Predicting the Arrival Time of an Interplanetary Shock Based on DSRT Spectrum Observations for the Corresponding Type II Radio Burst and a Blast Wave Theory

Since fast head-on coronal mass ejections and their associated shocks represent potential hazards to the space environment of the Earth and even other planets, forecasting the arrival time of the corresponding interplanetary shock is a priority in space weather research and prediction. Based on the radio spectrum observations of the 16-element array of the Daocheng Solar Radio Telescope (DSRT), the flagship instrument of the Meridian Project of China, during its construction, this study determines the initial shock speed of a type II solar radio burst on 2022 April 17 from its drifting speed in the spectrum. Assuming that the shock travels at a steady speed during the piston-driven phase (determined from the X-ray flux of the associated flare) and then propagates through interplanetary space as a blast wave, we estimate the propagation and arrival time of the corresponding shock at the orbit of the Solar Terrestrial Relations Observatory-A (STEREO-A). The prediction shows that the shock will reach STEREO-A at 14:31:57 UT on 2022 April 19. The STEREO-A satellite detected an interplanetary shock at 13:52:12 UT on the same day. The discrepancy between the predicted and observed arrival time of the shock is only 0.66 hr. The purpose of this paper is to establish a general method for predicting the shock’s propagation and arrival time from this example, which will be utilized to predict more events in the future based on the observations of ground-based solar radio spectrometers or telescopes like DSRT.


