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Data assimilation schemes blend observational data, with limited coverage, with a short term forecast to produce an analysis, which is meant to be the best estimate of the current state of the atmosphere. Appropriately specifying observation error statistics is necessary to obtain an optimal analysis. Observation error can originate from instrument error as well as the error of representation. While representation error is most commonly associated with unresolved scales and processes, this term is often considered to include contributions from pre-processing or quality control and errors associated with the observation operator. With a focus on practical operational implementation, this chapter aims to define the components of observation error, discusses their sources and characteristics, and provides an overview of current methods for estimating observation error statistics. We highlight the implicit assumptions of these methods, as well as their shortcomings. We will detail current operational practice for diagnosing observation error and accounting for correlated observation error. Finally, we provide a practical methodology for using these diagnostics, as well as the associated innovation-based observation impact, to optimize the assimilation of meteor radar observations in the upper atmosphere.

Coupled data assimilation (DA) provides a consistent framework for assimilating satellite observations that are sensitive to several components of the Earth system. In this paper, we focus on low-peaking infrared satellite channels that are sensitive to the lower atmosphere and Earth surface temperature (EST) over both ocean and land. Our atmospheric hybrid-4DVAR system [the Navy Global Environmental Model (NAVGEM)] is extended to include the following: 1) variability in the sea surface temperature (both diurnal variability and climatological perturbations to the ensemble members), 2) the coupled Jacobians of the radiative transfer model for the infrared sensors, and 3) the coupled covariances between the EST and the atmosphere. Our coupling approach is found to improve forecast accuracy and to provide corrections to the EST that are in balance with the atmospheric analysis. The largest impact of the coupling is found on near-surface atmospheric temperature and humidity in the tropics, but the impact extends all the way to the stratosphere. The role of each coupling element on the performance of the global atmospheric circulation model is investigated. Inclusion of variability in the sea surface temperature has the strongest positive impact on the forecast quality. Additional inclusion of the coupled Jacobian and ensemble-based coupled covariances led to further improvements in scores and to modification of the corrections to the ocean boundary layer. Coupled DA had significant impact on latent and sensible heat fluxes over land, locations of western boundary currents, and along the ice edge.

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.

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.

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.

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.

The lower atmosphere contributes significantly to the day-to-day variability of the ionosphere, especially during solar minimum conditions. Ionosphere/atmosphere model simulations that incorporate meteorology from data assimilation analysis products can be critically important for elucidating the physical processes that have substantial impact on ionospheric weather. In this study, the NCAR Whole Atmosphere Community Climate Model, extended version with specified dynamics (SD-WACCM-X) is coupled with an ionospheric model (Sami3 is Another Model of the Ionosphere) to study day-to-day variability in the ionosphere during January 2010. Lower atmospheric weather patterns are introduced into the SAMI3/SD-WACCM-X simulations using the 6-h Navy Operational Global Atmospheric Prediction System-Advanced Level Physics High Altitude (NOGAPS-ALPHA) data assimilation products. The same time period is simulated using the new atmospheric forecast model, the High Altitude Navy Global Environmental Model (HA-NAVGEM), a hybrid 4D-Var prototype data assimilation with the ability to produce meteorological fields at a 3-h cadence. Our study shows that forcing SD-WACCM-X with HA-NAVGEM better resolves the semidiurnal tides and introduces more day-to-day variability into the ionosphere than forcing with NOGAPS-ALPHA. The SAMI3/SD-WACCM-X/HA-NAVGEM simulation also more accurately captures the longitudinal variability associated with non-migrating tides in the equatorial ionization anomaly (EIA) region as compared to total electron content (TEC) maps derived from GPS data. Both the TEC maps and the SAMI3/SD-WACCM-X/HA-NAVGEM simulation show an enhancement in TEC over South America during 17–21 January 2010, which coincides with the commencement of a stratospheric warming event on 19 January 2010. Analysis of the SAMI3/SD-WACCM-X/HA-NAVGEM simulations indicates non-migrating tides (including DW4, DE2 and SW5) played a role during 17–21 January in shifting the phase of the wave-3 pattern in the ionosphere on these days. Constructive interference of wave-3 and wave-4 patterns in the E × B drifts contributed to the enhanced TEC in the South American longitude sector. The results of the study highlight the importance of high fidelity meteorology in understanding the day-to-day variability of the ionosphere.

