Matthew Carrier

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.

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.

On the Renormalization of the Covariance Operators

Many background error correlation (BEC) models in data assimilation are formulated in terms of a smoothing operator B, which simulates the action of the correlation matrix on a state vector normalized by respective BE variances. Under such formulation, B has to have a unit diagonal and requires appropriate renormalization by rescaling. The exact computation of the rescaling factors (diagonal elements of B )i s a computationally expensive procedure, which needs an efficient numerical approximation. In this study approximate renormalization techniques based on the Monte Carlo (MC) and Hadamard matrix (HM) methods and on the analytic approximations derived under the assumption of the local homogeneity (LHA) of B are compared using realistic BEC models designed for oceanographic applications. It is shown that although the accuracy of the MC and HM methods can be improved by additional smoothing, their computational cost remains significantly higher than the LHA method, which is shown to be effective even in the zeroth-order approximation. The next approximation improves the accuracy 1.5‐2 times at a moderate increase of CPU time. A heuristic relationship for the smoothing scale in two and three dimensions is proposed for the first-order LHA approximation.

Identifying cloud-uncontaminated AIRS spectra from cloudy FOV based on cloud-top pressure and weighting functions

Abstract An effort is made to increase the number of Advanced Infrared Sounder (AIRS) cloud-uncontaminated infrared data for regional mesoscale data assimilation and short-term quantitative precipitation forecast (QPF) applications. The cloud-top pressure from Moderate Resolution Imaging Spectroradiometer (MODIS) is utilized in combination with weighting functions (WFs) to develop a channel-based cloudy-data-removal algorithm. This algorithm identifies “clear channels” for which the brightness temperature (BT) values are not cloud contaminated. A channel-dependent cutoff pressure (COP) level is first determined based on the structure of the WF of each channel. It is usually below the maximum WF level. If the cloud top (as identified by a MODIS cloud mask) is above (below) the COP level of a channel, this channel is then deemed cloudy (clear) and removed (retained). Using this algorithm, a sizable increase of cloud-uncontaminated AIRS data can be obtained. There are more usable domain points for those chan...

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.

Background Error Correlation Modeling with Diffusion Operators

Many background error correlation (BEC) models in data assimilation are formulated in terms of a positive-definite smoothing operator B that is employed to simulate the action of correlation matrix on a vector in state space. In this chapter, a general procedure for constructing a BEC model as a rational function of the diffusion operator D is presented and analytic expressions for the respective correlation functions in the homogeneous case are obtained. It is shown that this class of BEC models can describe multi-scale stochastic fields whose characteristic scales can be expressed in terms of the polynomial coefficients of the model. In particular, the connection between the inverse binomial model and the well-known Gaussian model \(\mathbf{\mathsf{B}}_{g} =\exp \mathbf{\mathsf{D}}\) is established and the relationships between the respective decorrelation scales are derived.By its definition, the BEC operator has to have a unit diagonal and requires appropriate renormalization by rescaling. The exact computation of the rescaling factors (diagonal elements of B) is a computationally expensive procedure, therefore an efficient numerical approximation is needed. Under the assumption of local homogeneity of D, a heuristic method for computing the diagonal elements of B is proposed. It is shown that the method is sufficiently accurate for realistic applications, and requires 102 times less computational resources than other methods of diagonal estimation that do not take into account prior information on the structure of B.

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.