Effect of 2-m Temperature Data Assimilation in the CMA-MESO 3DVAR System

1.   Introduction

Numerical weather predication (NWP) is a critical technology for mesoscale weather forecasts. In China, theoretical, methodological, and numerical model investigations have long been highly valued, and widely influential research results have been obtained in terms of theory, methods, and numerical model developments (Xue and Chen, 2008; Ma et al., 2009; Zhang et al., 2019; Shen et al., 2020; Ma et al., 2021, 2022a). The China Meteorological Administration (CMA) mesoscale model (CMA-MESO) [formerly known as the GRAPES-MESO (Global and Regional Assimilation and PrEdiction System mesoscale numerical prediction)] (Xue and Chen, 2008) has been continuously improved over recent years. The CMA-MESO system with a 3-h assimilation cycle became operational in 2010 (Xu et al., 2013). In 2014, the horizontal resolution of the CMA-MESO system was increased from 15 to 10 km (Huang et al., 2017), and the original vertical resolution of 30 layers was improved to 50 layers. In 2020, the CMA-MESO system with 3-km resolution across the entire Chinese region played an important role in daily weather forecast operations (Huang et al., 2022; Ma et al., 2022b).

To improve capability in the forecasting extreme weather and near-surface meteorological elements, it is critical to develop a kilometer-scale data assimilation system and improve incorporation of as much small- and medium-scale information as possible in the initial conditions of numerical models (Gustafsson et al., 2018). The kilometer-scale CMA-MESO three-dimensional variational data assimilation (3DVAR) system was developed from the CMA global–regional integration variational assimilation framework (Xue and Chen, 2008; Ma et al., 2009). A framework of kilometer-scale 3DVAR has been developed to meet the needs of kilometer-scale numerical weather forecasting (Wang et al., 2018). The control variables in the kilometer-scale 3DVAR assimilation system comprise u wind, v wind, surface pressure (p_s), temperature (T), and relative humidity (RH), instead of the flow function (ψ), potential function (χ), and nonequilibrium dimensionless pressure (π), without consideration of the geostrophic equilibrium relationship between the control variables. The spatial correlation scale of the background error of the new control variable is smaller. A multiscale analysis scheme has been developed to analyze the small- and medium-scale systems, while taking into account correct description of the synoptic-scale environmental airflow (Wu et al., 2018). Concurrently, an additional large-scale constraint exists in the cost-function of 3DVAR (Yang et al., 2019; Wang et al., 2021), and a blending method has been implemented to merge large-scale information of global models with the mesoscale information of regional analysis (Zhuang et al., 2020). Furthermore, to compensate for the lack of a 3DVAR temporal dimension, and to adapt to the characteristics of the rapid development of small- and medium-scale information and short lifetime of mesoscale weather system, the kilometer-scale 3DVAR uses a rapid update assimilation and forecast cycle, with an assimilation interval of 1–3 h, and an incremental analysis update method to suppress noise in the fast cyclic process.

The CMA 3DVAR now actively considers assimilation of data with high spatiotemporal density data (e.g., radar, satellite, and automatic weather station observations). Radar radial wind and wind profile data are directly assimilated into the kilometer-scale 3DVAR. Radar reflectivity data, used in the cloud analysis system to obtain information on hydrometeors and latent heat tendency, are introduced into the model via a relaxation approximation (Zhu et al., 2017). Data from the newest of China’s Fengyun geostationary satellites (FY-4A) are also used in the kilometer-scale 3DVAR.

Approaches for surface data assimilation have also undergone continuous research and development since the release of the CMA-MESO system. For example, Ding et al. (2010) conducted experiments on the assimilation of surface wind data at 10-m height (hereafter, V_10m) in CMA-MESO based on the Monin–Obukhov similarity theory, and verified the effectiveness of V_10m data assimilation. Lian and Xue (2010) investigated and modified the surface pressure interpolation scheme in the CMA-MESO 3DVAR system, which effectively improved surface pressure data assimilation. Through the relationship between stability and difference in the low-level relative humidity of the model, Xu et al. (2021) improved the scheme for assimilation of relative humidity at 2-m height (hereafter, RH_2m) for observation sites with terrain elevation below that of the model in the CMA-MESO 3DVAR system, thereby improving the model system assimilation analysis and precipitation forecast.

