The Maintenance of Conservative Physical Laws Within Data Assimilation Systems

In many data assimilation applications, adding an error to represent forcing to certain dynamical equations may be physically unrealistic. Four-dimensional variational methods assume either an error in the dynamical equations of motion (weak constraint) or no error (strong constraint). The weak-constraint methodology proposes the errors to represent uncertainties in either forcing of the dynamical equations or parameterizations of dynamics. Dynamical equations that represent conservation of quantities (mass, entropy, momentum, etc.) may be cast in an analytical or control volume flux form containing minimal errors. The largest errors arise in determining the fluxes through control volume surfaces. Application of forcing errors to conservation formulas produces non-physical results (generation or destruction of mass or other properties), whereas application of corrections to the fluxes that contribute to the conservation formulas maintains the physically realistic conservation property while providing an ability to account for uncertainties in flux parameterizations. The results suggest that advanced assimilation systems must not be liberal in applying errors to conservative equations. Rather systems must carefully consider the points at which the errors exist and account for them correctly. Though careful accounting of error sources is certainly not an entirely new idea, this paper provides a focused examination of the problem and examines one possible solution within the 4D variational framework

On improving the accuracy of the M2 barotropic tides embedded in a high-resolution global ocean circulation model

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116867/1/ocemod_ASEnKF_tides_ngodocketal_2016.pd

Examining the Potential Impact of SWOT Observations In an Ocean Analysis-Forecasting System

NASA\u27s Surface Water and Ocean Topography (SWOT) satellite, scheduled for launch in 2020, will provide observations of sea surface height anomaly (SSHA) at a significantly higher spatial resolution than current satellite altimeters. This new observation type is expected to improve the ocean model mesoscale circulation. The potential improvement that SWOT will provide is investigated in this work by way of twin-data assimilation experiments using the Navy Coastal Ocean Model four-dimensional variational data assimilation (NCOM-4DVAR) system in its weak constraint formulation. Simulated SWOT observations are sampled from an ocean model run (referred to as the nature run) using an observation-simulator program provided by the SWOT science team. The SWOT simulator provides realistic spatial coverage, resolution, and noise characteristics based on the expected performance of the actual satellite. Twin-data assimilation experiments are run for a two-month period during which simulated observations are assimilated into a separate model (known as the background model) in a series of 96-h windows. The final condition of each analysis window is used to initialize a new 96-h forecast, and each forecast is compared to the nature run to determine the impact of the assimilated data. It is demonstrated here that the simulated SWOT observations help to constrain the model mesoscale to be more consistent with the nature run than the assimilation of traditional altimeter observations alone. The findings of this study suggest that data from SWOT may have a substantial impact on improving the ocean model forecast of mesoscale features and surface ocean velocity

Variational assimilation of Lagrangian data in oceanography

We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional space-time circulation of the ocean. This problem is solved using the four-dimensional variational technique and the adjoint method. In this problem the control vector is chosen as being the initial state of the dynamical system. The observed variables, namely the positions of the floats, are expressed as a function of the control vector via a nonlinear observation operator. This method has been implemented and has the ability to reconstruct the main patterns of the oceanic circulation. Moreover it is very robust with respect to increase of time-sampling period of observations. We have run many twin experiments in order to analyze the sensitivity of our method to the number of floats, the time-sampling period and the vertical drift level. We compare also the performances of the Lagrangian method to that of the classical Eulerian one. Finally we study the impact of errors on observations.Comment: 31 page

Generalized Inverse of a Reduced Gravity Primitive Equation Ocean Model and Tropical Atmosphere–Ocean Data

