Publication: A study of the entrainment function in models of Plinian columns: characteristics and calibration
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A study of the entrainment function in models of Plinian columns: characteristics and calibration

- Article in a journal -
 

Area
Geophysics

Author(s)
I. Charpentier , J. M. Espindola

Published in
Geophysical Journal International

Year
2005

Abstract
Many of the processes involved in volcanic eruptive columns may be described through physical models based on conservation laws in which a physical parametrization called the entrainment function plays an important role. The solution of inverse problems and the estimation of the characteristics of ancient eruptions are among the purposes of these models that require a better knowledge of the characteristics and properties of this function. The first part of the study shows that the three usual shapes chosen for this function yield apparently the same behaviour of the column. However, we prove that a piecewise constant shape may be unsuitable in optimization processes based on gradient methods. It also turns out that the parameters defining the entrainment function cannot be considered constant. In the second part of the paper, the unique parameter of the remaining two functions is viewed as dependent on the boundary conditions and specified with respect to them. A calibration of the entrainment function with respect to real data is achieved through a power law established between column height and discharge, the latter being related to velocity, radius and bulk density at the vent. According to a discussion on eruptive data, the construction of a mathematical parametrization for epsilon, with respect to boundary conditions and the heights of the vent and the tropopause, appears to be an unwarranted and difficult task since any new addition to the observed data will definitely modify the power law. A 4-D database covering the range of boundary conditions usually found in Plinian eruptions, together with an interpolation operator, are constructed in order to provide an approximated parameter for any set of boundary conditions in the range considered. Numerical results with a database of dimension 9(4) show that the approximated parameter allows one to recover column height very accurately.

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BibTeX
@ARTICLE{
         Charpentier2005Aso,
       doi = "10.1111/j.1365-246X.2005.02541.x",
       ad_area = "Geophysics",
       ad_tools = "Odyssee",
       ad_theotech = "Tangent",
       author = "Charpentier, I. and Espindola, J.M.",
       title = "A study of the entrainment function in models of {P}linian columns: characteristics
         and calibration",
       journal = "Geophysical Journal International",
       year = "2005",
       volume = "160",
       number = "3",
       pages = "1123--1130",
       month = "mar",
       abstract = "Many of the processes involved in volcanic eruptive columns may be described
         through physical models based on conservation laws in which a physical parametrization called the
         entrainment function plays an important role. The solution of inverse problems and the estimation of
         the characteristics of ancient eruptions are among the purposes of these models that require a
         better knowledge of the characteristics and properties of this function. The first part of the study
         shows that the three usual shapes chosen for this function yield apparently the same behaviour of
         the column. However, we prove that a piecewise constant shape may be unsuitable in optimization
         processes based on gradient methods. It also turns out that the parameters defining the entrainment
         function cannot be considered constant. In the second part of the paper, the unique parameter of the
         remaining two functions is viewed as dependent on the boundary conditions and specified with respect
         to them. A calibration of the entrainment function with respect to real data is achieved through a
         power law established between column height and discharge, the latter being related to velocity,
         radius and bulk density at the vent. According to a discussion on eruptive data, the construction of
         a mathematical parametrization for epsilon, with respect to boundary conditions and the heights of
         the vent and the tropopause, appears to be an unwarranted and difficult task since any new addition
         to the observed data will definitely modify the power law. A 4-D database covering the range of
         boundary conditions usually found in Plinian eruptions, together with an interpolation operator, are
         constructed in order to provide an approximated parameter for any set of boundary conditions in the
         range considered. Numerical results with a database of dimension 9(4) show that the approximated
         parameter allows one to recover column height very accurately.",
       issn = "0956-540X",
       id = "Charpentier2005Aso"
}


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