Although a considerable amount of research has been undertaken on assimilation of surface observational data, use of surface observations in NWP models remains a challenging problem owing to differences between the elevation of model terrain and that of actual observation sites. Some earlier studies considered the elevation differences between model terrain and actual observation sites (Ruggiero et al.,1996; Lazarus et al., 2002; Devenyi and Benjamin, 2003; Benjamin et al., 2004; Xu et al., 2007b, 2009; Shao and Min, 2019), while other studies did not on surface data assimilation schemes (Guo et al., 2002; Stensrud et al., 2009; Shao and Min, 2015). Urban (1996) argued that when the heights differed greatly, the best estimates of surface data cannot be obtained by simply interpolating the epitaxial model values. Pu et al. (2013) highlighted that the ensemble Kalman filter approach clearly performed better than 3DVAR over complex terrain because it is better to handle surface data in the presence of terrain misrepresentation. Xu et al. (2007a) studied the surface data assimilation scheme of Guo et al. (2002) and concluded that NWP forecast skill would be improved if surface observations were assimilated appropriately. The study also showed that temperature observations at 2-m height (hereafter, T_2m) had more noticeable impact than other meteorological variables on NWP model 24-h precipitation forecasts.

Because T_2m was found to be highly detrimental to model forecasts, T_2m was not assimilated into either the North American Regional Reanalysis project (Mesinger et al., 2006) or the model used for operational analysis and the 40-yr reanalysis project by the European Centre for Medium-Range Weather Forecasts (Simmons et al., 2004). Currently, China has more than 50,000 automatic weather stations in operation. The observational data they provide are important for mesoscale numerical models; therefore, many researchers from China focused on developing an appropriate T_2m assimilation scheme. For example, Xu et al. (2007b) added representative terrain error, which was related to differences between the surface elevation in the model and that of actual observation sites, to reduce the negative effects of elevation difference in assimilation of T_2m data. Xu et al. (2009) applied the temperature lapse rate (0.0065°C m⁻¹) to correct T_2m from the actual terrain to the model terrain, which partially mitigated the effect of terrain differences. Zhang et al. (2021) optimized the surface data assimilation correction scheme in the Weather Research and Forecasting 3DVAR system to improve the correction of T_2m and V_10m, thereby improving the model forecast.

In this study, based on previous research on surface data assimilation (Xu et al., 2007b, 2009), an assimilation scheme for T_2m was established and applied to the kilometer-scale CMA-MESO 3DVAR system, and individual case study and continuous experiments were carried out to assess the impact of the assimilation of T_2m data.

The remainder of the study is organized as follows. Section 2 briefly describes the assimilation scheme developed for T_2m data. Section 3 introduces the CMA-MESO 3DVAR system and describes the experimental setup. Section 4 presents the results of T_2m data assimilated using the assimilation scheme presented in Section 2 for the case of one rainfall process. Section 5 examines the impact of T_2m data assimilation on the basis of continuous experiments. Finally, a summary and our concluding remarks are provided in Section 6.

2.   Assimilation scheme for 2-m temperature data

If the elevation difference between an observation site and the model terrain is great, the analysis will use little of the observational information owing to the large observation error of the scheme (Xu et al., 2007b), while some erroneous observational information might be assimilated inappropriately in the scheme (Xu et al., 2009) when the temperature lapse rate value differs markedly from the actual value. With a small representative terrain error added to observational error, the combination of the two schemes can partly eliminate the above deficiencies caused by large elevation differences between observation sites and model terrain.

