Hans Ngodock - Academia.edu (original) (raw)

Papers by Hans Ngodock

Research paper thumbnail of Generalized inversion of the Gent-Cane model of the tropical Pacific with Tropical Atmosphere-Ocean (TAO) data

Research paper thumbnail of A 4DVAR System for the Navy Coastal Ocean Model. Part 2: Strong and Weak Constraint Assimilation Experiments with Real Observations in Monterey Bay

Research paper thumbnail of Assimilation de données et analyse de sensibilité. Une application à la circulation océanique

Research paper thumbnail of A 4DVAR System for the Navy Coastal Ocean Model. Part II: Strong and Weak Constraint Assimilation Experiments with Real Observations in Monterey Bay*

Http Dx Doi Org 10 1175 Mwr D 13 00220 1, May 28, 2014

A four-dimensional variational data assimilation (4DVAR) system was recently developed for the Na... more A four-dimensional variational data assimilation (4DVAR) system was recently developed for the Navy Coastal Ocean Model (NCOM). The system was tested in the first part of this study using synthetic surface and subsurface data. Here, a full range of real surface and subsurface data is considered following encouraging results from the preliminary test. The data include sea surface temperature and sea surface height from satellite, as well as subsurface observations from gliders deployed during the second Autonomous Ocean Sampling Network field experiment in California's Monterey Bay. Data assimilation is carried out with strong and weak constraints, and results are compared against independent observations. This study clearly shows that the 4DVAR approach improves the free-running model simulation and that the weak constraint experiment has lower analysis errors than does the strong constraint version. * Naval Research Laboratory Contribution Number JA/7320-13-13-1822.

Research paper thumbnail of Generalized Inverse of a Reduced Gravity Primitive Equation Ocean Model and Tropical Atmosphere Ocean Data

Monthly Weather Review, Jun 1, 2000

A nonlinear 2½-layer reduced gravity primitive equations (PE) ocean model is used to assimilate s... more 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.

Research paper thumbnail of AGU Oceans 2012 Poster : A Multi-Scale 3D Variational Data Assimilation Scheme (MS-3DVAR) in the Kurshio Extension

Research paper thumbnail of 4DVAR Assimilation of ADCP Data with the Navy Coastal Ocean Model using the Cycling Representer Method

Oceans 2007, 2007

4D-variational assimilation (4DVAR) is used to combine ADCP velocity observations with the Navy C... more 4D-variational assimilation (4DVAR) is used to combine ADCP velocity observations with the Navy Coastal Ocean model (NCOM) to obtain an optimal solution that minimizes a cost function containing the weighted squared errors of velocity measurements, initial conditions, boundary conditions, and model dynamics. However, in order to converge to the global minimum of this cost function, the ocean model (and its adjoint) must be linear. Ocean models, especially those that are designed to resolve baroclinic and mesoscale processes, are typically highly-nonlinear and must be linearized. Tangent linearization is a linearization method that is performed by expanding the nonlinear dynamics about a background field using the first order approximation of Taylor's expansion. The accuracy and stability of this tangent linearized model (TLM) is a very sensitive function of the background accuracy, the level of nonlinearity of the model, complexity of the bathymetry, and the complexity of the flow field. Therefore, in high-resolution coastal domains, the TLM is only going to be stable for a relatively short period of time.

Research paper thumbnail of A Weak Constraint 4D-Var Assimilation System for the Navy Coastal Ocean Model Using the Representer Method

Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. II), 2013

A 4D-Variational system was recently developed for assimilating ocean observations with the Navy ... more A 4D-Variational system was recently developed for assimilating ocean observations with the Navy Coastal Ocean Model. It is described here, along with initial assimilation experiments in the Monterey Bay using a combination of real and synthetic ocean observations. For testing a new assimilation system it is advantageous to use this combination of real and synthetic data over simplified cases of climatology and twin data. Assimilation experiments are carried out in a weak constraint formulation, with the model's external forcing assumed to be erroneous in addition to initial conditions. The system's ability to fit assimilated and non assimilated observations is assessed, as well as the consistency and relevance of the retrieved model forcing. Experiment results show that the assimilation system fits the data with relatively high prior errors in the initial conditions and surface forcing fluxes. However, the retrieved model forcing errors are well within the range of acceptable corrections according to an independent study.

