Local ensemble assimilation scheme with global constraints and conservation

Ensemble assimilation schemes applied in their original, global formulation respect linear conservation properties if the ensemble perturbations are set up accordingly. For realistic ocean systems, only a relatively small number of ensemble members can be calculated. A localization of the ensemble increment is therefore necessary to filter out spurious long-range correlations. The conservation of the global properties will be lost if the assimilation is performed locally, since the conservation requires a coupling between all model grid points which is removed by the localization. The distribution of ocean observations is often highly inhomogeneous. Systematic errors of the observed parts of the ocean state can lead to spurious adjustment of the non-observed parts via data assimilation and thus to a spurious increase or decrease in long-term simulations of global properties which should be conserved. In this paper, we propose a local assimilation scheme (with different variants and assumptions) which can satisfy global conservation properties. The proposed scheme can also be used for non-local observation operators. Different variants of the proposed scheme are tested in an idealized model and compared to the traditional covariance localization with an ad-hoc step enforcing conservation. It is shown that the inclusion of the conservation property reduces the total RMS error and that the presented stochastic and deterministic schemes avoiding error space rotation provide better results than the traditional covariance localization.     

Reconstructing late Eocene–lower Oligocene seismic facies framework of a rhythmic deposits from eastern China

Due to the apparent rhythmic characteristics of the stratigraphically complex unit formed of deltaic and mostly lacustrine deposits in Qianjiang depression (Jianghan basin), we used the seismic pattern proxies inside a seismic sequence, by analyzing the character of reflections (amplitude, continuity, and configuration) to detect the different seismic facies and to predict their depositional environmental settings. The depression fills are characterized by a distinct upward change in seismic facies; beginning with a fan facies in the bottom, followed by free facies occurring where thick salt sediments were presented, then convergent base-lapping facies, succeeded by chaotic facies and overlain by parallel to sub-parallel facies. The convergent base-lapping facies is the most common and the parallel and draping facies is restricted to slope areas shallower than 1000 m in water depth. Three depositional environments that range from fluvial, delta, to marine (lake) are predicted too. This paper lays the foundation for the development of a seismic sequence stratigraphic framework, and contributing to better understanding of the potential evaluation of hydrocarbon occurrence in the Eastern center of China.     

The effect of halogens on Zr diffusion and zircon dissolution in hydrous metaluminous granitic melts

