aerosol package

aerosol.functions module

Aerosol number-size distribution is assumed to be a pandas DataFrame where

index:

time, pandas.DatetimeIndex

columns:

size bin diameters in meters, float

values:

normalized concentration dN/dlogDp in cm-3, float

aerosol.functions.air_density(temp, pres)

Calculate air density

Parameters:

tempfloat or series of lenght n

absolute temperature (K)

presfloat or series of length n

absolute pressure (Pa)

Returns:

float or series of length n

air density (kg/m3)

aerosol.functions.air_viscosity(temp)

Calculate air viscosity using Enskog-Chapman theory

Parameters:

tempfloat or series

air temperature, unit: K

Returns:

float or series

viscosity of air, unit: m2 s-1

aerosol.functions.beta(dp, temp, pres, diffusivity, molar_mass)

Calculate Fuchs Sutugin correction factor

Sutugin et al. (1971): https://doi.org/10.1016/0021-8502(71)90061-9

Parameters:

dpfloat or series of lenght m

aerosol particle diameter(s), unit: m

tempfloat or series of lenght n

temperature, unit: K

presfloat or series of lenght n

pressure, unit: Pa

diffusivityfloat or series of length n

diffusivity of the gas that is condensing, unit: m2/s

molar_massfloat

molar mass of the condensing gas, unit: g/mol

Returns:

float or dataframe of shape (n,m)

Fuchs Sutugin correction factor for each particle diameter and temperature/pressure unit: m2/s

aerosol.functions.binary_diffusivity(temp, pres, Ma, Mb, Va, Vb)

Binary diffusivity in a mixture of gases a and b

Fuller et al. (1966): https://doi.org/10.1021/ie50677a007

Parameters:

tempfloat or series of length n

temperature, unit: K

presfloat or series of length n

pressure, unit: Pa

Mafloat

relative molecular mass of gas a, unit: dimensionless

Mbfloat

relative molecular mass of gas b, unit: dimensionless

Vafloat

diffusion volume of gas a, unit: dimensionless

Vbfloat

diffusion volume of gas b, unit: dimensionless

Returns:

float or series of length n

binary diffusivity, unit: m2 s-1

aerosol.functions.calc_bin_edges(dp)

Calculate bin edges given bin centers

Parameters:

dppandas series of lenght n

bin center diameters

Returns:

pandas series of lenght n+1

log bin edges

aerosol.functions.calc_coags(df, dp, temp, pres, dp_start=None)

Calculate coagulation sink

Kulmala et al (2012): doi:10.1038/nprot.2012.091

Parameters:

dfdataframe

Aerosol number size distribution

dpfloat or series of length m

Particle diameter(s) for which you want to calculate the CoagS, unit: m

tempfloat or series indexed by DatetimeIndex

Ambient temperature corresponding to the data, unit: K If single value given it is used for all data

presfloat or series indexed by DatetimeIndex

Ambient pressure corresponding to the data, unit: Pa If single value given it is used for all data

dp_startfloat or None

The smallest size that you consider as part of the coagulation sink If None (default) then the smallest size is from dp

Returns:

float or dataframe

Coagulation sink for the given diamater(s), unit: s-1

aerosol.functions.calc_conc(df, dmin, dmax, frac=0.5)

Calculate particle number concentration from aerosol number-size distribution

Parameters:

dfdataframe

Aerosol number-size distribution

dminfloat or series of length n

Size range lower diameter(s), unit: m

dmaxfloat or series of length n

Size range upper diameter(s), unit: m

fracfloat

Minimum fraction of available data when calculating a concentration point

Returns:

dataframe

Number concentration in the given size range(s), unit: cm-3

aerosol.functions.calc_cs(df, temp, pres)

Calculate condensation sink, assuming that the condensing gas is sulfuric acid in air with aerosol particles.

