Variational Assimilation of Satellite Cloud Water/Ice Path and Microphysics Scheme Sensitivity to the Assimilation of a Rainfall Case

Cloudy regions are often sensitive to important weather systems. At the same time, the development and distribution of cloud exerts considerable impacts on weather systems passing through these regions. Observational cloud information over such cloudy regions is directly linked with the analysis and simulation of weather systems (Errico et al., 2007).

Several current cloud analysis systems create an initial state, including hydrometeors, for NWP models, to reduce the uncertainty in cloud information. The main operational cloud analysis systems include, among others, the Local Analysis and Prediction System (Albers et al., 1997), the ARPS three-dimensional variational (3DVAR) or ARPS data analysis system (Hu et al., 2006a, 2006b), and the NOAA's Rapid Refresh and Rapid Update Cycling model (Benjamin et al., 2004). Such cloud analysis schemes are computationally fast and highly valuable for nowcasting systems.

However, these systems adopt traditional objective analytic methods involving the point-to-point adjustment of cloud water and cloud ice based on cloud information. These methods cannot take advantage of physical balance constraints. More studies are required to retrieve hydrometeors in balance with the model prognostic variables, using more advanced assimilation measures such as 3DVAR or diabatic digital filtering (Benjamin et al., 2004; Auligné et al., 2011).

Cloud information is mainly obtained by cloud radar, satellite observations and some surface observations. Previous studies (Sun and Crook, 2010; Auligné et al., 2011; Sun and Wang, 2013; Wang et al., 2013) have shown that the assimilation of radar observations can effectively improve the analysis fields and the numerical model forecast, particularly precipitation forecasts and the diagnostic analysis of associated cloud characteristics. However, regular radar is insensitive to non-precipitable clouds. In contrast, satellite remote sensing not only can detect precipitable clouds, but also are sensitive to them. With increasingly higher resolution cloud observations becoming available from satellite remote sensing (Jones et al., 2003; Minnis et al., 2012), the assimilation of satellite cloud observations has become a hot topic among researchers (Jones et al., 2003; McNally, 2009; Bauer et al., 2011; Pincus et al., 2011; Polkinghorne and Vukicevic, 2011; Migliorini, 2012; Okamoto et al., 2014).

Microphysics schemes in numerical models describe and simulate the mutual transformation and phase changes of various hydrometeor variables. These processes subsequently affect the environmental background through the feedback of sensible and latent heat fluxes and momentum transport. Thus, microphysics schemes are important for the simulation of cloud hydrometeors and the forecasting of environmental fields (Zhu et al., 2004; Zhu and Zhang, 2006; Rao et al., 2007; Bukovsky and Karoly, 2009). However, most previous studies have been based on simulations without initial cloud information (known as "cold start"), or from results that include model-simulated cloud information after a certain spin-up time (known as "hot start").

In the present study, the 3DVAR method is applied to assimilate cloud observations. Hydrometeor variables (cloud water and cloud ice mixing ratios) are added into the 3DVAR assimilation system as additional control variables. Hence, cloud information becomes available in the initial field for numerical simulations.

The structure of this paper is as follows: A brief introduction to the assimilation methodology, the modeling of the background error covariance of hydrometeors and the computational method for observational error variance are given in section 2. The experimental design is described in section 3, and the characteristics of the background error covariance for hydrometeors are discussed in section 4. In section 5, the distributions of cloud with and without cloud assimilation are compared and discussed. Diagnostic results with and without cloud assimilation are presented in section 6. The paper finishes with a summary and further discussion in section 7.

