Cloud Models

BeAR currently includes the following cloud descriptions:

The code also supports the mixing of different cloud models in a single retrieval.

Grey Cloud Model

The grey cloud layer model is the most simple cloud parametrisation available in BeAR. It puts a cloud layer with a certain geometric height and a wavelength-independent optical depth into the atmosphere. It is selected by using the keyword grey in the corresponding section in the forward_model.config file:

#Cloud model
grey

The location of the cloud layer is set by a cloud top pressure \(p_\mathrm{top}\) that is one of the free parameters of the model. The cloud bottom pressure \(p_\mathrm{bot}\) is determined by a free parameter \(b\), such that \(p_\mathrm{bot} = p_\mathrm{top} \, b\). The optical depth is divided between all atmospheric layers that lie between these two pressures.

A grey cloud model has in total three free parameters that have to be added to the prior config file in the following order:

  • (vertical) grey optical depth

  • cloud top pressure in bar

  • cloud bottom parameter \(b\)

It is sometimes not possible to constrain the bottom of the cloud deck properly. This is often the case when performing retrieval calculations for a transmission spectrum. In this case, BeAR has the option to use a fixed cloud bottom. This can be enabled by using the optional parameter fb after the cloud model:

#Cloud model
grey fb

By choosing this option, BeAR fixes the cloud bottom pressure at one atmospheric scale height below the cloud top. In this case, only two free parameters are required in the prior file:

  • (vertical) grey optical depth

  • cloud top pressure in bar

Kitzmann & Heng Non-Grey Cloud Model

This description of a non-grey cloud layer is based on analytical fits to the Mie efficiencies of the cloud particles presented by Kitzmann & Heng (2018). The Mie extinction efficiencies as a function of wavelength \(Q_\mathrm{ext}\) are described via:

\[Q_\mathrm{ext}(\lambda) = \frac{Q_1}{Q_0 x^{-a_0}_\lambda + x^{0.2}_\lambda} ,\]

where \(x_\lambda\) is the wavelength-dependent size parameter of the cloud particles, \(Q_1\) is a normalisation constant, \(Q_0\) determines the \(x_\lambda\) value at which \(Q_\mathrm{ext}\) is peaking, and \(a_0\) is the powerlaw index in the small particle limit, where Mie theory converges to the limit of Rayleigh scattering. The size parameter is a function of the particle radius \(a\) and the wavelength:

\[x_\lambda = 2 \pi a / \lambda .\]

The optical depth \(\tau_\lambda\) of the cloud is determined based on the number density of cloud particles \(n_c\) and the vertical extent of the cloud \(\Delta z\):

\[\tau(\lambda) = Q_\mathrm{ext}(\lambda) \pi a^2 n_c \Delta z .\]

Since, however, it is usually difficult to put good priors on the number density \(n_c\), BeAR instead uses the vertical optical depth at a reference wavelength \(\lambda_\mathrm{ref}\) to describe the optical depths as a function of wavelength:

\[\tau(\lambda) = \tau(\lambda_\mathrm{ref}) \frac{Q_\mathrm{ext}(\lambda)}{Q_\mathrm{ext}(\lambda_\mathrm{ref})} = \tau(\lambda_\mathrm{ref}) \frac{Q_0 x^{-a_0}_{\lambda_{\mathrm{ref}}} + x^{0.2}_{\lambda_\mathrm{ref}}}{Q_0 x^{-a_0}_\lambda + x^{0.2}_\lambda} .\]

By using the reference optical depth, the normalisation constant \(Q_1\) is not required anymore.

The non-grey cloud description is selected by using the keyword KHnongrey, followed by the reference wavelength in \(\mu\mathrm{m}\) in the corresponding section in the forward_model.config file:

#Cloud model
KHnongrey 1.0

The reference wavelength does not need to be within the wavelength range of the retrieval calculations.

