Jacobian mapping between vertical coordinate systems in data assimilation

2007 ◽  
Vol 133 (627) ◽  
pp. 1547-1558 ◽  
Author(s):  
Y. J. Rochon ◽  
L. Garand ◽  
D. S. Turner ◽  
S. Polavarapu
Keyword(s):  
Data Assimilation ◽  
Coordinate Systems ◽  
Vertical Coordinate

Two-way nesting ocean models with different vertical coordinates

2021 ◽  
Author(s):  
Jerome Chanut ◽  
James Harle ◽  
Tim Graham ◽  
Laurent Debreu
Keyword(s):  
Vertical Direction ◽  
Test Cases ◽  
Numerical Representation ◽  
Arbitrary Lagrangian Eulerian ◽  
Coordinate Systems ◽  
Vertical Coordinate ◽  
Terrain Following ◽  
New Feature ◽  
Polynomial Reconstruction ◽  
Horizontal Grid

<p>The NEMO platform possesses a versatile block-structured refinement capacity thanks to the AGRIF library. It is however restricted up to versions 4.0x, to the horizontal direction only. In the present work, we explain how we extended the nesting capabilities to the vertical direction, a feature which can appear, in some circumstances, as beneficial as refining the horizontal grid.</p><p>Doing so is not a new concept per se, except that we consider here the general case of child and parent grids with possibly different vertical coordinate systems, hence not logically defined from each other as in previous works. This enables connecting together for instance z (geopotential), s (terrain following) or eventually ALE (Arbitrary Lagrangian Eulerian) coordinate systems. In any cases, two-way exchanges are enabled, which is the other novel aspect tackled here.  </p><p>Considering the vertical nesting procedure itself, we describe the use of high order conservative and monotone polynomial reconstruction operators to remap from parent to child grids and vice versa. Test cases showing the feasibility of the approach are presented, with particular attention on the connection of s and z grids in the context of gravity flow modelling. This work can be considered as a preliminary step towards the application of the vertical nesting concept over major overflow regions in global realistic configurations. The numerical representation of these areas is indeed known to be particularly sensitive to the vertical coordinate formulation. More generally, this work illustrates the typical methodology from the development to the validation of a new feature in the NEMO model.</p>

scholarly journals Argo data assimilation into HYCOM with an EnOI method in the Atlantic Ocean

2014 ◽  
Vol 11 (4) ◽  
pp. 1733-1781
Author(s):  
D. Mignac ◽  
C. A. S. Tanajura ◽  
A. N. Santana ◽  
L. N. Lima ◽  
J. Xie
Keyword(s):  
Data Assimilation ◽  
Atlantic Ocean ◽  
Heat Content ◽  
Optimal Interpolation ◽  
Argo Data ◽  
Thermohaline Structure ◽  
Vertical Coordinate ◽  
Ocean Data Assimilation ◽  
First Time ◽  
Model Layer

Abstract. An ocean data assimilation system to assimilate Argo temperature (T) and salinity (S) profiles into HYCOM was constructed, implemented and evaluated for the first time in the Atlantic Ocean (78° S to 50° N and 98° W to 20° E). The system is based on the Ensemble Optimal Interpolation (EnOI) algorithm proposed by Xie and Zhu (2010), especially made to deal with the hybrid nature of HYCOM vertical coordinate system with multiple steps. The Argo T/S profiles were projected to the model vertical space to create pseudo-observed layer thicknesses (Δ pobs) which correspond to the model target densities. The first step was to assimilate Δ pobs considering the sub-state vector composed by the model layer thickness (Δ p) and the baroclinic velocity components. After that, T and S were assimilated separately. At last, T was diagnosed below the mixed layer to preserve the density of the model isopycnal layers. Five experiments were performed from 1 January 2010 until 31 December 2012: a control run without assimilation, and four assimilation runs considering different vertical localizations of T, S and Δ p. The assimilation experiments were able to significantly improve the thermohaline structure produced by the control run. They reduced the RMSD of T (S) calculated with respect to Argo independent data in 34.11% (43.56%) in comparison to the control run. In some regions, such as the west North Atlantic, substantial corrections in the 20 °C isotherm depth and the upper ocean heat content towards climatological states were achieved. The runs with vertical localization of Δ p showed positive impacts in the correction of the thermohaline structure and reduced the RMSD of T (S) from 0.993 °C (0.149 psu) to 0.905 °C (0.138 psu) for the whole domain with respect to the other assimilation runs.

scholarly journals Thickness-Weighted Averaging in Tidal Estuaries and the Vertical Distribution of the Eulerian Residual Transport

2019 ◽  
Vol 49 (7) ◽  
pp. 1809-1826 ◽  
Author(s):  
Knut Klingbeil ◽  
Johannes Becherer ◽  
Elisabeth Schulz ◽  
Huib E. de Swart ◽  
Henk M. Schuttelaars ◽  
...  
Keyword(s):  
Tidal Flow ◽  
Weighted Averaging ◽  
Correct Interpretation ◽  
Coordinate Systems ◽  
Unified Framework ◽  
Vertical Coordinate ◽  
One Dimensional ◽  
Tidal Estuaries ◽  
Residual Transport ◽  
The Vertical Distribution

