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Zhijin Li, Albert Barcilon, and I. M. Navon

Abstract

This work describes the dynamics of adjoint sensitivity perturbations that excite block onsets over the Pacific and Atlantic Oceans. Appropriate functions are derived for the blocking indices for these two regions and the model basic flow is constructed from Northern Hemisphere climatological data. The concepts of sensitivity analysis are extended to forced problems. This tool is used to investigate block onset due to atmospheric forcing, such as that resulting from tropical sea surface temperature anomalies. These linear studies are carried out in a hemispherical, primitive equations, θ-coordinate, two-layer model.

Results show that wind sensitivity perturbations less than 10 m s−1 and sensitivity forcing of vorticity sources of the order of 1.5 × 10−10 s−2 are sufficient to excite block onset. Both for the Pacific and Atlantic blocking, sensitivity perturbations and forcing perturbations, when expressed in terms of vertical vorticity, display a Rossby wave train structure mainly found on the southward flanks of the Pacific and Atlantic jets, that is, near the Philippines and the Caribbean regions.

From inferences based on the flow evolution of these sensitivity perturbations and with the help of potential vorticity analyses on the two constant potential temperature surfaces in this model, a dynamical framework that may explain Pacific and Atlantic block onsets is proposed. The nonuniform potential vorticity distribution in the jets, in particular the concentration of these gradients on potential vorticity waveguides, and the Lagrangian advection of potential vorticity by the eddies making up the stationary Rossby wave train and their energy propagation and convergence all conspire to play a key role in the growth of the synoptic-scale eddies supported by baroclinic as well as barotropic processes. It is proposed that the structural modification of the eddies in the wave train leads to the planetary structures that become associated with block onset. More specifically, the wave train in the Pacific evolves into a blocking dipole while the Atlantic block is found at the leading edge of the Rossby wave train across the Atlantic. Furthermore, this study shows that at the initial time the Pacific block displays a clear baroclinic structure while the wave train associated with the Atlantic block has a much more barotropic structure.

The significance of these results and their potential applications to predictions of blocking are discussed.

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Zhijin Li, Yi Chao, and James C. McWilliams

Abstract

An algorithm is proposed for the computation of streamfunction and velocity potential from given horizontal velocity vectors based on solving a minimization problem. To guarantee the uniqueness of the solution and computational reliability of the algorithm, a Tikhonov regularization is applied. The solution implies that the obtained streamfunction and velocity potential have minimal magnitude, while the given velocity vectors can be accurately reconstructed from the computed streamfunction and velocity potential. Because the formulation of the minimization problem allows for circumventing the explicit specification of separate boundary conditions on the streamfunction and velocity potential, the algorithm is easily applicable to irregular domains. By using an advanced minimization algorithm with the use of adjoint techniques, the method is computationally efficient and suitable for problems with large dimensions. An example is presented for coastal oceans to illustrate the practical application of the algorithm.

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Zhijin Li, I. M. Navon, and Yanqiu Zhu

Abstract

A set of four-dimensional variational data assimilation (4D-Var) experiments were conducted using both a standard method and an incremental method in an identical twin framework. The full physics adjoint model of the Florida State University global spectral model (FSUGSM) was used in the standard 4D-Var, while the adjoint of only a few selected physical parameterizations was used in the incremental method. The impact of physical processes on 4D-Var was examined in detail by comparing the results of these experiments. The inclusion of full physics turned out to be significantly beneficial in terms of assimilation error to the lower troposphere during the entire minimization process. The beneficial impact was found to be primarily related to boundary layer physics. The precipitation physics in the adjoint model also tended to have a beneficial impact after an intermediate number (50) of minimization iterations. Experiment results confirmed that the forecast from assimilation analyses with the full physics adjoint model displays a shorter precipitation spinup period. The beneficial impact on precipitation spinup did not result solely from the inclusion of the precipitation physics in the adjoint model, but rather from the combined impact of several physical processes. The inclusion of full physics in the adjoint model exhibited a detrimental impact on the rate of convergence at an early stage of the minimization process, but did not affect the final convergence.

