Manfred Wenzel

Testing a marine ecosystem model: sensitivity analysis and parameter optimization

A data assimilation technique is used with a simple but widely used marine ecosystem model to optimize poorly known model parameters. A thorough analysis of the a posteriori errors to be expected for the estimated parameters was carried out. The errors have been estimated by calculating the Hessian matrices for different problem formulations based on identical twin experiments. The error analysis revealed inadequacies in the formulation of the optimization problem and insufficiencies of the applied data set. Modifications of the actual problem formulation, which improved the accuracy of the estimated parameters considerably, are discussed. The optimization procedure was applied to real measurements of nitrate and chlorophyll at the Atlantic Bermuda site. The parameter optimization gave poor results. We suggest this to be due to features of the ecosystem that are unresolved by the present model formulation. Our results emphasize the necessity of an error analysis to accompany any parameter optimization study.

Variational Assimilation of Geosat Data into an Eddy-resolving Model of the Gulf Stream Extension Area

Abstract A variational inverse technique is applied to assimilate sea surface height (SSH) measurements into a simple eddy-resolving quasigeostrophic ocean model. The data used were measured by Geosat in the spring of 1987 in an area in the Gulf Stream extension. The assimilation technique minimizes the weighted least-squares difference between model and observations, while the dynamical model equations are satisfied exactly. Fitting the model to data by applying the adjoint technique allows us not only to solve for the best model trajectory in phase space but also the wind forcing and internal model parameters describing, for example, diffusion or stratification. The method is first tested systematically by performing a number of identical twin experiments with model-produced “observations.” A hierarchy of ocean models is then applied to test their performance in assimilating two repeat cycles of Geosat sea surface height (SSH) measurements. The most successful model is nonlinear and baroclinic. It can f...

The annual cycle of the global ocean circulation as determined by 4D VAR data assimilation

Abstract A method is presented that allows the estimation of a consistent oceanic circulation from hydrographic data using a coarse-resolution ocean model. The major difference to previous attempts to solve this well known problem in a global context lies in the application of a time dependent model that is optimized for a cyclo-stationary solution, i.e. the annual cycle is included and the interannual variability is minimized. Furthermore it is shown, that integral constraints on the large scale fluxes are important, when our goal is to get beyond the reproduction of the temperature and salinity measurements and is targeted at a realistic flow field. In order to estimate both the initial temperature and salinity fields as well as the surface forcing a new procedure is developed which is based on the adjoint technique. A sequence of sub-problems is constructed in which either the initial model state or the forcing fields are used as control variables. The corresponding cost functions are minimized iteratively by a gradient descent algorithm while each sub-problem involves several years of model integration per iteration. In this paper we report on two assimilation experiments. The first experiment, which uses temperature and salinity data only, fits the observations well. However, it was not very successful in reproducing our knowledge about the circulation and the transports. In the second experiment we gathered more a-priori knowledge in appropriate constraints and also utilize the sea surface height data from the TOPEX/Poseidon mission. Compared to assimilation attempts using stationary models our results clearly profit from taking into account the annual cycle as well as from optimizing the forcing. The remaining model-data misfit stays within the range of the expected errors and the retrieved forcing is, in general, consistent with prior estimates. Thus the model finally provides a reasonable seasonal cycle of the oceans heat as well as freshwater transport that is consistent with prior estimates. Most of the remaining discrepancies can be attributed to the coarse spatial resolution, while the large timestep obviously is not a problem.

On the Sensitivity of Field Reconstruction and Prediction Using Empirical Orthogonal Functions Derived from Gappy Data

AbstractEmpirical orthogonal function (EOF) analysis is commonly used in the climate sciences and elsewhere to describe, reconstruct, and predict highly dimensional data fields. When data contain a high percentage of missing values (i.e., gappy), alternate approaches must be used in order to correctly derive EOFs. The aims of this paper are to assess the accuracy of several EOF approaches in the reconstruction and prediction of gappy data fields, using the Galapagos Archipelago as a case study example. EOF approaches included least squares estimation via a covariance matrix decomposition [least squares EOF (LSEOF)], data interpolating empirical orthogonal functions (DINEOF), and a novel approach called recursively subtracted empirical orthogonal functions (RSEOF). Model-derived data of historical surface chlorophyll-a concentrations and sea surface temperature, combined with a mask of gaps from historical remote sensing estimates, allowed for the creation of true and observed fields by which to gauge the ...

The Global Ocean Mass Budget in 1993–2003 Estimated from Sea Level Change

Abstract The mass budget of the ocean in the period 1993–2003 is studied with a general circulation model. The model has a free surface and conserves mass rather than volume; that is, freshwater is exchanged with the atmosphere via precipitation and evaporation and inflow from land is taken into account. The mass is redistributed by the ocean circulation. Furthermore, the ocean’s volume changes by steric expansion with changing temperature and salinity. To estimate the mass changes, the ocean model is constrained by sea level measurements from the Ocean Topography Experiment (TOPEX)/Poseidon mission as well as by hydrographic data. The modeled ocean mass change within the years 2002–03 compares favorably to measurements from the Gravity Recovery and Climate Experiment (GRACE), and the evolution of the global mean sea level for the period 1993–2003 with annual and interannual variations can be reproduced to a 0.15-cm rms difference. Its trend has been measured as 3.37 mm yr−1 while the constrained model gi...

