tropy.analysis_tools¶

The tropy.analysis package is a collection of tools for dedicated analysis of scientific data. It has been especially used to explore atmospheric data, but the application to other types of data might be rather straight forward and meaningful.

tropy.analysis_tools.derived_variables¶

This module contains / will contain variables derived from some basic input fields. The name “basic” refers to the typical set of variables stored in climate or weather model output.

tropy.analysis_tools.derived_variables.calc_lwp(p, T, qv, qc, g=9.8, axis=-1)¶

Calculates the liquid water path.

Parameters

p (numpy array) – atmospheric pressure [hPa]
T (numpy array) – temperature [K]
qv (numpy array) – water vapor mixing ratio [kg / kg]
qc (numpy array) – liquid water mixing ratio [kg / kg]

Returns

lwp – liquid water path [g / m**2]

Return type

numpy array

Notes

hydrostatic approximation is used to convert vertical integration from pressure to height levels
impact of condesate mass on air density is ignored.

tropy.analysis_tools.grid_and_interpolation¶

tropy.analysis_tools.grid_and_interpolation.COSMO_mean_vertical_levels(Nlev)¶

Outputs the mean vertical levels of COSMO-DE taken from the model description of COSMO (see reference below).

Parameters

Nlev (int) –

number of vertical levels, i.e.

Nlev = 51 for intermediate half-levels (e.g. for w) Nlev = 50 for main levels (e.g. for u)

Returns

lev – mean vertical COSMO-DE levels

Return type

numpy array (1-dim)

References

M. Baldauf, J. Foerstner, S. Klink, T. Reinhardt, C. Schraff, A. Seifert und K. Stephan “Kurze Beschreibung des Lokal-Modells Kuerzestfrist COSMO-DE (LMK) und seiner Datenbanken auf dem Datenserver des DWD”, Version 1.6, Stand: 31. 03. 2011

Tabelle 1, Seite 29

tropy.analysis_tools.grid_and_interpolation.create_interpolation_index(lon1, lat1, lon2, lat2, xy=False)¶

Given georeference of two grids in lon and lat, an index is built to map a field on grid 1 to grid 2.

Parameters

lon1 (numpy array (2-dim)) – longitude of input grid 1
lat1 (numpy array (2-dim)) – latitude of input grid 1
lon2 (numpy array (2-dim)) – longitude of target grid 2
lat2 (numpy array (2-dim)) – latitude of target grid 2
xy (bool, optional, default = False) – switch if georef field are interpreted as local Cartesian coordinates: Then no internal transformation is used.

Returns

ir (numpy array, 2-dim, dtype = int) – index field for transforming rows
ic (numpy array, 2-dim, dtype = int) – index field for transforming columns

tropy.analysis_tools.grid_and_interpolation.curve_flow_filter(f, numberOfIterations=5)¶

Smoothing filter depending on isoline curvature. Interface for curvature flow filter from simpleITK toolkit.

Parameters

f (numpy array (2-dim)) – 2d field to be filtered (smoothed)
numberOfIterations (int, optional, default = 5) – number of iterations, increases smooting effect

Returns

f_sm – smoothed 2d field

Return type

numpy array (2-dim)

Notes

Only works if SimpleITK is installed !!!

tropy.analysis_tools.grid_and_interpolation.cutout_cluster(c, nc, nedge=30)¶

Makes a cutout of a categorial field c for an object of class / number nc.

Parameters

c (numpy array, 2-dim, dtype = int) – 2d categorial field
nc (int) – category number / class which is chosen
nedge (int, optional, default = 30) – number of edge pixels added / included

Returns

ccut – cutout of categorial field c

Return type

numpy array, 2-dim, dtype = int

tropy.analysis_tools.grid_and_interpolation.cutout_field4box(f, ind, bsize, **kwargs)¶

Cuts out a field based on center pix index and box size.

Parameters

f (2d or 3d numpy array) – the field to be cut out
ind (tuple or list) – center index of horizontal cutout
bsize (int) – size of the quadratic cutout box

Returns

fcut – resulting quadratic cutout

Return type

2d or 3d numpy array

tropy.analysis_tools.grid_and_interpolation.cutout_fields(fin, slices, vaxis=0)¶

Cuts out a field or a list of similar fields given row and column slices.

Parameters

fin (2d or 3d numpy array or list of fields) – the fields to be cut out
slices (tuple or list) – region slice such that the cutout is done as ((row1, row2), (col1, col2))
vaxis (int, optional, default = 0) – for 3d fields, axis which is still varying

Returns

fout – resulting cutout (possibly a list of cutted fields)

Return type

2d or 3d numpy array or list of fields

tropy.analysis_tools.grid_and_interpolation.get_index(p, lon, lat)¶

Given a point p the nearest grid point is returned.

