Solar Wind Driven from GONG Magnetograms in the Last Solar Cycle

In a previous study, Huang et al. (2023) used the Alfven Wave Solar atmosphere Model (AWSoM), one of the widely used solar wind models in the community, driven by ADAPT-GONG magnetograms to simulate the solar wind in the last solar cycle and found that the optimal Poynting flux parameter can be estimated from either the open field area or the average unsigned radial component of the magnetic field in the open field regions. It was also found that the average energy deposition rate (Poynting flux) in the open field regions is approximately constant. In the current study, we expand the previous work by using GONG magnetograms to simulate the solar wind for the same Carrington rotations and determine if the results are similar to the ones obtained with ADAPT-GONG magnetograms. Our results indicate that similar correlations can be obtained from the GONG maps. Moreover, we report that ADAPT-GONG magnetograms can consistently provide better comparisons with 1 AU solar wind observations than GONG magnetograms, based on the best simulations selected by the minimum of the average curve distance for the solar wind speed and density.

Accurately predicting the solar wind distribution at various locations in the heliosphere is one of the major objectives in the solar and heliosphere community, as well as the space weather community.The background solar wind plays a crucial role in determining the strength and arrival time of various drivers of space weather events, e.g., Coronal Mass Ejections (CMEs), Solar Energetic Particles (SEPs) and co-rotating interaction regions (CIRs).CIRs or CMEs can cause large geomagnetic disturbances (geomagnetic storms) that threaten advanced technology that we are highly reliant on.For example, the 1989 geomagnetic storm caused a widespread effect on the power grid system including a blackout of the Hydro-Québec system (Boteler 2019).
The photospheric magnetic field is the primarily used observational input for solar wind models.
There are two major types of observational products: synoptic magnetograms, which reconstruct the map from 27-day of magnetic field observations with some simple weighting factors (e.g., the Global Oscillation Network Group (GONG, Harvey et al. 1996) uses cos 4 of longitude) to ensure measurements taken at a particular time contribute most to that Carrington longitude in the synoptic map; and synchronic magnetograms, which take the photospheric magnetic field observations and apply surface flux transport models to simulate the evolution of the surface magnetic field while assimilating new observations.There are different observational sources used in both types of magnetograms, e.g., the Helioseismic Magnetic Imager (HMI, Schou et al. 2012) on the Solar Dynamics Observatory (SDO), the Michelson Doppler Imager (MDI, Scherrer et al. 1995) on the Solar and Heliospheric Observatory (SoHO), the GONG, the Mt.Wilson Observatory (MWO, Ulrich et al. 2002), the Synoptic Optical Long-term Investigations of the Sun (SOLIS, Keller et al. 2003) at the National Solar Observatory (NSO), and the Wilcox Solar Observatory (WSO, Babcock 1953;Scherrer et al. 1977).Also, there are different flux transport models, e.g., the Air Force Data Assimilative Photospheric flux Transport (ADAPT, Hickmann et al. (2015)), the Advective Flux Transport (AFT, Upton & Hathaway (2014b,a)), and the Lockheed Martin flux transport model (Schrijver & De Rosa 2003).
The input magnetogram has a strong impact on the simulated solar wind.Gressl et al. (2014) used four different magnetograms (MDI, NSO, MWO and GONG) to simulate the solar wind and showed that the choice of the synoptic map for the solar wind models significantly affects the model performance.Jian et al. (2015) compared multiple coronal and heliospheric models and different magnetograms and arrived at similar conclusions.Recently, Sachdeva et al. (2019) used the Alfvén Wave Solar atmosphere Model (AWSoM) to simulate solar minimum conditions and they noticed that the simulated solar wind based on the ADAPT-GONG magnetogram agrees better with observations, than the GONG magnetogram when all other model parameters are kept the same.Jin et al. (2022) assessed the influence of input magnetic maps on modeling the solar wind and concluded that it is important to consider the model uncertainty due to the imperfect magnetic field measurements.Sachdeva et al. (2021); Sachdeva et al. (2023) used AWSoM to simulate solar maximum conditions with different input magnetograms, and confirmed that the simulated solar wind at 1 AU can be very different when different input magnetograms are used.
In this study, we will expand our previous work (Huang et al. (2023), Paper I, hereafter) by simulating the solar wind using GONG magnetograms, for the same Carrington rotations that Paper I studied using ADAPT-GONG magnetograms.We then investigate how GONG maps affect the simulated solar wind at 1 AU during different phases of the last solar cycle.Both ADAPT-GONG and GONG magnetograms are widely used as the input magnetic field map for solar wind modeling.They take the same observations but construct the maps using different techniques.ADAPT-GONG applies the ADAPT surface flux transport model while GONG takes simple weighting factors.Systematically evaluating the model performance when driven by the two different maps can provide insights if a particular type of map provides better simulated solar wind, which is critical for real-time solar wind prediction.We will use AWSoM (Sokolov et al. 2013;van der Holst et al. 2014;Sokolov et al. 2021) to simulate the steady-state background solar wind.AWSoM is one of the widely used solar wind models in the community.It is open-source on GitHub (https://github.com/MSTEM-QUDA/SWMF)and can also be accessed via the runs-on-request service provided by the Community Coordinated Modeling Center (CCMC).AWSoM has been extensively validated with in-situ and remote observations under different solar wind conditions (Jin et al. 2012;Oran et al. 2013;Sachdeva et al. 2021;Huang et al. 2023;Szente et al. 2022Szente et al. , 2023)), as well as at different heliocentric distances including Parker Solar Probe locations (van der Holst et al. 2019(van der Holst et al. , 2022)).

METHODOLOGY
AWSoM is implemented in the BATS-R-US (Block Adaptive Tree Solar Wind Roe-type Upwind Scheme) code (Groth et al. 2000;Powell et al. 1999) within the Space Weather Modeling Framework (SWMF) (Tóth et al. 2005(Tóth et al. , 2012;;Gombosi et al. 2021).The main input of the model is the observed radial component of the photospheric magnetic field, a magnetogram, at the inner boundary.The density and temperature at the inner boundary are uniformly specified as n = 2 × 10 17 m −3 and T = 50, 000 K. AWSoM assumes that the pressure gradient and the nonlinear dissipation of the Alfvén wave turbulence are the only sources for accelerating and heating the solar wind, respectively.At the outer boundary, AWSoM applies a zero gradient condition allowing the super-fast magnetosonic solar wind to freely leave the domain.In depth discussions of the physics can be found in Sokolov et al. (2013);van der Holst et al. (2014van der Holst et al. ( , 2022)).
Significant progress has been made in understanding how the input parameters of AWSoM affect the simulation results recently.Jivani et al. (2023) used uncertainty quantification to study the effect of using different model parameters and determined the three major parameters impacting the simulated output.These are the Poynting flux parameter, associated with the energy input at the inner boundary for heating the corona and driving the solar wind; the perpendicular correlation length parameter, associated with how solar wind plasma gains energy from the Alfvén wave turbulence in the simulation domain; and the multiplicative factor for the input magnetogram, which is related to the uncertainty of the magnetic field observations.Paper I focused on the variation of the optimal value for the Poynting flux parameter in the last solar cycle and determined that it is linearly correlated with the area of the open field regions and anti-correlated with the average unsigned radial component of the magnetic field.
In this study, we apply the same approach as Paper I. We simulate the same Carrington rotations as Paper I, which are listed in Table 1, so that we can have a direct comparison between simulation results using the ADAPT-GONG and GONG maps.The ADAPT-GONG magnetograms are available at https://gong.nso.edu/adapt/maps/gong, and the GONG magnetograms can be accessed on https://gong.nso.edu/data/magmap/.We apply a similar approach as in Paper I and vary the the Poynting flux parameter between 0.3 and 1.2 MWm −2 T −1 with every 0.05 MWm −2 T −1 , except for two rotations, CR2137 and CR2198, in which the optimal values are outside the typical range.For Table 1.All the ADAPT-GONG and GONG magnetograms used in this study.For all the ADAPT-GONG maps, the 7th realization is picked as mentioned in Paper I.
to 5000 CPU hours (1120 cores running for about 3.5-4.5 hours) for the Intel 8280 "Cascade Lake" type CPU, leading to a total cost of about 800K CPU hours.
We use the curve distance, introduced by Sachdeva et al. (2019), between the simulation output and in situ observations at 1 AU to quantify the model performance.We select the optimal value of the Poynting flux parameter when the average of the curve distances of the solar wind density and velocity reaches its minimum, the same as Paper I.

