = 1}^n {(y_i - \bar y)^2 }$$

(4)

(e.g., Gilbert 1987). The variance of the lognormal distribution was estimated using the MVU estimator $\hat \sigma$ according to

$$\hat \sigma ^2 = \hat \mu ^2 \left[ {\exp \left( {s_y^2 } \right) - 1} \right].$$

(5)

RB

The RB estimator $\hat z(u)$ computes the value z at unsampled location u (a vector of spatial coordinates) as a weighted linear combination of multiquadric radial basis functions associated with surrounding observations:

$$\hat z(u) = \sum\limits_{i = 1}^n {w_i } (u)C(u_i - u), $$

(6)

where n is the number of sampled points in the data set,

$$C(u_i - u) = ((u_x - u_{ix} )^2 + (u_y - u_{iy} )^2 + e^2 )^{0.5} $$

(7)

is a basis function of the distance on the x-y plane between u and u _i modified by the arbitrary nonnegative constant e, and w _i is the weight assigned to each basis function (e.g., Watson 1992). The weights are found through the solution of a system of linear equations:

$$\sum\limits_{j = 1}^n {w_j (u)C(u_i - u_j ) + \mu = z(u_i )} ,\quad i = 1, \ldots ,n(u) $$

(8)

and

$$\sum\limits_{j = 1}^n {w_j (u)} = 0, $$

(9)

where μ is the Lagrange parameter to satisfy the condition that the weights sum to zero (Eq. (9)).

OK

OK estimates the value $\hat z(u)$ at unsampled location u (a vector of spatial coordinates) as a weighted linear combination of surrounding observations:

$$\hat z(u) = \sum\limits_{i = 1}^n {w_i (u)z(u_i )} , $$

(10)

where n is the number of sampled points in the data set, z(u _i ) is the value of the sampled point, and w _i is the weight assigned to each sampled point (e.g., Isaaks and Srivastava 1989). The weights are found through the solution of a system of linear equations:

$$\sum\limits_{j = 1}^n {w_j (u)\gamma (u_i - u_j ) + \mu } = \gamma (u_i - u),\quad i = 1, \ldots ,n(u) $$

(11)

and

$$\sum\limits_{j = 1}^n {w_j (u)} = 1, $$

(12)

where γ(u _i −u _j ) is the semivariogram model evaluated at the distance between points i and j and μ is the Lagrange parameter. Constraining the weights to sum to unity (Eq. (12) ) maintains the unbiasedness of the estimator. The spherical semivariogram model equation is

$$\gamma (u_i - u_j ) = \left\{ {\begin{array}{*{20}c} {1.5\frac{{u_i - u_j }}{a} - 0.5\left( {\frac{{u_i - u_j }}{a}} \right)^3 } \hfill & {{\rm if}\,(u_i - u_j ) \le a} \hfill \\ s \hfill & {{\rm if}\,(u_i - u_j ) > a} \hfill \\ n \hfill & {(u_i - u_j ) = 0} \hfill \\ \end{array}} \right. $$

(13)

where s, a, and n are the sill, range, and nugget effect, respectively, each determined from the statistical properties of the sampled data (e.g., Isaaks and Srivastava 1989). Additionally, the semivariogram can be used to calculate the estimation variance σ ²(u) as

$$\sigma ^2 (u) = \sum\limits_{i = 1}^{n(u)} {w_i \gamma (u_i - u) - u(\mu )} . $$

(14)

Appendix II: Recommendations for Accumulation Chamber $F_{{\rm CO}_2 }$ Measurements in Volcanic-Hydrothermal Environments

• 1. The IRGA should be calibrated with standard gases prior to $F_{{\rm CO}_2 }$ measurement, according to the suggestions of the IRGA manufacturer.

• 2. Water must be removed from the accumulation chamber air using an in-line desiccant (e.g., Mg(ClO₄)₂ or molecular sieve) before the air enters the IRGA.

• 3. Soil disturbance should be minimized during placement of the accumulation chamber on the soil surface to create a measurement footprint. A horizontally flat area should also be selected if possible. If necessary (e.g., an uneven soil surface is present), the researcher should create all measurement footprints within the survey area in a given order, and then return to the footprints to make the $F_{{\rm CO}_2 }$ measurements in the same order. This protocol should allow ample time for re-equilibration of gas flow following initial soil disturbance.

• 4. When the chamber is placed on the soil for $F_{{\rm CO}_2 }$ measurement, a seal must be obtained between the accumulation chamber and the soil to prevent chamber-atmosphere gas exchange.

• 5. Once the [CO₂]–t curve is obtained, the researcher should select the linear segment of the curve, the slope of which is used to calculate $F_{{\rm CO}_2 }$. The period of data collection must be sufficient to allow for adequate mixing of the atmospheric gas with the soil gas. The amount of time required for this to occur varies with $F_{{\rm CO}_2 }$. Short-term (a few seconds or less) changes in the [CO₂]–t curve should be ignored.

• 6. After a $F_{{\rm CO}_2 }$ measurement has been completed, the accumulation chamber measurement system should be flushed with atmospheric air before commencing a new measurement.

• 7. Soil temperature should be measured in conjunction with each $F_{{\rm CO}_2 }$ measurement.

• 8. The $F_{{\rm CO}_2 }$ survey should be conducted under meteorologically stable conditions. In particular, $F_{{\rm CO}_2 }$ measurements should not be made during and immediately following periods of rainfall.

• 9. To obtain datasets suitable for consistent geostatistical treatment, $F_{{\rm CO}_2 }$ measurements should be homogeneously distributed throughout the survey area (e.g., along measurement grids). Spatial clustering of measurements should be avoided when possible. Moreover, $F_{{\rm CO}_2 }$ measurements should be made in both areas of anomalously high $F_{{\rm CO}_2 }$ and background areas lacking CO₂ emissions of deep volcanic-hydrothermal origin.