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Xiaoxu Tian and Kayo Ide

Abstract

In this study, the tangent linear and adjoint (TL/AD) models for the Model for Prediction Across Scales (MPAS) Shallow Water (SW) component are tested and demonstrated. Necessary verification check procedures of TL/AD are included to ensure that the models generate correct results. The TL/AD models are applied to calculate the singular vectors (SVs) with a 48-h optimization time interval (OTI) under both the quasi-uniform-resolution (UR) and smoothly variable-resolution (VR) meshes in the cases of Hurricanes Sandy (2012) and Joaquin (2015). For the global domain, the VR mesh with 30 210 grid cells uses slightly fewer computational resources than the UR mesh with 40 962 cells. It is found that at the points before Hurricanes Sandy and Joaquin made sharp turns, the leading SV from the VR experiment show sensitivities in both areas surrounding the hurricane and those relatively far away, indicating the significant impacts from the environmental flows. The leading SVs from the UR experiments are sensitive to only areas near the storm. Forecasts by the nonlinear SW model demonstrate that in the VR experiment, Hurricane Sandy has a northwest turn similar to the case in the real world while the storm gradually disappeared in the UR experiment. In the case of Hurricane Joaquin, the nonlinear forecast with the VR mesh can generate a track similar to the best track, while the storm became falsely dissipated in the forecast with the UR mesh. These experiments demonstrate, in the context of SW dynamics with a single layer and no physics, the track forecasts in the cases of Hurricanes Sandy and Joaquin with the VR mesh are more realistic than the UR mesh. The SV analyses shed light on the key features that can have significant impacts on the forecast performances.

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Daryl T. Kleist and Kayo Ide

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An observing system simulation experiment (OSSE) has been carried out to evaluate the impact of a hybrid ensemble–variational data assimilation algorithm for use with the National Centers for Environmental Prediction (NCEP) global data assimilation system. An OSSE provides a controlled framework for evaluating analysis and forecast errors since a truth is known. In this case, the nature run was generated and provided by the European Centre for Medium-Range Weather Forecasts as part of the international Joint OSSE project. The assimilation and forecast impact studies are carried out using a model that is different than the nature run model, thereby accounting for model error and avoiding issues with the so-called identical-twin experiments.

It is found that the quality of analysis is improved substantially when going from three-dimensional variational data assimilation (3DVar) to a hybrid 3D ensemble–variational (EnVar)-based algorithm. This is especially true in terms of the analysis error reduction for wind and moisture, most notably in the tropics. Forecast impact experiments show that the hybrid-initialized forecasts improve upon the 3DVar-based forecasts for most metrics, lead times, variables, and levels. An additional experiment that utilizes 3DEnVar (100% ensemble) demonstrates that the use of a 25% static error covariance contribution does not alter the quality of hybrid analysis when utilizing the tangent-linear normal mode constraint on the total hybrid increment.

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Daryl T. Kleist and Kayo Ide

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This work describes the formulation of a hybrid four-dimensional ensemble--variational (4DEnVar) algorithm and initialization options utilized within the National Centers for Environmental Prediction global data assimilation system. Initialization schemes that are proposed for use are the tangent-linear normal mode constraint, weak constraint digital filter, and a combination thereof.

An observing system simulation experiment is carried out to evaluate the impact of utilizing hybrid 4DEnVar with various initialization techniques. The experiments utilize a dual-resolution configuration, where the ensemble is run at roughly half the resolution of the deterministic component. It is found that by going from 3D to 4D, analysis error is reduced for most variables and levels. The inclusion of a time-invariant static covariance when used without a normal mode–based strong constraint is found to have a small, positive impact on the analysis. The experiments show that the weak constraint digital filter degrades the quality of analysis, due to the use of hourly states to prescribe high-frequency noise. It is found that going from 3D to 4D ensemble covariances has a relatively larger impact in the extratropics, whereas the original inclusion of ensemble-based covariances was found to have the largest impact in the tropics. The improvements found in going from 3D to 4D covariances in the hybrid EnVar formulation are not as large as was found in Part I from the original introduction of the hybrid algorithm. The analyses generated by the 4D hybrid scheme are found to yield slightly improved extratropical height and wind forecasts, with smaller impacts on other variables and in general in the tropics.

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Padhraic Smyth, Kayo Ide, and Michael Ghil

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A mixture model is a flexible probability density estimation technique, consisting of a linear combination of k component densities. Such a model is applied to estimate clustering in Northern Hemisphere (NH) 700-mb geopotential height anomalies. A key feature of this approach is its ability to estimate a posterior probability distribution for k, the number of clusters, given the data and the model. The number of clusters that is most likely to fit the data is thus determined objectively.

A dataset of 44 winters of NH 700-mb fields is projected onto its two leading empirical orthogonal functions (EOFs) and analyzed using mixtures of Gaussian components. Cross-validated likelihood is used to determine the best value of k, the number of clusters. The posterior probability so determined peaks at k = 3 and thus yields clear evidence for three clusters in the NH 700-mb data. The three-cluster result is found to be robust with respect to variations in data preprocessing and data analysis parameters. The spatial patterns of the three clusters’ centroids bear a high degree of qualitative similarity to the three clusters obtained independently by Cheng and Wallace, using hierarchical clustering on 500-mb NH winter data: the Gulf of Alaska ridge, the high over southern Greenland, and the enhanced climatological ridge over the Rockies.

Separating the 700-mb data into Pacific (PAC) and Atlantic (ATL) sector maps reveals that the optimal k value is 2 for both the PAC and ATL sectors. The respective clusters consist of Kimoto and Ghil’s Pacific–North American (PNA) and reverse PNA regimes, as well as the zonal and blocked phases of the North Atlantic oscillation. The connections between our sectorial and hemispheric results are discussed from the perspective of large-scale atmospheric dynamics.

