scholarly journals Symmetric equations on the surface of a sphere as used by model GISS:IB

2018 ◽  
Vol 11 (11) ◽  
pp. 4637-4656
Author(s):  
Gary L. Russell ◽  
David H. Rind ◽  
Jeffrey Jonas
Keyword(s):  
Angular Momentum ◽  
Velocity Component ◽  
Initial Conditions ◽  
Spherical Surface ◽  
Domain Model ◽  
Orthogonal Axis ◽  
The North ◽  
Vector Calculus ◽  
Standard Vector ◽  
Cubed Sphere

Abstract. Standard vector calculus formulas of Cartesian three space are projected onto the surface of a sphere. This produces symmetric equations with three nonindependent horizontal velocity components. Each orthogonal axis has a velocity component that rotates around its axis (eastward velocity rotates around the north–south axis) and a specific angular momentum component that is the product of the velocity component multiplied by the cosine of axis' latitude. Angular momentum components align with the fixed axes and simplify several formulas, whereas the rotating velocity components are not orthogonal and vary with location. Three symmetric coordinates allow vector resolution and calculus operations continuously over the whole spherical surface, which is not possible with only two coordinates. The symmetric equations are applied to one-layer shallow water models on cubed-sphere and icosahedral grids, the latter being computationally simple and applicable to an ocean domain. Model results are presented for three different initial conditions and five different resolutions.

scholarly journals Symmetric Equations on the Surface of a Sphere as Used by Model GISS:IB

2018 ◽  
Author(s):  
Gary L. Russell ◽  
David H. Rind ◽  
Jeffrey Jonas
Keyword(s):  
Angular Momentum ◽  
Velocity Component ◽  
Initial Conditions ◽  
Spherical Surface ◽  
Domain Model ◽  
Orthogonal Axis ◽  
The North ◽  
Vector Calculus ◽  
Standard Vector ◽  
Cubed Sphere

Abstract. Standard vector calculus formulas of Cartesian three space are projected onto the surface of a sphere. This produces symmetric equations with three nonindependent horizontal velocity components. Each orthogonal axis has a velocity component that rotates around its axis (eastward velocity rotates around the north-south axis) and a specific angular momentum component that is the product of the velocity component times the cosine of axis' latitude. Angular momentum components align with the fixed axes and simplify several formulas, whereas the rotating velocity components are not orthogonal and vary with location. Three symmetric coordinates allow vector resolution and calculus operations continuously over the whole spherical surface, which is not possible with only two coordinates. The symmetric equations are applied to one-layer shallow water models on cubed-sphere and icosahedral grids, the latter being computationally simple and applicable to an ocean domain. Model results are presented for three different initial conditions and five different resolutions.

scholarly journals Spreading of warm ocean waters around Greenland as a possible cause for glacier acceleration

2012 ◽  
Vol 53 (60) ◽  
pp. 257-266 ◽  
Author(s):  
E. Rignot ◽  
I. Fenty ◽  
D. Menemenlis ◽  
Y. Xu
Keyword(s):  
Initial Conditions ◽  
Independent Study ◽  
Ocean Temperature ◽  
The North ◽  
Subsurface Ocean ◽  
Subsurface Waters ◽  
Glacier Flow ◽  
Horizontal Grid ◽  
Possible Cause

