The spin-up refers to the dynamic and thermal adjustments made at the initial stage of numerical integration in order to reach a statistical equilibrium
state. The analyses on the characteristics and effects of spin-ups are of great significance for optimizing the initial field of the model and
improving its forecast skills. In this paper, three different initial fields are used in the experiments: the analysis field of four-dimensional
variational (4D-VAR) assimilation, the 3
Norwegian scholar Bjerknes (1904) first explicitly proposed the theory of numerical forecasting in the early 20th century. After more than a century of development, it has become an effective way for studying climate change and its causes, as well as forecasting climate and weather. In addition, higher requirements have been also raised for the improvement of numerical forecast accuracy (Bauer et al., 2015; IPCC, 2013).
The numerical forecast accuracy is determined by a variety of factors. The European Centre for Medium-Range Weather Forecasts (ECMWF) concluded that the steady improvement of the numerical forecast in the past 30 years can be mainly attributed to the improvement of the forecast model itself, the application of more observation data, and the development of data assimilation technology (Linus and Erland, 2013). Among them, the performance of the forecast model is mainly determined by the model resolution, the accuracy of finite difference methods, and the representativeness of the physical process parameterization schemes. Observation data mainly depends on the development of monitoring technology, especially the application of satellite data. Data assimilation integrates observation data from different sources with model forecast elements so that the observation data can be comprehensively used by the models. The main purpose of data assimilation is to create a simulated atmosphere state closer to the real atmosphere, reduce the bias of the initial atmosphere condition, and thereby improve the quality of the initial field. In data assimilation, observation data from many sources are used. The uncertainties in the observation data, the inconsistencies among observation elements, and the model flaws (caused by model dynamic assumptions, interactions between physical processes, static data initialization and the radiation balance adjustment, etc.) can lead to inconsistencies between the assimilated new observation input data and the original data in the model. Therefore, the model needs to readjust the dynamic and thermal processes at the initial stage of integration until a new statistical equilibrium state is reached. This process is called the spin-up in numerical modeling, and the time required to reach a new equilibrium state is called the spin-up time (Wolcott and Warner, 1981; Kasahara et al., 1992; Séférian et al., 2016; Sheng et al., 2006; Liu et al., 2008; Xue et al., 2017). During the dynamic and thermal adjustment in the spin-up, spurious gravity waves can be triggered, causing a rapid increase in the root-mean-square error of the forecast variables in the model and an underestimation of the forecast precipitation (Wehbe et al., 2019; Qian et al., 2003). It leads to unreliable forecast results during the spin-up. Therefore, many studies generally do not consider the forecast results during the spin-up when evaluating the model forecasts (Lo et al., 2008; Kleczke et al., 2014; Xie et al., 2013; Zhao et al., 2012). If the spin-up time is too long in the operational model, it would inevitably affect the forecast accuracy of the model. In addition, the overlong spin-up in the climate model or the ocean model can consume excessive computing resources (Duben et al., 2014). Therefore, studying the spin-up characteristics and reducing the spin-up time are of great significance for improving the model forecast and saving computing resources.
Due to different types and usages of numerical models, the spin-up time in different models is greatly different. For example, in global climate models, glacial models, and ocean circulation models, the spin-ups usually take decades to hundreds of years (Scher and Messori, 2019; Danek et al., 2019; Rimac et al., 2017). However, in a regional climate model or a land surface model, only several weeks to several months are needed (Zhong et al., 2008; Rimac et al., 2017; Senatore et al., 2015; Giorgi and Mearns, 1999; Chen et al., 1997). In addition, the spin-up time is also affected by factors such as the simulation domain, the simulation season, and the circulation intensity (Anthes et al., 1989; Errico et al., 1987). The spin-up time of short-term weather forecast models is relatively short, usually several hours to about a dozen hours (Weiss et al., 2008; Souto et al., 2003; Kasahara et al., 1988). To reduce the impact of overlong spin-up on the accuracy of numerical forecasts, many technical methods have been developed to shorten the spin-up time. For example, the “Distorted Physics”, “Matrix method”, “Jacobian-free Newton–Krylov” are used in marine models (Bryan, 1984; Khatiwala et al., 2005; Knoll and Keyes, 2004), and the cloud analysis method for assimilating unconventional observation data such as satellites and radars is used in the short-term weather forecast model to improve the initial humidity field and cloud field, shorten the spin-up time, and improve the short-term precipitation forecast (Li et al., 2011, 2018; Zhu et al., 2017; Xue et al., 2003, 2017; Zhi et al., 2010; Carlin et al., 2017).