Introduction
Coronal mass ejection (CME) is a significant solar activity phenomenon in space weather.It can rapidly eject a large amount of magnetized plasma and magnetic flux from the corona into the solar wind in a short period.During their eruptions, CMEs can travel at speeds ranging from several tens to even thousands of kilometers per second (Yashiro et al. 2004;Webb & Howard 2012), potentially carrying mass from 10 13 to 10 16 g and releasing energy from 10 27 to 10 32 erg (Vourlidas et al. 2000(Vourlidas et al. , 2010)).Their occurrence rates depend on the corresponding solar activity level (Yashiro et al. 2008;Lamy et al. 2019;Song et al. 2021;Kumari et al. 2023), which increases from roughly 0.5 day −1 during solar minimum to 6 day −1 during solar maximum (Gopalswamy et al. 2003).CMEs originate primarily near the equatorial region during solar minimum, whereas they are ejected from all latitudes during solar maximum (Yashiro et al. 2004).When a CME propagates into the solar wind, it becomes an interplanetary CME (ICME; Light et al. 2020).As a manifestation of CMEs in interplanetary space, ICMEs are among the most significant sources of influence on the environment of Earth (and also other planets) and the nearby space.If the velocity of the ICME relative to the surrounding solar wind is higher than the plasma's characteristic speed, it will produce an interplanetary shock at the leading edge of the ICME (Cane et al. 1987;Ramesh et al. 2022).Fast ICMEs and their associated interplanetary shocks have the potential to accelerate solar energetic particles (Mondal et al. 2021) and cause severe disturbances and hazards to the Earth's space environment.When these shocks interact with the Earth's magnetosphere, they will compress the dayside magnetosphere, expose the spacecraft in the magnetosphere directly into the solar wind, and threaten spacecraft operations and astronaut safety.Furthermore, the compression generated by shocks can increase the southward magnetic field in ICMEs (Shen et al. 2021), which in turn amplifies their geomagnetic effects significantly (Wang et al. 2003;Xu et al. 2019).As a consequence, their combination can cause severe geomagnetic storms (Gómez et al. 2020) and lead to a series of follow-on effects in the Earth's radiation belts, ionosphere, up atmosphere, and so on.Thus, predicting the arrival time of interplanetary shocks is a primary task in space weather research and forecasting.
Currently, numerous models have been established to predict the arrival time of shocks.Generally speaking, these models can be divided into five categories: empirical models, drag-based models, shock-based models, magnetohydrodynamic models, and machine-learning models (Siscoe & Schwenn 2006; Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Zhao & Dryer 2014;Vourlidas et al. 2019).The shock-based models are the ones that pay more attention to the shock propagation theory.The shock time of arrival (STOA) model is one of the earliest developed and most widely used shock-based models (Dryer 1974;Dryer & Smart 1984;Smart & Shea 1985).This model utilizes type II radio bursts accompanied by solar flares for acquiring the initial speed of shocks from the frequency drift rate of the corresponding type II radio burst.Subsequently, the evolution mode of the shock speed is established to calculate the arrival time of the shock at Earth.It assumes that solar eruptions, like explosions from a single point source, will generate shocks.Shocks travel at a constant speed during the piston-driven phase before propagating outward as a blast wave.The velocity of the shock decays as ~- V R 1 2 in relation to the propagation distance R after the piston-driven phase.The influence of the wave's propagation direction with respect to the radial direction on the corresponding shock's arrival is considered in the STOA model.The STOA-2 model (Moon et al. 2002) is an updated version of the STOA model with refinements made in the relationship between shock velocity and distance.According to the STOA-2 model, the shock velocity decays according to a power law V ∼ R − N with the deceleration exponent determined by the initial shock velocity V is , i.e., N = 0.05 + 4 × 10 −4 V is .The STOA-2 model successfully eliminated some systematic dependence of the prediction error on the initial shock velocity revealed in the original STOA model used by Smith et al. (2000), decreased the number of events with prediction errors exceeding 20 hr from five to two, and reduced the rms error from 15.2 to 13.2 hr (Moon et al. 2002).The models of STOA and STOA-2 set a benchmark in predicting the interplanetary shock's propagation by blast-wave models.
CMEs are observed through coronagraphs as two-dimensional representations on the plane of the sky of the actual three-dimensional structures (Burkepile et al. 2004;Schwenn et al. 2005;Vršnak et al. 2007;Balmaceda et al. 2018).Consequently, the velocity of CMEs is usually underestimated due to the projection effect (Burkepile et al. 2004;Temmer et al. 2009).Previous attempts have tried to address the projection effect on the plane of the sky by utilizing simple geometric shapes (Leblanc et al. 2001;Michałek et al. 2003;Thernisien et al. 2006;Howard et al. 2008).However, the corrected speed could be overestimated, which often led to numerous CME events surpassing 3000 km s −1 or even reaching beyond 5000 km s −1 (Howard et al. 2008).Although the multiviewpoint observations or three-dimensional modeling can correct the projection effect (Liu et al. 2010;Lee et al. 2015;Wood et al. 2017;Balmaceda et al. 2018), these findings are limited to large or halo CMEs and are not based on a substantial number of events.Furthermore, the corrected CME velocity has not significantly improved the prediction accuracy of arrival times (Paouris et al. 2021).
Solar radio observations provide an additional approach for solar eruptions and their associated physical processes.Solar radio bursts are the intense solar radio emission in the radio wave range (McCready et al. 1947).Solar type II radio bursts appear as narrowband signals with slow frequency drifts in the dynamic solar radio spectra (Vršnak 2021).The spectral features of type II bursts are slow drifting in frequency lasting about 5 to 15 minutes.The structures of type II bursts usually consist of both fundamental (F) and harmonic (H) bands.The H frequency is approximately twice the F frequency (Vršnak et al. 2001).It is commonly thought that type II bursts are caused by plasma radiation, which is triggered by electrons that have been accelerated by shocks (Ma & Chen 2020; Ramesh et al. 2022;Hou et al. 2023;Koval et al. 2023).The radiation frequency of the F band is the local plasma frequency.Type II radio bursts are an important indicator to determine whether shocks driven by CMEs have been generated (Maguire et al. 2020;Chernov & Fomichev 2021).In combination with the appropriate coronal density model, the frequency drift rate of type II radio bursts can be used to estimate the corresponding shock's propagating speed (Vršnak et al. 2004).Especially, the shock speed obtained in this way would have less projection effect than that obtained in the while light coronagraph observations.This paper will establish a new method for predicting the arrival time of interplanetary shocks based on the spectrum observations of type II radio bursts.The Daocheng Solar Radio Telescope (DSRT), the iconic instrument of the Meridian Project of China, will observe solar radio emissions in both the spectrum and imaging with a working frequency of 150-450 MHz (Yan et al. 2023).DSRT was designed to be a circular array of 1 km diameter with 313 element antennas of 6 m aperture.With construction starting in 2019, a 16-element array had been finished along the circle in 2022 March.Then it recorded a type II radio burst on 2022 April 17.We will derive the initial shock speed directly from DSRT's spectral observations and apply it to the shock propagation theory to predict the corresponding shock's propagation and arrival time.The predicting method derived in this way is also applicable to other solar radio spectrometers or telescopes like DSRT.

