pos/pos_area.f90

The program pos_area

The program pos_area generates APs in 2 and 3 dimensions.

The 2-D version creates APs on a singular level with approximately) the same area, whereas 2 regions, fine (between lat_min and lat_max) and coarse (between lat_down and lat_up), with high and low spatial resolution, respectively, can be defined by different value of the mean distance between the APs, r_0 (in km).

In the 3-D case the problem is more complicated because the APs have to be distrubuted both horizontally and vertically. Therefore, a grid of vertical layers with variable thickness is defined. In each layer, the APs are uniformly distributed over the thickness of each layer by using sub-layers. The vertical grid and the thickness of the particular layers are motivated by the following ideas:

The ratio between the mean horizontal and vertical distance between the next neighbors, the so-called aspect ratio $\alpha$ , controls both the vertical and horizontal mixing intensity in the model. Furthermore, if correctly set, it guarantees not only that the horizontal and vertical resolution of the model are complementary chosen but also that the ratio between the horizontal and vertical diffusivity correctly describes mixing. Haynes et al. derived from observations and some theoretical ideas that $\alpha=250$ is a good choice for the lower stratosphere. Using the condition $\alpha=const$ (250 is the recommended value), the $\theta-$ grid can be created (recommended range: 1500> $\theta$ >350 K)
Because the criterion $\alpha=const$ cannot be applied for the troposphere (where much stronger vertical mixing is expected) and for the middle and upper stratosphere (where only an increase of the vertical diffusivity with the altitude can explain the profiles of the stratospheric age), we need an additional requirement to create the vertical grid, in particular for the $\zeta$ -coordinates. It seems plausible that the "volume" of every AP should contain "the same amount of information" or, because the number of APs in each layer is approximately the same, the "amount of information" per layer should be constant. The possible candidates for "the measure of information" could be the total mass of the layer or, that is physically stronger, the total entropy :
- $S\sim c_p n \ln\frac{\theta}{\theta_0}$
with, specific heat , air density , potential temperature $\theta$ and the reference potential temperature $\theta_0$ defined from the normal pressure and temperature. Here $\theta$ and are valid for the standard atmosphere. Thus, for a given horizonal resolution and aspect ratio $\alpha$ ,a layer near the tropical tropopause ( $\theta=380$ K is recommended) can be defined. Note that near this level, the maximum of entropy can be found ( $\theta$ increases whereas decreases with the altitude, so the product $n\ln\theta$ has a maximum). The amount of the entropy $\Delta S$ in this layers defines all other layers by assuming that $\Delta S=const$ in each layer. In this way the vertical grid $\zeta$ can be created. Note, that according to such a choice of the vertical axis, the lowest vertical diffusivity is near the entropy maximum ( $\approx$ 380 K) and that this diffusivity increases down- and upwards. This is in a general agreement with the expected profiles of the vertical diffusivity.

Furthermore, the vertical entropy flux ( $\sim \partial_z S(z)$ ) has its minimum near the tropical tropopause and increases with the distance from this level. Because one form of the entropy flux is the mass flux,this supports the mentioned increase of mixing with the distance from the entropy maximum.

The configuration file

The options to execute pos_area are set in the configuration file pos_area.inp:

1)  2004 11 20 12   ! Considered day (yyyy,mm,dd,ss)
2)  abc             ! Prefix (3 char) for output file
3)  outdir          ! Directory for output file  
4)  0.  90.0        ! External lat window (coarse)
5)  40. 90.0        ! Internal lat window (fine) 
6)  100.0           ! mean distance between APs for the coarse grid
7)  50.0            ! mean distance between APs for the fine grid
8)  zeta            ! vertical coordinate 
9)  2               ! generate vert axis (1-6)

1 = generate vertical axis with the same aspect ratio
2 = generate vertical axis with the same entropy increment and a constant horizontal resolution r_0
3 = generate vertical axis with the same entropy increment and variable horizontal resolution r_0(zeta)
4 = use ext. boundaries
5 = isentropic
6 = one-level

If 1 (same aspect ratio) is specified in line 9:

10) 10                   ! number of sublevels
11) 250.                 ! aspect ratio
12) 350.                 ! theta_min 
13) 800.                 ! theta_end

If 2 or 3 (same entropy increment) is specified in line 9:

10) 10                    ! number of sublevels
11) 250.                  ! aspect ratio
12) 380.                  ! theta0 
13) 100.                  ! p_ref
14) 150.,200.,1300.,1400. ! theta/zeta_range

Remarks:

p_ref=100 hPa is recommended but values between 100 and 200 hPa are also possible.

If 4 (use ext. boundaries) is specified in line 9:

10) 10                   ! number of sublevels

If 5 (isentropic) is specified in line 9:

10) 450.                 ! theta-level

If 6 (one-level) is specified in line 9:

10) 10                   ! number of sublevels
11) 450.                 ! theta-level