Bibliography - Shoaqing Zhang

1. Chang, Y-S, Anthony Rosati, Shoaqing Zhang, and Matthew J Harrison, February 2009: Objective analysis of monthly temperature and salinity for the world ocean in the 21st century: Comparison with World Ocean Atlas and application to assimilation validation. Journal of Geophysical Research, 114, C02014, doi:10.1029/2008JC004970.
   [ Abstract ]

   A new World Ocean atlas of monthly temperature and salinity, based on individual profiles for 2003–2007 (WOA21c), is constructed and compared with the World Ocean Atlas 2001 (WOA01), the World Ocean Atlas 2005 (WOA05), and the data assimilation analysis from the Coupled Data Assimilation (CDA) system developed by the Geophysical Fluid Dynamics Laboratory (GFDL). First, we established a global data management system for quality control (QC) of oceanic observed data both in real time and delayed mode. Delayed mode QC of Argo floats identified about 8.5% (3%) of the total floats (profiles) up to December 2007 as having a significant salinity offset of more than 0.05. Second, all QCed data were gridded at 1° by 1° horizontal resolution and 23 standard depth levels using six spatial scales (large and small longitudinal, latitudinal, and cross-isobath) and a temporal scale. Analyzed mean temperature in WOA21c is warm with respect to WOA01 and WOA05, while salinity difference is less evident. Consistent differences among WOA01, WOA05, and WOA21c are found both in the fully and subsampled data set, which indicates a large impact of recent observations on the existing climatologies. Root mean square temperature and salinity differences and offsets of the GFDL's CDA results significantly decrease in the order of WOA01, WOA05, and WOA21c in most oceans and depths as well. This result suggests that the WOA21c is of use for the collocated assessment approach especially for high-performance assimilation models on the global scale.

2. Zhang, Shoaqing, Matthew J Harrison, Anthony Rosati, and Andrew T Wittenberg, 2007: System Design and Evaluation of Coupled Ensemble Data Assimilation for Global Oceanic Climate Studies. Monthly Weather Review, 135(10), doi:10.1175/MWR3466.1.
   [ Abstract ]

   A fully coupled data assimilation (CDA) system, consisting of an ensemble filter applied to the Geophysical Fluid Dynamics Laboratory’s global fully coupled climate model (CM2), has been developed to facilitate the detection and prediction of seasonal-to-multidecadal climate variability and climate trends. The assimilation provides a self-consistent, temporally continuous estimate of the coupled model state and its uncertainty, in the form of discrete ensemble members, which can be used directly to initialize probabilistic climate forecasts. Here, the CDA is evaluated using a series of perfect model experiments, in which a particular twentieth-century simulation—with temporally varying greenhouse gas and natural aerosol radiative forcings—serves as a “truth” from which observations are drawn, according to the actual ocean observing network for the twentieth century. These observations are then assimilated into a coupled model ensemble that is subjected only to preindustrial forcings. By examining how well this analysis ensemble reproduces the “truth,” the skill of the analysis system in recovering anthropogenically forced trends and natural climate variability is assessed, given the historical observing network. The assimilation successfully reconstructs the twentieth-century ocean heat content variability and trends in most locations. The experiments highlight the importance of maintaining key physical relationships among model fields, which are associated with water masses in the ocean and geostrophy in the atmosphere. For example, when only oceanic temperatures are assimilated, the ocean analysis is greatly improved by incorporating the temperature–salinity covariance provided by the analysis ensemble. Interestingly, wind observations are more helpful than atmospheric temperature observations for constructing the structure of the tropical atmosphere; the opposite holds for the extratropical atmosphere. The experiments indicate that the Atlantic meridional overturning circulation is difficult to constrain using the twentieth-century observational network, but there is hope that additional observations—including those from the newly deployed Argo profiles—may lessen this problem in the twenty-first century. The challenges for data assimilation of model systematic biases and evolving observing systems are discussed.