Diffusion of Zr and zircon solubility in hydrous, containing approximately 4.5 wt% H₂O, metaluminous granitic melts with halogens, either 0.35 wt% Cl (LCl) or 1.2 wt% F (MRF), and in a halogen-free melt (LCO) were measured at 1.0 GPa and temperatures between 1,050 and 1,400 °C in a piston-cylinder apparatus using the zircon dissolution technique. Arrhenius equations for Zr diffusion in each hydrous melt composition are, for LCO with 4.4ǂ.4 wt% H₂O: % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacqWGebarcqGH9aqpcq % aIYaGmcqGGUaGlcqaI4aaocqaI4aaocqGHXcqScqaIWaamcqGGUaGl % cqaIWaamcqaIZaWmcqWG4baEcqaIXaqmcqaIWaamdaahaaWcbeqaai % abgkHiTiabiIda4aaakiGbcwgaLjabcIha4jabcchaWnaabmaabaWa % aSaaaeaacqGHsislcqaIXaqmcqaI0aancqaIWaamcqGGUaGlcqaIXa % qmcqGHXcqScqaIZaWmcqaIZaWmcqGGUaGlcqaI5aqoaeaacqWGsbGu % cqWGubavaaaacaGLOaGaayzkaaaaaa!571F! D = 2.88 ±0.03x10 ^{- 8} exp( [( - 140.1 ±33.9)/(RT)] )D = 2.88 \pm 0.03x10^{ - 8} \exp \left( {{{ - 140.1 \pm 33.9} \over {RT}}} \right) , for LCl with 4.5ǂ.5 wt% H₂O: % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacqWGebarcqGH9aqpcq % aIYaGmcqGGUaGlcqaIZaWmcqaIZaWmcqGHXcqScqaIWaamcqGGUaGl % cqaIWaamcqaI1aqncqWG4baEcqaIXaqmcqaIWaamdaahaaWcbeqaai % abgkHiTiabisda0aaakiGbcwgaLjabcIha4jabcchaWnaabmaabaWa % aSaaaeaacqGHsislcqaIYaGmcqaI1aqncqaI0aancqGGUaGlcqaI4a % aocqGHXcqScqaI2aGncqaI0aancqGGUaGlcqaIXaqmaeaacqWGsbGu % cqWGubavaaaacaGLOaGaayzkaaaaaa!5719! D = 2.33 ±0.05x10 ^{- 4} exp( [( - 254.8 ±64.1)/(RT)] )D = 2.33 \pm 0.05x10^{ - 4} \exp \left( {{{ - 254.8 \pm 64.1} \over {RT}}} \right) and for MRF with 4.9ǂ.3 wt% H₂O: % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacqWGebarcqGH9aqpcq % aIYaGmcqGGUaGlcqaI1aqncqaI0aancqGHXcqScqaIWaamcqGGUaGl % cqaIWaamcqaIZaWmcqWG4baEcqaIXaqmcqaIWaamdaahaaWcbeqaai % abgkHiTiabiwda1aaakiGbcwgaLjabcIha4jabcchaWnaabmaabaWa % aSaaaeaacqGHsislcqaIYaGmcqaIYaGmcqaIZaWmcqGGUaGlcqaI4a % aocqGHXcqScqaIXaqmcqaI1aqncqGGUaGlcqaI1aqnaeaacqWGsbGu % cqWGubavaaaacaGLOaGaayzkaaaaaa!5715! D = 2.54 ±0.03x10 ^{- 5} exp( [( - 223.8 ±15.5)/(RT)] )D = 2.54 \pm 0.03x10^{ - 5} \exp \left( {{{ - 223.8 \pm 15.5} \over {RT}}} \right) . Solubilities determined by the dissolution technique were reversed for LCO +4.5ǂ.5 wt% H₂O by crystallization of a Zr-enriched glass of LCO composition at 1,200 and 1,050 °C at 1.0 GPa. The solubility data were used to calculate partition coefficients of Zr between zircon and hydrous melt, which are given by the following expressions: for LCO % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacyGGSbaBcqGGUbGBcq % WGebardaqhaaWcbaGaemOwaOLaemOCaihabaGaemOEaONaemyAaKMa % emOCaiNaem4yamMaem4Ba8MaemOBa4Maei4la8IaemyBa0Maemyzau % MaemiBaWMaemiDaqhaaOGaeyypa0JaeGymaeJaeiOla4IaeGOnayJa % eG4mamZaaeWaaeaadaWcaaqaaiabigdaXiabicdaWiabicdaWiabic % daWiabicdaWaqaaiabdsfaubaaaiaawIcacaGLPaaacqGHsislcqaI % 1aqncqGGUaGlcqaI4aaocqaI3aWnaaa!5924! lnD_Zr^zircon/melt = 1.63( [10000/(T)] ) - 5.87\ln D_{Zr}^{zircon/melt} = 1.63\left( {{{10000} \over T}} \right) - 5.87 , for LCl % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacyGGSbaBcqGGUbGBcq % WGebardaqhaaWcbaGaemOwaOLaemOCaihabaGaemOEaONaemyAaKMa % emOCaiNaem4yamMaem4Ba8MaemOBa4Maei4la8IaemyBa0Maemyzau % MaemiBaWMaemiDaqhaaOGaeyypa0JaeGymaeJaeiOla4IaeGinaqJa % eG4naCZaaeWaaeaadaWcaaqaaiabigdaXiabicdaWiabicdaWiabic % daWiabicdaWaqaaiabdsfaubaaaiaawIcacaGLPaaacqGHsislcqaI % 0aancqGGUaGlcqaI3aWncqaI1aqnaaa!5920! lnD_Zr^zircon/melt = 1.47( [10000/(T)] ) - 4.75\ln D_{Zr}^{zircon/melt} = 1.47\left( {{{10000} \over T}} \right) - 4.75 and, for MRF by % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacyGGSbaBcqGGUbGBcq % WGebardaqhaaWcbaGaemOwaOLaemOCaihabaGaemOEaONaemyAaKMa % emOCaiNaem4yamMaem4Ba8MaemOBa4Maei4la8IaemyBa0Maemyzau % MaemiBaWMaemiDaqhaaOGaeyypa0JaeGymaeJaeiOla4IaeGinaqJa % eG4naCZaaeWaaeaadaWcaaqaaiabigdaXiabicdaWiabicdaWiabic % daWiabicdaWaqaaiabdsfaubaaaiaawIcacaGLPaaacqGHsislcqaI % 0aancqGGUaGlcqaI5aqocqaIXaqmaaa!591C! lnD_Zr^zircon/melt = 1.47( [10000/(T)] ) - 4.91\ln D_{Zr}^{zircon/melt} = 1.47\left( {{{10000} \over T}} \right) - 4.91 . Experiments on the same compositions, but with water contents down to 0.5 wt%, demonstrated reductions in both the diffusion coefficient of Zr and zircon solubility in the melt. The addition of halogens at the concentration levels studied to metaluminous melts has a small effect on either the diffusion of Zr in the melt, or the solubility of zircon at all water concentrations and temperatures investigated. At 800 °C, the calculated diffusion coefficient of Zr is lowest in LCl, 9᎒^-17 m² s^-1, and is highest in LCO, 4᎒^-15 m² s^-1. Extrapolation of the halogen-free solubility data to a magmatic temperature of 800 °C yields solubilities of approximately one-third of those directly measured in similar compositions, predicted by earlier studies of zircon dissolution and based upon analyses of natural rocks. This discrepancy is attributed to the higher oxygen fugacity of the experiments of this study compared with previous studies and nature, and the effect of oxygen fugacity on the structural role of iron in the melt, which, in turn, affects zircon solubility, but does not significantly affect Zr diffusion.     

