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

Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 1998.Includes bibliographical references (leaves 156-158).by François W. Primeau.Ph.D

Optimal parameters for the ocean's nutrient, carbon, and oxygen cycles compensate for circulation biases but replumb the biological pump

Accurate predictive modelling of the ocean's global carbon and oxygen cycles is challenging because of uncertainties in both biogeochemistry and ocean circulation. Advances over the last decade have made parameter optimization feasible, allowing models to better match observed biogeochemical fields. However, does fitting a biogeochemical model to observed tracers using a circulation with known biases robustly capture the inner workings of the biological pump? Here we embed a mechanistic model of the ocean's coupled nutrient, carbon, and oxygen cycles into two circulations for the current climate. To assess the effects of biases, one circulation (ACCESS-M) is derived from a climate model and the other from data assimilation of observations (OCIM2). We find that parameter optimization compensates for circulation biases at the expense of altering how the biological pump operates. Tracer observations constrain pump strength and regenerated inventories for both circulations, but ACCESS-M export production optimizes to twice that of OCIM2 to compensate for ACCESS-M having lower sequestration efficiencies driven by less efficient particle transfer and shorter residence times. Idealized simulations forcing complete Southern Ocean nutrient utilization show that the response of the optimized system is sensitive to the embedding circulation. In ACCESS-M, Southern Ocean nutrient and DIC trapping is partially short-circuited by unrealistically deep mixed layers. For both circulations, intense Southern Ocean production deoxygenates Southern-Ocean-sourced deep waters, muting the imprint of circulation biases on oxygen. Our findings highlight that the biological pump's plumbing needs careful assessment to predict the biogeochemical response to environmental changes, even when optimally matching observations.</p

Evaluating the benefits of bayesian hierarchical methods for analyzing heterogeneous environmental datasets: a case study of marine organic carbon fluxes

Large compilations of heterogeneous environmental observations are increasingly available as public databases, allowing researchers to test hypotheses across datasets. Statistical complexities arise when analyzing compiled data due to unbalanced spatial sampling, variable environmental context, mixed measurement techniques, and other reasons. Hierarchical Bayesian modeling is increasingly used in environmental science to describe these complexities, however few studies explicitly compare the utility of hierarchical Bayesian models to simpler and more commonly applied methods. Here we demonstrate the utility of the hierarchical Bayesian approach with application to a large compiled environmental dataset consisting of 5,741 marine vertical organic carbon flux observations from 407 sampling locations spanning eight biomes across the global ocean. We fit a global scale Bayesian hierarchical model that describes the vertical profile of organic carbon flux with depth. Profile parameters within a particular biome are assumed to share a common deviation from the global mean profile. Individual station-level parameters are then modeled as deviations from the common biome-level profile. The hierarchical approach is shown to have several benefits over simpler and more common data aggregation methods. First, the hierarchical approach avoids statistical complexities introduced due to unbalanced sampling and allows for flexible incorporation of spatial heterogeneitites in model parameters. Second, the hierarchical approach uses the whole dataset simultaneously to fit the model parameters which shares information across datasets and reduces the uncertainty up to 95% in individual profiles. Third, the Bayesian approach incorporates prior scientific information about model parameters; for example, the non-negativity of chemical concentrations or mass-balance, which we apply here. We explicitly quantify each of these properties in turn. We emphasize the generality of the hierarchical Bayesian approach for diverse environmental applications and its increasing feasibility for large datasets due to recent developments in Markov Chain Monte Carlo algorithms and easy-to-use high-level software implementations

Global-scale variations of the ratios of carbon to phosphorus in exported marine organic matter

The ratio of carbon (C) to phosphorus (P) in marine phytoplankton is thought to be constant throughout the worlds'oceans. Known as the Redfield ratio, this relationship describes the links between carbon and phosphorus cycling and marine ecosystems. However, variations in the stoichiometry of phytoplankton have recently been identified, in particular strong latitudinal variability. Here we assess the impact of this variability in the C:P ratio of biomass on the C:P ratio of organic matter that is exported to the deep ocean using a biogeochemical inverse-model based on a data-constrained ocean circulation model and a global database of dissolved inorganic carbon and phosphate measurements. We identify global patterns of variability in the C:P ratios of exported organic matter, with higher values in the nutrient-depleted subtropical gyres, where organic matter export is relatively low, and lower ratios in nutrient-rich upwelling zones and high-latitude regions, where organic matter export is high. This suggests that total carbon export is relatively constant throughout the oceans, in agreement with recent estimates of carbon fluxes. We conclude that the latitudinal patterns of C:P in exported organic matter are consistent with the large-scale stoichiometric variations in phytoplankton C:P. We suggest that a future expansion of nutrient-depleted waters could result in a shift to more efficient C export that compensates for the expected decline in productivity