Kulmala et al (2012): doi:10.1038/nprot.2012.091

Parameters:

dfpandas.DataFrame

aerosol number size distribution (dN/dlogDp)

temppandas.Series or float

Ambient temperature corresponding to the data, unit: K If single value given it is used for all data

prespandas.Series or float

Ambient pressure corresponding to the data, unit: Pa If single value given it is used for all data

Returns:

pandas.Series

condensation sink, unit: s-1

aerosol.functions.calc_formation_rate(df, dp1, dp2, gr, temp, pres)

Calculate particle formation rate

Kulmala et al (2012): doi:10.1038/nprot.2012.091

Parameters:

dfdataframe

Aerosol particle number size distribution

dp1float or series of length n

Lower diameter of the size range(s) Unit m

dp2float or series of length n

Upper diameter of the size range(s) Unit m

grfloat or series of length n

Growth rate for particles out of the size range(s), unit nm h-1

tempfloat or series

Ambient temperature corresponding to the data, unit K

presfloat or series

Ambient pressure corresponding to the data unit Pa

Returns:

dataframe

Particle formation rate(s) for the diameter range(s) Unit cm3 s-1

aerosol.functions.calc_ion_formation_rate(df_particles, df_negions, df_posions, dp1, dp2, gr_negions, gr_posions, temp, pres)

Calculate ion formation rate

Kulmala et al (2012): doi:10.1038/nprot.2012.091

Parameters:

df_particlesdataframe

Aerosol particle number size distribution

df_negionsdataframe

Negative ion number size distribution

df_posionsdataframe

Positive ion number size distribution

dp1float or series of length n

Lower diameter of the size range(s), unit: m

dp2float or series of length n

Upper diameter of the size range(s), unit: m

gr_negionsfloat or series of length n

Growth rate for negative ions out of the size range(s), unit: nm h-1

gr_posionsfloat or series of length n

Growth rate for positive ions out of the size range(s), unit: nm h-1

tempfloat or series

Ambient temperature corresponding to the data, unit: K

presor series

Ambient pressure corresponding to the data, unit: Pa

Returns:

dataframe

Negative ion formation rate(s), unit : cm3 s-1

dataframe

Positive ion formation rate(s), unit: cm3 s-1

aerosol.functions.calc_ion_production_rate(df_ions, df_particles, temp=293.15, pres=101325.0)

Calculate the ion production rate from measurements

Parameters:

df_ionsdataframe of shape (n,m)

negative or positive ion number size distribution unit cm-3

df_particlesdataframe of shape (n,m)

particle number size distribution unit cm-3

tempfloat or series of length n

ambient temperature unit K

presfloat or series of length n

ambient pressure unit Pa

Returns:

series of lenght n

ion production rate in cm-3 s-1

aerosol.functions.calc_ldsa(df)

Calculate total LDSA from number size distribution data

ICRP, 1994. Human respiratory tract model for radiological protection. A report of a task group of the international commission on radiological protection. Ann. ICRP 24 (1-3), 1-482

Parameters:

dfpandas.DataFrame

Aerosol number-size distribution

Returns:

pandas.DataFrame

Total LDSA for alveoli (“al”), trachea/bronchi (“tb”) head-airways (“ha”) and all combiend (“tot”) unit: um2 cm-3

aerosol.functions.calc_lung_df(dp)

Calculate lung deposition fractions for particle diameters

ICRP, 1994. Human respiratory tract model for radiological protection. A report of a task group of the international commission on radiological protection. Ann. ICRP 24 (1-3), 1-482

Parameters:

dppandas.Series

aerosol particle diameters unit: m

Returns:

pandas.DataFrame

Lung deposition fractions for alveoli (“DF_al”), trachea/bronchi (“DF_tb”) head-airways (“DF_ha”) and all combiend (“DF_tot”)

aerosol.functions.calc_tube_residence_time(tube_diam, tube_length, flowrate)

Calculate residence time in a circular tube

Parameters:

tube_diamfloat or series of length m

Inner diameter of the tube (m)

tube_lengthfloat or series of length m

Length of the tube (m)

flowratefloat or series of length n

Volumetric flow rate (lpm)

Returns:

float or dataframe of shape (n,m)

Residence time in seconds

aerosol.functions.coagulation_coef(dp1, dp2, temp, pres)

Calculate Brownian coagulation coefficient (Fuchs)

Parameters:

dp1float

first particle diameter, unit: m

dp2float or series of lenght m

second particle diameter, unit: m

tempfloat or series of lenght n

air temperature, unit: K

presfloat or series of lenght n

air pressure, unit: Pa

Returns:

float or dataframe of shape (n,m)

Brownian coagulation coefficient (Fuchs),

If dataframe is returned the columns correspond to diameter pairs (dp1,dp2) and are labeled by elements in dp2.

unit m3 s-1

aerosol.functions.cs2coags(cs, dp, m=-1.6)