Hydrometeor variables (cloud water and cloud ice mixing ratios) are added into the WRF 3DVAR assimilation system as additional control variables (analysis variables); and to assimilate cloud observations, the following additional terms are added to the 3DVAR cost function (Chen et al., 2015): \begin{eqnarray} \label{eq1} J_{\rm ice}&=&\dfrac{1}{2}({q}_{\rm ice}-{q}_{\rm ice,b})^{\rm T}{B}_{\rm ice}^{-1}({q}_{\rm ice}-{q}_{\rm ice, b})+\nonumber\\ &&\frac{1}{2}[{H}_{\rm I}({q}_{\rm ice})-{I}_{\rm o}]^{\rm T}{R}_{\rm ice}^{-1}[{H}_{\rm I}({q}_{\rm ice})-{I}_{\rm o}] ,(1)\\ \label{eq2} J_{\rm cloud}&=&\frac{1}{2}({q}_{\rm cloud}-{q}_{\rm cloud,b})^{\rm T}{B}_{\rm cloud}^{-1}({q}_{\rm cloud}-{q}_{\rm cloud,b})+\nonumber\\ &&\frac{1}{2}[{H}_{\rm L}({q}_{\rm cloud})-{L}_{\rm o}]^{\rm T}{R}_{\rm cloud}^{-1}[{H}_{\rm L}({q}_{\rm cloud})-{L}_{\rm o}] ,\quad (2)\end{eqnarray} where q _ice and q _cloud represent the cloud ice and cloud water mixing ratios of the atmospheric state, respectively; B _ice and B _cloud are the background error covariances of the cloud ice and cloud water mixing ratios, respectively; I _o and L _o are the cloud ice water path (CIP) and cloud liquid water path (CLP) from the Global Geostationary Gridded Cloud Products (G3C) of NASA's Langley Cloud and Radiation Research Group (Minnis, 2007; Minnis et al., 2008); R _ice and R _cloud are the observation error variances of the CIP and CLP, respectively; and H _I and H _L are the observation operators of the CIP and CLP, respectively.

Similar to most operational NWP centers, the background error covariance matrix B of hydrometeors (q _ice and q _cloud) is also modeled through a control variable transform (CVT): \begin{equation} {\rm d}{x}={Uv} , (3)\end{equation} where, dx is the analysis increment, v is the control variables, \begin{equation} {U}={U}_{\rm p}{U}_{\rm v}{U}_{\rm h} , (4)\end{equation} are a series of transforms, and UU ^T=B. Control variable transform (U) consists of a sequence of three transforms, the horizontal transform (U _h), vertical transform (U _v) and physical transform (U _p).

U _h is a recursive filter transform for imposing the horizontal correlations; the desired length scale for the U _h transform is estimated for each of the analysis control variables. For a 2D variable, the input analysis control variable for U _h is the output of U _p. For 3D-variables, the input analysis control variables for U _h are the outputs of U _v; so, for 3D variables, there is eigenmode dependence (Chen et al., 2013). Note that, here, for all the analysis control variables, the length scale does not vary horizontally.

U _v is the application of vertical correlations through the EOF of analysis control variables. Eigendecomposition is carried out for the vertical error covariance matrix in order to obtain the eigenvectors and eigenvalues. These eigenvalues and eigenvectors form the basis for the U _v transform.

U _p changes the control variables to model state variables using the statistical balance relationship. The control variables (v) in the data assimilation system will then be: \begin{equation} {v}=({\psi},{\chi}_{\rm u},{T}_{\rm u},{p}_{\rm su},{\rm RH}_{\rm u},{q}_{\rm ice-u},{q}_{\rm cloud-u}) , (5)\end{equation} where ψ is the stream function, χ _u is the unbalanced velocity potential, T _u is the unbalanced temperature, p _su is the unbalanced surface pressure, RH _u is the unbalanced pseudo relative humidity, q _ice-u is the unbalanced ice mixing ratio, and q _cloud-u is the unbalanced cloud water mixing ratio. The unbalanced variables are defined as the difference between the full variables and the balanced variables. The balanced part of hydrometeors (q) can be described as \begin{eqnarray} \label{eq3} {q}(i,j,k)&=&\sum_{l=1}^{N_k}{a}_{{\psi},{q}}(i,j,k,l){\psi}(i,j,l)+\nonumber\\[-0.5mm] &&\sum_{l=1}^{N_k}{a}_{{\chi}_{\rm u},{q}}(i,j,k,l){\chi}_{\rm u} (i,j,l)+\\[-0.5mm] &&\sum_{l=1}^{N_k}{a}_{{T}_{\rm u},{q}}(i,j,k,l){T}_{\rm u}(i,j,l))+\nonumber (6)\end{eqnarray} \begin{eqnarray} &&\sum_{l=1}^{N_k}{a}_{{\rm RH}_u,{q}}(i,j,k,l){\rm RH}_u(i,j,l)+\nonumber\\ &&{a}_{{p}_{\rm {su}},{q}}(i,j,k){p}_{\rm {su}}(i,j) . (7)\end{eqnarray} Here, q denotes hydrometeors (q _ice and q _cloud); the indices i and j run over the horizontal dimensions of the geographical domain; k and l run over the N_k vertical sigma levels; and a represents the regression coefficients between the variables, which form the basis for the U _p transform.

