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Geography Domain
Candidate:
PhDc. Niculiță Mihai
University Al. I Cuza Iași
Faculty of Geografie and Geology
Coordonator științific:
prof. univ. dr. Constantin Rusu
A framework for geomorphometric
analysis of landforms represented on
digital surface elevation terrain
models
Iași, 2012
1 Geomorphology, Geomorphometry and geomorphometric analysis
1.1 Geomorphology
Geomorphology, taken as it is: “ge”=Earth, „morphe”=form; “logos”=speech, is the science which study
the aspects/shapes of Earth’s surface (Chorley et al., 1984). Starting from the etymology, various
geomorphologists added content to this research direction. Chorley et al. (1984) suggests that the geomorphologic
approach revolve around two areas: one evolutionary/genetic (genesis and evolution of landforms) and other
functional (form-process relationships).
Geomorphologic approach has four branches (Chorley, 1966), which are consecutive or not, and which are the
realistic approach, of the daily geomorphology. The process which combine these specific approaches, giving
meaning and unity to the geomorphologic approach is the geomorphologic analysis.
1.2 Geomorphometry
Geomorphometry is the branch that deals with the study of the earth's surface forms (in this, etymology is
clear: morphometry of the Earth). It is considered an investigative method of geomorphology (Goudie et al.,
2005). New trends see Geomorphometry as a separate science (Pike, 2000, Pike et al., 2009). We believe that the
use of statistics, mathematics and computer science is not an argument for considering geomorphometry as
separate science, this trend of diversification of research methods being also present in other sciences (Biology -
Biomathematics, Biostatistics, Bioinformatics). At most, these types of diversity give rise to disciplinary or border
branches. Geomorphometry is "the science of quantitative analysis of land surface" (Pike, 1995, 2000),
"quantitative description and analysis of geometric-topological characteristics of the landscape" (Rasemann et al.,
2004).
The synthetic, but at the same time the most comprehensive presentation of geomorphometry is made by Evans
(1972), although currently the most cited reference is that of geomorfometrie Pike (2000).
1.3 Geomorphometric analysis
Already there are several monographic works (Wilson and Gallant, 2000; Hengl and Reuter, 2009), which
deals with important theoretical and methodological geomorphometric aspects, but the applications referred in this
monographs are closer to soil science, climatology-meteorology, hydrology, and so on, being actually a
characterization of measurable quantitative relationship between the elements of the earth's surface and some
physical-geographical components. The present approach of geomorphometric analysis, is seen as the construction
of models for the analysis of geomorphometric variables and objects/shapes, in order to use them in statistical,
geostatistic and spatial analysis, with applicability in geomorphometric control of geomorphologic processes, in
stating and testing work hypotheses in geomorphology, the geomorphometric and geomorphologic mapping and
regionalization. These analysis models, we associate with the concept of geomorphometric analysis and expand
the concept of geomorphologic analysis in geomorphology.
Going on the idea of general geomorphometry (terrestrial surface is considered as a whole) and specific
geomorphometry (considering only the specific parts of the earth's surfacet) geomorphometric analysis can be
applied to all land surfaces or to specific components (geomorphometric objects/landforms), by studying of
which, we can understand the formation and evolution under the influence of genetic factors.
In the analytical approach we use conceptual analysis in the first instance by separating the
concepts/components, then analyze them with the use of mathematical analysis, geometric analysis and statistical
analysis (descriptive statistics and inferential statistics). Segmentation/fragmentation is thus both at the formal and
conceptual level, hence geomorphometric analysis application opportunities in both mapping / geomorphologic
regionalization and landform development.
2 The digital framework for geomorphometric analysis of landforms from digital terrain altitude
surface models
Geomorphometry and geomorphometric analysis currently are closely related to digital terrain altitude
surface models and computer science, with views that the use of these, give to geomorphometry a separate
position (Hengl and Reuter, 2009). Whatever being the view, for or against this position, it is clear that
geomorphometry trend is towards automation and computerization of the acquisition, visualization and analysis of
geomorphometric data. Therefore we believe that theorizing should be doubled by its implementation in
digital/computer environment.
2.1 Flowchart for the process of geomorphometric analysis of landforms from digital terrain altitude
surface models Practical application of geomorphometric analysis involves a series of steps and sources that binds on the
idea of input - process - output. Fig. presents a flowchart of the steps of geomorphometric analysis. Input data,
respective a source of altitude, may be presented directly as DTASM, or may require the creation of one.
Identification of errors/uncertainty, creating a model of it/its and preprocessing for disposal is needed for both
situations of altitude source data. Derivation of geomorphometric variables and objects (and their characteristics)
follows, moment at which the stage of obtaining input data in the analysis is completed.
Based on a conceptual model, statistical methods can be applied to input spatial data, which may be
supplemented by additional data, unrelated to DTASM. Variety of methods of analysis is large, requiring
conceptualization of the relationship between variables/objects and processes geomorphometric/geomorphologic
situations.
The result of these methodological analysis is the output data, that can be used in different geomorphologic
analysis issues. The most common uses are predicting presence/rate of geomorphologic processes, the use of
physical models, testing hypotheses or objectification of geomorphologic mapping and geomorphologic
regionalization.
2.2 The digital environment used to support the process of geomorphometric analysis
Expansion of the modern computing capabilities make their use in science, as the standard research
methods, such as mathematics and statistics. Calculation occupies a fundamental position in computer science
(informatics), so this chapter will be an overview of current possibilities of using computer techniques and in
special GIS applications in support of geomorphometric analysis process, insisting on the need for
standardization, automation and use of open source applications. It should be noted that the material in this
chapter should be interpreted as part of the research methodology used in geomorphometric analysis applications.
Given the elements discussed in section 2.2 and the implementation flow chart discussed in section 2.1, a
GUI in QuantumGIS, was performed using Phyton scripting language, which sends commands (via scripts) to
GRASS, SAGA and R. This implementation was named GMORPHALYS (GeoMORPHometric Analysis). It can
be used both in Windows and Linux environments.