In this assimilation scheme, the T_2m data are classified into three categories. 1) If the elevation of a surface observation site is above the model terrain by more than 100 m, the T_2m data are assimilated in the same way as temperature sounding data with an additional representative error added to the observational error, thereby recognizing that T_2m data are greatly affected by the observational environment while sounding temperature data are not. 2) If the elevation of a surface observation site is above the model terrain, but by less than 100 m, the T_2m data are assimilated directly using the surface similarity theory assimilation operator described in the following, and the observational error remains unchanged. 3) If the elevation of a surface observation site is lower than the model terrain, the observed T_2m data are corrected from the site elevation to the 2-m level above the model terrain elevation using a temperature lapse rate of 0.0065°C m⁻¹. Then, they are assimilated by using the surface similarity theory assimilation operator with a small representative terrain error, which is related to the elevation difference between the model terrain and observation site.

The forward observation operator of the surface similarity theory is introduced subsequently. The surface similarity theory (Cheng, 1994) gives the following:

By integrating Eq. (1) with height, the potential temperature profile can be derived:

where $\theta$, ${\theta _z}$, and ${\theta _g}$ are potential temperature variables, ${\theta _{\text{z}}}$ and ${\theta _g}$ are the potential temperature at $z$ and ${z_0}$ above the ground, respectively, $\kappa = 0.4$ is the von Karman constant, and ${\varphi _h}$ is a function of the Richardson number (R_ib).

Parameter ${T_{\text{*}}}$ is the surface “friction” temperature, which can be expressed as follows:

where ${\theta _{\rm{a}}}$ is the potential temperature at ${z_{\rm{a}}}$ above the ground.

Because ${\varphi _h}$ is a function of ${{R}}_{{\rm{ib}}}$, ${\varphi _h}$ can be calculated from Eqs. (4)–(10). The critical Richardson number ${{R}}_{{\rm{ib}}}$ (= 0.2) is used to assess the state of stratification when calculating the function ${\varphi _h}$. The boundary layer height $h$ and the Monin–Obukhov length $L$ are both considered when determining instability:

where ${\rho _{\rm{a}}}$ is air density near the ground layer, ${u_{\text{*}}}$ is the surface “friction” velocity, ${H}_{\rm s}$ is the ground sensible heat flux, and ${c_p}$ is the heat capacity of air at constant pressure.

The Richardson number R_ib is given by the following:

where ${V_{\rm{a}}}$ is the wind speed over the ground or at the lowest layer of the model, for which height is ${z_{\rm{a}}}$, and $g = 9.8\;{\rm{m}} \; {{\rm{s}}^{ - 2}}$ is acceleration due to gravity.

This operator based on the surface similarity theory for T_2m observational data, together with the adjoint operator and the tangent linear operator were all coded and introduced into the CMA-MESO 3DVAR assimilation system.

The CMA-MESO model adopts terrain-following coordinates (Ma et al., 2009), temperature, humidity, and air pressure are specified for the model layers, while wind is specified for the half layers. The wind values are interpolated from the half layers to the model layers such that the operator calculation processing is conducted for the model layers.

3.   Experimental design

Experiments were performed by using the recent CMA-MESO system (version 5.1, released in 2021) that include 51 layers with unequal vertical spacing. The experiment consisted of data assimilation and forecasting at 3-h intervals, and 24-h forecasts at 0000 and 1200 UTC with cold or warm starts. Initial background and lateral boundary data were obtained from the NCEP 0.5° × 0.5° FNL 6-h forecast field. The surface observational data were acquired from the National Meteorological Information Centre.

Four groups of experiment were designed experiments CTL_c (cold start) and CTL_w (warm start) that were control experiment undertaken with the same parameter configuration as that of the operational CMA-MESO system and without T_2m data assimilation; experiments T2_c (cold start) and T2_w (warm start) were sensitivity experiments, which were the same as experiments CTL_c and CTL_w, but with T_2m data assimilated by using the T_2m data assimilation scheme described in Section 2. Experiments CTL_c and T2_c were performed with one-time data assimilation and a 24-h forecast. Experiments CTL_w and T2_w were performed with a 3-h cycle of data assimilation update, five cycles of data assimilation in total (at 0000, 0300, 0600, 0900, and 1200 UTC) for a warm start forecast at 1200 UTC.