Estimate coagulation sink from condensation sink

Parameters:

cspandas.Series

The condensation sink time series: unit s-1

dpfloat

Particle diameter for which CoagS is calculated, unit: nm

mfloat

Exponent in the equation

Returns:

coagspandas.Series

Coagulation sink time series for size dp

References

Kulmala et al (2012), doi:10.1038/nprot.2012.091

aerosol.functions.datenum2datetime(datenum)

Convert from matlab datenum to python datetime

Parameters:

datenumfloat or int

A serial date number representing the whole and fractional number of days from 1-Jan-0000 to a specific date (MATLAB datenum)

Returns:

pandas.Timestamp

aerosol.functions.datetime2datenum(dt)

Convert from python datetime to matlab datenum

Parameters:

dtdatetime object

Returns:

float

A serial date number representing the whole and fractional number of days from 1-Jan-0000 to a specific date (MATLAB datenum)

aerosol.functions.diam2mob(dp, temp, pres, ne)

Convert electrical mobility diameter to electrical mobility in air

Parameters:

dpfloat or series of lenght m

particle diameter(s), unit : m

tempfloat or series of length n

ambient temperature, unit: K

presfloat or series of length n

ambient pressure, unit: Pa

neint

number of charges on the aerosol particle

Returns:

float or dataframe of shape (n,m)

particle electrical mobility or mobilities, unit: m2 s-1 V-1

aerosol.functions.dma_mob2volts(Q, R1, R2, L, Z)

Cylindrical DMA voltage corresponding to mobility

Parameters:

Qfloat

sheath flow rate, unit lpm

R1float

inner electrode radius, unit m

R2float

outer electrode radius, unit m

Lfloat

effective electrode length, unit m

Zfloat

mobility, unit m2 s-1 V-1

Returns:

float

DMA voltage, unit V

aerosol.functions.dma_volts2mob(Q, R1, R2, L, V)

Theoretical selected mobility from cylindrical DMA

Parameters:

Qfloat

sheath flow rate, unit lpm

R1float

inner electrode radius, unit m

R2float

outer electrode radius, unit m

Lfloat

effective electrode length, unit m

Vfloat or series

applied voltage, unit V

Returns:

float or series

selected mobility, unit m2 s-1 V-1

aerosol.functions.dndlogdp2dn(df)

Convert from normalized number concentrations to unnormalized number concentrations.

Parameters:

dfdataframe

Aerosol number-size distribution (dN/dlogDp)

Returns:

dataframe

Aerosol number size distribution (dN)

aerosol.functions.eq_charge_frac(dp, N)

Calculate equilibrium charge fraction using Wiedensohler (1988) approximation

Parameters:

dpfloat

Particle diameter (m)

Nint

Amount of elementary charge in range [-2,2]

Returns:

float

Fraction of particles of diameter dp having N elementary charges

aerosol.functions.flow_velocity_in_pipe(tube_diam, flowrate)

Calculate fluid speed from the flow rate in circular tube

Parameters:

tube_diamfloat or series of lenght m

Diameter of circular tube (m)

flowratefloat or series of lenght n

Volumetric flow rate (lpm)

Returns:

float or dataframe of shape (n,m)

Speed of fluid (m/s)

aerosol.functions.ions2particles(neg_ions, pos_ions, temp=293.15, mob_ratio=None)

Estimate particle number size distribution from ions using Li et al. (2022)

Parameters:

neg_ionspandas dataframe

negative ion number size distribution

pos_ionspandas dataframr

positive ion number size distribution

tempfloat or series

ambient temperature in K

mob_ratiofloat

mobility ratio to be used, if None it is calculated from the ion data

Note that the ions should be overwhelmingly singly charged for the calculation to be accurate.

Returns:

pandas dataframe shape=(n,m)

estimated particle number size distribution

References

Li et al. (2022), https://doi.org/10.1080/02786826.2022.2060795

aerosol.functions.mean_free_path(temp, pres)

Calculate mean free path in air

Parameters:

tempfloat or series of length n

air temperature, unit: K

presfloat or series of length n

air pressure, unit: Pa

Returns:

float or series of length n

mean free path in air, unit: m

aerosol.functions.mob2diam(Zp, temp, pres, ne)

Convert electrical mobility to electrical mobility diameter in air

Parameters:

Zpfloat

particle electrical mobility or mobilities, unit: m2 s-1 V-1

tempfloat

ambient temperature, unit: K

presfloat

ambient pressure, unit: Pa

neinteger

number of charges on the aerosol particle

Returns:

float

particle diameter, unit: m

aerosol.functions.particle_diffusivity(dp, temp, pres)