Parameters

p (numpy array) – point in the 2d grid
lon (numpy array (2-dim)) – grid values of the 1st dimension (can be longitude, x, etc.)
lat (numpy array (2-dim)) – grid values of the 2nd dimension (can be latitude, y, etc.)

Returns

ir (numpy array (2-dim)) – row index (the 1st)
ic (numpy array (2-dim)) – column index (the 2nd)

tropy.analysis_tools.grid_and_interpolation.i2iset(v, i)¶

Returns an index set for a n-dim numpy array given an index i which points to a position within the same but flattened array.

It is assumed that the array was flattened in C-mode.

Parameters

v (numpy array (n-dim)) – field which determines the rank and shape
i (int) – input index which points to the position in v.flatten()

Returns

iset – index set which points to the position in v

Return type

tuple

Notes

This routine helps you to locate a maximum in a n-dimensional array using e.g. the np.argmax function.

tropy.analysis_tools.grid_and_interpolation.interpolate_field_to_hor_pos(pos, lon, lat, field, **kwargs)¶

Given a sequence of points (or just one) a field (2d or 3d) given a grid is interpolated to the new positions.

Parameters

pos (numpy array (2-dim)) – sequence of points given as np.array((x,y)) where x and y can be n-dimensional
lon (numpy array (2-dim)) – grid values of the 1st dimension (can be longitude, x, etc.)
lat (numpy array (2-dim)) – grid values of the 2nd dimension (can be latitude, y, etc.)
field (numpy array) – 2d or 3d field to be interpolated to pos
**kwargs (dict content) – keyword arguments for the griddata routine of the scipy.interpolate package can be passed through

Returns

f – field interpolated to the position sequence pos, f has the dimension n x Nlev, where n is the dimension of pos, Nlev the vertical dimension

Return type

numpy array

tropy.analysis_tools.grid_and_interpolation.ldiff(var, axis=-1)¶

Calculates difference of a field at adjacent levels. Now, wrapper for numpy.diff with default on last axis.

Parameters

var (numpy array (n-dim where n = [1,2,3])) – field; 1d, 2d or 3d array
axis (int, optional, default = -1) – axis used for layer avering

Returns

dvar – level difference

Return type

numpy array (n-dim where n = [1,2,3])

tropy.analysis_tools.grid_and_interpolation.ll2xy(lon, lat, lon0=10.0, lat0=50.0, R=6380.0)¶

Transformation between longitude and latitude and local Cartesian coordinates in west-east direction (x) and south-north direction (y). The local projection is called “sinusoidal”.

Parameters

lon (numpy array) – longitude
lat (numpy array) – latitude
lon0 (float, optional, default = 10.) – arbitrary initial longitude for x = 0
lat0 (float, optional, default = 50.) – arbitrary initial latitude for y = 0
R (float, optional, default = 6380.) – approximation for the radius of Earth

Returns

x (numpy array) – Cartesian coordinate in west-east direction (increasing towards the East)
y (numpy array) – Cartesian coordinate in south-north direction (increasing towards the North)

Notes

The unit of Earth’s radius determines the units of x and y. Default (km).

References

See https://en.wikipedia.org/wiki/Sinusoidal_projection for further info.

tropy.analysis_tools.grid_and_interpolation.ll2xyc(lon, lat, mlon=None, mlat=None, lon0=0, lat0=0.0)¶

Applies a centered version of ll2xy. The centering is around the mean lon/lat value and lon0, lat0 only define the x/y offset.

Parameters

lon (numpy array) – longitude
lat (numpy array) – latitude
mlon (float, optional, default = None) –
longitude center point of projection

if None then average of lon is used
mlat (float, optional, defaulft = None) –
latitutde center point of projection

if None then average of lat is used
lon0 (float, optional, default = 0.) – zero longitude (for x-offset)
lat0 (float, optional, default = 0.) – zero latitude (for y-offset)

Returns

x (numpy array) – x-coordinate
y (numpy array) – y-coordinate

tropy.analysis_tools.grid_and_interpolation.lmean(var, axis=-1)¶

Calculates the layer mean of a field.

Parameters

var (numpy array (n-dim where n = [1,2,3])) – field; 1d, 2d or 3d array
axis (int, optional, default = -1) – axis used for layer avering

Returns

varm – layer mean

Return type

numpy array (n-dim where n = [1,2,3])

tropy.analysis_tools.grid_and_interpolation.low2hres_region(region)¶

Based on low-res. region of MSG channels an correspoding HRV region is calculated.

