We have developed a method of animal localisation that detects the angle from a sensor towards the direction of an animal call. The method is as simple to use as deploying a conventional static sound recorder, but provides tracking information as well as sound recordings. The principal of operation is to detect the phase difference between microphones positioned closely together. The phase is detected by converting the signals to their analytic form with a Hilbert transform. The angle is then calculated from the phase difference, frequency and microphone separation. Angular measurements provide flight paths above the sensor, and can give details of activity and behaviour that are not possible with a single channel static recorder. We recorded flight paths for 5 bat species on a single night at a site in Denmark (Pipistrellus nathusii, Pipistrellus pygmaeus, Eptesicus serotinus, Myotis daubentonii and Nyctalus noctula). The median error in angular measurement for the species was between 3 and 7 degrees. Calls at high angles from normal, corresponding with a poor signal-to-noise ratio, had larger errors compared to calls recorded in the centre of the field of view. Locations in space could be estimated by combining angular measurements from two or more sensors.

Summary Climate change is a global threat to species, and their capacity to adapt could be limited by habitat fragmentation. Many initiatives to restore habitats, increase connectivity and/or ensure ‘functioning ecological networks’ are explicitly or implicitly trying to address this threat. However, existing methods of analysing networks mainly treat the landscape as static, and it is difficult to use these to plan restoration. We use a recent method to approximate the speed of a species’ range expansion through a landscape by an analogy to an electrical circuit, which takes into account both the rates of colonisation between patches and the rates at which occupied habitat produces new emigrants. Based on this, we propose and test two methods that can help to optimise the spatial arrangement of habitat for range expansion. First, high current flowing through a habitat patch indicates that it should be a priority for conservation, and this can be the basis of an algorithm for iteratively dropping the least valuable patches. Secondly, high power in a link between two patches indicates that it is a bottleneck in the circuit, and this can be the basis of an algorithm for iteratively adding new patches in the most efficient places. We show that these methods perform well for a variety of realistic landscape patterns, assuming known and fixed dispersal ability and source/target locations. The calculations involved for each parameter set are fast enough to be used as building blocks in a larger optimisation for practical planning of landscapes for multiple species. Thus, we lay the foundation for a new genre of systematic conservation planning, which efficiently proposes restoration as well as minimising loss.

We combine new and published satellite observations and the results of a coupled ice‐ocean model to provide the first estimate of changes in the quantity of ice floating in the global oceans and the consequent sea level contribution. Rapid losses of Arctic sea ice and small Antarctic ice shelves are partially offset by thickening of Antarctic sea ice and large Antarctic ice shelves. Altogether, 746 ± 127 km3 yr−1 of floating ice was lost between 1994 and 2004, a value that exceeds considerably the reduction in grounded ice over the same period. Although the losses are equivalent to a small (49 ± 8 μm yr−1) rise in mean sea level, there may be large regional variations in the degree of ocean freshening and mixing. Ice shelves at the Antarctic Peninsula and in the Amundsen Sea, for example, have lost 481 ± 38 km3 yr−1.

This letter describes the impulse response of a pulse-limited altimeter with an elliptical antenna pattern from a uniformly rough surface inclined at an angle to a sphere or, equivalently, from spherical surface and mispointed antenna. An integral for the impulse response is given, and analytic forms for the special cases of a mispointed circular antenna and a nadir-pointed elliptical antenna are derived. An analytic approximation for the case of small ellipticity and small surface gradient (or mispointing) are also given. The letter is illustrated with numerical examples that show the general effect of ellipticity on the impulse response. It also shows that in the practical case of the elliptical CryoSat-2 satellite SIRAL antenna, the analytic approximation is sufficiently accurate to provide a correction for the ellipticity for CryoSat-2 echoes from the ocean surface.