GMORPHALYS application can be used both in actual case studies and as a teaching tool because it
summarizes and presented as a staged process of geomorphometric analysis. It is available as a plugin for
Quantum GIS at http://www.geomorphologyonline.com/qgis/mniculita_qgis_repo.xml.
On running, the main window provides a number of settings, while pressing the OK button, the selected
operations to be carried out. Every option selection or completion of an additional window explains the options or
issue warnings in case of wrong selection.
3 Numerical models of land surface
Digital terrain model (DTM) is a general term that refers to the digital representation of ground surface
(Zhilin et al., 2005). This representation can be based on altitude, which can represent both landform and other
topographic details, hence the generic name of the field, but also other geomorphometric variables (slope,
exposition, shading). If we consider also the component of sub-surface (soil and geology), resulting in truly three-
dimensionality, indeed DTM term, is covered fully. Because DTM works nowadays only with ground land area
we believe that the best term is digital model of land surface (DMLS) is the most correct.
The numerical model of land surface elevation (DTASM) is the complete geomorphologic term, referring
to those digital representation of ground surface topography altitude. The shorter version, digital elevation model,
aka DEM is a specimen of DTM, which refers to the representation of land elevation (Pike et al., 2009). Although
generally is not a mistake to use any of the above options, there are situations, when it is important that a digital
representation of the terrain is a DTM, DEM or DTASM.
3.1 Mathematical models of terrain representation
Land surface is a rough surface and is an area of transition between the two environments (solid-fluid),
between which there are many areas of diffusion (boulders, underground cavities), and this limit area should be
considered double and orientable (Shary, 2008) (in terms of gravity we can not think to the negative part, below
the earth's surface, but the outside of it).
Analog and digital mapping of land surface model is made using a smooth model, sampling of the ground
and surface representation being made in certain well-defined three-dimensional measured positions and, between
which the interpolates is done according to distance: land surface is seen as a function of z (altitude) by x and y
(position, distance).
Measurement and representation of land surface elevation is achieved in a Cartesian coordinate system,
according to the coordinates x, y and z. Under this system, the altitude can be conceptualized and processed
mathematically and geometrically for digital representation and geomorphometric processing in several ways.
Digital models are used to represent land elevation are the raster, vector (height points or contour) and TIN.
3.2 Sources of altitude for creation of digital terrain surface altitude models
Photogrammetric stereorestitution is based on stereoscopic vision (Linder, 2006). Stereoscopic vision
allows estimation of the coordinates x, y, z of a point on the earth's surface, photographed (with a photographic
camera whose geometry is known) in at least two positions whose coordinates are known. The point on the earth's
surface must be spotted on both aerial photographs. Geometric relations established between photographic camera
geometry, a point on the earth's surface and aircraft position (aerotriangulation) allow the ortorectification of
aerial images and their transformation into orthophotographs. In the digital aerofotogrammetric stereorestitution
process, occur the following output data (Falkner and Morgan, 2002; Linder, 2006): orthophotographs which can
then be filtered and mosaicked and DTSAM from which contours can be obtained.
Hengl and Evans (2009) believes that after 20 years, the topographic materials become obsolete, some
elements of topography can fall under this category even earlier (dynamic elements such as hydrographic
network).
Satellite images obtained in the visible spectrum as stereographic pair can be used on the same principle
outlined above to derive elevation data, from the point sighted and stereoscopic geometric pattern. SPOT and
ASTER satellite imagery are commonly used to obtain DTSAM.
ASTER-GDEM numerical model available globally for land surface with a resolution of 30 m, is obtained
by stereorestitution of ASTER images (Abrams et al., No year) with a resolution of 15 m.
RADAR satellite images are obtained by scanning the earth's surface with a receiving antenna radar unit
lateral to moving direction above the earth's surface (Oliver and Quegan, 2004). Antenna size is consistent with
wave frequency, wave width and area covered by land area, making and launching of signal acquisition at short
intervals of time, to allow overlap of purchase. Distance to the surface of the earth is estimated from the time
difference and phase of two successive images.
3.3 Creating the digital terrain surface altitude models
When used as sources of altitude, the topographic map elevation data is discrete, but contain a continuity
model to estimate altitude. This model is given by using isolines, contours respectively. Interpolating the
intermediate values from the contour model is performed using mathematical interpolation, the elevation being
interpolated as a function of distance on the two axes x and y). The literature does not clearly specify a method for
obtaining digital models of the earth's surface by interpolating elevation contours, each user choosing interpolators
based on various aspects (availability of GIS interpolators in applications, and so on).
Most used interpolators are the nearest neighbor method, the Bilinear method, the Bicubic method, inverse
distance raised to the power method (IDW), bivariate spline functions with tension (RST) (Mitášová and
Hofierka, 1993; Mitasova and Hofierka, 1990, Neteler and Mitasova, No year), multiple levels of B-spline method
(SGM) (Lee et al., 1997), thin plate spline (TPS) (Donato and Belongia, 2002) and kriging interpolation.
The representation of landforms on topographic maps requires a series of operations to create a digital
model of land surface elevation. These operations can be grouped into three sets: operations of altitude
information densification, interpolation operations and preprocessing operations.
3.4 Errors and uncertainties associated with digital terrain surface models
From the point of view of an analysis of the errors, it should be noted that the error term can be used when
the actual value is known and it is compared with the estimated value. Most times, though, the actual value is not
known, even the most precise measurements having their errors. It is therefore preferable the term uncertainty of
the measurement, interpolation, calculation etc. When, however, we can calculate with some degree a a value of
difference between a range of values considered real and another set of estimated values, we can estimate the
error.
where A is the accuracy DTSAM, B are the characteristics of the land surface, M is the method of
obtaining DTSAM, R is the roughness of the ground, A is accuracy, D is the distribution, DN is the density of
data source, X representing other elements. Each of the components has influence on the error/uncertainty of
DTSAM.
