* The designed architecture of the NN performs better with respect to the fully connected architecture and with respect to the architecture distinguishing between different ARs.

* It is very important to evaluate the binary prediction based on the set of different metrics rather than focusing on a single one; the forecast may perform differently with respect to the baseline for different metrics.

* Inclusion of proxies characterizing ARs on the western limb and the far side improves the prediction built only on the AR characteristics.

* The most valuable characteristics for daily whole-Sun prediction of SPEs are the properties of the preceding 10 MeV proton flux. The addition of the SXR flux characteristics and the AR characteristics is equally-valuable for the forecast, while the radio burst counts do not improve the forecast performance.

* The constructed machine-learning-based forecast is very promising in situations when missing events is very undesirable. In particular, the ROC curve of the ML forecast is above the ROC curve of the operational forecast in the region of high true positive rate (for details, see Figure 3 in Sadykov et al., 2021).

The last key result is of special interest in terms of the development of the “all-clear” prediction of SPEs (i.e., the situation when having an event missed by the prediction algorithm is significantly more undesirable with respect to having a false alarm). In addition to the analysis of ROC curves, the developers introduced a score named the Weighted True Skill Statistic (WTSS):

$$WTSS(\alpha) = 1 - \frac{2}{\alpha + 1} \left( \alpha \frac{FN}{TP + FN} + \frac{FP}{TN + FP} \right) \quad (10)$$

In this equation, the TP is the number of correctly predicted SPEs, TN is the number of correctly-predicted no-SPEs, FN is the number of SPEs predicted as no-SPEs, FP is the number of no-SPEs predicted as SPEs, $\alpha$ is the parameter that indicates how strongly the missed event rate (FN/TP + FN) is penalized with respect to the false alarm rate (FP/TN + FP). The model developers concluded that WTSS score is larger for ML-based predictions with respect to operational forecasts for $\alpha > 1$ (i.e., for the situations when the missed event rate is penalized more with respect to the false alarm rate).

### 3.23. SAWS-ASPECS - SEP Advanced Warning System, Advanced Solar Particle Events Casting System

**Model developers:** The SEP Advanced Warning System (SAWS)-Advanced Solar Particle Events Casting System (ASPECS) forecasting system was developed by a consortium headed by A. Anastasiadis, through an ESA contract. The main developers of the ASPECS modules are as follows:

* Forecasting of SFs, CME likelihood and maximum CME speed per active region (Manolis K. Georgoulis, Evangelos Paouris)

* Forecasting of SEPs based on the prediction of SFs (Sigiava Aminalragia-Giamini)

* Nowcasting of SEPs based on SF, CME characteristics and combinations of both thereof (Athanasiou Papaioannou)

* Nowcasting/Forecasting of the expected peak flux of SEP events (Athanasiou Papaioannou)

* Nowcasting/Forecasting of the SEP time profile (Rami Vainio, Miikka Paassilta, Angels Aran)

**Model description:** The SEP Advanced Warning System (SAWS) is an ESA modular framework for forecasting SEP events, their characteristics and profiles. ASPECS is the first realization of this operational tool that collates and combines outputs from different modules providing predictions of SF and CME likelihood of occurrence, SEP event occurrence, expected peak flux and SEP time profile, all of which evolve with time. The system achieves this through the use of 3 modules. The predictions start with the SF forecasting based on near real-time SHARP (Bobra et al., 2014) outputs and continuously evolve through updates based on near-real time inputs (e.g., SF and CME data/characteristics) received by the system. Finally, for the first time the complete time profile of the SEP event at respective energies is provided in near real-time, utilizing both simulations and observations.

ASPECS incorporates two modes of operation. The *forecasting* and the *nowcasting*. The *forecasting* mode is the pre-event one, meaning that no event has actually taken place on the Sun, yet. The only input is the identification of an AR. The *nowcasting* mode is the post-event mode. In this case a SF, a CME, or a combination of both have taken place.

**Forecasting mode:** The input used is the SHARP output from the processing of the SDO/HMI data. Based on these, ASPECS delivers conditional flare probabilities complemented by information on CME probabilities and expected maximum CME speeds. Flare probabilities rely on the “effective connected magnetic field strength” ($B_{eff}$) prediction metric (Georgoulis and Rust, 2007). The CME likelihood relies on the published flare-to-CME association rates (Yashiro et al., 2005) and the maximum CME speed is directly defined by a relation between the $B_{eff}$-values and the recorded near-Sun CME velocities (Georgoulis, 2008). See also details on this approach in Anastasiadis et al. (2017). The statistics of flare prediction for ASPECS have been inferred from historical data covering the period September 2012 – December 2018, (2313 days in total), using the Flare Likelihood And Region Eruption forecasting (FLARECAST) property service (Georgoulis et al., 2021). Moreover, the statistics are built for a set of forecasting windows, namely for the next 6, 12, 24, 48 and 72 h. The outputs of ASPECS, for each AR, include
* The designed architecture of the NN performs better with respect to the fully connected architecture and with respect to the architecture distinguishing between different ARs.

* It is very important to evaluate the binary prediction based on the set of different metrics rather than focusing on a single one; the forecast may perform differently with respect to the baseline for different metrics.

