Estimating correlated observation error statistics using an ensemble transform Kalman filter

For certain observing types, such as those that are remotely sensed, the observation errors are correlated and these correlations are state- and time-dependent. In this work, we develop a method for diagnosing and incorporating spatially correlated and time-dependent observation error in an ensemble data assimilation system. The method combines an ensemble transform Kalman filter with a method that uses statistical averages of background and analysis innovations to provide an estimate of the observation error covariance matrix. To evaluate the performance of the method, we perform identical twin experiments using the Lorenz ’96 and Kuramoto-Sivashinsky models. Using our approach, a good approximation to the true observation error covariance can be recovered in cases where the initial estimate of the error covariance is incorrect. Spatial observation error covariances where the length scale of the true covariance changes slowly in time can also be captured. We find that using the estimated correlated observation error in the assimilation improves the analysis

Observation error statistics for Doppler radar radial wind superobservations assimilated into the DWD COSMO-KENDA system

Currently in operational numerical weather prediction (NWP) the density of high-resolution observations, such as Doppler radar radial winds (DRWs), is severely reduced in part to avoid violating the assumption of uncorrelated observation errors. To improve the quantity of observations used and the impact that they have on the forecast requires an accurate specification of the observation uncertainties. Observation uncertainties can be estimated using a simple diagnostic that utilises the statistical averages of observation-minus-background and observation-minus-analysis residuals. We are the first to use a modified form of the diagnostic to estimate spatial correlations for observations used in an operational ensemble data assimilation system. The uncertainties for DRW superobservations assimilated into the Deutscher Wetterdienst convection-permitting NWP model are estimated and compared to previous uncertainty estimates for DRWs. The new results show that most diagnosed standard deviations are smaller than those used in the assimilation, hence it may be feasible assimilate DRWs using reduced error standard deviations. However, some of the estimated standard deviations are considerably larger than those used in the assimilation; these large errors highlight areas where the observation processing system may be improved. The error correlation length scales are larger than the observation separation distance and influenced by both the superobbing procedure and observation operator. This is supported by comparing these results to our previous study using Met Office data. Our results suggest that DRW error correlations may be reduced by improving the superobbing procedure and observation operator; however, any remaining correlations should be accounted for in the assimilation

The role of airspeed variability in fixed-time, fuel-optimal aircraft trajectory planning

With the advent of improved aircraft situational awareness and the need for airlines to reduce their fuel consumption and environmental impact whilst adhering to strict timetables, fixed-time, fuel-optimal routing is vital. Here, the aircraft trajectory planning problem is addressed using optimal control theory. Two variants of a finite horizon optimal control formulation for fuel burn minimization are developed, subject to arrival constraints, an aerodynamic fuel-burn model, and a data-driven wind field. In the first variant, the control variable is expressed as a set of position-dependent aircraft headings, with the optimal control problem solved through a reduced gradient approach at a range of fixed airspeeds. The fuel optimal result is taken as the lowest fuel use recorded. In the second variant, both heading angle and airspeed are controlled. Results from three months of simulated flight routes between London and New York show that permitting optimised en-route airspeed variations leads to fuel savings of 0.5% on an average day (and up to 4% on certain days), compared with fixed airspeed flights. We conclude that significant fuel savings are possible if airspeeds are allowed to vary en route to take optimal advantage of the wind field

A pragmatic strategy for implementing spatially correlated observation errors in an operational system: an application to Doppler radial winds

Recent research has shown that high resolution observations, such as Doppler radar radial winds, exhibit spatial correlations. High resolution observations are routinely assimilated into convection permitting numerical weather prediction models assuming their errors are uncorrelated. To avoid violating this assumption observation density is severely reduced. To improve the quantity of observations used and the impact that they have on the forecast requires the introduction of full, correlated, error statistics. Some operational centres have introduced satellite inter-channel observation error correlations and obtained improved analysis’ accuracy and forecast skill scores. Here we present a strategy for implementing spatially correlated observation errors in an operational system. We then provide the first demonstration of the practical feasibility of incorporating spatially correlated Doppler radial wind error statistics in the Met Office numerical weather prediction system. Inclusion of correlated Doppler radial winds error statistics has little impact on the computation cost of the data assimilation system, even with a four-fold increase in the number of Doppler radial winds observations assimilated. Using the correlated observation error statistics with denser observations produces increments with shorter length scales than the control. Initial forecast trials show a neutral to positive impact on forecast skill overall, notably for quantitative precipitation forecasts. There is potential to improve forecast skill by optimising the use of Doppler radial winds and applying the technique to other observation types

