% Template GRASS newsletter - Article
% Language: Latex
%

% Head


\title{{\tt r.roughness} -- a new tool for morphometric analysis in GRASS}
\label{grohmann2}
%\subtitle{}
\author{by Carlos Henrique Grohmann}

\maketitle

\section{Introduction}
\label{sec:intro}

This article briefly describes {\tt r.roughness}, a shell script
written to calculate the surface roughness of raster surfaces. The
method is based on \cite{hobson:1972}, where roughness is defined as
the ratio between surface and plan area of square cells. This script
will create square sub-regions with size defined by the user; in each
sub-region, the real and planar areas will be calculated by {\tt
  r.surf.area}, and the results (points at the centre of sub-regions)
will be interpolated with {\tt v.surf.rst}. The user also can set the
tension and smooth parameters of interpolation.

\section{Surface Roughness}
\label{sec:roughness}

Surface roughness (or topographical roughness) was first introduced as
a morphometric parameter by \cite{stone+dugundji:1965} and
\cite{hobson:1967, hobson:1972}. To \cite{hobson:1972}, one possible
way to calculate it is the ratio between surface (real) area and flat
(plan) area of square cells; in this approach, flat surfaces would
present values close to 1, whilst in irregular ones the ratio shows a
curvilinear relationship which asymptotically approaches infinity as
the real areas increases. 

\begin{figure*}[hbt]
\begin{center}
 \begin{minipage}[t]{0.45\textwidth}  %[b] => Adjusts to \caption
  \begin{center}
   %name of your graphic, without the path AND in EPS format:
   \includegraphics[width=\textwidth]{images/shade_color}
   %caption of the figure
   \caption{Study area.}
   %label of the figure, which has to correspond to \ref{}:
   \label{fig:shade_color}
  \end{center}
 \end{minipage}
\hspace{.05\linewidth}                % Space between figures
 \begin{minipage}[t]{0.45\textwidth}  %[b] => Adjusts to \caption
  \begin{center}
   %name of your graphic, without the path AND in EPS format:
   \includegraphics[width=\textwidth]{images/rough500}
   %caption of the figure
   \caption{Surface roughness map, {\tt grid=500m}.}
   %label of the figure, which has to correspond to \ref{}:
   \label{fig:rough500}
   \end{center}
 \end{minipage}
\end{center}
\end{figure*}

Day (1979) describes surface roughness as the expression of
non-systematic variability of the topographic surface, and used the
dispersion of vector normals to surface plans as a roughness indicator
to discriminate tropical karst stiles.

\cite{ferrari+etal:1998} argue that surfaces with distinct
characteristics can present the same roughness value, due the
existence of interactions between the number and magnitude of terrain
irregularities. \cite{grohmann:2004}, considers this method useful for
morphological characterisation since it is mainly related with the
shape of land-forms and not its elevation;  thus, tectonically tilted
areas have their expression shown, while it could be masked in a
hypsometric map, as consequence of altimetric variations.

The method has been applied in studies related to morphology of lake
bottoms \citep{hakanson:1974}, as a discriminant of karstic areas
\citep{day:1979,karmann+etal:1996,ferrari+etal:1998}, for structural
compartimentation of sedimentary basins basement
\citep{grohmann+etal:2005}, in morphometric analysis of alkaline
massifs \citep{roldan+etal:2006,grohmann+etal:2007}, in structural
analysis of strike-slip shear zones \citep{steiner+etal:2006} and for
macro-geomorphological compartimentation
\citep{grohmann_riccomini:2006}.

\section{Usage and Examples}
\label{sec:usage}

The script has five options: {\tt map, grid, rough, tension} and {\tt
  smooth}. {\tt map} stands for the input raster surface and is the
only required option. {\tt grid} is the size of the sub-regions in
which roughness will be calculated; the default value is 1000m. {\tt
  rough} is the name for the output map; if a name is  not provided,
it will be set to {\tt input\_map\_name.roughness.grid\_size}. {\tt
  tension} and {\tt smooth} will be used by {\tt v.surf.rst} for
interpolation of roughness values; the default values are {\tt
  tension=40} and {\tt smooth=$0.1$}.

