Frank Pattyn

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GPL: General Power Law

What is GPL?

GPL is a computer program that calculates the shape of a valley cross-section based on a list of x,y values describing the valley cross section. Since its introduction by Svensson (1959), the power law curve y = a xb (with x and y horizontal and vertical direction respectively) has been widely used in morphological analysis of glacial trough cross profiles. The numerical constants a and b are obtained by a linear regression analysis of the logarithmic form of the power law curve (ln y = ln a + b ln x). The value b then gives a measure for the form of the cross section.

However, over the years this form of the power law has endured a lot of criticism. This criticism is well founded, since this particular form of the power law is not suitable for curve fitting in morphological analyses. Therefore, a general power law is proposed, of the form

y - y0 = a | x - x0 |b

with x0, y0 the coordinates of the origin of the cross profile. A unique and unbiased solution for this equation is obtained with a general least squares method, thereby minimizing the error between the cross profile data and the curve, and not between the logarithmic transform of the data and its regression line. This provides a robust way to characterize trough cross-section forms.

Synopsis of GPL

GPL is a program that estimates the shape of a valley cross-section according to the general power law: y - y0 = a | x - x0 |b

It was written by Frank Pattyn and Wim Van Huele, and described in "POWER LAW OR POWER FLAW?", by Pattyn and Van Huele. 1998. Earth Surface Processes and Landforms, 23: 761-767.

GPL inputs an ascii list of x-y coordinates, one point couple per line, and outputs the parameters x0, y0, a and b corresponding to the best fit curve.

Copyright Notice of GPL

Copyright (c) 1998, Frank Pattyn and Wim Van Huele (

You may refer to this software as:

Pattyn, F. and W. Van Huele (1998) Power Law or Power Flaw?, Earth Surface Processes and Landforms 23: 761-767.

This software is written by:

Department of Geography
Vrije Universiteit Brussel
Pleinlaan 2, B-1050 Brussel, BELGIUM

If you use this software for your scientific work or your publications, please don't forget to acknowledge explicitly the use of it.

Send me an e-mail if:

Legal matters, disclaimer of warranty, merchantability or fitness for any purpose: Permission to use, copy and distribute this software for any purpose without fee is hereby granted, provided that both the copyright notice and this permission notice appear in all copies, and that the name of GPL is not used in advertising or publicity pertaining to distribution of the software without specific, written prior permission. The Department of Geography (DGGF) and the Vrije Universiteit Brussel (VUB) make no representation about the suitability of this software for any purpose. It is provided "as is" without expressed or implied warranty. It is provided with no support and without obligation on the part of DGGF/VUB to assist in its use, correction, modification or enhancement.

Frank Pattyn and Wim Van Huele
Spetember 18, 1998

How to download GPL

GPL comes in three versions, i.e. one executable version for MacIntosh Power PC (not supported anymore), a PC (WIN32) version, and one source code version (written in C) primarily designed for use on a UNIX machine. However, if a C-compiler is available on your PC or Mac computer, the program source code can be compiled also..

You can obtain the Power MacIntosh version by downloading GPL.hqx, which can easily be unpacked. The PC version is WinZipped. The UNIX version is GPL.tar.gz which must be uncompressed and unpacked. All versions contain the program, a README file and some examples of valley cross-sections.


Pattyn, F. and Van Huele, W. (1998) Power law or power flaw? Earth Surface Processes and Landforms. 23: 761-767. (PDF)