4.1.1.1.1.7. pamtra2.hydrometeors.numberConcentration

4.1.1.1.1.7.1. Module Contents

4.1.1.1.1.7.1.1. Functions

fromSizeDistribution(sizeDistribution, sizeBoundsWidth)

convert size distribution [1/m4] to number concentration [1/m3]

monoDisperse(sizeCenter, Ntot, nBins)

constant distribution

monoDisperseWC(hydrometeorContent, mass)

constant distribution for a given water content

modifiedGamma(sizeCenter, sizeBoundsWidth, N0, lambd, mu, gamma)

classical modified gamma distribution

gamma(sizeCenter, sizeBoundsWidth, N0, lambd, mu)

classical gamma distribution

exponential(sizeCenter, sizeBoundsWidth, N0, lambd)

classical exponential distribution

exponentialMarshallPalmer(sizeCenter, sizeBoundsWidth, rainRate)

classical exponential distribution for rain following Marshall

exponentialField(sizeCenter, sizeBoundsWidth, temperature, lambd)

classical exponential distribution. N0 is estimated using

exponentialFieldWC(sizeCenter, sizeBoundsWidth, temperature, hydrometeorContent, massSizeA, massSizeB)

classical exponential distribution. N0 is estimated using

exponentialFieldReff(sizeCenter, sizeBoundsWidth, temperature, effectiveRadius)

classical exponential distribution. N0 is estimated using

exponentialN0WC(sizeCenter, sizeBoundsWidth, N0, hydrometeorContent, massSizeA=mass.powerLawLiquidPrefactor, massSizeB=mass.powerLawLiquidExponent)

classical exponential distribution constrained with N0 and LWC.

_exponentialField(temperature)

N0 is estimated using

_exponentialWC2Lambda(N0, WC, massSizeA, massSizeB)

Estimate lambda of exponential distribution from WC and Ntot

_exponentialReff2Lambda(effectiveRadius)

Estimate lambda of exponential distribution from effective radius

4.1.1.1.1.7.1.2. Attributes

_exponentialNtot2Lambda

fromSizeDistribution(sizeDistribution, sizeBoundsWidth)[source]

convert size distribution [1/m4] to number concentration [1/m3]

Parameters
  • sizeCenter (array_like) – particle size at center of size bin

  • sizeBoundsWidth (array_like) – particle size bin width

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

monoDisperse(sizeCenter, Ntot, nBins)[source]

constant distribution

Parameters
  • Ntot (array_like) – total number of particles for the whole size spectruum

  • nBins (int) – number of size bins

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

monoDisperseWC(hydrometeorContent, mass)[source]

constant distribution for a given water content

Parameters
  • hydrometeorContent (array_like) – hydrometeor water content [kg/m^3]

  • mass (array_like) – mass of hydrometeors [kg]

  • nBins (int) – number of size bins

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

modifiedGamma(sizeCenter, sizeBoundsWidth, N0, lambd, mu, gamma)[source]

classical modified gamma distribution

Parameters
  • sizeCenter (array_like) – particle size at center of size bin

  • sizeBoundsWidth (array_like) – particle size bin width

  • N0 (array_like) – N0 pre-factor

  • lambd (float or array_like) – lambda parameter

  • mu (float or array_like) – mu parameter

  • gamma (float or array_like) – gamma parameter

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

gamma(sizeCenter, sizeBoundsWidth, N0, lambd, mu)[source]

classical gamma distribution

Parameters
  • sizeCenter (array_like) – particle size at center of size bin

  • sizeBoundsWidth (array_like) – particle size bin width

  • N0 (array_like) – N0 pre-factor

  • lambd (float or array_like) – lambda parameter

  • mu (float or array_like) – mu parameter

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

exponential(sizeCenter, sizeBoundsWidth, N0, lambd)[source]

classical exponential distribution

Parameters
  • sizeCenter (array_like) – particle size at center of size bin

  • sizeBoundsWidth (array_like) – particle size bin width

  • N0 (array_like) – N0 pre-factor

  • lambd (float or array_like) – lambda parameter

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

exponentialMarshallPalmer(sizeCenter, sizeBoundsWidth, rainRate)[source]

classical exponential distribution for rain following Marshall Palmer, 1948.

