Ian S. Evans

Comparison of polynomial models for land surface curvature calculation

Curvature is a fundamental surface property whose application, for example in geomorphology and hydrology, has long been recognised. Its measurement from Digital Terrain Models (DTMs) has received less attention than that of slope, and there is even disagreement about which definitions of curvature are most applicable. Here these problems are related to semantic problems in the definition of the land surface, and three distinct algorithms for the three main gravity-related components of curvature are compared for both artificial and real surfaces. Quadratic-based algorithms are shown to give more stable results. Higher-order local surfaces (e.g. partial quartic) can fit more complex landform features, but are reliable only for very accurate data.

The selection of class intervals

The selection of class intervals, which can strongly affect the visual impression given by a map, is currently a totally anarchic branch of cartography. While practising cartographers have barely accustomed themselves to the routine techniques of class selection, recent work has widened the choice available and extended the opportunity to produce a desired bias. Systems of class intervals, apart from those fixed exogenously or in arbitrary fashion, are classified into idiographic or serial types, the latter being recommended here. Scale transformations leading towards symmetrical frequency distribu- tions are important and are required for proportional as well as graded symbolization. It is suggested that class intervals should not be optimized in relation to details of the statistical frequency distribution, but should be selected according to the overall shape of this distribution. For rectangular distributions, equal division of the range is appropriate: for dominantly unimodal distributions, intervals related to the standard deviation (on a scale which makes the distribution symmetrical): and for J-shaped distributions, geometric progressions to bases which are greater as skewness increases. Techniques are given for calibrating geometric progressions relative to the median, and for dealing with the special characteristics of percentages. An analysis of maps prepared by authors in various academic disciplines fails to show any rational or standardized procedures for the selection of class intervals. Evidently intuition, inspiration, revelation, mystical hunches, prejudices, legerdemain and predetermined ideas of what the class intervals should be have characterized the work of most map-makers ... Apparently many authors believe that maps are an art-form which allow liberties not admissible in verbal or tabular presentation. (Jenks and Coulson, 1963, p. 120)

Identification and characteristics of surge-type glaciers on Novaya Zemlya, Russian Arctic

We present a comprehensive new inventory of surge-type glaciers on the Novaya Zemlya archipelago, using high-resolution (up to 4 m) satellite imagery from 1976/77 (Hexagon), 1989 (Landsat TM), 2001 (Landsat ETM+) and 2006 (ASTER). A total of 692 glaciers and their forelands were observed for glaciological and geomorphological criteria indicative of glacier surging (e.g. looped moraines, heavy surface crevassing, surface potholes, thrust-block moraines, concertina eskers). This enabled the identification of 32 potential surge-type glaciers (compared with four previously identified) representing 4.6% of the total but 18% by glacier area. We assess the characteristics of surge-type glaciers. Surge-type glaciers are statistically different from non-surge-type glaciers in terms of their area, length, surface slope, minimum elevation, mid-range elevation and terminus type. They are typically long (median length 18.5 km), large (median area 106.8 km 2 ) outlet glaciers, with relatively low overall surface slopes (median slope 1.7°) and tend to terminate in water (marine or lacustrine). They are predominantly directed towards and located in the more maritime western region of the Russian Arctic, and we suggest that surge occurrence might be related to large and complex catchment areas that receive increased delivery of precipitation from the Barents Sea.

Abraded rock landforms (whalebacks) developed under ice streams in mountain areas

Like many mountain ranges, the Coast Mountains of British Columbia, Canada, have undergone both local and ice-sheet glaciation. Effects of ice sheets are concentrated along major valleys and on adjacent spurs and passes which carried strong flows of diffluent ice. The major valleys are broad glacial troughs with frequent rock basins. Their slopes are broken into rounded, steep-sided bosses whalebacks abraded on all sides: they are of the order of 100 m to 1 km long, and 10 m high. In the southern Coast Mountains, the distribution of these whalebacks is consistent with a proposed pattern of former ice streams 1.0–2.1 km thick, within the Cordilleran ice sheet. They are best developed where geological structures parallel the valley and thus the former ice-flow direction, but they are found on a range of lithologies and some are transverse to structure. The whalebacks provide an impression of glacial streamlining, and occasionally grade into rock drumlins. Roches moutonnees are rare in the major troughs. It is hypothesised that these whalebacks and rock drumlins develop under ice streams of Greenland or East Antarctic type, sliding rapidly over bedrock and exploiting rock weaknesses to produce streamlined features. Lee slopes are abraded when thick ice suppresses bed separation, even with rapid flow; basal ice of low viscosity would aid this suppression. Water pressures under the ice streams may have remained high, so that lee-side plucking was rare; such plucking is most likely where pressure fluctuates dramatically, and especially when lee cavities under active ice reach atmospheric pressure.