The experimental periods were 2–28 February 2020 (i.e., the Beijing Winter Olympic test system, covering the entire North China region (34.5°–44.5°N, 108°–124°E), model horizontal resolution is 1 km) and 5–20 July 2020 (i.e., the operational CMA-MESO test system, covering the entire China region (10°–60°N, 70°–145°E), model horizontal resolution: 3 km). The data used in the operational CMA-MESO system were also used in these experiments, including radiosonde reports (U, V, T, and RH), surface observations (p_s, RH, U, and V), buoy/ship reports (U, V, p_s, and RH), aircraft observations (U, V, and T), atmospheric motion vectors, ground-based occultation inversion precipitable amount data, radar radial wind, radar, and satellite data used in cloud analysis systems (Zhu et al., 2017), Global Navigation Satellite System Radio Occultation refractive index data, and FY-4A imager data.

4.   Case study

The period from 1200 UTC 11 July to 1200 UTC 12 July 2020 was chosen arbitrarily for a case study using the operational CMA-MESO test system. During this period, a large-scale precipitation event occurred in China, and for some regions in the south, the rainfall reached the intensity level of a rainstorm. There were 3642 observed T_2m data available for assimilation (Fig. 1) following early quality control (e.g., extreme value checking, consistency checking, and thinning). The terrain height data used in the model were derived from a global digital elevation model resulting from collaborative effort led by the staff at the US Geological Survey’s EROS Data Center in Sioux Falls (South Dakota, USA) and the elevations were spaced regularly at 30-arcsecond intervals (approximately 1 km). For 1844 observation sites, the actual elevation was higher than the comparative elevation of the model terrain, and the elevation difference was greater than +100 m at 113 sites. For 1798 observation sites, the actual elevation was lower than the comparative elevation of the model terrain, and the elevation difference was greater than −100 m at 346 sites. Most observation sites in the east–central (west) region of China have elevation above (below) that of the model terrain (Fig. 1).

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Fig  1.  Difference in elevation between the observation sites and model terrain (m).

The newly added assimilation operator must be validated for accuracy before it can be utilized. Figure 2 depicts the T_2m distribution of background and that derived from the background by the 2-m temperature similarity theoretical forward operator at 1200 UTC 11 July 2020. It can be seen that the distribution and values of the T_2m data obtained from the forward operator are broadly similar to those of the background T_2m data. Thus, it can be considered that the T_2m similarity theoretical forward operator is generally accurate.

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Fig  2.  Distributions of T_2m (K) at 1200 UTC 11 July 2020: (a) background and (b) derived from background by the forward observation operator.

According to the classical Taylor expansion formula, the approximation test formula for the tangent linear operator can be expressed as follows:

where $x$ is the state of the atmosphere and ${\rm{d}}x$ is the analysis increment, $F(\alpha )$ is a formula for the gradient coefficient $\alpha$, whose numerical value is close to 1, ${H'}$ is an approximate linearization of the forward (observation) operator $H$, and $\left\| {\;} \right\|$ represents the Frobenius norm of a matrix. Table 1 is the tangent operator test for the T_2m data assimilation. When $\alpha$ = 10⁻² – 10⁻⁴, the accuracy of the tangent linear approximation can exceed 7 digits, which is consistent with the conclusion that when $\alpha$ approaches 0, $F(\alpha )$ approaches 1. However, as $\alpha$ becomes increasingly small, the rounding error begins to affect the approximated results (Janisková and Lopez, 2013). The test results showed that the tangent linear operator is correct.

