Ichiro Fukumori

An approximate Kaiman filter for ocean data assimilation: An example with an idealized Gulf Stream model

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kaiman filter based on approximations of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the errors asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

A verification framework for interannual-to-decadal predictions experiments

Decadal predictions have a high profile in the climate science community and beyond, yet very little is known about their skill. Nor is there any agreed protocol for estimating their skill. This paper proposes a sound and coordinated framework for verification of decadal hindcast experiments. The framework is illustrated for decadal hindcasts tailored to meet the requirements and specifications of CMIP5 (Coupled Model Intercomparison Project phase 5). The chosen metrics address key questions about the information content in initialized decadal hindcasts. These questions are: (1) Do the initial conditions in the hindcasts lead to more accurate predictions of the climate, compared to un-initialized climate change projections? and (2) Is the prediction model’s ensemble spread an appropriate representation of forecast uncertainty on average? The first question is addressed through deterministic metrics that compare the initialized and uninitialized hindcasts. The second question is addressed through a probabilistic metric applied to the initialized hindcasts and comparing different ways to ascribe forecast uncertainty. Verification is advocated at smoothed regional scales that can illuminate broad areas of predictability, as well as at the grid scale, since many users of the decadal prediction experiments who feed the climate data into applications or decision models will use the data at grid scale, or downscale it to even higher resolution. An overall statement on skill of CMIP5 decadal hindcasts is not the aim of this paper. The results presented are only illustrative of the framework, which would enable such studies. However, broad conclusions that are beginning to emerge from the CMIP5 results include (1) Most predictability at the interannual-to-decadal scale, relative to climatological averages, comes from external forcing, particularly for temperature; (2) though moderate, additional skill is added by the initial conditions over what is imparted by external forcing alone; however, the impact of initialization may result in overall worse predictions in some regions than provided by uninitialized climate change projections; (3) limited hindcast records and the dearth of climate-quality observational data impede our ability to quantify expected skill as well as model biases; and (4) as is common to seasonal-to-interannual model predictions, the spread of the ensemble members is not necessarily a good representation of forecast uncertainty. The authors recommend that this framework be adopted to serve as a starting point to compare prediction quality across prediction systems. The framework can provide a baseline against which future improvements can be quantified. The framework also provides guidance on the use of these model predictions, which differ in fundamental ways from the climate change projections that much of the community has become familiar with, including adjustment of mean and conditional biases, and consideration of how to best approach forecast uncertainty.

Nature of global large-scale sea level variability in relation to atmospheric forcing : A modeling study

The relation between large-scale sea level variability and ocean circulation is studied using a numerical model. A global primitive equation model of the ocean is forced by daily winds and climatological heat fluxes corresponding to the period from January 1992 to January 1994. The physical nature of sea levels temporal variability from periods of days to a year is examined on the basis of spectral analyses of model results and comparisons with satellite altimetry and tide gauge measurements. The study elucidates and diagnoses the inhomogeneous physics of sea level change in space and frequency domain. At midlatitudes, large-scale sea level variability is primarily due to steric changes associated with the seasonal heating and cooling cycle of the surface layer. In comparison, changes in the tropics and high latitudes are mainly wind driven. Wind-driven variability exhibits a strong latitudinal dependence in itself. Wind-driven changes are largely baroclinic in the tropics but barotropic at higher latitudes. Baroclinic changes are dominated by the annual harmonic of the first baroclinic mode and is largest off the equator; variabilities associated with equatorial waves are smaller in comparison. Wind-driven barotropic changes exhibit a notable enhancement over several abyssal plains in the Southern Ocean, which is likely due to resonant planetary wave modes in basins semienclosed by discontinuities in potential vorticity. Otherwise, barotropic sea level changes are typically dominated by high frequencies with as much as half the total variance in periods shorter than 20 days, reflecting the frequency spectra of wind stress curl. Implications of the findings with regards to analyzing observations and data assimilation are discussed.

Effects of the Indonesian Throughflow on the Pacific and Indian Oceans

Abstract Effects of the Indonesian Throughflow (ITF) on the circulation and thermal structure of the Pacific and Indian Oceans are studied by comparing solutions of a near-global ocean general circulation model with open and closed Indonesian passages from 1981 to 1997. The ITF contributes to the maintenance of the model circulation system around eastern Australia and the southern Indian Ocean. Blockage of the ITF weakens the Indian Ocean South Equatorial Current and Agulhas Current and strengthens the East Australian Current. The ITF does not affect the Mindanao Current, but drains waters carried by this current into the Indian Ocean and thus reduces tropical–subtropical exchange in the North Pacific. Meanwhile, it helps maintain a stronger New Guinea Coastal Undercurrent and thus enhances tropical–subtropical exchange in the south. Water parcels traveling along the western boundary of the South Pacific cross the equator in the presence of the ITF but are confined to the Southern Hemisphere without the I...

