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All practical ensemble-based atmospheric data assimilation (DA) systems use localisation to reduce the damaging impact of spurious long-range correlations arising from the finite ensemble size. However, the form of the localisation function is generally ad-hoc, and requires expensive tuning to optimise the system. For the case of a single observation and known true background error correlation, we derive an expression for the localisation factor that minimises the expected root-mean-square (RMS) analysis error. Idealised tests show this formulation performs well for multiple observations provided their density is not too high. The width of the optimal localisation function scales with the width of the underlying correlation, but does not have the same shape. The optimal observation-space localisation for a single spatially integrating observation depends on the observation-to-gridpoint background error correlation, making it broader than the optimal localisation for point observations and potentially competitive with model-space localisation. A new form of hybrid DA is proposed in which localisation damps the sample correlations towards their climatological mean rather than zero, reducing the RMS error and potentially improving the dynamic balance of the analysis. The presence of variance errors causes the optimal localisation factor to depend on the ratio of observation to background error variance, and raises the possibility that a small amount of variance damping may be beneficial. For dense observations, a more elaborate theory is required, which will almost certainly depend on the observation network. We present some preliminary analysis of the features of the multi-observation problem, which for instance suggests that the optimal solution may involve different localisation factors in the numerator and denominator of the Kalman filter equation. We note that even optimal localisation gives an expected RMS error which exceeds that of perfect DA, contrary to the assumption made by 'deterministic' ensemble filters.

Ensemble forecasts aim to improve decision-making by predicting a set of possible outcomes. Ideally, these would provide probabilities which are both sharp and reliable. In practice, the models, data assimilation and ensemble perturbation systems are all imperfect, leading to deficiencies in the predicted probabilities. This paper presents an ensemble post-processing scheme which directly targets local reliability, calibrating both climatology and ensemble dispersion in one coherent operation. It makes minimal assumptions about the underlying statistical distributions, aiming to extract as much information as possible from the original dynamic forecasts and support statistically awkward variables such as precipitation. The output is a set of ensemble members preserving the spatial, temporal and inter-variable structure from the raw forecasts, which should be beneficial to downstream applications such as hydrological models. The calibration is tested on three leading 15-d ensemble systems, and their aggregation into a simple multimodel ensemble. Results are presented for 12 h, 1° scale over Europe for a range of surface variables, including precipitation. The scheme is very effective at removing unreliability from the raw forecasts, whilst generally preserving or improving statistical resolution. In most cases, these benefits extend to the rarest events at each location within the 2-yr verification period. The reliability and resolution are generally equivalent or superior to those achieved using a Local Quantile-Quantile Transform, an established calibration method which generalises bias correction. The value of preserving spatial structure is demonstrated by the fact that 3×3 averages derived from grid-scale precipitation calibration perform almost as well as direct calibration at 3×3 scale, and much better than a similar test neglecting the spatial relationships. Some remaining issues are discussed regarding the finite size of the output ensemble, variables such as sea-level pressure which are very reliable to start with, and the best way to handle derived variables such as dewpoint depression.

Statistical postprocessing techniques are nowadays key components of the forecasting suites in many national meteorological services (NMS), with, for most of them, the objective of correcting the impact of different types of errors on the forecasts. The final aim is to provide optimal, automated, seamless forecasts for end users. Many techniques are now flourishing in the statistical, meteorological, climatological, hydrological, and engineering communities. The methods range in complexity from simple bias corrections to very sophisticated distribution-adjusting techniques that incorporate correlations among the prognostic variables. The paper is an attempt to summarize the main activities going on in this area from theoretical developments to operational applications, with a focus on the current challenges and potential avenues in the field. Among these challenges is the shift in NMS toward running ensemble numerical weather prediction (NWP) systems at the kilometer scale that produce very large datasets and require high-density high-quality observations, the necessity to preserve space-time correlation of high-dimensional corrected fields, the need to reduce the impact of model changes affecting the parameters of the corrections, the necessity for techniques to merge different types of forecasts and ensembles with different behaviors, and finally the ability to transfer research on statistical postprocessing to operations. Potential new avenues are also discussed.

