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.

The presented study uses the recent colour aerial photographs, historical black and white aerial photographs, and detailed digital elevation model to assess the spatial distribution and long-term temporal dynamics of soil loss in agriculturally intensively exploited loess hilly land with a subcontinental temperate climate. The strongly eroded soils appear in the studied area as bright patterns, surrounded by darker soils, and they are well visible on aerial photos. Three approaches of interpretation of aerial photographs were tested: visual interpretation, pixel-based image classification, and object-based image classification. All three methods provided detailed maps of soil redistribution patterns. The bright areas as the areas of soil degradation characterized by erosion increased from 1949 until 2011 by 76%. A detailed map of areal erosion patterns was used for the validation of water erosion models. LS-factor of USLE and ED’ index of USPED were selected for expressing the relation of real erosion to the terrain. The relationship between surface morphology and real erosion is very complex, and the tested water erosion models do not express it sufficiently. Therefore, the first and second-order directional derivative of the surface elevations with respect to the tillage direction has been tested. The absolute value of the first-order directional derivative showed better results and better corresponded with the real erosion pattern than the other morphometric characteristics. The findings suggest that tillage is the dominant erosion factor in the area.

Umbrisols generally develop in a cool and humid climate. Therefore, occurrence of these soils in the Borská lowland of southwestern Slovakia is very uncommon, and this inspired the aim of this paper: Analysis of the natural conditions suitable for Umbrisol development. Umbrisols in the Borská lowland developed from aeolian quartz sands accumulated on Neogenne marine clay sediments. Their occurrence is connected with the groundwater table relatively close to the ground surface and this particularly determines Umbrisol genesis in this area. Sufficient input via organic matter is an important factor for formation of the umbric horizon, and only the rich herbaceous undergrowth of the prevailing planted pine and mixed pine-oak forests is capable of providing it. A growth of diep-rooted grass is closely connected with higher soil moisture content, and quite moist areas occur in the deeper inter-dunes depressions. Constant soil moisture in these sites is facilitated by water capillary elevation. While Umbrisols are transformed to Arenosols at increased altitude, they can be transformed to Gleysols in deep depressions. Herein, induced polarization provided suitable geophysical method for detection of arenic Umbrisol inclusions. Sharp transformation of the humus layer to dry non-polarized aeolian quartz sands enabled the surface horizon to be distinguished by induced polarization

One-decade-long observations of post-cut-off channel development and oxbow lake formation are presented to offer insight into the morphological response of the Morava River to neck cut-off. The main objectives were: calculation of the amount of sediment released to the channel by collapse of the meander neck; comparison of floodplain erosion and deposition rates before and after cut-off; and description of the rate and pattern of oxbow lake sedimentation. The amount of sediment released due to cut-off (~35 000 m³) equalled 2–5 years of sediment input by lateral erosion averaged for the past six decades. Bank erosion rates substantially exceeded long-term averages (0.63–6.21 m year⁻¹, post cut-off). Despite a low entrance angle, alluvial plugs in a newly formed oxbow lake were established within a few months. Between 2006 and 2016, sedimentation of the alluvial plugs proceeded at an average rate of 0.55 m year⁻¹, reflecting the time since cut-off and the frequency of overbank flows.

The solar angle of incidence is the angle between the sunlight and the normal on the impact surface. The lower the angle of incidence, the more sun radiation the surface can absorb. There are several methods for calculating of this angle. Determining the geographical location of the equivalent surface is one of the lesser-known options. The equivalent surface is a tangential plane to the Earth that is parallel to a reference inclined surface. The geographical coordinates of the point of tangency are clearly determined by the slope and aspect. Since the equivalent surface is horizontal, basic solar geometry equations apply. Unlike the conventional equations commonly used today, they provide easily interpretable results. The sunrise and sunset times for an inclined surface and the time of an extreme incidence angle can be calculated directly. Approximate calculations are not necessary. In addition, the geographical approach allows for the hour angle to be determined, as well as the tilt for a given azimuth of the solar panel that is perpendicular to direct sunlight. This new procedure sets the time for regular changes in the horizontal direction of the sun-tracker. The renaissance of the geographical approach for calculating the temporal characteristics, which allows for the use of simple equations and the interpretation of their results, can also benefit agriculture, forestry, land management, botany, architecture, and other sectors and sciences.