scholarly journals Computation of Stability Criterion for Fractional Ocean Circulation Box Model Using Optimal Routh—Hurwitz Conditions

2021 ◽  
Vol 2084 (1) ◽  
pp. 012021
Author(s):  
Yong Xian Ng ◽  
Chang Phang
Keyword(s):  
Dynamical Systems ◽  
Atlantic Ocean ◽  
Fractional Order ◽  
Ocean Circulation ◽  
Stability Criterion ◽  
Thermohaline Circulation ◽  
Real Life ◽  
Circulation Model ◽  
Box Model ◽  
The Stability

Abstract Atlantic ocean thermohaline circulation is a deep ocean circulation occur in the Atlantic ocean which shows mixed of salt and freshwater transportation. The ocean circulation box model is defined to cover the large-scale behavior of the thermohaline circulation. On the other hand, fractional order dynamical systems are more flexible and realistic for real-life problems if compare with integer order dynamical systems. Hence, research on the stability for fractional dynamical systems is still infant and more difficult to analyze analytically. In this paper, we will extend the ocean circulation 3-box model into fractional order and investigate stability criterion for this fractional model by applying fractional Routh-Hurwitz conditions. Routh-Hurwitz conditions allow us to find the range of adjustable control parameter F1 which can detect the stability criterion for the fractional ocean circulation model.

HOMOCLINIC BIFURCATION IN AN OCEAN CIRCULATION BOX MODEL

2002 ◽  
Vol 12 (04) ◽  
pp. 869-875 ◽  
Author(s):  
SVEN TITZ ◽  
TILL KUHLBRODT ◽  
ULRIKE FEUDEL
Keyword(s):  
Hopf Bifurcation ◽  
Ocean Circulation ◽  
Thermohaline Circulation ◽  
Homoclinic Bifurcation ◽  
Box Model ◽  
Qualitative Behavior ◽  
Unstable Periodic Orbit ◽  
Normal Form Theory ◽  
Form Theory ◽  
The Stability

The qualitative behavior of a conceptual ocean box model is investigated. It is a paradigmatic model of the thermohaline ocean circulation of the Atlantic. In a bifurcation study, the two occurring bifurcations, a saddle-node and a Hopf bifurcation, are computed analytically. Using normal form theory, it is shown that the latter bifurcation is always subcritical. The unstable periodic orbit emerging at the Hopf bifurcation vanishes in a homoclinic bifurcation. The results are interpreted with respect to the stability of the thermohaline circulation.

On the impact of sea ice in a global ocean circulation model

1997 ◽  
Vol 25 ◽  
pp. 111-115 ◽  
Author(s):  
Achim Stössel
Keyword(s):  
Southern Ocean ◽  
Sea Ice ◽  
Ocean Circulation ◽  
General Circulation ◽  
Thermohaline Circulation ◽  
Circulation Model ◽  
Deep Ocean ◽  
Global Ocean ◽  
Convective Activity ◽  
The Impact

This paper investigates the long-term impact of sea ice on global climate using a global sea-ice–ocean general circulation model (OGCM). The sea-ice component involves state-of-the-art dynamics; the ocean component consists of a 3.5° × 3.5° × 11 layer primitive-equation model. Depending on the physical description of sea ice, significant changes are detected in the convective activity, in the hydrographic properties and in the thermohaline circulation of the ocean model. Most of these changes originate in the Southern Ocean, emphasizing the crucial role of sea ice in this marginally stably stratified region of the world's oceans. Specifically, if the effect of brine release is neglected, the deep layers of the Southern Ocean warm up considerably; this is associated with a weakening of the Southern Hemisphere overturning cell. The removal of the commonly used “salinity enhancement” leads to a similar effect. The deep-ocean salinity is almost unaffected in both experiments. Introducing explicit new-ice thickness growth in partially ice-covered gridcells leads to a substantial increase in convective activity, especially in the Southern Ocean, with a concomitant significant cooling and salinification of the deep ocean. Possible mechanisms for the resulting interactions between sea-ice processes and deep-ocean characteristics are suggested.

A Near-Uniform Basin-Wide Sea Level Fluctuation of the Mediterranean Sea

2007 ◽  
Vol 37 (2) ◽  
pp. 338-358 ◽  
Author(s):  
Ichiro Fukumori ◽  
Dimitris Menemenlis ◽  
Tong Lee
Keyword(s):  
Atlantic Ocean ◽  
Mediterranean Sea ◽  
Sea Level ◽  
Ocean Circulation ◽  
Large Scale ◽  
Circulation Model ◽  
Level Fluctuation ◽  
Strait Of Gibraltar ◽  
Sea Level Fluctuation ◽  
The Mediterranean