Global and regional sea level change during the 20th century

Sea level variations prior to the launch of satellite altimeters are estimated by analyzing historic tide gauge records. Recently, a number of groups have reconstructed sea level by applying EOF techniques to fill missing observations. We complement this study with alternative methods. In a first step gaps in 178 records of sea level change are filled using the pattern recognition capabilities of artificial neural networks. Afterward satellite altimetry is used to extrapolate local sea level change to global fields. Patterns of sea level change are compared to prior studies. Global mean sea level change since 1900 is found to be 1.77±0.38 mm yr−1 on average. Local trends are essentially positive with the highest values found in the western tropical Pacific and in the Indian Ocean east of Madagascar where it reaches about +6 mm yr−1. Regions with negative trends are spotty with a minimum value of about −2 mm yr−1 south of the Aleutian Islands. Although the acceleration found for the global mean, +0.0042 ± 0.0092 mm yr−2, is not significant, local values range from −0.1 mm yr−2 in the central Indian Ocean to +0.1 mm yr−2 in the western tropical Pacific and east of Japan. These extrema are associated with patterns of sea level change that differ significantly from the first half of the analyzed period (i.e., 1900–1950) to the second half (1950–2000). We take this as an indication of long period oceanic processes that are superimposed to the general sea level rise.

Determining Diffusivities from Hydrographic Data by Inverse Methods with Applications to the Circumpolar Current

Several inverse models have recently been put forward for obtaining estimates of the unknown reference velocities on the basis of the balances for momentum, vorticity, heat and salt of the large scale geostrophic circulation in the ocean. Notable forerunners are the inverse method proposed by Wunsch (1978) and the β-spiral method of Stommel and Schott (1977). These have first been applied in strictly adiabatic versions in the North Atlantic (see also Wunsch and Grant 1982, Schott and Stommel 1978). Both approaches can be extended to diabatic conditions. For the β-spiral model the consideration of the diffusion terms in the balances for tracers and vorticity are conceptionally simple (e.g. Olbers et al. 1985, Bigg 1985). Also Wunsch’s method has been generalized in this respect (see e.g. Wunsch 1984). We should also mention Hogg’s model (Hogg 1987) which is an inversion of the advective-diffusive balances on two isopycnals subject to the geostrophic constraint between the isopycnals. The model was applied in the central North Atlantic.

Assimilation of TOPEX/Poseidon data in a global ocean model: differences in 1995–1996

Abstract Starting from an optimized climatological ocean model two response experiments are performed to study the impact of assimilating altimeter data on the ocean state. For this purpose TOPEX/Poseidon altimeter measurements from 1995 and 1996, respectively, are used. The model setup remains the same in the reference and the response experiments except the relative weight of the altimeter data is increased for the new assimilation experiments. Furthermore a cyclic repetition of altimeter data from the respective years will be used instead of a mean annual cycle. The analysis of the differences in the two ‘perpetual 1995’ and ‘perpetual 1996’ solutions shows that the changes in the optimal forcing are small and differences in the flow fields are noticeable only in the upper ocean. The model is able to follow the different sea surface height measurements by adjusting the upper ocean thermal and haline structures. The modelled steric height anomalies closely follow the TOPEX/Poseidon anomalies. These anomalies are mainly due to thermal expansion while the haline expansion is a second order effect in most parts of the global ocean. Nevertheless the latter cannot be neglected anywhere because it at least partly compensates the thermal.

Improved Estimates of the Oceanic Circulation Using the CHAMP Geoid

Ocean general circulation models which are constrained by altimetry data usually assimilate only temporal sea-surface height anomalies. It is known that this is not enough to correct the mean ocean state. Here we present first results of assimilating the full (absolute) dynamical topography into a steady state version of a finite element ocean model (FEOM) for the North Atlantic. This makes it possible to notably reduce the model-data misfit especially in the western part of the basin and in the southern Labrador Sea.

Assimilation of Altimeter and Geoid Data into a Global Ocean Model.

A dynamical global ocean model is used to determine the general circulation and its associated transports from data. As a reference a surface geostrophic velocity can be calculated from the slope of the sea surface height, which is measured by satellite altimetry. To get absolute values for the sea surface elevation relative to the equipotential surface we want to assimilate not only altimeter data but also geoid heights into our global ocean model. Until nowadays the assimilation of geoid heights has been done only in few cases, because the accuracy of the available gravity models is not sufficient. With the CHAMP satellite and future satellite missions we will get highly improved gravity models. Since these data are not available yet we use the EGM96 geoid models for our recent experiments. It is planned to esitmate corrections not only for the ocean model but also for the geoid models. We want to present the technique which will be used to assimilate the geoid data into the global ocean model.