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.

Data assimilation schemes combine observational data with a short-term model forecast to produce an analysis. However, many characteristics of the atmospheric states described by the observations and the model differ. Observations often measure a higher-resolution state than coarse-resolution model grids can describe. Hence, the observations may measure aspects of gradients or unresolved eddies that are poorly resolved by the filtered version of reality represented by the model. This inconsistency, known as observation representation error, must be accounted for in data assimilation schemes. In this paper the ability of the ensemble to predict the variance of the observation error of representation is explored, arguing that the portion of representation error being detected by the ensemble variance is that portion correlated to the smoothed features that the coarse-resolution forecast model is able to predict. This predictive relationship is explored using differences between model states and their spectrally truncated form, as well as commonly used statistical methods to estimate observation error variances. It is demonstrated that the ensemble variance is a useful predictor of the observation error variance of representation and that it could be used to account for flow dependence in the observation error covariance matrix.

A leading Data Assimilation (DA) technique in meteorology is 4D-Var which relies on the Tangent Linear Model (TLM) of the nonlinear model and its adjoint. The difficulty of building and maintaining traditional TLMs and adjoints of coupled ocean–wave–atmosphere–etc. models is daunting. On the other hand, coupled model ensemble forecasts are readily available. Here, we show how an ensemble forecast can be used to construct an accurate Local Ensemble TLM (LETLM) and adjoint of the entire coupled system. The method features a local influence region containing all the variables that could possibly influence the time evolution of some target variable(s) near the centre of the region. We prove that high accuracy is guaranteed provided that (i) the ensemble perturbations are governed by linear dynamics, and (ii) the number of ensemble members exceeds the number of variables in the influence region. The approach is illustrated in a simple coupled model. This idealized coupled model has some realistic features including reasonable predictability limits in the upper atmosphere, lower atmosphere, upper ocean and lower ocean of 10, 96, 160 and 335 days, respectively. In addition, the length-scale of eddies in the ocean is about one fifth of those in the atmosphere. The easy manner in which the adjoint is obtained from the LETLM is also described and illustrated by demonstrating how the LETLM adjoint predicts the high sensitivity of oceanic boundary-layer evolution to changes in the atmosphere. Finally, the feasibility of LETLMs for 4D-Var is demonstrated. Specifically, a case is considered with a 5-day data assimilation window in which nonlinear terms play a significant role in the evolution of forecast error; it is shown that the posterior mode delivered by 4D-Var with an LETLM, its adjoint and ten outer loops approximately recovers the true state in spite of a spatially sparse observational network.

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.

Recent studies have shown that day-to-day variability in thermospheric winds (100–300 km altitude) driven by meteorological variability from below affects ionospheric E and lower F regions, highlighting the need for accurate, continuous specification of day-to-day variability throughout the entire atmosphere for geospace weather prediction systems. To better understand the nature of forcing from below on the coupled thermosphere/ionosphere system, this study uses the Specified Dynamics Whole Atmosphere Community Climate Model eXtended (SD-WACCM-X) to quantify how the meteorology of the underlying atmosphere impacts the thermosphere. For this study, global meteorological specifications are produced by a high-altitude version of the Navy Global Environmental Model (NAVGEM-HA), which assimilates standard meteorological observations from the surface through the lower atmosphere, and satellite-based observations of temperature and constituents in middle atmosphere (MA) region 10–90 km altitude. Two SD-WACCM-X simulations for the January–February 2013 period are performed using NAVGEM-HA specifications produced with and without assimilation of MA observations. Results show that the availability of MA observations strongly constrains the modeled spectrum of planetary scale waves (zonal wavenumbers 1–3) in the thermosphere. Specifically, the amplitudes of the solar non-migrating DE3 tide and westward quasi-two day wave (Q2DW) are nearly twice as large in SD-WACCM-X simulations without MA observations compared to simulations with MA observations. Model diagnostics show that these differences are related to non-linear wave-wave interactions impacting the DE3 mode and to sources of baroclinic/barotropic instability near the summer mesospheric easterly jet impacting the Q2DW. This study highlights the importance of MA observations for constraining whole atmosphere models needed for next-generation space weather prediction capabilities.

