The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

[1] EGM2008 is a spherical harmonic model of the Earth's gravitational potential, developed by a least squares combination of the ITG-GRACE03S gravitational model and its associated error covariance matrix, with the gravitational information obtained from a global set of area-mean free-air gravity anomalies defined on a 5 arc-minute equiangular grid This grid was formed by merging terrestrial, altimetry-derived, and airborne gravity data Over areas where only lower resolution gravity data were available, their spectral content was supplemented with gravitational information implied by the topography EGM2008 is complete to degree and order 2159, and contains additional coefficients up to degree 2190 and order 2159 Over areas covered with high quality gravity data, the discrepancies between EGM2008 geoid undulations and independent GPS/Leveling values are on the order of ±5 to ±10 cm EGM2008 vertical deflections over USA and Australia are within ±11 to ±13 arc-seconds of independent astrogeodetic values These results indicate that EGM2008 performs comparably with contemporary detailed regional geoid models EGM2008 performs equally well with other GRACE-based gravitational models in orbit computations Over EGM96, EGM2008 represents improvement by a factor of six in resolution, and by factors of three to six in accuracy, depending on gravitational quantity and geographic area EGM2008 represents a milestone and a new paradigm in global gravity field modeling, by demonstrating for the first time ever, that given accurate and detailed gravimetric data, asingle global model may satisfy the requirements of a very wide range of applications

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2011JB008916

The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)

A major accomplishment of the recently completed Tropical Ocean-Global Atmosphere (TOGA) Program was the development of an ocean observing system to support seasonal-to-interannual climate studies. This paper reviews the scientific motivations for the development of that observing system, the technological advances that made it possible, and the scientific advances that resulted from the availability of a significantly expanded observational database. A primary phenomenological focus of TOGA was interannual variability of the coupled ocean-atmosphere system associated with El Nino and the Southern Oscillation (ENSO).Prior to the start of TOGA, our understanding of the physical processes responsible for the ENSO cycle was limited, our ability to monitor variability in the tropical oceans was primitive, and the capability to predict ENSO was nonexistent. TOGA therefore initiated and/or supported efforts to provide real-time measurements of the following key oceanographic variables: surface winds, sea surface temperature, subsurface temperature, sea level and ocean velocity. Specific in situ observational programs developed to provide these data sets included the Tropical Atmosphere-Ocean (TAO) array of moored buoys in the Pacific, a surface drifting buoy program, an island and coastal tide gauge network, and a volunteer observing ship network of expendable bathythermograph measurements. Complementing these in situ efforts were satellite missions which provided near-global coverage of surface winds, sea surface temperature, and sea level. These new TOGA data sets led to fundamental progress in our understanding of the physical processes responsible for ENSO and to the development of coupled ocean-atmosphere models for ENSO prediction.

/pdf/the-tropical-ocean-global-atmosphere-observing-system-a-c3sujtrlum.pdf

The Tropical Ocean‐Global Atmosphere observing system: A decade of progress

The South Atlantic Ocean receives waters from the North Atlantic, the Weddell Sea, and from the Circumpolar Current through the Drake Passage. The circumpolar and North Atlantic waters are of widely different characteristics (temperature, salinity, oxygen and nutrients) but of overlapping density ranges, and as they enter the South Atlantic are caught up in the circulation imposed by the winds and thermohaline processes. Interleaving of these different characteristics takes place in various ranges of depth and density, and more than a dozen vertical extrema are created in the tracer fields. These are spread by lateral flow in recognizable layers. These patterns as seen on vertical sections and on isopycnals can be taken to indicate the sense of flow in various areas and depths, and I have used them, with the density field, to add the barotropic component to the baroclinic flow defined by the density field. This gives the total geostrophic flow at all depths in a manner that appears to be consonant with the tracer patterns, and that satisfies continuity of mass. The resulting flow field has the traditional western boundary current from the Weddell Sea to the equator, beneath a poleward flow north of 50°S. In the upper waters the flow pattern shows a cyclonic gyre in the Weddell Sea, a northward flow from the Antarctic along the western boundary from 55°S to 40°S, an anticyclonic gyre between 15°S and 40°S, and an eastward flow near 10°S. Below the upper layer the axis of the anticyclonic gyre shifts southward, to 35°S at 1500 m, and at greater depths the gyre is confined to the Brazil Basin, west of the Mid-Atlantic Ridge and north of the Rio Grande Rise. Below the crest of the Mid-Atlantic Ridge in the Brazil Basin waters from the south flow northward along the Ridge, and part of them crosses the Ridge at or near the equator and returns southward in the eastern basin, joined by waters from the North Atlantic. The northward abyssal flow in the Brazil Basin is not confined to the western boundary but extends some distance across the basin, diverted only slightly at 3500 m by the small deep remnant of the overlying anticyclonic gyre. From 3000 to 4000 decibars the flow within the Weddell Sea and the Argentine Basin form a single cyclonic gyre and the flow within the Cape Basin is cyclonic below 3000 m.

