Bootstrap prediction intervals for autoregressive time series

The calculation of interval forecasts for highly persistent autoregressive (AR) time series based on the bootstrap is considered. Three methods are considered for countering the small-sample bias of least-squares estimation for processes which have roots close to the unit circle: a bootstrap bias-corrected OLS estimator; the use of the Roy–Fuller estimator in place of OLS; and the use of the Andrews–Chen estimator in place of OLS. All three methods of bias correction yield superior results to the bootstrap in the absence of bias correction. Of the three correction methods, the bootstrap prediction intervals based on the Roy–Fuller estimator are generally superior to the other two. The small-sample performance of bootstrap prediction intervals based on the Roy–Fuller estimator are investigated when the order of the AR model is unknown, and has to be determined using an information criterion.

Analytical and numerical solutions describing the inward solidification of a binary melt

We present a mathematical model describing the inward solidification of a slab, a circular cylinder and a sphere of binary melt kept below its equilibrium freezing temperature. The thermal and physical properties of the melt and solid are assumed to be identical. An asymptotic method, valid in the limit of large Stefan number is used to decompose the moving boundary problem for a pure substance into a hierarchy of fixed-domain diffusion problems. Approximate, analytical solutions are derived for the inward solidification of a slab and a sphere of a binary melt which are compared with numerical solutions of the unapproximated system. The solutions are found to agree within the appropriate asymptotic regime of large Stefan number and small time. Numerical solutions are used to demonstrate the dependence of the solidification process upon the level of impurity and other parameters. We conclude with a discussion of the solutions obtained, their stability and possible extensions and refinements of our study.

Communicating probabilistic information from climate model ensembles—lessons from numerical weather prediction

Climate model ensembles are widely heralded for their potential to quantify uncertainties and generate probabilistic climate projections. However, such technical improvements to modeling science will do little to deliver on their ultimate promise of improving climate policymaking and adaptation unless the insights they generate can be effectively communicated to decision makers. While some of these communicative challenges are unique to climate ensembles, others are common to hydrometeorological modeling more generally, and to the tensions arising between the imperatives for saliency, robustness, and richness in risk communication. The paper reviews emerging approaches to visualizing and communicating climate ensembles and compares them to the more established and thoroughly evaluated communication methods used in the numerical weather prediction domains of day-to-day weather forecasting (in particular probabilities of precipitation), hurricane and flood warning, and seasonal forecasting. This comparative analysis informs recommendations on best practice for climate modelers, as well as prompting some further thoughts on key research challenges to improve the future communication of climate change uncertainties.

Problems with binary pattern measures for flood model evaluation

As the calibration and evaluation of flood inundation models are a prerequisite for their successful application, there is a clear need to ensure that the performance measures that quantify how well models match the available observations are fit for purpose. This paper evaluates the binary pattern performance measures that are frequently used to compare flood inundation models with observations of flood extent. This evaluation considers whether these measures are able to calibrate and evaluate model predictions in a credible and consistent way, i.e. identifying the underlying model behaviour for a number of different purposes such as comparing models of floods of different magnitudes or on different catchments. Through theoretical examples, it is shown that the binary pattern measures are not consistent for floods of different sizes, such that for the same vertical error in water level, a model of a flood of large magnitude appears to perform better than a model of a smaller magnitude flood. Further, the commonly used Critical Success Index (usually referred to as F<2 >) is biased in favour of overprediction of the flood extent, and is also biased towards correctly predicting areas of the domain with smaller topographic gradients. Consequently, it is recommended that future studies consider carefully the implications of reporting conclusions using these performance measures. Additionally, future research should consider whether a more robust and consistent analysis could be achieved by using elevation comparison methods instead.

