ALBERT

Description: A data assimilation system (DAS) is described for global atmospheric reanalysis from 0- to 100-km altitude. We apply it to the 2014 austral winter of the Deep Propagating Gravity Wave Experiment (DEEPWAVE), an international field campaign focused on gravity wave dynamics from 0 to 100 km, where an absence of reanalysis above 60 km inhibits research. Four experiments were performed from April to September 2014 and assessed for reanalysis skill above 50 km. A four-dimensional variational (4DVAR) run specified initial background error covariances statically. A hybrid-4DVAR (HYBRID) run formed background error covariances from an 80-member forecast ensemble blended with a static estimate. Each configuration was run at low and high horizontal resolution. In addition to operational observations below 50 km, each experiment assimilated 105 observations of the mesosphere and lower thermosphere (MLT) every 6 h. While all MLT reanalyses show skill relative to independent wind and temperature measurements, HYBRID outperforms 4DVAR. MLT fields at 1-h resolution (6-h analysis and 1–5-h forecasts) outperform 6-h analysis alone due to a migrating semidiurnal (SW2) tide that dominates MLT dynamics and is temporally aliased in 6-h time series. MLT reanalyses reproduce observed SW2 winds and temperatures, including phase structures and 10–15-day amplitude vacillations. The 0–100-km reanalyses reveal quasi-stationary planetary waves splitting the stratopause jet in July over New Zealand, decaying from 50 to 80 km then reintensifying above 80 km, most likely via MLT forcing due to zonal asymmetries in stratospheric gravity wave filtering.

Description: The local ensemble tangent linear model (LETLM) provides an alternative method for creating the tangent linear model (TLM) and adjoint of a nonlinear model that promises to be easier to maintain and more computationally scalable than earlier methods. In this paper, we compare the ability of the LETLM to predict the difference between two nonlinear trajectories of the Navy’s global weather prediction model at low resolution (2.5° at the equator) with that of the TLM currently used in the Navy’s four-dimensional variational (4DVar) data assimilation scheme. When compared to the pair of nonlinear trajectories, the traditional TLM and the LETLM have improved skill relative to persistence everywhere in the atmosphere, except for temperature in the planetary boundary layer. In addition, the LETLM was, on average, more accurate than the traditional TLM (error reductions of about 20% in the troposphere and 10% overall). Sensitivity studies showed that the LETLM was most sensitive to the number of ensemble members, with the performance gradually improving with increased ensemble size up to the maximum size attempted (400). Inclusion of physics in the LETLM ensemble leads to a significantly improved representation of the boundary layer winds (error reductions of up to 50%), in addition to improved winds and temperature in the free troposphere and in the upper stratosphere/lower mesosphere. The computational cost of the LETLM was dominated by the cost of ensemble propagation. However, the LETLM can be precomputed before the 4DVar data assimilation algorithm is executed, leading to a significant computational advantage.

Description: An ensemble-based tangent linear model (TLM) is described and tested in data assimilation experiments using a global shallow-water model (SWM). A hybrid variational data assimilation system was developed with a 4D variational (4DVAR) solver that could be run either with a conventional TLM or a local ensemble TLM (LETLM) that propagates analysis corrections using only ensemble statistics. An offline ensemble Kalman filter (EnKF) is used to generate and maintain the ensemble. The LETLM uses data within a local influence volume, similar to the local ensemble transform Kalman filter, to linearly propagate the state variables at the central grid point. After tuning the LETLM with offline 6-h forecasts of analysis corrections, cycling experiments were performed that assimilated randomly located SWM height observations, based on a truth run with forced bottom topography. The performance using the LETLM is similar to that of the conventional TLM, suggesting that a well-constructed LETLM could free 4D variational methods from dependence on conventional TLMs. This is a first demonstration of the LETLM application within a context of a hybrid-4DVAR system applied to a complex two-dimensional fluid dynamics problem. Sensitivity tests are included that examine LETLM dependence on several factors including length of cycling window, size of analysis correction, spread of initial ensemble perturbations, ensemble size, and model error. LETLM errors are shown to increase linearly with correction size in the linear regime, while TLM errors increase quadratically. As nonlinearity (or forecast model error) increases, the two schemes asymptote to the same solution.

