DEFINITION MODULE EDepTParab;  

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

    Module  EDepTParab     (Version 1.0)

              Copyright (c) 1993 by Heike Lischke and Swiss
              Federal Institute of Technology Zźrich 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!
        !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!      
               
      Programming

          o Design
              H. Lischke         9/2/93

          o Implementation
              H. Lischke         9/2/93

              
          Swiss Federal Institute of Technology Zurich ETHZ
          CH-8952 Schlieren/Zurich
          Switzerland

          Last revision of definition:  9/2/93  HL

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

(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)
(* Methods EDDT1 and EDDT2   :                              *)
(*       ParabelExpectValueOfTempDep                        *)
(* Calculates expected value of piece wise linear dependence*)
(* function by first determining analytically dependence    *) 
(* function value of one day and then determining expected  *)
(* value of this function.                                  *)
(*                                                          *)
(* Input:                                                   *)  
(*   tempMue:    temperature mean (i.e. also mean daily mean*)                                             
(*   tempSigma:  temperature standard deviation             *)
(*                 (stdev), of daily  mean                  *) 
(*   amplMue:    mean of daily temp. amplitude              *)
(*   amplSigma   stdev. of daily temp. amplitude            *)
(*   idma:       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]        *)
(*   gr:         determines in how many stdevs distance from*)
(*               mean parabola approximation of normal      *)
(*               distribution density function is 0.        *)
(*               Suggested choice: 2.3                      *)
(* Output:                                                  *)  
(*  ParabelExpectValueOfTempDep: expected value             *)
(* EDDT1: tempMue and tempSigma from real daily temp. mean  *)
(* EDDT2: tempMue and tempSigma estimated from daily means  *)
(*        determined from (Tmin+Tmax)/2                     *)
(*&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*)

 PROCEDURE ParabelExpectValueOfTempDep(tempMue,tempSigma,    
                                amplMue,amplSigma:REAL;                            
                                idma :INTEGER;
                                threshold,
                                tempabAtThreshold: ARRAY OF REAL;
                                gr:                REAL):REAL; 


END EDepTParab.  