Chapter 3#

MICM Box Model with Multiple Grid Cells in Fortran#

In this third MUSICA Fortran example, we will extend the MICM box model from Chapter 2 to handle multiple grid cells in a single call to the MICM solver. This demonstrates how MUSICA can efficiently solve chemical mechanisms for multiple independent air masses simultaneously.

Each grid cell represents an independent set of well-mixed air masses, allowing us to model different atmospheric conditions (temperature, pressure, concentrations) and observe how the same chemical mechanism evolves differently under various conditions.

We will use the same analytical configuration files from Chapter 2 (config.json, species.json, and reactions.json) saved in the subdirectory configs/v0/analytical.

For reference, these files define:

A system of six chemical species: A, B, C, D, E, and F
Four reactions including two Arrhenius-type reactions and two user-defined rate reactions
The same mechanism will be solved simultaneously across multiple grid cells

To create a multiple grid cells box model, save the following Fortran code to a file named micm_multiple_grid_cells.F90:

Key differences from the single grid cell example in Chapter 2:

Grid Cell Configuration:

num_grid_cells is set to 3 instead of 1
Each grid cell can have different environmental conditions (temperature, pressure)
Each grid cell can start with different initial concentrations

Setting Conditions and Initial Values:

The state object now manages data for multiple grid cells using strides:

state%species_strides%variable provides the stride for accessing species data across cells
state%rate_parameters_strides%variable provides the stride for rate parameter data
Concentrations are stored in a flat array with stride-based indexing

! Different temperatures for each cell
do cell_id = 1, num_grid_cells
  state%conditions(cell_id)%temperature = 273.0 + (cell_id - 1) * 10.0
  state%conditions(cell_id)%pressure    = 1.0e5
  state%conditions(cell_id)%air_density = state%conditions(cell_id)%pressure / &
                                         (GAS_CONSTANT * state%conditions(cell_id)%temperature)
end do

Accessing Multi-Cell Data:

To access concentration data for a specific species in a specific grid cell:

cell_stride = state%species_strides%grid_cell
var_stride = state%species_strides%variable
cell_concentration = state%concentrations(1 + (cell_id - 1) * cell_stride + (species_index - 1) * var_stride)

Fortran’s 1-based indexing requires subtracting 1 from the 0-based cell_id and species_index to adjust offsets.

Simultaneous Solving:

A call to micm%solve with a state that represents multiple grid cells is only required once per time step; all grid cells are solved simultaneously in a multi-grid cell micm state.

call micm%solve(time_step, state, solver_state, solver_stats, error)

This is much more efficient than calling the solver separately for each grid cell, especially when dealing with large numbers of atmospheric grid cells in climate or weather models.

To build and run the example, follow the same build instructions as in Chapter 1 and 2. The compilation command would be:

gfortran -o micm_multiple_grid_cells micm_multiple_grid_cells.F90 -I<MUSICA_DIR>/include -L<MUSICA_DIR>/lib64 -lmusica-fortran -lmusica -lstdc++ -lyaml-cpp

Assuming you name the executable micm_multiple_grid_cells, you can run the program as follows:

 $ ./micm_multiple_grid_cells
Creating MICM solver with           3 grid cells...
Creating State for multiple grid cells...
Species in the mechanism:
Species Name:A, Index:           1
Species Name:B, Index:           2
Species Name:C, Index:           5
Species Name:D, Index:           3
Species Name:E, Index:           4
Species Name:F, Index:           6

Initial concentrations by grid cell:
Grid Cell 1 (T= 273.0K):
   1.000   1.000   1.000   1.000   1.000   1.000
Grid Cell 2 (T= 283.0K):
   2.000   2.000   2.000   2.000   2.000   2.000
Grid Cell 3 (T= 293.0K):
   0.500   0.500   0.500   0.500   0.500   0.500

Solving for all grid cells simultaneously...

Final concentrations by grid cell:
Grid Cell 1 (T= 273.0K):
   0.382   1.468   0.670   1.116   1.150   1.214
Grid Cell 2 (T= 283.0K):
   0.764   2.936   1.340   2.232   2.300   2.428
Grid Cell 3 (T= 293.0K):
   0.191   0.734   0.335   0.558   0.575   0.607

Solver completed successfully for all 3 grid cells!

The results differ in each grid cell due to the varying conditions.