3. Zhang, Shoaqing, Anthony Rosati, and Matthew J Harrison, in press: Detection of multi-decadal oceanic variability within a coupled ensemble data assimilation system. Journal of Geophysical Research. 11/06.
   [ Abstract ]

   This study examines the detectability of long time scale variability of oceanic heat content and salinity, based on the 20th-century (temperature only) and 21st-century (ARGO deploy for temperature and salinity) oceanic observing networks (OONs) by an oceanic data assimilation approach within the GFDL coupled data assimilation system. The assimilation algorithm is an ensemble filter. As an implementation of stochastic estimate theory, the filter solves for a temporally-varying joint probability density function (joint-PDF) of oceanic states by combining the observational PDF and a prior PDF derived from an oceanic general circulation model (GCM) that is coupled with an atmospheric GCM. A series of perfect-model experiments has been performed to examine the impact of temporally-varying radiative forcings, initial conditions (ICs) and OONs. A 20th-century simulation with temporally-varying greenhouse gas and natural aerosol (GHGNA) radiative forcings serves as the "truth" from which observations are drawn by the 20th-21st-century OONs. These oceanic observations were assimilated into the coupled climate model for targeting a 25-year climate variation (corresponding to 1976-2000 historical GHGNA records) starting from different ICs and with fixed-year/temporally-varying GHGNA forcings. Two sets of ICs called the controlled and the forced are used here, in which the former/latter was produced from a long time model integration with fixed-year/temporally-varying GHGNA radiative forcings.

4. Anderson, Jeffrey L., Bruce Wyman, Shoaqing Zhang, and T Hoar, 2005: Assimilation of surface pressure observations using an ensemble filter in an idealized global atmospheric prediction system. Journal of the Atmospheric Sciences, 62(8), doi:10.1175/JAS3510.1.
   [ Abstract ]

   An ensemble filter data assimilation system is tested in a perfect model setting using a low resolution Held-Suarez configuration of an atmospheric GCM. The assimilation system is able to reconstruct details of the model's state at all levels when only observations of surface pressure (PS) are available. The impacts of varying the spatial density and temporal frequency of PS observations are examined. The error of the ensemble mean assimilation prior estimate appears to saturate at some point as the number of PS observations available once every 24 h is increased. However, increasing the frequency with which PS observations are available from a fixed network of 1800 randomly located stations results in an apparently unbounded decrease in the assimilation's prior error for both PS and all other model state variables. The error reduces smoothly as a function of observation frequency except for a band with observation periods around 4 h. Assimilated states are found to display enhanced amplitude high-frequency gravity wave oscillations when observations are taken once every few hours, and this adversely impacts the assimilation quality. Assimilations of only surface temperature and only surface wind components are also examined. The results indicate that, in a perfect model context, ensemble filters are able to extract surprising amounts of information from observations of only a small portion of a model's spatial domain. This suggests that most of the remaining challenges for ensemble filter assimilation are confined to problems such as model error, observation representativeness error, and unknown instrument error characteristics that are outside the scope of perfect model experiments. While it is dangerous to extrapolate from these simple experiments to operational atmospheric assimilation, the resulrts also suggest that exploring the frequency with which observations are used for assimilation may lead to significant enhancements to assimilated state estimates.

5. Zhang, Shoaqing, Matthew J Harrison, Andrew T Wittenberg, Anthony Rosati, Jeffrey L Anderson, and Ventakramani Balaji, 2005: Initialization of an ENSO Forecast System using a parallelized ensemble filter. Monthly Weather Review, 133(11), doi:10.1175/MWR3024.1.
   [ Abstract ]

   As a first step toward coupled ocean–atmosphere data assimilation, a parallelized ensemble filter is implemented in a new stochastic hybrid coupled model. The model consists of a global version of the GFDL Modular Ocean Model Version 4 (MOM4), coupled to a statistical atmosphere based on a regression of National Centers for Environmental Prediction (NCEP) reanalysis surface wind stress, heat, and water flux anomalies onto analyzed tropical Pacific SST anomalies from 1979 to 2002. The residual part of the NCEP fluxes not captured by the regression is then treated as stochastic forcing, with different ensemble members feeling the residual fluxes from different years. The model provides a convenient test bed for coupled data assimilation, as well as a prototype for representing uncertainties in the surface forcing. A parallel ensemble adjustment Kalman filter (EAKF) has been designed and implemented in the hybrid model, using a local least squares framework. Comparison experiments demonstrate that the massively parallel processing EAKF (MPPEAKF) produces assimilation results with essentially the same quality as a global sequential analysis. Observed subsurface temperature profiles from expendable bathythermographs (XBTs), Tropical Atmosphere Ocean (TAO) buoys, and Argo floats, along with analyzed SSTs from NCEP, are assimilated into the hybrid model over 1980-2002 using the MPPEAKF. The filtered ensemble of SSTs, ocean heat contents, and thermal structures converge well to the observations, in spite of the imposed stochastic forcings. Several facets of the EAKF algorithm used here have been designed to facilitate comparison to a traditional three-dimensional variational data assimilation (3DVAR) algorithm, for instance, the use of a univariate filter in which observations of temperature only directly impact temperature state variables. Despite these choices that may limit the power of the EAKF, the MPPEAKF solution appears to improve upon an earlier 3DVAR solution, producing a smoother, more physically reasonable analysis that better fits the observational data and produces, to some degree, a self-consistent estimate of analysis uncertainties. Hybrid model ENSO forecasts initialized from the MPPEAKF ensemble mean also appear to outperform those initialized from the 3DVAR analysis. This improvement stems from the EAKF's utilization of anisotropic background error covariances that may vary in time.