Representation of model error in a convective-scale ensemble prediction system

In this paper ensembles of forecasts (of up to six hours) are studied from a convection-permitting model with a representation of model error due to unresolved processes. The ensemble prediction system (EPS) used is an experimental convection-permitting version of the UK Met Office’s 24- member Global and Regional Ensemble Prediction System (MOGREPS). The method of representing model error variability, which perturbs parameters within the model’s parameterisation schemes, has been modified and we investigate the impact of applying this scheme in different ways. These are: a control ensemble where all ensemble members have the same parameter values; an ensemble where the parameters are different between members, but fixed in time; and ensembles where the parameters are updated randomly every 30 or 60 min. The choice of parameters and their ranges of variability have been determined from expert opinion and parameter sensitivity tests. A case of frontal rain over the southern UK has been chosen, which has a multi-banded rainfall structure. The consequences of including model error variability in the case studied are mixed and are summarised as follows. The multiple banding, evident in the radar, is not captured for any single member. However, the single band is positioned in some members where a secondary band is present in the radar. This is found for all ensembles studied. Adding model error variability with fixed parameters in time does increase the ensemble spread for near-surface variables like wind and temperature, but can actually decrease the spread of the rainfall. Perturbing the parameters periodically throughout the forecast does not further increase the spread and exhibits “jumpiness” in the spread at times when the parameters are perturbed. Adding model error variability gives an improvement in forecast skill after the first 2–3 h of the forecast for near-surface temperature and relative humidity. For precipitation skill scores, adding model error variability has the effect of improving the skill in the first 1–2 h of the forecast, but then of reducing the skill after that. Complementary experiments were performed where the only difference between members was the set of parameter values (i.e. no initial condition variability). The resulting spread was found to be significantly less than the spread from initial condition variability alone.

Implications of model error for numerical climate prediction

Numerical climate models constitute the best available tools to tackle the problem of climate prediction. Two assumptions lie at the heart of their suitability: (1) a climate attractor exists, and (2) the numerical climate model's attractor lies on the actual climate attractor, or at least on the projection of the climate attractor on the model's phase space. In this contribution, the Lorenz '63 system is used both as a prototype system and as an imperfect model to investigate the implications of the second assumption. By comparing results drawn from the Lorenz '63 system and from numerical weather and climate models, the implications of using imperfect models for the prediction of weather and climate are discussed. It is shown that the imperfect model's orbit and the system's orbit are essentially different, purely due to model error and not to sensitivity to initial conditions. Furthermore, if a model is a perfect model, then the attractor, reconstructed by sampling a collection of initialised model orbits (forecast orbits), will be invariant to forecast lead time. This conclusion provides an alternative method for the assessment of climate models.

The potential of 1 h refractivity changes from an operational C-band magnetron-based radar for numerical weather prediction validation and data assimilation

Refractivity changes (ΔN) derived from radar ground clutter returns serve as a proxy for near-surface humidity changes (1 N unit ≡ 1% relative humidity at 20 °C). Previous studies have indicated that better humidity observations should improve forecasts of convection initiation. A preliminary assessment of the potential of refractivity retrievals from an operational magnetron-based C-band radar is presented. The increased phase noise at shorter wavelengths, exacerbated by the unknown position of the target within the 300 m gate, make it difficult to obtain absolute refractivity values, so we consider the information in 1 h changes. These have been derived to a range of 30 km with a spatial resolution of ∼4 km; the consistency of the individual estimates (within each 4 km × 4 km area) indicates that ΔN errors are about 1 N unit, in agreement with in situ observations. Measurements from an instrumented tower on summer days show that the 1 h refractivity changes up to a height of 100 m remain well correlated with near-surface values. The analysis of refractivity as represented in the operational Met Office Unified Model at 1.5, 4 and 12 km grid lengths demonstrates that, as model resolution increases, the spatial scales of the refractivity structures improve. It is shown that the magnitude of refractivity changes is progressively underestimated at larger grid lengths during summer. However, the daily time series of 1 h refractivity changes reveal that, whereas the radar-derived values are very well correlated with the in situ observations, the high-resolution model runs have little skill in getting the right values of ΔN in the right place at the right time. This suggests that the assimilation of these radar refractivity observations could benefit forecasts of the initiation of convection.

