Impact of oceanic circulation on biological carbon storage in the ocean and atmospheric pCO2

Author Posting. © American Geophysical Union, 2008. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Global Biogeochemical Cycles 22 (2008): GB3007, doi:10.1029/2007GB002958.We use both theory and ocean biogeochemistry models to examine the role of the soft-tissue biological pump in controlling atmospheric CO2. We demonstrate that atmospheric CO2 can be simply related to the amount of inorganic carbon stored in the ocean by the soft-tissue pump, which we term (OCS soft ). OCS soft is linearly related to the inventory of remineralized nutrient, which in turn is just the total nutrient inventory minus the preformed nutrient inventory. In a system where total nutrient is conserved, atmospheric CO2 can thus be simply related to the global inventory of preformed nutrient. Previous model simulations have explored how changes in the surface concentration of nutrients in deepwater formation regions change the global preformed nutrient inventory. We show that changes in physical forcing such as winds, vertical mixing, and lateral mixing can shift the balance of deepwater formation between the North Atlantic (where preformed nutrients are low) and the Southern Ocean (where they are high). Such changes in physical forcing can thus drive large changes in atmospheric CO2, even with minimal changes in surface nutrient concentration. If Southern Ocean deepwater formation strengthens, the preformed nutrient inventory and thus atmospheric CO2 increase. An important consequence of these new insights is that the relationship between surface nutrient concentrations, biological export production, and atmospheric CO2 is more complex than previously predicted. Contrary to conventional wisdom, we show that OCS soft can increase and atmospheric CO2 decrease, while surface nutrients show minimal change and export production decreases.While at MIT, I.M. was supported by the NOAA Postdoctoral Program in Climate and Global Change, administered by the University Corporation for Atmospheric Research

How does ocean biology affect atmospheric pCO2? Theory and models

Author Posting. © American Geophysical Union, 2008. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 113 (2008): C07032, doi:10.1029/2007JC004598.This paper examines the sensitivity of atmospheric pCO2 to changes in ocean biology that result in drawdown of nutrients at the ocean surface. We show that the global inventory of preformed nutrients is the key determinant of atmospheric pCO2 and the oceanic carbon storage due to the soft-tissue pump (OCS soft ). We develop a new theory showing that under conditions of perfect equilibrium between atmosphere and ocean, atmospheric pCO2 can be written as a sum of exponential functions of OCS soft . The theory also demonstrates how the sensitivity of atmospheric pCO2 to changes in the soft-tissue pump depends on the preformed nutrient inventory and on surface buffer chemistry. We validate our theory against simulations of nutrient depletion in a suite of realistic general circulation models (GCMs). The decrease in atmospheric pCO2 following surface nutrient depletion depends on the oceanic circulation in the models. Increasing deep ocean ventilation by increasing vertical mixing or Southern Ocean winds increases the atmospheric pCO2 sensitivity to surface nutrient forcing. Conversely, stratifying the Southern Ocean decreases the atmospheric CO2 sensitivity to surface nutrient depletion. Surface CO2 disequilibrium due to the slow gas exchange with the atmosphere acts to make atmospheric pCO2 more sensitive to nutrient depletion in high-ventilation models and less sensitive to nutrient depletion in low-ventilation models. Our findings have potentially important implications for both past and future climates.While at MIT, I.M. was supported by the NOAA Postdoctoral Program in Climate and Global Change, administered by the University Corporation for Atmospheric Research

Meteorological and oceanographic data collected during the ASREX 91 field experiment