* Inclusion of proxies characterizing ARs on the western limb and the far side improves the prediction built only on the AR characteristics.

* The most valuable characteristics for daily whole-Sun prediction of SPEs are the properties of the preceding 10 MeV proton flux. The addition of the SXR flux characteristics and the AR characteristics is equally-valuable for the forecast, while the radio burst counts do not improve the forecast performance.

* The constructed machine-learning-based forecast is very promising in situations when missing events is very undesirable. In particular, the ROC curve of the ML forecast is above the ROC curve of the operational forecast in the region of high true positive rate (for details, see Figure 3 in Sadykov et al., 2021).

The last key result is of special interest in terms of the development of the “all-clear” prediction of SPEs (i.e., the situation when having an event missed by the prediction algorithm is significantly more undesirable with respect to having a false alarm). In addition to the analysis of ROC curves, the developers introduced a score named the Weighted True Skill Statistic (WTSS):

$$WTSS(\alpha) = 1 - \frac{2}{\alpha + 1} \left( \alpha \frac{FN}{TP + FN} + \frac{FP}{TN + FP} \right) \quad (10)$$

In this equation, the TP is the number of correctly predicted SPEs, TN is the number of correctly-predicted no-SPEs, FN is the number of SPEs predicted as no-SPEs, FP is the number of no-SPEs predicted as SPEs, $\alpha$ is the parameter that indicates how strongly the missed event rate (FN/TP + FN) is penalized with respect to the false alarm rate (FP/TN + FP). The model developers concluded that WTSS score is larger for ML-based predictions with respect to operational forecasts for $\alpha > 1$ (i.e., for the situations when the missed event rate is penalized more with respect to the false alarm rate).

### 3.23. SAWS-ASPECS - SEP Advanced Warning System, Advanced Solar Particle Events Casting System

**Model developers:** The SEP Advanced Warning System (SAWS)-Advanced Solar Particle Events Casting System (ASPECS) forecasting system was developed by a consortium headed by A. Anastasiadis, through an ESA contract. The main developers of the ASPECS modules are as follows:

* Forecasting of SFs, CME likelihood and maximum CME speed per active region (Manolis K. Georgoulis, Evangelos Paouris)

* Forecasting of SEPs based on the prediction of SFs (Sigiava Aminalragia-Giamini)

* Nowcasting of SEPs based on SF, CME characteristics and combinations of both thereof (Athanasiou Papaioannou)

* Nowcasting/Forecasting of the expected peak flux of SEP events (Athanasiou Papaioannou)

* Nowcasting/Forecasting of the SEP time profile (Rami Vainio, Miikka Paassilta, Angels Aran)

**Model description:** The SEP Advanced Warning System (SAWS) is an ESA modular framework for forecasting SEP events, their characteristics and profiles. ASPECS is the first realization of this operational tool that collates and combines outputs from different modules providing predictions of SF and CME likelihood of occurrence, SEP event occurrence, expected peak flux and SEP time profile, all of which evolve with time. The system achieves this through the use of 3 modules. The predictions start with the SF forecasting based on near real-time SHARP (Bobra et al., 2014) outputs and continuously evolve through updates based on near-real time inputs (e.g., SF and CME data/characteristics) received by the system. Finally, for the first time the complete time profile of the SEP event at respective energies is provided in near real-time, utilizing both simulations and observations.

ASPECS incorporates two modes of operation. The *forecasting* and the *nowcasting*. The *forecasting* mode is the pre-event one, meaning that no event has actually taken place on the Sun, yet. The only input is the identification of an AR. The *nowcasting* mode is the post-event mode. In this case a SF, a CME, or a combination of both have taken place.

**Forecasting mode:** The input used is the SHARP output from the processing of the SDO/HMI data. Based on these, ASPECS delivers conditional flare probabilities complemented by information on CME probabilities and expected maximum CME speeds. Flare probabilities rely on the “effective connected magnetic field strength” ($B_{eff}$) prediction metric (Georgoulis and Rust, 2007). The CME likelihood relies on the published flare-to-CME association rates (Yashiro et al., 2005) and the maximum CME speed is directly defined by a relation between the $B_{eff}$-values and the recorded near-Sun CME velocities (Georgoulis, 2008). See also details on this approach in Anastasiadis et al. (2017). The statistics of flare prediction for ASPECS have been inferred from historical data covering the period September 2012 – December 2018, (2313 days in total), using the Flare Likelihood And Region Eruption forecasting (FLARECAST) property service (Georgoulis et al., 2021). Moreover, the statistics are built for a set of forecasting windows, namely for the next 6, 12, 24, 48 and 72 h. The outputs of ASPECS, for each AR, include
<figure><img src="image_11.png" /><figcaption>Fig. 10. An SDO/HMI magnetogram processed with SHARP (panel on the left hand side) and the corresponding outputs of ASPECS (panel on the right hand side). See text for details.</figcaption></figure>

the a) cumulative flare probability as a function of SF magnitude distributed over 28 classes (9 for each of the C, M and X-class flares and another one for X10+), b) the corresponding CME likelihood which is the product of the flare probabilities with the CME-flare association rate and the c) maximum CME speed. An example is presented in Fig. 10. The left panel shows SDO/HMI magnetogram processed with SHARP where ARs are clearly identified. The right panel incorporates all ASPECS’s outputs: flare probabilities (purple line), CME likelihood (orange line) and maximum CME speed. Moreover, the maximum CME likelihood is also provided.