6. Zhang, Shoaqing, Jeffrey L Anderson, Anthony Rosati, Matthew J Harrison, S P Khare, and Andrew T Wittenberg, 2004: Multiple time level adjustment for data assimilation. Tellus A, 56A(1), 2-15.
   [ Abstract PDF ]

   Time-stepping schemes in ocean-atmosphere models can involve multiple time levels. Traditional data assimilation implementation considers only the adjustment of the current state using observations available, i.e. the one time level adjustment. However, one time level adjustment introduces an inconsistency between the adjusted and unadjusted states into the model time integration, which can produce extra assimilation errors. For time-dependent assimilation approaches such as ensemble-based filtering algorithms, the persistent introduction of this inconsistency can give rise to computational instability and requires extra time filtering to maintain the assimilation. A multiple time level adjustment assimilation scheme is thus proposed, in which the states at times t and t- 1, t- 2, ... , if applicable, are adjusted using observations at time t. Given a leap frog time-stepping scheme, a low-order (Lorenz-63) model and a simple atmospheric (global barotropic) model are used to demonstrate the impact of the two time level adjustment on assimilation results in a perfect model framework with observing/assimilation simulation experiments. The assimilation algorithms include an ensemble-based filter (the ensemble adjustment Kalman filter, EAKF) and a strong constraint four-dimensional variational (4D-Var) assimilation method. Results show that the two time level adjustment always reduces the assimilation errors for both filtering and variational algorithms due to the consistency of the adjusted states at times t and t- 1 that are used to produce the future state in the leap frog time-stepping. The magnitude of the error reduction made by the two time level adjustment varies according to the availability of observations, the nonlinearity of the assimilation model and the strength of the time filter used in the model. Generally the sparser the observations in time, the larger the error reduction. In particular, for the EAKF when the model uses a weak time filter and for the 4D-Var method when the model is strongly nonlinear, two time level adjustment can significantly improve the performance of these assimilation algorithms.

7. Zhang, Shoaqing, and Jeffrey L Anderson, 2003: Impact of spatially and temporally varying estimates of error covariance on assimilation in a simple atmospheric model. Tellus A, 55A(2), 126-147.
   [ Abstract PDF ]

   The background error covariance (correlation) between model state variables is of central importance for implementing data assimilation and understanding model dynamics. Traditional approaches for estimating the background error covariance involve many heuristic approximations, and often the estimated covariance is flow-independent, i.e., only reflecting statistics of the climatological background. This study examines temporally and spatially varying estimates of error covariance in a spectral barotropic model using a Monte Carlo approach, an implementation of an ensemble square root filter called the ensemble adjustment Kalman filter (EAKF). The EAKF is designed to maintain as much information about the distribution of the prior state variables as possible, and results show that this method can produce reasonable estimates of error correlation structure with an affordable sample (ensemble) size. The impact of using temporally and spatially varying estimates of error covariance in the EAKF is examined by using the time and spatial mean error covariances derived from the EAKF in an ensemble optimal interpolation (OI) assimilation scheme. Three key results are: (1) for the same ensemble size, an ensemble filter such as the EAKF produces better assimilations since its flow-dependent error covariance estimates are able to reflect more about the synoptic-scale wave structure in the simulated flows; (2) an ensemble OI scheme can also produce reasonably good assimilation results if the time-invariate covariance matrix is chosen appropriately; (3) when using the EAKF to estimate the error covariance matrix for improving traditional assimilation algorithms such as variational analysis and OI, a relatively small ensemble size may be used to estimate correlation structure although larger ensembles produce progressively better results.

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