On the growth of errors in data assimilation systems

Considerable progress has taken place in numerical weather prediction over the last decade. It has been possible to extend predictive skills in the extra-tropics of the Northern Hemisphere during the winter from less than five days to seven days. Similar improvements, albeit on a lower level, have taken place in the Southern Hemisphere. Another example of improvement in the forecasts is the prediction of intense synoptic phenomena such as cyclogenesis which on the whole is quite successful with the most advanced operational models (Bengtsson (1989), Gadd and Kruze (1988)). A careful examination shows that there are no single causes for the improvements in predictive skill, but instead they are due to several different factors encompassing the forecasting system as a whole (Bengtsson, 1985). In this paper we will focus our attention on the role of data-assimilation and the effect it may have on reducing the initial error and hence improving the forecast. The first part of the paper contains a theoretical discussion on error growth in simple data assimilation systems, following Leith (1983). In the second part we will apply the result on actual forecast data from ECMWF. The potential for further forecast improvements within the framework of the present observing system in the two hemispheres will be discussed.

Evaluation of diagnostic molecular markers for DUS phenotypic assessment in the cereal crop, barley (Hordeum vulgare ssp. vulgare L.)

The deployment of genetic markers is of interest in crop assessment and breeding programmes, due to the potential savings in cost and time afforded. As part of the internationally recognised framework for the awarding of Plant Breeders’ Rights (PBR), new barley variety submissions are evaluated using a suite of morphological traits to ensure they are distinct, uniform and stable (DUS) in comparison to all previous submissions. Increasing knowledge of the genetic control of many of these traits provides the opportunity to assess the potential of deploying diagnostic/perfect genetic markers in place of phenotypic assessment. Here, we identify a suite of 25 genetic markers assaying for 14 DUS traits, and implement them using a single genotyping platform (KASPar). Using a panel of 169 UK barley varieties, we show that phenotypic state at three of these traits can be perfectly predicted by genotype. Predictive values for an additional nine traits ranged from 81 to 99 %. Finally, by comparison of varietal discrimination based on phenotype and genotype resulted in correlation of 0.72, indicating that deployment of molecular markers for varietal discrimination could be feasible in the near future. Due to the flexibility of the genotyping platform used, the genetic markers described here can be used in any number or combination, in-house or by outsourcing, allowing flexible deployment by users. These markers are likely to find application where tracking of specific alleles is required in breeding programmes, or for potential use within national assessment programmes for the awarding of PBRs.

PCR-based markers diagnostic for spring and winter seasonal growth habit in barley

Toward the ultimate goal of replacing field-based evaluation of seasonal growth habit, we describe the design and validation of a multiplex polymerase chain reaction assay diagnostic for allelic status at the barley (Hordeum vulgare ssp. vulgare L.) vernalization locus, VRN-H1 By assaying for the presence of all known insertion–deletion polymorphisms thought to be responsible for the difference between spring and winter alleles, this assay directly tests for the presence of functional polymorphism at VRN-H1 Four of the nine previously recognized VRN-H1 haplotypes (including both winter alleles) give unique profiles using this assay. The remaining five spring haplotypes share a single profile, indicative of function-altering deletions spanning, or adjacent to, the putative “vernalization critical” region of intron 1. When used in conjunction with a previously published PCR-based assay diagnostic for alleles at VRN-H2, it was possible to predict growth habit in all the 100 contemporary UK spring and winter lines analyzed in this study. This assay is likely to find application in instances when seasonal growth habit needs to be determined without the time and cost of phenotypic assessment and during marker-assisted selection using conventional and multicross population analysis.

A comprehensive benchmarking system for evaluating global vegetation models.

