pyPDAF.PDAF.local_weight

pyPDAF.PDAF.local_weight()

Get localisation weight for given distance, 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.

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)

  See also: PDAF-OMI wiki

• distance (float) – distance to observation

• nrows (int) – Number of rows in matrix A

• ncols (int) – Number of columns in matrix A

• a (ndarray[tuple[nrows, ncols, ...], np.float64]) – ensemble perturbation/anomaly matrix; this matrix is used when weighting is regulated by mean variance, i.e., rtype = 1. Array shape: (nrows, ncols)

• var_obs (double) – Observation variance

• verbose (int) – Verbosity flag

Returns:

weight – localisation weights

Return type:

double