Variational assimilation of Lagrangian data in oceanography

We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional space-time circulation of the ocean. This problem is solved using the four-dimensional variational technique and the adjoint method. In this problem the control vector is chosen as being the initial state of the dynamical system. The observed variables, namely the positions of the floats, are expressed as a function of the control vector via a nonlinear observation operator. This method has been implemented and has the ability to reconstruct the main patterns of the oceanic circulation. Moreover it is very robust with respect to increase of time-sampling period of observations. We have run many twin experiments in order to analyze the sensitivity of our method to the number of floats, the time-sampling period and the vertical drift level. We compare also the performances of the Lagrangian method to that of the classical Eulerian one. Finally we study the impact of errors on observations.Comment: 31 page

Sensitivity Analysis Applied To a Variational Data Assimilation of a Simulated Pollution Transport Problem

Understanding the impact of the changes in pollutant emission from a foreign region onto a target region is a key factor for taking appropriate mitigating actions. This requires a sensitivity analysis of a response function (defined on the target region) with respect to the source(s) of pollutant(s). The basic and straightforward approach to sensitivity analysis consists of multiple simulations of the pollution transport model with variations of the parameters that define the source of the pollutant. A more systematic approach uses the adjoint of the pollution transport model derived from applying the principle of variations. Both approaches assume that the transport velocity and the initial distribution of the pollutant are known. However, when observations of both the velocity and concentration fields are available, the transport velocity and the initial distribution of the pollutant are given by the solution of a data assimilation problem. As a consequence, the sensitivity analysis should be carried out on the optimality system of the data assimilation problem, and not on the direct model alone. This leads to a sensitivity analysis that involves the second-order adjoint model, which is presented in the present work. It is especially shown theoretically and with numerical experiments that the sensitivity on the optimality system includes important terms that are ignored by the sensitivity on the direct model. The latter shows only the direct effects of the variation of the source on the response function while the first shows the indirect effects in addition to the direct effects. Copyright © 2016 John Wiley & Sons, Ltd

Synoptic Forcing of the Korea Strait Transport

Korea Strait transport variations in the synoptic frequency band (2 20 days) are examined using results of a numerical 3-D primitive equation model, satellite observed sea-level variations. a linear barotropic adjoint dynamic model. and observed transports, The 3-D numerical model does not assimilate observations and the agreement with the observed transport implies that wind forcing is one of the main contributors to variations ill the Synoptic hand, The satellite observed and 3-D model sea-level indicate a sea-level response to wind stress along the cast Korean coast that propagates toward the Korea Strait and changes the sea-level slope across the strait. The adjoint results indicate that wind stress is most influential in the area east of Korea along with secondarily important area along the East China Sea shelf break south of Japan. The mechanism connecting wind stress to transport variations is a Kelvin wave propogation that changes sea-level slope across the strait. leading to the altered geostrophic transport through the strait. A strong southerly wind initially produces a sea-level set down along the east Korea coast and a sea-level increase along (tic shelf break. The set down propagates to the Korea Strait as a Kelvin wave. sea level across the strait changes, and the transport through the strait increases. Similarly, northerly wind stress produces. Set Lip along the Korea coast and subsequent decreased transport. Wind stresses across the Yellow and East China Seas are not a significant forcing mechanism since Kelvin waves would propagate away from the strait, Barotropic transport response to wind stress is rapid ton the order of 3 h), but the relatively slow development of the atmospheric forcing (oil the order of 1 2 days) modulates the response. Published by Elsevier Ltd

Generalized Inversion of the Gent-Cane Model of the Tropical Pacific With Tropical Atmosphere-Ocean (TAO) Data

We here describe the results of our latest effort to reanalyze TAO monthly mean Surface and subsurface temperature observations constrained by a tropical Pacific ocean model, and simultaneously to evaluate the physical consistency of the observations and the model. Both tasks are executed by weak-constraint, four-dimensional variational assimilation of the observations into the model. In this study our reanalysis employs the reduced-gravity Gent-Cane model, combined with the \u27KPP-interior\u27 parameterization of vertical turbulent fluxes. With the limited vertical resolution adopted in previous studies of this model, the \u27W4DVAR\u27 or inverse method fails to produce an acceptable reanalysis, as the dynamical residuals are too large locally ill space and time. Moreover, the objective significance test that is an essential product of the inversion rejects the model, even though the model is imposed only as a weak constraint, as convincingly as the even simpler Zebiak-Cane model was rejected (Bennett et al., 1998, 2000). In order to obtain a locally plausible reanalysis of the observations, we have to employ significantly finer vertical resolution. The calculations are extremely expensive and technically difficult, ill the interests of efficiency and convergence, we solve the fixed-interval smoothing problem for 3-month intervals (during the 1997-1998 El Ni (n) over tildeo, December 1996-March 1998), and we impose the continuity equations for layer thickness as strong constraints. We present detailed results for just one such experiment which shows the model in the best light. The resulting fits to the monthly-mean data are within our prior error assumptions and so constitute a highly plausible reanalysis. However, the significance test statistic for the inversion exceeds its expected value by many tens of standard deviations, forcing us to the inference that the model cannot ill fact be reconciled with the observations. The paradox of locally small residuals and a large test statistic is explained by an analysis of the degrees of freedom allowed in the weak constraints

