Assimilation of altimetric data in the mid-latitude oceans using the Singular Evolutive Extended Kalman filter with an eddy-resolving, primitive equation model

A new data assimilation scheme has been elaborated for ocean circulation models based on the concept of an evolutive, reduced-order Kalman filter. The dimension of the assimilation problem is reduced by expressing the initial error covariance matrix as a truncated series of orthogonal perturbations. This error sub-space evolves during the assimilation so as to capture the growing modes of the estimation error. The algorithm has been formulated in quite a general fashion to make it tractable with a large variety of ocean models and measurement types. In the present paper, we have examined three possible strategies to compute the evolution of the error subspace in the so-called Singular Evolutive Extended Kalman (SEEK) filter: the steady filter considers a time-independent error sub-space, the apprentice filter progressively enriches the error sub-space with the information learned from the innovation vector after each analysis step, and the dynamical filter updates the error sub-space according to the model dynamics. The SEEK filter has been implemented to assimilate synthetic observations of the surface topography in a non-linear, primitive equation model that uses density as vertical coordinate. A simplified box configuration has been adopted to simulate a Gulf Stream-like current and its associated eddies and gyres with a resolution of 20 km in the horizontal, and 4 levels in the vertical. The concept of twin experiments is used to demonstrate that the conventional SEEK filter must be complemented by a learning mechanism in order to model the misrepresented tail of the error covariance matrix. An approach based on the vertical physics of the isopycnal model, is shown particularly robust to control the velocity field in deep layers with surface observations only. The cost of the method makes it a suitable candidate for large-size assimilation problems and operational applications.     

A generalized model of pelagic biogeochemistry for the global ocean ecosystem. Part I: Theory

The set of equations for global ocean biogeochemistry deterministic models have been formulated in a comprehensive and unified form in order to use them in numerical simulations of the marine ecosystem for climate change studies (PELAGOS, PELAgic biogeochemistry for Global Ocean Simulations). The fundamental approach stems from the representation of marine trophic interactions and major biogeochemical cycles introduced in the European Regional Seas Ecosystem Model (ERSEM). Our theoretical formulation revisits and generalizes the stoichiometric approach of ERSEM by defining the state variables as Chemical Functional Families (CFF). CFFs are further subdivided into living, non-living and inorganic components. Living CFFs are the basis for the definition of Living Functional Groups, the biomass-based functional prototype of the real organisms. Both CFFs and LFGs are theoretical constructs which allow us to relate measurable properties of marine biogeochemistry to the state variables used in deterministic models. This approach is sufficiently generic that may be used to describe other existing biomass-based ecosystem model.     

Multigrid state vector for data assimilation in a two-way nested model of the Ligurian Sea

A system of two nested models composed by a coarse resolution model of the Mediterranean Sea, an intermediate resolution model of the Provençal Basin and a high resolution model of the Ligurian Sea is coupled with a Kalman-filter based assimilation method. The state vector for the data assimilation is composed by the temperature, salinity and elevation of the three models. The forecast error is estimated by an ensemble run of 200 members by perturbing initial condition and atmospheric forcings. The 50 dominant empirical orthogonal functions (EOF) are taken as the error covariance of the model forecast. This error covariance is assumed to be constant in time. Sea surface temperature (SST) and sea surface height (SSH) are assimilated in this system.     

A generalized model of pelagic biogeochemistry for the global ocean ecosystem. Part II: Numerical simulations

This paper presents a global ocean implementation of a multi-component model of marine pelagic biogeochemistry coupled on-line with an ocean general circulation model forced with climatological surface fields (PELAgic biogeochemistry for Global Ocean Simulations, PELAGOS). The final objective is the inclusion of this model as a component in an Earth System model for climate studies. The pelagic model is based on a functional stoichiometric representation of marine biogeochemical cycles and allows simulating the dynamics of C, N, P, Si, O and Fe taking into account the variation of their elemental ratios in the functional groups. The model also includes a parameterization of variable chlorophyll/carbon ratio in phytoplankton, carrying chl as a prognostic variable. The first part of the paper analyzes the contribution of non-local advective–diffusive terms and local vertical processes to the simulated chl distributions. The comparison of the three experiments shows that the mean chl distribution at higher latitudes is largely determined by mixing processes, while vertical advection controls the distribution in the equatorial upwelling regions. Horizontal advective and diffusive processes are necessary mechanisms for the shape of chl distribution in the sub-tropical Pacific. In the second part, the results have been compared with existing datasets of satellite-derived chlorophyll, surface nutrients, estimates of phytoplankton community composition and primary production data. The agreement is reasonable both in terms of the spatial distribution of annual means and of the seasonal variability in different dynamical oceanographic regions. Results indicate that some of the model biases in chl and surface nutrients distributions can be related to deficiencies in the simulation of physical processes such as advection and mixing. Other discrepancies are attributed to inadequate parameterizations of phytoplankton functional groups. The model has skill in reproducing the overall distribution of large and small phytoplankton but tends to underestimate diatoms in the northern higher latitudes and overestimate nanophytoplankton with respect to picoautotrophs in oligotrophic regions. The performance of the model is discussed in the context of its use in climate studies and an approach for improving the parameterization of functional groups in deterministic models is outlined.     