SIMULATION RESULTS
For clear one-to-one comparisons between the current study and our previous results using ADAPT-   The simulated solar wind becomes unphysical when the Poynting flux parameter is larger than a certain value for a CR2137 (near solar maximum).The threshold is around 0.7 MWm 2 T −1 in this study, slightly smaller than the 0.75 MWm 2 T −1 for the ADAPT-GONG magnetogram in Paper I.
We also identify a monotonic increase of the distance when the Poynting flux parameter is smaller or larger than the local optimal value, except for the distance value plot for the solar wind bulk velocity for CR2106 in Panel (a).The curve distance for the solar wind bulk velocity for CR2106 is monotonically declining.It is unclear if it has reached its minimum yet.But because we select the optimal value based on the average of the velocity and density curve distances, the optimal value is already identified.To save computational cost, we do not extend the range of Poynting flux parameter for this rotation to confirm if the distance for the velocity will increase after it reaches its minimum.The monotonic trend is also identified in Paper I, which again suggests that the selection of the optimal value is reliable.Moreover, compared to the ADAPT-GONG results reproduced from Paper I, we notice larger curve distances when GONG magnetograms are used, which is consistent with the discussion above.
In order to better quantify the differences between the curve distances obtained from ADAPT-GONG and GONG magnetograms, we list the minimum values of the average distance of the solar wind density and bulk velocity in Table 2.We confirm that for most of the rotations in the study (8 out of 9), the optimal runs based on ADAPT-GONG magnetograms give smaller minimum distance values than the GONG magnetograms, with only one exception for CR2154 when the GONG magnetogram provides a slightly better result than the ADAPT-GONG magnetogram.field regions is found to be 52.5 ±14.26 Wm −2 , while it is 47.42 ±13.12 Wm −2 for the ADAPT-GONG magnetograms in Paper I. They are essentially the same within the range of the standard error.To conclude, our study confirms that this behavior (small variations in the average deposition rate over time) is also valid when using the GONG magnetograms as the input for AWSoM.