As the roughness increases, the complexity of the surface is bigger and more points will be needed to
describe in detail the surface. Method of DTSAM production influence predominantly the errors, as well as the
source data, which will transfer their errors, but by propagation also to derivation of geomorphometric variables
and objects.
3.5 Digital terrain surface models freely available for Romania
SRTM (Shuttle Radar Topography Mission) mission was conducted by NASA (National Aeronautics and
Space Administration) in collaboration with the NGA (National Geospatial-Intelligence Agency), DLR (German
Aerospace Center) and ASI (Italian Space Agency). Flight which led to SRTM data acquisition took place from
11 to 22 February 2000 (Farr et al., 2007). SRTM data covers only the areas between 60 ° north latitude and 57 °
south latitude. NASA SRTM C-band data is presented in three versions: SRTM1 - represents initial data, with
resolution of ~30 m, available for free only for the U.S., SRTM3 - is the aggregated version of SRTM1 at a
resolution of ~90 m, by two methods, and SRTM30 - which is SRTM1 data aggregated at a resolution of ~1 km.
ASTER mission (Advanced Spaceborne Thermal Emission and Reflection Radiometer) is a satellite
mission data acquisition of thermal emissivity and land reflectance at resolutions ranging from 15.3 to 90 m
(Yamaguchi et al., 1998), a telescope mounted for additional stereographic image acquisition, enabling the
creation of DTASM, even in the absence of checkpoints on the ground, by measuring very precise satellite
ephemerides and instrument calibration (Fujisada et al., 2005).
3.5.3 Improving SRTM3 model for Romania
Interesting for landform studies in Romania, is the question: which of these DTSAM is most closely to the
real land surface elevation. It should be noted that SRTM is a DTSM containing human and vegetation features
altitude, while ASTER GDEM is a DTSAM. However ASTER GDEM has some influence of vegetation and
anthropogenic elements from the stereorestitution process, especially in the lowlands. To the errors of SRTM,
which can be identified by various methods, ASTER GDEM errors have a random component which hinders
correction.
Data presented for Romania does not confirm, nor deny the findings in the literature, about the validity of
SRTM model over ASTER GDEM model. It is required to use local derivatives analysis to determine which
model most closely represent land altitude in Romania.
3.5.3.1 Resampling SRTM3 In the literature it is argued the need of resampling ( downsampling) SRTM3 data in data SRTM1, because
of several reasons: SRTM3 decimated data suffer from the effect of "aliasing" and a resolution of 30 m is
consistent with other data such as Landsat and ASTER.
The results of the application of interpolation methods for resampling of SRTM3 USGS z coordinate points
spaced at 90 m to 30 m resolution related to SRTM1 (data validation was done by substraction from NASA
SRTM1 original data, for several test areas in US) indicate that resampling methods based on kriging give the best
values, so for eg. ordinary kriging is very flexible to apply because it can better control the level of generalization
(results are based on nugget 0, sill 60 and range 90) to MSB, where the maximum level (14) may not be exceeded.
4 Derivation of variables geomoprhometric
Geomorphometric variables are characteristic for general geomorphometry, and can be derived for any
point on the earth's surface (Evans, 1972, Pike et al., 2009).
4.1 General aspects on geomoprhometric variables
Land area is measured quantitatively by geomorphometric variables. To name these characteristics of
Earth's surface shape, in addition to variable, other terms have been used: attribute and parameter.
Variable is a quantity that can take a range of values used in an equation or function. Considering the
terrestrial as a continuous field, primary, secondary derivatives or various quantitative indices of the surface
characteristics, both scalar and vector, it looks normal, both mathematically and conceptually, that the term
variable to be used to express quantitative characteristics the Earth's surface.
Much of geomoprhometric derived variables using windows neighborhoods (known in the literature of
image processing and kernel windows or sliding windows, or windows were the center, the nucleus is concerned,
and its value is obtained by processing a number of neighbors), have variants of image processing filters form
(Olaya, 2009).These filters, are named in the image processing literature convolution filters, being a convolution
calculation, applied to two functions to third option in case f (z, x) and f (z, y) to obtain f (z) space. They are used
in processing images, by assigning a new value to each pixel in a sliding window, applying a weighted function
space.
4.2 Derivation of geomorphometric variables based on digital terrain altitude surface models
4.2.1 Primary derivatives The mathematical basis underlying the calculation of primary derivatives of altitude, is the earth's surface
field definition as a mathematical function. Given this mathematical representation and the fact that most sources
are represented by matrices of altitude, polynomial equations and differential equations were used to derive
formulas for calculating the derivatives of this type of numerical models of the earth's surface. These formulas are
valid only for rasters in Cartesian projections, for geographic projections being derived other formulas.
Mathematically speaking, the same type of calculation can be achieved by using image filters (for raster into
rectangular projections).
Calculus is based on calculating the derivative of a function (Meyer, 1970; Wainwright and Mulligan,
2004), in our case the function that describes the variation of land surface elevation.
The most important derivatives are the primary: slope, aspect (slope direction), shading, visibility factor,
descriptive statistics altitude, elevation amplitude.
4.2.2 Variables of the earth's surface shape
These variables have quantitative values, but they rather express qualitatively the earth's surface: land is
said to be rough, or smooth, but do not have a reliable measure of the boundary between smooth and rough.
Of these, roughness (fragmentation) is used most often, and is quantified by the terrain roughness indices.
4.2.3 Secondary derivatives Are represented by curvatures, mathematical demonstration of the existence and calculation of the
curvatures being given by Shary (1990) and Jordan (2007).Curvature (k) is seen as the inverse of the radius of the
circle shape Earth's surface, according to a plan called in differential geometry, normal section (Shary 1995, Olaya
2009).Since the normal section can be rotated in space, we can define an infinite system of curvatures, from which
may have significance geomorphometric, only a finite set. Establishing these curves is based on several criteria,
from which two are of practical importance.
Using land surface orientation criterion (resulting curvatures dependent on the slope) and their processes
directed by the gravitational force vector, normalization occurs two planes considered in terms of gravity, which
has a vertical component, and the angle x becomes 90 °, can be defined: vertical curvature Evans (1972), (in
profile) and horizontal curvature (contour plan or possibly level curve).
