Mantle Flow Trajectories in the Presence of Poorly Constrained Initial Conditions: Analysis of an Ensemble of Models

A crucial goal in geodynamics is the development of time-dependent earth models so that poorly known mantle convection parameters can be tested against observables gleaned from the geologic record. To this end one must construct model trajectories to link estimates of the current heterogeneity state to future or past flow structures via forward or inverse mantle convection models. Unfortunately, the current heterogeneity state which is derived from seismic imaging methods is subject to substantial uncertainty due to the finite resolution of seismic tomography. These uncertainties are likely to considerably affect the computed flow trajectory, in what is known as the butterfly effect. Here we study mantle convection models to assess the effects of varying initial conditions on the evolution of mantle flow. We perform twin experiments (Lorenz 1965), that is, we compute convection calculations with identical flow parameters but different initial temperature fields. A base temperature field is generated by allowing a mantle convection calculation to evolve until a statistical steady state is reached. This temperature field is then used to initialize our reference case. We proceed to modify this reference temperature field in a number of different forms to reflect tomographic choices of damping and smoothing. In all cases we track the divergence of the perturbed models from the reference model. Furthermore, we test the efficiency of surface velocity assimilation, following from the work of Colli et al (2015), in locking two convecting systems and driving their divergence to a minimum.

 

We also introduce a framework for the comparison of model output with geological observables. To this end, we perform a comparison between the dynamic topography maps of our reference and perturbed models. We calculate simple traditional metrics such as RMSE, correlation, difference fields and Taylor diagrams. Such traditional grid-point based error measures, however, suffer from the “double-penalty” problem and as such we introduce scale-decomposition methods that allow a computation of correlation, RMSE and ratios of variances for every spatial scale (see Surcel et al (2015), Casati et al (2005) for examples). Furthermore, we introduce object-based verification measures that identify and match uplift and subsidence objects in the dynamic topography maps for both reference and perturbed models similar to what a human observer would identify. Borrowing from the wealth of work in meteorology, we calculate SAL scores (Wernli et al 2008) and a Critical Success Index (Schaefer 1990). Finally, for successfully matched objects, a Procrustes shape analyis (Michaes et al 2007) is performed to compare the similarities in area, shape, orientation and intensity, after which a final score is calculated based on these properties. We believe that the measures introduced here represent the next step in geodynamics as mantle convection models become increasingly complex and more focus is placed on matching model observations with the geological record.