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Martin Losch and Carl Wunsch

Abstract

The possibility of using topography in a state estimation context as a control parameter is explored in a linear barotropic shallow water model. Along with its adjoint, the model is used to systematically assess the influence of the depth field on the modeled circulation in a steady state. Sensitivity of the flow field to the topography is greater in a partially blocked zonal channel than in a subtropical gyre. Hypothetical surface elevations are used to represent the types of data actually available. In neither case can all the details of the topography be recovered, showing that the relationship between topography and elevation does not have a unique inverse, and that many details of the topography are irrelevant to the particular physics under consideration.

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Ursula Schauer and Martin Losch

Abstract

Ocean water is freshwater with salt. The distribution of salt concentration in the ocean changes by addition and removal of freshwater in the form of precipitation, continental runoff, and evaporation, and by a flow of saline ocean water that gives rise to a salt flux divergence. Often, changes in salinity are described in terms of “freshwater content” changes and oceanic “freshwater transports,” defined as fractions of freshwater. But these freshwater fractions are arbitrary, because they are defined by a nonunique reference salinity. Also all temporal and spatial comparisons and anomalies of such freshwater fractions in the ocean depend on the choice of reference salinity in a nonlinear way, because in the definition of the fraction it appears in the denominator. Consequently, any conclusion based on the comparison of freshwater fractions is ambiguous. Since there is no definite physical constraint for a unique reference salinity, freshwater fractions are declared not useful for the assessment of the state of ocean regions and the associated changes. In the light of ongoing changes in the water cycle and the global nature of climate science, scientific results need to be expressed in a way so that they can be easily compared and integrated in a global perspective. To this end, we recommend to avoid freshwater fraction as a parameter describing the ocean state. Instead, one should use the terms of the salt budget to obtain unique results for quantifying and comparing salinity.

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Martin Losch and Patrick Heimbach

Abstract

Bottom topography, or more generally the geometry of the ocean basins, is an important ingredient in numerical ocean modeling. With the help of an adjoint model, it is shown that scalar diagnostics or objective functions in a coarse-resolution model, such as the transport through Drake Passage, the strength of the Atlantic Ocean meridional overturning circulation, the Deacon cell, and the meridional heat transport across 32°S, are sensitive to bottom topography as much as they are to surface boundary conditions. For example, adjoint topography sensitivities of the transport through Drake Passage are large in choke-point areas such as the Crozet–Kerguélen Plateau and south of New Zealand; the Atlantic meridional overturning circulation is sensitive to topography in the western boundary region of the North Atlantic Ocean and along the Scotland–Iceland Ridge. Many sensitivities are connected to steep topography and can be interpreted in terms of bottom form stress, that is, the product of bottom pressure and topography gradient. The adjoint sensitivities are found to agree with direct perturbation methods with deviations smaller than 30% for significant perturbations on time scales of 100 yr, so that the assumption of quasi linearity that is implicit in the adjoint method holds. The horizontal resolution of the numerical model affects the sensitivities to bottom topography, but large-scale patterns and the overall impact of changes in topography appear to be robust. The relative impact of changes in topography and surface boundary conditions on the model circulation is estimated by multiplying the adjoint sensitivities with assumed uncertainties. If the uncertainties are correlated in space, changing the surface boundary conditions has a larger impact on the scalar diagnostics than topography does, but the effects can locally be on the same order of magnitude if uncorrelated uncertainties are assumed. In either case, bottom topography variations within their prior uncertainties affect the solution of an ocean circulation model. To this extent, including topography in the control vector can be expected to compensate for identifiable model errors and, thus, to improve the solutions of estimation problems.