AbstractWe examine the pattern of spreading of warm subtropical-origin waters around Greenland for the years 1992–2009 using a high-resolution (4km horizontal grid) coupled ocean and sea-ice simulation. The simulation, provided by the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2) project, qualitatively reproduces the observed warming of subsurface waters in the subpolar gyre associated with changes of the North Atlantic atmospheric state that occurred in the mid-1990s. The modeled subsurface ocean temperature warmed by 1.5˚C in southeast and southwest Greenland during 1994–2005 and subsequently cooled by 0.5˚C; modeled subsurface ocean temperature increased by 2–2.5˚C in central and then northwest Greenland during 1997–2005 and stabilized thereafter, while it increased after 2005 by <0.5˚C in north Greenland. Comparisons with in situ measurements off the continental shelf in the Labrador and Irminger Seas indicate that the model initial conditions were 0.4˚C too warm in the south but the simulated warming is correctly reproduced; while measurements from eastern Baffin Bay reveal that the model initial conditions were 1.0˚C too cold in the northwest but the simulated ocean warming brought modeled temperature closer to observations, i.e. the simulated warming is 1.0˚C too large. At several key locations, the modeled oceanic changes off the shelf and below the seasonal mixed layer were rapidly transmitted to the shelf within troughs towards (model-unresolved) fjords. Unless blocked in the fjords by shallow sills, these warm subsurface waters had potential to propagate down the fjords and melt the glacier fronts. Based on model sensitivity simulations from an independent study (Xu and others, 2012), we show that the oceanic changes have very likely increased the subaqueous melt rates of the glacier fronts, and in turn impacted the rates of glacier flow.

scholarly journals Rotation and Flattening of Globular Clusters

1985 ◽  
Vol 113 ◽  
pp. 285-296 ◽  
Author(s):  
S. Michael Fall ◽  
Carlos S. Frenk
Keyword(s):  
Angular Momentum ◽  
Internal Rotation ◽  
Globular Clusters ◽  
Pressure Support ◽  
Initial Conditions ◽  
Anisotropic Pressure ◽  
Stellar Systems ◽  
Galactic Globular Clusters

Pease and Shapley (1917) first remarked on the apparent flattening of several Galactic globular clusters, a view that has been confirmed by many subsequent studies. Tidal stresses, internal rotation, and velocity anisotropies can cause deviations from sphericity in stellar systems. In general, we might expect globular clusters to have some angular momentum at the time of formation and, if they collapsed from flattened initial conditions, to have anisotropic pressure support. Since the velocity distributions within the clusters can be altered by a variety of internal and external processes, their shapes are expected to evolve. In this article, we review the methods for measuring ellipticities and the results that have emerged from such studies. Our main purpose, however, is to discuss the processes that determine the shapes of globular clusters and the ways in which they change with time.

scholarly journals Modelling the wintertime response to upper tropospheric and lower stratospheric ozone anomalies over the North Atlantic and Europe

2003 ◽  
Vol 21 (10) ◽  
pp. 2107-2118 ◽  
Author(s):  
I. Kirchner ◽  
D. Peters
Keyword(s):  
North Atlantic ◽  
General Circulation ◽  
Initial Conditions ◽  
Stratospheric Ozone ◽  
Circulation Model ◽  
Sensitivity Study ◽  
Boreal Winter ◽  
Radiative Processes ◽  
The North ◽  
The North Atlantic

Abstract. During boreal winter months, mean longitude-dependent ozone changes in the upper troposphere and lower stratosphere are mainly caused by different ozone transport by planetary waves. The response to radiative perturbation induced by these ozone changes near the tropopause on the circulation is unclear. This response is investigated with the ECHAM4 general circulation model in a sensitivity study. In the simulation two different mean January realizations of the ozone field are implemented in ECHAM4. Both ozone fields are estimated on the basis of the observed mean January planetary wave structure of the 1980s. The first field represents a 14-year average (reference, 1979–1992) and the second one represents the mean ozone field change (anomaly, 1988–92) in boreal extra-tropics during the end of the 1980s. The model runs were carried out pairwise, with identical initial conditions for both ozone fields. Five statistically independent experiments were performed, forced with the observed sea surface temperatures for the period 1988 to 1992. The results support the hypothesis that the zonally asymmetric ozone changes of the 80s triggered a systematic alteration of the circulation over the North Atlantic – European region. It is suggested that this feedback process is important for the understanding of the decadal coupling between troposphere and stratosphere, as well as between subtropics and extra-tropics in winter.Key words. Meteorology and atmospheric dynamics (general circulation; radiative processes; synoptic-scale meteorology)

scholarly journals The surprisingly small impact of magnetic fields on the inner accretion flow of Sagittarius A* fueled by stellar winds