We present a benchmark system for global vegetation models. This system provides a quantitative evaluation of multiple simulated vegetation properties, including primary production; seasonal net ecosystem production; vegetation cover, composition and 5 height; fire regime; and runoff. The benchmarks are derived from remotely sensed gridded datasets and site-based observations. The datasets allow comparisons of annual average conditions and seasonal and inter-annual variability, and they allow the impact of spatial and temporal biases in means and variability to be assessed separately. Specifically designed metrics quantify model performance for each process, 10 and are compared to scores based on the temporal or spatial mean value of the observations and a “random” model produced by bootstrap resampling of the observations. The benchmark system is applied to three models: a simple light-use efficiency and water-balance model (the Simple Diagnostic Biosphere Model: SDBM), and the Lund-Potsdam-Jena (LPJ) and Land Processes and eXchanges (LPX) dynamic global 15 vegetation models (DGVMs). SDBM reproduces observed CO2 seasonal cycles, but its simulation of independent measurements of net primary production (NPP) is too high. The two DGVMs show little difference for most benchmarks (including the interannual variability in the growth rate and seasonal cycle of atmospheric CO2), but LPX represents burnt fraction demonstrably more accurately. Benchmarking also identified 20 several weaknesses common to both DGVMs. The benchmarking system provides a quantitative approach for evaluating how adequately processes are represented in a model, identifying errors and biases, tracking improvements in performance through model development, and discriminating among models. Adoption of such a system would do much to improve confidence in terrestrial model predictions of climate change 25 impacts and feedbacks.

Description and process evaluation of pharmacists’ interventions in a pharmacist-led information technology-enabled multicentre cluster randomised controlled trial for reducing medication errors in general practice (PINCER trial)

Objective To undertake a process evaluation of pharmacists' recommendations arising in the context of a complex IT-enabled pharmacist-delivered randomised controlled trial (PINCER trial) to reduce the risk of hazardous medicines management in general practices. Methods PINCER pharmacists manually recorded patients’ demographics, details of interventions recommended, actions undertaken by practice staff and time taken to manage individual cases of hazardous medicines management. Data were coded and double entered into SPSS v15, and then summarised using percentages for categorical data (with 95% CI) and, as appropriate, means (SD) or medians (IQR) for continuous data. Key findings Pharmacists spent a median of 20 minutes (IQR 10, 30) reviewing medical records, recommending interventions and completing actions in each case of hazardous medicines management. Pharmacists judged 72% (95%CI 70, 74) (1463/2026) of cases of hazardous medicines management to be clinically relevant. Pharmacists recommended 2105 interventions in 74% (95%CI 73, 76) (1516/2038) of cases and 1685 actions were taken in 61% (95%CI 59, 63) (1246/2038) of cases; 66% (95%CI 64, 68) (1383/2105) of interventions recommended by pharmacists were completed and 5% (95%CI 4, 6) (104/2105) of recommendations were accepted by general practitioners (GPs), but not completed at the end of the pharmacists’ placement; the remaining recommendations were rejected or considered not relevant by GPs. Conclusions The outcome measures were used to target pharmacist activity in general practice towards patients at risk from hazardous medicines management. Recommendations from trained PINCER pharmacists were found to be broadly acceptable to GPs and led to ameliorative action in the majority of cases. It seems likely that the approach used by the PINCER pharmacists could be employed by other practice pharmacists following appropriate training.

The prevalence and nature of prescribing and monitoring errors in English general practice – a retrospective case note review

Objective To determine the prevalence and nature of prescribing and monitoring errors in general practices in England. Design Retrospective case note review of unique medication items prescribed over a 12 month period to a 2% random sample of patients. Mixed effects logistic regression was used to analyse the data. Setting Fifteen general practices across three primary care trusts in England. Data sources Examination of 6048 unique prescription items prescribed over the previous 12 months for 1777 patients. Main outcome measures Prevalence of prescribing and monitoring errors, and severity of errors, using validated definitions. Results Prescribing and/or monitoring errors were detected in 4.9% (296/6048) of all prescription items (95% confidence interval 4.4 - 5.5%). The vast majority of errors were of mild to moderate severity, with 0.2% (11/6048) of items having a severe error. After adjusting for covariates, patient-related factors associated with an increased risk of prescribing and/or monitoring errors were: age less than 15 (Odds Ratio (OR) 1.87, 1.19 to 2.94, p=0.006) or greater than 64 years (OR 1.68, 1.04 to 2.73, p=0.035), and higher numbers of unique medication items prescribed (OR 1.16, 1.12 to 1.19, p<0.001). Conclusion Prescribing and monitoring errors are common in English general practice, although severe errors are unusual. Many factors increase the risk of error. Having identified the most common and important errors, and the factors associated with these, strategies to prevent future errors should be developed based on the study findings.

Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Remote sensing observations often have correlated errors, but the correlations are typically ignored in data assimilation for numerical weather prediction. The assumption of zero correlations is often used with data thinning methods, resulting in a loss of information. As operational centres move towards higher-resolution forecasting, there is a requirement to retain data providing detail on appropriate scales. Thus an alternative approach to dealing with observation error correlations is needed. In this article, we consider several approaches to approximating observation error correlation matrices: diagonal approximations, eigendecomposition approximations and Markov matrices. These approximations are applied in incremental variational assimilation experiments with a 1-D shallow water model using synthetic observations. Our experiments quantify analysis accuracy in comparison with a reference or ‘truth’ trajectory, as well as with analyses using the ‘true’ observation error covariance matrix. We show that it is often better to include an approximate correlation structure in the observation error covariance matrix than to incorrectly assume error independence. Furthermore, by choosing a suitable matrix approximation, it is feasible and computationally cheap to include error correlation structure in a variational data assimilation algorithm.

The causes of prescribing errors in English general practices: a qualitative study

Aim: To examine the causes of prescribing and monitoring errors in English general practices and provide recommendations for how they may be overcome. Design: Qualitative interview and focus group study with purposive sampling and thematic analysis informed by Reason’s accident causation model. Participants: General practice staff participated in a combination of semi-structured interviews (n=34) and six focus groups (n=46). Setting: Fifteen general practices across three primary care trusts in England. Results: We identified seven categories of high-level error-producing conditions: the prescriber, the patient, the team, the task, the working environment, the computer system, and the primary-secondary care interface. Each of these was further broken down to reveal various error-producing conditions. The prescriber’s therapeutic training, drug knowledge and experience, knowledge of the patient, perception of risk, and their physical and emotional health, were all identified as possible causes. The patient’s characteristics and the complexity of the individual clinical case were also found to have contributed to prescribing errors. The importance of feeling comfortable within the practice team was highlighted, as well as the safety of general practitioners (GPs) in signing prescriptions generated by nurses when they had not seen the patient for themselves. The working environment with its high workload, time pressures, and interruptions, and computer related issues associated with mis-selecting drugs from electronic pick-lists and overriding alerts, were all highlighted as possible causes of prescribing errors and often interconnected. Conclusion: This study has highlighted the complex underlying causes of prescribing and monitoring errors in general practices, several of which are amenable to intervention.

The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data

The absorption spectra of phytoplankton in the visible domain hold implicit information on the phytoplankton community structure. Here we use this information to retrieve quantitative information on phytoplankton size structure by developing a novel method to compute the exponent of an assumed power-law for their particle-size spectrum. This quantity, in combination with total chlorophyll-a concentration, can be used to estimate the fractional concentration of chlorophyll in any arbitrarily-defined size class of phytoplankton. We further define and derive expressions for two distinct measures of cell size of mixed populations, namely, the average spherical diameter of a bio-optically equivalent homogeneous population of cells of equal size, and the average equivalent spherical diameter of a population of cells that follow a power-law particle-size distribution. The method relies on measurements of two quantities of a phytoplankton sample: the concentration of chlorophyll-a, which is an operational index of phytoplankton biomass, and the total absorption coefficient of phytoplankton in the red peak of visible spectrum at 676 nm. A sensitivity analysis confirms that the relative errors in the estimates of the exponent of particle size spectra are reasonably low. The exponents of phytoplankton size spectra, estimated for a large set of in situ data from a variety of oceanic environments (~ 2400 samples), are within a reasonable range; and the estimated fractions of chlorophyll in pico-, nano- and micro-phytoplankton are generally consistent with those obtained by an independent, indirect method based on diagnostic pigments determined using high-performance liquid chromatography. The estimates of cell size for in situ samples dominated by different phytoplankton types (diatoms, prymnesiophytes, Prochlorococcus, other cyanobacteria and green algae) yield nominal sizes consistent with the taxonomic classification. To estimate the same quantities from satellite-derived ocean-colour data, we combine our method with algorithms for obtaining inherent optical properties from remote sensing. The spatial distribution of the size-spectrum exponent and the chlorophyll fractions of pico-, nano- and micro-phytoplankton estimated from satellite remote sensing are in agreement with the current understanding of the biogeography of phytoplankton functional types in the global oceans. This study contributes to our understanding of the distribution and time evolution of phytoplankton size structure in the global oceans.

