PreMODIT

Last update: Jan 8th (2025) Hajime Kawahara

PreMODIT (Precomputation of Line Density + MODIT) is an enhanced algorithm building upon the foundations of MODIT. A key limitation of MODIT is its requirement to recalculate the lineshape density (LSD) from the complete transition information whenever the temperature or pressure conditions change. This approach necessitates storing all transition data in device memory, leading to inefficiencies in memory usage.

PreMODIT addresses this limitation by introducing a preprocessing step to compress line information prior to storage in device memory. This compression significantly reduces memory requirements.

PreMODIT precomputes a density field, referred to as the Line Base Density (LBD), which contains line information. When temperature and pressure are provided, the LBD is converted into LSD, enabling the calculation of opacity using the same method as MODIT. As a result, there is no need to use the molecular database (mdb) for LSD calculations each time. However, a trade-off is that the algorithm’s accuracy is constrained to a predefined temperature range. To accommodate this limitation, the auto_trange option is provided in OpaPremodit.

The functionality of auto_trange depends on the version of the default elower grid temperature range (degt) file. For more details, refer to premodit_trange. Users can specify the degt file version through the version_auto_trange option. Details of the PreMODIT algorithm will be described in Paper II.

from exojax.spec.opacalc import OpaPremodit
from jax import config
config.update("jax_enable_x64", True)
diffmode = 0
opa = OpaPremodit(mdb=mdbCO,
                  nu_grid=nus,
                  diffmode=diffmode,
                  auto_trange=[400.0, 1500.0])

This ensures an accuracy of 1% within the temperature range of 400–1500 K. It is important to note that enabling config.update(“jax_enable_x64”) configures JAX to utilize 64-bit precision; refer to the next section for details. Alternatively, 32-bit precision can also be used, as explained below.

For users who are well-acquainted with the PreMODIT algorithm, parameters can be specified directly using the manual_params option.

dE = 300.0 # cm-1
Tref = 400.0 # in Kelvin
Twt = 1000.0 # in Kelvin
opa = OpaPremodit(mdb=mdbCO,
                  nu_grid=nus,
                  diffmode=diffmode,
                  manual_params=[dE, Tref, Twt])

Visulization of the Line Base Density

The visualization of the LBD is shown below. For water, the LBD appears densely populated, whereas for CO, it is noticeably sparse.

from exojax.utils.grids import wavenumber_grid
from exojax.spec.api import MdbExomol
from exojax.plot.opaplot import plot_lbd

nu_grid, wav, resolution = wavenumber_grid(
    14500.0, 15500.0, 100000, unit="AA", xsmode="premodit"
)
mdb = MdbExomol(".database/H2O/1H2-16O/POKAZATEL/", nurange=nu_grid)
opa = OpaPremodit(mdb, nu_grid, auto_trange=[500.0, 1000.0], dit_grid_resolution=0.2)
lbd, midx, gegrid, gngamma, gn, R, pm = opa.opainfo
plot_lbd(lbd, gegrid, gngamma, gn, midx, nu_grid)
../_images/premodit_lbd_h2o.png 
nu_grid, wav, resolution = wavenumber_grid(
    22900.0, 27000.0, 200000, unit="AA", xsmode="premodit"
)
mdb = MdbExomol(".database/CO/12C-16O/Li2015/", nurange=nu_grid)
opa = OpaPremodit(mdb, nu_grid, auto_trange=[500.0, 1000.0], dit_grid_resolution=0.2)
lbd, midx, gegrid, gngamma, gn, R, pm = opa.opainfo
plot_lbd(lbd, gegrid, gngamma, gn, midx, nu_grid)
../_images/premodit_lbd_co.png

On 32bit and 64bit mode

We recommend using JAX’s 64-bit mode unless you are confident that 32-bit precision is sufficient for your specific application. While 64-bit mode requires more device memory and computational time, it provides greater numerical stability. If you plan to perform real retrievals, ensure that using 32-bit precision does not significantly impact the results. For initial analyses or cases where precision is critical, 64-bit mode is the safer option.

from jax import config
config.update("jax_enable_x64", True)

But, if you wanna try to use 32bit mode, use allow_32bit option.

    from jax import config
config.update("jax_enable_x64", False)
opa = OpaPremodit(mdb=mdbCO,
                  nu_grid=nus,
                  diffmode=diffmode,
                  auto_trange=[400.0, 1500.0]
                  allow_32bit=True)

Otherwise, you will see ValueError:

    from jax import config
config.update("jax_enable_x64", False)
opa = OpaPremodit(mdb=mdbCO,
                  nu_grid=nus,
                  diffmode=diffmode,
                  auto_trange=[400.0, 1500.0])
# -> JAX 32bit mode is not allowed. Use allow_32bit = True or ...

Changing the Resolution of the Broadening Parameters

By setting broadening_resolution option to {"mode": "manual", "value": 1.0}, OpaPremodit controls the resolution of the broadening parameters. The default value of {“mode”: “manual”, “value”: 0.2} might be overkilled for real exoplanet/brown dwarf spectrum analysis.

opa = OpaPremodit(mdb=mdb,
                  nu_grid=nu_grid,
                  diffmode=diffmode,
                  auto_trange=[500.0, 1500.0],
                  broadening_resolution={"mode": "manual", "value": 1.0})

You can check the grid overlaied on the data distribution by

opa.plot_broadening_parameters()
../_images/example_manual.png

Note that gamma in the above Figure is that at T = opa.Tref_broadening.

broadening_resolution = {"mode": "minmax", "value": None} using min/max values of the broadening parameters as grids

../_images/example_minmax.png

Single Broadening Parameter Set

By default, OpaPremodit constructs a grid for the broadening parameter. However, reducing the number of broadening grids can be advantageous for fitting purposes, as it decreases device memory usage. The memory usage scales with the product of the number of broadening grids, free parameters, atmospheric layers, wavenumber grid points, and the byte size of F64 or F32 precision.

To use a single broadening parameter, set the broadening_resolution option to {"mode": "single", "value": None}. When "value" is set to None, the median values of gamma_ref (the width in cm-1 at the reference pressure) and n_Texp (the temperature exponent) at 296 K are used.

In single broadening parameter mode, the reference temperature for broadening (Tref_broadening) remains fixed at 296 K. To specify custom values, provide gamma_ref and n_Texp at 296 K as a list in the format [gamma_ref, n_Texp] for the "value" field.

opa = OpaPremodit(mdb=mdb,
                  nu_grid=nu_grid,
                  diffmode=diffmode,
                  auto_trange=[500.0, 1500.0],
                  broadening_resolution={"mode": "single", "value": None})

In the above case, we assumed the median of broadening parameters of mdb. If you want to give the specific values use “single_broadening_parameters” option.

../_images/example_single.png