Global variations of local asymmetry in glacier altitude : separation of north-south and east-west components.

North-south and east-west differences in firn-line altitude, equilibrium-line altitude or middle altitudes of glaciers can be separated by regression on the cosine and sine of glacier aspect (accumulation area azimuth). Allowing for regional trends in altitude, the north-south differences expected from radiation and shade effects can be reliably quantified from World Glacier Inventory (WGI) data. The north-south differences are greater in sunnier climates, mid-latitudes and steeper relief. Local altitude differences between north- and south-facing glaciers are commonly 70-320 m. Such asymmetry is near-universal, although weak in the Arctic and tropics. East-west contrasts are less, and found mainly in the tropics and areas most exposed to strong winds. Altitude, latitude, glacier gradient and height range, calculable from most of the WGI data, are potential controls on the degree of north-south contrast, as well as surrogates for climatic controls (temperature, precipitation, radiation and cloudiness). An asymmetric sine-cosine power model is developed to describe the variation of north-south contrast with latitude. Multiple regression over 51 regions shows altitude and latitude to be the strongest controls of this contrast. Aspect-altitude analysis for former glaciers provides new evidence of cloudiness.

Apparent Fractal Dimensions from Continental Scale Digital Elevation Models Using Variogram Methods

It is often assumed that real land surfaces demonstrate the statistically self-affine scaling behaviour of fractional Brownian surfaces. Tests of this assumption against empirical data, however, show many deviations. Estimates of fractal properties vary between methods and over different scale ranges. So far, this empirical evidence has come from the analysis of variograms for DEMs representing areas up to tens of kilometres in diameter. Here we report results obtained by using variograms to analyse land surface DEMs at the continental scale, with a grid resolution of 30 arc seconds. Results reveal variogram curvature and breaks of slope, but also linear sections over distance lags of hundreds of kilometres. The estimated mean fractal dimension calculated from these sections is 2.66, substantially higher for all continents at these broad scales (around 200 km) than values calculated at the erosional landscape scale (around 200 m). Thus the land surface is not self-affine, and it is not clear that it follows any simple multifractal model. At the longest wavelengths, patterns found in the variograms appear to be related to broad tectonic features of the Earths surface. For the reader to assess their quality and generality, estimates of fractal dimension should always be accompanied by statements of the scale range covered and the goodness of fit to a log-linear relationship.

The Glacial Geomorphology and Surficial Geology of the South-West English Lake District

Abstract Please click here to download the map associated with this article. The glacial geomorphology of the south-west Lake District has been mapped over 98 km using 1:10,000 aerial photography, Google Earth images and a high resolution digital elevation model (NEXTMap). The area is subdivided into two map sheets (eastern and western) and includes Upper Eskdale, the Langdales, the valleys surrounding Wastwater and the neighbouring valley of Ennerdale. The maps include 9 surficial geology units in addition to the various geomorphological features. Suites of arcuate moraine ridges record the sequential retreat of topographically-controlled glaciers. Flutings, which may relate to radial outflow of ice from the central fells during the Late Devensian, are also present. ‘Paraglacially modified sediments and scree’ is the largest of the map units, reflecting the extensive occurrence of ancient and present-day hillslope processes in the region. More recent palaeo-glaciological reconstructions of the Younger Dryas (12.7—11.5 ka BP) ice extent in the Lake District remain spatially restricted, with many covering only small areas of the Lake District. Furthermore, these reconstructions suggest substantially different ice configurations. In particular, the south-west Lake District remains a key area of uncertainty. We use the geomorphological maps presented in this paper to produce new reconstructions of Younger Dryas ice extent in the south-west Lake District. We combine this with previously published reconstructions from across the whole Lake District to provide a complete regional Younger Dryas ice reconstruction.

