ISSN 0004-0894 © Royal Geographical Society (with The Institute of British Geographers) 2005

Area

(2005) 37.3, 341–350

Blackwell Publishing, Ltd.
Multi-scale landform characterization

Jochen Schmidt* and Robbie Andrew**

*National Institute for Water and Atmospheric Research (NIWA), PO Box 8602, Christchurch, New Zealand
Email: j.schmidt@niwa.co.nz
**Landcare Research, Palmerston North, New Zealand
Revised manuscript received 21 March 2005

One fundamental objective in geomorphometry is to extract signatures of geomorphologic
processes on different spatial scales from digital terrain models (DTMs) and to describe
the complexity of landforms as the synthesis of those individual imprints. We present an
approach for characterizing land surfaces on multiple, spatially varying local scales. We
approximate terrain surfaces locally to calculate surface derivatives at different window
sizes. Local scale behaviour diagrams are used to define dominant scale ranges and
multiple curvatures for each surface point. Multi-scale landform analysis leads to
improved models of surface derivatives and new landform classifications, applicable in
geomorphology, soil science and hydrology.

Key words:

terrain analysis, multi-scale analysis, digital terrain models, surface curvature

Introduction

The science and the art of quantitative interpretation
of landforms (geomorphometry) has a long history
and is probably one of the oldest sub-disciplines
in geomorphology (Pike 1995). It has long been
recognized that different landscape environments,
different geologic and tectonic settings, and climatic
characteristics are related to different geomorphologic
processes regimes and to different landform features.
In particular, the time–space coupling between
processes and forms has been heavily investigated,
relating the impact of geomorphic processes with
size and lifetime of landforms. Scale classification
schemes have been introduced (Dikau 1989), which
should be helpful in identifying landform features at
different spatial scales, related to their different
forming processes.
Landforms, however, are characterized by a multi-
tude of process imprints on different spatial scales.
That is why Chorley

et al

. (1984) introduced the
term ‘palimpsest’, describing landforms as a mix-
ture, an overlay, of the different process imprints
(Figure 1). This means a point in a landscape can
potentially carry more than one piece of information
(at one particular scale) about forming processes:
landforms in general have multi-scale characteristics
(Weissel

et al.

1994; Fisher

et al.

2004; Schmidt and
Hewitt 2004). One fundamental question of geo-
morphometry therefore is to find ways to extract
those individual signatures from numerical landform
representations like digital terrain models (DTMs)
and to describe landform complexity as the synthesis
of those individual imprints.
Therefore, various methods at different scales have
been developed and applied to analyse landforms
(Schmidt and Dikau 1999; Wilson and Gallant
2000). Surface derivatives like gradient and surface
curvature are heavily used terrain attributes in many
applications (Moore

et al

. 1991; Schmidt and Dikau
1999; Wilson and Gallant 2000). One fundamental
problem is that those parameters are heavily dependent
on the scale inherent in the calculation technique
(Figure 2, cf. Schmidt

et al

. 2003). Most of the recent
approaches, however, approximate this scale with
the given resolution of the DTMs used (as identified
as a limitation by Schneider 2001, for example). Few
attempts have been made to explicitly incorporate

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Schmidt and Andrew
Figure 1 Multiple scales in landforms. Hypothetical example of a landform as a result of a multitude of geomorphic
settings and processes. Different geomorphic processes acting at different characteristic length scales leaving their
signature in the landscape. Terrain therefore consists of a nested hierarchy (Dikau 1989) of those signatures
Figure 2 Scale dependence of local surface derivatives: an example for profile curvature. The figure shows a DTM
of a small catchment, top: original DTM, bottom: modified DTM with an added randomly distributed error (noise).
Curvature calculated at small scales (3 × 3 window) depict dominantly the noise in the modified DTM, whereas
curvature at larger scales depict the general landform character (the catchment form): the curvature images for
the 7 × 7 window are similar for the original and modified DTM