Research paper thumbnail of Incremental projection approach of regularization for inverse problems

Applied Mathematics & Optimization, 2015

Research paper thumbnail of On the direct assimilation of along-track sea surface height observations into a free-surface ocean model using a weak constraints four dimensional variational (4dvar) method

Quarterly Journal of the Royal Meteorological Society, 2015

Research paper thumbnail of Impact of Assimilating Surface Velocity Observations on the Model Sea Surface Height using the NCOM-4DVAR

Monthly Weather Review, 2015

Research paper thumbnail of Cycling the Representer Algorithm for Data Assimilation with the Lorenz Attractor

... model, and renders the cost of the representer method expensive for operational purposes. The... more ... model, and renders the cost of the representer method expensive for operational purposes. The accuracy of the TLM depends on the initial con-1(t) - xt) + ola,,r,,(t). (12) dition and model errors. The estimation of these errors is described in section 2. For completeness, the TLM ...

Research paper thumbnail of A 4DVAR System for the Navy Coastal Ocean Model. Part 1: System Description and Assimilation of Synthetic Observations in Monterey Bay

A 4D variational data assimilation system was developed for assimilating ocean observations with ... more A 4D variational data assimilation system was developed for assimilating ocean observations with the Navy Coastal Ocean Model. It is described in this paper, along with initial assimilation experiments in Monterey Bay using synthetic observations. The assimilation system is tested in a series of twin data experiments to assess its ability to fit assimilated and independent observations by controlling the initial conditions and/or the external forcing while assimilating surface and/or subsurface observations. In all strong and weak constraint experiments, the minimization of the cost function is done with both the gradient descent method (in the control space) and the representer method (observation space). The accuracy of the forecasts following the analysis and the relevance of the retrieved forcing correction in the case of weak constraints are evaluated. It is shown that the assimilation system generally fits the assimilated and nonassimilated observations well in all experiments, yielding lower forecast errors. * Naval Research Laboratory Contribution Number JA/7320-13-1821.

Research paper thumbnail of Cycling the Representer Algorithm for Variational Data Assimilation with the Lorenz Attractor

Monthly Weather Review, 2007

Realistic dynamic systems are often strongly nonlinear, particularly those for the ocean and atmo... more Realistic dynamic systems are often strongly nonlinear, particularly those for the ocean and atmosphere. Applying variational data assimilation to these systems requires a tangent linearization of the nonlinear dynamics about a background state for the cost function minimization. The tangent linearization may be accurate for limited time scales. Here it is proposed that linearized assimilation systems may be accurate if the assimilation time period is less than the tangent linear accuracy time limit. In this paper, the cycling representer method is used to test this assumption with the Lorenz attractor. The outer loops usually required to accommodate the linear assimilation for a nonlinear problem may be dropped beyond the early cycles once the solution (and forecast used as the background in the tangent linearization) is sufficiently accurate. The combination of cycling the representer method and limiting the number of outer loops significantly lowers the cost of the overall assimilation problem. In addition, this study shows that weak constraint assimilation corrects tangent linear model inaccuracies and allows extension of the limited assimilation period. Hence, the weak constraint outperforms the strong constraint method. Assimilated solution accuracy at the first cycle end is computed as a function of the initial condition error, model parameter perturbation magnitude, and outer loops. Results indicate that at least five outer loops are needed to achieve solution accuracy in the first cycle for the selected error range. In addition, this study clearly shows that one outer loop in the first cycle does not preclude accuracy convergence in future cycles.

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

Research paper thumbnail of Assimilation of HF Radar Observations in the Chesapeake–Delaware Bay Region Using the Navy Coastal Ocean Model (NCOM) and the Four-Dimensional Variational (4DVAR) Method

Coastal Ocean Observing Systems, 2015

Research paper thumbnail of A general approach to sensitivity studies in the geosciences

Sensitivity studies are an important application of numerical modelling. Several techniques are u... more Sensitivity studies are an important application of numerical modelling. Several techniques are used to carry out sensitivity studies, among them the derivation of the sensitivity via the adjoint model is one of the most powerful method. The aim of this paper is to show how to derive the sensitivity when both a mathematical model and data are simultaneously used. The method is applied to a model of oceanic circulation with altimetric data.

