Module sat_vapor_pres_mod¶

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¶

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(:,:,:)]

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(:,:,:)]

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(:,:,:)]

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¶

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

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]