Science at the policy interface: volcano-monitoring technologies and volcanic hazard management

Abstract

This paper discusses results from a survey of volcanologists carried out on the Volcano Listserv during late 2008 and early 2009. In particular, it examines the status of volcano monitoring technologies and their relative perceived value at persistently and potentially active volcanoes. It also examines the role of different types of knowledge in hazard assessment on active volcanoes, as reported by scientists engaged in this area, and interviewees with experience from the current eruption on Montserrat. Conclusions are drawn about the current state of monitoring and the likely future research directions, and also about the roles of expertise and experience in risk assessment on active volcanoes; while local knowledge is important, it must be balanced with fresh ideas and expertise in a combination of disciplines to produce an advisory context that is conducive to high-level scientific discussion.

Appendix

Preliminary tests

Initial exploration of the survey dataset was carried out to ascertain which parts were normally distributed (parametric tests are only appropriate for normally distributed datasets). Initially, histograms were examined for each variable (i.e. each question), and the skewness and kurtosis were calculated. These were rated as significant for the 5% level at z = 1.96 or greater (Field 2000). Kolmogorov–Smirnov and Shapiro–Wilk tests were carried out to compare the data to a normal distribution, and 5% significance was used to identify non-normally distributed datasets. Homogeneity of variance was assessed using Levene’s statistic, which looks for equal variances—an assumption of many parametric tests.

T tests

T tests are used to compare two means. They may be used either with different groups of participants (independent t test), or with the same group (dependent t test). It is the latter that have been used in this paper, since the same group of volcanologists answered all the questions, and these are discussed below. T tests are based on the null hypothesis that there is no systematic variation between the participants. The equation for the dependent t test is then

$$ t = D - \mu \_D/\left( {s\_D/\surd N} \right) $$

where, D is the mean difference between samples, μD is the difference expected assuming the null hypothesis, sD is the standard deviation and N is the number of samples. Dividing the standard deviations by the root of the number of samples calculates the estimated standard error. The t test thus measures the systematic variation in the samples relative to the unsystematic variation, therefore testing the model.

The z score and effect size

The z score is a way of approximating the normal distribution so that the deviations from the mean can be compared:

$$ {\text{z = }}\left( {{\text{X}} - \overline X } \right)/{\text{s}} $$

where, X is a data point, $\overline X$ is the mean of the population, and s is the standard deviation of the population.

The effect size, r, is calculated from the t statistic and the degrees of freedom:

$$ r = ({t^2}/\left( {{t^2} + df} \right) = z/\surd N $$

where, t is the t statistic, df is the number of degrees of freedom, z is the z score and N is the number of samples. A small effect is defined as r > 0.1, and a large one by r > 0.5 (Field 2000).

Non-parametric tests

Data that were not normally distributed—largely those that reflected strong opinions—were tested according to a variety of non-parametric methods. The Mann–Whitney test is similar to the independent t test and compares the median between two groups. It is thus only used for comparing two groups of data, but can be used as a test for the results of a Kruskal–Wallis test, in order to apply the Bonferroni correction (using a significance value of 0.05/number of tests). It is denoted here by ‘U’. The Kruskal–Wallis test, denoted by ‘H’, is the non-parametric equivalent of the Analysis of Variance—it compares the medians of several groups.

$$ H = \frac{{\left( {\frac{{12}}{{N\left( {N + 1} \right)}}} \right)\sum\nolimits_{{i = 1}}^k {R_i^2} }}{{{n_i}}} - 3\left( {N + 1} \right) $$

Here, R is the sum of ranks for each group, N is the total sample size and n is the sample size of a particular group. The Jonckeheere–Terpstra test for trends takes the analysis a step further, looking for trends within the ranked medians. It has been used where the groups are likely to impact the ordering of medians, and a value greater than 1.65 is considered significant (one tailed).

Spearman’s ρ is a non-parametric correlation that works by ranking the data and then applying the equation for Pearson’s correlation coefficient, R.

$$ R = {{\rm cov}_{{xy}}}/{s_x}{s_y} = \Sigma \left( {{\text{xi}} - x} \right)\left( {{\text{yi}} - y} \right)/\left( {N - 1} \right){s_x}{s_y} $$

Where this test has significance, it suggests that two variables are related to one another, and the sign of that relation. It does not however imply causality.

Factor analysis

Factor analysis seeks out latent variables within a multivariate dataset: these are underlying factors that influence the distribution of the data, but are not themselves measured variables. It works by calculating the correlation matrix between the variables and its eigenvalues, looking to maximise the variance accounted for by each corresponding eigenvector. The process is initially carried out as a principal components analysis, but with a specific number of factors being extracted: it is common practice to quote eigenvalues >1, in accordance with Kaiser’s criterion. The resulting component matrix is then rotated to ensure ease of interpretation. This study used a varimax orthogonal rotation, as it was considered unlikely that there would be correlation between factors. Stevens (1992) suggests that for a sample size of 150, a loading of more than about 0.4 is significant.

Reliability analysis

The reliability of the scales used in the questionnaire has been calculated using Cronbach’s alpha:

$$ \alpha = N2\overline {\text{Cov}} /\left( {\Sigma s_i^2 + \Sigma {\text{Co}}{{\text{v}}_i}} \right) $$

This is a measure of the magnitude of the variance and covariance in the data, weighted according to the number of items and the average covariance. There is some debate over the acceptable threshold, with 0.7 taken by many authors. However, it should be noted that reverse-scaled items or items measuring slightly different variables will lower the value of the alpha since it assumes that the items are all measuring the same thing. Thus, it is realistic to expect that some sets of variables will give a lower alpha than 0.7. For some parts of this questionnaire, Cronbach’s alpha was calculated using a normalised scale—the ratings given by the respondents were reversed in order to align the object of the scale as far as possible.