Ensemble estimation of background‐error variances in a three‐dimensional variational data assimilation system for the global ocean

Abstract

This paper studies the sensitivity of global ocean analyses to two flow-dependent formulations of the background-error standard deviations (σ b ) for temperature and salinity in a three-dimensional variational data assimilation (3D-Var) system. The first formulation is based on an empirical parameterization of σ b in terms of the vertical gradients of the background temperature and salinity fields, while the second formulation involves a more sophisticated approach that derives σ b from the spread of an ensemble of background states. The ensembles are created by explicitly perturbing both the surface fluxes (wind stress, fresh water and heat) used to force the model and the observations (temperature and salinity profiles) used in the assimilation process. The two formulations are compared in two cycled 3D-Var experiments for the period 1993-2000. In both experiments, the observation-error standard deviations (σ o ) are geographically dependent and estimated from a model-data comparison prior to assimilation. An additional 3D-Var experiment that employs the parametrized σ b but a simpler σ o formulation, and a control experiment involving no data assimilation, were also conducted and used for comparison.All 3D-Var experiments produce a significant reduction in the mean and standard deviation of the temperature and salinity innovations compared to those of the control experiment. The largest differences between the two σ b formulations occur in the upper 150 m, where the parametrized σ b are notably larger than the ensemble σ b . In this region, the innovation statistics are slightly better for the parametrized σ b . Statistical consistency checks indicate that both schemes underestimate σ b , the underestimation being stronger with the ensemble formulation. The error growth between cycles, however, is much reduced with the ensemble σ b , suggesting that the analyses produced with the ensemble σ b are in better balance than those produced with the parametrized σ b . This claim is supported by independent data comparisons involving model fields not directly constrained by the assimilated temperature and salinity profiles. In particular, sea-surface height (SSH) anomalies in the northwest Atlantic and zonal velocities in the equatorial Pacific are clearly better with the ensemble σ b than with the parametrized σ b . Results also show that while some aspects of those variables are improved with data assimilation (SSH anomalies and currents in the central and eastern Pacific), other aspects are degraded (SSH anomalies in the northwest Atlantic, currents in the western Pacific). Areas for improving the ensemble method and for making better use of the ensemble information are discussed.

NEMOTAM: tangent and adjoint models for the ocean modelling platform NEMO

“…OPATAM was initially developed for a Pacific Ocean configuration and targeted variational data assimilation applications in the framework of OPAVAR (Weaver et al, , 2005. OPATAM and OPAVAR were extended to other regional basins (Mediterranean Sea, Rémy, 1999; North Atlantic 1/3 • , Forget et al, 2008; South Atlantic 1 • ) and to the global ocean (ORCA 2 • , Daget et al, 2009). They were used for methodological studies such as control of the 3-D model error (Vidard, 2001), control of the surface forcing and open boundary conditions (Deltel, 2002;Vossepoel et al, 2003).…”

Weak constraint four-dimensional variational data assimilation in a model of the California Current System

“…Following the standard notation used in the meteorological and oceanographic literature (Ide et al, 1997;Daget et al, 2009), the ocean state vector will be denoted as x and comprises the model grid point values of temperature, salinity, two components of velocity, and sea surface height. The state vector x(t i ) is advanced forward in time by the forecast model, which is denoted as M so that x(t f ) = M(t i , t f ; x(t i ), f (t i , t f ), b(t i , t f )),…”

An Ensemble Ocean Data Assimilation System for Seasonal Prediction

“…Additionally, the model sea surface temperature (SST) field is strongly relaxed to model-gridded SST analysis products, so that the model SST is always close to the ''observed'' SST. This is often regarded as an important requirement for seasonal forecast initialization (e.g., Balmaseda et al 2008;Daget et al 2009). Specifically, the ratio of the model error standard deviation to that of the observations is 0.47 (this factor of 0.47 was established when POAMA-1 was initially developed through a process of tuning).…”

“…For a review of these systems, including a comparison of their methods and new developments in coupled model initialization [e.g., Geophysical Fluid Dynamics Laboratory (GFDL) coupled data assimilation (CDA) system; Zhang et al 2007], the reader is referred to Balmaseda et al (2009). Of these systems, some are based on three-dimensional variational (3DVAR) methods, some on univariate or multivariate optimal interpolation (OI), and some are variants of the ensemble Kalman filter (EnKF; Evensen 1994;Houtekamer and Mitchell 1998;Burgers et al 1998).…”