Papers by Alberta Albertella
Estimation of ocean circulation via assimilation of satellite measurements of dynamical ocean top... more Estimation of ocean circulation via assimilation of satellite measurements of dynamical ocean topography (DOT) into the global finite-element ocean model (FEOM) is investigated. The DOT was obtained by means of geodetic approach from carefully cross-calibrated multi-mission-altimeter data and GRACE gravity fields. The spectral consistency was achieved by means of the filtering applied on sea surface and geoid. Since the dynamical ocean topography is obtained from data types coming from different sources, different techniques can be employed for their assimilation into ocean circulation models. For example, the data can be combined and interpolated onto the model grid before they are used in assimilation. In this case special care needs to be taken concerning the specification of observational error statistics. The assimilation is performed by employing the local SEIK filter and various functions for observations error covariance are used. Finally we consider the effects of assimilat...
Monthly Weather Review, 2011
Ensemble Kalman filter methods are typically used in combination with one of two localization tec... more Ensemble Kalman filter methods are typically used in combination with one of two localization techniques. One technique is covariance localization, or direct forecast error localization, in which the ensemble-derived forecast error covariance matrix is Schur multiplied with a chosen correlation matrix. The second way of localization is by domain decomposition. Here, the assimilation is split into local domains in which the assimilation update is performed independently. Domain localization is frequently used in combination with filter algorithms that use the analysis error covariance matrix for the calculation of the gain like the ensemble transform Kalman filter (ETKF) and the singular evolutive interpolated Kalman filter (SEIK). However, since the local assimilations are performed independently, smoothness of the analysis fields across the subdomain boundaries becomes an issue of concern.
Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, 2000
ABSTRACT
Ocean Science, 2012
In this work we examine the impact of assimilation of multi-mission-altimeter data and the GRACE/... more In this work we examine the impact of assimilation of multi-mission-altimeter data and the GRACE/GOCE gravity fields into the finite element ocean model (FEOM), with the focus on the Southern Ocean circulation. In order to do so, we use the geodetic approach for obtaining the dynamical ocean topography (DOT), that combines the 5 multi-mission-altimeter data and the GRACE/GOCE gravity fields, and requires that both fields be spectrally consistent. The spectral consistency is achieved by filtering of the sea surface height and the geoid using profile approach. Combining the GRACE and GOCE data, a considerably shorter filter length resolving more DOT details can be used. In order to specify the spectrally consistent geodetic DOT we applied the 10 Jekeli-Wahr filter corresponding to 241 km, 121 km, 97 km and 81 km halfwidths for the GRACE/GOCE based gravity field model GOCO01S and to the sea surface. More realistic features of the ocean assimilation were obtained in the Weddel gyre area due to increased resolution of the data fields, particularly for temperature field at the 800 m depth compared to Argo data.
Journal of Geodesy, 2009
ABSTRACT Geoid models from the new generation of satellite gravity missions, such as GRACE and GO... more ABSTRACT Geoid models from the new generation of satellite gravity missions, such as GRACE and GOCE, in combination with sea surface from satellite altimetry allow to obtain absolute dynamic ocean topography with rather high spatial resolution and accuracy. However, this implies combination of data with fundamentally different characteristics and different spatial resolutions. Spectral consistency would imply the removal of the short-scale features of the altimetric sea surface height by filtering, to provide altimetric data consistent with the resolution of the geoid field. The goal must be to lose as little as possible from the high precision of the altimetric signal. Using a one-dimensional example we show how the spectrum is changing when a function defined only on a limited domain (ocean in the real case) is extended or not as to cover the complete domain (the whole sphere in the real case). The results depend on the spectral characteristics of the altimetric signal and of the applied filter. Referring to the periodicity condition, as it is requested in the case of Fourier analysis, the action of the two classical filters (Ideal Low Pass and Gauss filter) and of two alternative procedures (wavelets and Slepian) is studied.