The next step is to provide the probability of SEP occurrence (P(SEP)) based on the information delivered by the SF forecasting (i.e., the cumulative SF probabilities). The work flow is the following: for a given location of an AR, the SF forecasting module provides a Cumulative Distribution Function (CDF) over all 28 GOES SF classes (see Fig. 10). For this given AR location, the nearest historical SF events are identified. Then a probability distribution function for SEP occurrence is derived from these historical data. This forecasting module derives a P(SEP) which is essentially a conditional probability given that a flare with magnitude within a given range has also occurred. The product of the flare and SEP probabilities produces the final output per bin and the final P(SEP) is the sum of all binned probabilities.

**Nowcasting mode:** In the nowcasting mode, ASPECS incorporates the Probabilistic Solar Particle Event foRecasting (PROSPER) Model (Papaioannou et al., 2022). PROSPER applies a novel, data-driven methodology to predict SEP events probabilistically. The model comes with three modes of operation depending on the inputs available: (a) CME characteristics (width, speed);

(b) SF characteristics (longitude, magnitude) and (c) combinations of both CME and SF characteristics. The output is the corresponding P(SEP). The next step is to further infer the expected peak flux at two confidence levels, set to 50% and 90%, respectively. Following this, the SEP time profile is predicted and then scaled to the estimated peak flux values.

The SEP time profile is estimated based on the interplay of two solutions:(a) the Kahler-Ling (KL) (Kahler and Ling, 2017) fitting in which purely empirical fits to the time-intensity profiles or injection function convoluted with Green’s functions were explored (i.e., the method mentioned in the ADEPT model description in Section 3.1). In principle, Kahler and Ling (2017) used 14 SEP events and applied a modified Weibull function in order to fit the SEP time profile. We performed this investigation applying the function

$$F(t) = -I_0(\alpha/\beta)((t - t_0)/\beta)^{\alpha-1}\exp\{-(t - t_0)/\beta\} \quad (11)$$

where t is time (measured in hours) from the listed event onset, $I_0$ is a scaling parameter, $t_0$ is an offset from the time of the peak soft X-ray flux of the associated SF, and $\alpha$ and $\beta$ are parameters controlling the shape of the function. The dependence of the parameter’s fits ($\alpha, \beta$) with respect to solar longitude for a total of 217 SEP events has been explored. It seems that both parameters can be represented by simple, reproducible fits. In turn, these fits can be used to produce predicted (simulated) time-intensity SEP profiles (see Fig. 11, left panel).(b) A database of synthetic integral intensity SEP time profiles for a set of pre-defined test cases obtained by using the SOLar Particle ENgineering Code 2 (SOLPENCO2, see Section 3.29) software tool of the Universitat de Barcelona (Crosby et al., 2015; Aran et al., 2017). SOLPENCO2 is derived from
<figure><img src="image_11.png" /><figcaption>Fig. 10. An SDO/HMI magnetogram processed with SHARP (panel on the left hand side) and the corresponding outputs of ASPECS (panel on the right hand side). See text for details.</figcaption></figure>

the a) cumulative flare probability as a function of SF magnitude distributed over 28 classes (9 for each of the C, M and X-class flares and another one for X10+), b) the corresponding CME likelihood which is the product of the flare probabilities with the CME-flare association rate and the c) maximum CME speed. An example is presented in Fig. 10. The left panel shows SDO/HMI magnetogram processed with SHARP where ARs are clearly identified. The right panel incorporates all ASPECS’s outputs: flare probabilities (purple line), CME likelihood (orange line) and maximum CME speed. Moreover, the maximum CME likelihood is also provided.

The next step is to provide the probability of SEP occurrence (P(SEP)) based on the information delivered by the SF forecasting (i.e., the cumulative SF probabilities). The work flow is the following: for a given location of an AR, the SF forecasting module provides a Cumulative Distribution Function (CDF) over all 28 GOES SF classes (see Fig. 10). For this given AR location, the nearest historical SF events are identified. Then a probability distribution function for SEP occurrence is derived from these historical data. This forecasting module derives a P(SEP) which is essentially a conditional probability given that a flare with magnitude within a given range has also occurred. The product of the flare and SEP probabilities produces the final output per bin and the final P(SEP) is the sum of all binned probabilities.

**Nowcasting mode:** In the nowcasting mode, ASPECS incorporates the Probabilistic Solar Particle Event foRecasting (PROSPER) Model (Papaioannou et al., 2022). PROSPER applies a novel, data-driven methodology to predict SEP events probabilistically. The model comes with three modes of operation depending on the inputs available: (a) CME characteristics (width, speed);

(b) SF characteristics (longitude, magnitude) and (c) combinations of both CME and SF characteristics. The output is the corresponding P(SEP). The next step is to further infer the expected peak flux at two confidence levels, set to 50% and 90%, respectively. Following this, the SEP time profile is predicted and then scaled to the estimated peak flux values.