Research paper thumbnail of On the conservation of physical laws in weak constraint variational data assimilation

4-D variational methods assume either an error in the dynamical equations of motion (weak constra... more 4-D 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. However, in many applications adding an error to represent forcing to certain equations may be physically unrealistic. Dynamical equations that represent conservation of quantities (mass, entropy, momentum ?) 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 formulae produces nonphysical results (generation or destruction of mass or other properties), whereas application of corrections to the fluxes that contribute to the conservation formulae maintain the physically realistic conservation property while providing an ability to accoun...

Research paper thumbnail of Sensitivity studies in geophysical flows

The evolution of the geophysical environment is described by the classical laws of fluid dynamics... more The evolution of the geophysical environment is described by the classical laws of fluid dynamics and thermodynamics, but these are not sufficient to retrieve a geophysical episode since one should also take into account the observations. Data Assimilation Methods are the techniques which enable to use various sources of information for retrieving the state of the environment. We will show that the state of the geophysical fluid can be considered as the solution of an optimal control problem, and that it is computed by solving an optimality system (OS). If one wants to carry out a sensitivity study, it should be done not on the model itself but on the OS. Basically the sensitivity depends on the second order analysis of the model. A method for carrying sensitivity studies is given, then applied to a simple oceanic model. The comparison with first order sensitivity studies is discussed.

Research paper thumbnail of Validation of a Wave Data Assimilation System Based on SWAN

SWAN is one of the most broadly used models for wave predictions in the nearshore, with known and... more SWAN is one of the most broadly used models for wave predictions in the nearshore, with known and extensively studied limitations due to the physics and/or to the numerical implementation. In order to improve the performance of the model, a 4DVAR data assimilation system based on a tangent linear code and the corresponding adjoint from the numerical SWAN model has been developed at NRL(Orzech et. al., 2013), by implementing the methodology of Bennett 2002. The assimilation system takes into account the nonlinear triad and quadruplet interactions, depth-limited breaking, wind forcing, bottom friction and white-capping. Using conjugate gradient method, the assimilation system minimizes a quadratic penalty functional (which represents the overall error of the simulation) and generates the correction of the forward simulation in spatial, temporal and spectral domain. The weights are given to the output of the adjoint by calculating the covariance to an ensemble of forward simulations ac...

Research paper thumbnail of Generalized inversion of the Gent-Cane model of the tropical Pacific with Tropical Atmosphere-Ocean (TAO) data

Research paper thumbnail of A 4DVAR System for the Navy Coastal Ocean Model. Part 2: Strong and Weak Constraint Assimilation Experiments with Real Observations in Monterey Bay

Research paper thumbnail of Assimilation de données et analyse de sensibilité. Une application à la circulation océanique

Research paper thumbnail of A 4DVAR System for the Navy Coastal Ocean Model. Part II: Strong and Weak Constraint Assimilation Experiments with Real Observations in Monterey Bay*

Http Dx Doi Org 10 1175 Mwr D 13 00220 1, May 28, 2014

A four-dimensional variational data assimilation (4DVAR) system was recently developed for the Na... more A four-dimensional variational data assimilation (4DVAR) system was recently developed for the Navy Coastal Ocean Model (NCOM). The system was tested in the first part of this study using synthetic surface and subsurface data. Here, a full range of real surface and subsurface data is considered following encouraging results from the preliminary test. The data include sea surface temperature and sea surface height from satellite, as well as subsurface observations from gliders deployed during the second Autonomous Ocean Sampling Network field experiment in California's Monterey Bay. Data assimilation is carried out with strong and weak constraints, and results are compared against independent observations. This study clearly shows that the 4DVAR approach improves the free-running model simulation and that the weak constraint experiment has lower analysis errors than does the strong constraint version. * Naval Research Laboratory Contribution Number JA/7320-13-13-1822.

Research paper thumbnail of Generalized Inverse of a Reduced Gravity Primitive Equation Ocean Model and Tropical Atmosphere Ocean Data

Monthly Weather Review, Jun 1, 2000

A nonlinear 2½-layer reduced gravity primitive equations (PE) ocean model is used to assimilate s... more 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.

