A programme of research is described which will revolutionise the mathematical formulation of comprehensive Earth-System models, potentially leading to a step-change improvement in the reliability of our predictions of climate change, both globally and regionally. This programme of research is intended to make climate simulations more consistent both with the multi-scale nature of climate, and with related scaling symmetries of the partial differential equations which govern climate. This will be achieved by moving away from the traditional deterministic approach to the closure problem in computational fluid dynamics, and towards a more novel description of physical processes near and below the truncation scale of climate models, using contemporary nonlinear stochastic-dynamic mathematics. A detailed technical account of how this will be achieved in given in the full proposal. Leveraged on the proposer's many contacts in Europe and around the world, the aim of the proposed research is to produce the world's first Probabilistic Earth System Model. The consequences are enormous: a comprehensive climate model with reduced biases against observations, a model which will be capable of producing estimates of uncertainty in its own predictions, and a model which can make use of emerging energy-efficient probabilistic processor hardware. key to practical success as we approach the era of the exascale supercomputer. The development of the prototype Probabilistic Earth-System Model will open a new era of international scientific collaboration on climate model development, and has the potential to influence climate policy, on mitigation, adaptation and on geoengineering, a the highest governmental and intergovernmental levels.