psdModifiedGamma

Workspace.psdModifiedGamma(self: pyarts.arts._Workspace, psd_data: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Matrix]] = self.psd_data, dpsd_data_dx: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Tensor3]] = self.dpsd_data_dx, psd_size_grid: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Vector]] = self.psd_size_grid, pnd_agenda_input_t: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Vector]] = self.pnd_agenda_input_t, pnd_agenda_input: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Matrix]] = self.pnd_agenda_input, pnd_agenda_input_names: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.ArrayOfString]] = self.pnd_agenda_input_names, dpnd_data_dx_names: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.ArrayOfString]] = self.dpnd_data_dx_names, n0: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Numeric]] = std::numeric_limits<Numeric>::quiet_NaN(), mu: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Numeric]] = std::numeric_limits<Numeric>::quiet_NaN(), la: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Numeric]] = std::numeric_limits<Numeric>::quiet_NaN(), ga: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Numeric]] = std::numeric_limits<Numeric>::quiet_NaN(), t_min: Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Numeric], t_max: Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Numeric], picky: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Index]] = 0, verbosity: Optional[Union[pyarts.arts.WorkspaceVariable, pyarts.arts.Verbosity]] = self.verbosity) → None

Modified gamma distribution PSD using n0, mu, la and ga as parameters.

The modified gamma distribution is a 4-parameter (n0, mu, la and ga) distribution [Petty & Huang, JAS, 2011)]:

n(x) = n0 * x^mu * exp( -la*x^ga )

where x is particle size or mass.

The parameters can be given in two ways, either by pnd_agenda_input or as GIN arguments. The first option allows the parameter to vary, while in the second case the parameter gets a constant value. If a parameter is part of pnd_agenda_input, the corresponding GIN argument must be set to NaN (which is default). This means that the number of columns in pnd_agenda_input and the number of non-NaN choices for n0, mu, la and ga must add up to four.

Data in pnd_agenda_input are linked to the MGD parameters in term of order, the naming in pnd_agenda_input_names is free. If all four parameteras are specified by pnd_agenda_input, the data in the first column are taken as n0, the second column as mu etc. If a parameter is given as a GIN argument, the columns are just shifted with one position. For example, if mu and ga are specified as GIN arguments, pnd_agenda_input shall have two columns, with n0-values in the first one and la-values in the second one.

The GIN route is especially suitable for selecting special cases of MGD. For example, by setting mu=0 and ga=1, an exponential PSD is obtained:

n(x) = n0 * exp( -la * x )

With mu=1 and ga=1, the gamma PSD is obtained:

n(x) = n0 * x^mu * exp( -la * x )

There should be little overhead in using the method for exponential and gamma PSDs, there is an internal switch to dedicated expressions for those PSDs.

Derivatives can only be obtained for parameters that are specified by pnd_agenda_input.

If temperature is outside [ t_min , t_max ] psd=0 and dpsd=0 if picky=0, or an error is thrown if picky=1.

These requirements apply to the MGD parameters:

  1. la > 0

  2. ga > 0

Author(s): Patrick Eriksson

Parameters:

  • psd_data (Matrix, optional) – Particle size distribution values for a set of points. See psd_data, defaults to self.psd_data [OUT]

  • dpsd_data_dx (Tensor3, optional) – Partial derivates of psd_data. See dpsd_data_dx, defaults to self.dpsd_data_dx [OUT]

  • psd_size_grid (Vector, optional) – The particle sizes associated with psd_data. See psd_size_grid, defaults to self.psd_size_grid [IN]

  • pnd_agenda_input_t (Vector, optional) – Temperature input to one element of pnd_agenda_array. See pnd_agenda_input_t, defaults to self.pnd_agenda_input_t [IN]

  • pnd_agenda_input (Matrix, optional) – The variable input to one element of pnd_agenda_array. See pnd_agenda_input, defaults to self.pnd_agenda_input [IN]

  • pnd_agenda_input_names (ArrayOfString, optional) – Naming of (existing or expected) data in pnd_agenda_input. See pnd_agenda_input_names, defaults to self.pnd_agenda_input_names [IN]

  • dpnd_data_dx_names (ArrayOfString, optional) – Selection of partial derivatives of pnd_data. See dpnd_data_dx_names, defaults to self.dpnd_data_dx_names [IN]

  • n0 (Numeric, optional) – n0. Defaults to NaN [IN]

  • mu (Numeric, optional) – mu. Defaults to NaN [IN]

  • la (Numeric, optional) – la. Defaults to NaN [IN]

  • ga (Numeric, optional) – ga. Defaults to NaN [IN]

  • t_min (Numeric) – Low temperature limit to calculate a psd. [IN]

  • t_max (Numeric) – High temperature limit to calculate a psd. [IN]

  • picky (Index, optional) – Flag whether to be strict with parametrization value checks. Defaults to 0 [IN]

  • verbosity (Verbosity) – ARTS verbosity. See verbosity, defaults to self.verbosity [IN]