Three Modules for the Computation of Temperature Dependence over long Time Periods
=============================================================================

Publications:
------------
The files "EDepTOth.*", "EDepTParab.*", and "FirstCoeffP.*" contain the
MODULA-2 source-code of various methods  to determine expected
values of temperature dependence functions derived in

    (1) Lischke, H., Loeffler, T.J., Fischlin, A.
           Calculating Temperature Dependence over long Time Periods:
           Derivation of Methods.
           Ecol. Modelling, submitted

You can find comparisons and tests of these methods in

   (2)  Lischke, H., Loeffler, T.J., Fischlin, A.
           Calculating Temperature Dependence over long Time Periods:
           Comparison and Study of Methods.
           For. Agr. Meteorology, in press.

These two papers are also available as preprints no. 26 and 27 of the group
Systems Ecology at ETHZ (see our homepage).

Implementation:
---------------
The files "EDepTOth.DEF", "EDepTParab.DEF", and "FirstCoeffP.DEF"
(definition modules) are the modul-interfaces. They define e.g. the
interface of the subprograms, i.e. how the subprograms must be called
in a program.
The code itself is contained in the files "EDepTOth.MOD", "EDepTParab.MOD",
and "FirstCoeffP.MOD" (Implementation modules).

List of the methods (description cf.  (1) and (2); interface cf. "*.DEF"
files)

        METHOD   Module        Program
        ------------------------------------------------
        EDH        EDepTOth      EofDepofTmeanSigma
        EDHT1    EDepTOth      EofDepofTmeanSigmaParAppro
        EDDT1    EDepTParab   ParabelExpectValueOfTempDep
        EDHT2    EDepTOth      EofDepofTmeanSigmaParAppro
        EDDT2    EDepTParab   ParabelExpectValueOfTempDep
        EDM        EDepTOth      EofDepofTmeanSigma
        DAT        EDepTOth      DepFuncTmeanAmpl

In order to work with all methods published in (1), you need all
six files.
The methods are implemented in the programming language MODULA-2, the
successor of Pascal and the predecessor of Oberon-2.
For working with MODULA on Macintosh you can freely download the latest
version of MacMETH, the MODULA compiler developed by Wirth at the ETH
Zuerich (IP address see below).

It is easily possible to translate the MODULA-2 code to PASCAL and OBERON,
but also to other programming languages such as C or FORTRAN.
Actually, most of the code was initially developed in MATHEMATICA and
transfered by copy-paste to Modula.

You, resp. your compiler, have to provide the  following functions:

  FUNC.    Interface                                  Explanation           Used in Modul
  -----------------------------------------------------------------------
  PowerI (x: REAL; iexp: INTEGER): REAL;  real value to the
                                                               power of an           EDepTOth,
                                                               integer number      EDepTParab
  Rmin   (x1,x2: REAL): REAL;                   real minimum        EDepTParab
  Rmax   (x1,x2: REAL): REAL;                   real maximum       EDepTParab
  Ln       (x: REAL): REAL;                          Logarithmus to
                                                               base e                   EDepTParab
  Exp      (x: REAL): REAL;                         exponential func.   EDepTOth
  Sqrt    (x: REAL): REAL;                         Square root            EDepTOth,
                                                                                            FirstCoeffP
  Pi       Pi(): REAL;                                  Number PI             EDepTOth, 
                                                                                           FirstCoeffP

Copyright:
----------
Copyright (©) 1995,96 by Heike Lischke and Swiss Federal Institute of
Technology ZŸrich ETHZ.

 !! Note,  the implementations are tested in the bounds of  publication (2) !!

Please send remarks etc. to "lischke@ito.umnw.ethz.ch"

The code is freely available. We only require that you

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
         PLEASE cite these papers when you use these algorithms!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Thank you!

IP Address:
----------
In order to get further information about the work of Systems Ecology at ETHZ and for
downloading our software please visit (IP address 129.132.80.130)

            http://www.ito.umnw.ethz.ch/SysEcol/
or
            ftp://ftp.ito.umnw.ethz.ch



hl, tjl 5.8.96