Parameters: region (tuple of two tubles) – region slice for cuuting a field ((row1, row2), (col1, col2))
Returns: hrv_region
Return type: corresponding HRV region as ((row1, row2), (col1, col2))

Notes

Calculation

It is assumed that the hrv region is a dependent variable which depends on the low res region attribute That means: Given the low res region cutout hrv region is determined as corresponding cutout which

exactly fits with the low res region and

refers to the artifical hrv full disk of 11136 x 11136

low res pixel with the index (I,J) = (0,0) has a high res pixel with index (i_m, j_m) = (2,2) in the middle and (i_u, j_u) = (1,1) in the upper corner see doc “MSG Level 1.5 Image Data Format Description”, Fig.8 which then leads to the relation between the low res pixel (I,J) and its corresponding upper corner high res pixel (i_u, j_u): (i_u, j_u) = 3 * (I, J ) + 1

tropy.analysis_tools.grid_and_interpolation.make_add_edge(var)¶

Adds egde region to 2d data field. Values in added left and right column, and lower and upper row are linearily extrapolated from their neighbors.

Parameters: var (numpy array (2-dim)) – 2d variable field (Nrow, Ncols)
Returns: var_new – 2d variable field with added edge values (Nrows + 2, Ncols + 2)
Return type: numpy array (2-dim)

tropy.analysis_tools.grid_and_interpolation.make_hrv_upscaling(v)¶

A 2d field is upscaled to 3-fold higher resolution using linear interpolation. Edge values are determined by linear extrapolation.

Parameters: v (numpy array (2-dim)) – 2d variable field (Nrow, Ncols)
Returns: vhigh – variable field with 3-times higher resolution (3*Nrows, 3*Ncols)
Return type: numpy array (2-dim)

tropy.analysis_tools.grid_and_interpolation.make_index_set(nrows, ncols)¶

This simple routine makes an 2d index set for given row and column number of a 2d field.

Parameters

nrows (int) – number of rows
ncols (int) – number of columns

Returns

ii (numpy array, dtype = int) – 2d field of rows indices
jj (numpy array, dtype = int) – 2d field of column indices

tropy.analysis_tools.grid_and_interpolation.make_vert_cut(p1, p2, lon, lat, vg, **kwargs)¶

Makes a horizontal - vertical cut through a 3d field.

Parameters

p1 (list or numpy array) – 1st end of the cutting line (lon, lat)
p2 (list or numpy array) – 2nd end of the cutting line (lon, lat)
lon (numpy array (2-dim)) – longitude
lat (numpy array (2-dim)) – latitude
vg (numpy array (3-dim)) – 3d field to be interpolated
**kwargs (dict content) – keyword arguments for the griddata routine of the scipy.interpolate package can be passed through

Returns

s (numpy array (1-dim)) – distance of km from one to the other end of the cutting line
lo (numpy array (1-dim)) – longitude along the cut
la (numpy array (1-dim)) – latitude along the cut
v (numpy array (2-dim)) – field interpolated to the cutting line

Vertical levels are kept.

tropy.analysis_tools.grid_and_interpolation.mid2edge_gridvector(x_mid, x_edge0)¶

Converts an mid-point based grid vector into an edge-based grid vector.

Parameters

x_mid (numpy array (1-dim)) – mid-point-based grid vector (length N)
x_edge0 (float) – left edge

Returns

x_edge – edge-based grid vector (length N + 1)

Return type

numpy array (1-dim)

tropy.analysis_tools.grid_and_interpolation.region2slice(lon, lat, region)¶

Given a region of ((lon1,lon2),(lat1, lat2)) the routine provides a slicing ((row1, row2), (col1, col2)) than accomodates the region.

Parameters

lon (numpy array (2-dim)) – longitude
lat (numpy array (2-dim)) – latitude
region (tuple of two tubles) – ((lon1, lon2), (lat1, lat2))

Returns

slice – region slice for cuuting a field ((row1, row2), (col1, col2))

Return type

tuple of two tubles

tropy.analysis_tools.grid_and_interpolation.remap_field(lon, lat, f, dr=0.5)¶

Do nearest nearbor remapping on a simple equi-distant local cartesian coordiante grid.

Uses curvature flow filter for smoothing and pixel edge correction.

Parameters

lon (numpy array, (2-dim)) – longitude
lat (numpy array, (2-dim)) – latitude
f (numpy array, (2-dim)) – 2d field to be interpolated
dr (float, optional, default = 0.5) – grid spacing in km

Returns

xnew (numpy array, (2-dim)) – regridded, equi-distant x-coordinate in km
ynew (numpy array, (2-dim)) – regridded, equi-distant y-coordinate in km
fint (numpy array, (2-dim)) – remapped field

tropy.analysis_tools.grid_and_interpolation.simple_pixel_area(lon, lat, xy=False, uncertainty=False)¶

Approximates the grid box area of a lon - lat grid.