Description: A regionally enhanced global (REG) data assimilation (DA) method is proposed. The technique blends high-resolution model information from a single or multiple limited-area model domains with global model and observational information to create a regionally enhanced analysis of the global atmospheric state. This single analysis provides initial conditions for both the global and limited-area model forecasts. The potential benefits of the approach for operational data assimilation are (i) reduced development cost, (ii) reduced overall computational cost, (iii) improved limited-area forecast performance from the use of global information about the atmospheric flow, and (iv) improved global forecast performance from the use of more accurate model information in the limited-area domains. The method is tested by an implementation on the U.S. Navy’s four-dimensional variational global data assimilation system and global and limited-area numerical weather prediction models. The results of the monthlong forecast experiments suggest that the REG DA approach has the potential to deliver the desired benefits.

Description: Because of imperfections in ensemble data assimilation schemes, one cannot assume that the ensemble-derived covariance matrix is equal to the true error covariance matrix. Here, we describe a simple and intuitively compelling method to fit calibration functions of the ensemble sample variance to the mean of the distribution of true error variances, given an ensemble estimate. We demonstrate that the use of such calibration functions is consistent with theory showing that, when sampling error in the prior variance estimate is considered, the gain that minimizes the posterior error variance uses the expected true prior variance, given an ensemble sample variance. Once the calibration function has been fitted, it can be combined with ensemble-based and climatologically based error correlation information to obtain a generalized hybrid error covariance model. When the calibration function is chosen to be a linear function of the ensemble variance, the generalized hybrid error covariance model is the widely used linear hybrid consisting of a weighted sum of a climatological and an ensemble-based forecast error covariance matrix. However, when the calibration function is chosen to be, say, a cubic function of the ensemble sample variance, the generalized hybrid error covariance model is a nonlinear function of the ensemble estimate. We consider idealized univariate data assimilation and multivariate cycling ensemble data assimilation to demonstrate that the generalized hybrid error covariance model closely approximates the optimal weights found through computationally expensive tuning in the linear case and, in the nonlinear case, outperforms any plausible linear model.

Description: An ensemble-based linearized forecast model has been developed for data assimilation applications for numerical weather prediction. Previous studies applied this local ensemble tangent linear model (LETLM) to various models, from simple one-dimensional models to a low-resolution (~2.5°) version of the Navy Global Environmental Model (NAVGEM) atmospheric forecast model. This paper applies the LETLM to NAVGEM at higher resolution (~1°), which required overcoming challenges including 1) balancing the computational stencil size with the ensemble size, and 2) propagating fast-moving gravity modes in the upper atmosphere. The first challenge is addressed by introducing a modified local influence volume, introducing computations on a thin grid, and using smaller time steps. The second challenge is addressed by applying nonlinear normal mode initialization, which damps spurious fast-moving modes and improves the LETLM errors above ~100 hPa. Compared to a semi-Lagrangian tangent linear model (TLM), the LETLM has superior skill in the lower troposphere (below 700 hPa), which is attributed to better representation of moist physics in the LETLM. The LETLM skill slightly lags in the upper troposphere and stratosphere (700–2 hPa), which is attributed to nonlocal aspects of the TLM including spectral operators converting from winds to vorticity and divergence. Several ways forward are suggested, including integrating the LETLM in a hybrid 4D variational solver for a realistic atmosphere, combining a physics LETLM with a conventional TLM for the dynamics, and separating the LETLM into a sequence of local and nonlocal operators.