Bifurcation Structure of a Wind-Driven Shallow Water Model with Layer-Outcropping Abstract

The steady state bifurcation structure of the double-gyre wind-driven ocean circu-lation 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 Effect of Alongshore Topographic Variation and Bottom Friction on Shelf Wave Interactions

The theory of resonant interactions between continental shelf waves developed by Hsieh and Mysak to explain aspects of the shelf wave spectra observed on the Oregon shelf by Cutchin and Smith and Huyer et al. is extended to include the effect of bottom friction and alongshore topographic variation. The model equations are derived via a multiple-scale asymptotic expansion in which it is assumed that the alongshore topography varies over a length scale over which the nonlinear interactions make an order-one contribution to the dynamics. It is shown that alongshore topographic variability leads to a wavenumber mismatch in the wave resonance conditions. It is possible to identify a purely linear and nonlinear component to the wavenumber mismatch. The linear component can be identified simply as the topographic modulation in a WKB sense of the alongshore wavenumber. The nonlinear component of the wavenumber mismatch is a cumulative effect associated with the dynamic interactions between the waves occurring over regions of alongshore topographic variability. It is shown that even after a triad of initially maximally interacting shelf waves has traversed a topographic anomaly of finite alongshore extent, the energy exchange remains permanently suppressed and does not recover to its pretopographic efficiency. For some specialized alongshore topographic variations, the interaction equations can be solved exactly. An illustrative solution is presented for an isolated topographic feature superimposed on an Adams-Buchwald exponential shelf profile. Numerical solutions are presented for the purely dissipative wave interaction problem. For realistic values of the bottom friction parameter it is possible to almost completely damp out any interaction. It is suggested that the geographically localized nature of observed interacting shelf waves may in part be due to alongshore topographic detuning of the resonance conditions or strong frictional effects

Taxonomic resolution, ecotypes and the biogeography of Prochlorococcus.

In order to expand our understanding of the diversity and biogeography of Prochlorococcus ribotypes, we PCR-amplified, cloned and sequenced the 16S/23S rRNA ITS region from sites in the Atlantic and Pacific oceans. Ninety-three per cent of the ITS sequences could be assigned to existing Prochlorococcus clades, although many novel subclades were detected. We assigned the sequences to operational taxonomic units using a graduated scale of sequence identity from 80% to 99.5% and correlated Prochlorococcus diversity with respect to environmental variables and dispersal time between the sites. Dispersal time was estimated using a global ocean circulation model. The significance of specific environmental variables was dependent on the degree of sequence identity used to define a taxon: light correlates with broad-scale diversity (90% cut-off), temperature with intermediate scale (95%) whereas no correlation with phosphate was observed. Community structure was correlated with dispersal time between sample sites only when taxa were defined using the finest sequence similarity cut-off. Surprisingly, the concentration of nitrate, which cannot be used as N source by the Prochlorococcus strains in culture, explains some variation in community structure for some definitions of taxa. This study suggests that the spatial distribution of Prochlorococcus ecotypes is shaped by a hierarchy of environmental factors as well dispersal limitation

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 &gt; 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

Stratospheric mean residence time and mean age on the tropopause: Connections and implications for observational constraints

Stratospheric mean residence time  and mean age on the tropopause ΓΩ are shown to measure physically distinct aspects of stratospheric transport. Both ΓΩ and  are mean transit times through the stratosphere of air that enters through tropopause region Ω i  and exits through region Ω f , but they represent averages over different populations of fluid elements. The averaging for ΓΩ is based on the population of fluid elements exiting the stratosphere, while  is based on the population of Ω i  → Ω f  fluid elements residing in the stratosphere. Thus, ΓΩ is the mean age on exit, while is the expected mean residence time in the interior of the stratosphere. The physical basis for defining and robustly computing both timescales is the one-way stratosphere-to-troposphere flux of air labeled with the boundary-propagator Green function, . By re-expressing the boundary-value problem for in terms of first-order loss in a tropopause layer with a timescaleτ c  in the limit τ c  → 0, we show that both  and ΓΩ can be obtained as ratios of moments of  extrapolated to the tropopause. One obtains  = ΓΩ + 2Δ2/ΓΩ, where Δ quantifies the width of the transit-time distribution. Because the moments of  can be estimated from the mixing ratio of transient trace gases, it is in principle possible to estimate  from measurements of two independent transient tracers. The distinctness of  and ΓΩ is elucidated using idealized models