The multiple time scales over which physical processes interact in the global atmospheric climate models is a challenging problem for numerically evolving climate simulations. High performance computation offers a platform that can resolve climate simulations at unprecedented scales, allowing scientists to study climate processes that are out of reach to other forms of simulation. However, computing on these platforms requires special consideration in designing time evolving algorithms that can maintain throughput under the natural drag on simulation speed as well as the desirable properties of lowering power consumption per computation and rising model resolution. Implicit solvers can provide efficiency with scalable, optimized preconditioning, by enabling the simulation time step to be commensurate with the physical process being studied. We will demonstrate fully implicit methods for CAM-SE, running on GPUs, linking to the TRILINOS environment. The benefits of our approach are that climate scientists will be able to run climate simulations on GPU high performance computing systems, at time steps constrained by physical processes and not artificially imposed limits due to model resolution, with access to the latest solvers developed by a large and active community of experts.