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## Interpola
Emission Interpolation to a new mesh by using a conservative flux method

The new mesh is provided by the wrfinput file and the original grid with emissions are provided from wrfchem file

input files:

            wrfchemin.nc  ! A 12 hours emission file to be interpolated (0 to 11 hour or 12 to 23 hour)
            wrfinput      ! Domain where emissions will be interpolated can be a ge_em.d0?.nc file but the name should be wrfinput. 

output file:

            wrfchemi_00z_d01 or wrfchemi_12z_d01 ! 00z or 12z based on emissions file. 
                                                 ! d01, d02,... and date based on wrfinput
                                                 ! for geo_em.d0?.nc the dates are provided from wrfchemin.nc
            
wrfchemin.nc - file contain emissions starting with "E_" 

![Area to interpolate emissions](/assets/images/domain2int.png "Terrain and domain to interpolate")

![Source emissions](/assets/images/input_wrfchem.png "Emissions domain")

![Emissions result](/assets/images/output.png "Emissions in new domain")

## Mass conservative interpolation in overlaping grids
Emissions Inventories are generatred for represent global, regional or local emissions, air quality models domains are displayed in a different grid (dimensions and location) than the emissions. On other hand, emissions are a flux and it is necesary to use a mass conservative interpolation in order to avoid inconsistencies in the emissions. An example of overlaping grids is presented in the followgin figure.

![Grids overlaped](/assets/images/malla1.png "Modeling domain and emissions domain")

Grid with letters represents the new domain (it has coordinates dlat,dlon) and grid with numbers is the emissions (it has coordinates elat,elon). For N values in emission axis there are N+1 coordinates. 


For the new domain to interpolate the emissions the following variables are set (where `i` is in `x` axis and `j` in `y` axis):
 
 |  New domain   |   Emissions domain     | Type|
 |    ---        |    ---      | ---      | 
 | `ylat1=dlat(i ,j )` | `elat1= elat(ii,jj)` | unstagged |
 | `ylat2=dlat(i,j+1)` | `elat2= elat(ii,jj+1)`  |stagged lat|
 | `xlon1=dlon(i  ,j)` | `elon1= elon(ii,jj)` | unstagged | 
 | `xlon2=dlon(i+1,j)` | `elon2= elon(ii+1,jj)` |stagged long |
 
 The following figure presents the coordinates locations in each mesh.
 
 ![Grids overlaped with coordinates](/assets/images/malla2.png "Modeling domain --elat,elon-- and emissions domain --elon,elat--")

 In order to obtain the overlaped areas the following conditionals has to be evaluated:
 
            if(ylat1 .le. elat2 .and. ylat2 .ge. elat1) then
               alat=(min(ylat2,elat2)-max(ylat1,elat1))/(elat2-elat1)
            end if
            if(xlon1 .le. elon2 .and. xlon2 .ge. elon1)  then 
               alon=(min(xlon2,elon2)-max(xlon1,elon1))/(elon2-elon1)
            end if


The following procedure is followed in order to allocate the emissions in the new grid:

            alat=(min(ylat2,elat2)-max(ylat1,elat1))
            alon=(min(xlon2,elon2)-max(xlon1,elon1))
            area=max(0.,alat*alon)

![Computation](/assets/images/mallado.gif "Emissions domain asignation")


Emissions in cell:

- **A** are a flux emission fraction from 1, for
- **B** a flux  fractions from 1 and 2, and for 
- **C** fluxes from 2, 3 and 4 (not shown here), 
- **F** fluxes from 1 and 6, 
- **G** from 1, 2, 6 and 7 and 
- **H** from 2, 3, 7, 8, 4 and 9 (not shown here), and so on.