Versions of the Tempest Earth-system model with an interface to the ARKode library of additive Runge-Kutta methods from the SUNDIALS suite of solvers. These versions of Tempest+ARKode are used for evaluating approaches to implicit-explicit (IMEX) time integration of a non-hydrostatic atmosphere model using horizontally explicit vertically implicit (HEVI) approaches and splittings which include horizontally implicit terms. Additionally, Python scripts are included for processing and plotting results from Tempest+ARKode. Tempest: https://github.com/paullric/tempestmodel Tempest+ARKode: https://github.com/gardner48/tempestmodel SUNDIALS: https://computation.llnl.gov/projects/sundials The authors of Tempest are Paul Ullrich, Jorge E Guerra, Bryce Adelstein Lelbach, and Antonin Verlet Banide. The authors of the Tempest+ARKode interface and additional horizontally implicit splittings are by David J Gardner, Daniel R Reynolds, Francois P Hamon, and Carol S Woodward.