4.2.4 Complex derivatives Derivatives are complex variable geomorphometric that require consideration and physical mechanisms,
apart form the earth's surface.
Drainage length (slope / slope) is the length of flow, as stated by Horton (1945) that the length of water
flow on slopes up to the point where it is concentrated in a channel. The same author shows that its value is
approximately half way between whites, hence half the mutual drainage density.
Topographic moisture index (IUT) was derived from the physical model Topmodel (Beven and Kirkby,
1979), by attempting to define flow in soil (q) during a rain event intensity stationary condition independent of
time, function of upstream drainage area (DA) and the effective length of the curve orthogonal to the direction of
flow level (w):
Stream power index is a dimensionless power function of river erosion upstream drainage area and slope:
4.3 The problem of scale derivation of variables work geomoprhometric The variation of the value of geomoprhometric variables depending on the change in scale has two
components (Zhilin, 2008):
• scale, in scope, talk of local, regional or global, maintaining sampling step size x, y, z;
• scale measuring resolution and representation that involves changing the sampling step size x, y, z,
talking in small-scale (high resolution) or large scale (low resolution).
At present, the main methods of studying the influence of scale derivation and analysis work
geomoprhometric variables, consist of aggregation and de-aggregation of a set of data at lower resolutions, or
higher, to observe variability. Comparison between different resolution data acquisition is also used, but caution is
needed because in these cases the error can not be estimated with precision, and the findings may be inaccurate.
Multiple scale indices can be calculated by dividing the value of a variable computed at a local scale
geomorphometric (3x3 window) geomorphometric calculated value of a variable at a regional scale (9x9 window)
(an example of such an index is the index of topographic position) .An example of considering the scale, the
numerical model SRTM3 aggregation in the data set GMTED2010 (Danielson and Gesch, 2008, Danielson and G
Esch, 2011).
4.4 Errors and uncertainties associated with the derivation of geomorphometric variables Errors and uncertainties associated with the derivation of geomorphometric variables are grouped into two
components: the actual derivation errors associated with variables computing are introduced especially by
derivation algorithms and by error propagation due to errors introduced by numerical models. In general, the
theoretical study, using synthetic surfaces can eliminate errors due to numerical models, and allow analysis
introduced by calculation algorithm.
5 Delimitation of geomorphometric objects and their attributes
Geomorphometric objects are those areas of the earth's surface which are homogeneous according to
different criteria geometric/geomorphometrice or geomorphologic, these features being related to specific
geomorphometry (Pike et al., 2009, MacMillan and Shary, 2009).
5.1 Ontological, semantic and geomorphologic modeling of geomorphometric objects
Currently, ontology has two meanings (Corazzon, 2011).One defines ontology as a branch of philosophy
that studies the existence and the other in the language and knowledge systems, studying abstract entities
(Corazzon, 2011). Translated in geography (Mark et al., 1999) and more recently in geographical information
systems science (GIScience) (Smith and Mark, 2001), geographic ontology is purposeful studying geographical
partitioning of the world mezoscale for joining them to the associated scientific domain partitions (Smith and
Mark, 2001).
Geographical categories are both general and relevant to the field. In geomorphology and geomorphometry,
most typical application of ontology is done at the level of landforms (Mark and Smith, 2003). The notion
landform refers to the unit land area surfaces, which in terms of form, and the genesis and evolution have
homogeneous characteristics. Homogeneity of geometric and geomorphologic features, but also the limit of these
objects, is influenced by the scale of work, requiring consideration of notions such as vagueness, fuzzy, diffusivity
and hierarchy.
We conclude that an approach such as process-form system, just like in soil science there are soil-landscape
systems (Huggett, 1975) is best suited for studying the forms and the processes. These two terms are practically
intertwined, just the need of measuring and explaining, or modeling, leads to their separation. Each process is
discussed quantitatively in a formal context, and the opposite is true (or at least it should be).
At mezoscale-microscale limit, the simplest and comprehensive landform conceptual classification of a
riverine landscape predominantly shaped is the catena type (term introduced by Milne 1935, then expanded in
geomorphology and soil, Gennadiyev and Bockheim, 2006), with the easiest division in hills, slopes and channels.
Geomorphometry is not the only science dealing with surfaces, from this point of view there are some
theorizing in topology and computer science, specific points on surfaces that can be used for digital encoding of
surfaces, the raster model (Peucker and Douglas, 1975), or in the form of graphs, points and edges (Morse, 1968,
Mark, 1977; Rana, 2004).
5.2 Methods for delineating the geomorphometric objects Geomorphometric object delineation is done using various criteria, but often the automated classification,
according to G scale (Haggett et al., 1965) geomorphometric objects can fit both facets and any superior variants
and associations. This classification is defined at a scale or association of scales, and can be extended across G
scales only if using a hierarchical classification. The domain of geomorphometric classifications range from
micro-to mezoscale (MacMillan and Shary, 2009).
5.2.Supervised methods Supervised classification methods are used to create a classification tree based on a conceptual form-
geomorphologic process for classification and delineation of landforms in a given area. Supervision refers to the
fact that there is a semantic conceptualization and geomorphologic a priori, translate the variables used and their
associated thresholds (Hengl and Rossiter, 2003; MacMillan and Shary, 2009).
There are a number of supervised classification that by changing the classification thresholds can be
applied across the entire globe (eg. Iwahashi and Pike, 2007) or any areas of the world. There are supervised
classifications that are made only for areas where there are some landforms that are covered by classification, to
be defined.