The grid is treated as if it is an equidistant grid in local Cartesian coordinates on Earth’s surface (i.e. in x and y). The grid point is placed at each of the for corners of the grid box and the corresponding average area ist calculated.

Parameters

lon (numpy array (2-dim)) – longitude
lat (numpy array (2-dim)) – latitude
xy (bool, optional, default = False) – switch if lon & lat are interpreted as local Cartesian coordinates
uncertainty (bool, optional, default = False) –
switch if std of pixel area is output

Deviation are caused by effects of the not-rectangular grid.

Returns

a (numpy array (2-dim)) – grid box area
da (numpy array (2-dim), optional) – standard deviation of grid box area, if uncertainty == True

tropy.analysis_tools.grid_and_interpolation.spline_smooting(x, y, s=0.1, fixed_endpoints=True)¶

Smoothes a curve with smooting spline.

Parameters

x (numpy array (1-dim)) – abscissa values
y (numpy array (1-dim)) – ordinate values
s (float, optional, default = 0.1) – smooting parameter
fixed_endpoints (nool, optional, default = True) – switch, if endpoinds should be hold fixed

Returns

y_smooth – smoothed version of y

Return type

numpy array (1-dim)

Notes

Uses the function scipy.interpolate.UnivariateSpline.

tropy.analysis_tools.grid_and_interpolation.tube_cutout4box(v3d, i0, boxsize)¶

Performs tube cutout with given index set. The center index might not be constant.

Parameters

v3d (numpy array (3-dim)) – 3d field, 1st dimension is time (or variable)
i0 (list or numpy array (2-dim)) – center indices (irvec, icvec) index tuple, (row index vector, co index vector)
boxsize (int) – size of the quadratic cutout box

Returns

vtube – 3d tube, quadratic cutout in the last two dimensions

Return type

numpy array (3-dim)

Notes

This function can be used top make vertical cutouts, but a transpose command has to be applied before and after.

tropy.analysis_tools.grid_and_interpolation.xy2ll(x, y, lon0=10.0, lat0=50.0, R=6380)¶

Transformation between local Cartesian coordinates in west-east direction (x) and south-north direction (y) and longitude and latitude. This assumes a sinusoidal projection. Inversion of the function ll2xy.

Parameters

x (numpy array) – Cartesian coordinate in west-east direction (increasing towards the East)
y (numpy array) – Cartesian coordinate in south-north direction (increasing towards the North)
lon0 (float, optional, default = 10.) – arbitrary initial longitude for x = 0
lat0 (float, optional, default = 50.) – arbitrary initial latitude for y = 0
R (float, optional, default = 6380.) – approximation for the radius of Earth

Returns

lon (numpy array) – longitude
lat (numpy array) – latitude

Notes

The unit of Earth’s radius determines the units of x and y. Default (km).

References

See https://en.wikipedia.org/wiki/Sinusoidal_projection for further info.

tropy.analysis_tools.optical_flow¶

tropy.analysis_tools.parallax¶

tropy.analysis_tools.segmentation¶

tropy.analysis_tools.statistics¶

tropy.analysis_tools.thermodynamic_variables¶

Package for the calculation of several thermodynamical properties of moist air (including condensate).

ToDo

Some final tests of the routines should be done.
There was an issue with mixing ratio vs. specific humidity, but might be resolved …

tropy.analysis_tools.thermodynamic_variables.H2r(hrel, p, T)¶

Converts relative humidity H into mixing ratio r.

Parameters

hrel (numpy array) – relative humidity in [%]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]

Returns

es – water vapor pressure in [Pa]

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.absolute_humidity(r, p, T)¶

Calculates absolute humidity.

Parameters

r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]

Returns

rho_v – absolute humidity / m**3]

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.both_mass_fractions2mixing_ratios(qv, qw)¶

Converts water and the vapor mass fraction to condensed water and vapor mixing ratio.

Parameters

qv (numpy array) – water vapor mass fraction [kg / kg]
qw (numpy array) – condensed water mass fraction [kg / kg]

Returns

r (numpy array) – water vapor mixing ratio [kg / kg]
rw (numpy array) – condensed water mixing ratio [kg / kg]

tropy.analysis_tools.thermodynamic_variables.dew_point(r, p, T)¶

Calculates dew point temperature after Markowski book p 13 eq (2.25)

Parameters

r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]

Returns

Td – dew point temperature in [K]

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.dry_air_density(r, p, T)¶

Calculates dry air density.