Radio Spectrum and Measurements
The solar radio data used in this study were obtained during the construction period of DSRT on 2022 April 17.The soft X-ray flux data regarding flares in the 1.0-8.0Å band was obtained from the series of Geostationary Operational Environmental Satellites (GOES), which are operated by the National Oceanic and Atmospheric Administration (NOAA) of America. 7The solar wind and interplanetary magnetic field data observed by the Solar Terrestrial Relations Observatory-A (STEREO-A) satellite came from the STEREO database in the Coordinated Data Analysis Web (CDAWeb). 8The IDL program SSW_PLOT_WHERE.PRO in the SolarSoftware (SSW) package provides the relative positions between the STEREO satellites, the Sun, and the Earth.
Figure 1 is the radio spectrum observed by DSRT for the type II radio burst on 2022 April 17, together with the definitions of the lead edge, peak, and lag edge of the spectrum and the heliocentric distances of the radio source plotted versus time for the three strips.Figure 1(a) displays the dynamic radio spectrum from 03:27 to 03:38 UT.This event should be the first solar radio burst recorded by DSRT during its construction.Starting roughly from 03:28:15 UT at 420 MHz for the H band, this burst manifests as a fast frequency drifting and presents more features like type III bursts at the initial stage.However, for a frequency lower than 300 MHz, especially below 270 MHz, the drifting speed became evidently slow.Taking the lag edge, for example (red dots; defined in the following text), the frequency decreased from 269 MHz at 03:28:46 UT to 151 MHz at 03:31:33 UT.The average drifting speed is −0.707MHz s −1 , which is consistent with the frequency drift rate of a type II burst across the dynamic spectrum 1985).What is more, the F band appeared during this period, which has a frequency ratio of ∼0.5 with the H band.Although the whole burst might be a mixture of multiple kinds of bursts (II, III), this study concerns only the burst's characteristics in the frequency range of 150-270 MHz because it was a clear type II burst at these frequencies.The horizontal black band around 365 MHz in the spectrum is due to the noise-suppressed measurements adopted by DSRT at this interval.The horizontal white dashed line indicates the frequency sample of 231 MHz at which we will demonstrate the variations of the flux density along time.
As an example, Figure 1(b) shows the flux density (black solid line) versus time at a fixed frequency of 231 MHz.The onedimensional Gaussian fit to the flux density is shown as the red solid line.The vertical lines in red, blue, and yellow denote the lag time t l , peak time t c , and lead time t u of the spectrum, respectively; they represent the lag edge, peak, and lead edge of the H branch at a fixed frequency of 231 MHz for this type II radio burst event.
Here, the peak time t c corresponds to the peak location of the Gaussian fit.The lag and lead times t l and t u are obtained by identifying a percentage value of the Gaussian fit peak.The specific percentage values are selected to be consistent with the front and back edges of the H branch seen by the naked eye on the spectrum and found to be 5%-40% in this study.For this event, the lead edge is located where the rapid descent ends, the peak refers to the largest main peak in the spectrum, and the lag edge is usually around a small isolated peak lagging the main body of the spectrum (see Figure 1(b)).In the same way, we can calculate the peak time t c , lag time t l , and lead time t u for each frequency f i (where i is the index of the data points).There are 1730 frequencies from 140 to 403 MHz with a frequency resolution of 0.152 MHz.In order to get three smooth branches (lag, peak, and lead) of this spectrum, we compute the running averages of t l , t c , and t u between adjacent frequencies.Finally, we extract at 2 MHz intervals between 151 and 269 MHz and obtain 60 sets of (t li , t ci , t ui ) with 1 i 60.These three edges derived in this way are shown in Figure 1(a).Here, the lag edge, peak, and lead edge of the spectrum are indicated as the red, blue, and yellow dots, respectively.Figure 1(a) also displays the error bars of these three strips.Here, the error bars are calculated as the characteristic scale in frequency of the strip.For the peak and lag edge, this characteristic scale is the FWHM of the peak in the 1D Gaussian fit along the frequency, while for the lead edge, this characteristic scale refers to the scale of the transition region from the flux's sharp decrease to the platform of low variations ahead of the radio burst.
Type II radio bursts gradually shift from high to low frequencies in the radio dynamic spectrum (Vršnak et al. 2002), and the drift rate slows down as the frequency decreases.The relationship between the frequency of plasma radiation f and the electron density n is = ´f . Here a is the harmonic number, a = 1 represents the F band, and a = 2 denotes the H band; f is in KHz, and n is in cm −3 .In this paper, the H band of the type II radio bursts is evidently stronger than the F band, and all our analyses are carried out on the H band. Therefore, we set a = 2 in the following calculations.
The coronal density model provides a relationship between the radiation frequency of type II radio bursts and the height or location of shocks in the corona.Saito et al. (1977) introduced a coronal density model,