Third-order geomorphometric variables (derivatives): definition, computation and utilization of changes of curvatures

Third-order geomorphometric variables (based on third derivatives of the altitudinal field) have been neglected in geomorphometry, but their application to the delimitation of surface objects will lead to their increasing significance in future. New techniques of computation, presented and evaluated here, facilitate their use. This paper summarizes recent knowledge concerning definition, computation and geomorphologic interpretation of these variables. Formulae defining various third-order variables are unified based on the physical definition of slope gradient. Methods for their computation are compared from the point of view of method error and error generated by digital elevation model (DEM) inaccuracy. For exact mathematical test surfaces, the most natural and simple variant of the method of central differences (CD2) shows a method error 2–3 times smaller than the other methods used recently in geomorphometry. However, success in coping with DEM inaccuracy depends (for a given grid mesh) on the number and weighting of points from which the derivative is computed. This was tested for surfaces with varying degrees of random error. Here least squares-based methods are the most effective for mixed derivatives (especially for finer grids and less accurate DEMs), while a variant of the CD method, that repeats numerical evaluation of first derivatives (CD1), is the most successful for derivatives in cardinal directions. The CD2 method is generally the most successful for coarser grids where the method error is dominant. Utilization of third-order variables is documented from examples of terrain feature (ridge, valley and edge) extraction and from a first statistical test of the hypothesis that real segments of the land surface have a tendency to a constant value of some morphometric variable. For detection of (sharp) ridges and valleys, it is shown that the rate of change of tangential curvature is inadequate: rate of change of normal curvature is also required. A basic confirmation of the constant-value tendency is provided.

Glacier Distribution in the Alps: Statistical Modelling of Altitude and Aspect

Abstract Mass balance of glaciers in mountain areas varies not only with altitude and regional position but also with aspect, gradient, glacier size, glacier type and detailed topographic position. These factors are combined here in models of how glacier altitude varies, tested with data for the Alps edited from the World Glacier Inventory. An overall northward tendency in glacier numbers (toward 005 ± 4°) and lower altitudes (013 ± 5°) is maintained across a range of glacier sizes, types, altitudes and the major divisions of the Alps. Variation with aspect of glacier altitude (and, by implication, of glacier balance) in the Alps is essentially unimodal, and north‐facing glaciers average 220 m lower in middle altitude than south‐facing: 148 m in the Western Alps, 232 m in the West‐central, 252 m in the East‐central, and 268 m in the Eastern Alps. For smaller subdivisions, confidence intervals on estimates are broader and many differences lack statistical significance. Contrasts are greater in the higher massifs, with greater relief, and lower in cloudy, windward areas. There are small windrelated tendencies east of north along the northern and western fringes, but trends across space are weak: position is thus treated by subdivision into districts and groups. Mid‐altitude averages 2891 m overall and varies from 2552 to 3127 m for 27 glacier districts, and from 2124 to 3209 m for 103 glacier groups. Glacier mid‐altitude varies also with glacier form, nourishment, height range and area, which account for over two‐thirds of variance in combined models.

Climatogenic north-south asymmetry of local glaciers in Spitsbergen and other parts of the Arctic

Abstract Although World Glacier Inventory (WGI) data for 241 local glaciers (>1 km2 in area) in Svalbard show a mean aspect of 014˚ ± 24˚, their mid-altitudes are lowest for an aspect of 109˚ ± 46˚, which is inconsistent. Further data are generated here for the altitude, length and source aspect of 205 local glaciers (0.3–6.0 km long) in the main area of local glaciation in Svalbard, Nordenskiöld Land. All four mountain blocks have mean glacier source aspects of 356˚ to 018˚; the overall mean is 011˚ ± 8˚. Mid-altitudes are lowest at 042˚ ±21˚, predicted to be 53 m lower than on opposite aspects. Lowest altitudes are predicted at 009˚ to 030˚, averaging 157 m lower than on opposite aspects. These results show that local, land-terminating glaciers around 78˚ N are affected more by north-south radiation receipt contrasts than by wind effects, consistent with the trend found across most other Arctic regions. It is concluded that, although weaker than in mid-latitudes, contrasts due to slope climates are substantial even in Arctic glaciers. This is apparent only when small, steep glaciers are inventoried: WGI data are incomplete and users need to check the thresholds of coverage.