We use ERS‐2 and ENVISAT satellite radar altimetry to examine spatial and temporal changes in the rate of thinning of the Pine Island Glacier, West Antarctica, during the period 1995 to 2006. We show that the pattern of thinning has both accelerated and spread inland to encompass tributaries flowing into the central trunk of the glacier. Within the 5,400 km 2 central trunk, the average rate of volume loss quadrupled from 2.6 ± 0.3 km 3 yr −1 in 1995 to 10.1 ± 0.3 km 3 yr −1 in 2006. The region of lightly grounded ice at the glacier terminus is extending upstream, and the changes inland are consistent with the effects of a prolonged disturbance to the ice flow, such as the effects of ocean‐driven melting. If the acceleration continues at its present rate, the main trunk of PIG will be afloat within some 100 years, six times sooner than anticipated.

Knowledge of sea ice thickness is critical for the prediction of future climate, and for assessing the significance of changes in thickness. Sea ice thickness can be calculated from radar or laser satellite altimetry measurements of freeboard. However, a lack of knowledge of snow depth introduces significant uncertainties into these calculations. This paper compares the first coincident airborne laser and radar altimetry data over sea ice, collected during the Laser Radar Altimetry (LaRA) field campaign. LaRA was a flight of opportunity that provided valuable data to explore techniques to validate satellite measurements of ice freeboard, and the possibility of combining laser and radar measurements over snow covered sea ice to calculate the snow depth. Two new methods were created to analyse these data sets: a new radar retracker and a radar power simulator, which models radar returns from the laser data. We present the first quantitative analysis of data from the LaRA laser and radar altimeters, and demonstrate the potential of combining laser and radar altimetry to estimate snow depth. LaRA elevation estimates compare well with elevations from the radar altimeter onboard ERS-2 at the sub-meter level and the study provides lessons for future validation of satellite altimetry data over sea ice. Laser elevations are consistently higher than the radar elevations over snow covered sea ice. As LaRA was a flight of opportunity, no coincident in-situ measurements were available. Nevertheless, the difference between the reflecting surface of the laser and radar is consistent with snow depth from climatology and the analysis techniques developed in this paper will be useful for future radar and laser altimetry comparisons.

This paper describes the CryoSat satellite mission, due for launch in 2005, whose aim is to accurately determine the trends in Earth’s continental and marine ice fields. The paper’s purpose is to provide scientific users of the CryoSat data with a description of the design and operation of the SIRAL radar and the CryoSat platform, the data products, and the expected error budget. The ‘low-resolution mode’ (LRM), ‘synthetic aperture mode’ (SARM) and “synthetic aperture interferometric mode’ (SARInM) of the SIRAL radar are described, together with its system parameters, its antenna gain pattern and interferometer phase difference pattern, and its calibration modes. The orbit is described, together with the platform attitude and altitude control law and control systems, and the expected pointing and altitude knowledge. The geographical masks that are used to determine acquisitions in the three SIRAL modes are described. The SIRAL data products, and the processing applied to produce them, are described. Level 1b, level 2 and higher-level products are described in turn, with a particular emphasis on the new procedures applied to the SARInM and SARM processing over ice surfaces. The beam forming and multi-looking is summarised, and a description is given of the behaviour of the SARM and SARInM echoes over idealised surfaces. These inform descriptions of the elevation retrievals of the level 2 processing, including the SARInM retrieval of interferometric phase. The combination of these data, through cross-over analysis over continental ice sheets, and through averaging over sea-ice, to determine areal averages of ice sheet elevation change or sea-ice thickness, is described. The error budget in these higher-level products is described, together with its breakdown into errors arising from the instrument and errors arising from the retrievals. The importance of the co-variance of these errors in determining the final error is stressed. The description of the errors also includes a summary of the experiments required following the launch to validate the CryoSat mission data. An estimate of the mission performance over ice surfaces is made at various spatial scales, and it is concluded that even the relatively short, three-year duration of the CryoSat mission will allow it to make an important scientific contribution, particularly when combined with results from earlier satellite missions.

