Variational Data Assimilation for the Global Ocean - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 298

since the last analysis was made. Further, NCODA 3DVAR is globally relocatable
and has been integrated into the Coupled Ocean Atmosphere Mesoscale Prediction
System (COAMPS R

1 ),whichisusedbyNavyforrapidenvironmentalassessment.
In this mode of operation, the 3DVAR performs multi-scale analyses on nested,
successively higher resolution grids. Finally, NCODA provides the data assimilation
component for the WAVEWATCH wave model forecasting system at FNMOC
( Wittmann and Cummings 2005 ). In this mode of operation, NCODA computes
corrections to the model's two-dimensional wave spectra from assimilation of
satellite altimeter and wave buoy observations of significant wave height.
The examples used in the paper are taken from NCODA 3DVAR analyses cycling
with global HYCOM. Sections 13.2 and 13.3 of the paper describe the assimilation
method and techniques used to specify the error covariances. Section 13.4 lists
the ocean observing systems assimilated and outlines the data selection and data
pre-processing that is done for the real-time global forecast. Section 13.5 gives an
overview of the entire NCODA system, including the diagnostic suite. Section 13.6
presents some verification results from global HYCOM. Section 13.7 describes
future capabilities and applications of the NCODA 3DVAR system, while Sect. 13.8
gives a summary.

13.2 Method

The method used in NCODA is an oceanographic implementation of the Navy
Variational Atmospheric Data Assimilation System (NAVDAS), a 3DVAR tech-
nique developed for Navy numerical weather prediction (NWP) systems ( Daley
and Barker 2001 ). The oceanographic 3DVAR analysis variables are temperature,
salinity, geopotential (dynamic height), and u v vector velocity components. All

ocean variables are analyzed simultaneously in three dimensions. The horizon-
tal correlations are multivariate in geopotential and velocity, thereby permitting
adjustments to the mass fields to be correlated with adjustments to the flow
fields. The velocity adjustments (or increments) are in geostrophic balance with
the geopotential increments, which, in turn, are in hydrostatic agreement with
the temperature and salinity increments. The multivariate aspects of the 3DVAR
assimilation are discussed further in Sect. 13.3.3 .
The NCODA 3DVAR problem is formulated as:

;

x a D x b C P b H T . HP b H T C R/ 1 Œy H.x b / (13.1)

where x a is the analysis vector, x b is the background vector, P b is the positive-
definite background error covariance matrix, H is the forward operator, R is the
observation error covariance matrix, and y is the observation vector. At the present

is a registered trademark of the Naval Research Laboratory

1 COAMPS R