Table  1.  Tangent operator test for T_2m data assimilation

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$\alpha$	$F(\alpha )$ at the first iteration step	$F(\alpha )$at the final iteration step
1.0	1.00000020800675	0.999996474724146
10−1	1.00000002061261	0.999999647232695
10−2	1.00000000713101	0.999999964732025
10−3	1.00000003602014	0.999999996695718
10−4	0.999999987871595	0.999999999092994
10−5	1.00000383975878	0.999999971124763
10−6	0.999994210054727	1.00000025080709
10−7	1.00009050918172	1.00000025080709
10−8	1.00298163899401	1.00000824174737
10−9	1.02236247872679	0.999728577834389
10−10	1.44892641542912	1.00172703526248

 | Show Table

DownLoad: CSV

The adjoint operator ${H^ * }$ is developed on the basis of the tangent linear operator ${H'}$. The correctness of the adjoint operator is obtained by the following inner product:

At the final iteration step of the 3DVAR system,

The effective equivalent number exceeds 16 digits, which shows that the adjoint operator meets the accuracy requirements of the tangent adjoint test.

The temperature analysis increment at the model’s lowest layer (Fig. 3) is < 2 K in experiments CTL_c and CTL_w (Figs. 3a, c) but > 2 K somewhere in experiments T2_c and T2_w (Figs. 3b, d). The temperature incremental results of experiments CTL_c and T2_c are close to those of experiments CTL_w and T2_w, especially in those regions with the absolute maximum of the analysis increment. The isoline structure for the 0-K analysis increment of experiments T2_c and T2_w is comparable with that of experiments CTL_c and CTL_w, i.e., the absolute central value of the temperature analysis increment increases, and the area of positive values of the analysis increment in central and eastern regions of China expands. This finding demonstrates that assimilation of T_2m data has substantial impact on the analysis of temperature in the lowest layer of the model.

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Fig  3.  Temperature analysis increment (K) in the lowest layer of the model before and after T_2m data assimilation at 1200 UTC 11 July 2020: (a) CTL_c, (b) T2_c, (c) CTL_w, and (d) T2_w.

The innovation vector [observation minus background (O − B)] and analysis residual [observation minus analysis (O − A)] for T_2m data assimilated in experiment T2_w are illustrated in Fig. 4. The results of experiment T2_c are close to those of experiment T2_w; therefore, only the results of experiment T2_w are shown in Figs. 4, 5. Following background checking in the 3DVAR system, some observed T_2m data were discarded when the difference between observation and background larger than the observation error multiplied by 3.5. The volume of T_2m data assimilated in the eastern coastal region of China is larger than that assimilated in the northwest. There are more observation sites with an absolute value > 1.5 K in the innovation than in the analysis residual, and there is obvious negative deviation in the innovation near 35°N, whereas the manifested deviation is reduced and no longer visible in the analysis residual after assimilating the T_2m data. This finding demonstrates that the assimilation of T_2m data has reasonable and significant impact on the analysis of the low layer temperature.

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Fig  4.  Distributions of T_2m (K) innovation and analysis residuals in experiment T2_w at 1200 UTC 11 July 2020: (a) innovation and (b) analysis residual.

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Fig  5.  Probability distribution function (PDF) of T_2m (K) innovation (O − B) and analysis residual (O − A) in experiment T2_w at 1200 UTC 11 July 2020.

From the probability distribution function diagrams of the T_2m innovation (O − B) and analysis residual (O − A) (Fig. 5), it can be determined that the innovation vector has a clear and positive deviation, whereas the analysis residual has no clear positive deviation and is closer to a normal distribution.

The average deviation (Bias) and standard deviation profiles of the differences between background and radiosonde observation (radiosonde observation innovation) over the entire experimental region, and the differences between the analysis and radiosonde observation (radiosonde observation analysis residual) obtained from the four group of experiments at 1200 UTC 11 July 2020, are shown in Fig. 6. The standard deviations of the temperature and relative humidity analysis in the lower layer in experiments CTL_w and T2_w are smaller than those in experiments CTL_c and T2_c, i.e., the temperature and relative humidity analyses in experiments CTL_w and T2_w are closer to the observations.

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Fig  6.  (a1–d1) and (a3–d3) Deviation (Bias) and (a2–d2) and (a4–d4) standard deviation (Std) of the background and analysis versus radiosonde observations at 1200 UTC 11 July 2020. Columns 1 and 2: CTL_c and T2_c, columns 3 and 4: CTL_w and T2_w; (a1–a4): u (m s⁻¹), (b1–b4): v (m s⁻¹), (c1–c4): temperature (K), and (d1–d4): relative humidity (%). Black line: CTL_c or CTL_w, red line: T2_c or T2_w, solid line: innovation, and dotted line: analysis residual.

