Atmospheric predictability revisited

This article examines the potential to improve numerical weather prediction (NWP) by estimating upper and lower bounds on predictability by re-visiting the original study of Lorenz (1982) but applied to the most recent version of the European Centre for Medium Range Weather Forecasts (ECMWF) forecast system, for both the deterministic and ensemble prediction systems (EPS). These bounds are contrasted with an older version of the same NWP system to see how they have changed with improvements to the NWP system. The computations were performed for the earlier seasons of DJF 1985/1986 and JJA 1986 and the later seasons of DJF 2010/2011 and JJA 2011 using the 500-hPa geopotential height field. Results indicate that for this field, we may be approaching the limit of deterministic forecasting so that further improvements might only be obtained by improving the initial state. The results also show that predictability calculations with earlier versions of the model may overestimate potential forecast skill, which may be due to insufficient internal variability in the model and because recent versions of the model are more realistic in representing the true atmospheric evolution. The same methodology is applied to the EPS to calculate upper and lower bounds of predictability of the ensemble mean forecast in order to explore how ensemble forecasting could extend the limits of the deterministic forecast. The results show that there is a large potential to improve the ensemble predictions, but for the increased predictability of the ensemble mean, there will be a trade-off in information as the forecasts will become increasingly smoothed with time. From around the 10-d forecast time, the ensemble mean begins to converge towards climatology. Until this point, the ensemble mean is able to predict the main features of the large-scale flow accurately and with high consistency from one forecast cycle to the next. By the 15-d forecast time, the ensemble mean has lost information with the anomaly of the flow strongly smoothed out. In contrast, the control forecast is much less consistent from run to run, but provides more detailed (unsmoothed) but less useful information.

The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed and oral language) and numerical factors that include single-digit processing efficiency and multi-digit skills such as number system knowledge and estimation. This study of third graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in three significant arithmetic skills: basic calculation fluency, written multi-digit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill and their contributions are both independent of each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multi-digit skills. These findings indicate that many factors matter but multi-digit skills matter most in third grade mathematical achievement.

Estimation of sea surface temperature from the Spinning Enhanced Visible and Infra Red Imager, improved using numerical weather prediction

Most of the operational Sea Surface Temperature (SST) products derived from satellite infrared radiometry use multi-spectral algorithms. They show, in general, reasonable performances with root mean square (RMS) residuals around 0.5 K when validated against buoy measurements, but have limitations, particularly a component of the retrieval error that relates to such algorithms' limited ability to cope with the full variability of atmospheric absorption and emission. We propose to use forecast atmospheric profiles and a radiative transfer model to simulate the algorithmic errors of multi-spectral algorithms. In the practical case of SST derived from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) onboard Meteosat Second Generation (MSG), we demonstrate that simulated algorithmic errors do explain a significant component of the actual errors observed for the non linear (NL) split window algorithm in operational use at the Centre de Météorologie Spatiale (CMS). The simulated errors, used as correction terms, reduce significantly the regional biases of the NL algorithm as well as the standard deviation of the differences with drifting buoy measurements. The availability of atmospheric profiles associated with observed satellite-buoy differences allows us to analyze the origins of the main algorithmic errors observed in the SEVIRI field of view: a negative bias in the inter-tropical zone, and a mid-latitude positive bias. We demonstrate how these errors are explained by the sensitivity of observed brightness temperatures to the vertical distribution of water vapour, propagated through the SST retrieval algorithm.

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.

Are power calculations useful? A multicentre neuroimaging study

There are now many reports of imaging experiments with small cohorts of typical participants that precede large-scale, often multicentre studies of psychiatric and neurological disorders. Data from these calibration experiments are sufficient to make estimates of statistical power and predictions of sample size and minimum observable effect sizes. In this technical note, we suggest how previously reported voxel-based power calculations can support decision making in the design, execution and analysis of cross-sectional multicentre imaging studies. The choice of MRI acquisition sequence, distribution of recruitment across acquisition centres, and changes to the registration method applied during data analysis are considered as examples. The consequences of modification are explored in quantitative terms by assessing the impact on sample size for a fixed effect size and detectable effect size for a fixed sample size. The calibration experiment dataset used for illustration was a precursor to the now complete Medical Research Council Autism Imaging Multicentre Study (MRC-AIMS). Validation of the voxel-based power calculations is made by comparing the predicted values from the calibration experiment with those observed in MRC-AIMS. The effect of non-linear mappings during image registration to a standard stereotactic space on the prediction is explored with reference to the amount of local deformation. In summary, power calculations offer a validated, quantitative means of making informed choices on important factors that influence the outcome of studies that consume significant resources.

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

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.

Numerical analyses of Runge–Kutta implicit–explicit schemes for horizontally explicit, vertically implicit solutions of atmospheric models

With the prospect of exascale computing, computational methods requiring only local data become especially attractive. Consequently, the typical domain decomposition of atmospheric models means horizontally-explicit vertically-implicit (HEVI) time-stepping schemes warrant further attention. In this analysis, Runge-Kutta implicit-explicit schemes from the literature are analysed for their stability and accuracy using a von Neumann stability analysis of two linear systems. Attention is paid to the numerical phase to indicate the behaviour of phase and group velocities. Where the analysis is tractable, analytically derived expressions are considered. For more complicated cases, amplification factors have been numerically generated and the associated amplitudes and phase diagnosed. Analysis of a system describing acoustic waves has necessitated attributing the three resultant eigenvalues to the three physical modes of the system. To do so, a series of algorithms has been devised to track the eigenvalues across the frequency space. The result enables analysis of whether the schemes exactly preserve the non-divergent mode; and whether there is evidence of spurious reversal in the direction of group velocities or asymmetry in the damping for the pair of acoustic modes. Frequency ranges that span next-generation high-resolution weather models to coarse-resolution climate models are considered; and a comparison is made of errors accumulated from multiple stability-constrained shorter time-steps from the HEVI scheme with a single integration from a fully implicit scheme over the same time interval. Two schemes, “Trap2(2,3,2)” and “UJ3(1,3,2)”, both already used in atmospheric models, are identified as offering consistently good stability and representation of phase across all the analyses. Furthermore, according to a simple measure of computational cost, “Trap2(2,3,2)” is the least expensive.

An integrated study of urban microclimates in Chongqing, China: historical weather data, transverse measurement and numerical simulation

Chongqing is the largest central-government-controlled municipality in China, which is now under going a rapid urbanization. The question remains open: What are the consequences of such rapid urbanization in Chongqing in terms of urban microclimates? An integrated study comprising three different research approaches is adopted in the present paper. By analyzing the observed annual climate data, an average rising trend of 0.10◦C/decade was found for the annual mean temperature from 1951 to 2010 in Chongqing,indicating a higher degree of urban warming in Chongqing. In addition, two complementary types of field measurements were conducted: fixed weather stations and mobile transverse measurement. Numerical simulations using a house-developed program are able to predict the urban air temperature in Chongqing.The urban heat island intensity in Chongqing is stronger in summer compared to autumn and winter.The maximum urban heat island intensity occurs at around midnight, and can be as high as 2.5◦C. In the day time, an urban cool island exists. Local greenery has a great impact on the local thermal environment.Urban green spaces can reduce urban air temperature and therefore mitigate the urban heat island. The cooling effect of an urban river is limited in Chongqing, as both sides of the river are the most developed areas, but the relative humidity is much higher near the river compared with the places far from it.