The method to estimate the CIP and CLP observational error is that of (Desroziers et al., 2005). The observational error variance is the expectation of the observation minus the background, multiplied by the observation minus the analysis. First, the observation minus the background is estimated using observational departures from forecasts, which is the 6-h WRF cold forecast initiated from the GFS analysis. Second, using the observation minus the background to calculate the first guess of the observational error as the input to WRFDA (WRF model Data Assimilation system), the analyses are then obtained by assimilating cloud production into the 6-h WRF forecasts. Third, the observation minus the analysis is calculated. In this study, constants with values of 350 g m^-2 and 70 g m^-2 are used as the CIP and CLP observational errors. In addition, the values used here are close to those used by (Chen et al., 2015).

H _I and H _L, the observational operators of the CIP and CLP, are defined as \begin{eqnarray} \label{eq4} {H}_{\rm I}({q}_{\rm ice})&=&\frac{1}{g}\int_{p_{\rm cb}}^{p_{\rm ct}}{q}_{\rm ice}{\rm d}p ,(8)\\ \label{eq5} {H}_{\rm L}({q}_{\rm cloud})&=&\frac{1}{g}\int_{p_{\rm cb}}^{p_{\rm ct}}{q}_{\rm cloud}{\rm d}p , (9)\end{eqnarray} where g is gravitational acceleration, p _cb and p _ct are the observed cloud base pressure and cloud top pressure, respectively. The p _cb and p _ct, obtained from the G3C products (Minnis et al., 2008), are used to constrain the analysis increments inside the cloud regions.

The Yangtze River-Huaihe River valleys experienced a large-scale precipitation process from 0000 UTC 25 June to 1200 UTC 26 June 2014. As shown in Fig. 1a, the precipitation occurred over the area from southern Anhui Province to southern Jiangsu Province and Shanghai (denoted by the red box in Fig. 1a). The rain band was east-west oriented and the 24-h accumulated precipitation reached the level of a rainstorm (≥50 mm). The heaviest rainfall occurred between 0000 and 0600 UTC 26 June. Figure 1b shows the wind and divergence fields at 850 hPa, indicating clearly that this precipitation process was caused by a low-level shear line. A strong southwesterly low-level jet was located to the south of the shear line. As shown in Fig. 1c, there was sufficient water vapor along the low-level jet being brought into the region. A significant low-level convergence occurred to the front left of the jet axis, which was favorable for the development of heavy precipitation.