With one-time data assimilation, the wind (u and v), temperature, and relative humidity innovation deviations and standard deviations, as well as the analysis residual deviation in experiment CTL_c, are the same as those in experiment T2_c (columns 1 and 2 in Fig. 6), with their profile lines overlapping. The analysis residual standard deviation profiles of the wind (u and v) overlap in experiments CTL_c and T2_c, while the temperature and relative humidity analysis residual standard deviation profiles do not. These results indicate that one-time T_2m data assimilation affects the temperature and relative humidity analyses, but has only slight influence on the wind analysis. The lower-layer temperatures for experiment T2_c are closer to the sound observations, whose analysis deviation and standard deviation are smaller than those of experiment CTL_c.

At the end of the data assimilation cycle, the wind (u and v), temperature, relative humidity deviations, and standard deviations of the innovation and analysis residual for experiments CTL_w and T2_w (columns 3 and 4 in Fig. 6), are different. Their profiles do not completely overlap, and the difference is larger in the lower layer and smaller in the upper layer. This shows that by the end of the data assimilation cycle, T_2m data assimilation has varying degrees of influence on the analyses of temperature, wind, and relative humidity, with the impact on the lower layer greater than that on the upper layer. The low-level wind (u and v) and temperature of experiment T2_w are closer to the observations, with obviously smaller standard deviations than those of experiment CTL_w. Therefore, by the end of the data assimilation cycle, T_2m data assimilation can improve not only the temperature analysis but also wind analysis, which affects the entire atmosphere.

According to 6-h precipitation classification, the 6-h precipitation forecast results at 1200UTC 11 July 2020 (Figs. 7, 8 ) show that assimilation of T_2m data has a positive contribution to the precipitation forecast in the first 12 hours with a warm start. In comparison with the precipitation forecast of experiment CTL_w, the equitable threat score (ETS; Wei et al., 2020) value is higher and the Bias value is smaller for the precipitation forecast of experiment T2_w. The effect on the precipitation forecast is minor with a cold start when T_2m data are assimilated. The ETS and Bias values of the precipitation forecast in experiment CTL_c are close to those of the precipitation forecast in experiment T2_c. The ETS value of the precipitation forecast is higher with a warm start than with a cold start in the first 18 hours, except for the ETS value with thresholds of 0.1 mm (light rainfall), 13.0 mm (moderate rainfall), and 60.0 mm (torrential rainfall) in the 6–12-h precipitation forecast. Additionally, the bias value of the precipitation forecast is closer to 1 with a warm start than that with a cold start in the first 18 hours. Thus, the precipitation forecast is better with a warm start than that with a cold start, and the precipitation forecast with a warm start with T_2m data assimilation is best.

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Fig  7.  ETS values of 6-h accumulated simulated precipitation (mm) in the experimental region at 1200 UTC 11 July 2020 with a cold start (CTL_c and T2_c) and a warm start (CTL_w and T2_w): (a) 1200–1800, (b) 1800–0000, (c) 0000–0600, and (d) 0600–1200 UTC.

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Fig  8.  As in Fig. 7, but for bias values of 6-h accumulated simulated precipitation.

According to the precipitation forecast for the first 12-h beginning at 1200 UTC (Fig. 9), the main precipitation centers and precipitation ranges predicted by the four experiments are reasonably close to those of the observations, albeit with some minor differences.

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Fig  9.  Accumulated 6-h rainfall (mm) of (a, b) observation, (c, d) CTL_c, (e, f) T2_c, (g, h) CTL_w, and (i, j) T2_w during (a, c, e, g, i) 1200–1800 UTC and (b, d, f, h, j) 1800–0000 UTC 11 July 2020.

