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

Accounting for observation uncertainty and bias due to unresolved scales with the Schmidt-Kalman filter

Data assimilation combines observations with numerical model data, to provide a best estimate of a real system. Errors due to unresolved scales arise when there is a spatiotemporal scale mismatch between the processes resolved by the observations and model. We present theory on error, uncertainty and bias due to unresolved scales for situations where observations contain information on smaller scales than can be represented by the numerical model. The Schmidt-Kalman filter, which accounts for the uncertainties in the unrepresented processes, is investigated and compared with an optimal Kalman filter that treats all scales, and a suboptimal Kalman filter that accounts for the largescales only. The equation governing true analysis uncertainty is reformulated to include representation uncertainty for each filter. We apply the filters to a random walk model with one variable for large-scale processes and one variable for small-scale processes. Our new results show that the Schmidt-Kalman filter has the largest benefit over a suboptimal filter in regimes of high representation uncertainty and low instrument uncertainty but performs worse than the optimal filter. Furthermore, we review existing theory showing that errors due to unresolved scales often result in representation error bias. We derive a novel bias-correcting form of the Schmidt-Kalman filter and apply it to the random walk model with biased observations. We show that the bias-correcting Schmidt-Kalman filter successfully compensates for representation error biases. Indeed, it is more important to treat an observation bias than an unbiased error due to unresolved scales

Evaluating errors due to unresolved scales in convection permitting numerical weather prediction

In numerical weather prediction (NWP), observations and models are quantitatively compared for the purposes of data assimilation and forecast verification. The spatial and temporal scales represented by the observation and model may differ and this results in a scale mis‐match error which may be biased and correlated. The aim of this paper is to investigate the structure of representation error in convection‐permitting NWP models for four meteorological variables: temperature, specific humidity, zonal and meridional wind. We use high resolution data from the experimental Met Office London Model (approximately 300 m grid‐length) to simulate perfect observations and lower resolution model data. The scale mis‐match error and its bias, variance and correlation are calculated from the perfect observation and low‐resolution model equivalents. Our new results show that the scale mis‐match bias is significant in the boundary layer for temperature and specific humidity, whereas the variance is significant in the boundary layer for all analysed variables. Furthermore, they are shown to be related to the mismatch in the high‐ and low‐resolution orography. Contrary to previous studies using low‐resolution, (km‐scale) data, horizontal correlations are shown to be insignificant. However, all variables exhibit considerable vertical representation error correlation throughout the boundary layer; for temperature a significant positive vertical correlation persists for all model levels in the troposphere. Our results suggest that significant biases and vertical correlations exist that should be accounted for to give maximum observation impact in data assimilation and for fairness in model verification and validation

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

Comparing diagnosed observation uncertainties with independent estimates: a case study using aircraft‐based observations and a convection‐permitting data assimilation system

Aircraft can report in situ observations of the ambient temperature by using aircraft meteorological data relay (AMDAR) or these can be derived using mode‐select enhanced tracking data (Mode‐S EHS). These observations may be assimilated into numerical weather prediction models to improve the initial conditions for forecasts. The assimilation process weights the observation according to the expected uncertainty in its measurement and representation. The goal of this paper is to compare observation uncertainties diagnosed from data assimilation statistics with independent estimates. To quantify these independent estimates, we use metrological comparisons, made with in‐situ research‐grade instruments, as well as previous studies using collocation methods between aircraft (mostly AMDAR reports) and other observing systems such as radiosondes. In this study, we diagnose a new estimate of the vertical structure of the uncertainty variances using observation‐minus‐background and observation‐minus‐analysis statistics from a Met Office limited area three‐dimensional variational data assimilation system (3 km horizontal grid‐length, 3‐hourly cycle). This approach for uncertainty estimation is simple to compute but has several limitations. Nevertheless, the resulting diagnosed variances have a vertical structure that is like that provided by the independent estimates of uncertainty. This provides confidence in the uncertainty estimation method, and in the diagnosed uncertainty estimates themselves. In the future, our methodology, along with other results, could provide ways to estimate the uncertainty for the assimilation of aircraft‐based temperature observations

The Orphan Adhesion-GPCR GPR126 Is Required for Embryonic Development in the Mouse

Adhesion-GPCRs provide essential cell-cell and cell-matrix interactions in development, and have been implicated in inherited human diseases like Usher Syndrome and bilateral frontoparietal polymicrogyria. They are the second largest subfamily of seven-transmembrane spanning proteins in vertebrates, but the function of most of these receptors is still not understood. The orphan Adhesion-GPCR GPR126 has recently been shown to play an essential role in the myelination of peripheral nerves in zebrafish. In parallel, whole-genome association studies have implicated variation at the GPR126 locus as a determinant of body height in the human population. The physiological function of GPR126 in mammals is still unknown. We describe a targeted mutation of GPR126 in the mouse, and show that GPR126 is required for embryonic viability and cardiovascular development

Exploring the impact of dementia friendly ward environments on the provision of care: A qualitative thematic analysis

Dementia-friendly wards are recent developments to improve care for patients with dementia in acute hospitals. This qualitative study used focus groups to understand the impact of dementia friendly ward environments on nurses experiences of caring for acutely unwell patients with dementia. Qualified nurses and health care assistants working in an acute NHS Trust in England discussed their perceptions and experiences of working in a dementia-friendly ward environment. Four themes developed from the thematic analysis: (1) ‘It doesn’t look like a hospital’: A changed environment, (2) ‘More options to provide person-centred care’: No one size fits all, (3) ‘Before you could not see the patients’: A constant nurse presence and (4) ‘The ward remains the same’: Resistance to change. Recommendations and implementations for practice are discussed