emc2.simulator.psd.calc_mu_lambda

emc2.simulator.psd.calc_mu_lambda(model, hyd_type='cl', calc_dispersion=True, dispersion_mu_bounds=(2, 15), subcolumns=False)[source]

Calculates the \(\mu\) and \(\lambda\) of the gamma PSD given \(N_{0}\). The gamma size distribution takes the form:

\[N(D) = N_{0}e^{-\lambda D}D^{\mu}\]

Where \(N_{0}\) is the intercept, \(\lambda\) is the slope, and \(\mu\) is the dispersion.

Parameters
model: :py:mod:`emc2.core.Model`

The model to generate the parameters for.

hyd_type: str

The assumed hydrometeor type. Must be a hydrometeor type in Model.

calc_dispersion: bool

If False, the \(\mu\) parameter will be fixed at 1/0.09. If True and the hydrometeor type is “cl”, then the Martin et al. (1994) method will be used to calculate \(\mu\).

dispersion_mu_bounds: 2-tuple

The lower and upper bounds for the \(\mu\) parameter.

subcolumns: bool

If True, the fit parameters will be generated for the generated subcolumns rather than the model data itself.

Returns
——-
model: :py:mod:`emc2.core.Model`

The Model with the \(\lambda\) and \(\mu\) parameters added.

References

Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distribution: J. Climate Appl. Meteor., 22, 1764-1775

Martin, G.M., D.W. Johnson, and A. Spice, 1994: The Measurement and Parameterization of Effective Radius of Droplets in Warm Stratocumulus Clouds. J. Atmos. Sci., 51, 1823–1842, https://doi.org/10.1175/1520-0469(1994)051<1823:TMAPOE>2.0.CO;2