The spectral balances involved in shaping the short gravity wave region of the ocean wave-height spectrum have been the subject of recent physical models. In terms of the wind friction velocity u*, gravitational acceleration g and local wavenumber k, these models predict a wavenumber dependence of $k^{-\frac{7}{2}}$, where k = |k|, and a linear dependence on u* for the equilibrium range of gravity waves above the spectral peak. In this paper we present the results of an experimental determination of the wavenumber spectrum for the wavelength range of 0.2−1.6 m, based on stereophotogrammetric determinations from an oil platform under open ocean conditions.From our observations, for this wavenumber range, the one-dimensional equilibrium wavenumber spectrum was determined as \[ \phi (k_i) \sim \left(\frac{u^2_*k}{g}\right)^{\gamma} k^{-3}_{i}\;\;\;\;\;\;\;(i=1,2 \;\;\; K = (k_1,k_2)) \] where γ = 0.09±0.09 at the 95% confidence level. These limits embrace wind-independent approximations to the observed one-dimensional and two-dimensional wavenumber spectra of the form \[ \phi (k_i) \sim B k^{-3}_i \;\;\; (i = 1,2), \] and \[ \psi(k_i) \sim A k^{-4}, \] respectively, with B ∼ 10−4 and A ∼ 0.3 × 10−4 for $(u^2_*k_i/g)=10^{-2}$ and k = |k| is expressed in cycles/metre.The present findings do not support the wavenumber dependence predicted by the recent models in this wavenumber range and are at variance with their predicted dependence on the friction velocity. However, our observations are generally consistent with the radar reflectivity dependence on wind direction and wind speed under Bragg scattering conditions within our wavenumber range. The experimental observations also point out the potentially important role of wave-breaking of longer wave components in influencing the spectral levels of short gravity wave components.

Peer assessment typically requires students to judge peers' work against assessment criteria. We tested an alternative approach in which students judged pairs of scripts against one another in the absence of assessment criteria. First year mathematics undergraduates (N = 194) sat a written test of conceptual understanding of multivariable calculus, then assessed their peers' responses using pairwise comparative judgement. Inter-rater reliability was investigated by randomly assigning the students to two groups and correlating the two groups' assessments. Validity was investigated by correlating the peers' assessments with (i) expert assessments, (ii) novice assessments, and (iii) marks from other module tests. We found high validity and inter-rater reliability, suggesting that the students performed well as peer assessors. We interpret the results in the light of survey and interview feedback, and discuss directions for further research and development into the benefits and drawbacks of peer assessment without assessment criteria.

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The importance of improving students' understanding of core concepts in mathematics is well established. However, assessing the impact of different teaching interventions designed to improve students' conceptual understanding requires the validation of adequate measures. Here we propose a novel method of measuring conceptual understanding based on comparative judgement (CJ). Contrary to traditional instruments, the CJ approach allows test questions for any topic to be developed rapidly. In addition, CJ does not require a detailed rubric to represent conceptual understanding of a topic, as it is instead based on the collective knowledge of experts. In the current studies, we compared CJ to already established instruments to measure three topics in mathematics: understanding the use of p-values in statistics, understanding derivatives in calculus, and understanding the use of letters in algebra. The results showed that CJ was valid as compared to established instruments, and achieved high reliability. We conclude that CJ is a quick and efficient alternative method of measuring conceptual understanding in mathematics and could therefore be particularly useful in intervention studies.

The aim of this paper is to present a comparison of video- and sensor-based studies of swimming performance. The video-based approach is reviewed and contrasted to the newer sensor-based technology, specifically accelerometers based upon Micro-Electro-Mechanical Systems (MEMS) technology. Results from previously published swim performance studies using both the video and sensor technologies are summarised and evaluated against the conventional theory that upper arm movements are of primary interest when quantifying free-style technique. The authors conclude that multiple sensor-based measurements of swimmers' acceleration profiles have the potential to offer significant advances in coaching technique over the traditional video based approach.