A 12-km/4-km two-way nested configuration is used in the experiments, with 41 levels in the vertical direction. The model top is at 50 hPa and the time step is 30 s. A Lambert map projection is used. Physical parameterization schemes include the Kain-Fritsch cumulus parameterization scheme, the RRTM longwave radiation scheme, the Dudhia shortwave radiation scheme, and the YSU (Yonsei University) boundary layer scheme. Note that the cumulus scheme is turned off in the inner domain. All other schemes are the same for the outer and inner domains. The initial and boundary conditions are derived from GFS analysis. The model is initialized at 1800 UTC 24 June 2014, with a 12-h spin-up time, using the LIN (Lin et al., 1983) microphysics scheme. Data assimilation is conducted at 0600 UTC 25 June 2014 when the spin-up ends, and the model output at this time is taken as the background for assimilation. The integration is then continued for the next 24 hours, and stops at 0600 UTC 26 June 2014. Two sets of experiments are performed (Table 1). In the control experiments (EXP_CON), only the WMO's Global Telecommunications System (GTS) observations are assimilated. In the cloud assimilation experiments (EXP_CWP), both the regular GTS and CLP/CIP retrieved from G3C satellite remote sensing are assimilated (Minnis et al., 2011). Note that the four experiments in EXP_CON/EXP_CWP, with different microphysics schemes, employ the same analysis field with/without cloud assimilation. Quality control of satellite cloud data is performed using the same approach as (Chen et al., 2015).

Figure 1.  The (a) 24-h accumulated precipitation from 0600 UTC 25 to 0600 UTC 26 June 2014 (units: mm), and the (b) wind (vectors; units: m s$^-1$) and divergence fields (color-shaded; units: 10$^-5$ s$^-1$) and (c) water vapor mixing ratio (units: g kg$^-1$) at 850 hPa at 0600 UTC 25 June 2014. Red box in (a) is the rainfall area which will be analyzed in section 6.

Figure 2.  (a) Vertical distribution of the variables and balance part contribution to $q_\rm cloud$. (b) Vertical distribution of the variables and balance part contribution to $q_\rm ice$. (c) First-mode vertical eigenvectors of $q_\rm cloud$ and $q_\rm ice$. (d) Length scales of all control variables.

Figure 3.  The (a-c) CLP, (d-f) CIP and (g-i) CLP plus CIP at 0600 UTC 25 June (units: g m$^-2$): (a, d, g) satellite observation; (b, e, h) analysis fields of EXP_CON; (c, f, i) analysis fields of EXP_CWP.

Microphysics schemes have important impacts on cloud and precipitation simulation. In order to investigate the influence of cloud hydrometeors in analysis fields with and without cloud assimilation, four mixed-phase microphysics schemes [LIN (Lin et al., 1983), SBU-YLIN (Lin and Colle, 2011), WDM6 (Lim and Hong, 2010), and WSM6 (Hong et al., 2006)] are selected for sensitivity experiments in this study. These mixed-phase microphysics schemes include descriptions of water-phase particles such as cloud water, rain water etc., and ice-phase particles such as cloud ice, snow, graupel etc.

In this study, the 12-h and 24-h forecasts (valid for the same time), with initial conditions from both 0000 and 1200 UTC, are generated for a period of one month (0000 UTC 19 June to 0000 UTC 18 July 2014) using the WRF model for the 12-km domain. The initial and boundary conditions are interpolated from the GFS analysis. Thus, in all, 60 perturbations (forecast differences) are used as an input into the NMC method (National Meteorology Center; also named the NCEP method) (Parrish and Derber, 1992) for generating the background error covariance.

As mentioned before, the background error covariance is modeled through a CVT. This means that the CVT operators represent the major characteristics of the background error covariance.

Figures 2a and b present the vertical distribution of the variables and balance part contribution to hydrometeors (q _ice and q _cloud). The contribution of other variables to the balanced part of the cloud water mixing ratio (q _cloud) is mainly located below the middle troposphere (10th level) (Fig. 2a). The contribution of other variables to the balanced part of the cloud ice mixing ratio (q _ice) mainly occurs from the 25th to the 36th level (∼450 hPa to 150 hPa). The contributions of the other variables to hydrometeors mainly come from the temperature and relative humidity, largely because the generation of cloud and precipitation is closely connected to temperature and water vapor. However, the contribution of the balanced part (black line) to hydrometeors is very small, possibly because the background error covariance is derived from the forecast error of one month using the NMC method. The NMC method may average the mesoscale and microscale features. Note that the contribution of other variables to hydrometeors is small in the background error covariance, so the correlation between hydrometeors and other variables is not taken into consideration in this study.

Figure 2c displays the first-mode eigenvectors of the vertical EOF transform of q _ice and q _cloud. The first-mode eigenvector stands for the main vertical characteristic of the background error. From Fig. 2c, it can be seen that the maximum error of q _cloud occurs around the 8th level (∼700 hPa), and the error of q _cloud decreases rapidly as height increases above the 10th level, which indicates that the correlation between the upper and lower levels is weak and propagation attenuation is very fast. It can also be seen that the vertical error of q _ice occurs from the 27th level to the 35th level, the maximum error is at the 31st level (250 hPa), and the error decreases quickly both below and above the 31st level. The reason is that q _ice cannot form in the lower troposphere because of the higher temperature. As a result, q _ice occurs in the upper levels, but in small quantities, on account of the lack of water vapor there. Figure 2c also shows that the background errors of q _ice are negative and the background errors of q _cloud are positive. This indicates that the model forecast of q _ice has a negative deviation and the model forecast of q _cloud a positive deviation.

Length scale is one of the major parameters from a recursive filter transform of U _h, which represents the scope of influence of observations in data assimilation. Length scales of q _ice and q _cloud are eigenmode dependent, and the length scales of the top eigenmodes stand for the main vertical characteristic of the background error. Figure 2d shows clearly that the length scales of q _ice and q _cloud are significantly smaller than the stream function and velocity potential, as well as temperature and relative humidity. The length scales of q _ice and q _cloud (top 10 modes) are lower than 30 km, and the length scales of temperature (top 10 modes) are near to 50 km. As a result, the scope of influence of cloud observation is much less than wind observation, as well as temperature and moisture observation, in data assimilation.

Figure 3 presents the CLP and CIP from G3C, from EXP_CON without cloud assimilation, and from EXP_CWP with cloud assimilation, at the analysis time (0600 UTC 25 June). In addition, the differences in CLP and CLP between EXP_CWP and EXP_CON are shown in Fig. 4. It is clear that the CLP from EXP_CON without cloud assimilation is larger than the CLP from G3C observation in the main cloudy area, and the CLP from EXP_CWP with cloud assimilation is reduced in the main cloudy area. This is consistent with the model forecast of q _cloud having a positive deviation. The CIP from EXP_CON is much less than observed, while the CIP in EXP_CWP is increased and the values are more consistent with observation. This can also be explained by the negative deviation of the model forecast of q _ice. In general, the analysis of CLP and CIP from EXP_CWP with cloud assimilation is closer to observation than EXP_CON without cloud assimilation.

Figure 5 presents vertical cross sections of the zonal-average q _ice and q _cloud of the analysis field. The content of q _ice significantly increases at higher levels with cloud assimilation, and a large increase is located over the central area of the precipitation at 30^°-32^°N. The content of q _cloud increases only slightly over 30^°N with cloud assimilation. Cloud particles in solid ice phase (q _ice) appear near to 200-300 hPa, while cloud water in liquid phase (q _cloud) occurs at levels below 400 hPa. This vertical distribution is also consistent with the vertical characteristic of the background error.

Figure 4.  The difference in (a) CLP, (b) CLP and (c) CLP plus CIP between EXP_CWP and EXP_CON at 0600 UTC 25 June (units: g m$^-2$).

Figure 5.  Vertical cross sections of zonally averaged $q_\rm ice$ and $q_\rm cloud$ in the analysis fields (units: 10$^-5$ kg kg$^-1$): (a, c) EXP_CON without cloud assimilation; (b, d) EXP_CWP with cloud assimilation.

Figure 6.  Vertical cross sections of temporal evolution of horizontally averaged $q_\rm ice$ in the first 6 hours over the major rainy area (units: 10$^-5$ kg kg$^-1$): EXP_CON with the (a) LIN scheme, (c) SBU-YLIN scheme, (e) WDM6 scheme, and (g) WSM6 scheme; EXP_CWP with the (b) LIN scheme, (d) SBU-YLIN scheme, (f) WDM6 scheme, and (h) WSM6 scheme.

