Abstract

Difficulties in the assimilation of Lagrangian data arise because the state of the prognostic model is generally described in terms of Eulerian variables computed on a fixed grid in space, as a result there is no direct connection between the model variables and Lagrangian observations that carry time-integrated information. A method is presented for assimilating Lagrangian tracer positions, observed at discrete times, directly into the model. The idea is to augment the model with tracer advection equations and to track the correlations between the flow and the tracers via the extended Kalman filter. The augmented model state vector includes tracer coordinates and is updated through the correlations to the observed tracers.

The technique is tested for point vortex flows: an N _F point vortex system with a Gaussian noise term is modeled by its deterministic counterpart. Positions of N _D tracer particles are observed at regular time intervals and assimilated into the model. Numerical experiments demonstrate successful system tracking for (N _F , N _D ) = (2, 1), (4, 2), provided the observations are reasonably frequent and accurate and the system noise level is not too high. The performance of the filter strongly depends on initial tracer positions (drifter launch locations). Analysis of this dependence shows that the good launch locations are separated from the bad ones by Lagrangian flow structures (separatrices or invariant manifolds of the velocity field). The method is compared to an alternative indirect approach, where the flow velocity, estimated from two (or more) consecutive drifter observations, is assimilated directly into the model.

Abstract

Lagrangian measurements provide a significant portion of the data collected in the ocean. Difficulties arise in their assimilation, however, since Lagrangian data are described in a moving frame of reference that does not correspond to the fixed grid locations used to forecast the prognostic flow variables. A new method is presented for assimilating Lagrangian data into models of the ocean that removes the need for any commonly used approximations. This is accomplished by augmenting the state vector of the prognostic variables with the Lagrangian drifter coordinates at assimilation. It is shown that this method is best formulated using the ensemble Kalman filter, resulting in an algorithm that is essentially transparent for assimilating Lagrangian data. The method is tested using a set of twin experiments on the shallow-water system of equations for an unsteady double-gyre flow configuration. Numerical simulations show that this method is capable of correcting the flow even if the assimilation time interval is of the order of the Lagrangian autocorrelation time scale (T_L ) of the flow. These results clearly demonstrate the benefits of this method over other techniques that require assimilation times of 20%–50% of T_L , a direct consequence of the approximations introduced in assimilating their Lagrangian data. Detailed parametric studies show that this method is particularly effective if the classical ideas of localization developed for the ensemble Kalman filter are extended to the Lagrangian formulation used here. The method that has been developed, therefore, provides an approach that allows one to fully realize the potential of Lagrangian data for assimilation in more realistic ocean models.

Abstract

A basin-scale, reduced-gravity model is used to study how drifter launch strategies affect the accuracy of Eulerian velocity fields reconstructed from limited Lagrangian data. Optimal dispersion launch sites are found by tracking strongly hyperbolic singular points in the flow field. Lagrangian data from drifters launched from such locations are found to provide significant improvement in the reconstruction accuracy over similar but randomly located initial deployments. The eigenvalues of the hyperbolic singular points in the flow field determine the intensity of the local particle dispersion and thereby provide a natural timescale for initializing subsequent launches. Aligning the initial drifter launch in each site along an outflowing manifold ensures both high initial particle dispersion and the eventual sampling of regions of high kinetic energy, two factors that substantially affect the accuracy of the Eulerian reconstruction. Reconstruction error is reduced by a factor of ∼2.5 by using a continual launch strategy based on both the local stretching rates and the outflowing directions of two strong saddles located in the dynamically active region south of the central jet. Notably, a majority of those randomly chosen launch sites that produced the most accurate reconstructions also sampled the local manifold structure.

Abstract

Cross-stream mixing and Lagrangian transport caused by chaotic advection within a baroclinic (2½ layer) meandering jet are investigated. The quasi-steady meanders arise as a result of evolution from an initial small-amplitude instability. The investigation keys on the proposition, made in earlier work, that the cross-jet mixing and transport resulting from the meandering motions are maximized at a subsurface level. It is found that the results depend largely on the size of the shear between the two active layers (which are referred to as the upper and lower layer), as measured by a parameter α. For weak vertical shear (α greater than about 0.5) the primary instability is barotropic and there is no cross-jet transport in either of the active layers. Barriers to transport are identified as plateaus in the probability density function (PDF) of potential vorticity distributions. For stronger shear (α less than about 0.4), baroclinic instability comes into play, and the lower layer experiences barrier destruction followed by cross-jet exchange and mixing. The upper-layer barrier remains intact. The barrier destruction has a dynamical effect as evidenced by the decay of total variance of potential vorticity in the lower layer. Of interest is that the value of α estimated for the Gulf Stream lies in the range 0.4–0.5.