Correcting surface winds by assimilating high-frequency radar surface currents in the German Bight

Surface winds are crucial for accurately modeling the surface circulation in the coastal ocean. In the present work, high-frequency radar surface currents are assimilated using an ensemble scheme which aims to obtain improved surface winds taking into account European Centre for Medium-Range Weather Forecasts winds as a first guess and surface current measurements. The objective of this study is to show that wind forcing can be improved using an approach similar to parameter estimation in ensemble data assimilation. Like variational assimilation schemes, the method provides an improved wind field based on surface current measurements. However, the technique does not require an adjoint, and it is thus easier to implement. In addition, it does not rely on a linearization of the model dynamics. The method is validated directly by comparing the analyzed wind speed to independent in situ measurements and indirectly by assessing the impact of the corrected winds on model sea surface temperature (SST) relative to satellite SST.     

Filtering inertia-gravity waves from the initial conditions of the linear shallow water equations

A method for filtering inertia-gravity waves from elevation and depth-averaged velocity is described. This filtering scheme is derived from the linear shallow water equations for constant depth and constant Coriolis frequency. The filtered solution is obtained by retaining only the eigenvectors corresponding to the geostrophic equilibrium and by discarding explicitly the eigenvectors corresponding to the fast moving inertia-gravity waves. An alternative formulation is derived using a variational approach. Both filtering methods are tested numerically for a periodic domain with constant depth and the variational approach is implemented for a closed domain with large topographic variations. The filtering methods significantly reduce the amplitudes of the inertia-gravity waves while preserving the mean flow. The variational method is compared to the Incremental Analysis Update technique and the benefits of the variational filter are presented.     

Long-period waves in the vicinity of Onagawa Bay (I)

To investigate the response characteristics of a bay to tsunamis, field measurements of long-period waves have been carried out at Onagawa and Okachi Bays, both of which face the Pacific Ocean in northern Japan. In Onagawa Bay, the observed transfer function is in good agreement with the prediction based on the one-dimensional numerical model, in the period range larger than about 15 minutes. The response of shorter periods seems to be influenced by the two-dimensionality of the bay. The oscillations within Onagawa Harbor are also discussed with respect to the relative amplitude and phase at two stations inside the harbor and it is estimated that the reflection coefficient at the waterfront is about 0.7. In Okachi Bay, the oscillations in the period range larger than about 10 minutes could be explained by a Y-shaped model of the bay. The dominant oscillations offshore of these two-bays are found to be the mode with the motion predominantly in the direction normal to the shelf orientation, and the estimated power spectral density of incoming waves in deep water varies asf ^–2,f being the frequency. The waves of lateral modes, such as edge waves on the shelf, are small and of minor importance to generate bay oscillations of longer periods.     

