Multiple equilibria and low-frequency variability of wind-driven ocean models

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 1998The steady states of two models of the double-gyre wind-driven ocean circulation are studied. The link between the steady state solutions of the models and their time-mean and low-frequency variability is explored to test the hypothesis that both stable and unstable fixed points influence shape the model's attractor in phase space. The steady state solutions of a barotropic double-gyre ocean model in which the wind-stress curl input of vorticity is balanced primarily by bottom friction are studied. The bifurcations away from a unique and stable steady state are mapped as a function of two nondimensional parameters, (δI,δS), which can be thought of as measuring respectively the relative importance of the nonlinear advection and bottom damping of relative vorticity to the advection of planetary vorticity. A highly inertial branch characterized by a circulation with transports far in excess of those predicted by Sverdrup balance is present over a wide range of parameters including regions of parameter space where other solutions give more realistic flows. For the range of parameters investigated, in the limit of large Reynolds number, δI,δS → ∞, the inertial branch is stable and appears to be unique. This branch is anti-symmetric with respect to the mid-basin latitude like the prescribed wind-stress curl. For intermediate values of δI,δS, additional pairs of mirror image non-symmetric equilibria come into existence. These additional equilibria have currents which redistribute relative vorticity across the line of zero wind-stress curl. This internal redist~ibution of vorticity prevents the solution from developing the large transports that are necessary for the anti-symmetric solution to achieve a global vorticity balance. Beyond some critical Reynolds number, the nonsymmetric solutions are unstable to time-dependent perturbations. Time-averaged solutions in' this parameter regime have transports comparable in magnitude to those of the non-symmetric steady state branch. Beyond a turning point, where the non-symmetric steady state solutions cease to exist, all the computed time-dependent model trajectories converge to the anti-symmetric inertial runaway solution. The internal compensation mechanism which acts through explicitly simulated eddies is itself dependent explicit dissipation parameter. Using the reduced-gravity quasigeostrophic model an investigation of the link between the steady state solutions and the model's low-frequency variability is conducted. If the wind-stress curl is kept anti-symmetric, successive pairs of non-symmetric equilibria come into existence via symmetry-breaking pitchfork bifurcations as the model's biharmonic viscosity is reduced. Succesive pairs of mirror image equilibria have an additional half meander in the jet. The distinct energy levels of the steady state solutiOris can be understood in part by there different inter-gyre fluxes of vorticity. Those solutions with weak inter-gyre fluxes of vorticity have large and energetic recirculation cells which remove excess vorticity through bottom friction. Those solutions with strong inter-gyre fluxes of vorticity have much smaller and ·less energetic recirculation cells. A significant fraction of the variance (30%) of the interface height anomaly can be accounted by four coherent structures which point away from the time-mean state and towards four steady state solutions in phase space. After removing the variance which projects onto the four modes, the remaining variance is reduced predominantly at low-frequencies, showing that these modes are linked to the low-frequency variability of the model. Furthermore, the time-averaged flow fields within distinct energy ranges show distinct patterns which are in turn similar to the distinct steady state solutions

Stall Pattern Avoidance in Polynomial Product Codes

Product codes are a concatenated error-correction scheme that has been often considered for applications requiring very low bit-error rates, which demand that the error floor be decreased as much as possible. In this work, we consider product codes constructed from polynomial algebraic codes, and propose a novel low-complexity post-processing technique that is able to improve the error-correction performance by orders of magnitude. We provide lower bounds for the error rate achievable under post processing, and present simulation results indicating that these bounds are tight.Comment: 4 pages, 2 figures, GlobalSiP 201

