Climatology of estimated liquid water content and scaling factor for warm clouds using radar–microwave radiometer synergy
Authors: Vishwakarma Pragya , Delanoë Julien , Jorquera Susana , Martinet Pauline , Burnet Frederic , Bell Alistair , Dupont Jean-Charles 
Published: March 2023

Abstract. Cloud radars are capable of providing continuous high-resolution observations of clouds and now offer new capabilities within fog layers thanks to the development of frequency-modulated continuous-wave 95 GHz cloud radars. These observations are related to the microphysical properties of clouds. Power law relations in the form of Z=a⋅LWCb are generally used to estimate liquid water content (LWC) profiles. The constants a and b from the power law relation vary with the cloud type and cloud characteristics. Due to the variety of such parameterizations, selecting the most appropriate Z–LWC relation for a continuous cloud system is complicated. Additional information such as liquid water path (LWP) from a co-located microwave radiometer (MWR) is used to scale the LWC of the cloud profile. An algorithm for estimating the LWC of fog and warm clouds using 95 GHz cloud radar–microwave radiometer synergy in a variational framework is presented. This paper also aims to propose an algorithm configuration that retrieves the LWC of clouds and fog using radar reflectivity and a climatology of the power law parameters. To do so, variations in the scaling factor ln a (the logarithm of pre-factor a from power law relation) when MWR observations are available are allowed in each cloud profile to build a climatology of the scaling factor ln a that can be used when MWR observations are not available. The algorithm also accounts for attenuation due to cloud droplets.
In this algorithm formulation, the measure of uncertainty in the observations, the forward model, and the a priori information of desired variables acts as weights in the retrieved quantities.
These uncertainties in the retrieval are analyzed in the sensitivity analysis of the algorithm. The retrieval algorithm is first tested on a synthetic profile for different perturbations in sensitivity parameters. The sensitivity study has shown that this method is susceptible to LWP information because LWP is point information for the whole cloud column.
By further investigating the sensitivity analysis of various biases in LWP information, it was found that it is beneficial to incorporate LWP, even if it is biased, rather than not assimilate any LWP. The algorithm is then implemented in various cloud and fog cases at the SIRTA observatory to estimate LWC and the scaling factor. The scaling factor (ln a) changes for each cloud profile, and the range of ln a is consistent with suggested values in the literature.
The validation of such an algorithm is challenging, as we need reference measurements of LWC co-located with the retrieved values. During the SOFOG-3D campaign (southwest of France, October 2019 to March 2020), in situ measurements of LWC were collected in the vicinity of a cloud radar and a microwave radiometer, allowing comparison of retrieved and measured LWC. The comparison demonstrated that the cloud–fog heterogeneity played a key role in the assessment. The proposed synergistic retrieval algorithm is applied to 39 cloud and fog cases at SIRTA, and the behavior of the scaling factor is studied. This statistical analysis of scaling is carried out to develop a radar-only retrieval method. The climatology revealed that the scaling factor can be linked to the maximum reflectivity of the profile. From climatology, the statistical relations for the scaling factor are proposed for fog and clouds. Thanks to the variational framework, a stand-alone radar version of the algorithm is adapted from the synergistic retrieval algorithm, which incorporates the climatology of the scaling factor as a priori information to estimate the LWC of warm clouds. This method allows the LWC estimation using only radar reflectivity and climatology of the scaling factor.