## 4 Cloud Parameter Databases and Retrieval Methods
The solution of the inverse problem is another important aspect in these techniques that, in most of them, is addressed by searching in a large look-up table (LUT) for the value/parameter that best fits the radiancesobserved in the different spectral bands. The most widespread approach in the inversion procedure is based on the optimal estimation method (OEM) described by [74], in which attempts are made to maximize the probability of the retrieved state, conditional on the value of the measurements and any a priori knowledge. This is an iterative procedure in which convergence is sought by varying the first guess at each interaction [128]. Statistical techniques such as NN, deep learning (DL), and CNN have been widely applied to retrieve cloud parameters from satellite measurements [99; 118; 129; 130], proving, in some cases, to be an excellent alternative to variational retrieval, which is generally more expensive from a computational point of view. While neural networks are well suited to investigating the full nonlinearity of measurements, it is worth remembering that the NN itself is a statistical model. This makes it susceptible to similar problems associated with retrievals based on linear statistics. Estimating the error associated with network output is a rather complicated task, which is why physical retrieval is typically preferred, since it allows one to easily estimate the error by means of the covariance associated with the output [74]. Regarding the assessment of errors associated with the output of an NN, these are typically estimated on the basis of the total root mean square error (RMSE) evaluated on the training dataset. However, although reasonable in a linear case, this approach is not entirely satisfactory, as it does not allow for evaluating the error bars for the single output. As a result, the performance of the algorithm is not represented correctly if the performance is expected to degrade over a given range of input variables. Potential synergies between two or more datasets from independent observations of the same target offer important implications in the field of remote atmospheric sounding. For this reason, more and more attention is being paid to the study of optimized or innovative methods to combine two or more measured datasets. For example, a synergistic approach can be developed by applying an appropriate retrieval scheme that involves feeding multi-wavelength observations into a single input and then performing a simultaneous inversion of all observations, or via an a posteriori combination of stand-alone retrieval products from individual measurements. Ref. [131] compared these two strategies for data fusion in the case of multi-wavelength remote sensing observations and demonstrated the better performance of the synergistic inversion scheme. Applications for retrieving atmospheric profiles from IASI, MHS on MetOp-A, and AMSU-A are shown. The cloud masking problem has been addressed with several approaches, such as naive Bayes in PATMOS-x, threshold test sequences in MODIS C6 or some dynamic thresholding in CLARA. Cloud phase retrieval has also been addressed in the literature with several techniques. For example, it is determined as a function of a combined test between different channels and the cloud-top temperature in CLARA, whereas [132] describe a threshold algorithm in PATMOS-x. Refs. [133; 134] use a combination of four CTT-based tests, three infrared channels, 1.38 \(\upmu\)m, and cloud-effective data in MODIS C6. The cloud-effective data considered in [133; 134] include the cloud-effective radius, the effective temperature and the effective cloud amount defined as cloud fraction multiplied by cloud emissivity. The method developed by [40], however, is usually used to calculate the cloud-effective radius and cloud optical thickness. Furthermore, many retrieval algorithms have been evaluated/validated in several studies. Ref. [135] estimated the deviation between the collocated MYD06 product and the MODIS-based PATMOS-x microphysical retrievals.