A nonlinear 2½-layer reduced gravity primitive equations (PE) ocean model is used to assimilate sea surface temperature (SST) data from the Tropical Atmosphere–Ocean (TAO) moored buoys in the tropical Pacific. The aim of this project is to hindcast cool and warm events of this part of the ocean, on seasonal to interannual timescales. The work extends that of Bennett et al., who used a modified Zebiak–Cane coupled model. They were able to fit a year of 30-day averaged TAO data to within measurement errors, albeit with significant initial and dynamical residuals. They assumed a 100-day decorrelation timescale for the dynamical residuals. This long timescale for the residuals reflects the neglect of resolvable processes in the intermediate coupled model, such as horizontal advection of momentum. However, the residuals in the nonlinear PE model should be relatively short timescale errors in parameterizations. The scales for these residuals are crudely estimated from the upper ocean turbulence studies of Peters et al. and Moum. The assimilation is performed by minimizing a weighted least squares functional expressing the misfits to the data and to the model throughout the tropical Pacific and for 18 months. It is known that the minimum lies in the ‘‘data subspace’’ of the state or solution space. The minimum is therefore sought in the data subspace, by using the representer method to solve the Euler–Lagrange (EL) system. Although the vector space decomposition and solution method assume a linear EL system, the concept and technique are applied to the nonlinear EL system (resulting from the nonlinear PE model), by iterating with linear approximations to the nonlinear EL system. As a first step, the authors verify that sequences of solutions of linear iterates of the forward PE model do converge. The assimilation is also used as a significance test of the hypothesized means and covariances of the errors in the initial conditions, dynamics, and data. A ‘‘strong constraint’’ inverse solution is computed. However, it is outperformed by the ‘‘weak constraint’’ inverse. A cross validation by withheld data is presented, as well as an inversion with the model forced by the Florida State University winds, in place of a climatological wind forcing used in the former inversions

Application and comparison of Kalman filters for coastal ocean problems : an experiment with FVCOM

Author Posting. © American Geophysical Union, 2009. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 114 (2009): C05011, doi:10.1029/2007JC004548.Twin experiments were made to compare the reduced rank Kalman filter (RRKF), ensemble Kalman filter (EnKF), and ensemble square-root Kalman filter (EnSKF) for coastal ocean problems in three idealized regimes: a flat bottom circular shelf driven by tidal forcing at the open boundary; an linear slope continental shelf with river discharge; and a rectangular estuary with tidal flushing intertidal zones and freshwater discharge. The hydrodynamics model used in this study is the unstructured grid Finite-Volume Coastal Ocean Model (FVCOM). Comparison results show that the success of the data assimilation method depends on sampling location, assimilation methods (univariate or multivariate covariance approaches), and the nature of the dynamical system. In general, for these applications, EnKF and EnSKF work better than RRKF, especially for time-dependent cases with large perturbations. In EnKF and EnSKF, multivariate covariance approaches should be used in assimilation to avoid the appearance of unrealistic numerical oscillations. Because the coastal ocean features multiscale dynamics in time and space, a case-by-case approach should be used to determine the most effective and most reliable data assimilation method for different dynamical systems.P. Malanotte-Rizzoli and J. Wei were supported by the Office of Naval Research (ONR grant N00014-06-1- 0290); C. Chen and Q. Xu were supported by the U.S. GLOBEC/Georges Bank program (through NSF grants OCE-0234545, OCE-0227679, OCE- 0606928, OCE-0712903, OCE-0726851, and OCE-0814505 and NOAA grant NA-16OP2323), the NSF Arctic research grants ARC0712903, ARC0732084, and ARC0804029, and URI Sea Grant R/P-061; P. Xue was supported through the MIT Sea Grant 2006-RC-103; Z. Lai, J. Qi, and G. Cowles were supported through the Massachusetts Marine Fisheries Institute (NOAA grants NA04NMF4720332 and NA05NMF4721131); and R. Beardsley was supported through U.S. GLOBEC/Georges Bank NSF grant OCE-02227679, MIT Sea Grant NA06OAR1700019, and the WHOI Smith Chair in Coastal Oceanography

Improving surface tidal accuracy through two-way nesting in a global ocean model

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149151/1/ocemod_2019_twowaynesting_jeonetal.pdfDescription of ocemod_2019_twowaynesting_jeonetal.pdf : Main articl

Altimetry for the future: Building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the ‘‘Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Altimetry for the future: building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the “Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion