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This study applied the community NoahMP options (Niu et al., 2011) for soil moisture simulation. NoahMP was designed to facilitate climate predictions with physicalbased ensembles, and developed with substantial upgrades from the Noah LSM to better represent several parameters including surfacelayer radiation balances, snow depth, soil moisture and heat fluxes, leaf area–rainfall interaction, vegetation and canopy temperature distinction, soil column and drainage of soil, and runoff. Multiple parameterization options are available in NoahMP for key land–atmosphere interaction processes, such as snow, dynamic vegetation and surface water infiltration, and runoff. To better predict the climate, NoahMP is capable of coupling the NCEP’s Global Forecasting System and Climate Forecasting System. NoahMP contains four soil layers with thicknesses of 10, 30, 60, and 100 cm. In this paper, the default parameterization option of NoahMP (Table 1) was used to simulate soil moisture.
Parameterization option Physical configuration Vegetation model option: 4 Use table leaf area index (LAI); use maximum vegetation fraction Canopy stomatal resistance option: 1 BallBerry Soil moisture factor for stomatal resistance option: 1 Noah (soil moisture) Runoff and groundwater option: 1 TOPMODEL with groundwater (Niu et al., 2007) Surface layer drag coefficient option: 2 Original Noah (Chen97) Supercooled liquid water option: 1 No iteration (Niu and Yang, 2006) Frozen soil permeability option: 1 Linear effects, more permeable (Niu and Yang, 2006) Radiation transfer option: 1 Modified twostream Snow surface albedo option: 2 CLASS Rainfall and snowfall option: 1 Jordan (1991) Lower boundary of soil temperature option: 1 Zero heat flux from bottom Snow and soil temperature time scheme: 1 Semiimplicit Table 1. The NoahMP parameterization options used in this study
To obtain a reasonable initial condition, every land model requires a spinup period to reach the specific equilibrium state. We used the CLDAS atmospheric forcing described in Section 2.2 to drive a 20yr (1998–2018) spinup run with NoahMP, and the values of the last time were taken as the initial conditions on 1 January 1998. The produced soil moisture simulations were used as the background states for the following insitu soil moisture fusion experiments.

According to the EnOI scheme proposed by Evensen (2003), the analysis (
${{ X}^a}$ ) can be given as below:$$ { X}^{\rm a}={ X}^{\rm b}+{ K}\left({ Y}{ H} { X}^{\rm b}\right), $$ (1) where
${ X}^{\rm b} \in \mathbb{R}^{{N}_{m}}$ is the model forecast state,${ X}^{\rm a} \in \mathbb{R}^{{N}_{m}}$ is the analysis, N_{m} is the dimension of the model state vector,${ Y} \in \mathbb{R}^{{N}_{y}}$ is the observation vector, N_{y} is the number of observations, K is the gain matrix, and H is the observation operator. The gain matrix K is calculated by$$ { K}=\alpha({ {\rho}} \circ { B}) { H}^{\mathrm{T}}\left[\alpha { H}({ {\rho}} \circ { B}) { H}^{\mathrm{T}}+{ R}\right]^{1}, $$ (2) where
${ B} \in \mathbb{R}^{{N}_{m} \times {N}_{m}}$ is the ensembleestimated background error covariance matrix; R is the observation error covariance matrix; the localized ensembleestimated background error covariance matrix$\,{ {\rho}} \circ { B}$ is the Schür product of matrices ρ and B, which is a matrix whose (i, j) entries are given by$\, \rho_{i, j} \cdot {B}_{i, j}$ ; and$\alpha \in(0,1]$ is the parameter used to tune the different weights on the ensemble versus observations. The ensembleestimated background error covariance is estimated from the equation$$ { B}=\frac{{ A}^{\prime} { A}^{\prime {\mathrm{T}}}}{{N}1}, $$ (3) where
${ A}^{\prime}=\left[A^{\prime 1}, A^{\prime 2}, \ldots, A^{\prime N}\right]$ , N is the number of ensemble samples, and the kth element of A' is calculated by$$ A^{\prime k}=\left(X^{k}\frac{1}{N1} \sum\nolimits_{i=1}^{N} X^{i}\right). $$ (4) In the EnOI scheme, a relatively stationary ensemble of model state samples can be taken from a longterm ensemble of model perturbations (anomalies) generated from a longterm model run (Evensen, 2003). Without the need for an ensemble forecast, the EnOI scheme can typically save N times the computational cost than the EnKF. In fact, many previous studies have employed similar historical ensemble methods to simplify the ensemble generation procedure in the assimilation. For example, Pan et al. (2009) used downscaled forcing ensemble forecasts from the NOAA/NCEP Climate Forecast System (CFS) as the input forcing ensembles in their hydrological assimilation system. Pan and Wood (2009) proposed a patternbased sampling approach in which random samples were drawn from a historical rainfall database according to the pattern of the satellite rainfall, and Pan and Wood (2010) directly used the rainfall data from the Tropical Rainfall Measuring Mission (TRMM) satellite products as the rainfall ensembles to force their assimilation experiments. The selection of ensemble samples in this study is described in Section 4.2.
Another critical question in ensemblebased DA is the localization technique, which is a widely used solution to reduce sampling error, especially when the ensemble size is small (Hamill et al., 2001; Oke et al., 2007). We used the following fifthorder piecewise rational function (Gaspari and Cohn, 1999) to construct the localization matrix ρ:
$$ \rho (i, j)=C_{\rm o}\left({d_{i, j}} / d\right), $$ (5) where
$C_{\rm o}$ is defined as$$\begin{aligned} &C_{\rm o}(I)= \\ &\left\{\begin{split} &\frac{1}{4} I^{5}+\frac{1}{2} I^{4}+\frac{5}{8} I^{3}\frac{5}{3} I^{2}+1, \quad\quad\quad\quad\quad\;\; 0 \leqslant I \leqslant 1, \\ &\frac{1}{12} I^{5}\frac{1}{2} I^{4}+\frac{5}{8} I^{3}+\frac{5}{3} I^{2}5 I+4\frac{2}{3} I^{1}, \quad1 < I \leqslant 2, \\ &0, \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\;\quad 2 < I, \end{split}\right.\end{aligned} $$ (6) where
$I={d_{i, j}} / d$ , in which d is the localization length scale and${d_{i, j}}$ is the horizontal spatial distance between the ith and jth grid points. The localization length scale d indicates the significance range of a measurement. 
The evaluation criteria used in this study were the bias (Bias), rootmeansquare error (RMSE), and correlation coefficient (Corr), which are calculated as follows:
$$ {\rm Bias}=\frac{1}{N1}\sum _{i=1}^{N}({M}_{i}{O}_{i}), $$ (7) $$ {\rm RMSE}=\sqrt{\frac{\sum _{i=1}^{N}{({M}_{i}{O}_{i})}^{2}}{N1}}, $$ (8) $$ {\rm Corr}=\frac{\sum _{i=1}^{N}({M}_{i}\bar{M})({O}_{i}\bar{O})}{\sqrt{\sum _{i=1}^{N}{({M}_{i}\bar{M})}^{2}}\sqrt{\sum _{i=1}^{N}{({O}_{i}\bar{O})}^{2}}}, $$ (9) $$ \bar{O}=\frac{1}{N1}\sum _{i=1}^{N}{O}_{i}, $$ (10) $$ \bar{M}=\frac{1}{N1}\sum _{i=1}^{N}{M}_{i}, $$ (11) where
$ M $ is the simulated (merged) soil moisture to be evaluated,$ O $ represents the insitu soil moisture observations used for the evaluation,$ N $ is the number of observations,$ {O}_{i} $ is the ith observation,$ {M}_{i} $ is the simulated (merged) soil moisture collocated with the ith observation,$\bar {O}$ is the average value of all observations used for the evaluation, and$ \bar{M} $ is the average value of simulated (merged) soil moisture at all the collocated locations.