Fundamental quantitative methods of land surface analysis

Effective quantitative land surface analyses in soil science need scale-free land surface attributes (morphometric variables, MVs) to be introduced for making comparable results obtained at different scales. To investigate the problem in more detail, a conceptual scheme and curvatures studied earlier in Shary (1995) [Math. Geol. 27 (1995) 373] are further developed in this paper, formulae for a complete system of 12 curvatures and some other MVs are given, and modified Evans–Young algorithm for curvature calculation is described that does not emphasize grid directions. The conceptual scheme is based on that MVs often describe not the land surface itself, but rather the system “land surface+vector field”, where vector fields of common interest are gravitational field and solar irradiation. Correspondingly, morphometric variables and concepts may (1) refer to this system description (field-specific), or (2) be invariant with respect to any vector field (field-invariant), that is, describing the land surface itself, its geometrical form. From the other side, MVs and concepts may be (1) local, (2) regional, which need extended portions of a restricted part of land surface for their determination at a given point, or (3) global (planetary), when elevations of all the Earth are needed for their determination at a given point. Global MVs do not consist subject of this paper; so, the four classes of MVs are considered here: class A (local field-specific MVs), class B (regional field-specific), class C (local field-invariant), and class D (regional field-invariant). MVs of these classes permit description of geometrical land form, pre-requisits of surface runoff, thermal regime of slopes, and altitude zonality. Class A contains three independent MVs expressed by first derivatives of elevation Z by plan coordinates (slope steepness, slope direction, solar insolation) and seven curvatures expressed by second derivatives of Z; class C contains five curvatures; class B contains two variables (catchment and dispersal areas); MVs of class D are not introduced yet. Also, some non-system MVs of class A are described, sense of all MVs is described, and interrelationships between MVs are shown. Three curvatures are independent, not two, as this is often implied. It is experimentally shown that average depth of a depression defined in class B may not depend upon scale, while local MVs may not have limit values for large scales. Scale-free morphometric variables are defined here as those that have limit values for large scales. It is experimentally shown that maximal catchment area (class B) is a scale-free variable for thalwegs. These results show that local MVs are scale-specific (except elevation), but scale-free regional MVs might be introduced as a generalization of curvature concept. Two surface runoff accumulation mechanisms are considered in their relation to local and regional field-specific MVs; although the first one is generalized to a regional MV (catchment area), there is no regional MV for the second one description, although it is of great importance in soil science as describing slow profile changes. Geometrical forms were little studied in soil science; arguments are given that they may be useful for studying memory in soils, which is determined by temporal shifts between land surface formation and soil formation processes. The following topics are discussed: the current state of morphometry, an ambiguity in land form definitions, and a possibility to generalize curvature concept for regional scale-free MVs. The consideration is restricted by methods of the general geomorphometry; partial approaches are considered only by selection.

[1]  Robert Finn,et al.  Equilibrium Capillary Surfaces , 1985 .

[2]  E. Jong,et al.  Regional and catenary variations in properties of Borolls of southern Saskatchewan, Canada. , 1990 .

[3]  Dominique King,et al.  Predicting soil classes with parameters derived from relief and geologic materials in a sandstone region of the Vosges mountains (Northeastern France) , 1999 .

[4]  William L. Pan,et al.  Nitrogen use efficiency of winter wheat among landscape positions , 1995 .

[5]  Alex B. McBratney,et al.  Fuzzy‐c‐Means and Kriging for Mapping Soil as a Continuous System , 1992 .

[6]  Chi-Hua Huang.  Empirical Analysis of Slope and Runoff For Sediment Delivery from Interrill Areas , 1995 .

[7]  Jozef Krcho,et al.  Morphometric analysis of relief on the basis of geometric aspect of field theory , 1973 .

[8]  M. Poscolieri,et al.  The Digital Elevation Model of Italy for geomorphology and structural geology , 1992 .

[9]  T. G. Freeman,et al.  Calculating catchment area with divergent flow based on a regular grid , 1991 .

[10]  James C. Bell,et al.  Calibration and Validation of a Soil-Landscape Model for Predicting Soil Drainage Class , 1992 .

[11]  Eolian and Associated Pedogenic Features of the Jornada Basin Floor, Southern New Mexico , 1999 .

[12]  I. Moore,et al.  A contour‐based topographic model for hydrological and ecological applications , 1988, Earth surface processes and landforms.

[13]  D. P. Franzmeier,et al.  Landscape and pedogenesis of an oxisol-inceptisol-ultisol sequence in Southeastern Brazil , 1998 .

[14]  Dan Pennock,et al.  Landform classification and soil distribution in hummocky terrain , 1987 .

[15]  Stefan Hergarten,et al.  Process Modelling and Landform Evolution , 1998 .

[16]  K. Beven,et al.  THE PREDICTION OF HILLSLOPE FLOW PATHS FOR DISTRIBUTED HYDROLOGICAL MODELLING USING DIGITAL TERRAIN MODELS , 1991 .

[17]  R. Daniels,et al.  Landscape and Soil Property Effects on Corn Grain Yield Response to Tillage , 1989 .