The SEP time profile is estimated based on the interplay of two solutions:(a) the Kahler-Ling (KL) (Kahler and Ling, 2017) fitting in which purely empirical fits to the time-intensity profiles or injection function convoluted with Green’s functions were explored (i.e., the method mentioned in the ADEPT model description in Section 3.1). In principle, Kahler and Ling (2017) used 14 SEP events and applied a modified Weibull function in order to fit the SEP time profile. We performed this investigation applying the function

$$F(t) = -I_0(\alpha/\beta)((t - t_0)/\beta)^{\alpha-1}\exp\{-(t - t_0)/\beta\} \quad (11)$$

where t is time (measured in hours) from the listed event onset, $I_0$ is a scaling parameter, $t_0$ is an offset from the time of the peak soft X-ray flux of the associated SF, and $\alpha$ and $\beta$ are parameters controlling the shape of the function. The dependence of the parameter’s fits ($\alpha, \beta$) with respect to solar longitude for a total of 217 SEP events has been explored. It seems that both parameters can be represented by simple, reproducible fits. In turn, these fits can be used to produce predicted (simulated) time-intensity SEP profiles (see Fig. 11, left panel).(b) A database of synthetic integral intensity SEP time profiles for a set of pre-defined test cases obtained by using the SOLar Particle ENgineering Code 2 (SOLPENCO2, see Section 3.29) software tool of the Universitat de Barcelona (Crosby et al., 2015; Aran et al., 2017). SOLPENCO2 is derived from
<figure><img src="image_12.png" /><figcaption>Fig. 11. SAWS-ASPECS examples of different simulated SEP time-profiles at $E > 10$ MeV for parent solar events (e.g., SFs) distributed from –90 to 100 degrees, in longitude (panel on the left) and > 10 MeV synthetic proton intensity-time profiles provided by SOLPENCO2 for selected SEP events (panel on the right).</figcaption></figure>

the physics-based Shock-and-Particle (SaP) transport model (Aran et al., 2007; Pomoell et al., 2015) and uses the semi-empirical $Q(VR)$-relation (e.g., Aran et al.,

2006; Rodríguez-Gasén et al., 2014) to characterize the particle source function at the associated travelling shock. The outputs of this tool are simulated proton differential

<figure><img src="image_13.png" /><figcaption>Fig. 12. An example of SEPCaster model output. (a)-(c) Modeled time intensity profiles at three points of interests: Earth, STEREO A, and Mars. The thick-brown curve in (c) shows MAVEN/RAD flux of 60–100 MeV. (d) The modeled (red) and Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) observed (black) spectrum at 1 AU. The arrows indicate the roll-over energies. The figure is adapted from Li et al. (2021).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Fig. 11. SAWS-ASPECS examples of different simulated SEP time-profiles at $E > 10$ MeV for parent solar events (e.g., SFs) distributed from –90 to 100 degrees, in longitude (panel on the left) and > 10 MeV synthetic proton intensity-time profiles provided by SOLPENCO2 for selected SEP events (panel on the right).</figcaption></figure>

the physics-based Shock-and-Particle (SaP) transport model (Aran et al., 2007; Pomoell et al., 2015) and uses the semi-empirical $Q(VR)$-relation (e.g., Aran et al.,

2006; Rodríguez-Gasén et al., 2014) to characterize the particle source function at the associated travelling shock. The outputs of this tool are simulated proton differential

<figure><img src="image_13.png" /><figcaption>Fig. 12. An example of SEPCaster model output. (a)-(c) Modeled time intensity profiles at three points of interests: Earth, STEREO A, and Mars. The thick-brown curve in (c) shows MAVEN/RAD flux of 60–100 MeV. (d) The modeled (red) and Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) observed (black) spectrum at 1 AU. The arrows indicate the roll-over energies. The figure is adapted from Li et al. (2021).</figcaption></figure>
intensity-time profiles at selected locations in the inner
interplanetary space. SOLPENCO2 furnishes ASPECS
with predictions based on 10 SEPEM reference events<fnref n="13" />,
three of which have been re-modeled to reach an integral
energy of *E* > 300 MeV (by using GOES/HEPAD data)
and 2 new modeled cases. The right panel of Fig. 11 shows
the > 10 MeV profiles for a group of events (indicated in
the inset).

**Inputs:**

**Forecasting mode:**

* SDO/HMI SHARP magnetogram

* SF (magnitude, longitude)

**Nowcasting mode:**

* SF (magnitude, longitude)

* CME (speed, width)

* Particle flux

**Outputs:**

**Forecasting mode:**

* Beff

* Probabilities of SF occurrence,

* CME likelihood

* Maximum CME speed

* Probability of SEP occurrence

* Peak flux estimation at 50% and 90% CL

* SEP time profile

**Nowcasting mode:**

* Probability of SEP occurrence

* Peak flux estimation at 50% and 90% CL

* SEP time profile

**Free parameters:** None.

**Limitations and caveats:** ASPECS is a modular tool and incorporates several different modules. The final outcome is the SEP time profile, which evolves with time. The predictions are directly related to the probability of SEP occurrence. Once an SEP is expected to take place, the peak flux and the time profile are also predicted. The SEP time profile is provided for a set of integral energies from >10 to >300 MeV. For each integral energy ASPECS outputs the upper (90% CL) and the lower (50% CL) SEP time profiles. From these SEP time profiles, the peak fluxes can be estimated.