A truncated Newton-like incremental approach was introduced for examining the possibility of circumventing the detrimental aspects using the full physics in the adjoint model in 4D-Var but taking into account its positive aspects. This algorithm was based on the idea of the truncated Newton minimization method and the sequential cost function incremental method introduced by , consisting of an inner loop and an outer loop. The inner loop comprised the incremental method, while the outer loop consisted of the standard 4D-Var method using the full physics adjoint. The limited-memory quasi-Newton minimization method (L-BFGS) was used for both inner and outer loops, while information on the Hessian of the cost function was jointly updated at every iteration in both loops. In an experiment with a two-cycle truncated Newton-like incremental approach, the assimilation analyses turned out to be better than those obtained from either the standard 4D-Var or the incremental 4D-Var in all aspects examined. The CPU time required by this two-cycle approach was larger by 35% compared with that required by the incremental 4D-Var without almost any physics in the adjoint model, while the CPU time required by the standard 4D-Var with the full physics adjoint model was more than twice that required by the incremental 4D-Var. Finally, several hypotheses concerning the impact of using standard 4D-Var full physics on minimization convergence were advanced and discussed.

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Yi Chao, Zhijin Li, John D. Farrara, and Peter Hung

Abstract

A two-dimensional variational data assimilation (2DVAR) method for blending sea surface temperature (SST) data from multiple observing platforms is presented. This method produces continuous fields and has the capability of blending multiple satellite and in situ observations. In addition, it allows specification of inhomogeneous and anisotropic background correlations, which are common features of coastal ocean flows. High-resolution (6 km in space and 6 h in time) blended SST fields for August 2003 are produced for a region off the California coast to demonstrate and evaluate the methodology. A comparison of these fields with independent observations showed root-mean-square errors of less than 1°C, comparable to the errors in conventional SST observations. The blended SST fields also clearly reveal the finescale spatial and temporal structures associated with coastal upwelling, demonstrating their utility in the analysis of finescale flows. With the high temporal resolution, the blended SST fields are also used to describe the diurnal cycle. Potential applications of this SST blending methodology in other coastal regions are discussed.

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Zhijin Li, James C. McWilliams, Kayo Ide, and John D. Farrara

Abstract

A multiscale data assimilation (MS-DA) scheme is formulated for fine-resolution models. A decomposition of the cost function is derived for a set of distinct spatial scales. The decomposed cost function allows for the background error covariance to be estimated separately for the distinct spatial scales, and multi-decorrelation scales to be explicitly incorporated in the background error covariance. MS-DA minimizes the partitioned cost functions sequentially from large to small scales. The multi-decorrelation length scale background error covariance enhances the spreading of sparse observations and prevents fine structures in high-resolution observations from being overly smoothed. The decomposition of the cost function also provides an avenue for mitigating the effects of scale aliasing and representativeness errors that inherently exist in a multiscale system, thus further improving the effectiveness of the assimilation of high-resolution observations. A set of one-dimensional experiments is performed to examine the properties of the MS-DA scheme. Emphasis is placed on the assimilation of patchy high-resolution observations representing radar and satellite measurements, alongside sparse observations representing those from conventional in situ platforms. The results illustrate how MS-DA improves the effectiveness of the assimilation of both these types of observations simultaneously.

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Zhijin Li, Yi Chao, James C. McWilliams, and Kayo Ide

Abstract

A three-dimensional variational data assimilation (3DVAR) scheme has been developed within the framework of the Regional Ocean Modeling System (ROMS). This ROMS3DVAR enables the capability of predicting meso- to small-scale variations with temporal scales from hours to days in coastal oceans. To cope with particular difficulties that result from complex coastlines and bottom topography, unbalanced flows, and sparse observations, ROMS3DVAR includes novel strategies. These strategies include the implementation of three-dimensional anisotropic and inhomogeneous error correlations based on a Kronecker product, application of particular weak dynamic constraints, and implementation of efficient and reliable algorithms for minimizing the cost function. The formulation of ROMS3DVAR is presented here, and its implementation off the West Coast is currently under way.

