Attenuation =========== Especially at short wavelengths, reflectivity measurements, e.g. at X- and K-bands, are significantly attenuated by liquid water along their paths, while attenuation at S-Band is practically negligible :cite:`lengfeld2014`. To retrieve the intrinsic reflectivity, attenuation corrections have to be applied. For this purpose, we provide two procedures, a single radar and a dual radar attenuation correction. Single radar attenuation correction ----------------------------------- The single radar attenuation correction is a gate-by-gate correction developed by :cite:`kramer2008` and :cite:`jacobi2016` based on the iterative estimation of the relation between specific attenuation and the radar reflectivity. For this application, we can simply integrate wradlib_ into our package with :py:func:`wradlib.atten.correct_attenuation_constrained`, which calculates the path integrated attenuation. :cite:`jacobi2016` evaluated this attenuation correction for C-band weather radars of the german weather service (DWD). The parameters are i.a. wavelength dependent. We tuned the parameters for C-band and for X-band by ourselves using micro rain radar (MRR) measurements of multiple years covering 10252 fit values following the methodology introduced by :cite:`overeem2021rainfall`. The code below shows the simple possibility to integrate wradlib_ for single radar attenuation correction. .. _wradlib: https://docs.wradlib.org/en/latest/ .. code-block:: python from wradlib.atten import correct_attenuation_constrained, \ constraint_dbz, constraint_pia pia = correct_attenuation_constrained(refl.values, a_max=5.9e-6, a_min=2.71e-6, n_a=200, b_max=0.97, b_min=0.89, n_b=10, gate_length=0.25, constraints=[constraint_dbz, constraint_pia], constraint_args=[ [59.0], [constraint_pia_arg]] ) pia = xr.DataArray( data=pia, coords=refl.coords, dims=refl.dims, ) pia = pia.lawr.set_variable('pia') refl_corrected = refl + pia refl_corrected = refl_corrected.lawr.set_metadata(refl) tag_array(refl_corrected, "attenuation-corr-single") .. warning:: The function :py:func:`wradlib.atten.correct_attenuation_constrained` may return highly unstable results of path integrated attenuation. We added checks and warnings for the violation of thresholds and highly unstable results within the functional api (e.g. :py:func:`pylawr.functions.transform.correct_attenuation_lawr`). Dual radar attenuation correction --------------------------------- The dual radar attenuation correction :py:class:`~pylawr.transform.attenuation.AttenuationCorrectionDual` estimates the attenuation based on the maximum apparent attenuation comparing reflectivities of attenuation-influenced frequency bands (X-band) and observations from less attenuated radar systems (C-band) :cite:`lengfeld2016`. The reflectivities have to be on the same grid. One approach is to interpolate the reflectivities on a joint coarse grid, estimate the attenuation and interpolate the attenuation on the fine grid of the attenuation-influenced frequency band. To estimate the attenuation of the attenuation-influenced frequency band (X-band) with the less attenuated radar system (C-band) the maximum apparent attenuation :math:`K_{\mathrm{max}}` (dB) is used: .. math:: K_{\mathrm{max}} &= 10\cdot{}log[z_{\mathrm{C}} / z_{\mathrm{X}}] \\ &= Z_{\mathrm{C}} - Z_{\mathrm{X}} The attenuation should increase with increasing distance in theory. To get an increasing attenuation some regression is applied on :math:`K_{\mathrm{max}}`, e.g. the isotonic regression. For further information, refer to :cite:`lengfeld2016`. Note that the correction is only applied where the attenuated reflectivity is available, otherwise it would be possible that a reflectivity is created due to e.g. different radar resolution or incorrect alignment. The application of the dual attenuation correction by low-level-api is shown below with the attenuated reflectivity ``refl_attenuated`` (e.g. X-band) and the robust reflectivity ``refl_robust`` (e.g. C-band), both are type of :any:`xarray.DataArray`. .. code-block:: python # get grids of reflectivity fields grid_attenuated = get_verified_grid(refl_attenuated) grid_robust = get_verified_grid(refl_robust) # define coarse grid for the calculation # calculation on pattern area with dwd range resolution nr_ranges = int(round(grid_attenuated.nr_ranges * grid_attenuated.range_res / grid_robust.range_res)) grid = PolarGrid(grid_attenuated.center, nr_ranges=nr_ranges, range_res=grid_robust.range_res) # remap data on coarse grid remap = NearestNeighbor(1) remap.fit(grid_robust, grid) remapped_robust = remap.remap(refl_robust) remap.fit(grid_attenuated, grid) remapped_attenuated = remap.remap(refl_attenuated) # estimate the attenuation atten_corr = AttenuationCorrectionDual() atten_corr.fit(remapped_attenuated, remapped_robust) # remap attenuation data on fine grid remap.fit(grid, grid_attenuated) attenuation = remap.remap(atten_corr.attenuation) # correct the attenuation refl_corrected = refl_attenuated + attenuation refl_corrected = refl_corrected.lawr.set_metadata(refl_attenuated) tag_array(refl_corrected, "attenuation-corr-dual-isotonic") refl_corrected = refl_corrected.lawr.set_grid_coordinates(grid_attenuated) .. autosummary:: pylawr.transform.attenuation.AttenuationCorrectionDual Functional API -------------- For functional-api usage, you have to distinguish between single and dual attenuation correction: * **Single radar attenuation correction**: We have two methods for each radar type - :py:func:`~pylawr.functions.transform.correct_attenuation_dwd` (C-band) and :py:func:`~pylawr.functions.transform.correct_attenuation_lawr` (X-band). Both functions only need the :any:`xarray.DataArray` of the radar reflectivity. * **Dual radar attenuation correction**: The function :py:func:`~pylawr.functions.transform.correct_attenuation_dual` applies the dual attenuation correction and requires two arrays of simultaneous measured reflectivities of X-band and C-band. The function :py:func:`~pylawr.functions.transform.correct_attenuation` applies the single or dual radar attenuation correction depending if the second radar data (C-Band) is available. .. autosummary:: pylawr.functions.transform.correct_attenuation_lawr pylawr.functions.transform.correct_attenuation_dwd pylawr.functions.transform.correct_attenuation_dual pylawr.functions.transform.correct_attenuation