Journal of Geodesy, 1995
The recovery of the harmonic coefficients of the anomalous potential from a geodetic quantity sam... more The recovery of the harmonic coefficients of the anomalous potential from a geodetic quantity sampled over a regular grid is affected by the non-exact discrete orthogonality of spherical harmonics; larger errors occur for block-average quantities owing to the non-simple behaviour of the block-average operator when applied to spherical harmonics. Fourier coefficients, on the contrary, can be recovered by exact formulas
ISPRS Journal of Photogrammetry and Remote Sensing
After a cali for proposals for small satellite missions from thè Italian Space Agency (ASI), a gr... more After a cali for proposals for small satellite missions from thè Italian Space Agency (ASI), a group of Italian research teams and industries led by thè Politecnico di Milano proposed thè concept of SAGE, a mission aimed yJ^kLofLtheJìlarth-by means of -high-10wL SST, whieh-nreans that-the-satellite~orbit^is" determined by GPS, while thè non-gravitational perturbations are determined by a three-axes accelerometer. This is basically thè same concept of thè CHAMP mission . SAGE underwent a Phase A Study during thè year 1998 [ASI, 1998]. In this framework, thè task of thè Politecnico di Milano group was to analyze thè data by means of thè spacewise approach. The complete spacewise approach, besides studying new simulations of thè data to be expected from SAGE, requires to perforai thè inversion of Hill's equations, to forni average values on a regular grid over thè sphere and to recover thè gravity field coefficients. The simulations are requested in order to: assess thè accuracy of thè data obtained after thè inversion of Hill's equations introducing a realistic measurement noise; formulate thè overdetermined boundary value problem to be solved; determine indices enabling to evaluate thè performances of thè solution.
In WP4 the problem of quality assessment for GOCE data has been studied. Basically, procedures fo... more In WP4 the problem of quality assessment for GOCE data has been studied. Basically, procedures for outliers detection and removal have been identiied, from two diierent points of view. In Sec. 4.1 the problem was studied in a track-wise approach, by the group of POLIMI. In Sec. 4.2 the problem was studied in an area-wise approach by C.C.Tscherning (UCPH). While the track-wise approach can be applied to the data on-the--y, in the area-wise approach data of diierent types can be used as a whole. However, the second approach requires that characteristic values constant over an area be a-priori computed and subsequently updated as GOCE data become available. EE otvv os to mGal, Final Report
The geoid models from GRACE and soon GOCE in combination with sea surface geometry data from sate... more The geoid models from GRACE and soon GOCE in combination with sea surface geometry data from satellite altimetry allow to obtain a precise estimate of the absolute dynamic sea surface topography with rather high spatial resolution. However, this requires the combination of data with fundamentally different characteristics and different spatial resolutions. One of the central objectives must be to get altimetric data and the geoid spectrally consistent without loss of precision and/or resolution. Therefore it is necessary to find a representation common to the geoid model and to altimetry that allows to obtain spectral consistency by filtering the altimetric data. We try to design a filter for the altimetric data, using the spectral characteristics of the satellite gravimetric geoid, considering a “global” approach. It consists of the extension of the altimetric sea surface height so as to cover all of the Earth’s surface and the representation of the data in terms of spherical harmo...
Parole chiave > Filtro di Kalman, Minimi quadrati, Navigazione, solu-zione geodetica Riassunto... more Parole chiave > Filtro di Kalman, Minimi quadrati, Navigazione, solu-zione geodetica Riassunto > Da sempre si è ritenuto il filtro di Kalman un'ottima alter-nativa alle soluzioni minimi quadrati anche per stime richieste non in tempo reale: ciò è principalmente dovuto all'insostenibile carico nume-rico che la soluzione minimi quadrati necessariamente implica. In que-sto lavoro dimostriamo che con semplici accorgimenti è possibile rag-giungere soluzioni minimi quadrati equivalenti sia in termini di valori stimati che in termini di carico numerico richiesto. Abstract > Kalman filter is considered an efficient and valuable method alternative to the classic least squares algorithm even for no real time estimates, due to the huge computational load that least squares require. In this work we demonstrate how, by exploiting some simple expedients, we can obtain least squares solutions equivalent to Kalman solutions with comparable computational load. 1. Introduzione I prob...