**Access to model output or forecasts:** ASPECS is a web-based tool directly accessible via http://phobos-srv.space.noa.gr/. There are several options for the users: real-time predictions under the forecasting and the nowcasting

mode, run-on-demand functionalities that the user can uti-
ize and test the performance of the tool and its modules on
archived data. The only required input is a date. The inter-
face then searches the backend database, obtains the rele-
vant inputs and triggers the tool, and displays the
obtained outputs. JavaScript Object Notation (JSON) files
are produced and thus all outputs are directly reproducible.
SAWS-ASPECS is also available on the CCMC SEP
Scoreboards.

**Model validation:** Each module has been validated against an independent test sample. For PROSPER and the SEP time profiles the NASA/CCMC SEP challenge events<fnref n="14" /> were utilized. The results for PROSPER show a robust identification of the P(SEP) and the expected peak flux at CL of 50% and 90% in each module, while the SEP time profiles seem to bound well the actual SEP time profile.

3.24. SEPCaster

**Model developers:** Gang Li (UAH), Meng Jin (LMSAL/SETI).

**Model description:** SEPCaster is a new SEP model which couples the solar wind and CME model AWSOM with the particle acceleration and transport model IPATH. By coupling these two models together, the goal is to provide knowledge of the physics of the dynamics of an SEP event from the upper chromosphere of the Sun outward into the heliosphere and at Earth and beyond. SEPCaster is proposed to have two modes, one running in an automatic forecasting mode, and a mode for user-input data.

SEPCaster has been presented as a proof of concept in the paper Li et al. (2021). The model starts with modelling the upper chromosphere and coronal environment with AWSOM (van der Holst et al., 2014), where a steady state solar wind solution is found, using the Potential Field Source Surface (PFSS) as an initial condition and relaxed to MHD solution with local time-stepping. A CME is then initiated using a Gibson-Low (GL) flux rope (Gibson and Low, 1998). The GL flux rope parameters are calculated using EEGGL (Jin et al., 2017). This CME flux rope is then superposed onto the steady state background, and advanced through time. At each time step, a 2-D shock surface is obtained, with each point along the shock having its own shock parameters (compression ratio, obliquity angle, Mach number, and shock speed) and plasma information, which is then fed into the IPATH modules.

In the IPATH section of this paper (3.11), we discuss the three modules of that model. In the case of SEPCaster, the first module, the MHD module, is replaced with AWSOM, and the second module now takes information from the outputs of AWSOM. As these outputs are more complex, IPATH was modified to a 3-D cell structure from its 2-D parcel structure. The rest of the module functions in the same manner as the original IPATH, where each time step

<footnote n="13">¹³ http://www.sepem.eu/help/solpenco2_intro.html.</footnote>

<footnote n="14">¹⁴ https://ccmc.gsfc.nasa.gov/assessment/topics/SEP/campaign2020.php.</footnote>
intensity-time profiles at selected locations in the inner
interplanetary space. SOLPENCO2 furnishes ASPECS
with predictions based on 10 SEPEM reference events<fnref n="13" />,
three of which have been re-modeled to reach an integral
energy of *E* > 300 MeV (by using GOES/HEPAD data)
and 2 new modeled cases. The right panel of Fig. 11 shows
the > 10 MeV profiles for a group of events (indicated in
the inset).

Inputs:

Forecasting mode:

* SDO/HMI SHARP magnetogram

* SF (magnitude, longitude)

Nowcasting mode:

* SF (magnitude, longitude)

* CME (speed, width)

* Particle flux

Outputs:

Forecasting mode:

* Beff

* Probabilities of SF occurrence,

* CME likelihood

* Maximum CME speed

* Probability of SEP occurrence

* Peak flux estimation at 50% and 90% CL

* SEP time profile

Nowcasting mode:

* Probability of SEP occurrence

* Peak flux estimation at 50% and 90% CL

* SEP time profile

**Free parameters:** None.

**Limitations and caveats:** ASPECS is a modular tool and incorporates several different modules. The final outcome is the SEP time profile, which evolves with time. The predictions are directly related to the probability of SEP occurrence. Once an SEP is expected to take place, the peak flux and the time profile are also predicted. The SEP time profile is provided for a set of integral energies from >10 to >300 MeV. For each integral energy ASPECS outputs the upper (90% CL) and the lower (50% CL) SEP time profiles. From these SEP time profiles, the peak fluxes can be estimated.

**Access to model output or forecasts:** ASPECS is a web-based tool directly accessible via http://phobos-srv.space.noa.gr/. There are several options for the users: real-time predictions under the forecasting and the nowcasting

mode, run-on-demand functionalities that the user can uti-
lize and test the performance of the tool and its modules on
archived data. The only required input is a date. The inter-
face then searches the backend database, obtains the rele-
vant inputs and triggers the tool, and displays the
obtained outputs. JavaScript Object Notation (JSON) files
are produced and thus all outputs are directly reproducible.
SAWS-ASPECS is also available on the CCMC SEP
Scoreboards.

**Model validation:** Each module has been validated against an independent test sample. For PROSPER and the SEP time profiles the NASA/CCMC SEP challenge events<fnref n="14" /> were utilized. The results for PROSPER show a robust identification of the P(SEP) and the expected peak flux at CL of 50% and 90% in each module, while the SEP time profiles seem to bound well the actual SEP time profile.

