univertint

univertint(fs[, lnsp_code])
univertint(lnsp, fs[, levels])

Performs a vertical integration for pressure levels or ECMWF (hybrid) model levels.

Parameters

  • fs (Fieldset) – input fieldset

  • lnsp (Fieldset) – lnsp fieldset defined on model level 1

  • lnsp_code (number) – ecCodes paramId for lnsp

  • levels (list) – level range as a list of [top, bottom]

Return type

Fieldset containing one field only

univertint() has to be called in a different way depending on the type of vertical levels in fs.

  • Pressure levels: the function has to be called with the fs argument only.

  • Model levels:

    • when no lnsp is specified fs must also contain an lnsp field. In this case the optional lnsp_code can specify the ecCodes paramId used to identify the lnsp field (by default the value of 152 is used.

    • when lnsp is specified it defines the lnsp field.

    • the optional levels parameter is a list with two numbers [top, bottom] to specify the level range for the integration. If levels is not specified the vertical integration is performed for all the model levels in fs.

A missing value in any field will result in a missing value in the corresponding place in the output fieldset.

Computations

The computations are based on the following formula:

\[\int_{p_{top}}^{p_{bottom}} f \frac{dp}{g}\]

where:

  • f: input fieldset

  • p: pressure

  • g: acceleration of gravity (9.80665 m/s2).

The actual algorithm is slightly different on pressure and model levels.

For pressure levels the data is first sorted by pressure in ascending numerical order resulting in \(f_{i}\) fields on levels \(p_{i}\) i=0,…,N (with \(p_{i+1} > p_{i}\)). Then, to estimate the pressure differential we form N layers by using the pressures halfway between two levels. If we denote the halfway pressure between level i and i+1 by \(p^{*}_{i}\) we can write the layer sizes as follows:

\[ \begin{align}\begin{aligned}\Delta p_{0} = p^{*}_{0} - p_{0}\\\Delta p_{i} = p{*}_{i+1} - p^{*}_{i}\\\Delta p_{N} = p_{N} - p^{*}_{N-1}\end{aligned}\end{align} \]

and estimate the integral like this:

\[\sum_{i=0}^{N} f_{i} \frac{\Delta p_{i}}{g}\]

For model level data the vertical coordinate system definition is stored in the “pv” array in the GRIB header. A model level is defined on a “full level”, which lies in the layer between the two neighbouring “half levels”. Using lnsp and the “pv” array we can determine the \(\Delta p_{i}\) layer size for each level individually. The integral is then estimated in the same way as was shown above for pressure levels. Please note that you can use unithickness() to compute the layer sizes (the “thickness” in the function name actually means “layer size”). For more details about the model level definitions please visit this page.

Example
import metview as mv

# Retrieve cloud liquid water content
clwc = mv.retrieve(
   levtype="ml",
   levelist=[1,"to",137],
   param="clwc",
   date=-1,
   grid=[2,2]
)

# Retrieve lnsp
lnsp = mv.retrieve(
   levtype="ml",
   levelist=1,
   param="lnsp",
   date=-1,
   grid=[2,2]
)

# Compute total amount of liquid water
r = mv.univertint(lnsp,clwc)