The counterpropagating Rossby wave perspective on Kelvin Helmholtz instability as a limiting case of a Rayleigh shear layer with zero width

The Kelvin Helmholtz (KH) problem, with zero stratification, is examined as a limiting case of the Rayleigh model of a single shear layer whose width tends to zero. The transition of the Rayleigh modal dispersion relation to the KH one, as well as the disappearance of the supermodal transient growth in the KH limit, are both rationalized from the counterpropagating Rossby wave perspective.

The radial width of a coronal mass ejection between 0.1 and 0.4 AU estimated from the heliospheric imager on STEREO

On 15-17 February 2008, a CME with an approximately circular cross section was tracked through successive images obtained by the Heliospheric Imager (HI) instrument onboard the STEREO-A spacecraft. Reasoning that an idealised flux rope is cylindrical in shape with a circular cross-section, best fit circles are used to determine the radial width of the CME. As part of the process the radial velocity and longitude of propagation are determined by fits to elongation-time maps as 252±5 km/s and 70±5° respectively. With the longitude known, the radial size is calculated from the images, taking projection effects into account. The radial width of the CME, S (AU), obeys a power law with heliocentric distance, R, as the CME travels between 0.1 and 0.4 AU, such that S=0.26 R0.6±0.1. The exponent value obtained is compared to published studies based on statistical surveys of in situ spacecraft observations of ICMEs between 0.3 and 1.0 AU, and general agreement is found. This paper demonstrates the new opportunities provided by HI to track the radial width of CMEs through the previously unobservable zone between the LASCO field of view and Helios in situ measurements.

Performance of GPRS coding scheme detection under severe multipath and co-channel interference as a function of soft-bit width

The General Packet Radio Service (GPRS) has been developed for the mobile radio environment to allow the migration from the traditional circuit switched connection to a more efficient packet based communication link particularly for data transfer. GPRS requires the addition of not only the GPRS software protocol stack, but also more baseband functionality for the mobile as new coding schemes have be en defined, uplink status flag detection, multislot operation and dynamic coding scheme detect. This paper concentrates on evaluating the performance of the GPRS coding scheme detection methods in the presence of a multipath fading channel with a single co-channel interferer as a function of various soft-bit data widths. It has been found that compressing the soft-bit data widths from the output of the equalizer to save memory can influence the likelihood decision of the coding scheme detect function and hence contribute to the overall performance loss of the system. Coding scheme detection errors can therefore force the channel decoder to either select the incorrect decoding scheme or have no clear decision which coding scheme to use resulting in the decoded radio block failing the block check sequence and contribute to the block error rate. For correct performance simulation, the performance of the full coding scheme detection must be taken into account.

Movement time for motion-impaired users assisted by force-feedback: effects of movement amplitude, target width and gravity well width

This paper presents a study investigating how the performance of motion-impaired computer users in point and click tasks varies with target distance (A), target width (W), and force-feedback gravity well width (GWW). Six motion-impaired users performed point and click tasks across a range of values for A, W, and GWW. Times were observed to increase with A, and to decrease with W. Times also improved with GWW, and, with the addition of a gravity well, a greater improvement was observed for smaller targets than for bigger ones. It was found that Fitts Law gave a good description of behaviour for each value of GWW, and that gravity wells reduced the effect of task difficulty on performance. A model based on Fitts Law is proposed, which incorporates the effect of GWW on movement time. The model accounts for 88.8% of the variance in the observed data.

Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

Is DARTEL-based voxel-based morphometry affected by width of smoothing kernel and group size? A study using simulated atrophy

Purpose: To quantify to what extent the new registration method, DARTEL (Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra), may reduce the smoothing kernel width required and investigate the minimum group size necessary for voxel-based morphometry (VBM) studies. Materials and Methods: A simulated atrophy approach was employed to explore the role of smoothing kernel, group size, and their interactions on VBM detection accuracy. Group sizes of 10, 15, 25, and 50 were compared for kernels between 0–12 mm. Results: A smoothing kernel of 6 mm achieved the highest atrophy detection accuracy for groups with 50 participants and 8–10 mm for the groups of 25 at P < 0.05 with familywise correction. The results further demonstrated that a group size of 25 was the lower limit when two different groups of participants were compared, whereas a group size of 15 was the minimum for longitudinal comparisons but at P < 0.05 with false discovery rate correction. Conclusion: Our data confirmed DARTEL-based VBM generally benefits from smaller kernels and different kernels perform best for different group sizes with a tendency of smaller kernels for larger groups. Importantly, the kernel selection was also affected by the threshold applied. This highlighted that the choice of kernel in relation to group size should be considered with care.

