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Module sat_vapor_pres_mod

Contact:  Bruce Wyman
Reviewers: 
Change History: WebCVS Log

OVERVIEW

Routines for determining the saturation vapor pressure (ES) and the derivative of ES with respect to temperature.

This module contains routines for determining the saturation vapor pressure (ES) from lookup tables constructed using equations given in the Smithsonian tables. The ES lookup tables are valid between -160C and +100C (approx 113K to 373K). The values of ES are computed over ice from -160C to -20C, over water from 0C to 100C, and a blended value (over water and ice) from -20C to 0C. This version was written for non-vector machines. See the notes section for details on vectorization.

OTHER MODULES USED

constants_mod
      fms_mod

PUBLIC INTERFACE

Description summarizing public interface.
lookup_es:
For the given temperatures, returns the saturation vapor pressures.
lookup_des:
For the given temperatures, returns the derivative of saturation vapor pressure with respect to temperature.
compute_es:
For the given temperatures, computes the saturation vapor pressures.
sat_vapor_pres_init:
Initializes the lookup tables for saturation vapor pressure.

PUBLIC DATA

None.

PUBLIC ROUTINES

  1. lookup_es

    call lookup_es ( temp, esat )
    DESCRIPTION
    For the given temperatures these routines return the saturation vapor pressure (esat). The return values are derived from lookup tables (see notes below).


    INPUT
    temp    Temperature in degrees Kelvin.
       [real, dimension(scalar)]
       [real, dimension(:)]
       [real, dimension(:,:)]
       [real, dimension(:,:,:)]

    OUTPUT
    esat    Saturation vapor pressure in pascals. May be a scalar, 1d, 2d, or 3d array. Must have the same order and size as temp.
       [real, dimension(scalar)]
       [real, dimension(:)]
       [real, dimension(:,:)]
       [real, dimension(:,:,:)]

  2. lookup_des

    call lookup_des ( temp, desat )
    DESCRIPTION
    For the given temperatures these routines return the derivative of esat w.r.t. temperature (desat). The return values are derived from lookup tables (see notes below).


    INPUT
    temp    Temperature in degrees Kelvin.
       [real, dimension(scalar)]
       [real, dimension(:)]
       [real, dimension(:,:)]
       [real, dimension(:,:,:)]

    OUTPUT
    desat    Derivative of saturation vapor pressure w.r.t. temperature in pascals/degree. May be a scalar, 1d, 2d, or 3d array. Must have the same order and size as temp.
       [real, dimension(scalar)]
       [real, dimension(:)]
       [real, dimension(:,:)]
       [real, dimension(:,:,:)]

  3. compute_es

    es = compute_es ( temp )
    DESCRIPTION
    Computes saturation vapor pressure for the given temperature using the equations given in the Smithsonian Meteorological Tables. Between -20C and 0C a blended value over ice and water is returned.


    INPUT
    temp    Temperature in degrees Kelvin.
       [real, dimension(:)]
       [real, dimension(scalar)]
       [real, dimension(:,:)]
       [real, dimension(:,:,:)]

    OUTPUT
    es    Saturation vapor pressure in pascals. May be a scalar, 1d, 2d, or 3d array. Must have the same order and size as temp.
       [real, dimension(:)]
       [real, dimension(scalar)]
       [real, dimension(:,:)]
       [real, dimension(:,:,:)]

  4. sat_vapor_pres_init

    call sat_vapor_pres_init
    DESCRIPTION
    Initializes the lookup tables for saturation vapor pressure. This routine will be called automatically the first time lookup_es or lookup_des is called, the user does not need to call this routine. There are no arguments.


DATA SETS

None.

ERROR MESSAGES

FATAL in lookup_es
table overflow, nbad=##
Temperature(s) provided to the saturation vapor pressure lookup are outside the valid range of the lookup table (-160 to 100 deg C). This may be due to a numerical instability in the model. Information should have been printed to standard output to help determine where the instability may have occurred. If the lookup table needs a larger temperature range, then parameters in the module header must be modified.

REFERENCES

  1. Smithsonian Meteorological Tables Page 350.

COMPILER SPECIFICS

None.

PRECOMPILER OPTIONS

None.

LOADER OPTIONS

None.

TEST PROGRAM

test_sat_vapor_pres
use sat_vapor_pres_mod
implicit none

integer, parameter :: ipts=500, jpts=100, kpts=50, nloop=1
real, dimension(ipts,jpts,kpts) :: t,es,esn,des,desn
integer :: n

 generate temperatures between 120K and 340K
  call random_number (t)
  t = 130. + t * 200.

 initialize the tables (optional)
  call sat_vapor_pres_init

 compute actual es and "almost" actual des
   es = compute_es  (t)
  des = compute_des (t)

do n = 1, nloop
 es and des
  call lookup_es  (t, esn)
  call lookup_des (t,desn)
enddo

 terminate, print deviation from actual
  print *, 'size=',ipts,jpts,kpts,nloop
  print *, 'err es  = ', sum((esn-es)**2)
  print *, 'err des = ', sum((desn-des)**2)

contains

----------------------------------
 routine to estimate derivative

 function compute_des (tem) result (des)
 real, intent(in) :: tem(:,:,:)
 real, dimension(size(tem,1),size(tem,2),size(tem,3)) :: des,esp,esm
 real, parameter :: tdel = .01
    esp = compute_es (tem+tdel)
    esm = compute_es (tem-tdel)
    des = (esp-esm)/(2*tdel)
 end function compute_des
----------------------------------

end program test_sat_vapor_pres

KNOWN BUGS

No error checking is done to make sure that the size of the input and output fields match.


NOTES

1. Vectorization
To create a vector version the lookup routines need to be modified. The local variables: tmp, del, ind, should be changed to arrays with the same size and order as input array temp.

2. Construction of the ES tables
The tables are constructed using the saturation vapor pressure (ES) equations in the Smithsonian tables. The tables are valid between -160C to +100C with increments at 1/10 degree. Between -160C and -20C values of ES over ice are used, between 0C and 100C values of ES over water are used, between -20C and 0C blended values of ES (over water and over ice) are used.

There are three tables constructed: ES, first derivative (ES'), and second derivative (ES''). The ES table is constructed directly from the equations in the Smithsonian tables. The ES' table is constructed by bracketing temperature values at +/- 0.01 degrees. The ES'' table is estimated by using centered differencing of the ES' table.

3. Determination of es and es' from lookup tables
Values of the saturation vapor pressure (es) and the derivative (es') are determined at temperature (T) from the lookup tables (ES, ES', ES'') using the following formula. 
    es (T) = ES(t) + ES'(t) * dt + 0.5 * ES''(t) * dt**2
    es'(T) = ES'(t) + ES''(t) * dt

    where     t = lookup table temperature closest to T
             dt = T - t
4. Internal (private) parameters
These parameters can be modified to increase/decrease the size/range of the lookup tables. 
    tcmin   The minimum temperature (in deg C) in the lookup tables.
              [integer, default: tcmin = -160]

    tcmax   The maximum temperature (in deg C) in the lookup tables.
              [integer, default: tcmin = +100]

FUTURE PLANS

None.

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