Hans Ngodock

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

A nonlinear 2‰-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.

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

AbstractA 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 lowe...

Impact of Assimilating Ocean Velocity Observations Inferred from Lagrangian Drifter Data Using the NCOM-4DVAR*

AbstractEulerian velocity fields are derived from 300 drifters released in the Gulf of Mexico by The Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE) during the summer 2012 Grand Lagrangian Deployment (GLAD) experiment. These data are directly assimilated into the Navy Coastal Ocean Model (NCOM) four-dimensional variational data assimilation (4DVAR) analysis system in a series of experiments to investigate their impact on the model circulation. The NCOM-4DVAR is a newly developed tool for data analysis, formulated for weak-constraint data assimilation based on the indirect representer method. The assimilation experiments take advantage of this velocity data along with other available data sources from in situ and satellite measurements of surface and subsurface temperature and salinity. Three different experiments are done: (i) A nonassimilative NCOM free run, (ii) an assimilative NCOM run that utilizes temperature and salinity observations, and (iii) an assimilativ...

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

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.

Cycling the Representer Algorithm for Variational Data Assimilation with the Lorenz Attractor

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.

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

AbstractA 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.

Do Assimilated Drifter Velocities Improve Lagrangian Predictability in an Operational Ocean Model

The Lagrangian predictability of general circulation models is limited by the need for high-resolution data streams to constrain small-scale dynamical features. Here velocity observations from Lagrangian drifters deployedintheGulfofMexicoduringthesummer2012GrandLagrangianDeployment(GLAD)experiment are assimilated into the Naval Coastal Ocean Model (NCOM) 4D variational (4DVAR) analysis system to examine their impact on Lagrangian predictability. NCOM-4DVAR is a weak-constraint assimilation system using the indirect representer method. Velocities derived from drifter trajectories, as well as satellite and in situ observations, are assimilated. Lagrangian forecast skill is assessed using separation distance and angular differences between simulated and observed trajectory positions. Results show that assimilating drifter velocities substantially improvesthe model forecast shape and position of a Loop Currentring. These gains in mesoscale Eulerian forecast skill also improve Lagrangian forecasts, reducing the growth rate of separation distances between observed and simulated drifters by approximately 7.3kmday 21 on average, when compared with forecasts that assimilate only temperature and salinity observations. Trajectory angular differences are also reduced.

Cycling the Representer Method with Nonlinear Models

Realistic dynamic systems are often strongly nonlinear, particularly those for the ocean and atmosphere. Applying variational data assimilation to these systems requires the linearization of the nonlinear dynamics about a background state for the cost function minimization, except when the gradient of the cost function can be analytically or explicitly computed. Although there is no unique choice of linearization, the tangent linearization is to be preferred if it can be proven to be numerically stable and accurate. For time intervals extending beyond the scales of nonlinear event development, the tangent linearization cannot be expected to be sufficiently accurate. The variational assimilation would, therefore, not be able to yield a reliable and accurate solution. In this paper, the representer method is used to test this hypothesis with four different nonlinear models. The method can be implemented for successive cycles in order to solve the entire nonlinear problem. By cycling the representer method, it is possible to reduce the assimilation problem into intervals in which the linear theory is able to perform accurately. This study demonstrates that by cycling the representer method, the tangent linearization is sufficiently accurate once adequate assimilation accuracy is achieved in the early cycles. The outer loops that are usually required to contend with the linear assimilation of a nonlinear problem are not required beyond the early cycles because the tangent linear model is sufficiently accurate at this point. The combination of cycling the representer method and limiting the outer loops to one significantly lowers the cost of the overall assimilation problem. In addition, this study shows that weak constraint assimilation is capable of extending the assimilation period beyond the time range of the accuracy of the tangent linear model. That is, the weak constraint assimilation can correct the inaccuracies of the tangent linear model and clearly outperform the strong constraint method.

Impact of Assimilating Surface Velocity Observations on the Model Sea Surface Height Using the NCOM-4DVAR

AbstractThe assimilation of surface velocity observations and their impact on the model sea surface height (SSH) is examined using an operational regional ocean model and its four-dimensional variational data assimilation (4DVAR) analysis component. In this work, drifter-derived surface velocity observations are assimilated into the Navy’s Coastal Ocean Model (NCOM) 4DVAR in weak-constraint mode for a Gulf of Mexico (GoM) experiment during August–September 2012. During this period the model is trained by assimilating surface velocity observations (in a series of 96-h assimilation windows), which is followed by a 30-day forecast through the month of October 2012. A free-run model and a model that assimilates along-track SSH observations are also run as baseline experiments to which the other experiments are compared. It is shown here that the assimilation of surface velocity measurements has a substantial impact on improving the model representation of the forecast SSH on par with the experiment that assim...

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

Abstract The impact of HF radar observations on constraining and improving model forecasts of the coastal ocean circulation is examined using a very high resolution model and a 4DVAR data assimilation system. The latter can propagate the influence of these surface velocity measurements through all the model variables in space and time. Assimilation experiments with a high-resolution model show that, although the analysis is able to significantly reduce the models discrepancy to the observed surface velocities, the main challenge remains in providing more reliable atmospheric forcing fields to the coastal ocean model. However, using a very high resolution in the model can become a liability for the assimilation as the model would resolve small-scale circulation features that cannot be constrained by the available observations. An additional assimilation experiment with a reduced horizontal resolution with the same atmospheric forcing shows significant improvements in both the analysis and the forecast.