3.24. SEPCaster

**Model developers:** Gang Li (UAH), Meng Jin (LMSAL/SETI).

**Model description:** SEPCaster is a new SEP model which couples the solar wind and CME model AWSOM with the particle acceleration and transport model IPATH. By coupling these two models together, the goal is to provide knowledge of the physics of the dynamics of an SEP event from the upper chromosphere of the Sun outward into the heliosphere and at Earth and beyond. SEPCaster is proposed to have two modes, one running in an automatic forecasting mode, and a mode for user-input data.

SEPCaster has been presented as a proof of concept in the paper Li et al. (2021). The model starts with modelling the upper chromosphere and coronal environment with AWSOM (van der Holst et al., 2014), where a steady state solar wind solution is found, using the Potential Field Source Surface (PFSS) as an initial condition and relaxed to MHD solution with local time-stepping. A CME is then initiated using a Gibson-Low (GL) flux rope (Gibson and Low, 1998). The GL flux rope parameters are calculated using EEGGL (Jin et al., 2017). This CME flux rope is then superposed onto the steady state background, and advanced through time. At each time step, a 2-D shock surface is obtained, with each point along the shock having its own shock parameters (compression ratio, obliquity angle, Mach number, and shock speed) and plasma information, which is then fed into the IPATH modules.

In the IPATH section of this paper (3.11), we discuss the three modules of that model. In the case of SEPCaster, the first module, the MHD module, is replaced with AWSOM, and the second module now takes information from the outputs of AWSOM. As these outputs are more complex, IPATH was modified to a 3-D cell structure from its 2-D parcel structure. The rest of the module functions in the same manner as the original IPATH, where each time step

<footnote n="13">¹³ http://www.sepem.eu/help/solpenco2_intro.html.</footnote>

<footnote n="14">¹⁴ https://ccmc.gsfc.nasa.gov/assessment/topics/SEP/campaign2020.php.</footnote>
particles diffuse between nearby cells and some escape the shock complex - to be transported via the transport module. The transport is handled by a backward stochastic differential equation method. Cross-field diffusion can be included as a part of this process, but has been excluded to add in an ensemble simulation. This type of simulation, instead of assuming the observer is located at a singular point, it instead is located uniformly within a small angular region ~ 5° to 10°. The results for the model show little differences between considering either the perpendicular diffusion or ensemble simulation approach for cases when the observer is magnetically connected to the shock for extended periods of time.

A special case is made for the proposed forecasting mode, where EEGGL will determine flux rope location and flux rope parameters for all active regions, which will then all be initiated in separate runs. For each region, three CME options will be run: slow ($v_{cme}$ = 800 km s⁻¹), normal ($v_{cme}$ = 1000 km s⁻¹), and fast ($v_{cme}$ = 1200 km s⁻¹). These runs are passed into IPATH to provide a first-order prediction of a CME event’s or SEP event’s occurrence, as an “all-clear” measurement. Once a particular flare eruption has been observed, the model will accept a specific CME speed from an empirical relationship between flare class and CME speed.

**Inputs:**

* GONG diachronic magnetic maps (source region, erupting location, CME speed)

* Proton and electron temperatures ($T_i = T_e = 50,000$ K)

* Proton and electron number density ($n = 2 \times 10^{17} m^{-3}$)

* CME shock width, CME speed, and duration (user mode only)

**Outputs:**

* Time intensity profiles

* Particle Spectra

* All-clear

**Free parameters:** The Aflvén wave coronal heating parameters. Although these parameters could be constrained by the remote-sensing solar EUV observations and in situ solar wind measurements at 1 AU. Under the user mode, CME shock width, speed, and duration can be specified by the users to fine-tune event fitting.

**Limitations and caveats:** Although the standalone AWSOM MHD and IPATH simulations are already capable of running cases from the Sun to 1 AU, the current coupling between AWSOM and IPATH in the SEPCaster is limited to the first 6 h, beyond which a Parker-spiral field is assumed in the IPATH transport module. A fully coupling to cover the entire CME propagation in the heliosphere is being implemented/tested. Preliminary results of this full-scale coupling shows that the resulting particle spectra and intensity profile at certain heliospheric locations can be

different from the current 6-h-only coupling approach. SEP-Caster is not fully operational ready at the moment.

**Access to model output or forecasts:** SEPCaster is planned to be hosted on CCMC servers providing 24/7 real-time SEP forecasts.

**Model validation:** SEPCaster has participated in the community modelling validation challenge as part of SHINE and ISWAT, where a few example events were submitted. Once further effort has been made into development of the model, more validation can be done. Fig. 12 shows an example of SEPCaster model output based on a realistic event study of 2012 May 17 event (Li et al., 2021), in which the intensity profiles at different heliospheric longitudes and distances (i.e., Earth, STEREO A, Mars) are provided (Fig. 12a-c). In addition, by including the early-phase shock evolution in the lower corona, the SEPCaster model could provide the particle spectra from 100 keV to GeV. Fig. 12d shows a comparison between the modeled and observed particle spectra by PAMELA (Bruno et al., 2018).

