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Register a new userGlobal correlation matrix spectra of the surfacetemperature of the Oceans from Random MatrixTheory to Poisson fluctuations
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Anderson Barbosa A. L. R. Barbosa
Publication date
2020
fields
Physics
and research's language is
English
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In this work we use the random matrix theory (RMT) to correctly describethe behavior of spectral statistical properties of the sea surface temperatureof oceans. This oceanographic variable plays an important role in theglobalclimate system. The data were obtained from National Oceanic and Atmo-spheric Administration (NOAA) and delimited for the period 1982 to 2016.The results show that oceanographic systems presented specific $beta$ values thatcan be used to classify each ocean according to its correlation behavior. Thenearest-neighbors spacing of correlation matrix for north, central and south ofthe three oceans get close to a RMT distribution. However, the regions delim-ited in the Antarctic pole exhibited the distribution of the nearest-neighborsspacing well described by the Poisson model, which shows astatistical changeof RMT to Poisson fluctuations.
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We have analyzed the teleconnection of total cloud fraction (TCF) with global sea surface temperature (SST) in multi-model ensembles (MME) of the fifth and sixth Coupled Model Intercomparison Projects (CMIP5 and CMIP6). CMIP6-MME has a more robust and realistic teleconnection (TCF and global SST) pattern over the extra-tropics (R ~0.43) and North Atlantic (R ~0.39) region, which in turn resulted in improvement of rainfall bias over the Asian summer monsoon (ASM) region. CMIP6-MME can better reproduce the mean TCF and have reduced dry (wet) rainfall bias on land (ocean) over the ASM region. CMIP6-MME has improved the biases of seasonal mean rainfall, TCF, and outgoing longwave radiation (OLR) over the Indian Summer Monsoon (ISM) region by ~40%, ~45%, and ~31%, respectively, than CMIP5-MME and demonstrates better spatial correlation with observation/reanalysis. Results establish the credibility of the CMIP6 models and provide a scientific basis for improving the seasonal prediction of ISM.
Boundary layer turbulence in coastal regions differs from that in deep ocean because of bottom interactions. In this paper, we focus on the merging of surface and bottom boundary layers in a finite-depth coastal ocean by numerically solving the wave-averaged equations using a large eddy simulation method. The ocean fluid is driven by combined effects of wind stress, surface wave, and a steady current in the presence of stable vertical stratification. The resulting flow consists of two overlapping boundary layers, i.e. surface and bottom boundary layers, separated by an interior stratification. The overlapping boundary layers evolve through three phases, i.e. a rapid deepening, an oscillatory equilibrium and a prompt merger, separated by two transitions. Before the merger, internal waves are observed in the stratified layer, and they are excited mainly by Langmuir turbulence in the surface boundary layer. These waves induce a clear modulation on the bottom-generated turbulence, facilitating the interaction between the surface and bottom boundary layers. After the merger, the Langmuir circulations originally confined to the surface layer are found to grow in size and extend down to the sea bottom (even though the surface waves do not feel the bottom), reminiscent of the well-organized Langmuir supercells. These full-depth Langmuir circulations promote the vertical mixing and enhance the bottom shear, leading to a significant enhancement of turbulence levels in the vertical column.
We numerically study the level statistics of the Gaussian $beta$ ensemble. These statistics generalize Wigner-Dyson level statistics from the discrete set of Dyson indices $beta = 1,2,4$ to the continuous range $0 < beta < infty$. The Gaussian $beta$ ensemble covers Poissonian level statistics for $beta to 0$, and provides a smooth interpolation between Poissonian and Wigner-Dyson level statistics. We establish the physical relevance of the level statistics of the Gaussian $beta$ ensemble by showing near-perfect agreement with the level statistics of a paradigmatic model in studies on many-body localization over the entire crossover range from the thermal to the many-body localized phase. In addition, we show similar agreement for a related Hamiltonian with broken time-reversal symmetry.
The predictability of the atmosphere at short and long time scales, associated with the coupling to the ocean, is explored in a new version of the Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM), based on a 2-layer quasi-geostrophic atmosphere and a 1-layer reduced-gravity quasi-geostrophic ocean. This version features a new ocean basin geometry with periodic boundary conditions in the zonal direction. The analysis presented in this paper considers a low-order version of the model with 40 dynamical variables. First the increase of surface friction (and the associated heat flux) with the ocean can either induce chaos when the aspect ratio between the meridional and zonal directions of the domain of integration is small, or suppress chaos when it is large. This reflects the potentially counter-intuitive role that the ocean can play in the coupled dynamics. Second, and perhaps more importantly, the emergence of long-term predictability within the atmosphere for specific values of the friction coefficient occurs through intermittent excursions in the vicinity of a (long-period) unstable periodic solution. Once close to this solution the system is predictable for long times, i.e. a few years. The intermittent transition close to this orbit is, however, erratic and probably hard to predict. This new route to long-term predictability contrasts with the one found in the closed ocean-basin low-order version of MAOOAM, in which the chaotic solution is permanently wandering in the vicinity of an unstable periodic orbit for specific values of the friction coefficient. The model solution is thus at any time influenced by the unstable periodic orbit and inherits from its long-term predictability.
Consider a random vector $mathbf{y}=mathbf{Sigma}^{1/2}mathbf{x}$, where the $p$ elements of the vector $mathbf{x}$ are i.i.d. real-valued random variables with zero mean and finite fourth moment, and $mathbf{Sigma}^{1/2}$ is a deterministic $ptimes p$ matrix such that the spectral norm of the population correlation matrix $mathbf{R}$ of $mathbf{y}$ is uniformly bounded. In this paper, we find that the log determinant of the sample correlation matrix $hat{mathbf{R}}$ based on a sample of size $n$ from the distribution of $mathbf{y}$ satisfies a CLT (central limit theorem) for $p/nto gammain (0, 1]$ and $pleq n$. Explicit formulas for the asymptotic mean and variance are provided. In case the mean of $mathbf{y}$ is unknown, we show that after recentering by the empirical mean the obtained CLT holds with a shift in the asymptotic mean. This result is of independent interest in both large dimensional random matrix theory and high-dimensional statistical literature of large sample correlation matrices for non-normal data. At last, the obtained findings are applied for testing of uncorrelatedness of $p$ random variables. Surprisingly, in the null case $mathbf{R}=mathbf{I}$, the test statistic becomes completely pivotal and the extensive simulations show that the obtained CLT also holds if the moments of order four do not exist at all, which conjectures a promising and robust test statistic for heavy-tailed high-dimensional data.
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