Retrievals of sea surface temperature from infrared imagery: origin and form of systematic errors

We show that retrievals of sea surface temperature from satellite infrared imagery are prone to two forms of systematic error: prior error (familiar from the theory of atmospheric sounding) and error arising from nonlinearity. These errors have different complex geographical variations, related to the differing geographical distributions of the main geophysical variables that determine clear-sky brightness-temperatures over the oceans. We show that such errors arise as an intrinsic consequence of the form of the retrieval (rather than as a consequence of sub-optimally specified retrieval coefficients, as is often assumed) and that the pattern of observed errors can be simulated in detail using radiative-transfer modelling. The prior error has the linear form familiar from atmospheric sounding. A quadratic equation for nonlinearity error is derived, and it is verified that the nonlinearity error exhibits predominantly quadratic behaviour in this case.

Gene expression changes in phosphorus deficient potato (Solanum tuberosum L.) leaves and the potential for diagnostic gene expression markers

Background: There are compelling economic and environmental reasons to reduce our reliance on inorganic phosphate (Pi) fertilisers. Better management of Pi fertiliser applications is one option to improve the efficiency of Pi fertiliser use, whilst maintaining crop yields. Application rates of Pi fertilisers are traditionally determined from analyses of soil or plant tissues. Alternatively, diagnostic genes with altered expression under Pi limiting conditions that suggest a physiological requirement for Pi fertilisation, could be used to manage Pifertiliser applications, and might be more precise than indirect measurements of soil or tissue samples. Results: We grew potato (Solanum tuberosum L.) plants hydroponically, under glasshouse conditions, to control their nutrient status accurately. Samples of total leaf RNA taken periodically after Pi was removed from the nutrient solution were labelled and hybridised to potato oligonucleotide arrays. A total of 1,659 genes were significantly differentially expressed following Pi withdrawal. These included genes that encode proteins involved in lipid, protein, and carbohydrate metabolism, characteristic of Pi deficient leaves and included potential novel roles for genes encoding patatin like proteins in potatoes. The array data were analysed using a support vector machine algorithm to identify groups of genes that could predict the Pi status of the crop. These groups of diagnostic genes were tested using field grown potatoes that had either been fertilised or unfertilised. A group of 200 genes could correctly predict the Pi status of field grown potatoes. Conclusions: This paper provides a proof-of-concept demonstration for using microarrays and class prediction tools to predict the Pi status of a field grown potato crop. There is potential to develop this technology for other biotic and abiotic stresses in field grown crops. Ultimately, a better understanding of crop stresses may improve our management of the crop, improving the sustainability of agriculture.

