No abstract

The intent of this paper is to encourage improved numerical implementation of land models. Our contributions in this paper are two-fold. First, we present a unified framework to formulate and implement land model equations. We separate the representation of physical processes from their numerical solution, enabling the use of established robust numerical methods to solve the model equations. Second, we introduce a set of synthetic test cases (the laugh tests) to evaluate the numerical implementation of land models. The test cases include storage and transmission of water in soils, lateral sub-surface flow, coupled hydrological and thermodynamic processes in snow, and cryosuction processes in soil. We consider synthetic test cases as “laugh tests” for land models because they provide the most rudimentary test of model capabilities. The laugh tests presented in this paper are all solved with the Structure for Unifying Multiple Modeling Alternatives model (SUMMA) implemented using the SUite of Nonlinear and DIfferential/Algebraic equation Solvers (SUNDIALS). The numerical simulations from SUMMA/SUNDIALS are compared against (1) solutions to the synthetic test cases from other models documented in the peer-reviewed literature; (2) analytical solutions; and (3) observations made in laboratory experiments. In all cases, the numerical simulations are similar to the benchmarks, building confidence in the numerical model implementation. We posit that some land models may have difficulty in solving these benchmark problems. Dedicating more effort to solving synthetic test cases is critical in order to build confidence in the numerical implementation of land models.

Modeling the evolution of composition in a convecting mantle is difficult since the associated chemical diffusivity is very small. Consequently, compositional evolution is often modeled using the advection equation which is prone to overdiffusion and spurious oscillations unless special numerical schemes are employed. Similar errors can also occur while modeling the evolution of temperature, since mantle convection is advection dominated. One numerical scheme designed to minimize such errors is the tracer ratio method, in which Lagrangian tracers are used to track each composition in the system in addition to carrying local temperature values that are time dependent. However, tracer spacing may become very uneven during evolution, which can contribute to errors in mass and energy conservation. In this study, a tracer repositioning algorithm designed to promote even tracer coverage is presented and tested using over 400 calculations in a large thermal Rayleigh number/buoyancy ratio parameter space. In particular, the effect of tracer repositioning on mass and energy conservation errors is examined. In most cases, we find that energy errors are roughly an order of magnitude less than mass errors, regardless of tracer repositioning. However, in situations with substantial entrainment of compositionally distinct material, mass errors can be reduced by up to an order of magnitude if tracers are repositioned during model evolution. We also find that for a fixed buoyancy ratio, entrainment of basal material decreases as the thermal Rayleigh number increases.

Shear wave travel times in the Earth's deep mantle reveal broad steep‐sided seismologically distinct provinces lying on the core‐mantle boundary. The longevity and permanence of the two large principal provinces, located below the sites of present‐day Africa and the Pacific Ocean, have become a matter of great interest. Examination of the flood basalt record and kimberlite eruption dating suggests the presence of these provinces may disclose a deep mantle component with a compositionally distinct origin that plays a role in the generation of mantle plumes at preferred locations. By extension, the presence of these provinces may affect the supercontinent cycle. Implementing a mantle convection model featuring distinct continental lithosphere and a compositionally anomalous and intrinsically dense (CAID) component, we study the distribution and mobility of naturally forming, compositionally distinct provinces and their impact on model supercontinent assembly. We employ 2‐D Cartesian geometry calculations of thermochemical convection with extremely low compositional diffusion to model Earth‐like convective vigor on a global scale and find that an intrinsically dense mantle component generally aggregates into one or two broad provinces. The positions of the provinces are time dependent, but in many of our calculations the province locations are characterized by periods of fixity that reach several hundred million years. Eras of province and associated plume fixity are punctuated by periods of relatively rapid migration. A correlation between supercontinent position and the locations of CAID provinces is not supported by our findings. However, we find that the frequency of supercontinent assemblies increases when CAID provinces are present.

[1] A number of studies examining the influence of plates on mantle convection have concluded that planform and thermal structure are strongly influenced by plate geometry. However, studies that have modeled evolving plate geometries over periods greater than a mantle transit time indicate that mantle planform may not correlate with plate geometry. To assess the influence of plate boundary motion on mantle convection, we investigate convection in a plane-layer system featuring four polygon-shaped plates. New to this work, plate boundaries are moved at specified velocities that are consistent with the velocities associated with the convection driven flow in the system interior. Plate velocities are time dependent and use a force-balance method to ensure that plate motion neither drives nor resists the convection. The influence of the plate boundary motion on convection is compared in models featuring viscosity profiles that increase by factors of 30, 90, 300, and 1000 across the lower mantle. The effective Rayleigh numbers of these systems are held at a nearly constant value. We find that convection planform is sensitive to both divergent and convergent plate boundary motion for a system featuring as much as a 90-fold contrast in viscosity between the upper and lower mantle. However, as the viscosity stratification is increased, the response of the convection planform to the motion of divergent plate boundaries diminishes. In contrast, we find planform and specifically plume positions respond to the motion of convergent plate boundaries even when the lower mantle viscosity is 1000 times greater than the upper mantle viscosity.