Prediction of Staphylococcus aureus antimicrobial resistance by whole-genome sequencing

Whole-genome sequencing (WGS) could potentially provide a single platform for extracting all the information required to predict an organism’s phenotype. However, its ability to provide accurate predictions has not yet been demonstrated in large independent studies of specific organisms. In this study, we aimed to develop a genotypic prediction method for antimicrobial susceptibilities. The whole genomes of 501 unrelated Staphylococcus aureus isolates were sequenced, and the assembled genomes were interrogated using BLASTn for a panel of known resistance determinants (chromosomal mutations and genes carried on plasmids). Results were compared with phenotypic susceptibility testing for 12 commonly used antimicrobial agents (penicillin, methicillin, erythromycin, clindamycin, tetracycline, ciprofloxacin, vancomycin, trimethoprim, gentamicin, fusidic acid, rifampin, and mupirocin) performed by the routine clinical laboratory. We investigated discrepancies by repeat susceptibility testing and manual inspection of the sequences and used this information to optimize the resistance determinant panel and BLASTn algorithm. We then tested performance of the optimized tool in an independent validation set of 491 unrelated isolates, with phenotypic results obtained in duplicate by automated broth dilution (BD Phoenix) and disc diffusion. In the validation set, the overall sensitivity and specificity of the genomic prediction method were 0.97 (95% confidence interval [95% CI], 0.95 to 0.98) and 0.99 (95% CI, 0.99 to 1), respectively, compared to standard susceptibility testing methods. The very major error rate was 0.5%, and the major error rate was 0.7%. WGS was as sensitive and specific as routine antimicrobial susceptibility testing methods. WGS is a promising alternative to culture methods for resistance prediction in S. aureus and ultimately other major bacterial pathogens.

A review on Arctic sea ice predictability and prediction on seasonal-to-decadal timescales

Sea ice plays a crucial role in the earth's energy and water budget and substantially impacts local and remote atmospheric and oceanic circulations. Predictions of Arctic sea ice conditions a few months to a few years in advance could be of interest for stakeholders. This article presents a review of the potential sources of Arctic sea ice predictability on these timescales. Predictability mainly originates from persistence or advection of sea ice anomalies, interactions with the ocean and atmosphere and changes in radiative forcing. After estimating the inherent potential predictability limit with state-of-the-art models, current sea ice forecast systems are described, together with their performance. Finally, some challenges and issues in sea ice forecasting are presented, along with suggestions for future research priorities.

Advanced feature selection methods in multinominal dementia classification from structural MRI data

Recent studies showed that features extracted from brain MRIs can well discriminate Alzheimer’s disease from Mild Cognitive Impairment. This study provides an algorithm that sequentially applies advanced feature selection methods for findings the best subset of features in terms of binary classification accuracy. The classifiers that provided the highest accuracies, have been then used for solving a multi-class problem by the one-versus-one strategy. Although several approaches based on Regions of Interest (ROIs) extraction exist, the prediction power of features has not yet investigated by comparing filter and wrapper techniques. The findings of this work suggest that (i) the IntraCranial Volume (ICV) normalization can lead to overfitting and worst the accuracy prediction of test set and (ii) the combined use of a Random Forest-based filter with a Support Vector Machines-based wrapper, improves accuracy of binary classification.

Information and predictability: bookmakers, prediction markets and tipsters as forecasters

The more information is available, and the more predictable are events, the better forecasts ought to be. In this paper forecasts by bookmakers, prediction markets and tipsters are evaluated for a range of events with varying degrees of predictability and information availability. All three types of forecast represent different structures of information processing and as such would be expected to perform differently. By and large, events that are more predictable, and for which more information is available, do tend to be forecast better.

Evaluation of boundary-layer type in a weather forecast model utilising long-term Doppler lidar observations

Many studies evaluating model boundary-layer schemes focus either on near-surface parameters or on short-term observational campaigns. This reflects the observational datasets that are widely available for use in model evaluation. In this paper we show how surface and long-term Doppler lidar observations, combined in a way to match model representation of the boundary layer as closely as possible, can be used to evaluate the skill of boundary-layer forecasts. We use a 2-year observational dataset from a rural site in the UK to evaluate a climatology of boundary layer type forecast by the UK Met Office Unified Model. In addition, we demonstrate the use of a binary skill score (Symmetric Extremal Dependence Index) to investigate the dependence of forecast skill on season, horizontal resolution and forecast leadtime. A clear diurnal and seasonal cycle can be seen in the climatology of both the model and observations, with the main discrepancies being the model overpredicting cumulus capped and decoupled stratocumulus capped boundary-layers and underpredicting well mixed boundary-layers. Using the SEDI skill score the model is most skillful at predicting the surface stability. The skill of the model in predicting cumulus capped and stratocumulus capped stable boundary layer forecasts is low but greater than a 24 hr persistence forecast. In contrast, the prediction of decoupled boundary-layers and boundary-layers with multiple cloud layers is lower than persistence. This process based evaluation approach has the potential to be applied to other boundary-layer parameterisation schemes with similar decision structures.

