The improved robustness of multigrid elliptic solvers based on multiple semicoarsened grids

Multigrid convergence rates degenerate on problems with stretched grids or anisotropic operators, unless one uses line or plane relaxation. For 3-D problems, only plane relaxation suffices, in general. While line and plane relaxation algorithms are efficient on sequential machines, they are quite awkward and inefficient on parallel machines. A new multigrid algorithm is presented based on the use of multiple coarse grids, that eliminates the need for line or plane relaxation in anisotropic problems. This algorithm was developed and the standard multigrid theory was extended to establish rapid convergence for this class of algorithms. The new algorithm uses only point relaxation, allowing easy and efficient parallel implementation, yet achieves robustness and convergence rates comparable to line and plane relaxation multigrid algorithms. The algorithm described is a variant of Mulder's multigrid algorithm for hyperbolic problems. The latter uses multiple coarse grids to achieve robustness, but is unsuitable for elliptic problems, since its V-cycle convergence rate goes to one as the number of levels increases. The new algorithm combines the contributions from the multiple coarse grid via a local switch, based on the strength of the discrete operator in each coordinate direction

Parallelization of implicit finite difference schemes in computational fluid dynamics

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed

A Mechanisms-Based Approach to Detecting Recent Anthropogenic Hydroclimate Change

Both naturally occurring La Niña events and model-projected anthropogenic-driven global warming are associated with widespread drying in the subtropics to midlatitudes. Models suggest anthropogenic drying should already be underway but climate variability on interannual to multidecadal time scales can easily obscure any emerging trend, making it hard to assess the validity of the simulated forced change. Here, the authors address this problem by using model simulations and the twentieth-century reanalysis to distinguish between natural variability of, and radiatively forced change in, hydroclimate on the basis of the mechanisms of variations in the three-dimensional moisture budget that drive variations in precipitation minus evaporation (P 2 E). Natural variability of P 2 E is dominated by the El Niño–Southern Oscillation (ENSO) cycle and is "dynamics dominated" in that the associated global P2E anomalies are primarily driven by changes in circulation. This is quite well reproduced in the multimodel mean of 15 models used in the Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC AR4)/Coupled Model Intercomparison Project 3 (CMIP3). In contrast, radiatively forced P 2 E change is "thermodynamics mediated" in that the rise in specific humidity leads to intensified patterns of moisture transport and P 2 E. But, as for ENSO, the poleward shift of the storm tracks and mean meridional circulation cells also contribute to changes in P 2 E. However, La Niña and radiatively forced changes in the zonal mean flow are distinct in the tropics. These distinctions are applied to the post-1979 record of P 2 E in the twentieth-century reanalysis. ENSO-related variations strongly influence the observed P 2 E trend since 1979, but removal of this influence leaves an emerging pattern of P 2 E change consistent with the predictions of the IPCC AR4/CMIP3 models over this period together with, to some extent, consistent contributions from dynamical and thermodynamical mechanisms and consistent changes in the zonal mean circulation. The forced trends are currently weak compared to those caused by internal variability

Thermodynamic and Dynamic Mechanisms for Large-Scale Changes in the Hydrological Cycle in Response to Global Warming

The mechanisms of changes in the large-scale hydrological cycle projected by 15 models participating in the Coupled Model Intercomparison Project phase 3 and used for the Intergovernmental Panel on Climate Change’s Fourth Assessment Report are analyzed by computing differences between 2046 and 2065 and 1961 and 2000. The contributions to changes in precipitation minus evaporation, P − E, caused thermodynamically by changes in specific humidity, dynamically by changes in circulation, and by changes in moisture transports by transient eddies are evaluated. The thermodynamic and dynamic contributions are further separated into advective and divergent components. The nonthermodynamic contributions are then related to changes in the mean and transient circulation. The projected change in P − E involves an intensification of the existing pattern of P − E with wet areas [the intertropical convergence zone (ITCZ) and mid- to high latitudes] getting wetter and arid and semiarid regions of the subtropics getting drier. In addition, the subtropical dry zones expand poleward. The accentuation of the twentieth-century pattern of P − E is in part explained by increases in specific humidity via both advection and divergence terms. Weakening of the tropical divergent circulation partially opposes the thermodynamic contribution by creating a tendency to decreased P − E in the ITCZ and to increased P − E in the descending branches of the Walker and Hadley cells. The changing mean circulation also causes decreased P − E on the poleward flanks of the subtropics because the descending branch of the Hadley Cell expands and the midlatitude meridional circulation cell shifts poleward. Subtropical drying and poleward moistening are also contributed to by an increase in poleward moisture transport by transient eddies. The thermodynamic contribution to changing P − E, arising from increased specific humidity, is almost entirely accounted for by atmospheric warming under fixed relative humidity