Estimation of ocean circulation is investigated via assimilation of satellite measurements of dyn... more Estimation of ocean circulation is investigated via assimilation of satellite measurements of dynamical ocean topography (DOT) into the global finite-element ocean model (FEOM). The DOT was obtained by means of geodetic approach from carefully cross-calibrated multi-mission- altimeter data and GRACE/GOCE gravity fields. The spectral consistency was achieved by means of filtering applied on sea surface and geoid. The filter length is determened by the spatial resolution of the gravity field and corresponds to harmonic degree 60 for the GRACE-based gravity field model ITG03S. Combining the GRACE and GOCE data considerably shorter filter length resolving more DOT details can be used. This data filtered up to degree higher then 60 is also considered. The assimilation is performed by employing the local SEIK filter. Various functions for observation error covariance are used depending on the filtering applied to the data. The ocean model returns an optimized mean dynamical ocean topograp...
Celestial Mechanics & Dynamical Astronomy, 2002
An artificial satellite, flying in a purely gravitational field is a natural probe, such that, by... more An artificial satellite, flying in a purely gravitational field is a natural probe, such that, by a very accurate orbit determination, would allow a perfect estimation of the field. A true satellite experiences a number of perturbational, non-gravitational forces acting on the shell of the spacecraft; these can be revealed and accurately measured by a spaceborne accelerometer. If more accelerometers
Estimation of ocean circulation via assimilation of satellite measurements of dynamical ocean top... more Estimation of ocean circulation via assimilation of satellite measurements of dynamical ocean topography (DOT) into the global finite-element ocean model (FEOM) is investigated. The DOT was obtained by means of geodetic approach from carefully cross-calibrated multi-mission-altimeter data and GRACE gravity fields. The spectral consistency was achieved by means of the filtering applied on sea surface and geoid. Since the dynamical ocean topography is obtained from data types coming from different sources, different techniques can be employed for their assimilation into ocean circulation models. For example, the data can be combined and interpolated onto the model grid before they are used in assimilation. In this case special care needs to be taken concerning the specification of observational error statistics. The assimilation is performed by employing the local SEIK filter and various functions for observations error covariance are used. Finally we consider the effects of assimilat...
Surveys in Geophysics, 2011
In 2009 the European Space Agency satellite mission GOCE (Gravity Field and Steady-State Ocean Ci... more In 2009 the European Space Agency satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) was launched. Its objectives are the precise and detailed determination of the Earth’s gravity field and geoid. Its core instrument, a three axis gravitational gradiometer, measures the gravity gradient components V xx , V yy , V zz and V xz (second-order derivatives of
Surveys in Geophysics, 1993
The calculus of spherical harmonic representation of fields of geodetic interest is often perform... more The calculus of spherical harmonic representation of fields of geodetic interest is often performed by applying integral formulas to block-averaged quantities. Due to the dependence of the block areas on latitude, it is difficult to perform a rigorous computation; in this paper the effects of approximations related to the loss of orthogonality in the discretization and averaging procedures are numerically studied; a simple numerical approach to improve the efficiency of the estimates is presented.
Monthly Weather Review, 2011
Ensemble Kalman filter methods are typically used in combination with one of two localization tec... more Ensemble Kalman filter methods are typically used in combination with one of two localization techniques. One technique is covariance localization, or direct forecast error localization, in which the ensemble-derived forecast error covariance matrix is Schur multiplied with a chosen correlation matrix. The second way of localization is by domain decomposition. Here, the assimilation is split into local domains in which the assimilation update is performed independently. Domain localization is frequently used in combination with filter algorithms that use the analysis error covariance matrix for the calculation of the gain like the ensemble transform Kalman filter (ETKF) and the singular evolutive interpolated Kalman filter (SEIK). However, since the local assimilations are performed independently, smoothness of the analysis fields across the subdomain boundaries becomes an issue of concern.
Journal of Geodynamics, 2012
Estimation of ocean circulation is investigated via assimilation of satellite measurements of the... more Estimation of ocean circulation is investigated via assimilation of satellite measurements of the dynamic ocean topography (DOT) into the global finite-element ocean model (FEOM). The DOT was obtained by means of a geodetic approach from carefully cross-calibrated multi-mission altimeter data and GRACE gravity fields. The spectral consistency was achieved by consistently filtering both, the sea surface and the geoid. The
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Papers by Alberta Albertella