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François Colas, Xavier Capet, James C. McWilliams, and Zhijin Li

Abstract

A dynamical interpretation is made of the mesoscale eddy buoyancy fluxes in the Eastern Boundary Currents off California and Peru–Chile, based on regional equilibrium simulations. The eddy fluxes are primarily shoreward and upward across a swath several hundred kilometers wide in the upper ocean; as such they serve to balance mean offshore air–sea heating and coastal upwelling. In the stratified interior the eddy fluxes are consistent with the adiabatic hypothesis associated with a mean eddy-induced velocity advecting mean buoyancy and tracers. Furthermore, with a suitable gauge choice, the horizontal fluxes are almost entirely aligned with the mean horizontal buoyancy gradient, consistent with the advective parameterization scheme of Gent and McWilliams. The associated diffusivity κ is surface intensified, matching the vertical stratification profile. The fluxes span the across-shore band of high eddy energy, but their alongshore structure is unresolved because of sampling limitations. In the surface layer the eddy flux is significantly diabatic with a shallow eddy-induced circulation cell and downgradient lateral diapycnal flux. The dominant eddy generation process is baroclinic instability, but there are significant regional differences between the upwelling systems in the flux and κ that are not consistent with simple instability theory.

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Xin Jin, Changming Dong, Jaison Kurian, James C. McWilliams, Dudley B. Chelton, and Zhijin Li

Abstract

Observations, primarily from satellites, have shown a statistical relationship between the surface wind stress and underlying sea surface temperature (SST) on intermediate space and time scales, in many regions inclusive of eastern boundary upwelling current systems. In this paper, this empirical SST–wind stress relationship is utilized to provide a simple representation of mesoscale air–sea coupling for an oceanic model forced by surface winds, namely, the Regional Oceanic Modeling System (ROMS). This model formulation is applied to an idealized upwelling problem with prevailing equatorward winds to determine the coupling consequences on flow, SST, stratification, and wind evolutions. The initially uniform wind field adjusts through coupling to a cross-shore profile with weaker nearshore winds, similar to realistic ones. The modified wind stress weakens the nearshore upwelling circulation and increases SST in the coastal zone. The SST-induced wind stress curl strengthens offshore upwelling through Ekman suction. The total curl-driven upwelling exceeds the coastal upwelling. The SST-induced changes in the nearshore wind stress field also strengthen and broaden the poleward undercurrent. The coupling also shows significant impact on the developing mesoscale eddies by damaging cyclonic eddies more than anticyclonic eddies, which leads to dominance by the latter. Dynamically, this is a consequence of cyclones with stronger SST gradients that induce stronger wind perturbations in this particular upwelling problem and that are therefore generally more susceptible to disruption than anticyclones at finite Rossby number. The net effect is a weakening of eddy kinetic energy.

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William I. Gustafson Jr, Andrew M. Vogelmann, Zhijin Li, Xiaoping Cheng, Kyle K. Dumas, Satoshi Endo, Karen L. Johnson, Bhargavi Krishna, Tami Fairless, and Heng Xiao

Abstract

The U.S. Department of Energy’s Atmospheric Radiation Measurement (ARM) user facility recently initiated the Large-Eddy Simulation (LES) ARM Symbiotic Simulation and Observation (LASSO) activity focused on shallow convection at ARM’s Southern Great Plains (SGP) atmospheric observatory in Oklahoma. LASSO is designed to overcome an oft-shared difficulty of bridging the gap from point-based measurements to scales relevant for model parameterization development, and it provides an approach to add value to observations through modeling. LASSO is envisioned to be useful to modelers, theoreticians, and observationalists needing information relevant to cloud processes. LASSO does so by combining a suite of observations, LES inputs and outputs, diagnostics, and skill scores into data bundles that are freely available, and by simplifying user access to the data to speed scientific inquiry. The combination of relevant observations with observationally constrained LES output provides detail that gives context to the observations by showing physically consistent connections between processes based on the simulated state. A unique approach for LASSO is the generation of a library of cases for days with shallow convection combined with an ensemble of LES for each case. The library enables researchers to move beyond the single-case-study approach typical of LES research. The ensemble members are produced using a selection of different large-scale forcing sources and spatial scales. Since large-scale forcing is one of the most uncertain aspects of generating the LES, the ensemble informs users about potential uncertainty for each date and increases the probability of having an accurate forcing for each case.

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