Adjoint-Free 4D Variational Data Assimilation Into Regional Models

The ongoing trend towards parallelization in computer technologies propels ensemble methods toward the forefront of data assimilation studies in geophysics. Of particular interest are ensemble techniques which do not require the development of tangent linear numerical models and their adjoints for optimization. These “adjoint-free” methods detect effective search directions for optimization through direct perturbation of the numerical model across carefully chosen sets of states.Optimization proceeds by minimizing the cost functionwithin the sequence of subspaces spanned by these perturbations. In this chapter, an adjoint-free variational technique (a4dVar) is described and demonstrated in an application estimating initial conditions of two numerical models: the Navy Coastal Ocean Model (NCOM), and the surface wave model (WAM). It is shown that a4dVar is capable of providing forecast skill similar to that of conventional 4dVar at comparable computational expense while being less susceptible to excitation of ageostrophic modes that are not supported by observations. Prospects of further development of the a4dVar methods are discussed

A Primer on Global Internal Tide and Internal Gravity Wave Continuum Modeling in HYCOM and MITgcm

In recent years, high-resolution global three-dimensional ocean general circulation models have begun to include astronomical tidal forcing alongside atmospheric forcing. Such models can carry an internal tide field with a realistic amount of nonstationarity, and an internal gravity wave continuum spectrum that compares more closely with observations as model resolution increases. Global internal tide and gravity wave models are important for understanding the three-dimensional geography of ocean mixing, for operational oceanography, and for simulating and interpreting satellite altimeter observations. Here we describe the most important technical details behind such models, including atmospheric forcing, bathymetry, astronomical tidal forcing, self-attraction and loading, quadratic bottom boundary layer drag, parameterized topographic internal wave drag, shallow-water tidal equations, and a brief summary of the theory of linear internal gravity waves. We focus on simulations run with two models, the HYbrid Coordinate Ocean Model (HYCOM) and the Massachusetts Institute of Technology general circulation model (MITgcm). We compare the modeled internal tides and internal gravity wave continuum to satellite altimeter observations, moored observational records, and the predictions of the Garrett-Munk (1975) internal gravity wave continuum spectrum. We briefly examine specific topics of interest, such as tidal energetics, internal tide nonstationarity, and the role of nonlinearities in generating the modeled internal gravity wave continuum. We also describe our first attempts at using a Kalman filter to improve the accuracy of tides embedded within a general circulation model. We discuss the challenges and opportunities of modeling stationary internal tides, non-stationary internal tides, and the internal gravity wave continuum spectrum for satellite altimetry and other applications

Data assimilation considerations for improved ocean predictability during the Gulf of Mexico Grand Lagrangian Deployment (GLAD)

•Extensive drifter observations allow new understanding to data assimilation.•Background error covariance is the point at which assumptions have historically been placed.•Components of background error covariance are tested to determine impact.•Amplitude of background error covariance is a critical factor.•Time correlation in background errors must be considered in 3DVar and 4DVar.Ocean prediction systems rely on an array of assumptions to optimize their data assimilation schemes. Many of these remain untested, especially at smaller scales, because sufficiently dense observations are very rare. A set of 295 drifters deployed in July 2012 in the north-eastern Gulf of Mexico provides a unique opportunity to test these systems down to scales previously unobtainable. In this study, background error covariance assumptions in the 3DVar assimilation process are perturbed to understand the effect on the solution relative to the withheld dense drifter data. Results show that the amplitude of the background error covariance is an important factor as expected, and a proposed new formulation provides added skill. In addition, the background error covariance time correlation is important to allow satellite observations to affect the results over a period longer than one daily assimilation cycle. The results show the new background error covariance formulations provide more accurate placement of frontal positions, directions of currents and velocity magnitudes. These conclusions have implications for the implementation of 3DVar systems as well as the analysis interval of 4DVar systems