The 1991 Acoustic Surface Reverberation Experiment (ASREX 91) took place in November and December off the coast of British Columbia. As part of this experiment, three moorings were deployed to characterize the environmental background. The moorings consisted of a meteorological/oceanographic mooring designed to measure surface meteorology, current and temperature in the upper 120 meters, and nondirectional wave parameters and two wave moorings which were instrumented with pitch-roll buoys to characterize the directional wave spectrum. This report presents results from these three moorings. The conditions seen during the experiment were extremely rough, with wind speeds at 3.4m above the water surface reaching a maximum of 22 m/s and wave heights reaching a maximum of over 10 meters. The air-sea flux of heat was strongly cooling, and the mixed layer deepened over the course of the experiment from approximately 40 to approximately 70 meters. Spectra of the temperature showed a strong semidiurnal tidal signal associated with temperature excursions of several degrees C. The velocity signal showed strong inertial oscilations with amplitudes of 30-50 cm/s. Weaker low-frequency and semidiurnal tidal signals were also seen. The waves were very strong with significant wave heights of 5-6 meters persisting for up to 2 weeks at a time. Waves were generally out of the south or the west.Funding was provided by the Ocean Acoustics Program (Code 324OA) of the Office of Naval Research under contract N00014-91-J-1891

Meridional density gradients do not control the Atlantic overturning circulation

A wide body of modeling and theoretical scaling studies support the concept that changes to the Atlantic meridional overturning circulation (AMOC), whether forced by winds or buoyancy fluxes, can be understood in terms of a simple causative relation between the AMOC and an appropriately defined meridional density gradient (MDG). The MDG is supposed to translate directly into a meridional pressure gradient. Here two sets of experiments are performed using a modular ocean model coupled to an energy–moisture balance model in which the positive AMOC–MDG relation breaks down. In the first suite of seven model integrations it is found that increasing winds in the Southern Ocean cause an increase in overturning while the surface density difference between the equator and North Atlantic drops. In the second suite of eight model integrations the equation of state is manipulated so that the density is calculated at the model temperature plus an artificial increment ΔT that ranges from −3° to 9°C. (An increase in ΔT results in increased sensitivity of density to temperature gradients.) The AMOC in these model integrations drops as the MDG increases regardless of whether the density difference is computed at the surface or averaged over the upper ocean. Traditional scaling analysis can only produce this weaker AMOC if the scale depth decreases enough to compensate for the stronger MDG. Five estimates of the depth scale are evaluated and it is found that the changes in the AMOC can be derived from scaling analysis when using the depth of the maximum overturning circulation or estimates thereof but not from the pycnocline depth. These two depth scales are commonly assumed to be the same in theoretical models of the AMOC. It is suggested that the correlation between the MDG and AMOC breaks down in these model integrations because the depth and strength of the AMOC is influenced strongly by remote forcing such as Southern Ocean winds and Antarctic Bottom Water formation

Robust high-dimensional precision matrix estimation

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in high-dimensions, it cannot be used to obtain a precision matrix estimator. A popular high-dimensional estimator is the graphical lasso, but it lacks robustness. We consider the high-dimensional independent contamination model. Here, even a small percentage of contaminated cells in the data matrix may lead to a high percentage of contaminated rows. Downweighting entire observations, which is done by traditional robust procedures, would then results in a loss of information. In this paper, we formally prove that replacing the sample covariance matrix in the graphical lasso with an elementwise robust covariance matrix leads to an elementwise robust, sparse precision matrix estimator computable in high-dimensions. Examples of such elementwise robust covariance estimators are given. The final precision matrix estimator is positive definite, has a high breakdown point under elementwise contamination and can be computed fast

Changes in ocean vertical heat transport with global warming

Heat transport between the surface and deep ocean strongly influences transient climate change. Mechanisms setting this transport are investigated using coupled climate models and by projecting ocean circulation into the temperature-depth diagram. In this diagram, a “cold cell” cools the deep ocean through the downwelling of Antarctic waters and upwelling of warmer waters and is balanced by warming due to a “warm cell,” coincident with the interhemispheric overturning and previously linked to wind and haline forcing. With anthropogenic warming, the cold cell collapses while the warm cell continues to warm the deep ocean. Simulations with increasingly strong warm cells, set by their mean Southern Hemisphere winds, exhibit increasing deep-ocean warming in response to the same anthropogenic forcing. It is argued that the partition between components of the circulation which cool and warm the deep ocean in the preindustrial climate is a key determinant of ocean vertical heat transport with global warming

