BibTeX
@ARTICLE{
         Charpentier2005LSA,
       author = "Isabelle Charpentier and Juan Manuel Esp\'{i}ndola",
       title = "Local Sensitivity Analysis of a Numerical Model of Volcanic Plinian Columns through
         Automatic Differentiation",
       journal = "Mathematical Geology",
       year = "2005",
       volume = "37",
       number = "1",
       pages = "95--113",
       doi = "10.1007/s11004-005-8749-6",
       abstract = "Numerical simulation of geological phenomena are nowadays widely used to understand
         them. A good example are the numerous codes developed to model mass motion in different processes.
         Such models are approximations to the real phenomena because the physical conditions are simplified
         or because the values of the parameters intervening in the modeling are known only approximately.
         For this reason, an obligatory step in the application of these models is the assessment of their
         sensitivity to changes in the parameters. Sensitivity analysis is also required to evaluate the
         influence of the different input variables in the outcome of the model. In general this analysis is
         carried out by repeated computation of the model to different sets of input variables and settings
         of the model. A more fruitful procedure to carry out such analysis can be achieved by automatic
         differentiation. In this paper we illustrate such approach through its application to the model of
         an eruptive plinian column. The results of the analysis allow to assess, in a systematic and
         efficient manner, the relevance of the different boundary values and parameters of the model. The
         analysis reveals the effects on velocity, temperature, gas fraction, radius and ultimately column
         height, by changes in their boundary value (i.e. at the vent). The effect of changes in the value of
         the gas constants, density of pyroclasts and specific heat of the erupted material is also
         evidenced. Alternatively, the results can be regarded as a mean to estimate the values of the
         variables for different set of boundary values without recurring to new runs of the model. Automatic
         differentiation is shown to be a convenient scheme to obtain derivatives of model variables. This
         type of analysis forms in addition the basis for further work in inversion schemes.",
       ad_area = "Geophysics",
       ad_tools = "Odyssee"
}