Particle brownian diffusivity in air

Parameters:

dpfloat or series of lenght m

particle diameter, unit: m

tempfloat or series of lenght n

air temperature, unit: K

presfloat or series of lenght n

air pressure, unit: Pa

Returns:

float or dataframe of shape (n,m)

Particle Brownian diffusivity in air unit m2 s-1

aerosol.functions.particle_mean_free_path(dp, temp, pres)

Particle mean free path in air

Parameters:

dpfloat or series of length m

particle diameter, unit: m

tempfloat or series of length n

air temperature, unit: K

presfloat or series of length n

air pressure, unit: Pa

Returns:

float or dataframe of shape (n,m)

Particle mean free path, unit: m

aerosol.functions.particle_thermal_speed(dp, temp)

Particle thermal speed

Parameters:

dpfloat or series

particle diameter, unit: m

tempfloat or series

air temperature, unit: K

Returns:

float or dataframe

Particle thermal speed point, unit: m s-1

aerosol.functions.pipe_reynolds(tube_diam, flowrate, temp, pres)

Calculate Reynolds number in a tube

Parameters:

tube_diamfloat or series of length m

Inner diameter of the tube (m)

flowratefloat opr series of lenght n

Volumetric flow rate (lpm)

tempfloat

Temperature in K

presfloat

Pressure in Pa

Returns:

float or dataframe of shape (n,m)

Reynolds number

aerosol.functions.slipcorr(dp, temp, pres)

Slip correction factor in air

Parameters:

dpfloat or series of lenght m

particle diameter, unit m

tempfloat or series of length n

air temperature, unit K

presfloat or series of lenght n

air pressure, unit Pa

Returns:

float or dataframe fo shape (n,m)

For dataframe the index is taken from temperature or pressure series. Columns are particle diameters. unit dimensionless

Notes

Correction is done according to Mäkelä et al. (1996)

aerosol.functions.surf_dist(df)

Calculate the aerosol surface area size distribution

Parameters:

dfpandas.DataFrame

Aerosol number-size distribution

Returns:

pandas.DataFrame

Aerosol surface area-size distribution unit: m2 cm-3

aerosol.functions.thab_dp2volts(thab_voltage, dp)

Convert particle diameters to DMA voltages

Parameters:

thab_voltagefloat

Voltage at THA+ peak (V)

dpfloat or series

Particle diameters (m)

Returns:

float or series:

DMA voltage (V) corresponding to dp

Notes

See https://doi.org/10.1016/j.jaerosci.2005.02.009

Assumptions:

1. Sheath flow is air

2. Mobility standard used is THA+ monomer

3. T = 293.15 K and p = 101325 Pa

aerosol.functions.thab_volts2dp(thab_voltage, dma_voltage)

Convert DMA voltages to particle diameters

Parameters:

thab_voltagefloat

Voltage at THA+ peak (V)

dma_voltagefloat

DMA voltage (V)

Returns:

float:

particle diameter corresponding to DMA voltage (m)

Notes

See https://doi.org/10.1016/j.jaerosci.2005.02.009

Assumptions:

1. Sheath flow is air

2. Mobility standard used is THA+ monomer

3. T = 293.15 K and p = 101325 Pa

aerosol.functions.tubeloss(diam, flowrate, tubelength, temp, pres)

Calculate diffusional particle losses to walls of straight cylindrical tube assuming a laminar flow regime

Parameters:

diamfloat or series of length m

Particle diameters for which to calculate the losses, unit: m

flowratefloat or series of length n

unit: L/min

tubelengthfloat

Length of the cylindrical tube unit: m

tempfloat or series of length n

temperature unit: K

presfloat or series of lenght n

air pressure unit: Pa

Returns:

float or dataframe of shape (n,m)

Fraction of particles passing through. Each column represents diameter and each each row represents different temperature pressure and flowrate value

aerosol.functions.utc2solar(utc_time, lon, lat)

Convert utc time to solar time (solar maximum occurs at noon)

Parameters:

utc_timepandas Timestamp

lonfloat

Location’s longitude

latfloat

Location’s latitude

Returns:

pandas Timestamp

solar time

aerosol.functions.vol_dist(df)