The Global/Regional Assimilation Prediction System (GRAPES) is a numerical weather forecast model independently developed by the China Meteorological
Administration (CMA). It has become the core of the national numerical forecast operational system in China. Numerical Weather Prediction Center of
CMA has established a deterministic weather forecast model system with a global horizontal grid spacing of 25
The paper is organized as follows. In Sect. 2, the GRAPES_GFS forecasting system and the experiment settings for one case study are introduced. In Sect. 3, the main research results are presented. Finally, in Sect. 4, the main conclusions are given, and some issues about spin-ups are discussed.
GRAPES is a global numerical weather prediction system that is composed of an atmospheric model and a variational data assimilation system (3D-VAR/4D-VAR). The framework of the atmospheric model is a fully compressible non-hydrostatic dynamical one with semi-implicit and semi-Lagrangian time difference scheme. In the horizontal direction, the equidistant latitude–longitude grid system with the Arakawa-C grid and central differencing of second-order accuracy for variable staggering is used, and in the vertical direction, the height-based terrain-following coordinate with the Charney–Phillips staggering is adopted. Forecast variables of GRAPES_GFS include the dimensionless air pressure (Exner function), potential temperature, three-dimensional wind field components, and specific humidity. It also introduces the Piecewise Rational Method (PRM) scalars (Su et al., 2013) into the model, which is a scheme of water vapor advection. The physical parameterization schemes used in the GRAPES_GFS operation mainly include the long-wave and short-wave radiation schemes (the rapid radiative transfer model, RRTMG) (Morcrette et al., 2008; Pincus et al., 2003), the land surface scheme (the Common Land Model, CoLM) (Dai et al., 2003), the planetary boundary layer scheme (Medium-Range Forecast, MRF) (Hong and Pan, 1996), the deep and shallow cumulus convection parameterization scheme (the New Simplified Arakawa–Schubert, NSAS) (Arakawa and Schubert, 1974; Liu et al., 2015; Pan and Wu, 1995). The cloud physics scheme includes the macro cloud scheme dealing with the condensation process under the unsaturated condition of grid-average water vapor, a double-moment cloud microphysical scheme, and a cloud cover prognostic scheme (Chen et al., 2007; Ma et al., 2018). On 1 July 2018, the GRAPES global 4D-Var data assimilation system came into operation (Zhang et al., 2019), which is called version 2.3.1 of GRAPES_GFS (abbreviated as GRAPES_GFS2.3.1). The GRAPES_GFS2.3.1 version is adopted in this research.
In this paper, GRAPES_GFS2.3.1, with the operational forecast time of 00:00 UTC on 9 August 2019, is taken as an example, and three experiments
are set up to analyze the similarities and differences in the spin-up characteristics of the model using different initial fields. The settings are
shown in Table 1. In the first experiment, the analysis field provided by the 4D-VAR assimilation analysis system in the operational forecast at
21:00 UTC on 8 August 2019 is used as the initial field to directly perform model integration forecasts, and the initial time is 21:00 UTC on
8 August. This experiment is called G21. For the second experiment, called G00, its initial field adopts 3
Model setup of three experiments used in this study.
All three experiments are based on the GRAPES_GFS2.3.1 operational model, with a horizontal grid spacing of 0.25
In addition, the cloud-field information has not been saved during the restart in the current operation. To examine its impact on the accuracy of the later forecast, this study investigates the super typhoon “Lekima” (no. 1909) that landed in China during the selected forecast period, and the forecast differences in cloud, precipitation field, and typhoon track during Lekima between G00 and G21 are analyzed.
To analyze the spin-up characteristics of GRAPES_GFS2.3.1, the initial fields in F00, G21, and G00 are used to perform the integration, and the
temporal variations of the average total WVT and TT at different heights from 00:00 to 12:00 UTC are calculated, as shown in Fig. 1. Seen from
the figure, both the WVT and TT show sharp fluctuations at the initial stage of the integration in the three experiments, especially during the first
hour. After 3–6
Time evolution of global mean of the total water vapor tendency (WVT) and total temperature tendency (TT) at different vertical levels from 0 to 12
In G21 and G00, the variations of both WVT and TT are very consistent, indicating that G00 has inherited the temperature and humidity structure
of G21 well. However, G00 still needs to go through the spin-up during which a gradually stable adjustment process follows a sharp fluctuation at the early
stage of integration; i.e., the dynamic and thermal adjustments are required to reach a statistical equilibrium state in the model. At the initial
stage of integration in G00, the variation amplitudes of WVT and TT are smaller than those in G21, but greater than those in G21 after the 3
In GRAPES_GFS2.3.1, the total temperature tendency of the model (ALL) is determined by dynamic core (DYN), radiation process (RAD), turbulent
mixing in planetary boundary layer process (PBL), cumulus convection process (CONV) and cloud physical process (CLOUD). Among them, the total
temperature tendency of all physical processes (PHY) is defined as the sum of the last four items
(PHY
Time evolution of mean water vapor tendency (WVT) of the dynamical core and each physical process at 300, 500, and 925
In summary, in the middle and upper atmosphere, the fluctuation of WVT in G21 is weaker than that in F00, indicating the advantage of using the data assimilation cycling as the initial field. Both experiments quickly reach a quasi-equilibrium state after dramatic adjustments over several integration steps. The water vapor adjustment in spin-ups mainly occurs in the lower atmosphere of the model. The difference is mainly caused by different convection schemes. At the same time, different initial fields of the temperature and humidity structure may lead to a great difference in the dehumidification ability of convection. For G00 and G21, the WVTs of the dynamic and physical processes have roughly the same characteristics. At all of the three levels, the WVTs in G00 are slightly lower than those in G21.