[18]  Karl Auerswald,et al.  Using relief parameters in a discriminant analysis to stratify geological areas with different spatial variability of soil properties , 1999 .

[19]  A. N. Strahler.  Hypsometric (area-altitude) analysis of erosional topography. , 1952 .

[20]  L. Martz,et al.  Natural radionuclides in the soils of a small agricultural basin in the Canadian prairies and their association with topography, soil properties and erosion , 1990 .

[21]  R. V. Ruhe,et al.  Elements of the soil landscape. , 1960 .

[22]  F. R. Troeh,et al.  Landform Parameters Correlated to Soil Drainage 1 , 1964 .

[23]  C. Monreal,et al.  Sensitivity of Soil Enzyme Activities to Conservation Practices , 1998 .

[24]  B. J. Carter,et al.  Slope gradient and aspect effects on soils developed from sandstone in Pennsylvania , 1991 .

[25]  A. D. Gordon,et al.  Quantitative and Numerical Methods in Soil Classification and Survey. , 1978 .

[26]  Margaret Young,et al.  Statistical Characterization of Altitude Matrices by Computer. Report 5. Terrain Analysis: Program Documentation , 1978 .

[27]  Gary A. Peterson,et al.  Soil Attribute Prediction Using Terrain Analysis , 1993 .

[28]  G. G. Pohlman.  Soil Science Society of America , 1940 .

[29]  Alex B. McBratney,et al.  Soil pattern recognition with fuzzy-c-means : application to classification and soil-landform interrelationships , 1992 .

[30]  Ian S. Evans,et al.  Relations between land surface properties: Altitude, slope and curvature , 1999 .

[31]  A. R. Aandahl,et al.  The Characterization of Slope Positions and Their Influence on the Total Nitrogen Content of a Few Virgin Soils of Western Iowa , 1949 .

[32]  V. Klemeš.  Conceptualization and scale in hydrology , 1983 .

[33]  L. Martz,et al.  CATCH: a FORTRAN program for measuring catchment area from digital elevation models , 1988 .

[34]  F. Hole.  Geomorphology: Geomorphic Processes and Surficial Geology , 1975 .

[35]  F. Hole,et al.  Soil Science Society of America Meetings , 1970 .

[36]  Variation of Soil Water Storage across a Sand Plain Hillslope , 1995 .

[37]  William A. Reiners,et al.  Net Erosion on a Sagebrush Steppe Landscape as Determined by Cesium‐137 Distribution , 1991 .

[38]  I. Evans.  Statistical Characterization of Altitude Matrices by Computer. Report 6. An Integrated System of Terrain Analysis and Slope Mapping. , 1979 .

[39]  Keith C. Clarke,et al.  Scale-Based Simulation of Topographic Relief , 1988 .

[40]  N. McKenzie,et al.  Spatial prediction of soil properties using environmental correlation , 1999 .

[41]  G. Matheron.  Random Sets and Integral Geometry , 1976 .

[42]  Alex B. McBratney,et al.  Elucidation of soil-landform interrelationships by canonical ordination analysis , 1991 .

[43]  K. Beven,et al.  A physically based, variable contributing area model of basin hydrology , 1979 .

[44]  James C. Bell,et al.  Soil drainage class probability mapping using a soil-landscape model , 1994 .

[45]  L. Wilding,et al.  Close-interval spatial variability of Udertic Paleustalfs in East Central Texas. , 1990 .

[46]  E. Giusti.  Minimal surfaces and functions of bounded variation , 1977 .

[47]  P. A. Shary,et al.  Land surface in gravity points classification by a complete system of curvatures , 1995 .

[48]  Dennis Timlin,et al.  Spatial and temporal variability of corn grain yield on a hillslope , 1998 .

[49]  Andrea J. van Doorn,et al.  Two-plus-one-dimensional differential geometry , 1994, Pattern Recognition Letters.

[50]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[51]  Richard J. Chorley.  Spatial analysis in geomorphology , 1972 .

[52]  M. Costa-Cabral,et al.  Digital Elevation Model Networks (DEMON): A model of flow over hillslopes for computation of contributing and dispersal areas , 1994 .

[53]  G. F. Hall,et al.  LAND‐SURFACE MORPHOLOGY: 2. PREDICTING POTENTIAL LANDSCAPE INSTABILITY IN EASTERN OHIO , 1983 .

[54]  J. Maxwell.  L. On hills and dales: To the editors of the Philosophical Magazine and Journal , 1870 .

[55]  D. Zasłavsky,et al.  THE EFFECT OF SOIL SURFACE CURVATURE ON MOISTURE AND YIELD—BEER SHEBA OBSERVATION , 1981 .

[56]  Jean-Jacques Macaire,et al.  Relationship of the presence of a non-calcareous clay–loam horizon to DEM attributes in a gently sloping area , 1999 .

[57]  Ole H. Jacobsen,et al.  RELATIONS BETWEEN SPECIFIC SURFACE AREA AND SOIL PHYSICAL AND CHEMICAL PROPERTIES , 1996 .