Integrated spatio-temporal assessment and modelling of complex social–ecological systems is required to address global environmental challenges. However, the computational demands of this modelling are unlikely to be met by traditional Geographic Information System (GIS) tools anytime soon. I evaluated the potential of a range of high-performance computing (HPC) hardware and software tools to overcome these computational barriers. Performance advantages were quantified using a synthetic model. Four tests were compared, using: a) an Arc Macro Language (AML) GIS script on a single central processing unit (CPU); b) Python/NumPy on 1–256 CPU cores; c) Python/NumPy on 1–64 graphics processing units (GPUs) with high-level PyCUDA abstraction (GPUArray); and d) Python/NumPy on 1–64 GPUs with low-level PyCUDA abstraction (ElementwiseKernel). The GIS implementation effectively took 15.5 weeks to run. Python/NumPy on a single CPU core led to a speed-up of 59× compared to the GIS. On a single GPU, speed-ups of 1473× were achieved using GPUArray and 4881× using ElementwiseKernel. Parallel processing led to further performance enhancements. At best, the ElementwiseKernel module in parallel over 64 GPUs achieved a speed-up of 63,643×. Open source tools such as Python applied across a spectrum of HPC resources offer transformational and accessible performance improvements for integrated assessment and modelling. By reducing the computational barrier, HPC can lead to a step change in modelling sophistication, including the better representation of uncertainty, and perhaps even new modelling paradigms. However, migration to new hardware and software environments also has significant costs. Costs and benefits of HPC are discussed and code tools are provided to help others migrate to HPC and transform our ability to address global challenges through integrated assessment and modelling.