The same as Fig. 2 but for the results of temperature tendency. (values given in
In the middle and upper layers of the model, the dramatic change of the TT in F00 mainly occurs within the first half-hour of the integration (Fig. 3a
and d). Among all the TTs at the first integration step, the cloud physical process leads to the largest one, followed by convection process, and they
are related to the water vapor condensation process (Fig. 2a and d). For example, at 500
In G21, the TT in the middle and upper layers also experiences a dramatic adjustment in the first half-hour of the integration (Fig. 3b and e), and
the main reason for the fluctuation is the dehumidification and heating in the convection process, which is different from that in F00 caused by the
cloud physical process. The temperature increase caused by the convection process in G21 is 1 to 2.5
The characteristics of the TT variation in G00 are consistent with those in G21 (Fig. 3c, f and i). In the first few time steps, G00 also has an
adjustment process, with the adjustment amplitudes of TT close to half those in G21 at all levels. After half an hour, the temperature tends to be
relatively stable. The TT variation in G00 indicates that although G21 has undergone a 3
The comprehensive adjustment effect of the dynamic and the physical processes on the water vapor and temperature in the numerical model can be
presented by the cloud state. To reveal the dynamic and thermal adjustment processes in GRAPES_GFS2.3.1 system at the beginning of the integration
and the time required for the model to reach the statistical equilibrium state (spin-up time), this section uses the total grid number of cloud (TGNC)
in the model as the index for analyses. Although the cloud is changing locally, the total area covered by cloud can be regarded as a constant globally
on average. Therefore, TGNC is used as the analysis index, and the model is considered to have completed the spin-up when the TGNC gets relatively
stable. The total hydrometeors content (THC, THC
Vertical distribution of total number of cloud points at different forecast time simulated by F00
Distributions of all hydrometeor content at 400
Figure 4 shows the vertical distributions of TGNC at different lead times in three experiments. It can be seen that regardless of whether the
GRAPES_GFS2.3.1 model is cold-started with reanalysis data (F00, Fig. 4a) or warm-started with the 4D-VAR analysis field as the initial field (G21,
Fig. 4b), the TGNC experiences rapid generation and growth during the 3
In G00 (Fig. 4c), the growth of TGNC is found to be much slower than that in G21, especially for the TGNC of the middle and upper cloud. For example, at
3
Figure 5 shows the distributions of THC at 400
Distribution of water vapor content (WVC)
Experiments using the 4D-VAR analysis field to provide the initial field (Fig. 5e–h) show that the variation characteristics of THC at
400
Since G00 does not retain the cloud-field information after 3
To reveal the reason why the TGNC (Fig. 4) and the THC (Fig. 5) in the upper layers of the model in F00 are significantly higher than those in G21,
the difference of water vapor content and relative humidity at 400
It can be seen from Sect. 3.1 that the cloud-field information formed in the first 3
Figure 7 shows the zonal mean distributions of averaged column cloud water content (CCWC), the outgoing longwave (OLR) at the atmosphere top and the
downward longwave at ground (GDLW) level simulated by G21 and G00 from 00:00 to 03:00 UTC on 9 August 2019, as well as the distributions of difference
between them. It can be seen from Fig. 7a that the total zonal-averaged CCWC forecasted in G00 is systematically smaller than that forecasted in
G21. The areas with smaller CCWC are mainly located in the Southern Hemisphere storm track, tropical low-latitude areas, and midlatitude and
high-latitude areas in the Northern Hemisphere with active cloud. Among them, the area with the smallest CCWC is the active area of Southern
Hemisphere storm track, with the CCWC difference reaching 240
Zonal means and their differences of
The change in the calculation of the radiation flux induced by cloud would seriously affect the atmospheric temperature field and geopotential height
field. Figure 8 shows the difference distributions of the 500
Distribution of the differences (G00 minus G21) of temperature field
This section analyzes the biases of the cloud field, precipitation field, and the track of the super typhoon Lekima (no. 1909) and typhoon “Krosa” (No. 1910) in 2019 during the forecast period to evaluate the impact of the lost hydrometeor information on typhoon forecast operation in GRAPES_GFS2.3.1. During the forecast, Lekima and Krosa appear as double typhoons in the western Pacific. Lekima made landfall in northern China, while Krosa remained offshore. Since the conclusions for both Lekima and Krosa are the same, only Lekima will be presented in this study. Here, we show the impact on the cloud and precipitation of Lekima by the lost hydrometeor information on typhoon forecast operation of GRAPES_GFS2.3.1. In the last part, the path-forecast biases for the two typhoons are both given.