Ensemble methods are increasingly used in data assimilation for numerical weather prediction. These methods utilize sample covariance matrices that are subject to sampling error, which is commonly addressed by application of a localisation. The form of the localisation is usually ad-hoc. This paper presents results from applying a series of theoretically optimal localisations, derived for assimilating a single observation (sparse density), to a Gaussian model state. The theoretical localisations included are optimal localisation for a single true covariance (OSTC), optimal localisation for a variable true covariance (OVTC), which includes knowledge of the climatology and optimal hybrid localisation for a variable true covariance (HOVTC) which damps the difference from the mean covariance as opposed to the covariance itself. The optimal localisations and Gaussian localisation perform similarly for sparse observations. For dense observations, the theoretical assumptions do not hold, and the optimal localisations break down, but the Gaussian, which is retuned, continues to perform well. HOVTC localisation is shown to outperform traditional forms of localisation in the single observation cases. A tuned hybrid localisation is proposed based on the form of the optimal hybrid localisation and this is shown to perform well in all ranges of observation density and assimilation strengths. The paper shows that theoretically derived localisations can produce improved assimilation performance for a range of observation densities and assimilation strengths in a Gaussian model scenario. It provides the proof of concept that studying the optimal localisation can inform the improvement of localisation regimes for more complex models.

The Met Office in the United Kingdom has developed a completely new probabilistic postprocessing system called IMPROVER to operate on outputs from its operational numerical weather prediction (NWP) forecasts and precipitation nowcasts. The aim is to improve weather forecast information to the public and other stakeholders while better exploiting the current and future generations of underpinning kilometer-scale NWP ensembles. We wish to provide seamless forecasts from nowcasting to medium range, provide consistency between gridded and site-specific forecasts, and be able to verify every stage of the processing. The software is written in a modern modular framework that is easy to maintain, develop, and share. IMPROVER allows forecast information to be provided with greater spatial and temporal detail and a faster update frequency than previous postprocessing. Independent probabilistic processing chains are constructed for each meteorological variable consisting of a series of processing stages that operate on predefined grids and blend outputs from several NWP inputs to give a frequently updated, probabilistic forecast solution. Probabilistic information is produced as standard, with the option of extracting a most likely or yes–no outcome if required. Verification can be performed at all stages, although it is only currently switched on for the most significant stages when run in real time. IMPROVER has been producing real-time output since March 2021 and became operational in spring 2022.

Statistical postprocessing techniques are nowadays key components of the forecasting suites in many National Meteorological Services (NMS), with for most of them, the objective of correcting the impact of different types of errors on the forecasts. The final aim is to provide optimal, automated, seamless forecasts for end users. Many techniques are now flourishing in the statistical, meteorological, climatological, hydrological, and engineering communities. The methods range in complexity from simple bias corrections to very sophisticated distribution-adjusting techniques that incorporate correlations among the prognostic variables. The paper is an attempt to summarize the main activities going on this area from theoretical developments to operational applications, with a focus on the current challenges and potential avenues in the field. Among these challenges is the shift in NMS towards running ensemble Numerical Weather Prediction (NWP) systems at the kilometer scale that produce very large datasets and require high-density high-quality observations; the necessity to preserve space time correlation of high-dimensional corrected fields; the need to reduce the impact of model changes affecting the parameters of the corrections; the necessity for techniques to merge different types of forecasts and ensembles with different behaviors; and finally the ability to transfer research on statistical postprocessing to operations. Potential new avenues will also be discussed.

Objective To explore the prognostic significance of patient and disease characteristics on the survival of patients with metastatic cutaneous squamous cell carcinoma of the parotid gland at a tertiary care center in Halifax, Nova Scotia, Canada. Methods A retrospective chart review for all patients diagnosed with metastatic cutaneous squamous cell carcinoma to the parotid gland from January 2000 to December 2010. Multiple variables were examined related to: patient demographics, surgical details, non-surgical procedure details, and tumor pathologic description. Results A total of 54 patients [48 men (88%) and 6 women (12%)], with a median age at surgery of 78 years (range 47–93 years) were included in the study. All patients had a minimum follow up of 12 months or until deceased, with a median duration of follow up of 24 months. Predictors that were significant for cancer recurrence were pretreatment N-stage, pathologic neck node status, total number of positive neck nodes, and perineural invasion. Predictors that were significant for cancer death were the total number of positive neck nodes and perineural invasion. The remainder of the predictors including margin status were non-significant. Only age and nodal status were significant for both cancer death and recurrence on multivariate analysis. Conclusion Our results showed only two variables that remained significant on multivariate analysis were age and number of involved neck nodes, this finding suggests that re-resection of positive margins may not be necessary and that radiation therapy is the mainstay of treatment for positive margins.