2019 ◽  
Vol 492 (3) ◽  
pp. 3272-3293 ◽  
Author(s):  
S M Ressler ◽  
E Quataert ◽  
J M Stone
Keyword(s):  
Angular Momentum ◽  
Magnetic Fields ◽  
Event Horizon ◽  
Initial Conditions ◽  
Rotational Instability ◽  
Stellar Winds ◽  
Accretion Flow ◽  
Sagittarius A ◽  
Mhd Simulations ◽  
Sgr A

ABSTRACT We study the flow structure in 3D magnetohydrodynamic (MHD) simulations of accretion on to Sagittarius A* via the magnetized winds of the orbiting Wolf–Rayet stars. These simulations cover over 3 orders of magnitude in radius to reach ≈300 gravitational radii, with only one poorly constrained parameter (the magnetic field in the stellar winds). Even for winds with relatively weak magnetic fields (e.g. plasma β ∼ 106), flux freezing/compression in the inflowing gas amplifies the field to β ∼ few well before it reaches the event horizon. Overall, the dynamics, accretion rate, and spherically averaged flow profiles (e.g. density, velocity) in our MHD simulations are remarkably similar to analogous hydrodynamic simulations. We attribute this to the broad distribution of angular momentum provided by the stellar winds, which sources accretion even absent much angular momentum transport. We find that the magneto-rotational instability is not important because of (i) strong magnetic fields that are amplified by flux freezing/compression, and (ii) the rapid inflow/outflow times of the gas and inefficient radiative cooling preclude circularization. The primary effect of magnetic fields is that they drive a polar outflow that is absent in hydrodynamics. The dynamical state of the accretion flow found in our simulations is unlike the rotationally supported tori used as initial conditions in horizon scale simulations, which could have implications for models being used to interpret Event Horizon Telescope and GRAVITY observations of Sgr A*.

scholarly journals Response of Idealized Baroclinic Wave Life Cycles to Stratospheric Flow Conditions

2009 ◽  
Vol 66 (8) ◽  
pp. 2288-2302 ◽  
Author(s):  
Torben Kunz ◽  
Klaus Fraedrich ◽  
Frank Lunkeit
Keyword(s):  
Refractive Index ◽  
Initial Conditions ◽  
Spherical Geometry ◽  
Zonal Flow ◽  
Equation Model ◽  
Life Cycles ◽  
Baroclinic Wave ◽  
Flow Conditions ◽  
Mean Flow ◽  
The North

Abstract Dynamical stratosphere–troposphere coupling through a response of baroclinic waves to lower stratospheric flow conditions is investigated from an initial value approach. A series of adiabatic and frictionless nonlinear baroclinic wave life cycles in a midlatitude tropospheric jet with different initial zonal flow conditions in the stratosphere is simulated, using a dry primitive equation model with spherical geometry. When a stratospheric jet, located at various latitudes between 35° and 70°, is removed from the initial conditions, the wavenumber-6 life cycle behavior changes from the well-known LC1 to LC2 evolution, characterized by anticyclonic and cyclonic wave breaking, respectively. Linear theory, in terms of refractive index and the structure of the corresponding fastest-growing normal mode, is found to be unable to explain this stratosphere-induced LC1 to LC2 transition. This implies that altered nonlinear wave–mean flow interactions are important. The most significant stratosphere-induced change that extends into the nonlinear baroclinic growth stage is a region of downward wave propagation in the lower stratosphere associated with positive values of the squared refractive index near 20 km. Furthermore, it is demonstrated that the difference between the response of the tropospheric circulation to LC1 and LC2 life cycles closely resembles the meridional and vertical structure of the North Atlantic Oscillation (NAO), with positive (negative) NAO-like anomalies being driven by LC1 (LC2). Thus, a weakened stratospheric jet induces the generation of negative NAO-like anomalies in the troposphere, consistent with the observed stratosphere–NAO connection.

