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

Exploring the isopycnal mixing and helium–heat paradoxes in a suite of Earth system models

This paper uses a suite of Earth system models which simulate the distribution of He isotopes and radiocarbon to examine two paradoxes in Earth science, each of which results from an inconsistency between theoretically motivated global energy balances and direct observations. The helium–heat paradox refers to the fact that helium emissions to the deep ocean are far lower than would be expected given the rate of geothermal heating, since both are thought to be the result of radioactive decay in Earth's interior. The isopycnal mixing paradox comes from the fact that many theoretical parameterizations of the isopycnal mixing coefficient ARedi that link it to baroclinic instability project it to be small (of order a few hundred m² s⁻¹) in the ocean interior away from boundary currents. However, direct observations using tracers and floats (largely in the upper ocean) suggest that values of this coefficient are an order of magnitude higher. Helium isotopes equilibrate rapidly with the atmosphere and thus exhibit large gradients along isopycnals while radiocarbon equilibrates slowly and thus exhibits smaller gradients along isopycnals. Thus it might be thought that resolving the isopycnal mixing paradox in favor of the higher observational estimates of ARedi might also solve the helium paradox, by increasing the transport of mantle helium to the surface more than it would radiocarbon. In this paper we show that this is not the case. In a suite of models with different spatially constant and spatially varying values of ARedi the distribution of radiocarbon and helium isotopes is sensitive to the value of ARedi. However, away from strong helium sources in the southeastern Pacific, the relationship between the two is not sensitive, indicating that large-scale advection is the limiting process for removing helium and radiocarbon from the deep ocean. The helium isotopes, in turn, suggest a higher value of ARedi below the thermocline than is seen in theoretical parameterizations based on baroclinic growth rates. We argue that a key part of resolving the isopycnal mixing paradox is to abandon the idea that ARedi has a direct relationship to local baroclinic instability and to the so-called "thickness" mixing coefficient AGM

Estimating the contribution of strong daily export events to total pollutant export from the United States in summer

While the export of pollutants from the United States exhibits notable variability from day to day and is often considered to be “episodic,” the contribution of strong daily export events to total export has not been quantified. We use carbon monoxide (CO) as a tracer of anthropogenic pollutants in the Model of OZone And Related Tracers (MOZART) to estimate this contribution. We first identify the major export pathway from the United States to be through the northeast boundary (24–48°N along 67.5°W and 80–67.5°W along 48°N), and then analyze 15 summers of daily CO export fluxes through this boundary. These daily CO export fluxes have a nearly Gaussian distribution with a mean of 1100 Gg CO day−1 and a standard deviation of 490 Gg CO day−1. To focus on the synoptic variability, we define a “synoptic background” export flux equal to the 15 day moving average export flux and classify strong export days according to their fluxes relative to this background. As expected from Gaussian statistics, 16% of summer days are “strong export days,” classified as those days when the CO export flux exceeds the synoptic background by one standard deviation or more. Strong export days contributes 25% to the total export, a value determined by the relative standard deviation of the CO flux distribution. Regressing the anomalies of the CO export flux through the northeast U.S. boundary relative to the synoptic background on the daily anomalies in the surface pressure field (also relative to a 15 day running mean) suggests that strong daily export fluxes are correlated with passages of midlatitude cyclones over the Gulf of Saint Lawrence. The associated cyclonic circulation and Warm Conveyor Belts (WCBs) that lift surface pollutants over the northeastern United States have been shown previously to be associated with long-range transport events. Comparison with observations from the 2004 INTEX-NA field campaign confirms that our model captures the observed enhancements in CO outflow and resolves the processes associated with cyclone passages on strong export days. “Moderate export days,” defined as days when the CO flux through the northeast boundary exceeds the 15 day running mean by less than one standard deviation, represent an additional 34% of summer days and 40% of total export. These days are also associated with migratory midlatitude cyclones. The remaining 35% of total export occurs on “weak export days” (50% of summer days) when high pressure anomalies occur over the Gulf of Saint Lawrence. Our findings for summer also apply to spring, when the U.S. pollutant export is typically strongest, with similar contributions to total export and associated meteorology on strong, moderate and weak export days. Although cyclone passages are the primary driver for strong daily export events, export during days without cyclone passages also makes a considerable contribution to the total export and thereby to the global pollutant budget

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

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

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