Hannah Christensen (she/her)

Abstract:

The ‘signal-to-noise paradox’ for seasonal forecasts of the winter NAO is often described as an ‘underconfident’ forecast and measured using the ratio-of-predictable components metric (RPC). However, comparison of RPC with other measures of forecast confidence, such as spread-error ratios, can give conflicting impressions, challenging this informal description. We show, using a linear statistical model, that the ‘paradox’ is equivalent to a situation where the reliability diagram of any percentile forecast has a slope exceeding 1. The relationship with spread-error ratios is shown to be far less direct. We furthermore compute reliability diagrams of winter NAO forecasts using seasonal hindcasts from the European Centre for Medium-range Weather Forecasts and the UK Meteoro logical Office. While these broadly exhibit slopes exceeding 1, there is evidence of asymmetry between upper and lower terciles, indicating a potential violation of linearity/Gaussianity. The limitations and benefits of reliability diagrams as a diagnostic tool are discussed.

Abstract:

High-resolution numerical models have been used to develop statistical models of the enhancement of sea surface fluxes resulting from spatial variability of sea-surface wind. In particular, studies have shown that the flux enhancement is not a deterministic function of the resolved state. Previous studies focused on single geographical areas or used a single high-resolution numerical model. This study extends the development of such statistical models by considering six different high-resolution models, four different geographical regions, and three different ten-day periods, allowing for a systematic investigation of the robustness of both the deterministic and stochastic parts of the data-driven parameterization. Results indicate that the deterministic part, based on regressing the unresolved normalized flux onto resolved scale normalized flux and precipitation, is broadly robust across different models, regions, and time periods. The statistical features of the stochastic part of the model (spatial and temporal autocorrelation and parameters of a Gaussian process fit to the regression residual) are also found to be robust and not strongly sensitive to the underlying model, modelled geographical region, or time period studied. Best-fit Gaussian process parameters display robust spatial heterogeneity across models, indicating potential for improvements to the statistical model. These results illustrate the potential for the development of a generic, explicitly stochastic parameterization of sea-surface flux enhancements dependent on wind variability.

Abstract:

Numerical computer models play a key role in Earth science. They are used to make predictions on timescales ranging from short-range weather forecasts to multi-century climate projections. Computer models are also used as tools to understand the past, present, and future climate system, enabling numerical experiments to be carried out to explore physical processes of interest. To understand the behavior of these models, their formulation must be appreciated, including the simplifications and approximations employed in developing the model code.

Foremost among these approximations are the parametrization schemes used to represent subgrid scale physical processes. A useful mathematical formulation of parametrization often involves Reynolds averaging, whereby a flow described by the Navier–Stokes equations is separated into a slow, resolved component and a fast, unresolved component. On performing this decomposition, the component representing the unresolved, fast processes is shown to impact the resolved scale flow: It is this component that a parametrization seeks to represent.

Parametrization schemes encode the understanding of the salient physics needed to describe processes in the atmosphere and ocean and other components of the Earth system, such as land and ice. For example, finding the relationship between the Reynolds stresses and the mean fields of the system is the turbulence closure problem, which is common to both atmospheric and oceanic numerical models. Atmospheric parametrization schemes include those representing radiation, clouds and cloud microphysics, moist convection, gravity waves, and the boundary layer (which encompasses a representation of turbulent mixing). In the ocean, eddy processes must also be parametrized, including stirring and mixing due to both sub-mesoscale and mesoscale eddies. The similarities between the parametrization problem in atmospheric and oceanic models facilitate transfer of knowledge between these two communities, such that promising avenues of research in one community can in principle readily be adapted and adopted by the other.