\begin{figure*}[hbt]
\begin{center}
 \begin{minipage}[t]{0.45\textwidth}  %[b] => Adjusts to \caption
  \begin{center}
   %name of your graphic, without the path AND in EPS format:
   \includegraphics[width=\textwidth]{images/rough1000}
   %caption of the figure
   \caption{Surface roughness map, {\tt grid=1000m}.}
   %label of the figure, which has to correspond to \ref{}:
   \label{fig:rough1000}
  \end{center}
 \end{minipage}
\hspace{.05\linewidth}                % Space between figures
 \begin{minipage}[t]{0.45\textwidth}  %[b] => Adjusts to \caption
  \begin{center}
   %name of your graphic, without the path AND in EPS format:
   \includegraphics[width=\textwidth]{images/rough2000}
   %caption of the figure
   \caption{Surface roughness map, {\tt grid=2000m}.}
   %label of the figure, which has to correspond to \ref{}:
   \label{fig:rough2000}
   \end{center}
 \end{minipage}
\end{center}
\end{figure*}

The examples presented are from an area located in southeastern
Brazil, southern region of S\~ao Paulo State. Local geology consists
of NE-SW trending metapelitic and metacalcareous rocks where karstic
landscapes developed over the carbonatic rocks, with altimetric
differences up to 700m between non-carbonatic (pelitic, psamitic and
granitic) crests and karstic valley bottoms. NW-SE trending dikes cut
across the area and have a strong influence on geomorphological
development (Fig.~\ref{fig:shade_color}). Surface roughness was
calculated for grid sizes of 500, 1000 and 2000m.

With a grid size of 500m (Fig.~\ref{fig:rough500}), a good correlation
with land-forms can be seen. Higher roughness values are related with
the Bethary River valley, developed over a NW-SE trending dike. Also,
karstic valleys have smaller roughness values than non-carbonatic
crests. The general picture of the features present in
(Fig.~\ref{fig:rough500}) can be seen in the map for grid size of
1000m (Fig.~\ref{fig:rough1000}), although is not possible to
individualise the answer from each carbonatic unit. A grid of 2000m
(Fig.~\ref{fig:rough2000}) does not give much information, indicating
that land-forms within this area cannot be well described with a
wavelength this large.






\section{Concluding Remarks}
\label{sec:remarks}

Surface roughness is a useful parameter for morphological
compartimentation. {\tt r.roughness} is a shell script that automises
the process, but users must be aware that it uses {\tt r.surf.area} to
calculate both real and planar area for each grid cell (sub-regions)
and that raster resolution plays an important role on area
estimations.

The script is available through GRASS Wiki site \footnote{\url
  {http://grass.gdf-hannover.de/wiki/GRASS_AddOns}} in two versions:
{\tt r.roughness} for GRASS 6.1+ and {\tt r.roughness60} for GRASS
6.0.x.

\section{Acknowledgements}
\label{sec:thanks}

This work was supported by FAPESP grant 04/06260-5 (C.H.G. Doctor's
Degree Fellowship). The author is thankful to Tom\'as Senabre (Spain)
for his feedback which helped to improve the script usability.

\begin{footnotesize}
\begin{thebibliography}{99}

\bibitem[\protect\citeauthoryear{Day}{Day}{1979}]{day:1979}
M. J. Day (1979)
\newblock Surface roughness as a discriminator of tropical karst styles
\newblock {\em Zeitschrift f\"ur Geomorphologie},Suppl.-Bd.32:1-8.

\bibitem[\protect\citeauthoryear{Ferrari et al.}{Ferrari et al.}{1998}]{ferrari+etal:1998}
J. A. Ferrari, S. T. Hiruma, I. Karmann (1998)
\newblock {Caracteriza\c c\~ao morfom\'etrica de uma superf\'icie c\'arstica do Vale do Ribeira, S\~ao Paulo (N\'ucleo Caboclos - PETAR)}
\newblock {\em Revista do Instituto Geol\'ogico},19:9-17.

\bibitem[\protect\citeauthoryear{Grohmann}{Grohmann}{2004}]{grohmann:2004}
C. H. Grohmann (2004)
\newblock {Morphometric analysis in Geographic Information Systems: applications of free software GRASS and R}
\newblock {\em Computers \& Geosciences},30:1055-1067.
\newblock \url {http://dx.doi.org/10.1016/j.cageo.2004.08.002}

\bibitem[\protect\citeauthoryear{Grohmann et al.}{Grohmann et al.}{2005}]{grohmann+etal:2005}
C. H. Grohmann, C. Riccomini, F. Paula e Silva and H. K. Chang (2005)
\newblock {Compartimenta\c c\~ao tect\^onica da Bacia Bauru no centro-oeste do Estado de S\~ao Paulo}
\newblock {\em In:X Simp\'osio Nacional de Estudos Tect\^onicos / IV International Symposium on Tectonics, Curitiba-PR},{Boletim de Resumos Expandidos}:25-27.