### 3.25. SEPMOD - Solar Energetic Particle MODel

**Model developers:** Janet Luhmann (UC Berkeley), Christina Lee (UC Berkeley), Erika Palmerio (Predictive Science Inc.).

**Model description:** Solar Energetic Particle MODel (SEPMOD) (Luhmann et al., 2007; Luhmann et al., 2010) is a physics-based test particle code for modeling SEP proton events, that outputs differential protons flux time profiles in the energy range of 1–1000 MeV. A version modified for Integrated Solar Energetic Particle (Warning System) (ISEP) use also outputs integral proton fluxes in the channels >10, >30, >50, >60, >100, >300, >500, >750 MeV. SEPMOD assumes that SEP particles are accelerated at the shock created by a CME as it propagates outwards from the Sun. It requires inputs derived from a MHD solar wind and CME propagation model in the form of time sequences of observer-connected magnetic field lines and shock parameters on those field lines. Currently, SEPMOD uses outputs derived from the WSA-ENLIL coupled solar corona and solar wind model, where the geometrical ‘cone’ tool is used for parameterizing the CME clouds in ENLIL. SEPMOD then tracks test particles along the connected field lines from the MHD model shock source(s) to the observer. Its output is a SEP flux time profile at the observer’s location for the duration of the MHD simulation. Because the magnetic connection to the modeled ICME shock continues to be tracked past the observer to the MHD solar wind model outer boundary (usually 2 AU or 5 AU in ENLIL), periods of sunward-streaming SEPs are occasionally produced. SEPMOD has options to include additional sources of particles, such as those accelerated at a flare source and also ESP flux increases (ESP events) that may accompany the arrival of the shock, the latter of which is typically included in the runs. An example of a
particles diffuse between nearby cells and some escape the shock complex - to be transported via the transport module. The transport is handled by a backward stochastic differential equation method. Cross-field diffusion can be included as a part of this process, but has been excluded to add in an ensemble simulation. This type of simulation, instead of assuming the observer is located at a singular point, it instead is located uniformly within a small angular region ~ 5° to 10°. The results for the model show little differences between considering either the perpendicular diffusion or ensemble simulation approach for cases when the observer is magnetically connected to the shock for extended periods of time.

A special case is made for the proposed forecasting mode, where EEGGL will determine flux rope location and flux rope parameters for all active regions, which will then all be initiated in separate runs. For each region, three CME options will be run: slow ($v_{cme}$ = 800 km s⁻¹), normal ($v_{cme}$ = 1000 km s⁻¹), and fast ($v_{cme}$ = 1200 km s⁻¹). These runs are passed into IPATH to provide a first-order prediction of a CME event’s or SEP event’s occurrence, as an “all-clear” measurement. Once a particular flare eruption has been observed, the model will accept a specific CME speed from an empirical relationship between flare class and CME speed.

**Inputs:**

* GONG diachronic magnetic maps (source region, erupting location, CME speed)

* Proton and electron temperatures ($T_i = T_e = 50,000$ K)

* Proton and electron number density ($n = 2 \times 10^{17} m^{-3}$)

* CME shock width, CME speed, and duration (user mode only)

**Outputs:**

* Time intensity profiles

* Particle Spectra

* All-clear

**Free parameters:** The Aflvén wave coronal heating parameters. Although these parameters could be constrained by the remote-sensing solar EUV observations and in situ solar wind measurements at 1 AU. Under the user mode, CME shock width, speed, and duration can be specified by the users to fine-tune event fitting.

**Limitations and caveats:** Although the standalone AWSOM MHD and IPATH simulations are already capable of running cases from the Sun to 1 AU, the current coupling between AWSOM and IPATH in the SEPCaster is limited to the first 6 h, beyond which a Parker-spiral field is assumed in the IPATH transport module. A fully coupling to cover the entire CME propagation in the heliosphere is being implemented/tested. Preliminary results of this full-scale coupling shows that the resulting particle spectra and intensity profile at certain heliospheric locations can be

different from the current 6-h-only coupling approach. SEP-Caster is not fully operational ready at the moment.

**Access to model output or forecasts:** SEPCaster is planned to be hosted on CCMC servers providing 24/7 real-time SEP forecasts.

**Model validation:** SEPCaster has participated in the community modelling validation challenge as part of SHINE and ISWAT, where a few example events were submitted. Once further effort has been made into development of the model, more validation can be done. Fig. 12 shows an example of SEPCaster model output based on a realistic event study of 2012 May 17 event (Li et al., 2021), in which the intensity profiles at different heliospheric longitudes and distances (i.e., Earth, STEREO A, Mars) are provided (Fig. 12a-c). In addition, by including the early-phase shock evolution in the lower corona, the SEPCaster model could provide the particle spectra from 100 keV to GeV. Fig. 12d shows a comparison between the modeled and observed particle spectra by PAMELA (Bruno et al., 2018).

### 3.25. SEPMOD - Solar Energetic Particle MODel

**Model developers:** Janet Luhmann (UC Berkeley), Christina Lee (UC Berkeley), Erika Palmerio (Predictive Science Inc.).

