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Climate modeling is one of the grand challenges of computational science, and ocean modeling plays an important role in both understanding the current climatic conditions and predicting future climate change.
Sea level has been rising for the past century, and inhabitants of the Earth's coastal regions will want to understand and predict future sea level changes. In this study we present results from new simulations of the Goddard Institute for Space Studies (GISS) global atmosphere-ocean model from 1950 to 2099. Model results are compared with observed sea level changes during the past 40 years at 17 coastal stations around the world. Using observed levels of greenhouse gases between 1950 and 1990 and a compounded 0.5% annual increase in Co2 after 1990, model projections show that global sea level measured from 1950 will rise by 61 mm in the year 2000, by 212 mm in 2050, and by 408 mm in 2089. By 2089, two thirds of the global sea level rise will be due to thermal expansion and one third will be due to ocean mass changes. The spatial distribution of sea level rise is different than that projected by rigid lid ocean models.
A three-dimensional variational data assimilation scheme for the Regional Ocean Modeling System (ROMS), named ROMS3DVAR, has been described in the work of Li et al. (2008). In this paper, ROMS3DVAR is applied to the central California coastal region, an area characterized by inhomogeneity and anisotropy, as well as by dynamically unbalanced flows. A method for estimating the model error variances from limited observations is presented, and the construction of the inhomogeneous and anisotropic error correlations based on the Kronecker product is demonstrated. A set of single observation experiments illustrates the inhomogeneous and anisotropic error correlations and weak dynamic constraints used. Results are presented from the assimilation of data gathered during the Autonomous Ocean Sampling Network (AOSN) experiment during August 2003. The results show that ROMS3DVAR is capable of reproducing complex flows associated with upwelling and relaxation, as well as the rapid transitions between them. Some difficulties encountered during the experiment are also discussed.
With the growing power and shrinking cost of personal computers. the availability of fast ethernet interconnections, and public domain software packages, it is now possible to combine them to build desktop parallel computers (named Beowulf or PC clusters) at a fraction of what it would cost to buy systems of comparable power front supercomputer companies. This led as to build and assemble our own sys tem. specifically for climate ocean modeling. In this article, we present our experience with such a system, discuss its network performance, and provide some performance comparison data with both HP SPP2000 and Cray T3E for an ocean Model used in present-day oceanographic research.
A dynamical coupled ice-ocean numerical model for the marginal ice zone (MIZ) is suggested and used to study upwelling dynamics in the MIZ. The nonlinear sea ice model has a variable ice concentration and includes internal ice stress. The model is forced by stresses on the air/ocean and air/ice surfaces. The main coupling between the ice and the ocean is in the form of an interfacial stress on the ice/ocean interface. The ocean model is a linear reduced gravity model. The wind stress exerted by the atmosphere on the ocean is proportional to the fraction of open water, while the interfacial stress ice/ocean is proportional to the concentration of ice. A new mechanism for ice edge upwelling is suggested based on a geostrophic equilibrium solution for the sea ice medium. The upwelling reported in previous models invoking a stationary ice cover is shown to be replaced by a weak downwelling due to the ice motion. Most of the upwelling dynamics can be understood by analysis of the divergence of the across ice edge upper ocean transport. On the basis of numerical model, an analytical model is suggested that reproduces most of the upwelling dynamics of the more complex numerical model.
A coupled ice-ocean numerical model for the marginal ice zone is considered. The model consists of a nonlinear sea ice model and a two-layer (reduced gravity) ocean model. The dependence of the upwelling response on wind stress direction is discussed. The results confirm earlier analytical work. It is shown that there exist directions for which there is no upwelling, while other directions give maximum upwelling in terms of the volume of uplifted water. The ice and ocean is coupled directly through the stress at the ice-ocean interface. An interesting consequence of the coupling is found in cases when the ice edge is almost stationary. In these cases the ice tends to break up a few tenths of kilometers inside of the ice edge.
Results are presented of a series of numerical experiments in which an upper ocean model is driven by surface heat fluxes and stress fields derived from the FGGE SOP-1 GLAS analysis/forecast system (Halem, et al., 1982). The model results show that most changes in the mixed layer height and horizontal velocity occurs in the first days. On the other hand, changes in the temperature field take a longer time to develop. In the most realistic case (real initial conditions, instantaneous forcing fields from the atmospheric analysis), the resulting changes in temperature were larger than observed and the correlation between observed and predicted changes was poor. The deficiency in the forecast of SST changes may be due to several factors: lack of sufficient ocean resolution, improper initialization, lack of feedback between the ocean and the atmosphere and the absence of transports by the strong boundary currents, and perhaps unrealistic surface fluxes of heat and momentum. Unless these problems are alleviated it is not reasonable to perform coupled atmospheric ocean forecasts.
How does climate sensitivity vary with the magnitude of climate forcing? This question was investigated with the use of a modified coupled atmosphere-ocean model, whose stability was improved so that the model would accommodate large radiative forcings yet be fast enough to reach rapid equilibrium. Experiments were performed in which atmospheric CO2 was multiplied by powers of 2, from 1/64 to 256 times the 1950 value. From 8 to 32 times, the 1950 CO2, climate sensitivity for doubling CO2 reaches 8 C due to increases in water vapor absorption and cloud top height and to reductions in low level cloud cover. As CO2 amount increases further, sensitivity drops as cloud cover and planetary albedo stabilize. No water vapor-induced runaway greenhouse caused by increased CO2 was found for the range of CO2 examined. With CO2 at or below 1/8 of the 1950 value, runaway sea ice does occur as the planet cascades to a snowball Earth climate with fully ice covered oceans and global mean surface temperatures near 30 C.
