Stochastic modelling of unresolved eddy fluxes

A subgrid-scale parameterization scheme motivated by statistical closure theory, but employing statistics obtained from high-resolution direct numerical simulations, is applied to large eddy simulations of two-level quasigeostrophic turbulence on the sphere. It is shown that these parameterizations are consistent with the phenomenology of quasigeostrophic turbulence. The parameterizations consist of 2 × 2 dissipation and stochastic forcing covariance matrices at each wavenumber, with the off-diagonal elements of the matrices representing vertical mixing. Two flow regimes, characterized by their deformation scales, are considered, namely atmospheric and oceanic. In the former, the deformation scale is fully resolved, and the truncation scale is within the enstrophy cascading interial range. In the latter, the deformation scale is not fully resolved, and the truncation scale is within the energy cascading inertial range. It is demonstrated through numerical experiments that both stochastic and deterministic variants of the scheme give comparable results for the energy spectra in the atmospheric regime. In the oceanic regime, the stochastic variant again gives excellent results, but the deterministic variant is found to be numerically unstable.     

Modes of variability of Southern Hemisphere atmospheric circulation estimated by AGCMs

The seasonal mean variability of the atmospheric circulation is affected by processes with time scales from less than seasonal to interannual or longer. Using monthly mean data from an ensemble of Atmospheric General Circulation Model (AGCM) realisations, the interannual variability of the seasonal mean is separated into intraseasonal, and slowly varying components. For the first time, using a recently developed method, the slowly varying component in multiple AGCM ensembles is further separated into internal and externally forced components. This is done for Southern Hemisphere 500?hPa geopotential height from five AGCMs in the CLIVAR International Climate of the Twentieth Century project for the summer and winter seasons. In both seasons, the intraseasonal and slow modes of variability are qualitatively well reproduced by the models when compared with reanalysis data, with a relative metric finding little overall difference between the models. The Southern Annular Mode (SAM) is by far the dominant mode of slowly varying internal atmospheric variability. Two slow-external modes of variability are related to El Ni?o-Southern Oscillation (ENSO) variability, and a third is the atmospheric response to trends in external forcing. An ENSO-SAM relationship is found in the model slow modes of variability, similar to that found by earlier studies using reanalysis data. There is a greater spread in the representation of model slow-external modes in winter than summer, particularly in the atmospheric response to external forcing trends. This may be attributable to weaker external forcing constraints on SH atmospheric circulation in winter.     

Statistical dynamics of internal gravity waves-turbulence

Abstract

Numerical simulations of internal gravity waves-turbulence are carried out for the inviscid, viscous and forced-dissipative two-dimensional primitive equations using the spectral method. Some of the results are compared with the predictions of the eddy damped quasi-normal Markovian (EDQNM) closure for internal waves of Carnevale and Frederiksen, generalized for periodic boundary conditions and possible random forcing and dissipation. The EDQNM reduces to the Boltzman equation of resonant interaction theory in the continuum space limit and as the forcing and dissipation vanish. However, the limit is singular in the sense that as well as conserving total energy, E, and total cross-correlation between the vorticity and buoyancy fields, C, an additional conservation law, viz. z-momentum, P_z , occurs in the limit. This means that the resonant interaction equilibrium (RIE) solution of the Boltzmann equation differs from the statistical mechanical equilibrium (SME) solution of the EDQNM closure.

The statistical stability of the SME and RIE spectra for the primitive equations is tested by integrating the inviscid equations using initial realizations of these spectra with random phases. It is found that E and C are accurately conserved while P_z undergoes large amplitude variations. The approach to equilibrium of initial disequilibrium spectra is monitored by examining the evolution of the entropy. The increase and asymptotic approach to a constant value corresponding to complete chaos is consistent with the behaviour predicted by the EDQNM closure.

For the viscous decay and forced-dissipative experiments, the behaviour of the entropy is also consistent with that predicted by the EDQNM closure. There is approximate equipartition of potential and total kinetic energies throughout the integrations from initial conditions having equal potential and total kinetic energies and as well equal vertical and horizontal energies, but as expected, the ratio of horizontal to vertical kinetic energy increases with time to a value greater than unity.