Application of a SEEK filter to a 1D biogeochemical model of the Ligurian Sea: Twin experiments and real in-situ data assimilation

The Singular Evolutive Extended Kalman (SEEK) filter has been implemented to assimilate in-situ data in a 1D coupled physical-ecosystem model of the Ligurian Sea. The biogeochemical model describes the partly decoupled nitrogen and carbon cycles of the pelagic food web. The GHER hydrodynamic model (1D version) is used to represent the physical forcings. The data assimilation scheme (SEEK filter) parameterizes the error statistics by means of a set of empirical orthogonal functions (EOFs). Twin experiments are first performed with the aim to choose the suitable experimental protocol (observation and estimation vectors, number of EOFs, frequency of the assimilation,…) and to assess the SEEK filter performances. This protocol is then applied to perform real data assimilation experiments using the DYFAMED data base. By assimilating phytoplankton observations, the method has allowed to improve not only the representation of the phytoplankton community, but also of other variables such as zooplankton and bacteria that evolve with model dynamics and that are not corrected by the data assimilation scheme. The validation of the assimilation method and the improvement of model results are studied by means of suitable error measurements.     

Improving the physics of a coupled physical–biogeochemical model of the North Atlantic through data assimilation: Impact on the ecosystem

Several studies on coupled physical–biogeochemical models have shown that major deficiencies in the biogeochemical fields arise from the deficiencies in the physical flow fields. This paper examines the improvement of the physics through data assimilation, and the subsequent impact on the ecosystem response in a coupled model of the North Atlantic. Sea surface temperature and sea surface height data are assimilated with a sequential method based on the SEEK filter adapted to the coupling needs. The model domain covers the Atlantic from 20°S to 70°N at eddy-permitting resolution. The biogeochemical model is a NPZD-DOM model based on the P3ZD formulation. The results of an annual assimilated simulation are compared with an annual free simulation.With assimilation, the representation of the mixed layer depth is significantly improved in mid latitudes, even though the mixed layer depth is generally overestimated compared to the observations. The representation of the mean and variance of the currents is also significantly improved.The nutrient input in the euphotic zone is used to assess the data assimilation impact on the ecosystem. Data assimilation results in a 50% reduction of the input due to vertical mixing in mid-latitudes, and in a four- to six-fold increase of the advective fluxes in mid-latitudes and subtropics. Averaged zonally, the net impact is a threefold increase for the subtropical gyre, and a moderate (20–30%) decrease at mid and high latitudes.Surface chlorophyll concentration increases along the subtropical gyre borders, but little changes are detected at mid and high latitudes. An increase of the primary production appears along the Gulf Stream path, but it represents only 12% on average for mid and high latitudes. In the subtropical gyre centre, primary production is augmented but stays underestimated (20% of observations). These experiments show the benefits of physical data assimilation in coupled physical–biogeochemical applications.     

Lagrangian data in a high-resolution numerical simulation of the North Atlantic: I. Comparison with in situ drifter data

A model/data comparison was performed between simulated drifters from a high-resolution numerical simulation of the North Atlantic and a data set from in situ surface drifters. The comparison makes use of pseudo-Eulerian statistics such as mean velocity and eddy kinetic energy, and Lagrangian statistics such as integral time scales. The space and time distribution of the two data sets differ in the sense that the in situ drifters were released inhomogeneously in space and time while the simulated drifters were homogeneously seeded at the same time over a regular 1° grid. Despite this difference, the total data distributions computed over the complete data sets show some similarities that are mostly related to the large-scale pattern of Ekman divergence/convergence.Comparisons of eddy kinetic energy and root mean square velocity indicate that the numerical model underestimates the eddy kinetic energy in the Gulf Stream extension and in the ocean interior. In addition, the model Lagrangian time scales are longer in the interior than the in situ time scales by approximately a factor of 2. It is suggested that this is primarily due to the lack of high-frequency winds in the model forcing, which causes an underestimation of the directly forced eddy variability. Regarding the mean flow, the comparison has been performed both qualitatively and quantitatively using James' statistical test. The results indicate that over most of the domain, the differences between model and in situ estimates are not significant. However, some areas of significant differences exist, close to high-energy regions, notably around the Gulf Stream path, which in the model lies slightly north of the observed path, although its strength and structure are well represented overall. Mean currents close to the buffer zones, primarily the Azores Current, also exhibit significant differences between model results and in situ estimates. Possibilities for model improvement are discussed in terms of forcings, buffer zone implementations, turbulence and mixed layer parameterizations, in light of our model/data comparison.     