SUMMARY AND DISCUSSIONS
We use the GONG magnetograms to simulate the background solar wind with AWSoM in the last solar cycle.We simulate the same Carrington rotations and follow the same methodology as described in Paper I. We only change the values of the Poynting flux parameter and use the default values for all other parameters.We also apply the same criteria in selecting the optimal Poynting flux parameter: the minimum value of the average of the curve distances between the simulated and observed density and the solar wind bulk velocity at 1 AU.This provides a direct comparison between simulations using ADAPT-GONG and GONG magnetograms, respectively.
There are several similarities between the results obtained from ADAPT-GONG magnetograms and We notice that simulated solar wind driven by the ADAPT-GONG magnetograms generally agrees better with OMNI data at 1 AU than the results driven by GONG magnetograms.For example, exception could be due to the more complicated flux transport process in a very active Sun than a relatively quiet Sun, and the ADAPT algorithm may be inaccurate in that scenario.
Our study is an important step in using a first-principle solar wind model for real-time solar CR2137, the range is extended below 0.3 MWm −2 T −1 by adding extra points as [0.1, 0.125, 0.15, 0.175, 0.2, 0.25] MWm −2 T −1 ; and for CR2198, three extra points of[1.25,1.3, 1.35] MWm −2 T −1 are included.All other parameters are set with the default values.To be specific, the perpendicular correlation length parameter is set to 1.5×10 5 m T 1 2 .For the GONG magnetograms, we apply a scaling factor of 3.75 to account for the uncertainty of the synoptic magnetogram observations, especially the very weak field in high latitude regions.To be specific, we set the radial component of the magnetic field (B r ) to sign(B rGONG )*min(3.75•|B rGONG |, 5 + |B rGONG |), where B rGONG is the observed B r from the GONG magnetogram and the unit is in Gauss.This setting is consistent with previous studies(Cohen et al. 2007;Jin et al. 2012).Riley (2007) also applies a similar factor to study the open flux problem.AsHickmann et al. (2015) applied their scaling factor to derive the ADAPT-GONG magnetogram, we do not apply such a multiplicative factor for ADAPT-GONG magnetograms.There are 180 simulations in total in this study.Each simulation takes about 4000 -13 06:00 2018-10-13 06:04 2222 2019-10-2 02:00 2019-10-2 02:14 GONG maps (Paper I), we show figures similar to Paper I. We plot the AWSoM simulated solar wind (driven by GONG synoptic maps) for the same Carrington rotations: CR2106 near solar minimum in Figure 1, and CR2137 near solar maximum in Figure 2. Because we only change the values of the Poynting flux parameter of AWSoM, this figure clearly demonstrates the variations in the simulated solar wind results at 1 AU due to the different Poynting flux parameters.Similar to Figure 1 in Paper I, the simulations with different Poynting flux parameters are shown in blue and the optimal value of the Poynting flux parameter is highlighted in red.These figures share some similarities: the variations of the solar wind due to different Poynting flux parameters are smaller near solar minimum (CR2106) and larger near solar maximum (CR2137); and some Poynting flux parameters produceunphysical results for a relatively active Sun (CR2137).But there are some distinct differences: the simulated solar wind bulk velocity based on the GONG magnetograms (Panels (a) in Figures1 and 2) is significantly larger than the ADAPT-GONG magnetograms (Panels (b) in Figures1 and 2), while the density is about the same or slightly smaller.

Figure 1 .
Figure 1.Comparison between the AWSoM simulated solar wind (blue and red lines) and the hourly OMNI data (black lines) at 1 AU, for CR2106, which is near solar minimum in 2011.Each blue line is associated with a specific value of the Poynting flux parameter, and the red line highlights the simulated solar wind using the optimal Poynting flux parameter.Panel (a) is based on the GONG magnetogram, while Panel (b) is a reproduction based on the ADAPT-GONG magnetogram for the same Carrington Rotation from Paper I.

Figure 2 .
Figure 2.This figure shows a similar comparison as Figure 1 but for CR2137, which is near solar maximum in 2013.Panel (a) is based on the GONG magnetogram, while Panel (b) is a reproduction based on the ADAPT-GONG magnetogram from Paper I.
Figure 5.This figure is very similar to Figure 4 in Paper I. The average Poynting flux in the open

Figure 3 .
Figure 3.The variations of the distances as a function of different Poynting flux parameters.CR2106 is shown in Panel (a) while CR2137 is plotted in Panel (b).The relative curve distances for the solar wind density and velocity, as well as the average value of velocity and density distances are displayed from top to bottom, respectively.The black color is associated with the GONG magnetograms with the red star highlighting the optimal Poynting flux parameter value for the corresponding sub-figure, while the blue color is reproduced from Paper I for the ADAPT-GONG magnetogram results, with the yellow star highlighting the optimal Poynting flux parameter value.

Figures 1 Figure 4 .Figure 5 .
Figures 1 and 2 show that the simulated solar wind speed (from GONG magnetograms) is much wind prediction.Paper I and our results derived empirical formulas for the optimal Poynting flux parameter of AWSoM, and we show AWSoM can produce reasonable solar wind predictions at 1 AU, if the Poynting flux parameter is correctly set.Both Paper I and the current study cover only one Carrington rotation per year between 2011-2019.It is to be checked if the empirical formulas will hold if more rotations are included in the last solar cycle and/or other solar cycles are added.These questions will be addressed in future work.

Table 2 .
The minimum average distances for ADAPT-GONG and GONG magnetograms.