Abstract

Kinematic models predict that a coherent structure, such as a jet or an eddy, in an unsteady flow can exchange fluid with its surroundings. The authors consider the significance of this effect for a fully nonlinear, dynamically consistent, barotropic model of a meandering jet. The calculated volume transport associated with this fluid exchange is comparable to that of fluid crossing the Gulf Stream through the detachment of rings. Although the model is barotropic and idealized in other ways, the transport calculations suggest that this exchange mechanism may be important in lateral transport or potential vorticity budget analyses for the Gulf Stream and other oceanic jets. The numerically simulated meandering jet is obtained by allowing a small-amplitude unstable meander to grow until a saturated state occurs. The resulting flow is characterized by finite-amplitude meanders propagating with nearly constant speed, and the results clearly illustrate the stretching and stirring of fluid particles along the edges of the recirculation regions south of the meander crests and north of the troughs. The fluid exchange and resulting transport across boundaries separating regions of predominantly prograde, retrograde, and recirculating motion is quantified using a dynamical systems analysis. The geometrical structures that result from the analysis are shown to be closely correlated with regions of the flow that are susceptible to high potential vorticity dissipation. Moreover, in a related study this analysis has been used to effectively predict the entrainment and detrainment of particles to and from the jet.

Abstract

A single-layer, reduced-gravity, double-gyre primitive equation model in a 2000 km × 2000 km square domain is used to test the accuracy and sensitivity of time-dependent Eulerian velocity fields reconstructed from numerically generated drifter trajectories and climatology. The goal is to determine how much Lagrangian data is needed to capture the Eulerian velocity field within a specified accuracy. The Eulerian fields are found by projecting, on an analytic set of divergence-free basis functions, drifter data launched in the active western half of the basin supplemented by climatology in the eastern domain. The time-dependent coefficients are evaluated by least squares minimization and the reconstructed fields are compared to the original model output. The authors find that the accuracy of the reconstructed fields depends critically on the spatial coverage of the drifter observations. With good spatial coverage, the technique allows accurate Eulerian reconstructions with under 200 drifters deployed in the 1000 km × 1400 km energetic western region. The base reconstruction error, achieved with full observation of the velocity field, ranges from 5% (with 191 basis functions) to 30% (with 65 basis functions). Specific analysis of the relation between spatial coverage and reconstruction error is presented using 180 drifters deployed in 100 different initial configurations that maximize coverage extremes. The simulated drifter data is projected on 107 basis functions for a 50-day period. The base reconstruction error of 15% is achieved when drifters occupy approximately 110 (out of 285) 70-km cells in the western region. Reconstructions from simulated mooring data located at the initial positions of representative good and poor coverage drifter deployments show the effect drifter dispersion has on data voids. The authors conclude that with appropriate coverage, drifter data could provide accurate basin-scale reconstruction of Eulerian velocity fields.

Abstract

Eleven coupled climate–carbon cycle models used a common protocol to study the coupling between climate change and the carbon cycle. The models were forced by historical emissions and the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emissions Scenarios (SRES) A2 anthropogenic emissions of CO₂ for the 1850–2100 time period. For each model, two simulations were performed in order to isolate the impact of climate change on the land and ocean carbon cycle, and therefore the climate feedback on the atmospheric CO₂ concentration growth rate. There was unanimous agreement among the models that future climate change will reduce the efficiency of the earth system to absorb the anthropogenic carbon perturbation. A larger fraction of anthropogenic CO₂ will stay airborne if climate change is accounted for. By the end of the twenty-first century, this additional CO₂ varied between 20 and 200 ppm for the two extreme models, the majority of the models lying between 50 and 100 ppm. The higher CO₂ levels led to an additional climate warming ranging between 0.1° and 1.5°C.

All models simulated a negative sensitivity for both the land and the ocean carbon cycle to future climate. However, there was still a large uncertainty on the magnitude of these sensitivities. Eight models attributed most of the changes to the land, while three attributed it to the ocean. Also, a majority of the models located the reduction of land carbon uptake in the Tropics. However, the attribution of the land sensitivity to changes in net primary productivity versus changes in respiration is still subject to debate; no consensus emerged among the models.

