The impact of the M2 internal tide on data-assimilative model estimates of the surface tide

We use a synthetic data experiment to assess the accuracy of ocean tides estimated from satellite altimetry data, with emphasis on the impact of the phase-locked internal tide, which has a surface expression of several centimeters near its sites of genesis. Previous tidal estimates have regarded this signal as a random measurement error; however, it is deterministic and not scale-separated from the barotropic (surface) tide around complex bathymetric features. The synthetic data experiments show that the internal tide has a negligible impact on the barotropic tidal fields inferred under these circumstances, and the barotropic dissipation (a quadratic functional of the tidal fields) is in good agreement with the energetics of the three-dimensional regional primitive equations model which is the source of the synthetic data.     

Variational iteration solving method for El Nio phenomenon atmospheric physics of nonlinear model

1 IntroductionThe El Ni’o atmospheric physics oscillation is anabnormal phenomenon involved in the tropical Pacificocean- atmosphere interactions. Studies on the El Ni(ophenomenon are very attractive (Lin et al., 2000; Linet al., 2001, 2002; Wang, 2001; Feng et al., 2001;Feng et al., 2002; Liu et al., 2002; Wei and Chen,2003; Xie et al., 2002; Zhu et al., 2002; Pu et al.,2003; Gu et al., 2004; Yu and Liu, 2004). Lin and Mo(2004), Mo and Lin (2004) and Mo et al. (2004) alsostudied a s…     

Monitoring the Kuroshio Extension with Dynamically Constrained Synthesis of the Acoustic Tomography, Satellite Altimeter and in situ Data

A finite-difference quasigeostrophic (QG) model of an open ocean region has been employed to produce a dynamically constrained synthesis of acoustic tomography and satellite altimetry data with in situ observations. The assimilation algorithm is based upon the 4D variational data interpolation scheme controlled by the model's initial and boundary conditions. The data sets analyzed include direct and differential travel times measured at the array of five acoustic transceivers deployed by JAMSTEC in the region of the Kuroshio Extension in 1997, Topex/Poseidon altimetry, CTD soundings, and ADCP velocity profiles. The region monitored is located within the area 27.5°–36.5°N, 143°–155°. The results of assimilation show that mesoscale variability can be effectively reconstructed by five transceivers measuring direct and reciprocal travel times supported by relatively sparse in situ measurements. The misfits between model and data lie within the observational error bars for all the data types used in assimilation. We have compared the results of assimilation with the statistical inversion of travel time data and analyzed energy balances of the optimized model solution. Energy exchange between the depth-averaged and shear components of the observed currents reveals a weak decay of the barotropic mode at the rate of 0.2 ± 0.7⋅10⁻⁵ cm²/s³ due to topographic interaction. Mean currents in the region are unstable with an estimate of the available potential energy flux from the mean current to the eddies of 4.7 ± 2.3⋅10⁻⁵ cm²/s³. Kinetic energy transition has the same sign and is estimated as 2.8 ± 2.5⋅10⁻⁵ cm²/s³. Potential enstrophy is transferred to the mesoscale at a rate of 5.5 ± 2.7⋅10⁻¹⁸ s⁻³. These figures provide observational evidence of the properties of free geostrophic turbulence which were predicted by theory and observed in numerical experiments. This revised version was published online in July 2006 with corrections to the Cover Date.     

Parabolic Wave Propagation Modelling in Orthogonal Coordinate Systems

This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild-slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the confonnal system. The computational results show that the confonnal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical confonnal grid system.     

Data assimilation for a coastal area morphodynamic model: Morecambe Bay

This paper investigates the use of data assimilation in coastal area morphodynamic modelling using Morecambe Bay as a study site. A simple model of the bay has been enhanced with a data assimilation scheme to better predict large-scale changes in bathymetry observed in the bay over a 3-year period. The 2DH decoupled morphodynamic model developed for the work is described, as is the optimal interpolation scheme used to assimilate waterline observations into the model run. Each waterline was acquired from a SAR satellite image and is essentially a contour of the bathymetry at some level within the inter-tidal zone of the bay. For model parameters calibrated against validation observations, model performance is good, even without data assimilation. However the use of data assimilation successfully compensates for a particular failing of the model, and helps to keep the model bathymetry on track. It also improves the ability of the model to predict future bathymetry. Although the benefits of data assimilation are demonstrated using waterline observations, any observations of morphology could potentially be used. These results suggest that data assimilation should be considered for use in future coastal area morphodynamic models.     