In comparison with the 0–6-h observed precipitation, indicated by the black circle in Fig. 9a, the precipitation prediction of experiments with a cold start (Figs. 9c, e) is too strong, while the precipitation predicted by experiments with a warm start (Figs. 9g, i) is close to the observations. The precipitation predicted by experiment T2_w, shown by the purple circle, is smaller than that of experiment CTL_w, which is closer to the observations, whereas the precipitation predicted by experiment T2_w, indicated by the red circle, is slightly higher than that of experiment CTL_w, which is also closer to the observations.

For the 6–12-h precipitation forecast, the rain band (red circle in Fig. 9b) of experiment T2_w is the closest of the four experiments to the observations. The precipitation forecast in the purple circle for experiment T2_w is also closer to the observations. These results show that the forecast area and intensity of precipitation are improved in experiment T2_w with T_2m data assimilation, and more closely match the observations than those in experiment CTL_w.

5.   Evaluation of the effect of continuous experiments

Regional high-resolution model systems are focused on producing quantitative forecasts of precipitation, T_2m, and V_10m. The following is an analysis of precipitation, T_2m, and V_10m forecasts of continuous experiments for the two periods of interest (5–20 July 2020 and 2–28 February 2020). According to the analysis for the case study in Section 4, the analysis field and the short-term precipitation forecast with a warm start are better than that with a cold start. Therefore, the analysis in this section focuses solely on continuous experiments with a warm start.

5.1   Continuous experiments during 5–20 July 2020

The root mean square errors (RMSE) of the 3-h interval T_2m forecast and V_10m forecast (Fig. 10) show that the T_2m forecast RMSE value for the first 12 hours in experiment T2_w is smaller than that in experiment CTL_w, and that the V_10m forecast RMSE value for the first 6 hours in experiment T2_w is smaller than that in experiment CTL_w. The T_2m RMSE difference between experiment T2_w and CTL_w is greatest at the analysis time and gradually diminishes with increasing forecast time. The effect of the 6-h precipitation forecast (Fig. 11) is improved following T_2m data assimilation, and the ETS values with thresholds of 0.1 mm (light rainfall), 4.0 mm (moderate rainfall), and 13.0 mm (heavy rainfall) in the first 18 hours are improved. The T_2m data assimilation improves the forecasts of T_2m and V_10m primarily in the first 6 hours, while the effect on the precipitation forecast lasts longer, i.e., up to 18 h.

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Fig  10.  RMSEs of (a) T_2m (°C), (b) u (m s⁻¹), and (c) v (m s⁻¹) at 3-h intervals from 5–20 July 2020 with a warm start at 1200 UTC (CTL: experiment CTL_w and T2: experiment T2_w). The bars represent the 95% confidence level.

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Fig  11.  ETS values of 6-h accumulated simulated precipitation in the experimental region at 1200 UTC 5–20 July 2020 with a warm start (CTL: experiment CTL_w, T2: experiment T2_w): (a) 1200–1800,(b) 1800 0000, (c) 0000–0600, and (d) 0600–1200 UTC.

5.2   Continuous experiments from 2 to 28 February 2020

As can be seen in Figs. 10, 12, the T_2m RMSE value is greater in Fig.12, and the maximum value exceeds 4°C in experiment CTL_w (seen in Fig. 12, 21-h forecast). The T_2m data assimilation has a longer effect on the T_2m and V_10m forecasts and the effect is evident to 24 h. The T_2m forecast RMSE value in experiment T2_w is smaller than that in experiment CTL_w, and the T_2m RMSE value at the analysis time in experiment T2_w is 0.32°C lower than that in experiment CTL_w. The T_2m RMSE value for the first 15 hours in experiment T2_w is lower than that in experiment CTL_w, which passed the 95% confidence level. The V_10m (u and v) RMSE value of experiment T2_w is slightly higher than that of experiment CTL_w at the analysis time, while the V_10m (u and v) RMSE value of experiment T2_w at the other forecast time is lower and closer to the observations.

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Fig  12.  As in Fig. 10, but for a warm start at 1200 UTC 2–28 February 2020.