Curvatures can be used to classify local form as the trend of curvature. In literature there are indications of
various curvature threshold values to separate linear trend from the concave and convex hillslopes, the most
common being 1/600 m (Schmidt and Hewitt, 2004). Such classifications are: classification of Dikau (Dikau,
1988, Barsch and Dikau, 1989), classification of Wood (Wood, 1996), classification of Schmidt (Schmidt and
Hewitt, 2004) and complete classification of Shary (1995) , Shary and Sharaya (2006)
Complex classifications include besides curvature, slope and drainage area to delineate conceptual elements
of slopes in particular, the idea that the form itself can not completely classify, without making a topographic or
drainage position: Pennock's classification, extended Reuter (Pennock et al., 1987, Pennock, 2001; Reuter, 2003;
Reuter et al., 2006), and classification of MacMillan (MacMillan et al., 2000, MacMillan et al., 2003).
The complex classifications used are: global classification of Pike and Iwahashi (2007), classification of
Hammond Hammond (1954), Hammond (1964), Hammond-Dikau classification (Dikau et al., 1991; Dikau, 1995)
hierarchical classification of MacMillan et al. (2000).
Since Romania fall in the zone of the morphological and genetic temperate zone where river processes are
those governing land surface changes using a conceptual model such as catena based (toposequence) believe that
it is most useful to apply it for regional areas.
5.2.2 Non-supervised methods
Unsupervised methods involve the use of statistical methods for classification of landforms that are not
based on any a priori knowledge about it. However, most non-supervised classifications require as input the
number of classes. This can be calculated from the input data using different methods based on statistical
clustering of input data. Input data are the geomorphometric variables.
These classifications are recently introduced having a high potential to expand geomorphometric
classifications, which are specific to statistics, image processing and remote sensing (Chen, 2008; Nixon and
Aguado, 2008, Tso and Mather, 2009).However problems arise from the size of the area of application of these
methods because the results differ depending on the scope and statistical methods applied, while large sizes raster
requires computing resources.
The most used classifications of this type are multivariate classifications of cluster analysis type, specific to
image segmentation, edge detection or object oriented image (OBIA and GEOBIA).
5.2.3 Contextual merging
Especially for unsupervised classification, the results will not have a direct geomorphologic interpretation,
since these homogeneous morphological areas, regarding certain criteria, being a somewhat basic statistical
objects land area. Therefore, these items should be considered basic and should be merged into objects with
geomorphologic interpretability.
Statistical methods of classification presented can be used successfully in achieving the merging. Romstad
(2001) used cluster algorithms to merge the results of a classification for a steep slope eroded by a series of
streams and their alluvial cones of Spitsbergen.
Criticism of these methods is that they only aggregate results to previous classification without revealing a
high geomorphologic interpretability. Statistical methods give good results on different areas of small extent,
using statistical area making them sensitive to its variation. It is therefore ideal to use spatial adjacency to consider
geomorphometric adjacent spatial objects. In this way, if we analyze each object spatial relations with its
neighbors, we can identify their association patterns to obtain aggregate objects that have relevance and
geomorphology. Dikau (1990) proposed an aggregation hierarchy based on a set of river forms and Mackay et
al. (1992) performed a set of rules based on logical operators for prioritizing glacial landscape.
5.3 Obtaining variables of geomoprhometric objects Once obtained the classification and delineation of geomorphometric objects, an operation is to convert
them (if not already obtained directly in this format) in vector format. For each polygon representing an
geomorphometric object, we can calculate a number of variables: geometric variables such as (geo) morphometry
of the river and watershed and river network hierarchy (Horton, 1945), metric landscapes / land (Farina, 1998),
statistical variables, hypsometric variables such as hypsometric curve (Péguy, 1942), hypsometric integral
(Langbein, 1947) or hipsoclinic curve (Péguy, 1942).
5.4 Errors and uncertainties associated with derivation of variables of geomoprhometric objects
Lindsay and Evans (2008) analyze the effects of errors on DEM-derived river network variables
automatically, while some researchers use drainage network extracted from DTASM with different resolutions
and different sources to evaluate (Hancock, 2005)
Dikau (1999) question the need to delineate and highlight the field landforms that support the attempt to
extract them from maps or digital models through both predictive and by inference.
6 Statistical and spatial analysis methods used for geomorphometric analysis Statistics is a branch of applied mathematics, an "applied mathematics observational data" (Fisher, 1954),
"Uncertainty science that attempts to model the order in disorder" (Cress, 1991), considered "science, technology
and art of extract information from observational data, with emphasis on solving real world problems "(Wilcox,
2009). Modern statistics "provides a methodology for empirical science, being widely used in science and
technology as support for experimental methods, description and analysis, testing and validating hypotheses, etc..
The statistical approach is generally Standard (Wilcox, 2009).The first step is to acquire data that reflects a
sample of that population, the population is seen as all data of that type. Each sample value is a court case, an
object, an individual of a phenomenon, part of the population values phenomenon. Next, the representativeness of
the sample population is tested, the validity of this assumption, leading to the description of data by summarizing
them. The final step is to make statistical inferences (predictions, generalizations), using a probability model to
link findings from a population sample with a defined marginal error (Verzani, 2005).
In this case working with DTSAM, representing land surface elevation. This is a phenomenon random or
deterministic? Although the phenomena that lead to the formation of Earth surface are random, the evolution of
the earth's surface altitudes can find deterministic relations. DTSAM is obtained by interpolating a sample of the
population of altitudes of land surface.
6.1 Descriptive Statistics
Statistical theory is based on the idea that the phenomena can be studied using a data sample of that
phenomenon (intensity, shape), sample which although do not describe the entire population, allow analysis and
conclusions that reflects the whole population. In geomorphology land surface altitudes population is used, or
population of terrestrial surface slopes, landslides population in a given area, etc.. To describe these statistical
populations statistical measures like minimum, maximum, average, is used etc.. or tests to compare the theoretical
distribution with the distribution in question. The association of the theoretical distribution of a population is
based on the empirical analysis of this population distribution and conceptualization of the event that was
sampled.
6.2 Inferential statistics and statistical tests
Statistical tests are used primarily to answer the question: is the statistical variable calculated consistent
with the actual value of the entire population? Test procedures of the validity of this questions are known as
hypothesis testing. Hypothesis testing is done by testing statistical conditions, and taking into account two
possibilities:
• Null hypothesis, H0, is a statement that states a situation where statistical condition is true;
• Alternative hypothesis, Ha, defines what is accepted when the null hypothesis is rejected, the condition
does not apply.