Centennial variations in sunspot number, open solar flux and streamer belt width: 1. correction of the sunspot number record since 1874

We analyse the widely-used international/ Zürich sunspot number record, R, with a view to quantifying a suspected calibration discontinuity around 1945 (which has been termed the “Waldmeier discontinuity” [Svalgaard, 2011]). We compare R against the composite sunspot group data from the Royal Greenwich Observatory (RGO) network and the Solar Optical Observing Network (SOON), using both the number of sunspot groups, N{sub}G{\sub}, and the total area of the sunspots, A{sub}G{\sub}. In addition, we compare R with the recently developed interdiurnal variability geomagnetic indices IDV and IDV(1d). In all four cases, linearity of the relationship with R is not assumed and care is taken to ensure that the relationship of each with R is the same before and after the putative calibration change. It is shown the probability that a correction is not needed is of order 10{sup}−8{\sup} and that R is indeed too low before 1945. The optimum correction to R for values before 1945 is found to be 11.6%, 11.7%, 10.3% and 7.9% using A{sub}G{\sub}, N{sub)G{\sub}, IDV, and IDV(1d), respectively. The optimum value obtained by combining the sunspot group data is 11.6% with an uncertainty range 8.1-14.8% at the 2σ level. The geomagnetic indices provide an independent yet less stringent test but do give values that fall within the 2σ uncertainty band with optimum values are slightly lower than from the sunspot group data. The probability of the correction needed being as large as 20%, as advocated by Svalgaard [2011], is shown to be 1.6 × 10{sup}−5{\sup}.

Centennial variations in sunspot number, open solar flux and streamer belt width: 2. Comparison with the geomagnetic data

We investigate the relationship between interdiurnal variation geomagnetic activity indices, IDV and IDV(1d), corrected sunspot number, R{sub}C{\sub}, and the group sunspot number R{sub}G{\sub}. R{sub}C{\sub} uses corrections for both the “Waldmeier discontinuity”, as derived in Paper 1 [Lockwood et al., 2014c], and the “Wolf discontinuity” revealed by Leussu et al. [2013]. We show that the simple correlation of the geomagnetic indices with R{sub}C{\sub}{sup}n{\sup} or R{sub}G{\sub}{sup}n{\sup} masks a considerable solar cycle variation. Using IDV(1d) or IDV to predict or evaluate the sunspot numbers, the errors are almost halved by allowing for the fact that the relationship varies over the solar cycle. The results indicate that differences between R{sub}C{\sub} and R{sub}G{\sub} have a variety of causes and are highly unlikely to be attributable to errors in either R{sub}G{\sub} alone, as has recently been assumed. Because it is not known if R{sub}C{\sub} or R{sub}G{\sub} is a better predictor of open flux emergence before 1874, a simple sunspot number composite is suggested which, like R{sub}G{\sub}, enables modelling of the open solar flux for 1610 onwards in Paper 3, but maintains the characteristics of R{sub}C{\sub}.

Centennial variations in sunspot number, open solar flux and streamer belt width: 3. Modelling

From the variation of near-Earth interplanetary conditions, reconstructed for the mid-19th century to the present day using historic geomagnetic activity observations, Lockwood and Owens [2014] have suggested that Earth remains within a broadened streamer belt during solar cycles when the Open Solar Flux (OSF) is low. From this they propose that the Earth was immersed in almost constant slow solar wind during the Maunder minimum (c. 1650-1710). In this paper, we extend continuity modelling of the OSF to predict the streamer belt width using both group sunspot numbers and corrected international sunspot numbers to quantify the emergence rate of new OSF. The results support the idea that the solar wind at Earth was persistently slow during the Maunder minimum because the streamer belt was broad.

