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

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

Observational and numerical modeling constraints on the global ocean biological carbon pump

This study characterized ocean biological carbon pump metrics in the second iteration of the REgional Carbon Cycle Assessment and Processes (RECCAP2) project. The analysis here focused on comparisons of global and biome-scale regional patterns in particulate organic carbon (POC) production and sinking flux from the RECCAP2 ocean biogeochemical model ensemble against observational products derived from satellite remote sensing, sediment traps, and geochemical methods. There was generally good model-data agreement in mean large-scale spatial patterns, but with substantial spread across the model ensemble and observational products. The global-integrated, model ensemble-mean export production, taken as the sinking POC flux at 100 m (6.08 ± 1.17 Pg C yr−1), and export ratio defined as sinking flux divided by net primary production (0.154 ± 0.026) both fell at the lower end of observational estimates. Comparison with observational constraints also suggested that the model ensemble may have underestimated regional biological CO2 drawdown and air-sea CO2 flux in high productivity regions. Reasonable model-data agreement was found for global-integrated, ensemble-mean sinking POC flux into the deep ocean at 1,000 m (0.65 ± 0.24 Pg C yr−1) and the transfer efficiency defined as flux at 1,000 m divided by flux at 100 m (0.122 ± 0.041), with both variables exhibiting considerable regional variability. The RECCAP2 analysis presents standard ocean biological carbon pump metrics for assessing biogeochemical model skill, metrics that are crucial for further modeling efforts to resolve remaining uncertainties involving system-level interactions between ocean physics and biogeochemistry

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

The path-density distribution of oceanic surface-to-surface transport

 A novel diagnostic for advective-diffusive surface-to-surface paths is developed and applied to a global ocean model. The diagnostic provides, for the first time, a rigorous quantitative assessment of the great ocean conveyor's deep branch. A new picture emerges of a diffusive conveyor in which the deep North Pacific is a holding pen of long-residence-time water. Our diagnostic is the joint density, η, per unit volume and interior residence time, τ, of paths connecting two specified surface patches. The spatially integrated η determines the residence-time partitioned flux and volume of water in transit from entry to exit patch. We focus on interbasin paths from high-latitude water mass formation regions to key regions of re-exposure to the atmosphere. For non-overlapping patches, a characteristic timescale is provided by the residence time, τ ϕ, for which the associated flux distribution, ϕ, has its maximum. Paths that are fast compared to τ ϕ are organized by the major current systems, while paths that are slow compared to τ ϕ are dominated by eddy diffusion. Because ϕ has substantial weight in its tail for τ > τ ϕ, the fast paths account for only a minority of the formation-to-re-exposure flux. This conclusion is expected to apply to the real ocean based on recent tracer data analyses, which point to long eddy-diffusive tails in the ocean's transit-time distributions. The long-τ asymptotic path density is governed by two time-invariant patterns. One pattern, which we call the Deep North Pacific pattern, ultimately dominates a secondary redistribution pattern

Bifurcation structure of a wind-driven shallow water model with layer-outcropping

The steady state bifurcation structure of the double-gyre wind-driven ocean circulation is examined in a shallow water model where the upper layer is allowed to outcrop at the sea surface. In addition to the classical jet-up and jet-down multiple equilibria, we find a new regime in which one of the equilibrium solutions has a large outcropping region in the subpolar gyre. Time dependent simulations show that the outcropping solution equilibrates to a stable periodic orbit with a period of 8 months. Co-existing with the periodic solution is a stable steady state solution without outcropping.A numerical scheme that has the unique advantage of being differentiable while still allowing layers to outcrop at the sea surface is used for the analysis. In contrast, standard schemes for solving layered models with outcropping are non-differentiable and have an ill-defined Jacobian making them unsuitable for solution using Newton’s method. As such, our new scheme expands the applicability of numerical bifurcation techniques to an important class of ocean models whose bifurcation structure had hitherto remained unexplored

The diffusive ocean conveyor

 We use a novel path-density transport diagnostic to trace out the deep branch of the ocean conveyor in a global circulation model. Our results suggest that the majority of the world's deep water is not transported back to the surface along the current systems of the standard great ocean conveyor (GOC). Standard GOC routes are evident only for waters with interior residence times, τ, less than about a thousand years, accounting for less than a quarter of the ventilation-to-re-exposure flux. Waters with longer τ are spread across the deep oceans by the “diffusive conveyor” and, by τ ∼ 3000 years, organized into a characteristic deep-North-Pacific pattern that is dominated by eddy diffusion. The observed depletion of oxygen and 14C in the deep N Pacific is consistent with a diffusive conveyor and should not be interpreted as evidence of an advective terminus of the GOC deep branch

Global teleconnections in the oceanic phosphorus cycle: Patterns, paths, and timescales

Nutrient transport and productivity teleconnections with the Southern Ocean are diagnosed in a data-assimilated circulation model coupled to a jointly optimized simple phosphorus cycling model. The North Atlantic has the strongest extratropical teleconnections with the Southern Ocean: phosphate (PO4) last utilized in the Southern Ocean sustains 29 ± 6% of the subpolar and 14 ± 6% of the subtropical, new production in the North Atlantic. A PO4 path-density diagnostic shows that these teleconnections are mediated by thermocline paths and reveals that most paths to anywhere north of 40°S lie in the deep Pacific. Forcing nearly complete Southern-Ocean nutrient utilization increases the overall number of paths to anywhere north of 40°S, but reduces the number of paths from the Pacific to the North Atlantic by trapping nutrients in return paths to the Southern Ocean. At the same time, the mean export-to-uptake transit times to anywhere north of 40°S increase, while the mean transit times to the North Atlantic decrease. Correspondingly, the amount of North-Atlantic production sustained by Southern-Ocean export increases in spite of decreased total production in response to Southern-Ocean nutrient trapping. The distributions of export-to-uptake, export-to-surface, and surface-to-surface transit times are computed and summarized in terms of their mean transit times and their mean interior residence times. The combined particle and advective–diffusive transport of nutrients is characterized by broad, skewed transit-time distributions, which result in mean residence times much longer than the mean transit times, in turn much longer than the most probable transit times