In a strongly coupled data assimilation (DA), a cross-fluid covariance is specified that allows measurements from a coupled fluid (e.g., atmosphere) to directly impact analysis increments in a target fluid (e.g., ocean). The exhaustive solution to this coupled DA problem calls for a covariance where all available measurements can influence all grid points in all fluids. Solution of such a large algebraic problem is computationally expensive, often calls for a substantial rewrite of existing fluid-specific DA systems, and, as shown in this paper, can be avoided. The proposed interface solver assumes that covariances between coupled measurements and target fluid are often close to null (e.g., between stratospheric observations and the deep ocean within a 6-h forecast cycle). In the interface solver, two separate DA solvers are run in parallel: one that produces an analysis solution in the atmosphere, and one in the ocean. Each system uses a coupled observation vector where in addition to resident measurements in the target fluid it also includes nonresident measurements in the coupled fluid that are likely to have significant influence on the analysis in the target fluid (interface measurements). An ensemble-based method is employed and a localization function for coupled ensembles is proposed. Using a coupled model for the Mediterranean Sea (in a twin setting), it is demonstrated that (i) the solution of the interface solver converges to the exhaustive solution and (ii) that in presence of poorly known error covariances, the interface solver can be configured to produce a more accurate solution than an exhaustive solver.

The wind extraction due to assimilation of stratospheric trace gas (tracer) data is examined using a 4D-Var (four-dimensional variational) data assimilation system based on the shallow water equations coupled to the tracer continuity equation. The procedure is outlined as follows. First, a nature run is created, simulating middle stratospheric winter conditions. Second, ozone (O3), nitrous oxide (N2O), and water vapor (H2O) (treated in this study as passive tracers) are initialized using Aura Microwave Limb Sounder (MLS) mixing ratios at 850 K potential temperature and are advected by the nature run winds. Third, the initial dynamical conditions are perturbed by using a 6 h offset. Fourth, simulated hourly tracer observations on the full model grid are assimilated with a 4D-Var system in which tracer and winds are coupled via the adjoint of the tracer continuity equation. Multiple assimilation experiments are performed by varying the amount of random observation error added to the simulated measurements. Finally, the wind extraction potential (WEP) is calculated as the reduction of the vector wind root mean square error (RMSE) relative to the maximum possible reduction. For a single 6 h assimilation cycle with the smallest observation error, WEP values are ~60% for all three tracers, while 10-day multi-cycle simulations result in WEP of ~90%, wind errors of ~0.3 m s−1, and height errors of ~13 m. There is therefore sufficient information in the tracer fields to almost completely constrain the dynamics, even without direct assimilation of dynamical information. When realistic observation error is added (based on MLS precisions at 10 hPa), the WEP after 10 days is 90% for O3, 87% for N2O, and 72% for H2O. O3 and N2O provide more wind information than H2O due to stronger background gradients relative to the MLS precisions. The RMSE for wind reach a minimum level of ~0.3–0.9 m s−1 for the MLS precisions, suggesting a limit to which realistic tracers could constrain the winds, given complete global cover age. With higher observation noise levels, the WEP values decrease, but the impact on the winds is still positive up to noise levels of 100% (relative to the global mean value) when compared to the case of no data assimilation.