On the Total Geostrophic Circulation of the South Pacific Ocean: Flow Patterns, Tracers and Transports

OPA is a primitive equation model of both the regional and global ocean circulation. It is intended to be a flexible tool for studying ocean and its interactions with the others components of the earth climate system (atmosphere, sea-ice, biogeochemical tracers, ...) over a wide range of space and time scale. Prognostic variables are the three-dimensional velocity field and the thermohaline variables. The distribution of variables is a threedimensional Arakawa-C-type grid using prescribed zor s-levels. Various physical choices are available to describe ocean physics, including a 1.5 turbulent closure for the vertical mixing. OPA is interfaced with a sea-ice model, a passive tracer model and, via the OASIS coupler, with several atmospheric general circulation models. In addition, it can be run on many different computers, including shared and distributed memory multiprocessor computers.

OPA 8.1 Ocean General Circulation Model reference manual

TOPEX/POSEIDON is the first space mission specifically designed and conducted for studying the circulation of the world's oceans. A state-of-the-art radar altimetry system is used to measure the precise height of sea level, from which information on the ocean circulation is obtained. The satellite, launched on August 10, 1992, has been making observations of the global oceans with unprecedented accuracy since late September 1992. To meet the stringent measurement accuracy required for ocean circulation studies, a number of innovative improvements have been made to the mission design, including the first dual-frequency space-borne radar altimeter capable of retrieving the ionospheric delay of the radar signal, a three-frequency microwave radiometer for retrieving the signal delay caused by the water vapor in the troposphere, an optimal model of the Earth's gravity field and multiple satellite tracking systems for precision orbit determination. Additionally, the satellite also carries two experimental instruments to demonstrate new technologies: a single-frequency solid-state altimeter for the technology of low-power, low-weight altimeter and a Global Positioning System receiver for continuous,precise satellite tracking. The performance of the mission's measurement system has been tested by numerous verification studies. The results indicate that the root-sum-square accuracy of a single-pass sea level measurement is 4.7 cm for the TOPEX system and 5.1 cm for the POSEIDON system; both are more than a factor of 2 better than the requirement of 13.7 cm. This global data set is being analyzed to improve understanding of the global ocean circulation as well as the ocean tides, geodesy, and geodynamics, and ocean wind and waves. The mission is designed to last for at least 3 years with a possible extension to 6 years. The multiyear global data set will go a long way toward understanding the ocean circulation and its variability in relation to climate change. A summary of the mission's systems and their performance as well as the mission's science team is presented.

TOPEX/POSEIDON mission overview

On December 7, 2001, the Jason-1 satellite was successfully launched by a Boeing Delta II rocket from the Vandenberg site in California, USA. Its main mission was to maintain the high accuracy altimeter measurements, provided since 1992 by TOPEX/Poseidon (T/P), ensuring continuity in observing and monitoring the ocean for intraseasonal to interannual changes, mean sea level, tides, and so forth. Despite four times less mass and power, the Jason-1 system has been designed to have the same performances as T/P, measuring sea surface topography at the centimeter level. This new Centre National d'Etudes Spatiales/National Aeronautics and Space Administration (CNES/NASA) mission also provides near real-time data for sea state and ocean forecast. The first 10 months of the Jason mission were dedicated to the verification of the system performance and cross-calibration with T/P measurements. A complete CALVAL plan was conducted by the Science and Project Teams of the mission based on in situ and regional experime...

The Jason-1 Mission Special Issue: Jason-1 Calibration/Validation

Absolute calibration of Jason-1 and TOPEX/Poseidon altimeters in Corsica

Until now, most satellite altimetry studies of the coastal ocean have been based on along-track data from a single mission, whereas up to four missions were operative in 2002–2005 Here, to monitor the coastal ocean we have applied specialized corrections and dedicated processing strategies to compute a multimission data set at a mean distance of 32 km of the coast The resulting altimetric data set is compared with sea level data from three in situ stations over a coastal zone of the northwestern Mediterranean The mean rms difference between this data set and the sea level stations is 29 cm against 37 cm when using the AVISO altimetric product Comparison of altimeter-derived geostrophic velocities with a mooring also shows that the spatial and temporal variability of the surface current field is well reproduced The agreement with in situ measurements extends to intraseasonal time scales showing a significant improvement compared to previous studies in the 50 km coastal-band

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2008GL033488

Exploiting the potential of an improved multimission altimetric data set over the coastal ocean

The double geodetic Corsica site, which includes Ajaccio-Aspretto and Cape Senetosa (40 km south Ajaccio) in the western Mediterranean area, has been chosen to permit the absolute calibration of radar altimeters It has been developed since 1998 at Cape Senetosa and, in addition to the use of classical tide gauges, a GPS buoy is deployed every 10 days under the satellites ground track (10 km off shore) since 2000 The 2002 absolute calibration campaign made from January to September in Corsica revealed the necessity of deploying different geodetic techniques on a dedicated site to reach an accuracy level of a few mm: in particular, the French Transportable Laser Ranging System (FTLRS) for accurate orbit determination, and various geodetic equipment as well as a local marine geoid, for monitoring the local sea level and mean sea level TOPEX/Poseidon altimeter calibration has been performed from cycle 208 to 365 using M-GDR products, whereas Jason-1 altimeter calibration used cycles from 1 to 45 using I-GD

Y. Menard

Papers

TOPEX/POSEIDON mission overview

The Jason-1 Mission Special Issue: Jason-1 Calibration/Validation

Absolute calibration of Jason-1 and TOPEX/Poseidon altimeters in Corsica

Exploiting the potential of an improved multimission altimetric data set over the coastal ocean

Absolute Calibration of Jason-1 and TOPEX/Poseidon Altimeters in Corsica Special Issue: Jason-1 Calibration/Validation