wradlib.dp.rhohv_noise_correction

wradlib.dp.rhohv_noise_correction(rho, snr)

wradlib.dp.rhohv_noise_correction(rho: DataArray, snr)

Correct correlation coefficient (\(\rho_{HV}\)) for receiver noise bias.

This function applies a noise-bias correction to the polarimetric correlation coefficient assuming additive, uncorrelated noise in the horizontal and vertical radar channels with equal noise power.

The correction is based on the covariance-based noise contamination model for polarimetric radar observables [Gourley et al., 2006], where finite SNR leads to a downward bias in the estimated correlation coefficient.

Parameters:

• rho (array_like) – Measured complex correlation coefficient magnitude (\(\rho_{HV}\)).

• snr (array_like) – Signal-to-noise ratio in dB for the corresponding radar channel. Must be expressed in dB.

Returns:

rho_c (array_like) – Noise-corrected correlation coefficient.

Notes

The correction assumes additive, uncorrelated noise in the H and V channels and approximates the effect of noise on the covariance-based estimator of the correlation coefficient.

The formulation is a simplified SNR-dependent approximation derived from the noise bias model presented in [Gourley et al., 2006].

In the original formulation (Eq. 6), the bias correction includes additional dependence on differential reflectivity (\(Z_{DR}\)) and separate noise contributions in the H and V channels.

The present implementation neglects \(Z_{DR}\)-dependent terms and assumes symmetric noise conditions, resulting in the approximation:

rho_c ≈ rho * sqrt(1 + 1 / SNR_lin)

where SNR_lin = 10^(SNR / 10).