Reducing noise associated with the Monte Carlo Independent Column Approximation for weather forecasting models

The Monte Carlo Independent Column Approximation (McICA) is a flexible method for representing subgrid-scale cloud inhomogeneity in radiative transfer schemes. It does, however, introduce conditional random errors but these have been shown to have little effect on climate simulations, where spatial and temporal scales of interest are large enough for effects of noise to be averaged out. This article considers the effect of McICA noise on a numerical weather prediction (NWP) model, where the time and spatial scales of interest are much closer to those at which the errors manifest themselves; this, as we show, means that noise is more significant. We suggest methods for efficiently reducing the magnitude of McICA noise and test these methods in a global NWP version of the UK Met Office Unified Model (MetUM). The resultant errors are put into context by comparison with errors due to the widely used assumption of maximum-random-overlap of plane-parallel homogeneous cloud. For a simple implementation of the McICA scheme, forecasts of near-surface temperature are found to be worse than those obtained using the plane-parallel, maximum-random-overlap representation of clouds. However, by applying the methods suggested in this article, we can reduce noise enough to give forecasts of near-surface temperature that are an improvement on the plane-parallel maximum-random-overlap forecasts. We conclude that the McICA scheme can be used to improve the representation of clouds in NWP models, with the provision that the associated noise is sufficiently small.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

Be careful how you ask! Using focus groups and nominal group technique to explore the barriers to learning

Schools have a legal duty to make reasonable adjustments for disabled pupils who experience barriers to learning. Inclusive approaches to data collection ensure that the needs of all children who are struggling are not overlooked. However, it is important that the methods promote sustained reflection on the part of all children, do not inadvertently accentuate differences between pupils, and do not allow individual needs to go unrecognized. This paper examines more closely the processes involved in using Nominal Group Technique to collect the views of children with and without a disability on the difficulties experienced in school. Data were collected on the process as well as the outcomes of using this technique to examine how pupil views are transformed from the individual to the collective, a process that involves making the private, public. Contrasts are drawn with questionnaire data, another method of data collection favoured by teachers. Although more time-efficient this can produce unclear and cursory responses. The views that surface from pupils need also to be seen within the context of the ways in which schools customize the data collection process and the ways in which the format and organization of the activity impact on the responses and responsiveness of the pupils.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Gulliver, medium, technique

In the four Parts of Gulliver’s Travels the narrator attends closely to the manual skills, crafts and techniques of the different countries visited and to the materials and instruments by which they are mediated. The patterned, motif-like presentation of these observations and their rich contextual background, historical and literary, indicate their special significance. These references to technique play an important, previously underappreciated roll in Gulliver. They form a thematic connection between its embodied, sensual, compulsive descriptions of the world and its socio-political satire, the latter focusing on technocratic, professionalized statecraft. They are crucial to the peculiar fullness with which Swift’s writing imagines different communities of practice, different ecologies of mind.