With Laplacian viscous dissipation and thermal diffusivity, the statistical steady states produced in the forced-dissipative experiments have k^?3 power laws for k≧7. A comparison with the power laws for kinetic energy and passive scalar variance produced in a numerical simulation of the two-dimensional passive scalar problem is also presented.     

Nonlinear stability of baroclinic flows over topography

Abstract

A new nonlinear stability criterion is derived for baroclinic flows over topography in spherical geometry. The stability of a wide class of exact three-dimensional nonlinear steady state solutions subject to arbitrary disturbances is established. The resonance condition, at the highest total wavenumber, for the steady state solutions and the stability criteria for baroclinic flow in the absence of topography provide the boundaries of the regions of stability in the presence of topography. The analogous results for flow on periodic or infinite beta planes incorporating non-orthogonal function large scale flows are also discussed.     

Black-legged kittiwakes as indicators of environmental change in the North Sea: Evidence from long-term studies

Top predators, particularly seabirds, have repeatedly been suggested as indicators of marine ecosystem status. One region currently under pressure from human fisheries and climate change is the North Sea. Standardized seabird monitoring data have been collected on the Isle of May, an important seabird colony in the northwestern North Sea, over the last 10-20 years. Over this period oceanographic conditions have varied markedly, and between 1990 and 1999 a major industrial fishery for sandlance (Ammodytes marinus), the main prey of most seabird species, was prosecuted nearby. Sandlance fishing grounds close to seabird colonies down the east coast of the UK were closed in 2000 in an attempt to improve foraging opportunities for breeding seabirds, particularly black-legged kittiwakes (Rissa tridactyla). Initially this closure seemed to be beneficial for kittiwakes with breeding success recovering to pre-fishery levels. However, despite the ban continuing, kittiwakes and many other seabird species in the North Sea suffered severe breeding failures in 2004. In this paper, we test the predictive power of four previously established correlations between kittiwake breeding success and climatic/trophic variables to explain the observed breeding success at the Isle of May in 2004. During the breeding season, kittiwakes at this colony switch from feeding on 1+ group to 0 group sandlance, and results up until 2003 indicated that availability of both age classes had a positive effect on kittiwake breeding success. The low breeding success of kittiwakes in 2004 was consistent with the late appearance and small body size of 0 group sandlance, but at odds with the two variables likely to operate via 1 group availability (lagged winter sea surface temperature and larval sandlance cohort strength in 2003). The reason for the discrepancy is currently unknown, but analysis of 1 group sandlance body composition indicated that lipid content in 2004 was extremely low, and thus fish eaten by kittiwakes during pre-breeding and early incubation were likely to be of poor quality. Monitoring of reproductive success of kittiwakes, although useful, was clearly not sufficient to tease apart the complex causation underlying the 2004 event. Monitoring programs such as this, therefore, need to be complemented by detailed research to identify the mechanisms involved, and to attribute and predict the effects of natural and human-induced environmental change.     

Teleconnections and predictive characteristics of Australian seasonal rainfall

A new methodology is proposed that allows patterns of interannual covariability, or teleconnections, between the intraseasonal and slow components of seasonal mean Australian rainfall and the corresponding components in the Southern Hemisphere atmospheric circulation to be estimated. In all seasons, the dominant rainfall–circulation teleconnections in the intraseasonal component are shown to have the characteristic features associated with well-known intraseasonal dynamical and statistical atmospheric modes and their relationship with rainfall. Thus, for example, there are patterns of interannual covariability that reflect rainfall relationships with the intraseasonal Southern Annular Mode, the Madden-Julian Oscillation and wavenumber 3 and 4 intraseasonal modes of variability. The predictive characteristics of the atmospheric circulation–rainfall relationship are shown to reside with the slow components. In all seasons, we find rainfall–circulation teleconnections in the slow components related to the El Niño-Southern Oscillation. Each season also has a coupled mode, with a statistically significant trend in the time series of the atmospheric component that appears to be related to recent observed trends in rainfall. The slow Southern Annular Mode also features in association with southern Australian rainfall, especially during austral winter and spring. There is also evidence of an influence of Indian Ocean sea surface temperature variability on rainfall in southeast Australia during austral winter and spring.