Thermodynamic and Dynamic Mechanisms for Large-Scale Changes in the Hydrological Cycle in Response to Global Warming

The mechanisms of changes in the large-scale hydrological cycle projected by 15 models participating in the Coupled Model Intercomparison Project phase 3 and used for the Intergovernmental Panel on Climate Change’s Fourth Assessment Report are analyzed by computing differences between 2046 and 2065 and 1961 and 2000. The contributions to changes in precipitation minus evaporation, P − E, caused thermodynamically by changes in specific humidity, dynamically by changes in circulation, and by changes in moisture transports by transient eddies are evaluated. The thermodynamic and dynamic contributions are further separated into advective and divergent components. The nonthermodynamic contributions are then related to changes in the mean and transient circulation. The projected change in P − E involves an intensification of the existing pattern of P − E with wet areas [the intertropical convergence zone (ITCZ) and mid- to high latitudes] getting wetter and arid and semiarid regions of the subtropics getting drier. In addition, the subtropical dry zones expand poleward. The accentuation of the twentieth-century pattern of P − E is in part explained by increases in specific humidity via both advection and divergence terms. Weakening of the tropical divergent circulation partially opposes the thermodynamic contribution by creating a tendency to decreased P − E in the ITCZ and to increased P − E in the descending branches of the Walker and Hadley cells. The changing mean circulation also causes decreased P − E on the poleward flanks of the subtropics because the descending branch of the Hadley Cell expands and the midlatitude meridional circulation cell shifts poleward. Subtropical drying and poleward moistening are also contributed to by an increase in poleward moisture transport by transient eddies. The thermodynamic contribution to changing P − E, arising from increased specific humidity, is almost entirely accounted for by atmospheric warming under fixed relative humidity

Coupled climate model simulations of Mediterranean winter cyclones and large-scale flow patterns

The study aims to evaluate the ability of global, coupled climate models to reproduce the synoptic regime of the Mediterranean Basin. The output of simulations of the 9 models included in the IPCC CMIP3 effort is compared to the NCEP-NCAR reanalyzed data for the period 1961–1990. The study examined the spatial distribution of cyclone occurrence, the mean Mediterranean upper- and lower-level troughs, the inter-annual variation and trend in the occurrence of the Mediterranean cyclones, and the main large-scale circulation patterns, represented by rotated EOFs of 500 hPa and sea level pressure. The models reproduce successfully the two maxima in cyclone density in the Mediterranean and their locations, the location of the average upper- and lower-level troughs, the relative inter-annual variation in cyclone occurrences and the structure of the four leading large scale EOFs. The main discrepancy is the models' underestimation of the cyclone density in the Mediterranean, especially in its western part. The models' skill in reproducing the cyclone distribution is found correlated with their spatial resolution, especially in the vertical. The current improvement in model spatial resolution suggests that their ability to reproduce the Mediterranean cyclones would be improved as well