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.

Time-dependent variational data assimilation allows the possibility of extracting wind information from observations of ozone or other trace gases. Since trace gas observations are not available at sufficient resolution for deriving feature-track winds, they must be combined with model background information to produce an analysis. If done with time-dependent variational assimilation, wind information may be extracted via the adjoint of the linearized tracer continuity equation. This paper presents idealized experiments that illustrate the mechanics of tracer–wind extraction and demonstrate some of the limitations of this procedure. We first examine tracer–wind extraction using a simple one-dimensional advection equation. The analytic solution for a single trace gas observation is discussed along with numerical solutions for multiple observations. The limitations of tracer–wind extraction are then explored using highly idealized ozone experiments performed with a development version of the Navy Global Environmental Model (NAVGEM) in which globally distributed hourly stratospheric ozone profiles are assimilated in a single 6 h update cycle in January 2009. Starting with perfect background ozone conditions, but imperfect dynamical conditions, ozone errors develop over the 6 h background window. Wind increments are introduced in the analysis in order to reduce the differences between background ozone and ozone observations. For "perfect" observations (unbiased and no random error), this results in root-mean-square (RMS) vector wind error reductions of up to ~4 m s−1 in the winter hemisphere and tropics. Wind extraction is more difficult in the summer hemisphere due to weak ozone gradients and smaller background wind errors. The limitations of wind extraction are also explored for observations with imposed random errors and for limited sampling patterns. As expected, the amount of wind information extracted degrades as observation errors or data voids increase. In the case of poorly specified observation error covariances, assimilation of ozone data with imposed errors may result in increased RMS wind error, since the assimilation is constrained too tightly to the noisy observations.

We present a study of horizontal winds in the mesosphere and lower thermosphere (MLT) during the boreal winters of 2009–2010 and 2012–2013 produced with a new high-altitude numerical weather prediction (NWP) system. This system is based on a modified version of the Navy Global Environmental Model (NAVGEM) with an extended vertical domain up to ∼116 km altitude coupled with a hybrid four-dimensional variational (4DVAR) data assimilation system that assimilates both standard operational meteorological observations in the troposphere and satellite-based observations of temperature, ozone and water vapor in the stratosphere and mesosphere. NAVGEM-based MLT analyzed winds are validated using independent meteor radar wind observations from nine different sites ranging from 69°N–67°S latitude. Time-averaged NAVGEM zonal and meridional wind profiles between 75 and 95 km altitude show good qualitative and quantitative agreement with corresponding meteor radar wind profiles. Wavelet analysis finds that the 3-hourly NAVGEM and 1-hourly radar winds both exhibit semi-diurnal, diurnal, and quasi-diurnal variations whose vertical profiles of amplitude and phase are also in good agreement. Wavelet analysis also reveals common time-frequency behavior in both NAVGEM and radar winds throughout the Northern extratropics around the times of major stratospheric sudden warmings (SSWs) in January 2010 and January 2013, with a reduction in semi-diurnal amplitudes beginning around the time of a mesospheric wind reversal at 60°N that precedes the SSW, followed by an amplification of semi-diurnal amplitudes that peaks 10–14 days following the onset of the mesospheric wind reversal. The initial results presented in this study demonstrate that the wind analyses produced by the high-altitude NAVGEM system accurately capture key features in the observed MLT winds during these two boreal winter periods. © 2016. This is the authors’ accepted and refereed manuscript to the article. Locked until 24.12.2018 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Wind extraction from stratospheric ozone (O3) assimilation is examined using a hybrid ensemble 4-D variational assimilation (4DVar) shallow water model (SWM) system coupled to the tracer advection equation. Stratospheric radiance observations are simulated using global observations of the SWM fluid height (Z), while O3 observations represent sampling by a typical polar-orbiting satellite. Four ensemble sizes were examined (25, 50, 100, and 1518 members), with the largest ensemble equal to the number of dynamical state variables. The optimal length scale for ensemble localization was found by tuning an ensemble Kalman filter (EnKF). This scale was then used for localizing the ensemble covariances that were blended with conventional covariances in the hybrid 4DVar experiments. Both optimal length scale and optimal blending coefficient increase with ensemble size, with optimal blending coefficients varying from 0.2–0.5 for small ensembles to 0.5–1.0 for large ensembles. The hybrid system outperforms conventional 4DVar for all ensemble sizes, while for large ensembles the hybrid produces similar results to the offline EnKF. Assimilating O3 in addition to Z benefits the winds in the hybrid system, with the fractional improvement in global vector wind increasing from ∼ 35 % with 25 and 50 members to ∼ 50 % with 1518 members. For the smallest ensembles (25 and 50 members), the hybrid 4DVar assimilation improves the zonal wind analysis over conventional 4DVar in the Northern Hemisphere (winter-like) region and also at the Equator, where Z observations alone have difficulty constraining winds due to lack of geostrophy. For larger ensembles (100 and 1518 members), the hybrid system results in both zonal and meridional wind error reductions, relative to 4DVar, across the globe.