Planetary impact craters have a high degree of radial symmetry. This hampers efforts to identify the azimuthal impact direction for most craters - the radially symmetric component of an impact crater swamps any asymmetries that may be present. We demonstrate how the asymmetric component can be isolated and the direction of the asymmetries quantified using a two-dimensional eigenfunction expansion over a circular domain. The complex coefficients of expansion describe the magnitude and phase (angular alignment) of each term. From the analysis of hypervelocity impact craters formed in the laboratory, with impact angles ranging from 0 degrees to 50 degrees from the surface normal, we show that asymmetries which reveal the impact direction are still present at just 10 degrees from the surface normal, and that the phase of one complex coefficient of expansion, c(11), indicates the impact direction. Analysis of the lunar crater Hadley shows bilateral symmetry in the radially asymmetric component, which may be due to oblique impact. The 31-km lunar ray crater Kepler has morphological features that indicate the azimuthal impact direction. Coefficient c(11) gives an azimuthal impact direction similar to that expected from the morphology, although post-impact gravitational collapse and slumping obscure the result to some degree. Ray craters may provide a means of testing the method for smaller 'simple' craters when data are available.

This paper describes the echo from a beamforming interferometric altimeter from a uniformly scattering surface inclined at an angle to a sphere, underlain by a uniformly scattering volume. The rough "surface" impulse response and the echo and interferometric cross product are determined as functions of the beam direction and the vector surface gradient. These expressions are used to determine the multilooked echo and interferometric phase from such a system. The "effective" number of looks and the multilooked echo coherence, which determine the statistics of the echo power and the interferometric phase, are defined. The dependence of the multilooked echo power and interferometric phase are investigated as functions of the surface vector gradient, surface roughness, volume scattering, and SNR. These behaviors are illustrated using values based on a practical system. The precision of the elevation measurement is examined in the light of the effective number of looks and the coherence of the multilooked echo and cross product. Some conclusions concerning the practical recovery of the range from the echo power are discussed.

Crater morphology in a ductile target can reveal some properties of the impacting particle. Simple measurements alone, such as the crater depth and diameter are limited in potential because the complete morphology is not considered. Detailed shape measurements, made by comparing stereo Scanning Electron Micrographs, can be reduced to a parameter set based on an orthogonal expansion over a circular domain, allowing quantitative comparisons between craters that consider the complete morphology. Most high-velocity impact craters are circular (have a circular rim), enabling us to make a model using only the radially symmetric terms from the orthogonal functions set. Shape parameters can be plotted on a feature space diagram, where similar shaped craters form clusters which can be analysed statistically. The method has been applied to laboratory impacts using a two-stage light-gas gun to fire mineral grains at an aluminium alloy target and glass beads over the velocity range 1–6kms−1. The minerals kamacite and enstatite can be distinguished from crater morphology by this method and we have shown that the shape of impact craters change over the velocity range 1–6kms−1 as well as simply the depth to diameter ratio.

High-resolution topography has recently become available for a number of planetary bodies such as the Moon, Venus, Mercury and particularly Mars, with the 32nd-degree global Martian topography from the Mars Orbital Laser Altimeter on Mars Global Surveyor. Gridded digital elevation models (DEMs) of impact craters can be extracted from these data, and provide an extensive record of planetary impact crater morphologies. It may not be immediately obvious, however, how crater DEMs can be compared, particularly if there are many thousands of individual measurements. Comparison is greatly simplified if the measurements are reduced to an eigenfunction expansion, using the coefficients of expansion for quantitative shape comparison. Four eigenvalue expansions are compared for their suitability: a one-dimensional Fourier sine expansion of a crater cross-section; a two-dimensional Fourier sine expansion; the eigenfunctions of a vibrating circular membrane; and the Zernike polynomials. All are found to be suitable except the two-dimensional Fourier expansion, which fails to converge well on the data because of inappropriate geometry. Expansion spectra of four Martian impact craters, each representing a different class of planetary crater morphology, are calculated with the three suitable methods. The relevance of symmetry (about the crater centre for cross-sections and radial symmetry for two-dimensional expansions) is discussed. Finally, a preliminary survey of Martian impact crater shapes is made, using eigenfunction expansion, which shows three distinct clusters of Martian crater morphology.

We describe a new project to obtain a global characterisation of Martian impact crater morphology from the 1/16 degree MOLA topography dataset. A new mathematical method applicable to both symmetric and asymmetric craters is used.