= ´´+
´- where n represents the electron density in cm −3 units, r denotes the distance from the Sun in units of solar radius (R s ), and N is the multiplicative factor, which is often taken to be 10 for the active region corona and 3 for the quiet corona.We need to remember that this density model is only applied to the low corona within 5.5 R s (Saito et al. 1977).In this study, we attempt to put forward an empirical method for determining the factor of N in the Saito density model.First, we try each value of N from 3 to 10 and compute the radial distances (with errors derived from the frequency error) of the spectrum's peak strip based on the coronal density models with different N.Then, a line fitting to these radial distance-time (r-t) points would yield the average speed with an error bar, which is the shock's initial propagation speed derived from the peak drifting (abbreviated as V peak ).The speed error bar is computed from the distance error.Figure 2 shows the variations of V peak along N. The average V peak is 1139 km s −1 , as shown by the horizontal dotted line, and the corresponding matching N for this average V peak is N = 6.2, as shown by the vertical dashed line.On the other hand, the average of these N is 6.5, which is shown as the vertical dashed-dotted line.The median location between these two vertical lines (N = 6.2 and 6.5) yields N = 6.35, i.e., the red vertical solid line in Figure 2, which we think would reflect the overall average effects after taking into account both densities and speeds derived from the model.Therefore, we adopt N = 6.35 for the corona density model, i.e., Equation (1), in this study.
After the density model is settled, we can determine the height or radial distance in the corona where the shock occurs.We compute the radial distances for the lag edge, peak, and lead edge in the frequency range of 151-269 MHz. Figure 1(c) displays the variations of these heliocentric distances plotted versus time.The red, blue, and yellow points denote the heliocentric distances for the lag edge, peak, and lead edge of the spectrum, respectively.A line fitting to these r-t points would yield the average speeds for them, which are v lag = 1159 ± 26 km s −1 for the lag edge, v peak = 1146 ± 48 km s −1 for the peak, and v lead = 1171 ± 43 km s −1 for the lead edge.Figure 1(c) also shows the error bars of these heliocentric distances, which are derived from the frequency error bars of the strips (lag edge, peak, and lead edge).
We can see that the derived speeds for these three strips are very close, and the differences between them could be neglected.Considering the fact that the peak strip stands for the radiation center of the radio signals, we take v peak = 1146 ± 48 km s −1 as the initial shock speed in its radial direction associated with this type II burst.The start moment for the peak strip in the spectrum is t peak0 = 03:29:56 UT, which is believed to be the initial time of the shock.The corresponding initial position, r peak0 = 1.29 R s , can be obtained from Figure 1(c).

Blast-wave Model
Cavaliere & Messina (1976) studied the self-similar solutions for the shock propagation through different density profiles.According to their theory, the speed of the fast blast wave decays as t -( ) t 1 3 when the density decreases as r −2 .Here, the constant τ is the duration time of the initial blast.This r −2 decreasing of the solar wind density is a good approximation in the far-Sun region (Parker 1960).After that, the shock starts to decrease.Furthermore, Pinter & Dryer (1990)   2) for this average V peak .The vertical dasheddotted line represents the average value (6.5) of these N (from 3 to 10), and the red vertical solid line represents the N = 6.35 adopted in this study, which is the median location between N = 6.2 and 6.5.
these studies led to an approximate analytic solution for the speed of an interplanetary blast wave along time t: Here v 0 is the initial shock speed lasting from t = 0 to t = τ (piston-driven phase), and w sw is the background solar wind speed.That is, the shock propagates at a constant speed during the piston-driven phase.After that, the shock decelerates as a blast wave with its speed decaying as t - ( ) . By integrating Equation (2) over time, the leading front position of the blast wave can be expressed as where r 0 is the integral constant associated with the initial position of the shock front (at t = 0).Then, the kinematic process of the shock in the interplanetary space can be predicted.

Effect of the Propagation Direction
The shock-front shape and the propagation direction also contribute to its arrival time.In the models of STOA and STOA-2, the shock speed at an angle θ from the flare radial direction is assumed to be R where V R is the the wave speed along the flare radial direction, and V θ is the the shock-front speed at an angle θ from the flare radial direction (Smart & Shea 1985).Zhao & Feng (2014) studied 551 solar disturbance events of solar cycle 23 and found that the effect of propagation direction could be expressed as This relation was adopted in their developed SPM2 model to transform the shock-front speed in its main propagation direction to the expected front speed along the target direction.In this study, we will adopt Equation (5) to account for the angle of the shockwave propagation with respect to its radial direction.

Inputs and Forecast of the Model
To sum up, the input parameters for the prediction model developed in this study include the initial shock speed v 0 and initial shock location r 0 at the start time t 0 , the shock propagation angle θ with respect to its radial direction, the background solar wind speed w sw , and the duration time τ.For this event, we take t 0 = t peak0 = 03:29:56 UT on 2022 April 17, with r peak0 = 1.29 R s .We take the start time of the peak strip as the initial time of the shock.Although the start of the lag edge (t lag0 = 03:28:46 UT) is a little earlier than this moment, their difference is only 1.17 minutes.Here, θ is the angle between the shock normal direction and the target direction along which we want to make predictions.Figure 3 depicts the relative locations of the Sun (yellow circle), the Earth (green circle), and the STEREO satellite (red circle for STEREO-A and blue circle for STEREO-B) at the moment of 03:29:56 UT on 2022 April 17.The black arrow marks the normal direction of the solar source (N12E88) of the associated active region for this radio burst and indicates the corresponding shock's normal propagation direction.It is apparent that the shock originated from the eastern limb of the Sun and propagated far away from both STEREO-B and the near-Earth satellites.STEREO-A turns out to be the closest satellite along its propagation direction.Therefore, we will predict the shock's propagation along the direction from the Sun to STEREO-A and check the in situ observations of the STEREO-A satellite to determine whether and when the interplanetary shock would reach it.
The heliographic longitude and latitude of STEREO-A are −32°.14and −7°.24 at the moment of the radio burst.From the  R S .The remaining unknown input parameters are w sw and τ.The in situ observations at STEREO-A give w sw = 430 km s −1 at the start time of the radio burst.The duration time τ is often estimated from the X-ray flux of the associated flares (Dryer & Smart 1984;Smart & Shea 1985).The same as previous studies, we take τ as the lasting time of the X-ray flux higher than 0.5 times the log of the maximum flux above the pre-event background.This burst is associated with an X1.1 solar flare starting at 03:17:00 UT and ending at 03:51:00 UT on 2022 April 17. Figure 4 displays the soft X-ray flux variations observed by the GOES 12 satellite for this flare.The red curve illustrates the soft X-ray flux in the 0.5-4.0Å band, whereas the blue curve represents the soft X-ray flux in the 1.0-8.0Å band.In the 1.0-8.0Å band, the lower horizontal black solid line represents the stable pre-event background flux level.Meanwhile, the upper horizontal black solid line represents the maximum flux.The middle horizontal black solid line indicates that the soft X-ray flux has decreased to 0.5 of the log of the maximum flux above the pre-event background.Finally, the cyan double-headed arrow illustrates the duration time of τ = 1.23 hr.
Inputting v 0 , r 0 , t 0 , w sw , and τ into the blast-wave model (Equations ( 2) and (3)), we can obtain the predicted kinematic process of the shock.Figure 5 displays the trajectory of the shock as it propagates through interplanetary space along the Sun-STEREO-A direction.The upper panel indicates the heliocentric distances of the shock along time, while the lower panel shows its propagation speeds along time.The shock maintained a constant speed during the piston-driven phase with the propagation distance changing linearly with time (red sections of curves).After that, the shock propagated as a blast wave in interplanetary space; its propagation speed decreased gradually with time, and the corresponding propagation distance increased nonlinearly (black sections of curves).As shown in the upper panel, the red diamond denotes the initial position of the shock (r 0 ), while the red triangle shows that the blast wave reached the STEREO-A satellite orbit by prediction.In the lower panel of Figure 5, the red square represents the initial velocity of the shock (v 0 ), while the red circle displays the propagation speed of the shock at the distance of STEREO-A.The model predicted that the shock would reach the STEREO-A satellite orbit at 14:31:57 UT on 2022 April 19 with a total transit time of 59.03 hr.The shock's propagation speed at the STEREO-A orbit predicted by the model was 598 km s −1 .