This paper evaluates a strategy for the assimilation of satellite radiance observations with the local ensemble transform Kalman filter (LETKF) data assimilation scheme. The assimilation strategy includes a mechanism to select the radiance observations that are assimilated at a given grid point and an ensemble-based observation bias-correction technique. Numerical experiments are carried out with a reduced (T62L28) resolution version of the model component of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS). The observations used for the evaluation of the assimilation strategy are AMSU-A level 1B brightness temperature data from the Earth Observing System (EOS) Aqua spacecraft. The assimilation of these observations, in addition to all operationally assimilated nonradiance observations, leads to a statistically significant improvement of both the temperature and wind analysis in the Southern Hemisphere. This result suggests that the LETKF, combined with the proposed data assimilation strategy for the assimilation of satellite radiance observations, can efficiently extract information from radiance observations.

In this paper, the spatiotemporally changing nature of predictability is studied in a reduced-resolution version of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS), a state-of-the-art numerical weather prediction model. Atmospheric predictability is assessed in the perfect model scenario for which forecast uncertainties are entirely due to uncertainties in the estimates of the initial states. Uncertain initial conditions (analyses) are obtained by assimilating simulated noisy vertical soundings of the “true” atmospheric states with the local ensemble Kalman filter (LEKF) data assimilation scheme. This data assimilation scheme provides an ensemble of initial conditions. The ensemble mean defines the initial condition of 5-day deterministic model forecasts, while the time-evolved members of the ensemble provide an estimate of the evolving forecast uncertainties. The observations are randomly distributed in space to ensure that the geographical distribution of the analysis and forecast errors reflect predictability limits due to the model dynamics and are not affected by inhomogeneities of the observational coverage. Analysis and forecast error statistics are calculated for the deterministic forecasts. It is found that short-term forecast errors tend to grow exponentially in the extratropics and linearly in the Tropics. The behavior of the ensemble is explained by using the ensemble dimension (E dimension), a spatiotemporally evolving measure of the evenness of the distribution of the variance between the principal components of the ensemble-based forecast error covariance matrix. It is shown that in the extratropics the largest forecast errors occur for the smallest E dimensions. Since a low value of the E dimension guarantees that the ensemble can capture a large portion of the forecast error, the larger the forecast error the more certain that the ensemble can fully capture the forecast error. In particular, in regions of low E dimension, ensemble averaging is an efficient error filter and the ensemble spread provides an accurate prediction of the upper bound of the error in the ensemble-mean forecast.