\bibitem[\protect\citeauthoryear{Grohmann \& Riccomini}{Grohmann \& Riccomini}{2006}]{grohmann_riccomini:2006}
C. H. Grohmann and C. Riccomini (2006)
\newblock {An\'alise regional de rugosidade de relevo}
\newblock {\em In:XLIII Congresso Brasileiro de Geologia, Aracaju-SE} Anais:97.

\bibitem[\protect\citeauthoryear{Grohmann et al.}{Grohmann et al.}{2007}]{grohmann+etal:2007}
C. H. Grohmann, C. Riccomini and F. M. Alves (2007)
\newblock {SRTM-based morphotectonic analysis of the Po\c cos de Caldas Alkaline Massif, southeastern Brazil}
\newblock {\em Computers \& Geosciences (in press).}
\newblock \url {http://dx.doi.org/10.1016/j.cageo.2006.05.002}

\bibitem[\protect\citeauthoryear{Hakanson}{Hakanson}{1974}]{hakanson:1974}
L. Hakanson (1974)
\newblock A mathematical model for establishing numerical values of topographical roughness for lake bottoms
\newblock {\em Geografiska Annaler. Series A, Physical Geography},56:183-200.

\bibitem[\protect\citeauthoryear{Hobson}{Hobson}{1967}]{hobson:1967}
R. D. Hobson (1967)
\newblock {FORTRAN IV programs to determine the surface roughness in topography for the CDC 3400 computer}
\newblock {\em Computer Contribution 14, State Geol. Survey Kansas}, 28p.

\bibitem[\protect\citeauthoryear{Hobson}{Hobson}{1972}]{hobson:1972}
R. D. Hobson (1972)
\newblock Surface roughness in topography: quantitative approach
\newblock {\em In:Chorley, R.J., 1972. Spatial analysis in geomorphology}, 225-245.

\bibitem[\protect\citeauthoryear{Karmann et al.}{Karmann et al.}{1996}]{karmann+etal:1996}
I. Karmann, R. F. Pereira and J. A. Ferrari (1996)
\newblock {\'Indice de rugosidade: par\^ametro morfom\'etrico da intensidade de relevo. Exemplo do carste da bacia do Rio Una, Bahia}
\newblock {\em In: XXXIX Congresso Brasileiro de Geologia, Salvador},Anais:575-579.

\bibitem[\protect\citeauthoryear{Roldan et al.}{Roldan et al.}{2006}]{roldan+etal:2006}
L. F. Roldan, S. S. Steiner, C. H. Grohmann and R. Machado (2006)
\newblock {An\'alise morfom\'etrica da regi\~ao do Domo de Lages, SC}
\newblock {\em In:XLIII Congresso Brasileiro de Geologia, Aracaju-SE} Anais:266.

\bibitem[\protect\citeauthoryear{Steiner et al.}{Steiner et al.}{2006}]{steiner+etal:2006}
S. S. Steiner, R. Machado and C. H. Grohmann, C. H. (2006)
\newblock {An\'alise morfom\'etrica da estrutura divergente na regi\~ao do Rio Para\'iba do Sul, Rio de Janeiro}
\newblock {\em In:XLIII Congresso Brasileiro de Geologia, Aracaju-SE} Anais:97.

\bibitem[\protect\citeauthoryear{Stone and Dugundji}{Stone and Dugundji}{1965}]{stone+dugundji:1965}
R. O. Stone and J. Dugundji (1965)
\newblock {A study of microrelief -- its mapping, classification and quantification by means of a Fourier analysis}
\newblock {\em Engineering Geology},1:89-187.

%\bibitem[\protect\citeauthoryear{}{}{}]{}

\end{thebibliography}
\end{footnotesize}


\address{Carlos Henrique Grohmann\\
  Institute of Geosciences \\
  University of S\~ao Paulo, Brazil\\
  \url{http://www.igc.usp.br}\\
  \email{guano AT usp br}}

%%% Local Variables: 
%%% mode: latex
%%% TeX-master: main_document.tex
%%% End: 