Nightside studies of coherent HF Radar spectral width behaviour

A previous case study found a relationship between high spectral width measured by the CUTLASS Finland HF radar and elevated electron temperatures observed by the EISCAT and ESR incoherent scatter radars in the postmidnight sector of magnetic local time. This paper expands that work by briefly re-examining that interval and looking in depth at two further case studies. In all three cases a region of high HF spectral width (>200 ms−1) exists poleward of a region of low HF spectral width (<200 ms^{−1}). Each case, however, occurs under quite different geomagnetic conditions. The original case study occurred during an interval with no observed electrojet activity, the second study during a transition from quiet to active conditions with a clear band of ion frictional heating indicating the location of the flow reversal boundary, and the third during an isolated substorm. These case studies indicate that the relationship between elevated electron temperature and high HF radar spectral width appears on closed field lines after 03:00 magnetic local time (MLT) on the nightside. It is not clear whether the same relationship would hold on open field lines, since our analysis of this relationship is restricted in latitude. We find two important properties of high spectral width data on the nightside. Firstly the high spectral width values occur on both open and closed field lines, and secondly that the power spectra which exhibit high widths are both single-peak and multiple-peak. In general the regions of high spectral width (>200 ms−1) have more multiple-peak spectra than the regions of low spectral widths whilst still maintaining a majority of single-peak spectra. We also find that the region of ion frictional heating is collocated with many multiplepeak HF spectra. Several mechanisms for the generation of high spectral width have been proposed which would produce multiple-peak spectra, these are discussed in relation to the data presented here. Since the regions of high spectral width are observed both on closed and open field lines the use of the boundary between low and high spectral width as an ionospheric proxy for the open/closed field line boundary is not a simple matter, if indeed it is possible at all.

Occurrence probability, width and number of steps of cusp precipitation for fully pulsed reconnection at the dayside magnetopause

We discuss the characteristics of magnetosheath plasma precipitation in the “cusp” ionosphere for when the reconnection at the dayside magnetopause takes place only in a series of pulses. It is shown that even in this special case, the low-altitude cusp precipitation is continuous, unless the intervals between the pulses are longer than observed intervals between magnetopause flux transfer event (FTE) signatures. We use FTE observation statistics to predict, for this case of entirely pulsed reconnection, the occurrence frequency, the distribution of latitudinal widths, and the number of ion dispersion steps of the cusp precipitation for a variety of locations of the reconnection site and a range of values of the local de-Hoffman Teller velocity. It is found that the cusp occurrence frequency is comparable with observed values for virtually all possible locations of the reconnection site. The distribution of cusp width is also comparable with observations and is shown to be largely dependent on the distribution of the mean reconnection rate, but pulsing the reconnection does very slightly increase the width of that distribution compared with the steady state case. We conclude that neither cusp occurrence probability nor width can be used to evaluate the relative occurrence of reconnection behaviors that are entirely pulsed, pulsed but continuous and quasi-steady. We show that the best test of the relative frequency of these three types of reconnection is to survey the distribution of steps in the cusp ion dispersion characteristics.

On the speed of the eddy-driven jet and the width of the Hadley cell in the Southern Hemisphere

A strong correlation between the speed of the eddy-driven jet and the width of the Hadley cell is found to exist in the Southern Hemisphere, both in reanalysis data and in twenty-first-century integrations from the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report multimodel archive. Analysis of the space–time spectra of eddy momentum flux reveals that variations in eddy-driven jet speed are related to changes in the mean phase speed of midlatitude eddies. An increase in eddy phase speeds induces a poleward shift of the critical latitudes and a poleward expansion of the region of subtropical wave breaking. The associated changes in eddy momentum flux convergence are balanced by anomalous meridional winds consistent with a wider Hadley cell. At the same time, faster eddies are also associated with a strengthened poleward eddy momentum flux, sustaining a stronger westerly jet in midlatitudes. The proposed mechanism is consistent with the seasonal dependence of the interannual variability of the Hadley cell width and appears to explain at least part of the projected twenty-first-century trends.

Rossby wave propagation on potential vorticity fronts with finite width

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here an approximate correction is derived for the case of a finite width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.