Stochastic Superparameterization and Multiscale Filtering of Turbulent Tracers

Yoonsang Lee* , Andrew J. Majda and Di Qi
Courant Institute

Data assimilation combines a numerical forecast model and observations to provide the best statistical estimate of the state of interest. In this paper we are concerned with data assimilation of the passive tracer advected in turbulent flows using a low-order forecast model. The turbulent flows which contain anisotropic and inhomogeneous structures such as jets are typical in geophysical turbulent flows in atmosphere and ocean sciences. Stochastic superparameterization, which is a seamless multiscale method developed for large-scale models of atmosphere and ocean models without scale-gap between the resolved and unresolved scales, generates large-scale turbulent velocity fields using a significantly smaller degree of freedoms compared to a direct fine resolution numerical simulation. In a large-scale model of the tracer transport, the tracer is advected by the large- scale velocity field generated by the superparameterization with a parameterization of eddies, an additional eddy diffusion given by an anisotropic biharmonic diffusion. To alleviate the problem of mixed observations of the resolved and unresolved scales, we use an ensemble multiscale data assimilation which provides estimates of the resolved scales using mixed observations. The low-order model is 250 times cheaper than the fine resolution solution and thus enables to increase the number of ensembles for accurate predictions of prior distributions. We test the multiscale data assimilation method for the passive tracer model advected by two-layer quasigeostrophic turbulent flows. Numerical experiments show positive results in the estimation of the resolved scales of the tracer.

*Preference: Oral