Abstract
Stochastic methods are a crucial area in contemporary climate research and
are increasingly being used in comprehensive weather and climate prediction
models as well as reduced order climate models. Stochastic methods are used as
subgrid-scale parameterizations as well as for model error representation,
uncertainty quantification, data assimilation and ensemble prediction. The need
to use stochastic approaches in weather and climate models arises because we
still cannot resolve all necessary processes and scales in comprehensive
numerical weather and climate prediction models. In many practical applications
one is mainly interested in the largest and potentially predictable scales and
not necessarily in the small and fast scales. For instance, reduced order
models can simulate and predict large scale modes. Statistical mechanics and
dynamical systems theory suggest that in reduced order models the impact of
unresolved degrees of freedom can be represented by suitable combinations of
deterministic and stochastic components and non-Markovian (memory) terms.
Stochastic approaches in numerical weather and climate prediction models also
lead to the reduction of model biases. Hence, there is a clear need for
systematic stochastic approaches in weather and climate modelling. In this
review we present evidence for stochastic effects in laboratory experiments.
Then we provide an overview of stochastic climate theory from an applied
mathematics perspectives. We also survey the current use of stochastic methods
in comprehensive weather and climate prediction models and show that stochastic
parameterizations have the potential to remedy many of the current biases in
these comprehensive models.
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