## 2 Data and Method
### Methods
#### 2.3.4 Rain Area Delineation Method Based on PNN  
With the ground observations of the rain gauge network over the Yangtze River Basin, the PNN-based rain area delineation method was established according to the following steps:  
(1) The multi-channel TBs stored in TRMM 1B11 datasets were extracted and pre-processed. First, the multi-channel TBs at the nine channels (including the vertical and horizontal polarization at 10.7, 19.4, 37.0 and 85.5 GHz, and the vertical polarization at 21.3 GHz), as well as the geo-locations of each pixel were extracted using the \"hdftool\" of the MATLAB 2009a software, generating a dataset composed of the latitude, longitude and the TBs at the nine channels of each pixel. Then, this dataset was resampled to 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\) spatial resolution using the nearest neighboring method provide by ArcGIS software. (2) Three parameters, which have the potential to distinguish the rainfall areas from underlying surface, were derived from the resampled TBs. The first parameter is the polarization-corrected temperature (PCT) at 85 GHz (termed PCT\({}_{85}\)). PCT was proposed by [PERSON] [19] to delineate the rain areas based on the scattering effect of raindrops on the high-frequency microwave radiation, as well as the difference of the microwave polarization between the land surface and rain areas. High values of PCT usually indicate intense raindrops in the clouds and a high probability of raining. [PERSON] [33] investigated the relationship between the occurrence of rain and the PCT at different frequencies, and the results indicated that the PCT at 85 GHz was sensitive to light precipitation and more suitable for the delineation of the rain areas than other channels. PCT\({}_{85}\) can be calculated using Equation (4):  
\[\mathit{PCT}_{85}=\mathit{TB}_{85^{\prime}}+\mu^{*}(\mathit{TB}_{85^{\prime}} -\mathit{TB}_{85^{\prime}H}) \tag{4}\]  
In this equation, \(\mathit{TB}_{85^{\prime}H}\) is the horizontally polarized brightness temperature at 85 GHz and \(\upmu\) is a constant value (0.818), according to [PERSON] _et al._[34]. The second one is the difference of TBs at high frequency and low frequency (termed TD). [PERSON], [PERSON], [PERSON] and [PERSON] [25] pointed out that the TBs of land surface (except snow, desert) at high frequency is higher or similar in comparison with those at low frequency; therefore, the TD tends to be  
Figure 2: The structure of the probabilistic neural network. positive over no rain areas. However, because of the serious scattering effect of the raindrops on high-frequency microwave radiation, the TBs at high frequency showed a substantial decrease, leading to negative TD over rain areas. Therefore, the TD is a promising indicator of rain areas. In this study, the vertically polarized TBs at 37 GHz (high frequency) and 19 GHz (high frequency) were used to calculate TD according to the research of [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [22]. The third variable is the sum of TBs at 37 and 19 GHz (termed TS). Because the emissivity of water is much lower than land surface, the water body usually shows low TBs, which is similar to rain areas. As addressed by [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [22], the sum of TBs at 37 and 19 GHz (TS) was an effective indicator to identify the water body, which usually showed a much lower value of TS than other land surface and rain areas. (3) The three parameters calculated in Step (2) were collocated with the ground observations measured by the rain gauges. For the pixel \(i\) (with a spatial resolution of \(0.1^{\circ}\times 0.1^{\circ}\)), the rain gauges located inside pixel \(i\) were first selected, and then, the mean value of the selected rain gauge observations was calculated as the true precipitation for this pixel. Pixels containing at least one rain gauge were selected to establish and validate the PNN-based rain area delineation method.