Abstract A new basin-wide oscillation of the Mediterranean Sea is identified and analyzed using sea level observations from the Ocean Topography Experiment (TOPEX)/Poseidon satellite altimeter and a numerical ocean circulation model. More than 50% of the large-scale, nontidal, and non-pressure-driven variance of sea level can be attributed to this oscillation, which is nearly uniform in phase and amplitude across the entire basin. The oscillation has periods ranging from 10 days to several years and has a magnitude as large as 10 cm. The model suggests that the fluctuations are driven by winds at the Strait of Gibraltar and its neighboring region, including the Alboran Sea and a part of the Atlantic Ocean immediately to the west of the strait. Winds in this region force a net mass flux through the Strait of Gibraltar to which the Mediterranean Sea adjusts almost uniformly across its entire basin with depth-independent pressure perturbations. The wind-driven response can be explained in part by wind setup; a near-stationary balance is established between the along-strait wind in this forcing region and the sea level difference between the Mediterranean Sea and the Atlantic Ocean. The amplitude of this basin-wide wind-driven sea level fluctuation is inversely proportional to the setup region’s depth but is insensitive to its width including that of Gibraltar Strait. The wind-driven fluctuation is coherent with atmospheric pressure over the basin and contributes to the apparent deviation of the Mediterranean Sea from an inverse barometer response.

scholarly journals Manganese in the west Atlantic Ocean in the context of the first global ocean circulation model of manganese

2017 ◽  
Vol 14 (5) ◽  
pp. 1123-1152 ◽  
Author(s):  
Marco van Hulten ◽  
Rob Middag ◽  
Jean-Claude Dutay ◽  
Hein de Baar ◽  
Matthieu Roy-Barman ◽  
...  
Keyword(s):  
Atlantic Ocean ◽  
Ocean Circulation ◽  
Surface Waters ◽  
Manganese Oxides ◽  
Essential Element ◽  
Circulation Model ◽  
Global Ocean ◽  
Background Concentration ◽  
Elevated Concentration ◽  
The West

Abstract. Dissolved manganese (Mn) is a biologically essential element. Moreover, its oxidised form is involved in removing itself and several other trace elements from ocean waters. Here we report the longest thus far (17 500 km length) full-depth ocean section of dissolved Mn in the west Atlantic Ocean, comprising 1320 data values of high accuracy. This is the GA02 transect that is part of the GEOTRACES programme, which aims to understand trace element distributions. The goal of this study is to combine these new observations with new, state-of-the-art, modelling to give a first assessment of the main sources and redistribution of Mn throughout the ocean. To this end, we simulate the distribution of dissolved Mn using a global-scale circulation model. This first model includes simple parameterisations to account for the sources, processes and sinks of Mn in the ocean. Oxidation and (photo)reduction, aggregation and settling, as well as biological uptake and remineralisation by plankton are included in the model. Our model provides, together with the observations, the following insights: – The high surface concentrations of manganese are caused by the combination of photoreduction and sources contributing to the upper ocean. The most important sources are sediments, dust, and, more locally, rivers. – Observations and model simulations suggest that surface Mn in the Atlantic Ocean moves downwards into the southward-flowing North Atlantic Deep Water (NADW), but because of strong removal rates there is no elevated concentration of Mn visible any more in the NADW south of 40° N. – The model predicts lower dissolved Mn in surface waters of the Pacific Ocean than the observed concentrations. The intense oxygen minimum zone (OMZ) in subsurface waters is deemed to be a major source of dissolved Mn also mixing upwards into surface waters, but the OMZ is not well represented by the model. Improved high-resolution simulation of the OMZ may solve this problem. – There is a mainly homogeneous background concentration of dissolved Mn of about 0.10–0.15 nM throughout most of the deep ocean. The model reproduces this by means of a threshold on particulate manganese oxides of 25 pM, suggesting that a minimal concentration of particulate Mn is needed before aggregation and removal become efficient. – The observed distinct hydrothermal signals are produced by assuming both a strong source and a strong removal of Mn near hydrothermal vents.

scholarly journals Obstacles and benefits of the implementation of a reduced rank smoother with a high resolution model of the Atlantic ocean

2012 ◽  
Vol 9 (2) ◽  
pp. 1187-1229 ◽  
Author(s):  
N. Freychet ◽  
E. Cosme ◽  
P. Brasseur ◽  
J.-M. Brankart ◽  
E. Kpemlie
Keyword(s):  
Atlantic Ocean ◽  
Ocean Circulation ◽  
Three Dimensional ◽  
Circulation Model ◽  
Point Of View ◽  
Optimal Interpolation ◽  
The North ◽  
Observation Network ◽  
North Brazil ◽  
Resolution Model

