The modified gamma distribution PSD

The form of the modified gamma distribution (MGD) used here is as follows:

\[\frac{N(X)}{dX} = N \frac{\nu}{\Gamma(1 + \alpha)}\lambda^{\nu(1 + \alpha)} D^{\nu(1 + \alpha) - 1} \cdot \exp \{-(\lambda D)^\nu\}.\]

The distribution is described by four parameters:

  1. The intercept parameter \(N\)
  2. The slope parameter \(\lambda\)
  3. The shape parameter \(\alpha\)
  4. The parameter \(\nu\)
class parts.scattering.psd.modified_gamma.ModifiedGamma(size_parameter, intercept_parameter=None, alpha=None, lmbd=None, nu=None)[source]

Bases: parts.scattering.psd.arts.arts_psd.ArtsPSD

The ModifiedGamma class describes the size distribution of scattering particles in an atmosphere using the four parameters of the particle size distribution.

evaluate(x)[source]

Computes the values of this modified gamma distribution evaluated at the given size grid x.

Parameters:

x(numpy.array): Array containing the values of the size parameter at which to evaluate the PSD.

Returns:

PSDData object containing the numeric PSD data obtained by evaluating this PSD at the given values of the size parameter.
get_mass_density()[source]

Computes the mass density :math: rho_m for the given bulk elements using

\[\rho_m = a \cdot M(b).\]

where \(a\) and \(b\) are the coefficients of the mass-size relation of the size parameter.

Returns:

numpy.ndarray containing the mass density corresponding to each volume element described by the PSD.
get_moment(p, reference_size_parameter=None)[source]

Computes the \(p\) th moment \(M(p)\) of the PSD using

\[M(p) = \frac{N}{\lambda} \frac{\Gamma (1 + \alpha + p / \nu )} {\Gamma({1 + \alpha})}.\]
Parameters:
p(np.float): Which moment of the PSD to compute.
Raises:
Exception: If any of the parameters of the PSD is not set.
moment_names

The free parameters of the PSD.

pnd_call_agenda

ARTS agenda that contains the call to the WSM that computed this PSD.