Errors in dynamical fields inferred from oceanographic cruise data: Part I. The impact of observation errors and the sampling distribution

Diagnostic studies of ocean dynamics based on the analysis of oceanographic cruise data are usually quite sensitive to observation errors, to the station distribution and to the synopticity of the sampling. Here we present an error analysis of the first two sources. The third one is evaluated in Part II of this work (J. Mar. Sys. (2005), this issue). For observed variables and those linearly related to them, we use the Optimal Statistical Interpolation (OI) formulation. For variables which are not linearly related to observed variables (e.g., the vertical velocity), we carry out numerical experiments in a consistent way with OI statistics. Best results are obtained when some kind of scale selection or spatial filtering is applied in order to suppress small scales that cannot be properly resolved by the station distribution.The formulation is first applied to a high resolution (SeaSoar) sampling aimed to the recovery of mesoscale features in a region of large spatial variability (noise-to-signal fraction of the order of 0.002). Fractional errors (rms error divided by the standard deviation of the field) are estimated in about 2% for dynamic height and between 4% and 20% for geostrophic vorticity and vertical velocity. For observed variables, observation errors and sampling limitations are shown to contribute in similar amounts to total errors. For derived variables, sampling errors are by far the dominant contribution. For less dense samplings (e.g., equally spaced CTD stations), fractional errors are about 6% for dynamic height and between 15% and 30% for geostrophic vorticity and vertical velocity. For this sampling strategy, errors of all variables are mostly associated with sampling limitations.     

A numerical transport model for predicting the distributions of Cd, Cu, Ni, Pb and Zn in the southern North Sea: the sensitivity of model results to the uncertainties in the magnitudes of metal inputs

A new transport model for metals (named NOSTRADAMUS) has been developed to predict concentrations and distributions of Cd, Cu, Ni, Pb and Zn in the southern North Sea. NOSTRADAMUS is comprised of components for water, inorganic and organic suspended particulate matter transport; a primary production module contributes to the latter component. Metal exchange between dissolved (water) and total suspended particulate matter (inorganic + organic) phases is driven by distribution coefficients. Transport is based on an existent 2-D vertically integrated model, incorporating a 35 × 35 km grid. NOSTRADAMUS is largely driven by data obtained during the Natural Environment Research Council North Sea Project (NERC NSP). The sensitivity of model predictions to uncertainties in the magnitudes of metal inputs has been tested. Results are reported for a winter period (January 1989) when plankton production was low. Simulated ranges in concentrations in regions influenced by the largest inflows, i.e. the NE English coast and the Southern Bight, are similar to the ranges in the errors of the concentrations estimated at the northern and southern open sea boundaries of the model. Inclusion of uncertainties with respect to atmospheric (up to ± 54%) and riverine (± 30%) inputs makes little difference to the calculated concentrations of both dissolved and particulate fractions within the southern North Sea. When all the errors associated with the inputs are included there is good agreement between computed and observed concentrations, and that for dissolved and particulate Cd, Cu and Zn, and dissolved Ni and Pb, many of the observations fall within, or are close to, the range of values generated by the model. For particulate Pb, model simulations predict concentrations of the right order, but do not reproduce the large scatter in actual concentrations, with simulated concentrations showing a bias towards lower values compared to those observed. A factor which could have contributed to observed concentrations, and which is not included in the model, is considered to be a substantial benthic input of dissolved lead during this winter period, coupled to a rapid and extensive scavenging of the dissolved lead to particles. Significant reductions in riverine and aeolian inputs of total Cd and Cu of 70% and 50%, respectively, consistent with aims of North Sea Conferences, are predicted to lead to minor decreases (~ 10%) in water column concentrations of dissolved and particulate Cd and Cu, except near river sources, where maximum reductions of ~ 30–40% may occur.