Parameters

r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]

Returns

rho_d – dry air density in [kg / m**3]

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.dry_air_potential_temperature(r, p, T)¶

Calculates dry air potential temperature.

Parameters

r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]

Returns

theta_d – dry air potential temperature (K)

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.equivalent_potential_temperature(r, p, T, eq=15)¶

Calculates equivalent potential temperature. after Bolton (1980) MWR 108, p.1046, eq. (43)

Davies-Jones (2009) MWR137, eq. (6.3)

also using either one of (15), (21) or (22)

Parameters

r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]
eq (int, optional, default = 15) – which eq. of Bolton (1980) to be chosen for lifting condensation level temperature eq in [15, 21, 22]

Returns

theta_E – equivalent potential temperature

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.lifting_condensation_level_temperature(r, p, T, eq=15)¶

Calculates lifting condensation level temperature. after Bolton (1980) MWR 108, p.1046, eq. (15), (21) or (22)

Parameters

r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]
eq (int, optional, default = 15) – which eq. of Bolton (1980) to be chosen eq in [15, 21, 22]

Returns

TL – lifting condensation level temperature in [K]

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.moist_gas_constant(r)¶

Calculates gas constant of moist air.

Parameters: r (float or numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
Returns: R_m – gas constant of moist air [J / kg / K]
Return type: float or numpy array

tropy.analysis_tools.thermodynamic_variables.moist_potential_temperature(r, p, T)¶

Calculates moist air potential temperature.

Parameters

r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]

Returns

theta_m – moist air potential temperature (K)

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.moist_specific_heat(r)¶

Calculates specific heat at constant pressure of moist air.

Parameters: r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
Returns: c_pm – specific heat at constant pressure of moist air
Return type: numpy array

tropy.analysis_tools.thermodynamic_variables.relative_humidity(r, p, T)¶

Calculates relative humidity.

Parameters

r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]

Returns

H – relative humidity in [%]

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.saturation_over_ice(T, method='PK')¶

Calculates saturation water vapor pressure over ice.

Parameters

T (numpy array) – temperature [K]
method (str, optional, default = 'PK') – use an equation which approximates the vapor pressure over ice method in [‘PK’, ‘Murphy’]

Returns

es – water vapor pressure in [Pa]

Return type

numpy array

Notes

‘PK’ refers to Pruppacher and Klett (1997) ‘Murphy’ refers to Murphy and Koop (2005) eq. (7)

References

Murphy, D. M., and T. Koop (2005), Review of the vapour pressures of ice and supercooled water for atmospheric applications, Quart. J. Roy. Meteor. Soc., 131(608), 1539-1565, doi:10.1256/qj.04.94.

tropy.analysis_tools.thermodynamic_variables.saturation_pressure(T)¶

Calculates saturation water vapor pressure after Bolton (1980) MWR 108, p.1046, eq. (10)

Parameters: T (numpy array) – temperature [K]
Returns: es – water vapor pressure in [Pa]
Return type: numpy array

tropy.analysis_tools.thermodynamic_variables.specific_humidity(r)¶

Calculates specific humidity.

Parameters: r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
Returns: q – specific humidity i.e. vapor mass per moist air mass [kg / kg]
Return type: numpy array

tropy.analysis_tools.thermodynamic_variables.thermodynamic_constants()¶

Sets some thermodynamic constants.

Parameters: None –
Returns: const – set of thermodynamic constans saved in dictionary
Return type: dict

tropy.analysis_tools.thermodynamic_variables.total_density(r, r_w, p, T)¶

Calculates total density of moist air with hydrometeors.

Parameters

r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
r_w (numpy array) – mixing ratio of condensed water i.e. condensed water mass per dry air mass in [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]

Returns

rho_d – dry air density in [kg / m**3]

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.water_vapor_pressure(r, p, T)¶

Calculates water vapor pressure.

Parameters

r (numpy array) – mixing ratio i.e. vapor mass per dry air mass in [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]

Returns

e – water vapor pressure in [Pa]

Return type

numpy array

tropy.analysis_tools.thermodynamic_variables.watermass_fraction2rw(qw, r)¶

Converts water mass fraction to condensed water mixing ratio.

Parameters

qw (numpy array) – condensed water mass fraction [kg / kg]
r (numpy array) – mixing ration of water vapor [kg / kg]
p (numpy array) – total gas pressure [Pa]
T (numpy array) – temperature [K]

Returns

rw – condensed water mixing ratio [kg / kg]

Return type

numpy array