Unsupervised Deep Learning for Massive MIMO Hybrid Beamforming

Hybrid beamforming is a promising technique to reduce the complexity and cost of massive multiple-input multiple-output (MIMO) systems while providing high data rate. However, the hybrid precoder design is a challenging task requiring channel state information (CSI) feedback and solving a complex optimization problem. This paper proposes a novel RSSI-based unsupervised deep learning method to design the hybrid beamforming in massive MIMO systems. Furthermore, we propose i) a method to design the synchronization signal (SS) in initial access (IA); and ii) a method to design the codebook for the analog precoder. We also evaluate the system performance through a realistic channel model in various scenarios. We show that the proposed method not only greatly increases the spectral efficiency especially in frequency-division duplex (FDD) communication by using partial CSI feedback, but also has near-optimal sum-rate and outperforms other state-of-the-art full-CSI solutions.Comment: Submitted to IEEE Transactions on Wireless Communication

Rejuvenating the ocean: mean ocean radiocarbon, CO2 release, and radiocarbon budget closure across the last deglaciation

Abstract. Radiocarbon is a tracer that provides unique insights into the ocean's ability to sequester CO2 from the atmosphere. While spatial patterns of radiocarbon in the ocean interior can indicate the vectors and timescales for carbon transport through the ocean, estimates of the global average ocean–atmosphere radiocarbon age offset (B-Atm) place constraints on the closure of the global carbon cycle. Here, we apply a Bayesian interpolation method to compiled B-Atm data to generate global interpolated fields and mean ocean B-Atm estimates for a suite of time slices across the last deglaciation. The compiled data and interpolations confirm a stepwise and spatially heterogeneous “rejuvenation” of the ocean, suggesting that carbon was released to the atmosphere through two swings of a “ventilation seesaw” operating between the North Atlantic and both the Southern Ocean and the North Pacific. Sensitivity tests using the Bern3D model of intermediate complexity demonstrate that a portion of the reconstructed deglacial B-Atm changes may reflect “phase-attenuation” biases that are unrelated to ocean ventilation and that arise from independent atmospheric radiocarbon dynamics instead. A deglacial minimum in B-Atm offsets during the Bølling–Allerød could partly reflect such a bias. However, the sensitivity tests further demonstrate that when correcting for such biases, ocean “ventilation” could still account for at least one-third of deglacial atmospheric CO2 rise. This contribution to CO2 rise appears to have continued through the Younger Dryas, though much of the impact was likely achieved by the end of the Bølling–Allerød, indicating a key role for marine carbon cycle adjustment early in the deglacial process. Our global average B-Atm estimates place further new constraints on the long-standing mystery of global radiocarbon budget closure across the last deglaciation and suggest that glacial radiocarbon production levels are likely underestimated on average by existing reconstructions. </jats:p

Global estimate of submarine groundwater discharge based on an observationally constrained radium isotope model

© The Author(s), 2014. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Geophysical Research Letters 41 (2014): 8438–8444, doi:10.1002/2014GL061574.Along the continental margins, rivers and submarine groundwater supply nutrients, trace elements, and radionuclides to the coastal ocean, supporting coastal ecosystems and, increasingly, causing harmful algal blooms and eutrophication. While the global magnitude of gauged riverine water discharge is well known, the magnitude of submarine groundwater discharge (SGD) is poorly constrained. Using an inverse model combined with a global compilation of 228Ra observations, we show that the SGD integrated over the Atlantic and Indo-Pacific Oceans between 60°S and 70°N is (12 ± 3) × 1013 m3 yr−1, which is 3 to 4 times greater than the freshwater fluxes into the oceans by rivers. Unlike the rivers, where more than half of the total flux is discharged into the Atlantic, about 70% of SGD flows into the Indo-Pacific Oceans. We suggest that SGD is the dominant pathway for dissolved terrestrial materials to the global ocean, and this necessitates revisions for the budgets of chemical elements including carbon.This work was supported by the Ministry of Oceans and Fisheries, Korea, through the Korea Institute of Marine Science and Technology (KIMST) (20120176) and National Research Foundation (NRF) of Korea (2013R1A2A1A05004343 and 2013R1A1A1058203). Charette and Moore's contributions were supported by the US National Science Foundation through the GEOTRACES project