The behavior and possible past evolution of fully coupled atmosphere and ocean model of Titan are investigated. It is found that Titan's surface temperature was about 20 K cooler at 4 Gyr ago and will be about 5 K warmer 0.5 Gyr in the future. The change in solar luminosity and the conversion of oceanic CH4 to C2H6 drive the evolution of the ocean and atmosphere over time. Titan appears to have experienced a frozen epoch about 3 Gyr ago independent of whether an ocean is present or not. This finding may have important implications for understanding the inventory of Titan's volatile compounds.
Oceanic convective plumes modeled with a thermobaric large-eddy simulation and driven by conditions similar to those of the Greenland Sea are compared to observations from ERS-1 Synthetic Aperture Radar (SAR) data from the Greenland Sea for the winter of 1992. In both form and size the two representations are seen to compare favorably. The plume-filled area of the SAR image occupies a region about 20 km by 90 km at the ice edge of the open water in 'Nordbukta', the large seasonal ice retreat, in the 'Odden' ice protuberance in the southern Greenland gyre. In the SAR data the plumes appear to be ice covered while the convective-return areas are open.
A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N. In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions I up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.
A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model of Zebiak and Cane. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.
The primary goals of the authors are to build an intuition for assimilation techniques and to investigate the impact of variable altimeter topography on simple or complex oceanic models. In particular, applying various techniques and sensitivity studies to model and data constraints plays a key role. We are starting to use quasi-geostrophic, semigeostrophic, and primitive-equation (PE) models and to test the schemes in regions of interest to the World Ocean Circulation Experiment (WOCE), as well as in the northeast Atlantic and the Mediterranean. The impact of scatterometer wind forcing on the results is also investigated. The use of Geosat, European Remote Sensing satellite (ERS-1), and TOPEX/POSEIDON altimetry data is crucial in fine tuning the models and schemes to the selected areas of interest.
Results are presented for two greenhouse gas experiments of the Goddard Institute for Space Studies Atmosphere-Ocean Model (AOM). The computed trends of surface pressure, surface temperature, 850, 500 and 200 mb geopotential heights and related temperatures of the model for the time frame 1960-2000 are compared to those obtained from the National Centers for Environmental Prediction observations. A spatial correlation analysis and mean value comparison are performed, showing good agreement. A brief general discussion about the statistics of trend detection is presented. The domain of interest is the Northern Hemisphere (NH) because of the higher reliability of both the model results and the observations. The accuracy that this AOM has in describing the observed regional and NH climate trends makes it reliable in forecasting future climate changes.
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It is shown that the (cumulus) convective processes in the tropics may be described by a one-dimensional cloud model, while the near-surface ocean may similarly be described by a one-dimensional mixed-layer model. The coupling is achieved through a sea surface flux budget combined with the flux parameterizations implied by Monin-Obukhov similarity theory. The coupled one-dimensional atmosphere-ocean model is applied to the equilibrium situation in which all temperatures reach a steady state. For the ocean, the fluxes must vanish in equilibrium, but the atmosphere maintains a stable lapse rate by balancing cumulonimbus heating against net radiative cooling. All water precipitating from cumulonimbus clouds must have evaporated from the sea. It is shown that this equilibrium system is closed and determinable solely in terms of the solar constant.
A partial differential equation model is defined for ocean meteorological prediction and synoptic analysis. The Kalman filter used for data assimilation is described and applied to the one-dimensional linear barotropic quasi-geostrophic model with periodic and open boundary conditions. The model accounts for eddy scale dynamics in the ocean. The assumptions made in the forecast model are discussed, along with comparisons of the error variances expected with the filter and from an objective analysis method. The effectiveness of the Kalman filter is demonstrated and subsequent efforts to extend the filter to two dimensions are indicated.
Prognostic numerical models for atmospheric and oceanic circulations require initial fields, boundary conditions, and forcing functions in addition to a consistent set of partial differential equations, including a state relation and equations expressing conservation of mass, momentum, and energy. Depending on the horizontal domain to be modeled, the horizontal boundary conditions are either physically obvious or extremely difficult to specify consistently. If the entire atmosphere is modeled, periodic horizontal boundary conditions are appropriate. On the other hand, the physical horizontal boundaries on the entire ocean are solid walls. Obviously, the normal velocity at a solid wall is zero while the specification of the tangential velocity depends on the mathematical treatment of the horizontal viscous terms. Limitations imposed by computer capacity and cost, as well as research interests, have led to the use of limited area models to study flows in the atmosphere and ocean. The limited area models do not have physical horizontal boundaries, merely numerical ones. Correctly determining these open boundary conditions for limited-area numerical models has both intrigued and frustrated numerical modelers for decades. One common approach is to use the closed or solid wall boundary conditions for a limited-area model. The argument given for this approach is that the boundary conditions affect flow near the walls but that none of these effects are propagated into the interior. Therefore, one chooses a big enough domain that the central region of interest is not corrupted by the boundary flow. Research in progress to model the North Atlantic circulation vividly illustrates the pitfalls of this approach. Two model runs are compared: (1) the southern boundary at 20S between latitudes 0 and 40W is artificially closed; and (2) the same boundary is specified as open with an inward transport of 15 Sv (determined from a global model with the same physics) uniformly spread across the boundary. A comparison of both runs is presented.