The feasibility of extracting wind information from stratospheric ozone observations is tested using ensemble Kalman filter (EnKF) data assimilation (DA) and a global shallow water model that includes advection of an ozone-like tracer. Simulated observations are created from a truth run (TR) that resembles the Northern Hemisphere winter stratosphere with a polar vortex disturbed by planetary-scale wave forcing. Ozone observations mimic sampling of a polar-orbiting satellite, while geopotential height observations are randomly placed in space and time. EnKF experiments are performed assimilating ozone, height, or both, over a 10-day period. The DA is also implemented using two different pairs of flow variables: zonal and meridional wind (EnKF-uv) and stream function and velocity potential (EnKF-ψχ). Each experiment is tuned for optimal localization length, while the ensemble spread is adaptively inflated using the TR. The experiments are evaluated using the maximum wind extraction potential (WEP). Ozone only assimilation improves winds (WEP = 46% for EnKF-uv, and 58% for EnKF-ψχ), but suffers from spurious gravity wave generation. Application of nonlinear normal mode initialization (NMI) greatly reduces the unwanted imbalance and increases the WEP for EnKF-uv (84%) and EnKF-ψχ (81%). Assimilation of only height observations also improved the winds (WEP = 60% for EnKF-uv, and 69% for EnKF-ψχ), with much less imbalance compared to the ozone experiment. The assimilation of both height and ozone performed the best, with WEP increasing to ~87% (~90% with NMI) for both EnKF-uv and EnKF-ψχ, demonstrating that wind extraction from ozone assimilation can be beneficial even in a data-rich environment. Ozone assimilation particularly improves the tropical winds, which are not well constrained by height observations due to lack of geostrophy.

The wind extraction due to assimilation of trace gas (tracer) data is examined using a 4D-Var data assimilation system based on the shallow water equations coupled to the tracer continuity equation. The procedure is outlined as follows. First, a Nature Run is created, simulating middle stratospheric winter conditions. Second, ozone (O3), nitrous oxide (N2O), and water vapor (H2O) (treated in this study as passive tracers) are initialized using Microwave Limb Sounder (MLS) mixing ratios at 850 K potential temperature and advected by the Nature Run winds. Third, the initial dynamical conditions are perturbed by using a 6 h offset. Fourth, observations based on the simulated tracer data are then assimilated with a 4D-Var system in which the tracer and winds are coupled via the adjoint of the tracer continuity equation. Finally, the wind extraction potential (WEP) is calculated as the reduction of the Root Mean Square (RMS) vector wind error due to tracer assimilation relative to the total possible reduction from the initial perturbed conditions. For a single 6 h assimilation cycle of "perfect" tracer (unbiased and no imposed random errors), WEP values are 70% for O3, 49% for N2O and 16% for H2O. O3 and N2O provide more wind information than H2O due to stronger background gradients relative to the tracer precisions. 10 day multi-cycle simulations with "perfect" tracer result in WEP of 98% for O3, 97% for N2O, and 90% for H2O. There is therefore sufficient information in these fields to nearly completely specify the dynamics, even without assimilation of dynamical information. For assimilation of tracer observations with realistic random noise (based on MLS precision at 10 hPa), the WEP after 10 days decreases to 57% for O3, 42% for N2O, and 28% for H2O. The root-mean-square (RMS) wind errors level out at ~ 1–2 m s−1 for these runs, suggesting a limit to which realistic tracers could constrain the winds, given complete global coverage. With higher observation noise levels, the WEP values decrease further, with negative WEP occurring in cases of very large errors for H2O, indicating that assimilation of very noisy observations may worsen the wind fields.