6.3 Multivariate statistics
Multivariate statistical methods include methods such as regression, principal component analysis and
classification by cluster analysis.
6.4 Geostatistics (spatial statistics)
In short, Cressie (1991) describe the spatial statistics as statistical analysis using the spatial locations
defined by the positions x, y, z in a Cartesian system for example) and values of phenomena observed in these
locations (eg. altitude z observed in locations defined above).
Application of geostatistics is based on a series of statistical assumptions (Cressie, 1991). Thus,
independence and independent distribution of data is the basis of any geospatial method, but there is not always
possible to sample such data. Therefore there are a number of models based on a number of assumptions, and used
to implement the geostatistic methods.
Flow of geostatistic analysis requires initial exploratory spatial analysis of geostatistic assumptions
argument. If assumptions of normality is accepted, we can proceed to analyze the correlation between variables,
and possibly if present, using principal component analysis for the extraction of components that explain as much
variance, and still not be collinear to use regression. If assumptions of normality is not supported, but also in the
case of different scales and distributions of variables, the variables are transformed using z scores.
Subsequently, based on the variogram and semivariogram, kriging can be used, as a method of
interpolation / prediction of spatial data based on variogram modeling, and using equation of the model to
estimate the values of the independent variable (Cress, 1989; Cress, 1991 ).Kriging can be translated as optimal
prediction (Cress, 1989).
Variogram modeling and kriging assumptions are similar to the interpolation, by considering space distance
as a parameter of estimation of variance and estimation of variable Z in spatial locations s (Cress, 1989).
However, kriging is applied, depending on a number of assumptions that go beyond spatial interpolations. These
are: presence / absence of anisotropy, presence / absence of trend, presence / absence of spatial autocorrelation,
presence / absence of spatially correlated error and the presence / absence of stationarity.
7 Case studies of the applicability analysis geomoprhometric
7.1 Statistical analysis DTASM representing global land area and national
Currently there are a number of datasets with global coverage of altitude, both for land and for the
submerged areas. Sources used to obtain these DTASM vary, but generally they were obtained by generalization
given by interpolation of data from digitized topographic maps. Another important source is SRTM (SRTM30 and
GMTED2010), and for bathymetry, acoustic surveys and satellite gravity data inversion (Smith and Sandwell,
1997).
Histogram analysis of altitudes of planet Earth and Mars (on which the presence of water in a geological
period is assumed and supported by the presence of valleys and coastline) is interesting to reveal the influence of
planetary processes on altitude.
In Romania, the histogram of DTSAM SRTM3 resampled at 30 m show a similar distribution with the
overall global situation. Most frequently altitudes occur between 0-200 m, with maximum centered on 90 m
Secondary peak is centered around 25 m
7.2 Use of variables in modeling geomorphologic control of geomorphologic processes
7.2.1 Geomorphometric control of soil erosion
Soil erosion is an important geomorphologic process which has a strong geomorphometric control , but its
occurrence, intensity and evolution is defined by the use of the land. Geomorphometric control translates into a
potential of occurrence and intensity of the phenomenon.
Geomorphometric control of soil erosion, and other factors influence can be modeled using USLE
Wischmeier and Smith (1978), existing also with Romanian variant (Moţoc et al., 1979).
USLE model implementation on DTASM require a number of changes to the model imposed by the fact
that compared to data determined by Cs, erosion model USLE / RUSLE proved to underestimate erosion (Warren
et al., 2005). Therefore Mitasova et al. (1996); Mitasova and Mitas (1999), Warren et al. (2005) have developed
two models, RUSLE3D and USPED (Unit Stream Power Erosion Deposition) to overcome the problems of
DTASM model.
Specific geomorphometry can be used to delineate the landforms, respective geomorphometric landform
classifications, for ex. using curvatures, which controls the flow of water from Earth's surface (Shary et al.,
2002).Eelementary forms of slopes, can control acceleration or deceleration, thus governing erosion, or
accumulation (Martz and DeJong, 1991). Valleys, where erosion is minimal as potential can be removed from
USLE modeling. The same situation is also characteristic for concave slope profiles, where depositional potential
is high, while on concave slopes the concentration of runoff potential is high.
7.2.2 Geomorphometric control of landslides
Landslides are geomorphologic processes involving the gravitational flow of materials from surface crust
due to various causes that generate instability of these materials (Ritter et al., 2001). Geomorphometric control is
not the only process control, but it is easier to include in probabilistic models and can be used as covariate
togehter with other factors (Brenning, 2005), Chung , 2006, Carrara and Pike, 2008), Gao and Brown, 2010).The
most used and flexible approach is the probabilistic multinomial logistic regression.
The data set used in the current analysis is comprised from the delineation of debris-flow type formations in
the area of Călimani Mountains, provided by Olimpiu Pop (Department of Geography, University Babes-Bolyai
University in Cluj Napoca). The database is not multi-temporal, but is extracted from ortorectificated images
(ANCPI, edition 2004-2006). Therefore, to validate the modeling, was included in the analysis only a rectangular
area, which is part of a larger complex phenomenon that is inventoried. Modeling validation was done externally,
depending on the results of modeling of the spatially restricted database.
Sensitivity testing of the multinomial logistic regression model to errors due DTSAM, was assessed using a
random error as a Gaussian surface with average 0 and standard deviation 1, with values ranging from 0 to 40,
introduced into the DTASM. Introducing this error and with the propagation in the derivation of geomorphometric
variables, the model supported by Akaike criterion has significance levels of partial coefficients> 0.01, however
the area under the ROC curve was changed from 0.74 to 0.666.
7.2.3 Uncertainty introduced by the geomorphometric variables Since the input data in the models presented above are particularly geomorphometric is of great importance
estimation uncertainty introduced by different ways of calculating the variables geomorphometric eventually and
DTSAM (Niculita, 2011).