Calculate the aerosol volume size distribution

Parameters:

dfpandas.DataFrame

Aerosol number-size distribution

Returns:

pandas.DataFrame

Aerosol volume-size distribution unit: m3 cm-3

aerosol.plotting module

aerosol.plotting.generate_log_ticks(min_exp, max_exp)

Generate ticks and ticklabels for log axis

Parameters:

min_expint

The exponent in the smallest power of ten

max_expint

The exponent in the largest power of ten

Returns:

numpy.array

minor tick values

numpy.array

major tick values

list of strings

major tick labels (powers of ten)

aerosol.plotting.generate_timeticks(t_min, t_max, minortick_interval, majortick_interval, ticklabel_format)

Parameters:

t_minpandas timestamp

t_maxpandas timestamp

majortick_intervalpandas date frequency string

See for all options here: https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#offset-aliases

minortick_intervalpandas date frequency string

ticklabel_formatpython date format string

See for all options here: https://docs.python.org/3/library/datetime.html#strftime-and-strptime-format-code

Returns:

pandas DatetimeIndex

minor tick values

pandas DatetimeIndex

major tick values

pandas Index containing strings

major tick labels

aerosol.plotting.plot_aerosol_dist(v, ax, cmap=<matplotlib.colors.LinearSegmentedColormap object>, norm=<matplotlib.colors.Normalize object>, xminortick_interval='1H', xmajortick_interval='2H', xticklabel_format='%H:%M')

Plot aerosol particle number-size distribution surface plot

Parameters:

vpandas.DataFrame or list of pandas.DataFrames

Aerosol number size distribution (continuous index)

axaxes object

axis on which to plot the data

cmapmatplotlib colormap

Colormap to use, default is rainbow

normmatplotlib.colors norm

Define how to normalize the colors. Default is linear normalization

xminortick_intervalpandas date frequency string

See for all options here: https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#offset-aliases

xmajortick_intervalpandas date frequency string

xticklabel_formatstr

See for all options here: https://docs.python.org/3/library/datetime.html#strftime-and-strptime-format-code

Returns:

colorbar handle

aerosol.plotting.rotate_xticks(ax, degrees)

Parameters:

axmatplotlib axes

degreesint or float

number of degrees to rotate the xticklabels

aerosol.plotting.set_legend_outside(ax, handles=None, labels=None, fs=10)

Put legend outside axes (upper right corner)

Parameters:

axAxes

axes to add the legend to

handleslist of handles

list of lines or points in the legend

labelslist of strings

labels for the legend entries

fsint

font size

Returns:

Legend

aerosol.plotting.show_matrix_values(ax, matrix, text_format='%d', text_color='white')

Plot numerical values on top of the cells when visualizing a matrix with imshow()

Parameters:

axmatplotlib.axes

matrixnumpy 2d-array

text_formatstr

text_colorstr

aerosol.plotting.subplot_aerosol_dist(vlist, grid, cmap=<matplotlib.colors.LinearSegmentedColormap object>, norm=<matplotlib.colors.Normalize object>, xminortick_interval='1H', xmajortick_interval='2H', xticklabel_format='%H:%M', keep_inner_ticklabels=False, hspace_padding=None, vspace_padding=None, subplot_labels=None, label_color='black', label_size=10, column_titles=None, fill_order='row', **kwargs)

Plot aerosol size distributions (subplots)

Parameters:

vlistlist of pandas.DataFrames

Aerosol size distributions (continuous index)

gridtuple (rows,columns)

define number of rows and columns

cmapmatplotlib colormap

Colormap to use, default is rainbow

normmatplotlib.colors norm

Define how to normalize the colors. Default is linear normalization

xminortick_intervalstr

A pandas date frequency string. See for all options here: https://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#offset-aliases

xmajortick_intervalstr

A pandas date frequency string

xticklabel_formatstr

Date format string. See for all options here: https://docs.python.org/3/library/datetime.html#strftime-and-strptime-format-code

keep_inner_ticklabelsbool

If True, use ticklabels in all subplots. If False, use ticklabels only on outer subplots.

subplot_paddingnumber or None

Adjust space between subplots

subplot_labelslist of str or None

The labels to put to labels the subplots with

label_colorstr

label_sizefloat

column_titleslist of strings or None

fill_orderstr

“rows” fills the subplots row by row “columns” fills the subplots column by column

**kwargsoptional parameters passed to matplotlib imshow()

Returns:

figure object

array of axes objects

colorbar handle