AbstractThis paper presents thickness-weighted averaging (TWA) in generalized vertical coordinates as a unified framework for a variety of existing tidal-averaging concepts in seas and estuaries. Vertical profiles of resulting residual quantities depend on the specific vertical coordinate, which is held fixed during the averaging process. This dependence is demonstrated through the application to one-dimensional analytical tidal flow with sediment transport, to field observations from a tidal channel, and to model results from a two-dimensional estuary. The use of different coordinate systems provides complementary views on the residual dynamics and stresses the importance of a correct interpretation of residual quantities obtained by tidal averaging.

scholarly journals Argo data assimilation into HYCOM with an EnOI method in the Atlantic Ocean

Ocean Science ◽  
2015 ◽  
Vol 11 (1) ◽  
pp. 195-213 ◽  
Author(s):  
D. Mignac ◽  
C. A. S. Tanajura ◽  
A. N. Santana ◽  
L. N. Lima ◽  
J. Xie
Keyword(s):  
Data Assimilation ◽  
Atlantic Ocean ◽  
Heat Content ◽  
Ocean Model ◽  
Optimal Interpolation ◽  
Argo Data ◽  
Thermohaline Structure ◽  
Vertical Coordinate ◽  
Ocean Data Assimilation ◽  
Hybrid Coordinate Ocean Model

Abstract. An ocean data assimilation system to assimilate Argo temperature (T) and salinity (S) profiles into the HYbrid Coordinate Ocean Model (HYCOM) was constructed, implemented and evaluated for the first time in the Atlantic Ocean (78° S to 50° N and 98° W to 20° E). The system is based on the ensemble optimal interpolation (EnOI) algorithm proposed by Xie and Zhu (2010), especially made to deal with the hybrid nature of the HYCOM vertical coordinate system with multiple steps. The Argo T–S profiles were projected to the model vertical space to create pseudo-observed layer thicknesses (Δ pobs), which correspond to the model target densities. The first step was to assimilate Δ pobs considering the sub-state vector composed by the model layer thickness (Δ p) and the baroclinic velocity components. After that, T and S were assimilated separately. Finally, T was diagnosed below the mixed layer to preserve the density of the model isopycnal layers. Five experiments were performed from 1 January 2010 to 31 December 2012: a control run without assimilation, and four assimilation runs considering the different vertical localizations of T, S and Δ p. The assimilation experiments were able to significantly improve the thermohaline structure produced by the control run. They reduced the root mean square deviation (RMSD) of T and S calculated with respect to Argo independent data in 34 and 44%, respectively, in comparison to the control run. In some regions, such as the western North Atlantic, substantial corrections in the 20 °C isotherm depth and the upper ocean heat content towards climatological states were achieved. The runs with a vertical localization of Δ p showed positive impacts in the correction of the thermohaline structure and reduced the RMSD of T (S) from 0.993 °C (0.149 psu) to 0.905 °C (0.138 psu) for the whole domain with respect to the other assimilation runs.

scholarly journals Efficient Ensemble Covariance Localization in Variational Data Assimilation

2011 ◽  
Vol 139 (2) ◽  
pp. 573-580 ◽  
Author(s):  
Craig H. Bishop ◽  
Daniel Hodyss ◽  
Peter Steinle ◽  
Holly Sims ◽  
Adam M. Clayton ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Efficient Algorithm ◽  
Grid Point ◽  
Three Dimensional ◽  
Localization Length ◽  
Length Scale ◽  
Grid Spacing ◽  
Computationally Efficient ◽  
Vertical Coordinate ◽  
Separable Product

Abstract Previous descriptions of how localized ensemble covariances can be incorporated into variational (VAR) data assimilation (DA) schemes provide few clues as to how this might be done in an efficient way. This article serves to remedy this hiatus in the literature by deriving a computationally efficient algorithm for using nonadaptively localized four-dimensional (4D) or three-dimensional (3D) ensemble covariances in variational DA. The algorithm provides computational advantages whenever (i) the localization function is a separable product of a function of the horizontal coordinate and a function of the vertical coordinate, (ii) and/or the localization length scale is much larger than the model grid spacing, (iii) and/or there are many variable types associated with each grid point, (iv) and/or 4D ensemble covariances are employed.

Reference Coordinate System Requirements for Geophysics

1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender
Keyword(s):  
Coordinate System ◽  
Polar Motion ◽  
Main Part ◽  
Measurement Techniques ◽  
Reference Points ◽  
Angular Motion ◽  
Coordinate Systems ◽  
Axis Of Rotation ◽  
The Earth ◽  
Fixed System

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

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