Time-dependent variational data assimilation allows the possibility of extracting wind information from observations of long-lived trace gases. Since trace gas observations are not available at sufficient resolution for deriving feature-track winds, they must be combined with model background information to produce an analysis. If done with time-dependent variational assimilation, wind information may be extracted via the adjoint of the linearized tracer continuity equation. This paper presents idealized experiments that illustrate the mechanics of tracer-wind extraction and demonstrate some of the limitations of this procedure. We first examine tracer-wind extraction using a simple one-dimensional advection equation. The analytic solution for a single trace gas observation is discussed along with numerical solutions for multiple observations. The limitations of tracer-wind extraction are then explored using highly idealized ozone experiments performed with a development version of the Navy Global Environmental Model (NAVGEM) in which stratospheric globally-distributed hourly stratospheric ozone profiles are assimilated in a single 6-h update cycle in January 2009. Starting with perfect background ozone conditions, but imperfect dynamical conditions, ozone errors develop over the 6-h background window. Wind increments are introduced in the analysis in order to reduce the differences between background ozone and ozone observations. For "perfect" observations (unbiased and no random error), this results in root mean square (RMS) vector wind error reductions of up to ∼ 3 m s−1 in the winter hemisphere and tropics. Wind extraction is more difficult in the summer hemisphere due to weak ozone gradients and smaller background wind errors. The limitations of wind extraction are also explored for observations with imposed random errors and for limited sampling patterns. As expected, the amount of wind information extracted degrades as observation errors or data voids increase. In the case of poorly specified observation error covariances, assimilation of ozone data with imposed errors may result in erroneous wind increments, since the assimilation is constrained too tightly to the noisy observations.

This paper is a description of the analysis of blockage corrections for bodies of revolution for the slotted-wall configuration of the National Transonic Facility (NTF) at the NASA Langley Research Center (LaRC). A wall correction method based on the measured wall signature is used. Test data from three different-sized blockage bodies and four wall ventilation settings were analyzed at various Mach numbers and unit Reynolds numbers. The results indicate that with the proper selection of the boundary condition parameters, the wall correction method can predict blockage corrections consistent with the wall measurements for Mach numbers as high as 0.95.

The new wall pressure measurement system and the TWICS wall correction system for the 14x22-Ft subsonic tunnel are described. Results from a recent semispan test and a full-span test are presented. Comparison with existing classical methods of correction is shown. A modification of the TWICS code to treat the effect due to a deflected wake from a high-lift wing is also discussed. The current implementation of TWICS for the 14x22-Ft tunnel is shown to be an improvement over existing methods.

This paper describes the new wall pressure measurement system and data-quality monitoring software installed at 14x22 Ft subsonic tunnel at the NASA Langley Research Center. The monitoring software was developed to enable measurement and control of the variability of the reference pressures and approximately 400 tunnel wall pressure measurements. Variability of the system, based upon data acquired over a year of wind tunnel tests and calibrations, is presented. The level of variation of the wall pressure measurements is shown to be predictable.

This report documents the experimental study for four different three-dimensional turbulent flows. The investigation focuses on near wall measurements in these flows. Several experimental techniques are used in the studies; however, the bulk of the investigation focuses on a three-orthogonal-velocity-component fiber-optic laser Doppler anemometer (3D-LDA) system. The control volume of the 3D-LDA is on the order of 50 micrometer in size, or a y(+) distance of around 2.3 units. An auxiliary small boundary layer wind tunnel (auxiliary tunnel) and a low speed linear compressor cascade wind tunnel (cascade tunnel) are utilized in this study. One of four flow experiments is done in the auxiliary tunnel the other three are in the cascade tunnel. The first three-dimensional turbulent flow is a vortical flow created by two half-delta wing vortex generators. Near wall secondary flow features are found. The second flow is an investigation of the first quarter chord tip gap flow in the cascade tunnel. Strong three-dimensional phenomena are found. The third flow investigated is the inflow to the compressor cascade with the moving wall. The experiment records shear layer interaction between the upstream flow and moving wall. Finally the fourth flow investigated is the inflow to the compressor cascade with the moving wall with half-delta wing vortex generators attached. Phase-averaged data reveal asymmetrical vortex structures just downstream of the vortex generators. This is the first time near wall turbulence data have been taken on these types of flows.