The Value of Initialization on Decadal Timescales: State-Dependent Predictability in the CESM Decadal Prediction Large Ensemble

2020 ◽  
Vol 33 (17) ◽  
pp. 7353-7370
Author(s):  
H. M. Christensen ◽  
J. Berner ◽  
S. Yeager
Keyword(s):  
Time Scale ◽  
Initial Conditions ◽  
Heat Content ◽  
Atlantic Multidecadal Oscillation ◽  
Forced Response ◽  
Climate Change Signal ◽  
Seasonal Forecasts ◽  
The North ◽  
State Dependent ◽  
Start Dates

AbstractInformation in decadal climate prediction arises from a well-initialized ocean state and from the predicted response to an external forcing. The length of time over which the initial conditions benefit the decadal forecast depends on the start date of the forecast. We characterize this state-dependent predictability for decadal forecasts of upper ocean heat content in the Community Earth System Model. We find regionally dependent initial condition predictability, with extended predictability generally observed in the extratropics. We also detect state-dependent predictability, with the year of loss of information from the initialization varying between start dates. The decadal forecasts in the North Atlantic show substantial information from the initial conditions beyond the 10-yr forecast window, and a high degree of state-dependent predictability. We find some evidence for state-dependent predictability in the ensemble spread in this region, similar to that seen in weather and subseasonal-to-seasonal forecasts. For some start dates, an increase of information with lead time is observed, for which the initialized forecasts predict a growing phase of the Atlantic multidecadal oscillation. Finally we consider the information in the forecast from the initial conditions relative to the forced response, and quantify the crossover time scale after which the forcing provides more information. We demonstrate that the climate change signal projects onto different patterns than the signal from the initial conditions. This means that even after the crossover time scale has been reached in a basin-averaged sense, the benefits of initialization can be felt locally on longer time scales.

scholarly journals Sources of Uncertainty in Future Projections of the Carbon Cycle

2016 ◽  
Vol 29 (20) ◽  
pp. 7203-7213 ◽  
Author(s):  
Alan J. Hewitt ◽  
Ben B. B. Booth ◽  
Chris D. Jones ◽  
Eddy S. Robertson ◽  
Andy J. Wiltshire ◽  
...  
Keyword(s):  
Carbon Cycle ◽  
Climate Models ◽  
Climate Model ◽  
Initial Conditions ◽  
Carbon Fluxes ◽  
Global Ocean ◽  
Lead Times ◽  
Carbon Uptake ◽  
The North ◽  
Ocean Carbon

Abstract The inclusion of carbon cycle processes within CMIP5 Earth system models provides the opportunity to explore the relative importance of differences in scenario and climate model representation to future land and ocean carbon fluxes. A two-way analysis of variance (ANOVA) approach was used to quantify the variability owing to differences between scenarios and between climate models at different lead times. For global ocean carbon fluxes, the variance attributed to differences between representative concentration pathway scenarios exceeds the variance attributed to differences between climate models by around 2025, completely dominating by 2100. This contrasts with global land carbon fluxes, where the variance attributed to differences between climate models continues to dominate beyond 2100. This suggests that modeled processes that determine ocean fluxes are currently better constrained than those of land fluxes; thus, one can be more confident in linking different future socioeconomic pathways to consequences of ocean carbon uptake than for land carbon uptake. The contribution of internal variance is negligible for ocean fluxes and small for land fluxes, indicating that there is little dependence on the initial conditions. The apparent agreement in atmosphere–ocean carbon fluxes, globally, masks strong climate model differences at a regional level. The North Atlantic and Southern Ocean are key regions, where differences in modeled processes represent an important source of variability in projected regional fluxes.

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