Time evolution of the sum of averaged column cloud water content (CCWC) and column cloud ice content (CCIC) at the typhoon Lekima region (22–34
Figure 9 shows the evolutions of the averaged CCWC and column cloud ice content (CCIC) within the main cloud area of Lekima (22–34
Distribution of the differences (G00 minus G21) of 3-hourly and 24
Figure 10 shows the difference distributions of both 3 and 24
It can be found from Fig. 10d that the lack of cloud-field information has a significant impact on the simulation of the accumulated precipitation in
the first 24
Time evolution of the forecasted track errors of G00 and G21 experiments for the typhoons Lekima and Krosa during the forecast period of 72
Figure 11 shows the forecast track evolution of Lekima and Krosa in G00 and G21 within the lead time of 72
Overall, G21 performs better than G00 in the track forecasts of Lekima and Krosa within the lead time of 72
To analyze the characteristics of the spin-up at the early stage of integration in GRAPES_GFS2.3.1, this study adopted three different initial
fields, namely the 4D-VAR analysis field (G21), the field obtained by interrupting and restarting the 4D-VAR analysis field after 3
All three experiments using different initial fields show that the spin-up of GRAPES_GFS2.3.1 has to go through two stages: the dramatic adjustment in
the initial half-hour of integration and the slow dynamic and thermal adjustment afterwards. In the middle and lower layers of the model, the spin-up
takes 6
The GRAPES_GFS2.3.1 using its own analysis field as the initial field (G21) is gentler in the water vapor and temperature adjustment in the spin-up than the GRAPES_GFS2.3.1 using FNL reanalysis data for cold start (F00), and the time required is slightly shorter. Due to the different structures of temperature and humidity in the two initial fields, the differences of physical processes in the model spin-up adjustment are obvious, especially regarding the convections and cloud physical processes. However, the differences in dynamic processes are not obvious. G00 needs to repeat the spin-up. Its dynamic and thermal adjustments are similar to that in G21. The temperature and humidity adjustment in G00 is slightly weaker than that in G21, and its spin-up is slightly shorter.
In G00, the cloud-field information is not retained during the current operation of GRAPES_GFS2.3.1. It shows that G00 significantly underestimates
the atmospheric CCWC and CCIC at the early stage of forecast, which would affect the calculation accuracy of radiation and result in systematic
positive biases in temperature and geopotential height fields at 500
Regarding the influence of the lost cloud-field information in the GRAPES_GFS2.3.1 operation on the forecast results, this paper mainly analyzes the differences of simulation results between G21 and G00, and evaluates the possible changes brought to the GRAPES_GFS2.3.1. But an in-depth analysis of how the simulation results can improve the forecast performance is absent in this paper. The reason is that the forecast biases of the numerical model result from a combination of various factors, and it is difficult to explain the improvement of the GRAPES_GFS2.3.1 forecast system just with a single case. Therefore, a batch of experiments are needed later in our future study. Since the absence of cloud-field information at a single time can bring systematic biases to the simulated temperature field and geopotential height field, in the cycling numerical forecasting operational system, the cloud-field information that has formed should be retained as much as possible. Moreover, the temperature and humidity structure in the initial field, especially the water vapor, can significantly affect the dynamic and physical processes in the numerical model. Thus, in addition to the improvement of dynamic and physical processes, more attention should be paid to the assimilation of water vapor data, to improve the data quality of water vapor in the initial field of GRAPES_GFS2.3.1.
The model simulation data used in this study are available at
ZM and CZ designed the experiments and ZM carried them out. ZM developed the model code and performed the simulations. ZM prepared the manuscript with contributions from all co-authors.
The authors declare that they have no conflict of interest.
We thank the reviewers for their thoughtful comments that helped to improve the paper. We thank Nanjing Hurricane Translation for reviewing the English-language quality of this paper.
This research has been supported by the National Key R&D Program on Monitoring, Early Warning and Prevention of Major Natural Disasters (grant nos. 2017YFC1501406 and 2017YFC1501403), the National Natural Science Foundation of China (grant nos. 41925022 and 91837204), and the State Key Laboratory of Earth Surface Processes and Resource Ecology.
This paper was edited by Olivier Marti and reviewed by two anonymous referees.