integrate

integrate(fs[, area_or_mask])

Computes the average of each field in fs over an area.

Parameters

  • fs (Fieldset) – input fieldset

  • area_or_mask (list or Fieldset) – list defining an area as [North, West, South, East] or fieldset defining a mask

Return type

number or ndarray or None

If fs contains only one field a number is returned. If there is more than one field a numpy array is returned. Missing values in the input fieldset are bypassed in this calculation. For each field for which there are no valid values None is returned.

  • If fs is the only argument the integration is done on all grid points.

  • If area_or_mask is a list it defines an area as [North, West, South, East] for the integration:

    import metview as mv
europe = [75,-12.5,35,42.5]
x = mv.integrate(field, europe)

  • If area_or_mask is a fieldset it is used as a mask and the integration is performed only on the grid points where the mask values are non zero. area_or_mask should contain either one or as many fields as there are in fs. If it has a single field then the mask is applied to all fields in fs. If it has the same number of fields as fs, then a different mask is applied to each input field. The example below shows how to use integrate() with a land-sea mask retrieved from MARS:

    import metview as mv

# read grib data on a 1 degree by 1 degree grid
f = mv.read("my_fs.grib")

# retrieve land-sea mask from MARS on the same grid
lsm = mv.retrieve(
   type="an",
   date=-1,
   param="lsm",
   grid=[1,1],
   levtype="sfc"
)

# make sure values are either 0 or 1
lsm = lsm > 0.5

# compute the average value on land and on sea
land = mv.integrate(f, lsm)
sea = mv.integrate(f, not lsm)

Note

The computations are based on the following approximation of the grid cell areas:

\[A_{i} = 2 R^{2} cos\phi_{i} sin(\frac{\Delta\phi_{i}}{2}) \Delta\lambda_{i}\]

where:

  • R is the radius of the Earth

  • \(\phi_{i}\) is the latitude of the i-th grid cell

  • \(\Delta\phi_{i}\) is the size of the grid cells in latitude

  • \(\Delta\lambda_{i}\) is the size of the i-th grid cell in longitude.

integrate() then supposes that \(\Delta\phi_{i}\) is constant and the weighted average over the area is computed as:

\[\frac {\sum_{i}f_{i} A_{i}}{\sum_{i}A_{i}} = \frac {\sum_{i}f_{i}cos\phi_{i}\Delta\lambda_{i}}{\sum_{i}cos\phi_{i}\Delta\lambda_{i}}\]

The formula above is only used for reduced or regular latitude-longitude and Gaussian grids. For all other grid types integrate() simply returns the mathematical average of the values (just like average() does).

Warning

Please note that for Gaussian grids the formula can only be only regarded as an approximation since \(\Delta\phi_{i}\) is not constant!