A24B-01 INVITED
Theoretical Advances in Sequential Data Assimilation for the Atmosphere and Oceans
We concentrate here on two aspects of advanced Kalman--filter-related methods: (i) the stability of the forecast- assimilation cycle, and (ii) parameter estimation for the coupled ocean-atmosphere system. The nonlinear stability of a prediction-assimilation system guarantees the uniqueness of the sequentially estimated solutions in the presence of partial and inaccurate observations, distributed in space and time; this stability is shown to be a necessary condition for the convergence of the state estimates to the true evolution of the turbulent flow. The stability properties of the governing nonlinear equations and of several data assimilation systems are studied by computing the spectrum of the associated Lyapunov exponents. These ideas are applied to a simple and an intermediate model of atmospheric variability and we show that the degree of stabilization depends on the type and distribution of the observations, as well as on the data assimilation method. These results represent joint work with A. Carrassi, A. Trevisan and F. Uboldi. Much is known by now about the main physical mechanisms that give rise to and modulate the El-Nino/Southern- Oscillation (ENSO), but the values of several parameters that enter these mechanisms are an important unknown. We apply Extended Kalman Filtering (EKF) for both model state and parameter estimation in an intermediate, nonlinear, coupled ocean-atmosphere model of ENSO. Model behavior is very sensitive to two key parameters: (a) "mu", the ocean-atmosphere coupling coefficient between the sea-surface temperature (SST) and wind stress anomalies; and (b) "delta-s", the surface-layer coefficient. Previous work has shown that "delta- s" determines the period of the model's self-sustained oscillation, while "mu' measures the degree of nonlinearity. Depending on the values of these parameters, the spatio-temporal pattern of model solutions is either that of a delayed oscillator or of a westward propagating mode. Assimilation of SST data from the NCEP- NCAR Reanalysis-2 shows that the parameters can vary on fairly short time scales and switch between values that approximate the two distinct modes of ENSO behavior. Rapid adjustments of these parameters occur, in particular, during strong ENSO events. Ways to apply EKF parameter estimation efficiently to state-of-the-art coupled ocean-atmosphere GCMs will be discussed. These results arise from joint work with D. Kondrashov and C.-j. Sun.
A24B-02 INVITED
4D-Var or Ensemble Kalman Filter
We consider the relative advantages of two advanced data assimilation systems, 4D-Var and ensemble Kalman filter (EnKF), currently in use or considered for operational implementation. We explore the impact of tuning assimilation parameters such as the assimilation window length and background error covariance in 4D-Var, the variance inflation in EnKF, and the effect of model errors and reduced observation coverage in both systems. For short assimilation windows EnKF gives more accurate analyses. Both systems reach similar levels of accuracy if long windows are used for 4D-Var, and for infrequent observations, when ensemble perturbations grow nonlinearly and become non-Gaussian, 4D-Var attains lower errors than EnKF. Results obtained with variations of EnKF using operational models and both simulated and real observations are reviewed. A table summarizes the pros and cons of the two methods.
A24B-03
Adaptive Spatially-varying Variance Inflation in an Ensemble Filter
Ensemble filters are subject to errors arising from model deficiencies, representativeness error, and sampling
error. In general, these errorslead to a systematic underestimate of the ensemble variance. This in turn can lead
to reduced assimilation accuracy, insufficient spread for forecasts, and filter divergence in the worst case. Simple
heuristic algorithms like inflation have been used to ameliorate this problem. However, it can be difficult to select
appropriate inflation
magnitudes. Even worse, if the spatial density of observations
is not uniform, the inflation required in heavily observed regions
can lead to filter divergence in sparsely observed regions.
A hierarchical Bayesian algorithm that uses observations to
produce a spatially- and temporally-varying inflation field has
been developed to address this problem. The algorithm is implemented
in the Data Assimilation Research Testbed and has been applied to
a wide variety of global and regional prediction models. In this
talk, results will be shown for assimilations using a global climate
model (NCAR's Community Atmospheric Model) and the standard
set of operational NWP observations. One month ensemble assimilations
with and without adaptive inflation are compared and contrasted.
The algorithm is successful in producing larger inflation in
regions where dense observations make this necessary. A particular
challenge occurs in areas where different observation types may
have slightly different bias relative to the model.