Estimating interchannel observation-error correlations for IASI radiance data in the Met Office system

The optimal utilisation of hyper-spectral satellite observations in numerical weather prediction is often inhibited by incorrectly assuming independent interchannel observation errors. However, in order to represent these observation-error covariance structures, an accurate knowledge of the true variances and correlations is needed. This structure is likely to vary with observation type and assimilation system. The work in this article presents the initial results for the estimation of IASI interchannel observation-error correlations when the data are processed in the Met Office one-dimensional (1D-Var) and four-dimensional (4D-Var) variational assimilation systems. The method used to calculate the observation errors is a post-analysis diagnostic which utilises the background and analysis departures from the two systems. The results show significant differences in the source and structure of the observation errors when processed in the two different assimilation systems, but also highlight some common features. When the observations are processed in 1D-Var, the diagnosed error variances are approximately half the size of the error variances used in the current operational system and are very close in size to the instrument noise, suggesting that this is the main source of error. The errors contain no consistent correlations, with the exception of a handful of spectrally close channels. When the observations are processed in 4D-Var, we again find that the observation errors are being overestimated operationally, but the overestimation is significantly larger for many channels. In contrast to 1D-Var, the diagnosed error variances are often larger than the instrument noise in 4D-Var. It is postulated that horizontal errors of representation, not seen in 1D-Var, are a significant contributor to the overall error here. Finally, observation errors diagnosed from 4D-Var are found to contain strong, consistent correlation structures for channels sensitive to water vapour and surface properties.

Care homes’ use of medicines study: prevalence, causes and potential harm of medication errors in care homes for older people

Introduction: Care home residents are at particular risk from medication errors, and our objective was to determine the prevalence and potential harm of prescribing, monitoring, dispensing and administration errors in UK care homes, and to identify their causes. Methods: A prospective study of a random sample of residents within a purposive sample of homes in three areas. Errors were identified by patient interview, note review, observation of practice and examination of dispensed items. Causes were understood by observation and from theoretically framed interviews with home staff, doctors and pharmacists. Potential harm from errors was assessed by expert judgement. Results: The 256 residents recruited in 55 homes were taking a mean of 8.0 medicines. One hundred and seventy-eight (69.5%) of residents had one or more errors. The mean number per resident was 1.9 errors. The mean potential harm from prescribing, monitoring, administration and dispensing errors was 2.6, 3.7, 2.1 and 2.0 (0 = no harm, 10 = death), respectively. Contributing factors from the 89 interviews included doctors who were not accessible, did not know the residents and lacked information in homes when prescribing; home staff’s high workload, lack of medicines training and drug round interruptions; lack of team work among home, practice and pharmacy; inefficient ordering systems; inaccurate medicine records and prevalence of verbal communication; and difficult to fill (and check) medication administration systems. Conclusions: That two thirds of residents were exposed to one or more medication errors is of concern. The will to improve exists, but there is a lack of overall responsibility. Action is required from all concerned.

A generalised Bayesian instrumental variable approach under student t-distributed errors with application

Bayesian analysis is given of an instrumental variable model that allows for heteroscedasticity in both the structural equation and the instrument equation. Specifically, the approach for dealing with heteroscedastic errors in Geweke (1993) is extended to the Bayesian instrumental variable estimator outlined in Rossi et al. (2005). Heteroscedasticity is treated by modelling the variance for each error using a hierarchical prior that is Gamma distributed. The computation is carried out by using a Markov chain Monte Carlo sampling algorithm with an augmented draw for the heteroscedastic case. An example using real data illustrates the approach and shows that ignoring heteroscedasticity in the instrument equation when it exists may lead to biased estimates.

An environmental uncertainty-based diagnostic reference tool for evaluating the performance of supply chain value streams

This research has responded to the need for diagnostic reference tools explicitly linking the influence of environmental uncertainty and performance within the supply chain. Uncertainty is a key factor influencing performance and an important measure of the operating environment. We develop and demonstrate a novel reference methodology based on data envelopment analysis (DEA) for examining the performance of value streams within the supply chain with specific reference to the level of environmental uncertainty they face. In this paper, using real industrial data, 20 product supply value streams within the European automotive industry sector are evaluated. Two are found to be efficient. The peer reference groups for the underperforming value streams are identified and numerical improvement targets are derived. The paper demonstrates how DEA can be used to guide supply chain improvement efforts through role-model identification and target setting, in a way that recognises the multiple dimensions/outcomes of the supply chain process and the influence of its environmental conditions. We have facilitated the contextualisation of environmental uncertainty and its incorporation into a specific diagnostic reference tool.