Authigenic uranium in foraminiferal coatings : a proxy for ocean redox chemistry

Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Paleoceanography 27 (2012): PA3227, doi:10.1029/2012PA002335.The rate of uranium accumulation in oceanic sediments from seawater is controlled by bottom water oxygen concentrations and organic carbon fluxes—two parameters that are linked to deep ocean storage of CO2. To investigate glacial-interglacial changes in what is known as authigenic U, we have developed a rapid method for its determination as a simple addition to a procedure for foraminiferal trace element analysis. Foraminiferal calcite acts as a low U substrate (U/Ca < 15 nmol/mol) upon which authigenic U accumulates in reducing sediments. We measured a downcore record of foraminiferal U/Ca from ODP Site 1090 in the South Atlantic and found that U/Ca ratios increase by 70–320 nmol/mol during glacial intervals. There is a significant correlation between U/Ca records of benthic and planktonic foraminiferal species and between U/Ca and bulk sediment authigenic U. These results indicate that elevated U/Ca ratios are attributable to the accumulation of authigenic U coatings in sediments. Foraminiferal Mn/Ca ratios were lower during the glacial intervals, suggesting that the observed U accumulation on the shells is not directly linked to U incorporation into secondary manganese phases. Thus, foraminiferal U/Ca ratios may provide useful information on past changes in sediment redox conditions.R.B. was funded by the Winston Churchill Foundation, and H.E. was funded by the UK Natural Environment Research Council and the European Research Council.2013-03-0

Strong latitudinal patterns in the elemental ratios of marine plankton and organic matter

Nearly 75 years ago, Alfred C. Redfield observed a similarity between the elemental composition of marine plankton in the surface ocean and dissolved nutrients in the ocean interior. This stoichiometry, referred to as the Redfield ratio, continues to be a central tenet in ocean biogeochemistry, and is used to infer a variety of ecosystem processes, such as phytoplankton productivity and rates of nitrogen fixation and loss2-4. Model, field and laboratory studies have shown that different mechanisms can explain both constant and variable ratios of carbon to nitrogen and phosphorus among ocean plankton communities. The range of C/N/P ratios in the ocean, and their predictability, are the subject of much active research. Here we assess global patterns in the elemental composition of phytoplankton and particulate organic matter in the upper ocean, using published and unpublished observations of particulate phosphorus, nitrogen and carbon from a broad latitudinal range, supplemented with elemental data for surface plankton populations. We show that the elemental ratios of marine organic matter exhibit large spatial variations, with a global average that differs substantially from the canonical Redfield ratio. However, elemental ratios exhibit a clear latitudinal trend. Specifically, we observed a ratio of 195:28:1 in the warm nutrient-depleted low-latitude gyres, 137:18:1 in warm, nutrient-rich upwelling zones, and 78:13:1 in cold, nutrient-rich high-latitude regions. We suggest that the coupling between oceanic carbon, nitrogen and phosphorus cycles may vary systematically by ecosystem. © 2013 Macmillan Publishers Limited. All rights reserved

Characterizing Transport between the Surface Mixed Layer and the Ocean Interior with a Forward and Adjoint Global Ocean Transport Model

The theory of first-passage time distribution functions and its extension to last-passage time distribution functions are applied to the problem of tracking the movement of water masses to and from the surface mixed layer in a global ocean general circulation model. The first-passage time distribution function is used to determine in a probabilistic sense when and where a fluid element will make its first contact with the surface as a function of its position in the ocean interior. The last-passage time distribution is used to determine when and where a fluid element made its last contact with the surface. A computationally efficient method is presented for recursively computing the first few moments of the first- and last-passage time distributions by directly inverting the forward and adjoint transport operator. This approach allows integrated transport information to be obtained directly from the differential form of the transport operator without the need to perform lengthy multitracer time integration of the transport equations. The method, which relies on the stationarity of the transport operator, is applied to the time-averaged transport operator obtained from a three-dimensional global ocean simulation performed with an OGCM. With this approach, the author (i) computes surface maps showing the fraction of the total ocean volume per unit area that ventilates at each point on the surface of the ocean, (ii) partitions interior water masses based on their formation region at the surface, and (iii) computes the three-dimensional spatial distribution of the mean and standard deviation of the age distribution of water