!copyright (C) 2001  MSC-RPN COMM  %%%RPNPHY%%%
*** S/P PROF5

      SUBROUTINE PROF5(EQ,EE,UD) 1
*
*
#include "impnone.cdk"
*
*
      REAL A1,A2,A3,C1,C2,EE,EQ,EY,E45,FE,P,SIGMA,SQRT2P,T1,T2
      REAL UD,X,Y
*
*AUTHOR
*          Jack Kain and JM Fritsch (Oct 14,1990)
*
*REVISION
* 001      Stephane Belair (1994)
*
*OBJECT
*          integrates the area under the curve in the Gaussian
*          Distribution to determine the fractional entrainment
*          and detrainment rates given EQ, the critical fraction
*          of environmental air for neutral buoyancy.
*
*ARGUMENTS
*
*          - Input -
* EQ       is the fraction between 0 and 1 given to the equation
*
*          - Output -
* EE       fractional entrainment rate
* UD       fraction detrainment rate
*
*NOTES
*
*          The numerical approximation to the integral is taken
*          from "Handbook of Mathematical Functions with formulas,
*          graphs and mathematical tables" ED. by Abramowitz
*          and Stegun, Nat'l Bureau of Standards Applied Mathematics
*          Series. June, 1964., May, 1968.  Jack Kain
*
**
C
      DATA SQRT2P,A1,A2,A3,P,SIGMA,FE/2.506628,0.4361836,-0.1201676,
     *0.9372980,0.33267,0.166666667,0.202765151/
c
      X=(EQ-0.5)/SIGMA
      Y=6.*EQ-3.
      EY=EXP(Y*Y/(-2))
      E45=EXP(-4.5)
      T2=1./(1.+P*ABS(Y))
      T1=0.500498
      C1=A1*T1+A2*T1*T1+A3*T1*T1*T1
      C2=A1*T2+A2*T2*T2+A3*T2*T2*T2
*
      IF(Y.GE.0.)THEN
        EE=SIGMA*(0.5*(SQRT2P-E45*C1-EY*C2)+SIGMA*(E45-EY))
     *     -E45*EQ*EQ/2.
        UD=SIGMA*(0.5*(EY*C2-E45*C1)+SIGMA*(E45-EY))
     *     -E45*(0.5+EQ*EQ/2.-EQ)
      ELSE
        EE=SIGMA*(0.5*(EY*C2-E45*C1)+SIGMA*(E45-EY))
     *     -E45*EQ*EQ/2.
        UD=SIGMA*(0.5*(SQRT2P-E45*C1-EY*C2)+SIGMA*(E45-EY))
     *     -E45*(0.5+EQ*EQ/2.-EQ)
      ENDIF
*
      EE=EE/FE
      UD=UD/FE
*
*
      RETURN
      END