Validation of In Situ Observations
Figure 6 displays the magnetic field and plasma data observed by STEREO-A during 2022 April 18-20.The panels from top to bottom are the magnetic field magnitude (B T ), the three magnetic components (B r , B t , and B n in RTN coordinates), the magnetic field elevation angle (θ B ), the magnetic field azimuthal angle (j B ), the solar wind bulk speed (V p ), the proton temperature (T p ), the proton number density (N p ), the solar wind dynamic pressure (P dy ), the total pressure (P t ), and the plasma beta (β).The red solid line denotes the arrival of the shock at the STEREO-A satellite orbit at 13:52:12 UT on 2022 April 19 as observed by STEREO-A.At this moment, parameters including B T , V p , T p , N p , P dy , and P t present a sharp rise, indicating a fast forward interplanetary shock.
However, we need to clarify the relationship between this interplanetary shock at STEREO-A and the solar radio burst studied here.We check all CMEs recorded by SOHO/LASCO from 2022 April 16 to 189 and find only three candidate CMEs: CME1 (2022 April 16 10:00:05 UT), CME2 (2022 April 17 03:48:05 UT), and CME3 (2022 April 17 16:24:06 UT).The other CMEs are both narrow (angular width <90°) and slow (linear speed <600 km s −1 ).CME1 was a western limb CME with a central position angle at 272°.Therefore, this CME would not hit STEREO-A due to the large angular separation between them (probably exceeding 120°).CME2 was associated with our studied solar radio burst here.CME3 originated southwest of the Sun with a central position angle of 208°, and the associated solar flare was located at S30W67.Therefore, the angular separation between the main propagation direction of CME3 and STEREO-A would exceed 100°, leading to a miss of STEREO-A, too.What is more, if this was the CME causing the shock on April 19 at STEREO-A, then the transit time was 45.47 hr (from April 17 16:24:06 UT to April 19 13:52:12 UT).The average propagation speed from the Sun to STEREO-A would be 914 km s −1 , which was much larger than the CME's speed observed by SOHO/LASCO (575 km s −1 ).Besides these, the April 19 shock at STEREO-A was not caused by the corotating interaction region as seen from Figure 6.In a word, the radio burst we studied here, associated with CME2, is the only potential "culprit" for the interplanetary shock detected by STEREO-A at 13:52:12 UT on 2022 April 19.
Our prediction, based on a combination of spectral observations of type II radio bursts and blast-wave theory, indicates that the shock will reach the STEREO-A satellite orbit at 14:31:57 UT on 2022 April 19, shown as the blue dashed line in Figure 6.Our prediction is only 0.66 hr later.No obvious ICME signatures, e.g., enhanced helium abundance, depressed proton temperature, and smooth strong magnetic fields, were observed during this time interval.It is likely that the main body of the corresponding ICME missed STEREO-A due to the large angular separation between them.

Conclusion
In this research, we studied a complex type II radio burst on 2022 April 17 based on the spectrum of the 16-element array of the DSRT, the iconic instrument of the Meridian Project of China.The primary results are as follows.
1. Based on the drifting speed of the spectrum of this type II radio burst and an appropriate coronal density model, we estimated the initial propagation speed for the type II burst-producing shock in the radial direction, which was 1146 ± 48 km s −1 for this event.2. Then a blast-wave model was adopted to predict the propagation of the corresponding shock in interplanetary space along the STEREO-A direction.The model predicted that the shock would reach the STEREO-A satellite at 14:31:57 UT on 2022 April 19, which was only 0.66 hr later than the in situ recorded shock arrival of STEREO-A.
Through this case study, we have established a general prediction method for the interplanetary shock's propagation and arrival time in the heliosphere.The DSRT had completed the preliminary construction and began normal observations since 2023 September.More and more radio bursts will soon be observed by this world-leading solar radio telescope.The derived prediction model has great potential to be tested and trained by a large number of cases and finally developed to be an automatic data-driven predicting model for type II burstproducing interplanetary shocks based on the real-time data streaming of DSRT.

