The new-generation operational numerical forecast system of the China Meteorological Administration, the GRAPES (Chen et al., 2008; Zhang and Shen, 2008; Ma et al., 2009; He et al., 2019a) model version 3.0, and its three-dimensional variational assimilation system has been applied in modeling many weather phenomena. These phenomena include extreme weather events, typhoons, sandstorms, and floods (Xu et al., 2012; An et al., 2016; Wang et al., 2016). We have implemented two VarQC methods (Flat-VarQC and Huber-VarQC) within the GRAPES m3DVAR system. Here, we discuss these model confiurations, and we will examine the posterior analysis of the mass fields from these VarQC methods in section 4.
Figure 2 shows the domain used in the simulation experiments. The simulation domain is defined by a 351 × 251 grid in the horizontal, with a meridional and zonal spacing of 20 km. In the vertical, the domain is broken into 31 levels, with a model top pressure of 10 hPa. The operational forecasts from the Global Forecast System (GFS) are used to construct the initial and lateral boundary conditions (ICs and LBCs) used for running the GRAPES model.
Figure 2. Simulation domain (10°−60°N, 70°−140°E) used in running the GRAPES model for the real-data experiments of VarQC methods. The red shade shows the verified domain (18°−40°N, 100°−125°E).
We have selected a region over east China (domain shaded in red in Fig. 2) for validation of the VarQC methods established in this paper. This region was selected because the high terrain over west China, particularly over the Tibetan Plateau, induces complex thermodynamic and dynamical effects (Wang and Zeng, 2012; Bao and Zhang, 2013; He et al., 2019b) that make it difficult to obtain accurate simulations.
Both idealized and real-data experiments are performed. Tables 1 and 2 describe the configurations of the idealized experiments used to examine the robustness of using the different VarQC methods to handle the outliers. The CTRL1 control experiment assimilates the actual pressure observations of 12 sounding sites, which are referred to as “normal pressures”. Some of these 500-hPa and 850-hPa level normal pressure observations are then replaced with outlier pressure values (underlined in Table 1). We will refer to these replaced observations as “outlier pressures” observations. Any pressure not equal to a specified level’s pressure will be treated as an outlier. For example, if an observed pressure at the 500-hPa height is not equal to 500 hPa, then that observation is an outlier. These outliers centered at the specified level are created by adding/subtracting a random draw from a uniform distribution within [1, 2]. The pressure errors (Table 1) from the observation report at 500 hPa (0.7766), 850 hPa (0.7975), and other levels (not shown) are consistent in the idealized experiments. We examine the impact of assimilating these outlier pressures with/without VarQC using the experiments given in Table 2 and detailed in section 4.1. The CTRL1 and CTRL1-Outlier experiments do not utilize any VarQC algorithms, whereas the Flat-Outlier and Huber-Outlier experiments respectively utilize the Flat-VarQC and Huber-VarQC methods.
Sounding site number The observed and artificial pressures Pressures and error
(0.7766) at 500-hPa level
Pressures and error
(0.7975) at 850-hPa level
1 501.085 851.633 2 500.000 848.206 3 498.441 851.506 4 500.000 851.002 5 501.408 848.148 6 500.000 851.356 7 500.000 851.612 8 500.000 851.001 9 500.000 851.165 10 500.000 851.679 11 500.000 850.000 12 500.000 850.000
Table 1. The rebuilding outliers (underlined) for pressure (units: hPa) on sounding sites.
Experiment name VarQC schemes Observations CTRL1 Without VarQC Normal pressures CTRL1-Outlier Without VarQC Outlier pressures Flat-Outlier With Flat-VarQC Outlier pressures Huber-Outlier With Huber-VarQC Outlier pressures
Table 2. Summary of the idealized experiment for different variational quality control.
