wradlib.dp.kdp_from_phidp(phidp, winlen=7, dr=1.0, method='lanczos_conv', skipna=True, **kwargs)

Retrieves \(K_{DP}\) from \(Phi_{DP}\).

In normal operation the method uses convolution to estimate \(K_{DP}\) (the derivative of \(Phi_{DP}\)) with Low-noise Lanczos differentiators (method=’lanczos_conv’). The results are very similar to the moving window linear regression (method=’lstsq’), but the former is much faster.

The \(K_{DP}\) retrieval will return NaNs in case at least one value in the moving window is NaN. By default, the remaining gates are treated by using local linear regression where possible.

Please note that the moving window size winlen is specified as the number of range gates. Thus, this argument might need adjustment in case the range resolution changes. In the original publication ([Vulpiani et al., 2012]), the value winlen=7 was chosen for a range resolution of 1km.

Uses derivate to calculate the derivation. See for additional kwargs.


The function is designed for speed by allowing to process multiple dimensions in one step. For this purpose, the RANGE dimension needs to be the LAST dimension of the input array.

  • phidp (numpy.ndarray) – multi-dimensional array, note that the range dimension must be the last dimension of the input array.

  • winlen (int) – Width of the window (as number of range gates)

  • dr (float) – gate length in km

  • method (str) – Defaults to ‘lanczos_conv’. Can also take one of ‘lanczos_dot’, ‘lstsq’, ‘cov’, ‘cov_nan’, ‘matrix_inv’.

  • skipna (bool) – Defaults to True. Local Linear regression removing NaN values using valid neighbors > min_periods

Keyword Arguments

min_periods (int) – Minimum number of valid values in moving window for linear regression. Defaults to winlen // 2 + 1.


out (numpy.ndarray) – array of \(K_{DP}\) with the same shape as phidp


>>> import wradlib
>>> import numpy as np
>>> import matplotlib.pyplot as pl
>>> pl.interactive(True)
>>> kdp_true = np.sin(3 * np.arange(0, 10, 0.1))
>>> phidp_true = np.cumsum(kdp_true)
>>> phidp_raw = phidp_true + np.random.uniform(-1, 1, len(phidp_true))
>>> gaps = np.concatenate([range(10, 20), range(30, 40), range(60, 80)])
>>> phidp_raw[gaps] = np.nan
>>> kdp_re = wradlib.dp.kdp_from_phidp(phidp_raw)
>>> line1 = pl.plot(np.ma.masked_invalid(phidp_true), "b--", label="phidp_true")  # noqa
>>> line2 = pl.plot(np.ma.masked_invalid(phidp_raw), "b-", label="phidp_raw")  # noqa
>>> line3 = pl.plot(kdp_true, "g-", label="kdp_true")
>>> line4 = pl.plot(np.ma.masked_invalid(kdp_re), "r-", label="kdp_reconstructed")  # noqa
>>> lgnd = pl.legend(("phidp_true", "phidp_raw", "kdp_true", "kdp_reconstructed"))  # noqa
>>> pl.show()