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Martin Losch, René Redler, and Jens Schröter

Abstract

The recovery of the oceanic flow field from in situ data is one of the oldest problems of modern oceanography. In this study, a stationary, nonlinear inverse model is used to estimate a mean geostrophic flow field from hydrographic data along a hydrographic section. The model is augmented to improve these estimates with measurements of the absolute sea-surface height by satellite altimetry. Measurements of the absolute sea-surface height include estimates of an equipotential surface, the geoid. Compared to oceanographic measurements, the geoid is known only to low accuracy and spatial resolution, which restricts the use of sea-surface height data to applications of large-scale phenomena of the circulation. Dedicated satellite missions that are designed for high precision, high-resolution geoid models are planned and/or in preparation. This study, which relies on twin experiments, assesses the important contribution of improved geoid models to estimating the mean flow field along a hydrographic section. When the sea-surface height data are weighted according to the error estimates of the future highly accurate geoid models GRACE (Gravity Recovery And Climate Experiment) and GOCE (Gravity Field and Steady-State Ocean Circulation Explorer), integrated fluxes of mass and temperature can be determined with an accuracy that is improved over the case with no sea-surface height data by up to 55%. With the error estimates of the currently best geoid model EGM96, the reduction of the estimated flux errors does not exceed 18%.

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Martin Losch, Alistair Adcroft, and Jean-Michel Campin

Abstract

The advent of high-precision gravity missions presents the opportunity to accurately measure variations in the distribution of mass in the ocean. Such a data source will prove valuable in state estimation and constraining general circulation models (GCMs) in general. However, conventional GCMs make the Boussinesq approximations, a consequence of which is that mass is not conserved. By use of the height–pressure coordinate isomorphism implemented in the Massachusetts Institute of Technology general circulation model (MITGCM), the impact of non-Boussinesq effects can be evaluated. Although implementing a non-Boussinesq model in pressure coordinates is relatively straightforward, making a direct comparison between height and pressure coordinate (i.e., Boussinesq and non-Boussinesq) models is not simple. However, a careful comparison of the height coordinate and the pressure coordinate solutions ensures that only non-Boussinesq effects can be responsible for the observed differences. As a yardstick, these differences are also compared with those between the Boussinesq hydrostatic and models in which the hydrostatic approximation has been relaxed, another approximation commonly made in GCMs. Model errors (differences) caused by the Boussinesq and hydrostatic approximations are demonstrated to be of comparable magnitude. Differences induced by small changes in subgrid-scale parameterizations are at least as large. Therefore, non-Boussinesq and nonhydrostatic effects are most likely negligible with respect to other model uncertainties. However, because there is no additional cost incurred in using a pressure coordinate model, it is argued that non-Boussinesq modeling is preferable simply for tidiness. It is also concluded that even coarse-resolution GCMs can be sensitive to small perturbations in the dynamical equations.

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Yosef Ashkenazy, Hezi Gildor, Martin Losch, and Eli Tziperman

Abstract

Between ~750 and 635 million years ago, during the Neoproterozoic era, the earth experienced at least two significant, possibly global, glaciations, termed “Snowball Earth.” While many studies have focused on the dynamics and the role of the atmosphere and ice flow over the ocean in these events, only a few have investigated the related associated ocean circulation, and no study has examined the ocean circulation under a thick (~1 km deep) sea ice cover, driven by geothermal heat flux. Here, a thick sea ice–flow model coupled to an ocean general circulation model is used to study the ocean circulation under Snowball Earth conditions. The ocean circulation is first investigated under a simplified zonal symmetry assumption, and (i) strong equatorial zonal jets and (ii) a strong meridional overturning cell are found, limited to an area very close to the equator. The authors derive an analytic approximation for the latitude–depth ocean dynamics and find that the extent of the meridional overturning circulation cell only depends on the horizontal eddy viscosity and β (the change of the Coriolis parameter with latitude). The analytic approximation closely reproduces the numerical results. Three-dimensional ocean simulations, with reconstructed Neoproterozoic continental configuration, confirm the zonally symmetric dynamics and show additional boundary currents and strong upwelling and downwelling near the continents.

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Marc H. Taylor, Martin Losch, Manfred Wenzel, and Jens Schröter

Abstract

Empirical 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 performance of EOF approaches. Only DINEOF and RSEOF were found to be appropriate for gappy data reconstruction and prediction. DINEOF proved to be the superior approach in terms of accuracy, especially for noisy data with a high estimation error, although RSEOF may be preferred for larger data fields because of its relatively faster computation time.