The daily RMSE analysis of the T_2m forecast value (Fig. 13) reveals that the RMSE value for T_2m for the same forecast period varies on different days. The T_2m forecast RMSE value of experiment T2_w is lower than that of experiment CTL_w, and the T_2m RMSE difference between the two experiments at different times is different. At the analysis time, experiment T2_w has a much lower T_2m RMSE value than experiment CTL_w. The T_2m RMSE difference between the two experiment groups diminishes as the prediction time increases. The T_2m prediction for the first 15 hours in experiment T2_w is more accurate than that of experiment CTL_w, as shown in Fig. 8, i.e., as the forecast time increases, the effect of T_2m data assimilation gradually diminishes.

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Fig  13.  As in Fig. 10, but for T_2m (°C) daily from 2–28 February 2020.

The assimilation of T_2m data improves the precipitation forecast (Fig. 14). In the first 18 hours for every 6-h precipitation forecast, the ETS values for thresholds with 0.1 mm (light rainfall), 4.0 mm (moderate rainfall), and 13.0 mm (heavy rainfall) are obviously improved. The duration of the positive effect of T_2m data assimilation on precipitation forecasts in winter or summer can be seen to be around 18 h.

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Fig  14.  As in Fig. 11, but for a warm start at 1200 UTC 2–28 February 2020.

6.   Conclusions and discussion

Surface observational data represent one of the most important sources of data for regional rapid-cycle assimilation and forecast systems, and they play an ever-increasing role in regional high-resolution NWP models. To improve both the analysis and forecast skill of the high-resolution CMA-MESO system and the application capability of T_2m observational data, a T_2m data assimilation scheme was established in the CMA-MESO 3DVAR system. The T_2m data were divided into three types for assimilation according to the height difference between the model terrain and the station terrain. Analysis of individual case study and continuous experiments involving the T_2m data assimilation scheme led to the following conclusions.

(1) The T_2m data assimilation forward calculation operator was established based on surface similarity theory, and the T_2m data obtained by the T_2m data assimilation operator were broadly consistent with the background T_2m distribution. The results of the tangent linear operator and the adjoint operator test for the T_2m data assimilation showed that the tangent linear operator and the adjoint operator were correct and met the accuracy requirements. The innovation and analysis residual had Gaussian distributions and the analysis increment value was reasonable.

(2) The one-time assimilation of T_2m observational data produced notable impact on the analysis of the temperature and relative humidity fields, but only slight influence on the wind field analysis; therefore, it had little impact on the precipitation forecast. The analyses of the temperature, wind, and relative humidity fields were influenced at the end of data assimilation cycle when the T_2m data were assimilated. The analyses of the low-level temperature and wind fields were more accurate, and the area and intensity of the precipitation forecast in the first 12 hours were improved.

(3) Results of the continuous experiments showed that assimilation of T_2m data improved the T_2m, V_10m, and precipitation forecasts. With increasing forecast time, the improvement effect on the T_2m and V_10m fields diminished gradually. The T_2m data assimilation produced a clear positive impact on the precipitation forecast in the first 18 hours.

The improvement effect of the T_2m data assimilation on the T_2m forecast was greater in the continuous experiment from 2 to 28 February 2020 than that in the continuous experiment from 5 to 20 July 2020, and duration of the the impact was also longer, which might be related to season, model resolution, and analysis area size. Further studies on this topic will be undertaken in the future.

In comparison with the previous work, the representative terrain error was reduced properly in this study, but the question of how best to obtain the error of terrain representation was not considered. Additionally, only the overall results of T_2m data assimilation are discussed, without more comprehensive comparisons of the three treatments of T_2m data assimilation. Therefore, future studies should pay more attention to T_2m data assimilation in regions of complex terrain, and include consideration of the effects of the representative terrain error value.

Acknowledgments

We are grateful to Dr. Yongzhu Liu from the China Meteorological Administration’s Earth System Numerical Prediction Centre who contributed to the completion of this work. We thank the anonymous reviewers and editors for their thoughtful comments that helped us to improve the manuscript.