Parameters
  • sizeCenter (array_like) – particle size at center of size bin

  • sizeBoundsWidth (array_like) – particle size bin width

  • rainRate (array_like) – rain rate in mm/hour!

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

exponentialField(sizeCenter, sizeBoundsWidth, temperature, lambd)[source]

classical exponential distribution. N0 is estimated using Field et al. (2005 QJRM, end of page 2008 + end of page 2009 for the relation between N_0 and N_0,23) n_0 = n_0(T)

Parameters
  • sizeCenter (array_like) – particle size at center of size bin

  • sizeBoundsWidth (array_like) – particle size bin width

  • temperature (array_like) – ambient temperature [K]

  • lambd (float or array_like) – lambda parameter

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

exponentialFieldWC(sizeCenter, sizeBoundsWidth, temperature, hydrometeorContent, massSizeA, massSizeB)[source]

classical exponential distribution. N0 is estimated using Field et al. (2005 QJRM, end of page 2008 + end of page 2009 for the relation between N_0 and N_0,23) n_0 = n_0(T). Lambda is estimated from the WC which requires a power law mass-size relation.

Parameters
  • sizeCenter (array_like) – particle size at center of size bin

  • sizeBoundsWidth (array_like) – particle size bin width

  • temperature (array_like) – ambient temperature [K]

  • hydrometeorContent (array_like) – hydrometeor water content [kg/m^3]

  • massSizeA (float) – pre-factor mass-size power law

  • massSizeB (float) – exponent mass-size power law

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

exponentialFieldReff(sizeCenter, sizeBoundsWidth, temperature, effectiveRadius)[source]

classical exponential distribution. N0 is estimated using Field et al. (2005 QJRM, end of page 2008 + end of page 2009 for the relation between N_0 and N_0,23) n_0 = n_0(T). Lambda is estimated from the effective radius.

Parameters
  • sizeCenter (array_like) – particle size at center of size bin

  • sizeBoundsWidth (array_like) – particle size bin width

  • temperature (array_like) – ambient temperature [K]

  • effectiveRadius (array_like) – hydrometeor effective radius

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

exponentialN0WC(sizeCenter, sizeBoundsWidth, N0, hydrometeorContent, massSizeA=mass.powerLawLiquidPrefactor, massSizeB=mass.powerLawLiquidExponent)[source]

classical exponential distribution constrained with N0 and LWC.

Parameters
  • sizeCenter (array_like) – particle size at center of size bin

  • sizeBoundsWidth (array_like) – particle size bin width

  • N0 (array_like) – N0 pre-factor

  • hydrometeorContent (array_like) – hydrometeor water content [kg/m^3]

  • massSizeA (float) – pre-factor mass-size power law (Default value = mass.powerLawLiquidPrefactor)

  • massSizeB (float) – exponent mass-size power law (Default value = mass.powerLawLiquidExponent)

Returns

number concentration – calculated number concentration (NOT normalized, i.e. unit is 1/m3 instead of 1/m4)

Return type

array_like

_exponentialField(temperature)[source]

N0 is estimated using Field et al. (2005 QJRM, end of page 2008 + end of page 2009 for the relation between N_0 and N_0,23) n_0 = n_0(T)

Parameters

temperature (array_like) – ambient temperature [K]

Return type

N0

_exponentialWC2Lambda(N0, WC, massSizeA, massSizeB)[source]

Estimate lambda of exponential distribution from WC and Ntot

Parameters
  • N0 (array_like) – N0 pre-factor

  • WC (array_like) – hydrometeor water content [kg/m3]

  • massSizeA (float) – pre-factor mass-size power law

  • massSizeB (float) – exponent mass-size power law

Return type

lambda

_exponentialNtot2Lambda[source]
_exponentialReff2Lambda(effectiveRadius)[source]

Estimate lambda of exponential distribution from effective radius

Parameters

effectiveRadius (array_like) – hydrometeor effective radius

Return type

lambda