http:www.image.ucar.edu/DAReS/DART
A24B-04 INVITED
Towards the development of an on-line model error identification system for land surface models
Due to the complexity of potential error sources in land surface models, the accurate specification of model error parameters has emerged as a major challenge in the development of effective land data assimilation systems. While several on-line procedures for estimating model error parameters - based on the statistical analysis of filtering innovations - have been introduced for geophysical models, such procedures have not been widely applied to land surface models. A frequently cited concern is the computation burden of iteratively adjusting model error parameters until theoretical expectations for innovation statistics (e.g. temporally white and normalized variance of one) are met. Classical, closed-form approaches for the on-line identification of linear model error could greatly reduce this computational burden; however their applicably to nonlinear land surface models is unclear. Using a series of synthetic twin experiments and an Ensemble Kalman filter, this paper will present a framework for diagnosing the magnitude of error in hydrologic model forecasts and/or hydrologic remote sensing retrievals. Results will demonstrate the potential of applying classical adaptive filtering approaches (originally derived for purely linear systems) to land surface models. Particular attention will be paid to potential differences between highly nonlinear and chaotic atmospheric models and nonlinear, but ultimately dissipative, land surface model and the implications of these differences on the development of an on-line system for identification of model error parameters. Preliminary real data results (based on the assimilation of remotely-sensed surface soil moisture retrievals into a land surface model forced by satellite-based precipitation) will be used to underscore the potential value of the approach in an operational setting.
A24B-05 INVITED
Estimates of Error of Representation for Data Assimilation
Errors in model estimates of the state of the ocean or atmosphere can be partitioned roughly into three components: the long time and space scale component, possibly with nonzero mean, designated as bias; that part of the error attributable to forcing, boundary or initial conditions that can be described in terms of the model physics, designated as model error and that part of the difference that can be considered as a random process that cannot be represented in terms of the model physics. We designate this last source of error as representation error. Examples are variability of western boundary currents and mesoscale eddies in coarsely resolved ocean models. This last component is an important one in large-scale ocean simulations. Here we describe the process of estimation of the statistics of representation error, and the incorporation of those statistics into practical data assimilation systems.
A24B-06
Bottom Topography Correction by Assimilation of Tsunami Simulation Model and Tide Gauge Data With Particle Filter
We demonstrate the results of applying the sequential data assimilation (SDA) to a tsunami simulation model. A shallow water equations model and tide gauge data are employed in DA. Most of our concerns in DA are paid to validate information on depths of sea bottom. The reason is that bottom topography data sets are erroneous and depths affect propagation speed of tsunamis, which results in inaccurate tsunami forecasts. Because the depths are included in the simulation model as boundary condition, we can modify the depths by putting them into state vector. Specifically, we allow for an error term in the bottom topography and its statistical inference is carried out through DA. The filtering method used in SDA is the particle filter (PF) due to the computational and statistical reasons. The PF is also an ensemble based assimilation procedure, and then it has a similar algorithmic structure with the ensemble Kalman filter (EnKF). However, there exist some different characteristics between them. In this study, we conducted three types of numerical experiment and analysis: twin experiment of bottom topography correction, bottom topography estimation based on real tide gauge data of Okushiri tsunami in 1993. The result of twin experiment shows the effectiveness of our DA. The result of DA to real data suggests that almost all part of Yamato Rises is shallower than the average of available data sets (four data sets at hand). We also discuss the differences among raw data, bottom topography data sets and obtained depths by DA.
A24B-07
Simultaneous Assimilation of Physical and Biological Observations into a 3D Coupled Marine Ecosystem Model Using Joint and Dual Kalman Filtering
Two assimilation systems based on a suboptimal extended Kalman filter have been developed to simultaneously assimilate physical and biochemical data into a complex ecosystem model of the Eastern Mediterranean. The three-dimensional ecosystem model is composed of two on-line coupled sub-models: the Princeton Ocean Model (POM) and the European Regional Seas Ecosystem Model (ERSEM). The filter is a variant of the extended Kalman filter which operates with low-rank error covariance matrices to reduce computational burden. Two different approaches have been considered: the "joint approach" and the "dual approach". In the first approach, one filter is used in which the state vector of the filter is composed of all prognostic variables of POM and ERSEM models. Basically, the numerical models are integrated forward in time to produce the (physical and biochemical) forecasts. The observations are then assimilated jointly to correct all forecast variables using the cross-correlations between all physical and biochemical forecast errors, which simultaneously provides the analyses for the physics and for the ecology. The dual approach consists of two filters, operating separately on the physics and on the ecology. We describe the two assimilation systems and discuss results of assimilation experiments.
A24B-08
Applications of bred vectors in NASA GMAO ocean assimilation system
Bred vectors (BV) are generated for the use of initial ensemble perturbations for NASA GMAO coupled ensemble forecasting system (GCEF) and for the purpose of improving the ensemble prediction of seasonal-to-interannual variability. Currently, four pairs of BVs are generated with different rescaling norms and with one-month rescaling period with GCEF. In this study, we explore the applications and potential impact of the oceanic component of the bred vectors in NASA GMAO oceanic data assimilation system. BVs are applied as a shortcut to provide the structures of flow-dependent background error covariance and used to augment the background error covariance in the assimilation system (the optimal interpolation scheme). In this hybrid assimilation framework, the error correlation is modified to have seasonal and regional-dependent structures. Our preliminary results suggest that BVs have positive impact on the local structures of the corrections for both temperature and salinity fields. Other issues of utilizing the BV structures in the assimilation system will be addressed in the talk.