Contrasts in sedimentation flux below the southern California Current in late 1996 and during the El Niño event of 1997–1998

The vertical flux of particulate matter at 330 m depth in San Lázaro Basin off southern Baja California ranged from 63 to 587 mg m⁻² d⁻¹ between August and November 1996. Organic carbon contents were between 5.6 and 14.8%, yielding flux rates of 9–40 mgC m⁻² d⁻¹. In December 1997 and January 1998, at the height of the strong El Niño event, the respective fluxes (47–202 mg m⁻² d⁻¹ and 3–8 mgC m⁻² d⁻¹) were comparable. The February–June 1998 records, however, revealed sharply reduced mass (1–6 mg m⁻² d⁻¹) and organic carbon (0.2–0.8 mgC m⁻² d⁻¹) fluxes. The organics collected in 1996 were predominantly autochthonous (δ¹³C=−22‰; C/N=8). The variations in δ¹⁵N (8.3–11.0‰) suggest an alternation of new and regenerated production, possibly associated with fluctuations in the intensity of deep mixing during that autumn. The relatively high organic matter fluxes in December 1997 appear to be associated with regenerated production. The average composition from February to June 1998 (δ¹³C=−23.6‰; ¹⁵N=11.7‰; C/N=10.5) indicates degraded material of marine origin. The maximum δ¹⁵N value found (14‰) suggests that deeper, denitrified waters were brought to the surface and possibly advected laterally. Regime changes in the waters of the basin occur at 6–10 week intervals, evidenced by concurrent shifts in most of the measured parameters, including fecal pellet types and metal chemistry. The marine snow-dominated detritus collected showed a shift from a mixed diatom-rich-radiolarian-coccolith assemblage in late 1996 to a coccolith-dominated assemblage, including the contents of fecal pellets, during the 1997–1998 El-Niño period. T–S profiles, plankton analysis and chlorophyll contents of the upper water column indicated that the strong phytoplankton bloom, normally associated with seasonal upwelling along the Pacific coast of Baja, did not occur during the spring of 1998. The persistence of oligotrophic conditions during the 1997–1998 El Niño event favored the dominance of nanoplankton and reduced the vertical flux of particles.     

Cloud filling of ocean colour and sea surface temperature remote sensing products over the Southern North Sea by the Data Interpolating Empirical Orthogonal Functions methodology

Optical remote sensing data is now being used systematically for marine ecosystem applications, such as the forcing of biological models and the operational detection of harmful algae blooms. However, applications are hampered by the incompleteness of imagery and by some quality problems. The Data Interpolating Empirical Orthogonal Functions methodology (DINEOF) allows calculation of missing data in geophysical datasets without requiring a priori knowledge about statistics of the full dataset and has previously been applied to SST reconstructions. This study demonstrates the reconstruction of complete space–time information for 4 years of surface chlorophyll a (CHL), total suspended matter (TSM) and sea surface temperature (SST) over the Southern North Sea (SNS) and English Channel (EC). Optimal reconstructions were obtained when synthesising the original signal into 8 modes for MERIS CHL and into 18 modes for MERIS TSM. Despite the very high proportion of missing data (70%), the variability of original signals explained by the EOF synthesis reached 93.5% for CHL and 97.2% for TSM. For the MODIS TSM dataset, 97.5% of the original variability of the signal was synthesised into 14 modes. The MODIS SST dataset could be synthesised into 13 modes explaining 98% of the input signal variability. Validation of the method is achieved for 3 dates below 2 artificial clouds, by comparing reconstructed data with excluded input information. Complete weekly and monthly averaged climatologies, suitable for use with ecosystem models, were derived from regular daily reconstructions. Error maps associated with every reconstruction were produced according to Beckers et al. (2006). Embedded in this error calculation scheme, a methodology was implemented to produce maps of outliers, allowing identification of unusual or suspicious data points compared to the global dynamics of the dataset. Various algorithm artefacts were associated with high values in the outlier maps (undetected cloud edges, haze areas, contrails, and cloud shadows). With the production of outlier maps, the data reconstruction technique becomes also a very efficient tool for quality control of optical remote sensing data and for change detection within large databases.