## 2 Materials and Methods
### Introduction of Data Processing Methods  
#### 2.2.1 Forwards and Inversion Algorithm  
The atmospheric temperature and humidity profile is the basic physical quantity to describe the thermodynamic and dynamic processes of the atmosphere. The atmospheric  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Date**} & \multirow{2}{*}{**Type**} & \multicolumn{2}{c}{**Precipitation**} \\ \cline{4-5}  & & & **Start Time** & **Duration** \\ \hline  
anuary 2020 & Clear day & / & / \\ \hline \hline \end{tabular}
\end{table}
Table 1: Schedule of field experiments of meteorological observations.  
detection of MWR can be divided into two stages, namely, forwards modeling and inversion (Figure 2). The forwards process refers to calculating the radiant brightness temperature through known historical sounding data, including ground water vapour pressure, atmospheric pressure and dew point temperature and atmospheric pressure at different altitudes. In the forwards stage, historical radiosonde observations should be interpolated into 58 high-level layers. Subsequently, according to the atmospheric microwave absorption characteristics, the atmospheric absorption coefficients at different heights can be obtained. Finally, a radiative transfer model is used to calculate the brightness temperature of each layer of atmospheric radiation to the surface at 35 sampling frequencies [26]. In this study, the radiative transfer model was solved using MonoRTM (Atmospheric and Environmental Research, Inc., Lexington, KY, USA), and descending BT can be expressed as follows [27; 28].  
\[T_{\theta,f}=T_{\infty}\cdot\tau(z_{0},\infty)+\int\limits_{z_{0}}^{\infty}K_{a }(z)T(z)\tau(z_{0},z)\sec(\theta)\;\mathrm{d}z \tag{1}\]  
\[\tau(z_{0},z)=\exp\left[-\int_{z_{0}}^{z}K_{a}(z)\sec\theta\;\mathrm{d}z\right] \tag{2}\]  
where \(T_{\theta f}\) denotes the radiation brightness temperature received by the microwave radiometer, \(\tau(z_{0},\infty)\) and \(\tau(z_{0},z)\) denote the atmospheric transmittance from the ground-based MWR antenna \(z_{0}\) to the universe and that from \(z_{0}\) to height \(z\). \(T_{\infty}\) denotes the cosmic background radiation temperature and can be taken as 3 K. \(K_{a}\) (z) denotes the volumetric absorption coefficient. \(\theta\) denotes the zenith angle of MWR.  
For the inversion algorithm, the information obtained by ground-based MWR is the radiation energy reaching the ground through layer-by-layer atmospheric buffing, absorption, reflection, and scattering. The relationship between the MWR-obtained radiation energy and atmospheric parameters can be constructed by statistical regression and neural network algorithms. The essence of artificial neural network calculation theory is the nonlinear statistical regression between a set of prediction indices. Some scholars have shown that the neural network algorithm has good performance in solving the nonlinear relationship be  
Figure 2: Flow chart of remote sensing atmospheric detection by MWR.  
tween atmospheric temperature, humidity, and atmospheric liquid water and water vapour content. It has a fast operation speed and a higher inversion accuracy than the statistical regression algorithm. Thus, a neural network (NN) is trained and developed to construct the nonlinear relationship between atmospheric parameters and the obtained brightness temperature (BT) [29; 30]. In this study, atmospheric vertical structures such as temperature, humidity, water density and liquid water content were derived through a built-in back-propagation (BP) neural network-based model. The historical radiosonde observations for NN training were obtained from Darlag, Qinghai Meteorological Administration (2011-2018) [31]. Detailed information can be found in the work of [PERSON] et al. [31].