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file_format: mystnb
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(_users_continuum)=
# Continuum

The [MT_CKD continuum](https://github.com/AER-RC/MT_CKD) is a fortran program which calculates the continuum
absorption due to water vapour, nitrogen, oxygen, carbon dioxide, and ozone over the wavenumber range 0-20,000 cm{sup}`-1`.

## Basic Usage

The MT_CKD continuum can be added to a model atmosphere as a constituent.
See the example in [Quick Start](_quickstart).

The atmosphere must contain constituents that define the H2O, CO2, and O3 VMR profiles. By default, it is assumed that
these species have been added to the atmosphere with the keys "H2O", "CO2", and "O3". Different key names can be used
by setting `h2o_name`, `co2_name`, and `o3_name` in the initialization of {py:class}`sasktran2_ext.continuum.MTCKDContinuum`.
Temperature and pressure profiles must also be set in the atmosphere.

```{note}
The MT_CKD continuum accounts for contributions to the absorption further than 25 cm{sup}`-1` from the centre
wavenumber of each line. When combining the continuum with line-by-line absorption from optical properties such as
{py:class}`sasktran2.optical.hitran.HITRANAbsorber` it is recommended to leave the `line_contribution_width` parameter
at its default value of 25.
```

## Weighting Functions

Weighting functions are calculated with respect to pressure and temperature as well as H2O, CO2, and O3 VMR. In the output
the weighting functions have `continuum` in their variable names to indicate they are the portion of the species derivative
resulting from the continuum. For example, if we perform a calculation with the continuum,

```{code-cell}
:tags: ["remove-cell"]
import numpy as np
import sasktran2 as sk
from sasktran2_ext.continuum import MTCKDContinuum

config = sk.Config()
config.emission_source = sk.EmissionSource.Standard
config.single_scatter_source = sk.SingleScatterSource.NoSource

altitude_grid = np.arange(0, 65001, 1000.0)

geometry = sk.Geometry1D(
    0.6,
    0,
    6327000,
    altitude_grid,
    sk.InterpolationMethod.LinearInterpolation,
    sk.GeometryType.Spherical,
)

viewing_geo = sk.ViewingGeometry()
viewing_geo.add_ray(sk.GroundViewingSolar(0.6, 0, 0.8, 200000))

wavenum = np.arange(530, 550, 0.01)

atmosphere = sk.Atmosphere(geometry, config, wavenumber_cminv=wavenum)
sk.climatology.us76.add_us76_standard_atmosphere(atmosphere)
for species in ["H2O", "O3", "CO2"]:
    hitran_db = sk.optical.database.OpticalDatabaseGenericAbsorber(sk.database.StandardDatabase().path(f"hitran/{species}/sasktran2/6e786d8451a300f48627c3239314a9c9214b44bb.nc"))
    atmosphere[species] = sk.climatology.mipas.constituent(species, hitran_db)
atmosphere["emission"] = sk.constituent.ThermalEmission()
atmosphere["surface_emission"] = sk.constituent.SurfaceThermalEmission(300, 0.9)
atmosphere["continuum"] = MTCKDContinuum()

engine = sk.Engine(config, geometry, viewing_geo)
output = engine.calculate_radiance(atmosphere)
```

```{code}
import numpy as np
import sasktran2 as sk
from sasktran2_ext.continuum import MTCKDContinuum

config = sk.Config()
config.emission_source = sk.EmissionSource.Standard
config.single_scatter_source = sk.SingleScatterSource.NoSource

altitude_grid = np.arange(0, 65001, 1000.0)

geometry = sk.Geometry1D(
    0.6,
    0,
    6327000,
    altitude_grid,
    sk.InterpolationMethod.LinearInterpolation,
    sk.GeometryType.Spherical,
)

viewing_geo = sk.ViewingGeometry()
viewing_geo.add_ray(sk.GroundViewingSolar(0.6, 0, 0.8, 200000))

wavenum = np.arange(530, 550, 0.01)

atmosphere = sk.Atmosphere(geometry, config, wavenumber_cminv=wavenum)
sk.climatology.us76.add_us76_standard_atmosphere(atmosphere)
for species in ["H2O", "O3", "CO2"]:
    hitran_db = sk.database.HITRANDatabase(
        molecule=species,
        start_wavenumber=530,
        end_wavenumber=550,
        wavenumber_resolution=0.01,
        reduction_factor=1,
        backend="sasktran2",
        profile="voigt"
    )
    atmosphere[species] = sk.climatology.mipas.constituent(species, hitran_db)
atmosphere["emission"] = sk.constituent.ThermalEmission()
atmosphere["surface_emission"] = sk.constituent.SurfaceThermalEmission(300, 0.9)
atmosphere["continuum"] = MTCKDContinuum()

engine = sk.Engine(config, geometry, viewing_geo)
output = engine.calculate_radiance(atmosphere)
```

and look at the output,

```{code-cell}
:tags: ["remove-cell"]
import xarray as xr
xr.set_options(display_max_rows=20)
```
```{code-cell}
print(output)
```

there are two weighting functions related to ozone, `wf_O3_vmr` and `wf_continuum_O3_vmr`.
The first contains the ozone weighting function contribution due to line-by-line absorption and
the second is the contribution from continuum absorption.