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Mahdi Mohammadi-Aragh, Martin Losch, and Helge F. Goessling

Abstract

Sea ice models have become essential components of weather, climate, and ocean models. A realistic representation of sea ice affects the reliability of process representation, environmental forecast, and climate projections. Realistic simulations of sea ice kinematics require the consideration of both large-scale and finescale geomorphological structures such as linear kinematic features (LKF). We propose a multiscale directional analysis (MDA) that diagnoses the spatial characteristics of LKFs. The MDA is different from previous analyses in that it (i) does not detect LKFs as objects, (ii) takes into account the width of LKFs, and (iii) estimates scale-dependent orientation and intersection angles. The MDA is applied to pairs of deformation fields derived from satellite remote sensing data and from a numerical model simulation with a horizontal grid spacing of ~4.5 km. The orientation and intersection angles of LKFs agree with the observations and confirm the visual impression that the intersection angles tend to be smaller in the satellite data compared to the model data. The MDA distributions can be used to compare satellite data and numerical model fields using conventional metrics such as a Euclidean distance, the Bhattacharyya coefficient, or the Earth mover’s distance. The latter is found to be the most meaningful metric to compare distributions of LKF orientations and intersection angles. The MDA proposed here provides a tool to diagnose if modified sea ice rheologies lead to more realistic simulations of LKFs.

Open access
Qinghua Yang, Martin Losch, Svetlana N. Losa, Thomas Jung, and Lars Nerger

Abstract

The sensitivity of assimilating sea ice thickness data to uncertainty in atmospheric forcing fields is examined using ensemble-based data assimilation experiments with the Massachusetts Institute of Technology General Circulation Model (MITgcm) in the Arctic Ocean during November 2011–January 2012 and the Met Office (UKMO) ensemble atmospheric forecasts. The assimilation system is based on a local singular evolutive interpolated Kalman (LSEIK) filter. It combines sea ice thickness data derived from the European Space Agency’s (ESA) Soil Moisture Ocean Salinity (SMOS) satellite and Special Sensor Microwave Imager/Sounder (SSMIS) sea ice concentration data with the numerical model. The effect of representing atmospheric uncertainty implicit in the ensemble forcing is assessed by three different assimilation experiments. The first two experiments use a single deterministic forcing dataset and a different forgetting factor to inflate the ensemble spread. The third experiment uses 23 members of the UKMO atmospheric ensemble prediction system. It avoids additional ensemble inflation and is hence easier to implement. As expected, the model-data misfits are substantially reduced in all three experiments, but with the ensemble forcing the errors in the forecasts of sea ice concentration and thickness are smaller compared to the experiments with deterministic forcing. This is most likely because the ensemble forcing results in a more plausible spread of the model state ensemble, which represents model uncertainty and produces a better forecast.

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Paul R. Holland, Nicolas Bruneau, Clare Enright, Martin Losch, Nathan T. Kurtz, and Ron Kwok

Abstract

Unlike the rapid sea ice losses reported in the Arctic, satellite observations show an overall increase in Antarctic sea ice concentration over recent decades. However, observations of decadal trends in Antarctic ice thickness, and hence ice volume, do not currently exist. In this study a model of the Southern Ocean and its sea ice, forced by atmospheric reanalyses, is used to assess 1992–2010 trends in ice thickness and volume. The model successfully reproduces observations of mean ice concentration, thickness, and drift, and decadal trends in ice concentration and drift, imparting some confidence in the hindcasted trends in ice thickness. The model suggests that overall Antarctic sea ice volume has increased by approximately 30 km3 yr−1 (0.4% yr−1) as an equal result of areal expansion (20 × 103 km2 yr−1 or 0.2% yr−1) and thickening (1.5 mm yr−1 or 0.2% yr−1). This ice volume increase is an order of magnitude smaller than the Arctic decrease, and about half the size of the increased freshwater supply from the Antarctic Ice Sheet. Similarly to the observed ice concentration trends, the small overall increase in modeled ice volume is actually the residual of much larger opposing regional trends. Thickness changes near the ice edge follow observed concentration changes, with increasing concentration corresponding to increased thickness. Ice thickness increases are also found in the inner pack in the Amundsen and Weddell Seas, where the model suggests that observed ice-drift trends directed toward the coast have caused dynamical thickening in autumn and winter. Modeled changes are predominantly dynamic in origin in the Pacific sector and thermodynamic elsewhere.

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