Diagnosing observation error correlations for Doppler radar radial winds in the Met Office UKV model using observation-minus-background and observation-minus-analysis statistics

With the development of convection-permitting numerical weather prediction the efficient use of high-resolution observations in data assimilation is becoming increasingly important. The operational assimilation of these observations, such as Doppler radar radial winds (DRWs), is now common, though to avoid violating the assumption of uncorrelated observation errors the 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 the full, potentially correlated, error statistics. In this work, observation error statistics are calculated for the DRWs that are assimilated into the Met Office high-resolution UK model using a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. This is the first in-depth study using the diagnostic to estimate both horizontal and along-beam observation error statistics. The new results obtained show that the DRW error standard deviations are similar to those used operationally and increase as the observation height increases. Surprisingly the estimated observation error correlation length-scales are longer than the operational thinning distance. They are dependent both on the height of the observation and on the distance of the observation away from the radar. Further tests show that the long correlations cannot be attributed to the background error covariance matrix used in the assimilation, although they are, in part, a result of using superobservations and a simplified observation operator. The inclusion of correlated error statistics in the assimilation allows less thinning of the data and hence better use of the high-resolution observations

Diagnosing horizontal and inter-channel observation error correlations for SEVIRI observations using observation-minus-background and observation-minus-analysis statistics

It has been common practice in data assimilation to treat observation errors as uncorrelated; however, meteorological centres are beginning to use correlated inter-channel observation errors in their operational assimilation systems. In this work, we are the first to characterise inter-channel and spatial error correlations for Spinning Enhanced Visible and Infrared Imager (SEVIRI) observations that are assimilated into the Met Office high-resolution model. The errors are calculated using a diagnostic that calculates statistical averages of observation-minus-background and observation-minus-analysis residuals. This diagnostic is sensitive to the background and observation error statistics used in the assimilation, although, with careful interpretation of the results, it can still provide useful information. We find that the diagnosed SEVIRI error variances are as low as one-tenth of those currently used in the operational system. The water vapour channels have significantly correlated inter-channel errors, as do the surface channels. The surface channels have larger observation error variances and inter-channel correlations in coastal areas of the domain; this is the result of assimilating mixed pixel (land-sea) observations. The horizontal observation error correlations range between 30 km and 80 km, which is larger than the operational thinning distance of 24 km. We also find that estimates from the diagnostics are unaffected by biased observations, provided that the observation-minus-background and observation-minus-analysis residual means are subtracted

Marker effects and examination reliability: a comparative exploration from the perspectives of generalizability theory, Rasch modelling and multilevel modelling

This study looked at how three different analysis methods could help us to understand rater effects on exam reliability. The techniques we looked at were: generalizability theory (G-theory) item response theory (IRT): in particular the Many-Facets Partial Credit Rasch Model (MFRM) multilevel modelling (MLM) We used data from AS component papers in geography and psychology for 2009, 2010 and 2011 from Edexcel.</p

A Spatio-Temporal Point Process Model for Ambulance Demand

Ambulance demand estimation at fine time and location scales is critical for fleet management and dynamic deployment. We are motivated by the problem of estimating the spatial distribution of ambulance demand in Toronto, Canada, as it changes over discrete 2-hour intervals. This large-scale dataset is sparse at the desired temporal resolutions and exhibits location-specific serial dependence, daily and weekly seasonality. We address these challenges by introducing a novel characterization of time-varying Gaussian mixture models. We fix the mixture component distributions across all time periods to overcome data sparsity and accurately describe Toronto's spatial structure, while representing the complex spatio-temporal dynamics through time-varying mixture weights. We constrain the mixture weights to capture weekly seasonality, and apply a conditionally autoregressive prior on the mixture weights of each component to represent location-specific short-term serial dependence and daily seasonality. While estimation may be performed using a fixed number of mixture components, we also extend to estimate the number of components using birth-and-death Markov chain Monte Carlo. The proposed model is shown to give higher statistical predictive accuracy and to reduce the error in predicting EMS operational performance by as much as two-thirds compared to a typical industry practice