## 2 Dataset, Models and Method
### Models  
CALDAS (Figure 1) has three subsystems: (1) a land-atmosphere coupled mesoscale model (ARPS-SiB2); (2) a Land Data Assimilation System (LDAS); and (3) a Cloud Microphysics Data Assimilation System (CMDAS). Here, the combinations of the ARPS-SiB2-LDAS and ARPS-SiB2-LDAS-CMDAS models are named LDAS-A and CALDAS, respectively. All three models (_i.e._, ARPS-SiB2, LDAS-A, and CALDAS) shared the same atmosphere-land couple model (_i.e._, ARPS-SiB2) and same settings of physics and parameterizations. ARPS-SiB2 model simulation was a simple dynamical downscaling of GCM analysis data. The only difference between ARPS-SiB2 and LDAS-A simulations is that LDAS-A used additional satellite observed soil moisture contents compared to ARPS-SiB2. Similarly, the only difference between LDAS-A and CALDAS simulations is that CALDAS used additional satellite observed cloud data. Detailed information and formulations on LDAS-A and CALDAS are given in [11,12], respectively; however, the following sections provide a brief explanation of their formulation. The Advanced Regional Prediction System (ARPS) is a comprehensive regional- to storm-scale prediction model, and its atmospheric prediction component is a three-dimensional nonhydrostatic compressible model [15]. The LDAS consists of the Simple Biosphere model version 2 (SiB2) [16], which functions as a model operator for LDAS as well as the land surface scheme for ARPS, together with a physics-based radiative transfer model as the observation operator, and an Ensemble Kalman Filter (EnKF) [17] as the assimilation algorithm. A land surface radiative transfer algorithm has been developed based on the large contrast between the dielectric constants of dry soil (\(\sim\)4) and water (\(\sim\)80) for lower microwave frequencies (_i.e._, 1-15 GHz). By neglecting atmospheric and rainfall effects and by assuming that the reflection at the surface is much less than the radiation from the surface and vegetation layers at lower frequencies, the brightness temperature \(T_{b}\) at the satellite level is given by [18]:  
\[T_{b}=(1-R_{p})*T_{s}*\exp(-\tau_{c})+(1-\omega_{c})*T_{c}*(1-\exp(-\tau_{c})) \tag{1}\]  
here, \(R_{p}\) is the surface reflectivity and \(T_{s}\) is the surface physical temperature (K), \(\omega_{c}\) is the single-scattering albedo of the canopy, \(\tau_{c}\) is the vegetation optical thickness and \(T_{c}\) is the canopy temperature (K). In the field of hydrology, the EnKF has been applied to soil moisture estimation and it has been found to perform well against the variational assimilation method [19, 20]. An overview of the EnKF for soil moisture assimilation is given below. Consider X=\([w_{1},\ w_{2},\ w_{3}]^{T}\) as a state variable and the first estimate, for which \(w_{1}\), \(w_{2}\) and \(w_{3}\) are the soil moisture contents of the surface, root and deep soil layers, respectively. The first estimate is used to create an ensemble of size (\(N\)) by adding pseudo-random noise with known statistics. By dropping the time notation, each member of state variable \(X_{i}\) is given by  
\[X_{i}= \bar{X}+e_{i}\qquad e_{i}(i=1,2....N)\sim N(0,P) \tag{2}\]  
Figure 1: Schematic diagram of the Coupled Atmosphere and Land Data Assimilation System (CALDAS). where \(e_{i}\) is the random error vector of each member obtained from a multivariate Gaussian distribution with zero mean and error covariance matrix P, and \(\bar{X}\) is the expectation of the first estimate X. In the forecast step, the forecast state member \(X_{i}^{f}\) is determined from the nearest analysis state member \(X_{i}^{a}\) according to  
\[X_{i}^{f}= M(X_{i}^{a})+u_{i}\qquad u_{i}\sim N(0,Q) \tag{3}\]  
where M is the model operator and \(u_{i}\) is the model error vector of each member, obtained from a multivariate Gaussian distribution with zero mean and error covariance matrix Q.