Impact of the Midlatitude Storm Track on the Upper Pacific Ocean

Transient eddies in the atmosphere induce a poleward transport of heat and moisture. A moist static energy budget of the surface layer is determined from the NCEP reanalysis data to evaluate the impact of the storm track. It is found that the transient eddies induce a cooling and drying of the surface layer with a monthly mean maximum of 60 W m−2. The cooling in the midlatitudes extends zonally over the entire basin. The impact of this cooling and drying on surface heat fluxes, sea surface temperature (SST), water mass transformation, and vertical structure of the Pacific is investigated using an ocean model coupled to an atmospheric mixed layer model. The cooling by atmospheric storms is represented by adding an eddy-induced transfer velocity to the mean velocity in an atmospheric mixed layer model. This is based on a parameterization of tracer transport by eddies in the ocean. When the atmospheric mixed layer model is coupled to an ocean model, realistic SSTs are simulated. The SST is up to 3 K lower due to the cooling by storms. The additional cooling leads to enhanced transformation rates of water masses in the midlatitudes. The enhanced shallow overturning cells affect even tropical regions. Together with realistic SST and deep winter mixed layer depths, this leads to formation of homogeneous water masses in the upper North Pacific, in accordance to observations

Atmospheric Circulation Response to an Instantaneous Doubling of Carbon Dioxide Part I: Model Experiments and Transient Thermal Response in the Troposphere

This study aims to understand the dynamical mechanisms driving the changes in the general circulation of the atmosphere due to increased carbon dioxide (CO2) by looking into the transient step-by-step adjustment of the circulation. The transient atmospheric adjustment is examined using the National Center for Atmospheric Research Community Atmospheric Model Version 3 coupled to a slab ocean model and the CO2 concentration in the atmosphere is uniformly and instantaneously doubled. The thermal structure and circulation response is well established after one year of integration with the magnitudes gradually increasing afterwards towards quasi-equilibrium. Tropical upper tropospheric warming occurs in the first month. The expansion of the warming in the middle and upper troposphere to the subtropics occurs later and is found to be primarily dynamically-driven due to the intensification of transient eddy momentum flux convergence and resulting anomalous descending motion in this region. The poleward displacement of the midlatitude tropospheric jet streams occurs together with the change in eddy momentum flux convergence but only after the intensification of the subpolar westerlies in the stratosphere. The results demonstrate the importance of the tropospheric eddies in setting up the extratropical tropospheric response to global warming

Northern Hemisphere winter snow anomalies: ENSO, NAO and the winter of 2009/10

Winter 2009/10 had anomalously large snowfall in the central parts of the United States and in northwestern Europe. Connections between seasonal snow anomalies and the large scale atmospheric circulation are explored. An El Niño state is associated with positive snowfall anomalies in the southern and central United States and along the eastern seaboard and negative anomalies to the north. A negative NAO causes positive snow anomalies across eastern North America and in northern Europe. It is argued that increased snowfall in the southern U.S. is contributed to by a southward displaced storm track but further north, in the eastern U.S. and northern Europe, positive snow anomalies arise from the cold temperature anomalies of a negative NAO. These relations are used with observed values of NINO3 and the NAO to conclude that the negative NAO and El Niño event were responsible for the northern hemisphere snow anomalies of winter 2009/10

Atmospheric Circulation Response to an Instantaneous Doubling of Carbon Dioxide. Part II: Atmospheric Transient Adjustment and Its Dynamics

The dynamical mechanisms underlying the transient circulation adjustment in the extratropical atmosphere after the instantaneous doubling of carbon dioxide are investigated using the National Center for Atmospheric Research Community Atmosphere Model version 3 coupled to a Slab Ocean Model. It is shown that the transient process during the first few months of integration is important in setting up the extratropical circulation response in equilibrium such as the poleward shift of the tropospheric jet streams. Three phases are found during the transient thermal/dynamical adjustment in the Northern Hemisphere: 1) a radiatively driven easterly anomaly in the subpolar stratosphere, 2) an acceleration of the westerly anomaly in the subpolar stratosphere as a result of anomalous planetary-scale eddy momentum flux convergence, and 3) a “downward migration” of the westerly anomaly from the lower stratosphere to the troposphere, followed by the tropospheric jet shift. Several proposed mechanisms for inducing the poleward shift of the tropospheric jet streams are examined. No significant increase in eddy phase speed is found. The rise in tropopause height appears to lead the tropospheric jet shift but no close relation is observed. The length scale of transient eddies does increase but does not lead the tropospheric jet shift. Finally, the tropospheric jet shift can be captured by changes in the index of refraction and the resulting anomalous eddy propagation in the troposphere