DEFINITION MODULE EDepTOth;  

  (*******************************************************************

    Module  EDepTOth     (Version 1.0)

              Copyright (c) 1992 by Heike Lischke and Swiss
              Federal Institute of Technology ZŸrich ETHZ

     References to equations, figures and tables in the comments
     refer to:              
              
        !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!      
              Lischke, H., Loeffler, T.J., Fischlin, A.:
              Calculating temperature dependence over long time periods:
              Derivation of methods. Ecol. Modelling, in press.
              
              PLEASE cite this paper when you use these algorithms!
        !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!       
         Version written for:
              MacMETH_V3.2    (1-Pass Modula-2 implementation)

      Purpose (*.  purpose  .*)
              
      Remarks (*.  remarks.  .*)
              
      Programming

          o Design
              H. Lischke         6/8/93

          o Implementation
              H. Lischke         6/8/93

              
          Swiss Federal Institute of Technology Zurich ETHZ
          CH-8092 Zurich
          Switzerland

          Last revision of definition:  6/8/93  HL

  *******************************************************************)

TYPE whichDayOfDataset=(first,middle,last);
(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
(* Dependence function value (dep) :                        *)
(*       DepFunc                                            *)
(* Calculates value of piece wise linear approximation of   *)
(* dependence function                                      *)
(* Input:                                                   *)  
(*   temp:       current temperature value                  *)
(*   idmax:       number of grid points of dep. func.       *)
(*               approximation                              *)
(*   threshold:  x-(Temp.)-values of grid points of dep.    *)
(*               function approximation  [0..idma-1]        *)
(*   tempabAtThreshold:  y-values of grid points of dep.    *)
(*               function approximation  [0..idma-1]        *)
(* Output:                                                  *)  
(*  DepFunc: dep. func value                                *)
(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
PROCEDURE DepFunc( temp:REAL;
                   idmax:INTEGER;
                   threshold,tempabAtThreshold: ARRAY OF REAL):REAL;
 
 
 
(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
(*Error function value :                                    *)
(*       ErrorFunction                                      *)
(* Calculates by series expansion value of error function,  *)
(* i.e.                                                     *)
(* Erf()= 2/sqrt(Pi) integral from 0 to x over e^(-t^2) dt  *)
(* Input:                                                   *)  
(*   x:        upper integral boundary                      *)
 (* Output:                                                 *)  
(*  ErrorFunction: error func value                         *)
(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
PROCEDURE ErrorFunction( x:REAL ):REAL; 



(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
(* Methods EDH and EDM  :                                   *)
(*       EofDepofTmeanSigma                                 *)
(* Calculates expected value of piece wise linear dependence*)
(* function explicitly                                      *)
(*                                                          *)
(* Input:                                                   *)  
(*   mue:        temperature mean                           *) 
(*   s    :      temperature standard deviation             *)
(*   idmax:       number of grid points of dep. func.       *)
(*               approximation                              *)
(*   threshold:  x-(Temp.)-values of grid points of dep.    *)
(*               function approximation  [0..idma-1]        *)
(*   tempabAtThreshold:  y-values of grid points of dep.    *)
(*               function approximation  [0..idma-1]        *)
(* Output:                                                  *)  
(*  EofDepofTmeanSigma: expected value                      *)
(*                                                          *)
(* EDH: mue and s of hourly temperatures                    *)
(* EDM: mue and s of daily mean temperatures                *)
(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
PROCEDURE EofDepofTmeanSigma( mue,s: REAL;
                            idmax:INTEGER;
                            threshold,tempabAtThreshold: ARRAY OF REAL):REAL;
 
 
(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
(* Methods EDHT1 and EDHT2  :                               *)
(*       EofDepofTmeanSigmaParAppro                         *)
(* Calculates expected value of piece wise linear dependence*)
(* function using  average temperature and standard         *)
(* deviation  which are estimated from mean and variance    *)
(* of daily mean  and amplitude                             *)
(*                                                          *)
(* Input:                                                   *)  
(*   mueTb:      temperature mean                           *) 
(*   sTb    :    standard deviation  of daily means         *)
(*   mueAmpl:    mean of daily amplitudes                   *)
(*   sAmpl:      standard deviation of daily amplitudes     *)
(*   idmax:      number of grid points of dep. func.        *)
(*               approximation                              *)
(*   threshold:  x-(Temp.)-values of grid points of dep.    *)
(*               function approximation  [0..idma-1]        *)
(*   tempabAtThreshold:  y-values of grid points of dep.    *)
(*               function approximation  [0..idma-1]        *)
(* Output:                                                  *)  
(*  EofDepofTmeanSigmaParAppro: expected value              *)
(*                                                          *)
(* EDHT1: recorded mueTb                                    *)
(* EDH: mueTb reconstructed from Tmin and                   *)
(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
PROCEDURE EofDepofTmeanSigmaParAppro (  mueTb,sTb,mueAmpl,sAmpl: REAL;
                            idmax:INTEGER;
                            threshold,tempabAtThreshold: ARRAY OF REAL):REAL;
 
 
(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
(* Method DAT :                                             *)
(*       DepFuncTmeanAmpl                                   *)
(* Calculates dependence function of mean daily triangle    *) 
(*                                                          *)
(* Input:                                                   *)  
(*   avtemp:     temperature mean                           *) 
(*   ampl    :   mean temperature amplitude                 *)
(*   idmax:       number of grid points of dep. func.       *)
(*               approximation                              *)
(*   threshold:  x-(Temp.)-values of grid points of dep.    *)
(*               function approximation  [0..idma-1]        *)
(*   tempabAtThreshold:  y-values of grid points of dep.    *)
(*               function approximation  [0..idma-1]        *)
(* Output:                                                  *)  
(*  DepFuncTmeanAmpl:dep. funct. of mean daily triangle     *)
(*                                                          *)
 (*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
 PROCEDURE DepFuncTmeanAmpl( avtemp ,ampl:REAL;
                            idmax:INTEGER;
                            threshold,tempabAtThreshold: ARRAY OF REAL):REAL; 

(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
             

END EDepTOth.