On Finite Rank Deformations of Wigner Matrices II: Delocalized Perturbations

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices. We assume that the matrix entries have finite fourth moment and extend the results by Capitaine, Donati-Martin, and F\'eral for perturbations whose eigenvectors are delocalized.Comment: We explained some proofs in greater detail, corrected several small misprints, and updated the bibliograph

An assessment of the surface turbulent heat fluxes from the NCEP reanalysis over western boundary currents

With the completion of the NCEP-NCAR and ECMWF reanalyses there are now global representations of air-sea surface heat fluxes with sufficient spatial and temporal resolution to be useful in characterizing the air-sea interaction associated with individual weather systems, as well as in developing global-scale oceanic heat and moisture budgets. However, these fluxes are strongly dependent on the numerical models used, and, as a result, there is a clear need to validate them against observations. Accurate air-sea heat flux estimates require a realistic representation of the atmospheric boundary layer, and the implementation of an appropriate surface flux parameterization. Previous work at high latitudes has highlighted the shortcomings of the surface turbulent heat flux parameterization used in the NCEP-NCAR reanalysis during high wind speed conditions, especially when combined with large air-sea temperature differences. Here the authors extend this result through an examination of the air-sea heat fluxes over the western boundary currents of the North Atlantic and North Pacific Oceans. These are also regions where large transfers of heat and moisture from the ocean to the atmosphere take place. A comparison with in situ data shows that the surface layer meteorological fields are reasonably well represented in the NCEP-NCAR reanalysis, but the turbulent heat flux fields contain significant systematic errors. It is argued that these errors are associated with shortcomings in the bulk flux algorithm employed in the reanalysis. Using the NCEP-NCAR reanalysis surface layer meteorological fields and a more appropriate bulk flux algorithm, "adjusted'' fields for the sensible and latent heat fluxes are presented that more accurately represent the air-sea exchange of heat and moisture over the western boundary currents

A parameterization of Greenland's tip jets suitable for ocean or coupled climate models

Greenland's tip jets are low-level, high wind speed jets forced by an interaction of the synoptic-scale atmospheric flow and the steep, high orography of Greenland. These jets are thought to play an important role in both preconditioning for, and triggering of, open-ocean convection in the Irminger Sea. However, the relatively small spatial scale of the jets prevents their accurate representation in the relatively low resolution (~1 degree) atmospheric (re-)analyses which are typically used to force ocean general circulation models (e.g. ECMWF ERA-40 and NCEP reanalyses, or products based on these). Here we present a method of ‘bogussing’ Greenland's tip jets into such surface wind fields and thus, via bulk flux formulae, into the air-sea turbulent flux fields. In this way the full impact of these mesoscale tip jets can be incorporated in any ocean general circulation model of sufficient resolution. The tip jet parameterization is relatively simple, making use of observed linear gradients in wind speed along and across the jet, but is shown to be accurate to a few m s-1 on average. The inclusion of tip jets results in a large local increase in both the heat and momentum fluxes. When applied to a 1-dimensional mixed-layer model this results in a deepening of the winter mixed-layer of over 300 m. The parameterization scheme only requires 10 meter wind speed and mean sea level pressure as input fields; thus it is also suitable for incorporation into a coupled atmosphere-ocean climate model at the coupling stage

An easterly tip jet off Cape Farewell, Greenland. II: Simulations and dynamics

An easterly tip jet that occurred on 21 February 2007 off Cape Farewell, Greenland, is examined. In Part I of this article aircraft observations were described. Now, in Part II, numerical simulations and an analysis of the dynamical forcing mechanisms are presented. The simulations make use of a limited-area 12 km resolution configuration of the Met Office's Unified Model. Sea-surface temperatures and sea-ice concentrations have been replaced using the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) product, addressing a boundary-layer temperature bias, while roughness lengths over sea ice have been updated, addressing a wind-speed bias. These modifications ensured a reasonably accurate simulation: generally within 1–2 K and 2–3 m s-1 when compared with dropsonde observations. A momentum-budget analysis along a curved locus through the core of the jet has been derived. Off southeast Greenland, the easterly tip jet was in cross-jet geostrophic balance, but was being accelerated downstream by an along-jet pressure gradient. Over the curved part of the locus, as the jet rounded Cape Farewell, a cross-jet residual suggests that the jet was unbalanced at the height of the jet core. This residual decreases with height so that an approximate gradient wind balance applies in the upper part of the jet. The anticyclonic curvature, characteristic of easterly tip jets, was caused by a dramatic decrease in the cross-jet pressure-gradient force at the end of the barrier, after which the jet aligned with the synoptic-scale isobars and returned to approximate geostrophic balance. The momentum budget is shown to be robust and applicable to other cases

Eigenvalues of block structured asymmetric random matrices

We study the spectrum of an asymmetric random matrix with block structured variances. The rows and columns of the random square matrix are divided into $D$ partitions with arbitrary size (linear in $N$). The parameters of the model are the variances of elements in each block, summarized in $g\in\mathbb{R}^{D\times D}_+$. Using the Hermitization approach and by studying the matrix-valued Stieltjes transform we show that these matrices have a circularly symmetric spectrum, we give an explicit formula for their spectral radius and a set of implicit equations for the full density function. We discuss applications of this model to neural networks