physics_funcs.cc

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/* Copyright (C) 2002-2012
   Patrick Eriksson <Patrick.Eriksson@chalmers.se>
   Stefan Buehler   <sbuehler@ltu.se>

   This program is free software; you can redistribute it and/or modify it
   under the terms of the GNU General Public License as published by the
   Free Software Foundation; either version 2, or (at your option) any
   later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
   USA. */




/*===========================================================================
  === File description 
  ===========================================================================*/

/*===========================================================================
  === External declarations
  ===========================================================================*/

#include <cmath>
#include <stdexcept>
#include "physics_funcs.h"
#include "messages.h"          
#include "mystring.h"
#include "physics_funcs.h"

extern const Numeric BOLTZMAN_CONST;
extern const Numeric DEG2RAD;
extern const Numeric PLANCK_CONST;
extern const Numeric SPEED_OF_LIGHT;



/*===========================================================================
  === The functions (in alphabetical order)
  ===========================================================================*/

Numeric barometric_heightformula ( //output is p1
                                   //input
                                   const Numeric& p, 
                                   const Numeric& dh
                                   )

{
 /* taken from: Seite „Barometrische Höhenformel“. In: Wikipedia, 
 * Die freie Enzyklopädie. Bearbeitungsstand: 3. April 2011, 20:28 UTC.
 * URL: http://de.wikipedia.org/w/index.php?title=Barometrische_H%C3%B6henformel&oldid=87257486 
 * (Abgerufen: 15. April 2011, 15:41 UTC) 
 */

  
  //barometric height formula
  Numeric M = 0.02896; //mean molar mass of air [kg mol^-1]
  Numeric g = 9.807; //earth acceleration [kg m s^-1]
  Numeric R = 8.314; //universal gas constant [J K^−1 mol^−1]
  Numeric T = 253; //median tropospheric reference temperature [K]
    
  // calculation
  Numeric p1 = p * exp(-(-dh)/(R*T/(M*g)));
  
  return p1;
  
}




Numeric dinvplanckdI(
        const Numeric&  i,
        const Numeric&  f )
{
  assert( i >= 0 );
  assert( f > 0 );

  static const Numeric a = PLANCK_CONST / BOLTZMAN_CONST;
  static const Numeric b = 2 * PLANCK_CONST / ( SPEED_OF_LIGHT*SPEED_OF_LIGHT );

  const Numeric d    = b * f*f*f / i;
  const Numeric binv = a * f / log( d + 1 );

  return binv*binv / ( a * f * i * (1/d+1) ); 
}




void fresnel(
             Complex&   Rv,
             Complex&   Rh,
       const Complex&   n1,
       const Complex&   n2,
       const Numeric&   theta )
{
  const Numeric theta1 = DEG2RAD * theta;
  const Numeric costheta1 = cos( theta1 );
  const Numeric costheta2 = cos( asin( n1.real() * sin(theta1) / n2.real() ) );

  Complex a, b;
  a  = n2 * costheta1;
  b  = n1 * costheta2;
  Rv = ( a - b ) / ( a + b );
  a  = n1 * costheta1;
  b  = n2 * costheta2;
  Rh = ( a - b ) / ( a + b );
}



Numeric invplanck(
        const Numeric&  i,
        const Numeric&  f )
{
  if (i < 0)
  {
      ostringstream os;
      os << "Conversion to Planck brightness temperature failed: Radiance must be >= 0.\n"
      << "r = " << i;
      throw runtime_error(os.str());
  }

//  assert( i >= 0 );
  assert( f > 0 );

  static const Numeric a = PLANCK_CONST / BOLTZMAN_CONST;
  static const Numeric b = 2 * PLANCK_CONST / ( SPEED_OF_LIGHT*SPEED_OF_LIGHT );

  return   ( a * f ) / log( (b*f*f*f)/i + 1.0 );
}




Numeric invrayjean(
        const Numeric&  i,
        const Numeric&  f )
{
  assert( f > 0 );

  static const Numeric   a = SPEED_OF_LIGHT*SPEED_OF_LIGHT/(2*BOLTZMAN_CONST);

  return  ( a * i ) / ( f * f );
}



Numeric number_density(  
        const Numeric&   p,
        const Numeric&   t )
{
  assert( p >= 0 );
  assert( t > 0 );
  return   p / ( t * BOLTZMAN_CONST );
}




Numeric planck( 
        const Numeric&   f, 
        const Numeric&   t )
{
  assert( t >= 0 );
  assert( f > 0 );

  if( t == 0 )
    { return 0; }

  else
    {
    static const Numeric a = 2 * PLANCK_CONST / (SPEED_OF_LIGHT*SPEED_OF_LIGHT);
    static const Numeric b = PLANCK_CONST / BOLTZMAN_CONST;
  
    return  ( a * f*f*f ) / ( exp( (b*f)/t ) - 1.0 );
    }
}




Numeric rayjean(
        const Numeric&  f,
        const Numeric&  t )
{
  assert( f > 0 );

  static const Numeric   a = SPEED_OF_LIGHT*SPEED_OF_LIGHT/(2*BOLTZMAN_CONST);

  return  ( f * f ) / ( a * t );
}