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.

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.

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.

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.

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

No abstract

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.

Abstract. 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 (O 3 ), nitrous oxide (N 2 O), and water vapor (H 2 O) (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 O 3 , 87 % for N 2 O, and 72 % for H 2 O. O 3 and N 2 O provide more wind information than H 2 O 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.