Description: Extraction of wind and temperature information from stratospheric ozone assimilation is examined within the context of the Navy Global Environmental Model (NAVGEM) hybrid 4-D variational assimilation (4D-Var) data assimilation (DA) system. Ozone can improve the wind and temperature through two different DA mechanisms: (1) through the “flow-of-the-day” ensemble background error covariance that is blended together with the static background error covariance and (2) via the ozone continuity equation in the tangent linear model and adjoint used for minimizing the cost function. All experiments assimilate actual conventional data in order to maintain a similar realistic troposphere. In the stratosphere, the experiments assimilate simulated ozone and/or radiance observations in various combinations. The simulated observations are constructed for a case study based on a 16-day cycling truth experiment (TE), which is an analysis with no stratospheric observations. The impact of ozone on the analysis is evaluated by comparing the experiments to the TE for the last 6 days, allowing for a 10-day spin-up. Ozone assimilation benefits the wind and temperature when data are of sufficient quality and frequency. For example, assimilation of perfect (no applied error) global hourly ozone data constrains the stratospheric wind and temperature to within ∼ 2 m s−1 and ∼ 1 K. This demonstrates that there is dynamical information in the ozone distribution that can potentially be used to improve the stratosphere. This is particularly important for the tropics, where radiance observations have difficulty constraining wind due to breakdown of geostrophic balance. Global ozone assimilation provides the largest benefit when the hybrid blending coefficient is an intermediate value (0.5 was used in this study), rather than 0.0 (no ensemble background error covariance) or 1.0 (no static background error covariance), which is consistent with other hybrid DA studies. When perfect global ozone is assimilated in addition to radiance observations, wind and temperature error decreases of up to ∼ 3 m s−1 and ∼ 1 K occur in the tropical upper stratosphere. Assimilation of noisy global ozone (2 % errors applied) results in error reductions of ∼ 1 m s−1 and ∼ 0.5 K in the tropics and slightly increased temperature errors in the Northern Hemisphere polar region. Reduction of the ozone sampling frequency also reduces the benefit of ozone throughout the stratosphere, with noisy polar-orbiting data having only minor impacts on wind and temperature when assimilated with radiances. An examination of ensemble cross-correlations between ozone and other variables shows that a single ozone observation behaves like a potential vorticity (PV) “charge”, or a monopole of PV, with rotation about a vertical axis and vertically oriented temperature dipole. Further understanding of this relationship may help in designing observation systems that would optimize the impact of ozone on the dynamics.

Description: The effect on weather forecast performance of incorporating ensemble covariances into the initial covariance model of the four-dimensional variational data assimilation (4D-Var) Naval Research Laboratory Atmospheric Variational Data Assimilation System-Accelerated Representer (NAVDAS-AR) is investigated. This NAVDAS-AR-hybrid scheme linearly combines the static NAVDAS-AR initial background error covariance with a covariance derived from an 80-member flow-dependent ensemble. The ensemble members are generated using the ensemble transform technique with a (three-dimensional variational data assimilation) 3D-Var-based estimate of analysis error variance. The ensemble covariances are localized using an efficient algorithm enabled via a separable formulation of the localization matrix. The authors describe the development and testing of this scheme, which allows for assimilation experiments using differing linear combinations of the static and flow-dependent background error covariances. The tests are performed for two months of summer and two months of winter using operational model resolution and the operational observational dataset, which is dominated by satellite observations. Results show that the hybrid mode data assimilation scheme significantly reduces the forecast error across a wide range of variables and regions. The improvements were particularly pronounced for tropical winds. The verification against radiosondes showed a greater than 0.5% reduction in vector wind RMS differences in areas of statistical significance. The verification against self-analysis showed a greater than 1% reduction from verifying against analyses between 2- and 5-day lead time at all eight vertical levels examined in areas of statistical significance. Using the Navy's summary of verification results, the Navy Operational Global Atmospheric Prediction System (NOGAPS) scorecard, the improvements resulted in a score (+1) that justifies a major system upgrade.