New bounds on the condition number of the Hessian of the preconditioned variational data assimilation problem

Data assimilation algorithms combine prior and observational information, weighted by their respective uncertainties, to obtain the most likely posterior of a dynamical system. In variational data assimilation the posterior is computed by solving a nonlinear least squares problem. Many numerical weather prediction (NWP) centers use full observation error covariance (OEC) weighting matrices, which can slow convergence of the data assimilation procedure. Previous work revealed the importance of the minimum eigenvalue of the OEC matrix for conditioning and convergence of the unpreconditioned data assimilation problem. In this article we examine the use of correlated OEC matrices in the preconditioned data assimilation problem for the first time. We consider the case where there are more state variables than observations, which is typical for applications with sparse measurements, for example, NWP and remote sensing. We find that similarly to the unpreconditioned problem, the minimum eigenvalue of the OEC matrix appears in new bounds on the condition number of the Hessian of the preconditioned objective function. Numerical experiments reveal that the condition number of the Hessian is minimized when the background and observation lengthscales are equal. This contrasts with the unpreconditioned case, where decreasing the observation error lengthscale always improves conditioning. Conjugate gradient experiments show that in this framework the condition number of the Hessian is a good proxy for convergence. Eigenvalue clustering explains cases where convergence is faster than expected

Chandra Observations of Associates of η\eta Car: I. Luminosities

The region around the $\eta$ Car nebula has three OB associations, which contain a Wolf-Rayet star and several massive O3 stars. An early Chandra ACIS-I image was centered on $\eta$ Car and includes Trumpler 16 and part of Trumpler 14. The Chandra image confirms the well-known result that O and very early B stars are X-ray sources with L$_X$ $\simeq$ 10$^{-7} \times$ L$_{bol}$ over an X-ray luminosity range of about 100. Two new anomalously strong X-ray sources have been found among the hot star population, Tr 16-244, a heavily-reddened O3 I star, and Tr 16-22, a heavily-reddened O8.5 V star. Two stars have an unusually large L$_X$/L$_{bol}$: HD 93162, a Wolf-Rayet star (and possible binary), and Tr 16-22, a possible colliding wind binary In addition, a population of sources associated with cool stars is detected. In the color-magnitude diagram, these X-ray sources sit above the sequence of field stars in the Carina arm. The OB stars are on average more X-ray luminous than the cool star X-ray sources. X-ray sources among A stars have similar X-ray luminosities to cooler stars, and may be due to cooler companions. Upper limits are presented for B stars which are not detected in X-rays. These upper limits are also the upper limits for any cool companions which the hot stars may have. Hardness ratios are presented for the most luminous sources in bands 0.5 to 0.9 keV, 0.9 to 1.5 keV, and 1.5 to 2.04 kev. The available information on the binary nature of the hot stars is discussed, but binarity does not correlate with X-ray strength in a simple way.Comment: accepted by Ap

Defining the eco-enzymological role of the fungal strain <i>Coniochaeta</i> sp. 2T2.1 in a tripartite lignocellulolytic microbial consortium

Coniochaeta species are versatile ascomycetes that have great capacity to deconstruct lignocellulose. Here, we explore the transcriptome of Coniochaeta sp. strain 2T2.1 from wheat straw-driven cultures with the fungus growing alone or as a member of a synthetic microbial consortium with Sphingobacterium multivorum w15 and Citrobacter freundii so4. The differential expression profiles of carbohydrate-active enzymes indicated an onset of (hemi)cellulose degradation by 2T2.1 during the initial 24 hours of incubation. Within the tripartite consortium, 63 transcripts of strain 2T2.1 were differentially expressed at this time point. The presence of the two bacteria significantly upregulated the expression of one galactose oxidase, one GH79-like enzyme, one multidrug transporter, one laccase-like protein (AA1 family) and two bilirubin oxidases, suggesting that inter-kingdom interactions (e.g. amensalism) take place within this microbial consortium. Overexpression of multicopper oxidases indicated that strain 2T2.1 may be involved in lignin depolymerization (a trait of enzymatic synergism), while S. multivorum and C. freundii have the metabolic potential to deconstruct arabinoxylan. Under the conditions applied, 2T2.1 appears to be a better degrader of wheat straw when the two bacteria are absent. This conclusion is supported by the observed suppression of its (hemi)cellulolytic arsenal and lower degradation percentages within the microbial consortium