# Multi-Sensor Precipitation Estimation from Space: Data Sources, Methods and Validation
## 3 Physical Basis of Multi-Sensor Precipitation Estimation
### PMW-Based Precipitation Estimation  
PMW observations are physically linked to precipitation. PMW sensors capture the upwelling MW radiation emitted from the Earth's surface, which is then attenuated by the atmosphere. Precipitation particles are the main source of attenuation. The emission of radiation from precipitation particles results in an increase in the signal, while the scattering due to hydrometeors reduces the radiation. The type and size of the hydrometeors detected by PMW sensors depend on the frequency of the upwelling radiation. Above 85 GHz, ice scattering dominates. Below about 22 GHz, absorption is the primary mechanism affecting the transfer of MW radiation. Between 19.3 and 85.5 GHz, the common PMW sensor channel range (such as 19.35, 22.235, 37.0, and 85.5 GHz), radiation interacts with the main types of hydrometeors, water particles or droplets (liquid or frozen). Over oceans, the background microwave signals remain constantly low (emissivity, \(\varepsilon\), \(\sim\)0.4-0.5), and the presence of precipitation (\(\varepsilon\) = \(\sim\)0.8) enhances the microwave signals. The enhanced signals can be decomposed to retrieve precipitation at low-frequency bands (\(<\)20 GHz). Land surface emissivities, however, are heterogenous in space and comparable in magnitude to precipitation (\(\varepsilon\) = 0.7-0.9), challenging the accurate retrieval of precipitation. Additionally, the presence of ice particles causes a reduction in microwave signals at frequencies \(>\)35 GHz as a result of scattering effects [(77; 78)]. In addition, high-frequency PMW observations (about \(>\) 183 GHz) can provide the ability to retrieve precipitation over regions such as coastlines and areas with snow/ice. Thus, PWV-based precipitation estimation involves two distinct processes: emission from rain droplets and scattering by precipitating ice particles. Several PMW-based approaches have been proposed considering the two processes. [PERSON] [(71)] developed a statistical-physical algorithm that considers the scattering effects at  
Figure 2: GPM constellation. The left figure was obtained from [[https://gpm.nasa.gov/image-gallery/gpm](https://gpm.nasa.gov/image-gallery/gpm)]([https://gpm.nasa.gov/image-gallery/gpm](https://gpm.nasa.gov/image-gallery/gpm)) (accessed on 1 December 2024). 85 GHz over land, which was additionally combined with the emissions at 19/37- GHz over oceans. This algorithm was mainly applied in the Special Sensor Microwave/Imager (SSM/I) and Special Sensor Microwave Imager/Sounder (SSMIS). [PERSON] et al. (2019); [PERSON] et al. (2020) proposed the GPROF algorithm, based on Bayesian theory. This Bayesian approach was used to create an a priori database of observed cloud and the hydrometeor profiles. GPROF has undergone significant evolution and enhancement since [PERSON] et al. 's work [PERSON] et al. (2019); [PERSON] et al. (2020); [PERSON] et al. (2020); K  
data using the cumulative histogram matching method. The combined passive microwave-infrared (PMIR) algorithm, as described by [PERSON] et al. (2017) and [PERSON] (2012), utilizes a cumulative histogram matching approach to establish an IR Tb-PMW-rain-rate relationship, enabling the provision of PMW-calibrated IR estimates of precipitation. This algorithm operates under the assumption that colder clouds are associated with higher rainfall amounts compared to warmer clouds, indicating a monotonically increasing precipitation rate with decreasing Tb. Additionally, it assumes that the IR Tb exhibits a similar cumulative frequency as the PMW precipitation estimate at specific spatial and temporal scales. The equations expressing the PMM are as follows.