Discussions
The observation of type II radio bursts in radio spectra serves as a crucial tool in determining the generation of CME-driven shocks, as well as tracing their movement and propagation in the space between the Sun and the Earth.Solar radio observations are a very useful complement to white-light observations.In this sense, studying the frequency spectra of type II radio bursts can significantly enhance the ability to predict and alert against disastrous space weather effects related to solar and interplanetary shocks.
Previous studies indicated that type II radio bursts may originate from both the leading edge and the area of the interaction front between the flanks of a CME-driven shock and the coronal streamer (Cho et al. 2008;Majumdar et al. 2021;Koval et al. 2023).Coronal streamers not only contribute to the generation of type II radio bursts but also affect the morphology of type II radio bursts in the dynamic spectrum during the shock propagation (Feng et al. 2012;Kong et al. 2012), which would lead to errors in the spectrum fitting.Furthermore, the spectrum itself lacks the directional information of propagation about the associated shock.This will be compensated for by the radio imaging observations, which are the biggest advantage of DSRT after its construction.Furthermore, the background solar wind velocity stated in this paper is a constant value.The model can be improved by taking into account the radial variations of the background solar wind speed, which is also the goal of the next attempt.

Figure 1 .
Figure 1.(a) Dynamic radio spectrum of the 2022 April 17 type II radio burst observed by DSRT with the lag edge (red dots), peak (blue dots), and lead edge (yellow dots) of the spectrum.(b)The lag edge, peak, and lead edge of the spectrum at a fixed frequency of 231 MHz determined by a one-dimensional Gaussian fit along time for the H branch of this radio burst.The peak time, lag time, and lead time at the sample frequency are represented by t c , t l , and t u , respectively.(c) The heliocentric distances and their error bars of the radio source plotted vs. time for the three strips (lag edge, peak, and lead edge) of the radio burst spectrum together with the corresponding initial shock speeds derived from the spectrum drifting.
investigated the effect of the background solar wind speed w sw on the shock's propagation.As pointed out by Corona-Romero et al. (2015),

Figure 2 .
Figure2.The derived initial shock speeds with error bars based on the drifting of the peak strip in the spectrum (V peak ) plotted vs. different values of N in the Saito density model.The horizontal dotted line denotes the average of V peak , and the vertical dashed line is the matching N (6.2) for this average V peak .The vertical dasheddotted line represents the average value (6.5) of these N (from 3 to 10), and the red vertical solid line represents the N = 6.35 adopted in this study, which is the median location between N = 6.2 and 6.5.

Figure 3 .
Figure 3.The relative locations of the Sun (yellow circle), the Earth (green circle), and the STEREO satellites (red and blue circles) on 2022 April 17.The black arrow indicates the source location and the propagation direction of the shock.Figure 4. The soft X-ray flux variations of the X1.1 solar flare on 2022 April 17 observed by the GOES 17 satellite.

Figure 4 .
Figure 3.The relative locations of the Sun (yellow circle), the Earth (green circle), and the STEREO satellites (red and blue circles) on 2022 April 17.The black arrow indicates the source location and the propagation direction of the shock.Figure 4. The soft X-ray flux variations of the X1.1 solar flare on 2022 April 17 observed by the GOES 17 satellite.

Figure 5 .
Figure5.The kinematic process of the shock wave along the Sun-STEREO-A direction predicted by the blast-wave model.Shown are the shock's heliocentric distances plotted vs. time (upper panel) and its propagation speeds vs. time (lower panel).The red sections of the curves denote the piston-driven phase, and the black sections denote the blast-wave deceleration phase.The red diamond denotes the initial position of the blast wave (r 0 ), and the red square represents the initial velocity of the blast wave (v 0 ).The red triangle denotes the shock's arrival at STEREO-A, and the red circle represents the corresponding shock's propagation speed at STEREO-A.

Figure 6 .
Figure 6.Interplanetary and solar wind parameters from the instruments on STEREO-A from 2022 April 18 to 2022 April 20.The blue dashed line denotes the predicted arrival time of the shock at STEREO-A (i.e., 14:31:57 UT on 2022 April 19), and the red solid line denotes the actual arrival time of the shock (13:52:12 UT on 2022 April 19).