Research paper thumbnail of AGU Oceans 2012 Poster : A Multi-Scale 3D Variational Data Assimilation Scheme (MS-3DVAR) in the Kurshio Extension

Research paper thumbnail of 4DVAR Assimilation of ADCP Data with the Navy Coastal Ocean Model using the Cycling Representer Method

Oceans 2007, 2007

4D-variational assimilation (4DVAR) is used to combine ADCP velocity observations with the Navy C... more 4D-variational assimilation (4DVAR) is used to combine ADCP velocity observations with the Navy Coastal Ocean model (NCOM) to obtain an optimal solution that minimizes a cost function containing the weighted squared errors of velocity measurements, initial conditions, boundary conditions, and model dynamics. However, in order to converge to the global minimum of this cost function, the ocean model (and its adjoint) must be linear. Ocean models, especially those that are designed to resolve baroclinic and mesoscale processes, are typically highly-nonlinear and must be linearized. Tangent linearization is a linearization method that is performed by expanding the nonlinear dynamics about a background field using the first order approximation of Taylor's expansion. The accuracy and stability of this tangent linearized model (TLM) is a very sensitive function of the background accuracy, the level of nonlinearity of the model, complexity of the bathymetry, and the complexity of the flow field. Therefore, in high-resolution coastal domains, the TLM is only going to be stable for a relatively short period of time.

Research paper thumbnail of A Weak Constraint 4D-Var Assimilation System for the Navy Coastal Ocean Model Using the Representer Method

Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. II), 2013

A 4D-Variational system was recently developed for assimilating ocean observations with the Navy ... more A 4D-Variational system was recently developed for assimilating ocean observations with the Navy Coastal Ocean Model. It is described here, along with initial assimilation experiments in the Monterey Bay using a combination of real and synthetic ocean observations. For testing a new assimilation system it is advantageous to use this combination of real and synthetic data over simplified cases of climatology and twin data. Assimilation experiments are carried out in a weak constraint formulation, with the model's external forcing assumed to be erroneous in addition to initial conditions. The system's ability to fit assimilated and non assimilated observations is assessed, as well as the consistency and relevance of the retrieved model forcing. Experiment results show that the assimilation system fits the data with relatively high prior errors in the initial conditions and surface forcing fluxes. However, the retrieved model forcing errors are well within the range of acceptable corrections according to an independent study.

Research paper thumbnail of Incremental projection approach of regularization for inverse problems

Applied Mathematics & Optimization, 2015

Research paper thumbnail of On the direct assimilation of along-track sea surface height observations into a free-surface ocean model using a weak constraints four dimensional variational (4dvar) method

Quarterly Journal of the Royal Meteorological Society, 2015

Research paper thumbnail of Impact of Assimilating Surface Velocity Observations on the Model Sea Surface Height using the NCOM-4DVAR

Monthly Weather Review, 2015

Research paper thumbnail of Cycling the Representer Algorithm for Data Assimilation with the Lorenz Attractor

... model, and renders the cost of the representer method expensive for operational purposes. The... more ... model, and renders the cost of the representer method expensive for operational purposes. The accuracy of the TLM depends on the initial con-1(t) - xt) + ola,,r,,(t). (12) dition and model errors. The estimation of these errors is described in section 2. For completeness, the TLM ...

Research paper thumbnail of A 4DVAR System for the Navy Coastal Ocean Model. Part 1: System Description and Assimilation of Synthetic Observations in Monterey Bay

A 4D variational data assimilation system was developed for assimilating ocean observations with ... more A 4D variational data assimilation system was developed for assimilating ocean observations with the Navy Coastal Ocean Model. It is described in this paper, along with initial assimilation experiments in Monterey Bay using synthetic observations. The assimilation system is tested in a series of twin data experiments to assess its ability to fit assimilated and independent observations by controlling the initial conditions and/or the external forcing while assimilating surface and/or subsurface observations. In all strong and weak constraint experiments, the minimization of the cost function is done with both the gradient descent method (in the control space) and the representer method (observation space). The accuracy of the forecasts following the analysis and the relevance of the retrieved forcing correction in the case of weak constraints are evaluated. It is shown that the assimilation system generally fits the assimilated and nonassimilated observations well in all experiments, yielding lower forecast errors. * Naval Research Laboratory Contribution Number JA/7320-13-1821.