Using Green's Functions to Calibrate an Ocean General Circulation Model

Abstract Greens functions provide a simple yet effective method to test and to calibrate general circulation model (GCM) parameterizations, to study and to quantify model and data errors, to correct model biases and trends, and to blend estimates from different solutions and data products. The method is applied to an ocean GCM, resulting in substantial improvements of the solution relative to observations when compared to prior estimates: overall model bias and drift are reduced and there is a 10%–30% increase in explained variance. Within the context of this optimization, the following new estimates for commonly used ocean GCM parameters are obtained. Background vertical diffusivity is (15.1 ± 0.1) × 10−6 m2 s−2. Background vertical viscosity is (18 ± 3) × 10−6 m2 s−2. The critical bulk Richardson number, which sets boundary layer depth, is Ric = 0.354 ± 0.004. The threshold gradient Richardson number for shear instability vertical mixing is Ri0 = 0.699 ± 0.008. The estimated isopycnal diffusivity coeff...

Distinguishing the Roles of Natural and Anthropogenically Forced Decadal Climate Variability: Implications for Prediction

Abstract Given that over the course of the next 10–30 years the magnitude of natural decadal variations may rival that of anthropogenically forced climate change on regional scales, it is envisioned that initialized decadal predictions will provide important information for climate-related management and adaptation decisions. Such predictions are presently one of the grand challenges for the climate community. This requires identifying those physical phenomena—and their model equivalents—that may provide additional predictability on decadal time scales, including an assessment of the physical processes through which anthropogenic forcing may interact with or project upon natural variability. Such a physical framework is necessary to provide a consistent assessment (and insight into potential improvement) of the decadal prediction experiments planned to be assessed as part of the IPCCs Fifth Assessment Report.

Assimilation of TOPEX/Poseidon altimeter data into a global ocean circulation model: How good are the results?

The feasibility of assimilating satellite altimetry data into a global ocean general circulation model is studied. Three years of TOPEX/Poseidon data are analyzed using a global, three-dimensional, nonlinear primitive equation model. The assimilations success is examined by analyzing its consistency and reliability measured by formal error estimates with respect to independent measurements. Improvements in model solution are demonstrated, in particular, properties not directly measured. Comparisons are performed with sea level measured by tide gauges, subsurface temperatures and currents from moorings, and bottom pressure measurements. Model representation errors dictate what can and cannot be resolved by assimilation, and its identification is emphasized.

NASA supercomputer improves prospects for ocean climate research

Estimates of ocean circulation constrained by in situ and remotely sensed observations have become routinely available during the past five years, and they are being applied to myriad scientific and operational problems [Stammer et al., 2002]. Under the Global Ocean Data Assimilation Experiment (GODAE), several regional and global estimates have evolved for applications in climate research, seasonal forecasting, naval operations, marine safety, fisheries, the offshore oil industry coastal management, and other areas. This article reports on recent progress by one effort, the consortium for Estimating the Circulation and Climate of the Ocean (ECCO), toward a next-generation synthesis of ocean and sea-ice data that is global, that covers the full ocean depth, and that permits eddies.

State estimation improves prospects for ocean research

Rigorous global ocean state estimation methods can now be used to produce dynamically consistent time-varying model/data syntheses, the results of which are being used to study a variety of important scientific problems. Figure 1 shows a schematic of a complete ocean observing and synthesis system that includes global observations and state-of-the-art ocean general circulation models (OGCM) run on modern computer platforms. A global observing system is described in detail in Smith and Koblinsky [2001],and the present status of ocean modeling and anticipated improvements are addressed by Griffies et al. [2001]. Here, the focus is on the third component of state estimation: the synthesis of the observations and a model into a unified, dynamically consistent estimate.

Atmospheric and oceanic excitation of length-of-day variations during 1980-2000

[1] Although nontidal changes in the Earth’s length-of-day on timescales of a few days to a few years are primarily caused by changes in the angular momentum of the zonal winds, other processes can be expected to cause the length-of-day to change as well. Here the relative contribution of upper atmospheric winds, surface pressure, oceanic currents, and ocean-bottom pressure to changing the length-of-day during 1980–2000 is evaluated using estimates of atmospheric angular momentum from the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis project, estimates of the angular momentum of the zonal winds in the upper atmosphere from the United Kingdom Meteorological Office, and estimates of oceanic angular momentum from the Estimating the Circulation and Climate of the Ocean consortium’s simulation of the general circulation of the oceans. On intraseasonal timescales, atmospheric surface pressure, oceanic currents, and ocean-bottom pressure are found to be about equally important in causing the length-of-day to change, while upper atmospheric winds are found to be less important than these mechanisms. On seasonal timescales, the upper atmospheric winds are more important than the sum of currents and bottom pressure in causing the length-of-day to change and, except at the annual frequency, are even more important than surface pressure changes. On interannual timescales, oceanic currents and ocean-bottom pressure are found to be only marginally effective in causing the length-ofday to change. INDEX TERMS: 1223 Geodesy and Gravity: Ocean/Earth/atmosphere interactions (3339); 1239 Geodesy and Gravity: Rotational variations; 3319 Meteorology and Atmospheric Dynamics: General circulation; 4532 Oceanography: Physical: General circulation; KEYWORDS: Earth rotation, length-ofday, oceanic angular momentum