Abstract. Most of oceanographic operational centers use three-dimensional data assimilation schemes to produce reanalyses. We investigate here the benefits of a smoother, i.e. a four-dimensional formulation of statistical assimilation. A square-root sequential smoother is implemented with a tropical Atlantic ocean circulation model. A simple twin experiment is performed to investigate its benefits, compared to its corresponding filter. Results show that the smoother leads to a better estimation of the ocean state, both on statistical (i.e. mean error level) and dynamical point of view. Smoothed states are more in phase with the dynamics of the reference state, an aspect that is nicely illustrated with the chaotic dynamics of the north-Brazil rings. We also show that the smoother efficiency is strongly related to the filter configuration. One of the main obstacles to implement the smoother is then to accurately estimate the error covariances of the filter. Considering this, benefits of the smoother are also investigated with a configuration close to situations that can be managed by operational centers systems, where covariances matrices are fixed (optimal interpolation). We define here a simplified smoother scheme, called half-fixed basis smoother, that could be implemented with current reanalysis schemes. Its main assumption is to neglect the propagation of the error covariances matrix, what leads to strongly reduce the cost of assimilation. Results illustrate the ability of this smoother to provide a solution more consistent with the dynamics, compared to the filter. The smoother is also able to produce analyses independently of the observation frequency, so the smoothed solution appears more continuous in time, especially in case of a low frenquency observation network.

scholarly journals Effect of vegetation on the Late Miocene ocean circulation

2006 ◽  
Vol 2 (4) ◽  
pp. 605-631 ◽  
Author(s):  
G. Lohmann ◽  
M. Butzin ◽  
A. Micheels ◽  
T. Bickert ◽  
V. Mosbrugger
Keyword(s):  
Ocean Circulation ◽  
North Atlantic ◽  
Late Miocene ◽  
Land Surface ◽  
General Circulation ◽  
Thermohaline Circulation ◽  
Hydrological Cycle ◽  
Circulation Model ◽  
The North ◽  
The North Atlantic

Abstract. A weak and shallow thermohaline circulation in the North Atlantic Ocean is related to an open Central American gateway and exchange with fresh Pacific waters. We estimate the effect of vegetation on the ocean general circulation using the atmospheric circulation model simulations for the Late Miocene climate. Caused by an increase in net evaporation in the Miocene North Atlantic, the North Atlantic water becomes more saline which enhances the overturning circulation and thus the northward heat transport. This effect reveals a potentially important feedback between the ocean circulation, the hydrological cycle and the land surface cover for Cenozoic climate evolution.

scholarly journals Chaos synchronization of a fractional nonautonomous system

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Zakia Hammouch ◽  
Toufik Mekkaoui
Keyword(s):  
Dynamic Behavior ◽  
Fractional Order ◽  
Chaotic System ◽  
Stability Criterion ◽  
Chaos Synchronization ◽  
Phase Locked Loop ◽  
Numerical Results ◽  
The Other ◽  
Fractional Systems ◽  
The Stability

AbstractIn this paper we investigate the dynamic behavior of a nonautonomous fractional-order biological system.With the stability criterion of active nonlinear fractional systems, the synchronization of the studied chaotic system is obtained. On the other hand, using a Phase-Locked-Loop (PLL) analogy we synchronize the same system. The numerical results demonstrate the efiectiveness of the proposed methods

scholarly journals Obstacles and benefits of the implementation of a reduced-rank smoother with a high resolution model of the tropical Atlantic Ocean

Ocean Science ◽  
2012 ◽  
Vol 8 (5) ◽  
pp. 797-811
Author(s):  
N. Freychet ◽  
E. Cosme ◽  
P. Brasseur ◽  
J.-M. Brankart ◽  
E. Kpemlie
Keyword(s):  
Atlantic Ocean ◽  
Ocean Circulation ◽  
Three Dimensional ◽  
Circulation Model ◽  
Optimal Interpolation ◽  
Tropical Atlantic ◽  
Tropical Atlantic Ocean ◽  
The North ◽  
North Brazil ◽  
Resolution Model

Abstract. Most of oceanographic operational centers use three-dimensional data assimilation schemes to produce reanalyses. We investigate here the benefits of a smoother, i.e. a four-dimensional formulation of statistical assimilation. A square-root sequential smoother is implemented with a tropical Atlantic Ocean circulation model. A simple twin experiment is performed to investigate its benefits, compared to its corresponding filter. Despite model's non-linearities and the various approximations used for its implementation, the smoother leads to a better estimation of the ocean state, both on statistical (i.e. mean error level) and dynamical points of view, as expected from linear theory. Smoothed states are more in phase with the dynamics of the reference state, an aspect that is nicely illustrated with the chaotic dynamics of the North Brazil Current rings. We also show that the smoother efficiency is strongly related to the filter configuration. One of the main obstacles to implement the smoother is then to accurately estimate the error covariances of the filter. Considering this, benefits of the smoother are also investigated with a configuration close to situations that can be managed by operational center systems, where covariances matrices are fixed (optimal interpolation). We define here a simplified smoother scheme, called half-fixed basis smoother, that could be implemented with current reanalysis schemes. Its main assumption is to neglect the propagation of the error covariances matrix, what leads to strongly reduce the cost of assimilation. Results illustrate the ability of this smoother to provide a solution more consistent with the dynamics, compared to the filter. The smoother is also able to produce analyses independently of the observation frequency, so the smoothed solution appears more continuous in time, especially in case of a low frenquency observation network.

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