A non-grey cloud model has in total six free parameters that have to be added to the prior config file in the following order:

  • (vertical) optical depth at the reference wavelength

  • \(Q_1\)

  • \(a_0\)

  • particle size \(a\) in microns

  • cloud top pressure in bar

  • cloud bottom parameter \(b\)

The location of the cloud layer is set by a cloud top pressure \(p_\mathrm{top}\) that is one of the free parameters of the model. The cloud bottom pressure \(p_\mathrm{bot}\) is determined by a free parameter \(b\), such that \(p_\mathrm{bot} = p_\mathrm{top} \, b\). The optical depth is divided between all atmospheric layers that lie between these two pressures.

It is sometimes not possible to constrain the bottom of the cloud deck properly. This is often the case when performing retrieval calculations for a transmission spectrum. In this case, BeAR has the option to use a fixed cloud bottom. This can be enabled by using the optional parameter fb after the cloud model and the reference wavelength:

#Cloud model
KHnongrey 1.0 fb

By choosing this option, BeAR fixes the cloud bottom pressure at one atmospheric scale height below the cloud top. In this case, only five free parameters are required in the prior file:

  • (vertical) optical depth at the reference wavelength

  • \(Q_1\)

  • \(a_0\)

  • particle size \(a\)

  • cloud top pressure in bar

Power-Law Cloud Model

This cloud model uses a power law to describe the wavelength-dependent optical depth of the cloud layer. It uses the optical depth at a reference wavelength as normalisation:

\[\tau(\lambda) = \tau(\lambda_\mathrm{ref}) \frac{\lambda^e}{\lambda_\mathrm{ref}^e} ,\]

where \(e\) is the exponent of the power law. To simulate Rayleigh scattering, for example, \(e=-4\).

The power-law cloud model is selected by using the keyword power_law, followed by the reference wavelength in \(\mu\mathrm{m}\) in the corresponding section in the forward_model.config file:

#Cloud model
power_law 1.0

The reference wavelength does not need to be within the wavelength range of the retrieval calculations.

A non-grey cloud model has in total four free parameters that have to be added to the prior config file in the following order:

  • (vertical) optical depth at the reference wavelength

  • power-law exponent \(e\)

  • cloud top pressure in bar

  • cloud bottom parameter \(b\)

The location of the cloud layer is set by a cloud top pressure \(p_\mathrm{top}\) that is one of the free parameters of the model. The cloud bottom pressure \(p_\mathrm{bot}\) is determined by a free parameter \(b\), such that \(p_\mathrm{bot} = p_\mathrm{top} \, b\). The optical depth is divided between all atmospheric layers that lie between these two pressures.

It is sometimes not possible to constrain the bottom of the cloud deck properly. This is often the case when performing retrieval calculations for a transmission spectrum. In this case, BeAR has the option to use a fixed cloud bottom. This can be enabled by using the optional parameter fb after the cloud model:

#Cloud model
power_law 1.0 fb

By choosing this option, BeAR fixes the cloud bottom pressure at one atmospheric scale height below the cloud top. In this case, only two three parameters are required in the prior file:

  • (vertical) optical depth at the reference wavelength

  • power-law exponent \(e\)

  • cloud top pressure in bar

Mixing different cloud models

BeAR also has the ability to use multiple clouds simultaneously. For example, to perform a retrieval with grey cloud layer and a second cloud with a power-law optical depth to simulate, for example, a haze-like behaviour, the following can be used as configuration in the forward_model.config file:

#Cloud model
grey
power_law 1.0 fb

BeAR will call the cloud models in the order they appear in this list. Clouds can also be overlapping in pressure.

In the prior configuration file, the free parameters have to appear in the same order as the cloud models listed in forward_model.config.

Thus, for the example above, the following priors need to be listed:

  • grey optical depth

  • cloud top pressure in bar

  • cloud bottom parameter

  • optical depth at the reference wavelength

  • power-law exponent

  • cloud top pressure in bar