The most used sources for uncertainty estimating are synthetic surfaces, obtained by applying mathematical
formulas on a matrix of coordinates. To illustrate an estimation of uncertainty, we have chosen a sinusoidal
surface (which reproduces a riverine generic landscape) and a surface of Gaussian random field (mean 0 and
standard deviation 1), whose elevation values were scaled between values of 0.1 and 100 m
Variability introduced by the calculation of geomoprhometric variables can be up to 81.48%, but most
commonly in 16.11% of the estimated final result of the model (Niculita, 2011).Speaking about the propagation of
these errors, from slope to topographic moisture index is not very high (Temme et al., 2009).
Using average values obtained from the calculation using different algorithms for geomorphometric
variables may be a technique designed to optimize and minimize errors that may occur as a result of choosing a
particular algorithm.
7.3 Detection of morphological changes Detection of morphological changes was argued by various authors Evans et al. (2009), James et al. (2012)
for introducing time dimension in geomorphologic analysis. Cartographic sources are useful materials because
they are sources of data on spatial distribution of earlier stages of geomorphologic processes and forms. In
addition to horizontal position information of interpreted aspects (whites, banks, slopes), the information
contained in model elevation contours can be used to interpolate a DTASM and the use of difference technology
(James et al., 2012). If some sources are based on geodetic mapping (is built on a network of geodetic surveying),
others do not have these features, so it requires an analysis of the use of these data in geomorphology, using the
DTASM difference method.
To analyze these issues for Romania were used topographic maps available in the Department of
Geography, Faculty of Geography and Geology, Alexandru Ioan Cuza University of Iasi (1:25,000 scale
topographic maps, first edition 1960-1965, and the second edition 1983-1985) and army plans, at 1:20 000 scale
drawing provided by community geospatial.org ( http://earth.unibuc.ro/download/planurile-directoare-de-tragere )
for three test areas: the Caiuti section in the Trotus valley, erosion formations in the area of Păltinoasa-Berchişeşti
and Negoiu - Pietricelu - Călimani mining area
DTSAM difference method is very useful in revealing the changes occurring in the surface crust. In this
approach the quality and accuracy of data sources is essential as directly affect the conclusions. In order to have a
significant geomorphologic analysis, there is need for an analysis of the errors (the differences between DTSAM
must be consistent with the geomorphologic evolution of the area) to reveal the existence of deviations of vertical
or horizontal surface. Any vertical or horizontal variations can be corrected if they have the same magnitude
throughout the area studied. Un-uniformity of these variations make it impossible to use these data sources to
reveal geomorphologic changes. Particular attention should be paid to the resolution of studied surface whose
minimum wavelength must be smaller than the landforms studied.
7.4 Analysis of cuesta landforms from the Moldavian Plateau Structural landforms Moldavian Plateau are dominated by cuestas and structural valleys (Ionita, 2000).
Against this structural background, sculptural forms degrade structural landforms. Main features of the landscape
of cuestas are asymmetry (Davis and Snyder, 1898; Selby, 1985) and monoclinal shifting (Thornbury, 1966),
present in the Moldavian Plateau, with a number of local features.
Ionita (2000) proposed the theory of double asymmetry, given that geological strata bend (8-12 m 1 km) to
the southeast ("deep") with orientation ("strike") west-east (~ N45E) and manifested by the presence of two types
of cuesta assymetry.
In the context described above, geomorphometric analysis is able to present the case surprised on DTASM
by geomorphometric analysis.This would include general geomorphometry analysis, ie pixel aspect analysis and
specific geomorphometry by the delimitation of cuesta hillslopes and analysis of their aspect.
Methodology for classifying the cuesta landforms is described in Niculiţă (2011).
General (pixel level) and specific (the geomorphometric objects) geomorphometry of the Moldavian
Plateau, through descriptive analysis of the distribution of slopes exhibition (floodplains, riverbeds and ridges
were removed), reveals the following:
• the entire surface of the plateau, is dominated by the eastern and western exposure pixels, followed by the
south and then the north;
• at the level of hillslopes geomorphometric objects the situation repeats, which reinforces the conclusion
that in the Moldavian Plateau "second order asymmetry" is a reality;
• about the distribution in the subdivisions of the Moldavian Plateau, the "second order asymmetry" is most
evident in the Jijia Plain Hills, Central Moldavian Plateau and Tutova Hills, the rest of subunits sharing the two
types of asymmetries in a similar manner.
Analyzing the organization of cuestia hillslopes, one can identify a number of types of cuestas:
• typical cuestas, developed with one scarp slope and one reverse slope, of only one of the two
asymmetries;
• composite cuestas, which develops two types of scarp slopes, and two reverse, of both types of
asymmetries.
Compound cuestas generally occur through the evolution of reconsequnt and obsequent valleys in the
generation of primary obsequnet cuestas apeared as a consequence of monoclinal displacement. It is the example
of the Hilly Plain of Jijia, where cuestas of first order, came as a result of the monoclinal movement of Jijia and
Bahlui rivers, to south, as this process evolves, the two river tributaries imposing appearance of hillslopes specific
to the second order asymmetry .
Compound cuestas are very common, with various combinations of slopes, requiring a further hierarchy of
cuesta slopes, according to the hierarchy of the river, and possibly reconstruction of the primary level of cuestas.
7.5 Geomorphometric mapping of landforms in Romania Geomorphologic mapping is seen as a purpose of geomorphologic research in some countries (Evans,
2005), or descriptive approach part of the earth's surface forms (Richards, 2005). In addition to using GIS in
digital geomorphologic map drawing (Rădoane and Rădoane, 2007, Michael et al., 2008; Dobre et al., 2011),
modern geomorphometry results (Wilson and Gallant, 2000; Hengl and Reuter, 2009) have potential to address
concerns that the geomorphologic mapping tended to make the transition to "art", "Ikebana" and "knowledge
landscape" (Yatsu, 1966) more than to the geomorphology. This is true for both large scale and small scale work
for. From this point of view, there is huge potential in the coverage of large areas at small scales by
geomorphometric mapping .
