Solution of a Model for the Oceanic Pycnocline Depth: Scaling of Overturning Strength and Meridional Pressure Difference

We present an analysis of the model by Gnanadesikan [1999] for the pycnocline depth in the ocean. An analytic solution for the overturning strength as a function of the meridional pressure difference is derived and used to discuss their mutual scaling. We show that scaling occurs only in two unphysical regimes of the model. In the absence of the Southern Ocean (SO) processes, i.e. for a northern overturning cell, the volume transport is proportional to the square root of the pressure difference. Linear scaling is seen when the overturning is restricted entirely to the SO, i.e. when no northern downwelling exists. For comparison, we present simulations with the coupled climate model CLIMBER-3$\alpha$ which show linear scaling over a large regime of pressure differences in the North Atlantic (NA). We conclude that the pycnocline model is not able to reproduce the linear scaling between its two central variables, pressure and volume transport.Comment: Geophysical Research Letters (2004), accepted. See also http://www.pik-potsdam.de/~ander

How does ocean ventilation change under global warming?

International audienceSince the upper ocean takes up much of the heat added to the earth system by anthropogenic global warming, one would expect that global warming would lead to an increase in stratification and a decrease in the ventilation of the ocean interior. However, multiple simulations in global coupled climate models using an ideal age tracer which is set to zero in the mixed layer and ages at 1 yr/yr outside this layer show that the intermediate depths in the low latitudes, Northwest Atlantic, and parts of the Arctic Ocean become younger under global warming. This paper reconciles these apparently contradictory trends, showing that the decreases result from changes in the relative contributions of old deep waters and younger surface waters. Implications for the tropical oxygen minimum zones, which play a critical role in global biogeochemical cycling are considered in detail

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

Delayed baroclinic response of the Antarctic circumpolar current to surface wind stress

Author Posting. © Science in China Press, 2008. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Science in China Series D: Earth Sciences 51 (2008): 1036-1043, doi:10.1007/s11430-008-0074-8.Antarctic Circumpolar Current (ACC) responds to the surface windstress via two processes, i.e., instant barotropic process and delayed baroclinic process. This study focuses on the baroclinic instability mechanism in ACC. That is, the strengthening of surface zonal windstress causes the enhanced tilting of the isopycnal surface, which leads to the intense baroclinic instability. Simultaneously, the mesoscale eddies resulting from the baroclinic instability facilitate the transformation of mean potential energy to eddy energy, which causes the remarkable decrease of the ACC volume transport with the 2-year lag time. This delayed negative correlation between the ACC transport and the zonal windstress may account for the steadiness of the ACC transport in these two decades.Supported by NSCF Outstanding Young Scientist Award (Grant No. 40625017) and the National Basic Research Program of China (Grant No. 2006CB403604). The research was also supported by W. Alan Clark Chair from Woods Hole Oceanographic Institution for RXH and NOAA GLERL contribution No. 1462 for J

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

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

Model projections of the North Atlantic thermohaline circulation for the 21st century assessed by observations

Most climate models predict a weakening of the North Atlantic thermohaline circulation for the 21st century when forced by increasing levels of greenhouse gas concentrations. The model spread, however, is rather large, even when the forcing scenario is identical, indicating a large uncertainty in the response to forcing. In order to reduce the model uncertainties a weighting procedure is applied considering the skill of each model in simulating hydrographic properties and observation-based circulation estimates. This procedure yields a “best estimate” for the evolution of the North Atlantic THC during the 21st century by taking into account a measure of model quality. Using 28 projections from 9 different coupled global climate models of a scenario of future CO2 increase (SRESA1B) performed for the upcoming fourth assessment report of the Intergovernmental Panel on Climate Change, the analysis predicts a gradual weakening of the North Atlantic THC by 25(±25)% until 2100