Figure 7.  Vertical cross sections of 2D wind vectors (vectors; units: m s$^-1$), divergence fields (color-shaded; units: 10$^-5$ s$^-1$) and cloud hydrometeors (lines; hydrometeor boundary defined by a threshold mixing ratio of 0.005 g kg$^-1$) along 121$^\circ$E of the 3-h forecast of EXP_CON with the (a) LIN scheme, (c) SBU-YLIN scheme, (e) WDM6 scheme, (g) WSM6 scheme; and EXP_CWP with the (b) LIN scheme, (d) SBU-YLIN scheme, (f) WDM6 scheme, and (h) WSM6 scheme.

Figure 8.  The difference in the 3-h precipitable water forecast (units: mm) between EXP_CON and GFS analysis with the (a) LIN scheme, (c) SBU-YLIN scheme, (e) WDM6 scheme, and (g) WSM6 scheme; and the difference between EXP_CWP and EXP_CON with the (b) LIN scheme, (d) SBU-YLIN scheme, (f) WDM6 scheme, and (h) WSM6 scheme.

The vertical cross section of the temporal evolution of horizontally averaged q _ice in the first six hours over the major rainy area (Fig. 6) suggests that, no matter which microphysics scheme is used, q _ice is always smaller in EXP_CON than observed. The content of q _ice in EXP_CWP with cloud assimilation is effectively increased at the analysis time; however, q _ice gradually decreases with an increase in the forecast time and eventually becomes similar to that in EXP_CON.

Focusing on the differences in q _ice between different microphysics schemes in EXP_CWP with cloud assimilation, it is found that the increased q _ice sustains longest when WDM6 is used and the increased q _ice decreases quickly when SBU-YLIN is applied. The content of q _ice in the experiment with the WDM6 scheme becomes equivalent to that in the control experiment after 120 minutes; whereas in the experiment with the SBU-YLIN scheme, q _ice becomes similar to that in the control experiment after 30 minutes. A similar pattern is also found for q _cloud, although it can sustain a little longer than q _ice.

Noting that the correlation between hydrometeors (q _ice and q _cloud) and other model variables are not taken into account, and there is no difference between the analysis of EXP_CWP and EXP_CON, except for q _ice and q _cloud, this section focuses on how the cloud information is passed to other variables, and then how these impact the forecasting of precipitation.

The vertical cross section of vertical velocity along the center of the precipitation (121^°E) of the 3-h forecast (Fig. 7) shows that, in EXP_CON without cloud assimilation, there is no distinct convergence and ascending motion in lower levels, and ascending motion only occurs at a higher level (300 hPa). It is difficult for precipitation to develop under such a condition. In EXP_CWP with cloud assimilation, strong convergence at lower levels (850 hPa to 400 hPa) and divergence at a higher level (300 hPa) are accompanied by significant ascending motion over the central area of precipitation (30.3^°-31.3^°N). This circulation pattern promotes lifting and condensation of water vapor in the atmosphere, and the content of cloud hydrometeors is larger than that in EXP_CON.

In EXP_CWP, low-level convergence and ascending motion are weakest when SBU-YLIN is used. Subsequently, the lifting and condensation of water vapor is weak and cloud hydrometeors are small. In contrast, low-level convergence and ascending motion are strong when WDM6 is used. Significant lifting and condensation of water vapor in the atmosphere result in large amounts of cloud hydrometeors and deep cloud layers, which are favorable for precipitation development.

Precipitable water represents total column water vapor in the atmosphere. Figure 8 shows the difference in the 3-h forecast of precipitable water between EXP_CON and GFS, and the difference between EXP_CWP and EXP_CON. Compared with GFS analysis, the atmosphere is drier over the rainy area in EXP_CON; whereas, in EXP_CWP with cloud assimilation, precipitable water is effectively increased over the drier area in EXP_CON.

Cloud assimilation can significantly improve the model simulation of precipitable water, but there is little difference in the distribution of precipitable water between experiments with different microphysics schemes.