Eddy saturation and frictional control of the Antarctic Circumpolar Current

The Antarctic Circumpolar Current is the strongest current in the ocean and has a pivotal impact on ocean stratification, heat content, and carbon content. The circumpolar volume transport is relatively insensitive to surface wind forcing in models that resolve turbulent ocean eddies, a process termed “eddy saturation.” Here a simple model is presented that explains the physics of eddy saturation with three ingredients: a momentum budget, a relation between the eddy form stress and eddy energy, and an eddy energy budget. The model explains both the insensitivity of circumpolar volume transport to surface wind stress and the increase of eddy energy with wind stress. The model further predicts that circumpolar transport increases with increased bottom friction, a counterintuitive result that is confirmed in eddy-permitting calculations. These results suggest an unexpected and important impact of eddy energy dissipation, through bottom drag or lee wave generation, on ocean stratification, ocean heat content, and potentially atmospheric CO2

Thermobaric control of gravitational potential energy generation by diapycnal mixing in the deep ocean

Sources and sinks of gravitational potential energy (GPE) play a rate-limiting role in the large scale ocean circulation. A key source is turbulent diapycnal mixing, whereby irre- versible mixing across isoneutral surfaces is enhanced by turbulent straining of these surfaces. This has motivated international observational efforts to map diapycnal mixing in the global ocean. However, in order to accurately relate the GPE supplied to the large scale circulation by diapycnal mixing to the mixing energy source, it is first necessary to determine the ratio, ξ , of the GPE generation rate to the available potential energy dissipation rate associated with turbulent mixing. Here, the link between GPE and hydro- static pressure is used to derive the GPE budget for a com- pressible ocean with a nonlinear equation of state. The role of diapycnal mixing is isolated and from this a global cli- matological distribution of ξ is calculated. It is shown that, for a given source of mixing energy, typically three times as much GPE is generated if the mixing takes place in bottom waters rather than in the pycnocline. This is due to GPE destruction by cabbelling in the pycnocline, as opposed to thermobaric enhancement of GPE generation by diapycnal mixing in the deep ocean

Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm

Over the past five decades, k-means has become the clustering algorithm of choice in many application domains primarily due to its simplicity, time/space efficiency, and invariance to the ordering of the data points. Unfortunately, the algorithm's sensitivity to the initial selection of the cluster centers remains to be its most serious drawback. Numerous initialization methods have been proposed to address this drawback. Many of these methods, however, have time complexity superlinear in the number of data points, which makes them impractical for large data sets. On the other hand, linear methods are often random and/or sensitive to the ordering of the data points. These methods are generally unreliable in that the quality of their results is unpredictable. Therefore, it is common practice to perform multiple runs of such methods and take the output of the run that produces the best results. Such a practice, however, greatly increases the computational requirements of the otherwise highly efficient k-means algorithm. In this chapter, we investigate the empirical performance of six linear, deterministic (non-random), and order-invariant k-means initialization methods on a large and diverse collection of data sets from the UCI Machine Learning Repository. The results demonstrate that two relatively unknown hierarchical initialization methods due to Su and Dy outperform the remaining four methods with respect to two objective effectiveness criteria. In addition, a recent method due to Erisoglu et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms (Springer, 2014). arXiv admin note: substantial text overlap with arXiv:1304.7465, arXiv:1209.196

The ocean's gravitational potential energy budget in a coupled climate model

This study examines, in a unified fashion, the budgets of ocean gravitational potential energy (GPE) and available gravitational potential energy (AGPE) in the control simulation of the coupled atmosphere–ocean general circulation model HadCM3. Only AGPE can be converted into kinetic energy by adiabatic processes. Diapycnal mixing supplies GPE, but not AGPE, whereas the reverse is true of the combined effect of surface buoyancy forcing and convection. Mixing and buoyancy forcing, thus, play complementary roles in sustaining the large scale circulation. However, the largest globally integrated source of GPE is resolved advection (+0.57 TW) and the largest sink is through parameterized eddy transports (-0.82 TW). The effect of these adiabatic processes on AGPE is identical to their effect on GPE, except for perturbations to both budgets due to numerical leakage exacerbated by non-linearities in the equation of state