Kuroshio extension variability explored through assimilation of TOPEX/POSEIDON altimeter data into a quasi-geostrophic model

Mesoscale features in the eastward extension of the Kuroshio were investigated using assimilation of TOPEX/POSEIDON (T/P) data into a three-layer quasi-geostrophic model. The T/P data exhibited an elongated state of the southern recirculation gyre in 1993–95 and 1997, between whose two periods the gyre had a contracted state in 1995–96. A few stationary eddies were located in the southern gyre during the contracted state. The baroclinic instability, which was indicated by the phase shift from the uppermost-to the lowest-layer anomalies toward the downstream side, was evident near the Kuroshio Extension (KE) path. Since the instability never appeared in the artificial model without bottom topography, the topographic barrier for the eastward flow in the lowest layer was a necessary condition for the instability. The instability synchronized with the transition in the western region of the KE axis from the elongated to the contracted states. This evolution was interpreted as if the baroclinic instability played some part in the KE states and was a trigger for the transition from the elongated to the contracted states.     

A Unified Variational Principle of Fluid Mechanics and Application on Solitary Subdomain or Point

-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as follows, the establishment of the functional and the variational principle is easy, it can change various problems of fluid mechanics derived by basic equations into a unified optimization problem, and the solution is the optimum one in some sense. According to the OMWR for the solitary subdomain, this paper uses UVPFM onto any solitary subdomain and gives the solution of the hydrodynamics equation which is suitable only for that solitary subdomain. According to the OMWR for solitary point, this paper uses UVPFM to any solitary point and gives the solution of the hydrodynamics equation (point solution) which is suitable only for that solitary point. As the solution for the solitary subdomain or solitary point is developed independently, the compatibility with other subdomain or other points, do     

A Reconstruction of Observed Profiles in the Sea East of Japan Using Vertical Coupled Temperature-Salinity EOF Modes

It is important to estimate hard-to-observe parameters in the ocean interior from easy-to-observe parameters. This study therefore demostrates a reconstruction of observed temperature and salinity profiles of the sea east of Japan (30°≈40°N, 140°≈150°E). The reconstruction was done by estimating suboptimal state from several values of the observed profiles and/or sea surface dynamic height (SDH) calculated from the profiles. The estimation used a variational method with vertical coupled temperature-salinity empirical orthogonal function (EOF) modes. Profiles of temperature and salinity in the subtropical region are effectively reconstructed from in situ temperature profile data, or sea surface temperature (SST) and SDH. For example, the analyzed temperature field from SST and SDH has an accuracy to within 1°C in the subtropical region. Salinity in the sea north of Kuroshio, however, is difficult to estimate because of its complex variability which is less correlated with temperature than in the subtropical region. Sea surface salinity is useful to estimate the subsurface structure. We also show the possibility that the estimation is improved by considering nonlinearity in the equation calculating SDH from temperature and salinity analysis values in order to examine the misfit between analysis and observation. Analysis using TOPEX/POSEIDON altimetry data instead of SDH was also performed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar)

I present the derivation of the Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar), which is developed for adopting a non-diagonal background error covariance matrix in nonlinear variational analyses (i.e., analyses employing a non-quadratic cost function). POpULar is based on the idea of a linear preconditioned conjugate gradient method widely adopted in ocean data assimilation systems. POpULar uses the background error covariance matrix as a preconditioner without any decomposition of the matrix. This preconditioning accelerates the convergence. Moreover, the inverse of the matrix is not required. POpULar therefore allows us easily to handle the correlations among deviations of control variables (i.e., the variables which will be analyzed) from their background in nonlinear problems. In order to demonstrate the usefulness of POpULar, we illustrate two effects which are often neglected in studies of ocean data assimilation before. One is the effect of correlations among the deviations of control variables in an adjoint analysis. The other is the nonlinear effect of sea surface dynamic height calculation required when sea surface height observation is employed in a three-dimensional ocean analysis. As the results, these effects are not so small to neglect.