Out of the 12 assimilated sounding sites, 10 sites are scattered around East China, near the middle and lower reaches of the Yangtze River (Fig. 3a). The remaining two sounding sites are located on the Korean Peninsula. Considering that observations that are sufficiently close can be used for "buddy checks" (Auligné, 2014) during VarQC, the observations of sites 11 and 12 were not constructed as outliers (Table 1) since they are far from the other 10 sites. The pressure values from sites 1, 3, and 5 at the 500-hPa level, as well as the pressure values from sites 1 to 10 at the 850-hPa level, were constructed as outliers (Table 1). Note that the pressures set as outliers would not be rejected by CQC. In other words, these outliers would be assimilated in all experiments, except for the CTRL1 experiment. Apart from CTRL1, which assimilates the normal pressures from 12 sounding sites without using VarQC, the other three experiments assimilate the same outlier pressures by using different quality control methods.
Figure 3. (a) Positions of sounding sites used in the robustness experiments. (b) Vertical profiles of RMSE of geopotential height for CTRL1 (red line), CTRL1-Outlier (green line), Flat-Outlier (blue line), and Huber-Outlier (black line). (c) Vertical distribution of observation weights at the sounding sites in the Huber-Outlier experiment. The top (bottom) of each x-coordinate shows the total number of the assimilated pressures (the site number).
The configurations of the three real-data VarQC assimilation experiments are listed in Table 3. These experiments spanned the entire month of August in 2015 by using the fitted transition points from the training observations in 2013. Unlike the earlier idealized experiments, which only assimilated pressure observations, these real data experiments assimilated GTS observations. The GTS observation types include TEMP, SYNOP, AIREP, SHIP, and SATOB, and are assimilated using a 6-hour assimilation window into the three experiments. Furthermore, all three experiments are performed using the cold start method. The analyses are performed each day at 0000, 0600, 1200, and 1800 UTC. The experiments utilize the old BgQC threshold limit to evaluate the impacts of existing long-tails observations (identified in Fig. 1).
Experiment names Quality control Observations CTRL2 Without VarQC GTS observations Flat-VarQC With Flat-VarQC GTS observations Huber-VarQC With Huber-VarQC GTS observations
Table 3. Summary of simulation experiments for different variational quality control schemes.
In this study, the Flat-VarQC was turned on during the first iteration of the 3DVAR cost function optimization in every cycle of the assimilation experiments. This first-iteration activation is unlike earlier work where VarQC’s modification to the 3DVAR cost function was only introduced after iterating the cost function minimization a specified number of times (Anderson and Järvinen, 1999). This late-inclusion in earlier work was done to prevent convergence issues. We were able to activate the Flat-VarQC algorithm in the first iteration because we did not experience convergence issues in most cases. The only time where we experienced convergence issues is represented in Fig. 8b. We were able to mostly avoid convergence issues because the first iterations’ innovations were relatively small, meaning that the starting point of the Flat-VarQC-modified cost function minimization should be within or near the convex region containing the cost function’s global minima. Future work can investigate whether we should turn on the Flat-VarQC at a later iteration step.
It should be noted that for the real-data experiments listed in Table 3, the innovations of specific humidity in the Huber-VarQC experiment cannot be effectively fitted by a Gaussian plus flat or a Huber norm OEDM in the statistics due to its unknown non-Gaussian property (Pires et al., 2010). To reduce the possibility of the Huber-VarQC experiment producing analyses that are worse than the CTRL2 experiment, while keeping VarQC active for specific humidity, we opted to use the OEDM that is closer to the traditionally prescribed Gaussian observation error distribution: the Gaussian plus flat OEDM. Thus, specific humidity observations in the Huber-VarQC are assimilated using the Gaussian plus flat OEDM, while all other observations are assimilated using Huber norm OEDM. In other words, the Huber-VarQC experiment utilized a hybrid of both Gaussian plus flat and Huber norm OEDMs.
|Sounding site number||The observed and artificial pressures|
|Pressures and error |
(0.7766) at 500-hPa level
|Pressures and error |
(0.7975) at 850-hPa level