The multination, high-resolution field study of Meteorology And Diffusion Over Non-Uniform Areas (MADONA) was conducted by scientists from the United States, the United Kingdom, Germany, Denmark, Sweden, and the Netherlands at Porton Down, Salisbury, Wiltshire, United Kingdom, during September and October 1992. The host of the field study was the Chemical and Biological Defence Establishment (CBDE, now part of Defence Evaluation and Research Agency) at Porton Down. MADONA was designed and conducted for high-resolution meteorological data collection and diffusion experiments using smoke, sulphurhexaflouride (SF₆), and propylene gas during unstable, neutral, and stable atmospheric conditions in an effort to obtain terrain-influenced meteorological fields, dispersion, and concentration fluctuation measurements using specialized sensors and tracer generators. Thirty-one days of meteorological data were collected during the period 7 September–7 October and 27 diffusion experiments were conducted from 14 to 23 September 1992. Puffs and plumes of smoke and SF₆ were released simultaneously for most of the experiments to gauge the resultant diffusion and concentration behavior. Some 44 meteorological and aerosol sensors and four source generators were used during each day of the field study. This array of sensors included 14 towers of wind cups and vanes, 10 sonic anemometer/thermometers, one boundary layer sonde, two lidar, one ion sensor, the CBDE Weather Station, and several one-of-a-kind sensors. Simulations of airflow and diffusion over the MADONA topography (a 9 km by 7.5 km area) were made with a variety of models. Wind fields and wind-related parameters were simulated with several high-resolution (microalpha scale) wind flow models. A tally of the various data-gathering activities indicates that the execution of MADONA was highly successful. Preliminary use of the datasets shows the high quality and depth of the MADONA database. This well-documented database is suitable for the evaluation and validation of short-range/near-field wind and diffusion models/codes. The database was originally placed on CD-ROM in a structured way by CBDE, Porton Down. The database is now available from the Risø National Laboratory, Denmark.

Abstract

Eight earth system models of intermediate complexity (EMICs) are used to project climate change commitments for the recent Intergovernmental Panel on Climate Change’s (IPCC’s) Fourth Assessment Report (AR4). Simulations are run until the year 3000 a.d. and extend substantially farther into the future than conceptually similar simulations with atmosphere–ocean general circulation models (AOGCMs) coupled to carbon cycle models. In this paper the following are investigated: 1) the climate change commitment in response to stabilized greenhouse gases and stabilized total radiative forcing, 2) the climate change commitment in response to earlier CO₂ emissions, and 3) emission trajectories for profiles leading to the stabilization of atmospheric CO₂ and their uncertainties due to carbon cycle processes. Results over the twenty-first century compare reasonably well with results from AOGCMs, and the suite of EMICs proves well suited to complement more complex models. Substantial climate change commitments for sea level rise and global mean surface temperature increase after a stabilization of atmospheric greenhouse gases and radiative forcing in the year 2100 are identified. The additional warming by the year 3000 is 0.6–1.6 K for the low-CO₂ IPCC Special Report on Emissions Scenarios (SRES) B1 scenario and 1.3–2.2 K for the high-CO₂ SRES A2 scenario. Correspondingly, the post-2100 thermal expansion commitment is 0.3–1.1 m for SRES B1 and 0.5–2.2 m for SRES A2. Sea level continues to rise due to thermal expansion for several centuries after CO₂ stabilization. In contrast, surface temperature changes slow down after a century. The meridional overturning circulation is weakened in all EMICs, but recovers to nearly initial values in all but one of the models after centuries for the scenarios considered. Emissions during the twenty-first century continue to impact atmospheric CO₂ and climate even at year 3000. All models find that most of the anthropogenic carbon emissions are eventually taken up by the ocean (49%–62%) in year 3000, and that a substantial fraction (15%–28%) is still airborne even 900 yr after carbon emissions have ceased. Future stabilization of atmospheric CO₂ and climate change requires a substantial reduction of CO₂ emissions below present levels in all EMICs. This reduction needs to be substantially larger if carbon cycle–climate feedbacks are accounted for or if terrestrial CO₂ fertilization is not operating. Large differences among EMICs are identified in both the response to increasing atmospheric CO₂ and the response to climate change. This highlights the need for improved representations of carbon cycle processes in these models apart from the sensitivity to climate change. Sensitivity simulations with one single EMIC indicate that both carbon cycle and climate sensitivity related uncertainties on projected allowable emissions are substantial.

ABSTRACT

Regional climate modeling addresses our need to understand and simulate climatic processes and phenomena unresolved in global models. This paper highlights examples of current approaches to and innovative uses of regional climate modeling that deepen understanding of the climate system. High-resolution models are generally more skillful in simulating extremes, such as heavy precipitation, strong winds, and severe storms. In addition, research has shown that fine-scale features such as mountains, coastlines, lakes, irrigation, land use, and urban heat islands can substantially influence a region’s climate and its response to changing forcings. Regional climate simulations explicitly simulating convection are now being performed, providing an opportunity to illuminate new physical behavior that previously was represented by parameterizations with large uncertainties. Regional and global models are both advancing toward higher resolution, as computational capacity increases. However, the resolution and ensemble size necessary to produce a sufficient statistical sample of these processes in global models has proven too costly for contemporary supercomputing systems. Regional climate models are thus indispensable tools that complement global models for understanding physical processes governing regional climate variability and change. The deeper understanding of regional climate processes also benefits stakeholders and policymakers who need physically robust, high-resolution climate information to guide societal responses to changing climate. Key scientific questions that will continue to require regional climate models, and opportunities are emerging for addressing those questions.