pyPDAF.PDAF.local_weights

pyPDAF.PDAF.local_weights()

Get a vector of localisation weights for given distances, cut-off radius, support radius, weighting type, and weighting function.

This function is used in the analysis step of a filter to computes a localisation weight.

Typically, in domain-localised filters, the function is called in user-supplied py__prodRinvA_l_pdaf(). In LEnKF, this function is called in user-supplied py__localize_covar_pdaf().

This function is usually only used without PDAF-OMI.

This function is a vectorised version of pyPDAF.PDAF.local_weight() without any regulations.

Parameters:

  • wtype (int) –

    type of weight function:

    • wtype=0: unit weight (weight=1 up to distance=cradius)

    • wtype=1: exponential decrease (weight=1/e at distance=sradius; weight=0 for distance>cradius)

    • wtype=2: 5th order polynomial (Gaspari and Cohn 1999; weight=0 for distance>cradius)

  • rtype (int) –

    type of regulated weighting:

    • rtype/=1: no regulation

    • rtype=1: regulated by variance of the matrix A and the observation variance

  • cradius (float) – cut-off radius where weight = 0 beyond the cradius

  • sradius (float) –

    support radius of localisation function. This depends on wtype:

    • wtype=0: sradius is not used

    • wtype=1: weight = \(e^{-\frac{distance}{sradius}}\)

    • wtype=2: weight = 0 if distance > sradius

      else weight = f(distance ,sradius)

  • dim (int) – Size of distance and weight arrays

  • distance (ndarray[np.float64, ndim=1]) – distance to observation Array shape: (dim)

  • verbose (int) – Verbosity flag

Returns:

weight – Array for localisation weights Array shape: (dim)

Return type:

ndarray[np.float64, ndim=1]