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Reining in the butterfly effect: construction of robust global mantle flow trajectories, their assessment through dynamic topography histories via object-based image processing methods derived from meteorology and a case study of Southern African topographic uplift
Reining in the butterfly effect: construction of robust global mantle flow trajectories, their assessment through dynamic topography histories via object-based image processing methods derived from meteorology and a case study of Southern African topographic uplift
In the past, fluid dynamicists obtained analytical solutions for simplified versions of the equations governing mantle flow. However, in recent times, numerical solutions of these equations as well as their graphical representation have been enabled by computational and visualization advances. These developments have led to the construction of high resolution, time-dependent models capable of simulating realistic mantle convection scenarios and creating time trajectories of mantle flow. Two main modelling approaches have been so far employed: mantle circulation models (MCMs) which simulate mantle flow forward in time starting from a randomly chosen past state of the mantle, and the adjoint method which reconstructs past mantle flow starting from an estimate of the mantle present-day state as derived from seismic tomography. In both cases, the starting (initial) conditions are not well known. On the other hand, the mantle is in a category of systems that exhibit chaotic behaviour. The implication of this behaviour is that uncertainties in the initial condition of a time-dependent mantle model grow and propagate through the entire model thus leading to the construction of incorrect mantle flow trajectories. This is referred to as the \textit{butterfly effect}. However, geodynamicists have learned that if knowledge of the surface velocity field is available and if this information is assimilated into a mantle model, it is possible to overcome the butterfly effect and construct robust trajectories. A key geologic observation against which such trajectories can be tested is the Earth's dynamic topography that is increasingly well-mapped by geologists. There is, however, a dearth of high-quality metrics that allow one to compare dynamic topography effectively. Meteorologists have extensively studied forecast verification methods including the Taylor diagram, power ratio, scale-separation techniques and object-based verification and it is possible to adapt these metrics to dynamic topography. In this work, I verify, using synthetic forward models of mantle flow, that velocity assimilation leads to the construction of robust, accurate mantle flow trajectories. I then compute dynamic topography responses from the constructed trajectories and I adapt a number of meteorological forecast verification tools to assess dynamic topography. Importantly, I develop and object-based, image processing metric with which dynamic topography maps can be evaluated. Finally, I apply these metrics to results from a set of state-of-the-art, recently published adjoint simulations of mantle flow. In a twin experiment setup, I use these metrics to explore model performance for a case study focused on the dynamic topography high located in southern Africa. The results of the study show that these metrics provide a powerful way of analysing dynamic topography behaviour of global geodynamic models.
Geophysics, geodynamics, mantle convection, dynamic topography, geology, meteorology, model assessment, forecasting
Taiwo, Ayodeji Abdul-Razaq
2023
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Taiwo, Ayodeji Abdul-Razaq (2023): Reining in the butterfly effect: construction of robust global mantle flow trajectories, their assessment through dynamic topography histories via object-based image processing methods derived from meteorology and a case study of Southern African topographic uplift. Dissertation, LMU München: Faculty of Geosciences
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Abstract

In the past, fluid dynamicists obtained analytical solutions for simplified versions of the equations governing mantle flow. However, in recent times, numerical solutions of these equations as well as their graphical representation have been enabled by computational and visualization advances. These developments have led to the construction of high resolution, time-dependent models capable of simulating realistic mantle convection scenarios and creating time trajectories of mantle flow. Two main modelling approaches have been so far employed: mantle circulation models (MCMs) which simulate mantle flow forward in time starting from a randomly chosen past state of the mantle, and the adjoint method which reconstructs past mantle flow starting from an estimate of the mantle present-day state as derived from seismic tomography. In both cases, the starting (initial) conditions are not well known. On the other hand, the mantle is in a category of systems that exhibit chaotic behaviour. The implication of this behaviour is that uncertainties in the initial condition of a time-dependent mantle model grow and propagate through the entire model thus leading to the construction of incorrect mantle flow trajectories. This is referred to as the \textit{butterfly effect}. However, geodynamicists have learned that if knowledge of the surface velocity field is available and if this information is assimilated into a mantle model, it is possible to overcome the butterfly effect and construct robust trajectories. A key geologic observation against which such trajectories can be tested is the Earth's dynamic topography that is increasingly well-mapped by geologists. There is, however, a dearth of high-quality metrics that allow one to compare dynamic topography effectively. Meteorologists have extensively studied forecast verification methods including the Taylor diagram, power ratio, scale-separation techniques and object-based verification and it is possible to adapt these metrics to dynamic topography. In this work, I verify, using synthetic forward models of mantle flow, that velocity assimilation leads to the construction of robust, accurate mantle flow trajectories. I then compute dynamic topography responses from the constructed trajectories and I adapt a number of meteorological forecast verification tools to assess dynamic topography. Importantly, I develop and object-based, image processing metric with which dynamic topography maps can be evaluated. Finally, I apply these metrics to results from a set of state-of-the-art, recently published adjoint simulations of mantle flow. In a twin experiment setup, I use these metrics to explore model performance for a case study focused on the dynamic topography high located in southern Africa. The results of the study show that these metrics provide a powerful way of analysing dynamic topography behaviour of global geodynamic models.