Geomorphologic mapping is done by associating forms the earth's surface (quantified by geomorphometry)
with geomorphologic processes Evans, 2005, models that can be associated to systems of shape-process (similar
to what Huggett, 1975, in soil science suggests as oil- land systems), or aerial photo-interpretation of images. We
present a geomorphometric map of the Iasi region at 1:100 000 scale (L-35-32) obtained by different approaches
of geomorphometric techniques. Evans (2005) considers "morphometric maps" as the graphical representation of
geomorphometric variables such as slope or curvature, and so on (quantitative expression of Earth's surface
shape), while morphographic maps graphically describe morphology (study of form), qualitative expression of the
form of land area (Waters, 1956; Savigear, 1965; Savigear, 1967).
Such a map can be used on the aggregation of geomorphometric classes of curvatures in landforms.
It can be concluded that the separation of geomorphometric objects and their aggregation in landforms, has
the potential of objectification of the delimitation of the landforms and automation of procedures so that they can
cover large areas in small scale study.
7.6 Geomorphometric regionalization of landforms in Romania Regionalization is a method of analysis in geography which aims to delineate areas where spatial variation
of geographic features vary sufficiently weak for those areas to be considered homogeneous (Fenneman, No year,
Berry, 1964). Although considered a historical part of geography, regionalization remains useful, for practical
applications of resource management or human intervention.
Most often, criticism of regionalization is given by the subjectivity of criteria for establishing boundaries
between regions, and the inability to identify a complete set of criteria by which a region to be precisely defined in
space. The concept of multi-scale, affects the geomorphologic regionalization, with different hierarchies that can
be applied in regionalization. In this approach ideal is to delineate areas as small as possible and then using
statistical methods, to group them in the higher regions to be objective and well-defined.
By geomorphometric regionalization, we understand the geomorphologic regionalization based on
geomorphometry of the Earth surface. Statistical methods of classification can be used to obtain a more connected
data to itself, rather than to subjectivity of the specialist (Etzelmüller et al., 2007).Statistical methods applied to
geomorphometric data should not completely replace the specialist, but it should facilitate its work, especially by
being able to automate extraction of geomorphometric limits (Chai et al., 2009).Need for statistical results arise
from the difficulty of the specialist in defining properly the form of the earth's surface using topographic maps or
shading DTSAM.
Statistical classification can be applied both to pixels (as general geomorphometry approach) and for
geomorphometric objects (as for specific geomorphometry approach). The second approach may be more useful,
and can be integrated into hierarchical agglomeration methods (Minar et al., 2011).
8 Conclusions
This paper aims at substantiating the concept of geomorphometric analysis as a method of working in
Geomorphology, but also in other fields of endeavor in geosciences.Regardless of the location, geomorphometry
as a branch / working method in geomorphology, or as specific science, altitude and land surface variables that
describe its shape are considered basic information of land. Beside the applicability of geomorphometric variables
in statistical modeling of natural processes, the quantitative quantification of Earth's surface shape interest
geomorphologists on various issues, among which the most typical are analyzing the geomorphologic changes,
correlating of morphology with geomorphologic evolution, geomorphlogic mapping and regionalization .
The fundamenting of geomorphometric analysis concept is based on a flowchart that includes the different
stages in the process of analysis:
• creating sources of altitude as numerical models of terrain altitude;
• derivation of geomoprhometric variables based on numerical models of the terrain altitude;
• delineation of geomoprhometric objects based on numerical models of the terrain altitude;
• the use of variables and objects as input in statistical, geostatistical and spatial techniques with finality in
geomorphology.
Numerical models of the earth's surface elevation are the main source of information of altitudes underlying
quantitative analysis of land surface shape. Altitude sources are varied, as also the methodologies for creating
digital models of the earth's surface elevation, for Romania we present and validate methodology to refine freely
available SRTM data. We performed also a description of completing data for elevation topographic maps for
obtaining valid numerical models of the terrain elevation.
Geomorphometric variables quantify land surface form, ranging from simple statistical analysis of altitude,
variables related to water floe, radiation and wind on the earth's surface. In addition to the multitude of
geomorphometric variables, the calculation of these varies greatly, which can have repercussions on their use in
statistical or physical models. The evaluation of geomorphometric variables associated uncertainty derivation is
very important in this respect being shown a series of case studies on estimating soil erosion or the probability of
occurrence of landslides.
Geomorphometric objects are relatively homogeneous areas following various criteria of form of the earth's
surface, which are candidates for landforms. Geomorphometric landform classification methodologies are aimed
at delimiting geomorphometric objects, both using supervised systems by a certain type of landforms previously
conceptualized and unsupervised by applying statistical methods and image segmentation. For Romania is
presented supervised classification methodology for geomorphometric analysis of cuesta landforms from the
Moldavian Plateau.
DTSAM emergence of global coverage opens up the possibility of global and national landform analysis.
This reveals a number of issues concerning geomorphologic evolution of the system, especially if it can be
achieved compared with other planets altitude distribution.
Statistical methods, geostatistical and spatial analysis are indispensable for geomorphometric and
geomorphologic analysis. Sources variability and elevation influence of geomorphometric variable value,
following the calculation algorithm was analyzed, both for estimating soil erosion using USLE model and logistic
regression as a method for probabilistic modeling of landslide occurrence.
Detection of morphological changes by the difference of DTASM is a technique that can be used
successfully in the study of geomorphologic evolution of floodplains and anthropogenic landscape in the last
decade. For the validity of the analysis there is need for accurate modeling of DTSAM surface that can reveal any
deficiencies in data sources. Morphological changes by DTASM difference method was applied to Romanian
topographic maps from various editions.
Geomorphometric mapping is a technique for geomorphologic mapping objectification, in this regard is
presented as a case study, the geomorphometric map of the region Iasi, scale 1:100 000 (L, 35-32).
Geomorphometric regionalization can be improved as precision and objectivity for geomorphologic
regionalization. Statistical methods can be used to clarify the boundaries, the specialist remaining to complete the
regionalization.