The accumulated precipitation verification, based on the Fraction Skill Score (FSS; Roberts and Lean, 2008), over the major rainy area (red box in Fig. 1a), is discussed in this subsection. The observed precipitation is from the China Hourly Merged Precipitation Analysis, operationally produced by the China Meteorological Administration (Shen et al., 2014).

The time series of hourly accumulated precipitation (Fig. 9) shows that the observed precipitation experienced an increasing-decreasing process, and weak double peaks of precipitation of less than 2 mm h^-1 appeared during the first 12 hours. During the latter 12 hours, precipitation gradually increased and reached its peak value at hour 23. In EXP_CON, the accumulated precipitation with all four microphysics schemes is very small in the first 8 hours, and the time of precipitation occurs 4 hours earlier than observed, though the increasing trend of precipitation after 12 hours is reproduced. In contrast, in EXP_CWP, precipitation in the first 12 hours and the two weak peaks are better simulated with all four microphysics schemes, and the time of peak precipitation is closer to the observation than EXP_CON.

Figure 10 presents the FSS for hourly precipitation over 1 mm and 2 mm simulated by each individual experiment. Note that the FSS is lower in the first 7 hours in EXP_CON without cloud assimilation, and gradually becomes higher after 7 hours. Obviously, the FSS in EXP_CWP with cloud assimilation significantly improves, particularly in the first 7 hours. It is found that, without cloud assimilation, the LIN scheme gives the best results, followed by the SBU-YLIN scheme; and with cloud assimilation, the FSS improves in all the experiments with different schemes; the most significant improvement is found in the experiment with WDM6, while the experiment with SBU-YLIN shows the smallest improvement. This is consistent with the increased q _ice sustaining longest when WDM6 is used and the increased q _ice decreasing quickly when SBU-YLIN is applied.

Figure 9.  Time series of hourly precipitation for OBS, EXP_CON and EXP_CWP with different microphysics schemes (units: mm).

Figure 10.  The FSS of hourly accumulated precipitation with the thresholds of 1 mm h$^-1$ and 2 mm h$^-1$: (a) LIN; (b) SBU-YLIN; (c) WDM6; (d) WSM6.

In this study we apply WRFDA-3DVAR to assimilate satellite CLP and CIP. The background error covariance of hydrometeors (q _cloud and q _ice) is modeled through a CVT, and the characteristics of the background error covariance for hydrometeors are discussed. The impacts of cloud assimilation on the simulation of a strong precipitation process over the Yangtze River-Huaihe River valleys using four microphysics schemes are then investigated.

In terms of the characteristics of the background error covariance for cloud control variables, it is shown that the contributions of temperature and relative humidity to hydrometeors are predominant, albeit very small. It can be seen that the vertical error of q _ice occurs around 250 hPa and the vertical error of q _cloud around 700 hPa. It is also found that the model forecast of q _ice has a negative deviation and the model forecast of q _cloud has a positive deviation. The distribution and increment of cloud hydrometeors in EXP-CWP with cloud assimilation, which shows significant improvement, are consistent with the characteristics of the background error covariance.

It is found that low-level convergence and upward motion are both more significant in the experiment with the WDM6 scheme than with the other schemes, and the assimilated cloud information can sustain for longer when using WDM6. Meanwhile, both upward motion and low-level convergence are weakest in the experiment with the SBU-YLIN scheme, and the assimilated cloud information disappears quickly. This partly explains why only a small improvement is found in the experiment with the SBU-YLIN scheme, why the FSS for precipitation is lowest in this experiment, and why the most significant improvement is found in the experiment with the WDM6 scheme.

It should be noted that the background error covariance of hydrometeors used in this study is modeled through a CVT via the NMC method, and the background error covariance is isotropic, homogeneous and static. An anisotropic, inhomogeneous and flow-dependent background error covariance is important for data assimilation, especially for cloudy data assimilation. So, variational-ensemble hybrid data assimilation with hydrometeor control variables based on the extended control variables method will be studied in future work.