# Multi-Sensor Precipitation Estimation from Space: Data Sources, Methods and Validation
## 3 Physical Basis of Multi-Sensor Precipitation Estimation
### Adjustment-Ratio-Based Method  
A technique based on the adjustment ratio (AR) was proposed to calibrate or adjust the rain rates inferred from GEO IR data using PMW estimates [114]. It is assumed that PMW-based estimates provide accurate instantaneous precipitation but have limited spatial and temporal sampling, while IR estimates offer extensive spatial coverage and sampling frequencies but contain significant systematic errors. The objective is therefore to generate rainfall estimates superior to either of these individual approaches. The AR can be calculated based on coincident PMW and IR data by employing the following equations:  
\[P_{\text{PMW}} =f_{4}(Tb_{\text{PMW}}) \tag{7}\] \[P_{\text{IR}} =f_{5}(Tb_{\text{IR}})\] (8) \[\text{AR} =\frac{P_{\text{PMW}}}{P_{\text{IR}}} \tag{9}\]  
where \(Tb_{\text{PMW}}\) represents a cloud parameter derived from PMW (e.g., the Scattering Index in [PERSON]'s work); \(P_{\text{IR}}\) represents the precipitation rate estimated based on the coincident IR; \(f_{4}(Tb_{\text{PMW}})\) represents the relationship between \(P_{\text{PMW}}\) and \(Tb_{\text{PMW}}\) (e.g., the Goddard Scattering Algorithm); and \(f_{5}(Tb_{\text{IR}})\) represents the relationship between \(P_{\text{IR}}\) and \(Tb_{\text{IR}}\) (e.g., GPI). It is thus necessary to ensure that PMW and IR are constructed from nearly coincident data. In addition, it is necessary to use a moving average (e.g., 5 \(\times\) 5 grid box) before calculating the ARs to produce a smooth field of coefficients. Finally, the spatial array of ARs is then multiplied by the original IR estimates to produce the calibrated estimates using a simple assigned threshold technique (235 K).  
The AR-based method is commonly employed for obtaining monthly precipitation estimates, such as those acquired using the adjusted GPI (AGPI) algorithm [115]. AGPI utilizes matched PMW and GEO IR datasets to generate an AR map that can subsequently be applied to IR precipitation estimate fields in order to produce adjusted estimations. All the available IR data can then be utilized for obtaining precipitation estimates, while a secondary IR-based mean of precipitation can be constructed solely using the spatiotemporally corresponding IR data during PMW overpasses. The AGPI algorithm preserves the typically low bias of PMW estimates along with ensuring smoothness and temporal coverage from GEO IR data. The AGPI was successfully employed to construct global monthly precipitation analyses for the Global Precipitation Climatology Project (GPCP) [116; 117; 118; 119]. Additionally, during the production process, small fractions were utilized to generate pentad and daily precipitation analyses. Subsequently, [PERSON] and [PERSON] [120] as well as [PERSON] et al. [121] developed more sophisticated approaches based on AGPI, termed by the latter as the Universally AGPI (UAGPI) method, wherein the optimization of the IR threshold \(f_{2}(Tb_{\text{IR}})\) is incorporated. Furthermore, the AR method can be applied to adjust satellite precipitation estimates using gauged data (e.g., [25; 122]).