Roger Daley

NAVDAS: Formulation and Diagnostics

Abstract The Naval Research Laboratory Atmospheric Variational Data Assimilation System (NAVDAS) is a three-dimensional variational data assimilation suite for generating atmospheric state estimates to satisfy a variety of navy needs. These needs range from global initial conditions for navy global prediction models to environmental input into forward-deployed shipboard tactical decision aids. In common with many other U.S. Navy applications, the NAVDAS system has been designed to be robust, flexible, and portable. In particular, it can perform central site global assimilation on massively parallel machines as well as local data assimilation on workstations with the same code. NAVDAS is an observation space algorithm. The preconditioned conjugate gradient method is used as the descent algorithm to minimize the three-dimensional cost function. The number of iterations required to reach convergence is minimized through the use of dual block diagonal preconditioners with Choleski decomposition. Vertical eige...

Estimating Model-Error Covariances for Application to Atmospheric Data Assimilation

Abstract Forecast-error statistics have traditionally been used to investigate model performance and to calculate analysis weights for atmospheric data assimilation. Forecast error has two components: the model error, caused by model imperfections, and the predictability error, which is due to the model generation of instabilities from an imperfectly defined initial state. Traditionally, these two error sources have been difficult to separate. The Kalman filter theory assumes that the model error is additive white (in time) noise, which permits the separation of the model and predictability error. Progress can be made by assuming that the model-error statistics are homogeneous and stationary, an assumption that is more justifiable for the model-error statistics than for the forcast-error statistics. A methodology for estimating the homogeneous, stationary component of the model- error covariance is discussed and tested in a simple data-assimilation system.

Development of NAVDAS-AR: formulation and initial tests of the linear problem

A 4-D implementation of an observation space variational data assimilation system is under development at the Marine Meteorology Division of the Naval Research Laboratory (NRL). The system is an extension of the current US Navy 3-D operational data assimilation system, the NRL Atmospheric Variational Data Assimilation System (NAVDAS). The new system, NAVDAS-AR, where AR stands for accelerated representer, is similar in many respects to the European Centre for Medium-Range Weather Forecasts (ECMWF) 4DVAR system. However, NAVDAS-AR is based on a weak constraint observation space, while the ECMWF system is based on a strong constraint model space. In this paper the formulation of NAVDAS-AR is described in detail and preliminary results with a perfect model assumption and comparisons with the operational NAVDAS are presented.

Singular Vector Calculations with an Analysis Error Variance Metric

Abstract Singular vectors of the navys global forecast model are calculated using an initial norm consistent with an estimate of analysis error variance provided by the Naval Research Laboratorys (NRL) Atmospheric Variational Data Assimilation System (NAVDAS). The variance estimate is based on a decomposition of the block diagonal preconditioner for the conjugate-gradient descent algorithm used in NAVDAS. Because the inverse square root of the operator that defines the variance norm is readily computed, the leading singular vectors are obtained using a standard Lanczos algorithm, as with diagonal norms such as total energy. The resulting singular vectors are consistent with the expected distribution of analysis errors. Compared with singular vectors based on a total energy norm, the variance singular vectors at initial time have less amplitude over well-observed areas, as well as greater amplitude in the middle and upper troposphere. The variance singular vectors are in some ways similar to the full cov...

The Effect of Serially Correlated Observation and Model Error on Atmospheric Data Assimilation

Abstract Observation error statistics are required in most atmospheric data assimilation systems. While observation errors are often assumed to be spatially correlated, serial correlations have received virtually no attention. In this article, the effect of serially correlated observation error is examined in the context of Kalman filter theory. It is shown that for spatially uncorrelated observation errors, serial correlations will only be detrimental for rapid-sampling instruments or low-flow regimes. In standard Kalman filter theory, it is assumed that the model error is not serially correlated. This assumption has been questioned in the past. In this article, certain types of serially correlated model errors are shown to have a serious detrimental effect on atmospheric data assimilation. It is also suggested that certain performance diagnostics may be capable of detecting serial correlations.

The Analysis of Synoptic Scale Divergence by a Statistical Interpolation Procedure

Abstract The direct analysis of the divergent component of the wind has traditionally been difficult. The higher quality datasets now available offer an opportunity to produce meaningful analyses of the divergent wind. The present work considers how the statistical interpolation objective analysis formalism can be generalized to improve the analysis of the divergent wind. The formulation of the prediction error correlation is modified to be weakly divergent instead of completely nondivergent. This formulation is tested on several lower-order analysis systems. The spectral characteristics of the analysis operators are determined and a simple case study is performed with real data. The results suggest that the present formulation is likely to improve the analysis of the divergent wind field.

The Lagged Innovation Covariance: A Performance Diagnostic for Atmospheric Data Assimilation

Abstract The goal of atmospheric data assimilation is to determine the most accurate representation of the signal from the available observations. The optimality of a data assimilation scheme measures how much information has been extracted from the observations. It is possible to quantify the optimality of the scheme using on-line performance diagnostics. Such a diagnostic is the proposed lagged innovation covariance procedure. This diagnostic has been developed from Kalman filter theory. Its characteristics are examined using a simple scalar model, a univariate one-dimensional linear advection model, and a linear quasigeostrophic model. The model results are compared with actual lagged innovation covariances derived from the innovation sequences of an operational data assimilation system.

Estimates of Global Analysis Error from the Global Weather Experiment Observational Network

Abstract Objective analysis provides a regular representation of the atmospheric state for numerical forecasting and climate studies. The present observing system has numerous deficiencies which present analysis techniques can only partly remedy. Consequently, objective analyses contain error—referred to here as E0. The present experiment provides estimates of E0. The experiment is based on the OSSE (Observation System Simulation Experiment) concept. Time mean and transient errors are calculated and displayed as a function of altitude, latitude, longitude and also spectrally. The experimental results show substantial analysis errors south of 60°S and in the stratosphere. For some variables, the relative error below 850 mb and in the tropics is also large.

A Baroclinic Finite-Element Model for Regional Forecasting with the Primitive Equations

Abstract A baroclinic primitive equations model is formulated using a variable resolution finite-element discretization in all three space dimensions. The horizontal domain over which the model is integrated is a rectangle on a polar stereographic projection which approximately covers the Northern Hemisphere. A wall boundary condition is imposed at this rectangular boundary giving rise to a well-posed initial boundary value problem. The mesh is specified to be of Cartesian product form with arbitrary non-uniform spacing. By choosing the mesh to be uniformly high over an area of interest and degrading smoothly away from this area, it is possible to use the model to produce a high-resolution local forecast for a limited time period. This choice of mesh avoids the noise problems of a so-called nested grid. A semi-implicit time discretization is used for efficiency. Some results for forecast periods of 24 and 48 h are also given to demonstrate its viability in an operational context.

Estimating the Wind Field from Chemical Constituent Observations: Experiments with a One-Dimensional Extended Kalman Filter

Abstract Modern data assimilation algorithms such as the four-dimensional variational algorithm or the extended Kalman filter (EKF) can, in theory, estimate the wind field from chemical constituent observations. This seems to be possible because of the wind-constituent coupling in the chemical transport equation. This paper examines this possibility by applying an EKF to the one-dimensional constituent transport equation and to a prognostic, linear wind model. Generally, both transport and wind models are assumed to be perfect. Tangent linear (TLM) and adjoint models for the chemical transport model are developed and examined. A set of preliminary experiments was performed assuming perfect winds and examining the propagation of constituent errors. For this case, it was shown that the analysis of the constituent in zones of strong convergence can only be determined from nearby observations inside the zone; but the situation is much more favorable in divergent zones. This was shown to be consistent with obs...