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

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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

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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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Eric Simonnet, Michael Ghil, Kayo Ide, Roger Temam, and Shouhong Wang

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Successive bifurcations—from steady states through periodic to aperiodic solutions—are studied in a shallow-water, reduced-gravity, 2½-layer model of the midlatitude ocean circulation subject to time-independent wind stress. The bifurcation sequence is studied in detail for a rectangular basin with an idealized spatial pattern of wind stress. The aperiodic behavior is studied also in a North Atlantic–shaped basin with realistic continental contours. The bifurcation sequence in the rectangular basin is studied in Part I, the present article. It follows essentially the one reported for single-layer quasigeostrophic and 1½-layer shallow-water models. As the intensity of the north–south-symmetric, zonal wind stress is increased, the nearly symmetric double-gyre circulation is destabilized through a perturbed pitchfork bifurcation. The low-stress steady solution, with its nearly equal subtropical and subpolar gyres, is replaced by an approximately mirror-symmetric pair of stable equilibria. The two solution branches so obtained are named after the inertial recirculation cell that is stronger, subtropical or subpolar, respectively. This perturbed pitchfork bifurcation and the associated Hopf bifurcations are robust to changes in the interface friction between the two active layers and the thickness H 2 of the lower active layer. They persist in the presence of asymmetries in the wind stress and of changes in the model's spatial resolution and finite-difference scheme. Time-dependent model behavior in the rectangular basin, as well as in the more realistic, North Atlantic–shaped one, is studied in Part II.

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Eric Simonnet, Michael Ghil, Kayo Ide, Roger Temam, and Shouhong Wang

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The time-dependent wind-driven ocean circulation is investigated for both a rectangular and a North Atlantic–shaped basin. Multiple steady states in a 2½-layer shallow-water model and their dependence on various parameters and other model properties were studied in Part I for the rectangular basin. As the wind stress on the rectangular basin is increased, each steady-state branch is destabilized by a Hopf bifurcation. The periodic solutions that arise off the subpolar branch have a robust subannual periodicity of 4–5 months. For the subtropical branch, the period varies between sub- and interannual, depending on the inverse Froude number F 2 defined with respect to the lower active layer's thickness H 2. As F 2 is lowered, the perturbed-symmetric branch is destabilized baroclinically, before the perturbed pitchfork bifurcation examined in detail in Part I occurs. Transition to aperiodic behavior arises at first by a homoclinic explosion off the isolated branch that exists only for sufficiently high wind stress. Subsequent global and local bifurcations all involve the subpolar branch, which alone exists in the limit of vanishing wind stress. Purely subpolar solutions vary on an interannual scale, whereas combined subpolar and subtropical solutions exhibit complex transitions affected by a second, subpolar homoclinic orbit. In the latter case, the timescale of the variability is interdecadal. The role of the global bifurcations in the interdecadal variability is investigated. Numerical simulations were carried out for the North Atlantic with earth topography-5 minute (ETOPO-5) coastline geometry in the presence of realistic, as well as idealized, wind stress forcing. The simulations exhibit a realistic Gulf Stream at 20-km resolution and with realistic wind stress. The variability at 12-km resolution exhibits spectral peaks at 6 months, 16 months, and 6–7 years. The subannual mode is strongest in the subtropical gyre; the interannual modes are both strongest in the subpolar gyre.

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Alvaro de la Cámara, Ana M. Mancho, Kayo Ide, Encarna Serrano, and Carlos R. Mechoso

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Transport in the lower stratosphere over Antarctica has been studied in the past by means of several approaches, such as contour dynamics or Lyapunov exponents. This paper examines the problem by means of a new Lagrangian descriptor, which is referred to as the function M. The focus is on the southern spring of 2005, which allows for a comparison with previous analyses based on Lyapunov exponents. With the methodology based on the function M, a much sharper depiction of key Lagrangian features is achieved and routes of large-scale horizontal transport across the vortex edge are captured. These results highlight the importance of lobe dynamics as a transport mechanism across the Antarctic polar vortex.

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Matthew J. Hoffman, Takemasa Miyoshi, Thomas W. N. Haine, Kayo Ide, Christopher W. Brown, and Raghu Murtugudde

Abstract

An advanced data assimilation system, the local ensemble transform Kalman filter (LETKF), has been interfaced with a Regional Ocean Modeling System (ROMS) implementation on the Chesapeake Bay (ChesROMS) as a first step toward a reanalysis and improved forecast system for the Chesapeake Bay. The LETKF is among the most advanced data assimilation methods and is very effective for large, nonlinear dynamical systems with sparse data coverage. Errors in the Chesapeake Bay system are due more to errors in forcing than errors in initial conditions. To account for forcing errors, a forcing ensemble is used to drive the ensemble states for the year 2003. In the observing system simulation experiments (OSSEs) using the ChesROMS-LETKF system presented here, the filter converges quickly and greatly reduces the analysis and subsequent forecast errors in the temperature, salinity, and current fields in the presence of errors in wind forcing. Most of the improvement in temperature and currents comes from satellite sea surface temperature (SST), while in situ salinity profiles provide improvement to salinity. Corrections permeate through all vertical levels and some correction to stratification is seen in the analysis. In the upper Bay where the nature-run summer stratification is −0.2 salinity units per meter, stratification is improved from −0.01 per meter in the unassimilated model to −0.16 per meter in the assimilation. Improvements are seen in other parts of the Bay as well. The results from the OSSEs are promising for assimilating real data in the future.

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