Impacts of increasing the aerosol complexity in the Met Office global numerical weather prediction model.

The inclusion of the direct and indirect radiative effects of aerosols in high-resolution global numerical weather prediction (NWP) models is being increasingly recognised as important for the improved accuracy of short-range weather forecasts. In this study the impacts of increasing the aerosol complexity in the global NWP configuration of the Met Office Unified Model (MetUM) are investigated. A hierarchy of aerosol representations are evaluated including three-dimensional monthly mean speciated aerosol climatologies, fully prognostic aerosols modelled using the CLASSIC aerosol scheme and finally, initialised aerosols using assimilated aerosol fields from the GEMS project. The prognostic aerosol schemes are better able to predict the temporal and spatial variation of atmospheric aerosol optical depth, which is particularly important in cases of large sporadic aerosol events such as large dust storms or forest fires. Including the direct effect of aerosols improves model biases in outgoing long-wave radiation over West Africa due to a better representation of dust. However, uncertainties in dust optical properties propagate to its direct effect and the subsequent model response. Inclusion of the indirect aerosol effects improves surface radiation biases at the North Slope of Alaska ARM site due to lower cloud amounts in high-latitude clean-air regions. This leads to improved temperature and height forecasts in this region. Impacts on the global mean model precipitation and large-scale circulation fields were found to be generally small in the short-range forecasts. However, the indirect aerosol effect leads to a strengthening of the low-level monsoon flow over the Arabian Sea and Bay of Bengal and an increase in precipitation over Southeast Asia. Regional impacts on the African Easterly Jet (AEJ) are also presented with the large dust loading in the aerosol climatology enhancing of the heat low over West Africa and weakening the AEJ. This study highlights the importance of including a more realistic treatment of aerosol–cloud interactions in global NWP models and the potential for improved global environmental prediction systems through the incorporation of more complex aerosol schemes.

How do I know if my forecasts are better? Using benchmarks in Hydrological ensemble prediction

The skill of a forecast can be assessed by comparing the relative proximity of both the forecast and a benchmark to the observations. Example benchmarks include climatology or a naïve forecast. Hydrological ensemble prediction systems (HEPS) are currently transforming the hydrological forecasting environment but in this new field there is little information to guide researchers and operational forecasters on how benchmarks can be best used to evaluate their probabilistic forecasts. In this study, it is identified that the forecast skill calculated can vary depending on the benchmark selected and that the selection of a benchmark for determining forecasting system skill is sensitive to a number of hydrological and system factors. A benchmark intercomparison experiment is then undertaken using the continuous ranked probability score (CRPS), a reference forecasting system and a suite of 23 different methods to derive benchmarks. The benchmarks are assessed within the operational set-up of the European Flood Awareness System (EFAS) to determine those that are ‘toughest to beat’ and so give the most robust discrimination of forecast skill, particularly for the spatial average fields that EFAS relies upon. Evaluating against an observed discharge proxy the benchmark that has most utility for EFAS and avoids the most naïve skill across different hydrological situations is found to be meteorological persistency. This benchmark uses the latest meteorological observations of precipitation and temperature to drive the hydrological model. Hydrological long term average benchmarks, which are currently used in EFAS, are very easily beaten by the forecasting system and the use of these produces much naïve skill. When decomposed into seasons, the advanced meteorological benchmarks, which make use of meteorological observations from the past 20 years at the same calendar date, have the most skill discrimination. They are also good at discriminating skill in low flows and for all catchment sizes. Simpler meteorological benchmarks are particularly useful for high flows. Recommendations for EFAS are to move to routine use of meteorological persistency, an advanced meteorological benchmark and a simple meteorological benchmark in order to provide a robust evaluation of forecast skill. This work provides the first comprehensive evidence on how benchmarks can be used in evaluation of skill in probabilistic hydrological forecasts and which benchmarks are most useful for skill discrimination and avoidance of naïve skill in a large scale HEPS. It is recommended that all HEPS use the evidence and methodology provided here to evaluate which benchmarks to employ; so forecasters can have trust in their skill evaluation and will have confidence that their forecasts are indeed better.