Research paper thumbnail of Cycling the Representer Algorithm for Variational Data Assimilation with the Lorenz Attractor

Monthly Weather Review, 2007

Realistic dynamic systems are often strongly nonlinear, particularly those for the ocean and atmo... more Realistic dynamic systems are often strongly nonlinear, particularly those for the ocean and atmosphere. Applying variational data assimilation to these systems requires a tangent linearization of the nonlinear dynamics about a background state for the cost function minimization. The tangent linearization may be accurate for limited time scales. Here it is proposed that linearized assimilation systems may be accurate if the assimilation time period is less than the tangent linear accuracy time limit. In this paper, the cycling representer method is used to test this assumption with the Lorenz attractor. The outer loops usually required to accommodate the linear assimilation for a nonlinear problem may be dropped beyond the early cycles once the solution (and forecast used as the background in the tangent linearization) is sufficiently accurate. The combination of cycling the representer method and limiting the number of outer loops significantly lowers the cost of the overall assimilation problem. In addition, this study shows that weak constraint assimilation corrects tangent linear model inaccuracies and allows extension of the limited assimilation period. Hence, the weak constraint outperforms the strong constraint method. Assimilated solution accuracy at the first cycle end is computed as a function of the initial condition error, model parameter perturbation magnitude, and outer loops. Results indicate that at least five outer loops are needed to achieve solution accuracy in the first cycle for the selected error range. In addition, this study clearly shows that one outer loop in the first cycle does not preclude accuracy convergence in future cycles.

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

Research paper thumbnail of Assimilation of HF Radar Observations in the Chesapeake–Delaware Bay Region Using the Navy Coastal Ocean Model (NCOM) and the Four-Dimensional Variational (4DVAR) Method

Coastal Ocean Observing Systems, 2015

Research paper thumbnail of A general approach to sensitivity studies in the geosciences

Sensitivity studies are an important application of numerical modelling. Several techniques are u... more Sensitivity studies are an important application of numerical modelling. Several techniques are used to carry out sensitivity studies, among them the derivation of the sensitivity via the adjoint model is one of the most powerful method. The aim of this paper is to show how to derive the sensitivity when both a mathematical model and data are simultaneously used. The method is applied to a model of oceanic circulation with altimetric data.

Research paper thumbnail of On the conservation of physical laws in weak constraint variational data assimilation

4-D variational methods assume either an error in the dynamical equations of motion (weak constra... more 4-D 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. However, in many applications adding an error to represent forcing to certain equations may be physically unrealistic. Dynamical equations that represent conservation of quantities (mass, entropy, momentum ?) 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 formulae produces nonphysical results (generation or destruction of mass or other properties), whereas application of corrections to the fluxes that contribute to the conservation formulae maintain the physically realistic conservation property while providing an ability to accoun...

Research paper thumbnail of Sensitivity studies in geophysical flows

The evolution of the geophysical environment is described by the classical laws of fluid dynamics... more The evolution of the geophysical environment is described by the classical laws of fluid dynamics and thermodynamics, but these are not sufficient to retrieve a geophysical episode since one should also take into account the observations. Data Assimilation Methods are the techniques which enable to use various sources of information for retrieving the state of the environment. We will show that the state of the geophysical fluid can be considered as the solution of an optimal control problem, and that it is computed by solving an optimality system (OS). If one wants to carry out a sensitivity study, it should be done not on the model itself but on the OS. Basically the sensitivity depends on the second order analysis of the model. A method for carrying sensitivity studies is given, then applied to a simple oceanic model. The comparison with first order sensitivity studies is discussed.

Research paper thumbnail of Validation of a Wave Data Assimilation System Based on SWAN

SWAN is one of the most broadly used models for wave predictions in the nearshore, with known and... more SWAN is one of the most broadly used models for wave predictions in the nearshore, with known and extensively studied limitations due to the physics and/or to the numerical implementation. In order to improve the performance of the model, a 4DVAR data assimilation system based on a tangent linear code and the corresponding adjoint from the numerical SWAN model has been developed at NRL(Orzech et. al., 2013), by implementing the methodology of Bennett 2002. The assimilation system takes into account the nonlinear triad and quadruplet interactions, depth-limited breaking, wind forcing, bottom friction and white-capping. Using conjugate gradient method, the assimilation system minimizes a quadratic penalty functional (which represents the overall error of the simulation) and generates the correction of the forward simulation in spatial, temporal and spectral domain. The weights are given to the output of the adjoint by calculating the covariance to an ensemble of forward simulations ac...