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.