A generalized vertical coordinate for 3D marine models

Vertical coordinate transformation is used in ocean modelling to provide good representation of the flow near bottom and free surface boundaries and to allow the concentration of grid points in regions of high gradient. A natural treatment of impermeability boundary conditions is achieved by considering transformations which fit the surface and bottom boundaries. This paper develops the governing equations of shallow sea hydrodynamics for a generalised vertical coordinate transformation, which embraces all formulations commonly used in ocean modelling, and allows greater freedom to concentrate grid points in regions of high gradient. In addition to the popular sigma coordinates, various hybrid "sigma-z" coordinate transformations, defined for ad hoc applications, are reviewed. Conservative formulations are proposed for the governing equations, including the pressure gradient and horizontal diffusion terms

A coastal ocean model intercomparison study for a three-dimensional idealised test case

Several coastal ocean models have been used to compute the circulation on the Northwest European Continental Shelf. Five of them, developed within the European Union, are compared in the scope of an idealised three-dimensional test case, dealing with the geostrophic adjustment of a freshwater cylinder. As the central eddy adjusts, unstable baroclinic vortices start to grow. All the models are able to produce such unstable vortices. However, two of them produce an order-two instability, which is in accordance with a previous laboratory experiment, while the others exhibit an order- four instability. Using a simple scaling analysis, it is seen that the azimuthal wavenumber depends on the ratio of the kinetic energy to the available potential energy. It appears that the discrepancy in the azimuthal wavenumber is mainly due to the effect of the discretisation of the horizontal advection of momentum which could produce significant decrease of the total kinetic energy

Calibration and validation of a generic multisensor algorithm for mapping of total suspended matter in turbid waters

Mapping of total suspended matter concentration (TSM) can be achieved from space-based optical sensors and has growing applications related to sediment transport. A TSM algorithm is developed here for turbid waters, suitable for any ocean colour sensor including MERIS, MODIS and SeaWiFS. Theory shows that use of a single band provides a robust and TSM-sensitive algorithm provided the band is chosen appropriately. Hyperspectral calibration is made using seaborne TSM and reflectance spectra collected in the southern North Sea. Two versions of the algorithm are considered: one which gives directly TSM from reflectance, the other uses the reflectance model of Park and Ruddick (2005) to take account of bidirectional effects.Applying a non-linear regression analysis to the calibration data set gave relative errors in TSM estimation less than 30% in the spectral range 670–750 nm. Validation of this algorithm for MODIS and MERIS retrieved reflectances with concurrent in situ measurements gave the lowest relative errors in TSM estimates, less than 40%, for MODIS bands 667 nm and 678 nm and for MERIS bands 665 nm and 681 nm. Consistency of the approach in a multisensor context (SeaWiFS, MERIS, and MODIS) is demonstrated both for single point time series and for individual images

Effect of a waveband shift on chlorophyll retrieval from MERIS imagery of inland and coastal waters

A chlorophyll-retrieval algorithm for use with imagery from the Medium Resolution Imaging Spectrometer (MERIS) aboard ENVISAT relying on wavebands centred at 665, 705 and 775 nm was described in a previous paper (Gons et al. 2002, J. Plankton Res., 24, 947–951). The present study reexamined the performance for the current nominal setting to 708.75 nm of the previously envisaged 705 nm band. Validation of the algorithm with revised coefficients gave the same standard error of estimate for the inland and coastal waters as in the original work. The algorithm has been transcribed for direct application with the MERIS level-2 standard product ‘water-leaving reflectance’. By this correction, chlorophyll estimation will generally improve, especially for high concentrations.

A chlorophyll-retrieval algorithm for satellite imagery (Medium Resolution Imaging Spectrometer) of inland and coastal waters

A chlorophyll (Chl) a retrieval algorithm, originally developed for spectral subsurface irradiance reflectance determined from above-water shipboard measurements, was adapted for use with satellite imagery to be acquired by the MERIS (Medium Resolution Imaging Spectrometer) instrument. This MERIS algorithm was calibrated for Chl a concentrations in the range 3–185 mg m-3 using spectral reflectance calculated from shipboard measurements on the IJssel Lagoon (The Netherlands). Next, the algorithm was validated for various inland and coastal waters covering this concentration range. Despite the lower spectral resolution of MERIS as compared to the shipboard spectroradiometer, the standard error of estimate is expected to be similar, i.e. 9 mg m-3 of Chl a in mesotrophic and eutrophic lakes, rivers, estuaries and coastal waters.

Optical teledetection of chlorophyll <i>a</i> in estuarine and coastal waters

A hand-held spectroradiometer was used for above-water determination of subsurface spectral irradiance reflectance in the Scheldt Estuary (Belgium/The Netherlands), the North Sea off the Belgian coast, and the Hudson/Raritan Estuary (New York/New Jersey). On the North Sea the measurement conditions were adverse, and elsewhere broken cloud caused considerable spectral variation. Despite this variation the retrieval of chlorophyll a (Chl-a) from three reflectance spectra at all sampling stations was stable. The algorithm calibrated for the freshwater IJssel Lagoon (The Netherlands) proved to be applicable to these estuarine and coastal waters (N = 30; standard error of estimate = 7 mg m-3 for corrected Chl-a ranging from 1 to 93 mg m-3)

Seaborne measurements of near infrared water-leaving reflectance: the similarity spectrum for turbid waters

Theory and seaborne measurements are presented for the near infrared (NIR: 700-900 nm) water-leaving reflectance in turbid waters. According to theory, the shape of the NIR spectrum is determined largely by pure water absorption and is thus almost invariant. A ‘‘similarity’’ NIR reflectance spectrum is defined by normalization at 780 nm. This spectrum is calculated from seaborne reflectance measurements and is compared with that derived from laboratory water absorption measurements. Factors influencing the shape of the similarity spectrum are analyzed theoretically and by radiative transfer simulations. These simulations show that the similarity spectrum is valid for waters ranging from moderately turbid (e.g., water-leaving reflectance at 780 nm of order 10-4 or total suspended matter concentration of order 0.3 g m-3) to extremely turbid (e.g., reflectance at 780 nm of order 10-1 or total suspended matter of order 200 g m-3). Measurement uncertainties are analyzed, and the air-sea interface correction is shown to be critical for low reflectances. Applications of the NIR similarity spectrum to atmospheric correction of ocean color data and to the quality control of seaborne, airborne, and spaceborne reflectance measurements in turbid waters are outlined