## 4 Challenges in Rainfall Estimation by CMLs
### Baseline Estimates  
The estimation of the baseline is of great importance in the operational flow of rainfall inversion by CMLs as it determines whether non-rain-induced attenuation can be accurately eliminated. As for baseline estimation approaches that require dry and wet period classification, though several methods based on different principles have been proposed for the classification of dry and wet periods, there remain difficulties in accurately determining whether rainfall exists along the path of CMLs at the current time. Since we only acquired RSL data (and in some cases TSL as well), it is difficult to determine what factors are responsible for the attenuation variations produced in the paths of the CMLs. Scintillation effects and multipath effects due to, for example, changes in the refractive index of air, may also lead to anomalous fluctuations in signal attenuation during dry periods, which may be incorrectly judged as wet periods. In addition, water films that accumulate on the antenna due to dew or after rainfall may produce false positives. Coarse RSL quantization also limits the ability of CMLs to detect light rain, especially for low-frequency short CMLs. These undoubtedly pose a negative impact on classification accuracy.  
Moreover, for conventional empirical threshold-based classification methods, a priori information is required to make a comprehensive calibration of thresholds in order to obtain comparatively high dry and wet period detection capabilities simultaneously. Machine learning methods typically have a higher classification accuracy but require large, labeled datasets for training. However, on the one hand, it is not always the case that dedicated rain sensors exist in the vicinity of CMLs to provide rainfall data; on the other hand, due to the inhomogeneity of the rainfall distribution, the dataset is usually unbalanced (much fewer data in the wet period than in the dry period), which not only implies that it takes more time to collect enough wet period data, but also leads to the requirement of balancing the training set using undersampling or oversampling methods, which may contribute to overfitting or poorer performance of the model.  
After dry and wet period classifications, the baseline will be determined by the dry period attenuation over a period of time around the rainfall event. In contrast, methods to estimate the baseline without dry and wet period information usually dynamically update the statistical values of attenuation in past time periods as the baseline. This may be a  
Figure 5: Minimum detectable rain rate of CMLs at different quantization resolutions, path lengths and frequencies. Notably, the \(\gamma\)-\(R\) relation is referenced from the ITU-R model and the minimum detectable rain rate for most short CMLs below 10 GHz exceeds the upper limit of the color bar.  
reasonable reference as the historical information on attenuation is able to reflect the classic state of CMLs working in the dry period. The problem is the fact that the baseline for the wet period will not remain constant but will vary with some regularity, and could possibly be quite different from the past dry period attenuation due to phenomena caused by rainfall such as increased water vapor, decreased temperatures, changes in the device conditions, etc. However, subject to the coarse sampling and quantization resolution of the RSL, most researchers have to ignore, to varying degrees, changes in the baseline during wet periods.