**Model description:** Solar Energetic Particle MODel (SEPMOD) (Luhmann et al., 2007; Luhmann et al., 2010) is a physics-based test particle code for modeling SEP proton events, that outputs differential protons flux time profiles in the energy range of 1–1000 MeV. A version modified for Integrated Solar Energetic Particle (Warning System) (ISEP) use also outputs integral proton fluxes in the channels >10, >30, >50, >60, >100, >300, >500, >750 MeV. SEPMOD assumes that SEP particles are accelerated at the shock created by a CME as it propagates outwards from the Sun. It requires inputs derived from a MHD solar wind and CME propagation model in the form of time sequences of observer-connected magnetic field lines and shock parameters on those field lines. Currently, SEPMOD uses outputs derived from the WSA-ENLIL coupled solar corona and solar wind model, where the geometrical ‘cone’ tool is used for parameterizing the CME clouds in ENLIL. SEPMOD then tracks test particles along the connected field lines from the MHD model shock source(s) to the observer. Its output is a SEP flux time profile at the observer’s location for the duration of the MHD simulation. Because the magnetic connection to the modeled ICME shock continues to be tracked past the observer to the MHD solar wind model outer boundary (usually 2 AU or 5 AU in ENLIL), periods of sunward-streaming SEPs are occasionally produced. SEPMOD has options to include additional sources of particles, such as those accelerated at a flare source and also ESP flux increases (ESP events) that may accompany the arrival of the shock, the latter of which is typically included in the runs. An example of a
<figure><img src="image_14.png" /><figcaption>Fig. 13. Example of a WSA-ENLIL-SEPMOD application. (a) Snapshot of a WSA-ENLIL run, showing results for the solar wind radial speed on the ecliptic plane. (b) Corresponding view of a few shock parameters that are used as input for SEPMOD, i.e. the difference between shock and ambient speed and the compression ratio. (c) Example results at the STEREO-A spacecraft compared to spacecraft data, from top to bottom: Magnetic field magnitude, solar wind speed, solar wind density, and SEP fluxes at three sample energies. The plot shows results for four different WSA-ENLIL-SEPMOD runs, and the results reported in panels (a) and (b) correspond to Run4 in panel (c). More details on these simulations and comparisons with observations throughout the inner heliosphere can be found in Palmerio et al. (2022).</figcaption></figure>

recent WSA-ENLIL-SEPMOD application is shown in Fig. 13.

When applying and evaluating SEPMOD results, it is important to consider that the underlying MHD modeled ICME shock and heliospheric field line descriptions are just as critical to the performance of SEPMOD as the treatment details within the SEPMOD code itself. In this case, limitations that have particularly important impacts on the SEP-MOD results using ENLIL with cone model CMEs include the location of the ENLIL inner boundary of 21.5 Rs, where below this region (e.g., ~5–10 Rs) the early strong CME shock formation occurs, and the lack of an internal magnetic field description within the cone model CMEs. These limitations affect the modeled SEP time profile onset times and the ICME shock formation and evolution (e.g. timing, shape, strength), respectively. In particular, the current 21.5 Rs inner boundary location affects the modeling of GLE events, which are inferred to originate at heights of a few Rs. Future enhancements to SEPMOD will enable the inclusion of surface sources (e.g., flares) and mappings, as well as coronal mirroring of SEPs below the 21.5 Rs boundary.

In SEPMOD itself, protons are injected into the solar wind on the sequence of observer-connected field lines from the MHD model with a prescribed seed population (energy and angular distribution, and flux) that depends on the MHD model shock properties on the field lines. The energy distribution is currently specified by a standard power law for the diffusive acceleration process based on the shock compression ratio, while the injected flux depends on the shock velocity jump according to an empirical result by Lario et al. (1998). The assumed angular distributions of the injected particles are isotropic. This seed population

is then tracked as it adiabatically propagates along the modeled magnetic field without further scattering to the observer site within the MHD simulation domain. Particle propagation includes any mirroring dictated by the field topology along the particle trajectories. Each time a new magnetic connection to a shock is indicated for either the next field line in the MHD model sampling sequence or the appearance of a new ICME shock connection, SEP-MOD injects a new burst of test particles, diluted by $1/r^2$ due to radial expansion of the volume into which the injection occurs. The particles are transported and the results of these impulsive injections are then integrated at the observer location at each time step to achieve the modeled SEP event time profile. SEPMOD includes two additional optional components that 1) represent particles accelerated by the flare source at the Sun at the start of the event and 2) the ESP increase due to the ICME shock passing Earth. If the observer is located within a few tenths of an AU of the shock source and the shock is moving at greater than 300 km/s, an energy-dependent (softer spectrum) ESP flux enhancement is applied that increases as the shock is approached (Luhmann et al., 2017).

**Inputs:** WSA-ENLIL input parameters:

* Magnetogram

* CME 'cone' cloud parameters (angular width, latitude, longitude, speed at 21.5Rs, time at 21.5Rs)

SEPMOD inputs from post-processing of ENLIL:

* Shock information from ENLIL

* Magnetic field connectivity information from ENLIL
<figure><img src="image_14.png" /><figcaption>Fig. 13. Example of a WSA-ENLIL-SEPMOD application. (a) Snapshot of a WSA-ENLIL run, showing results for the solar wind radial speed on the ecliptic plane. (b) Corresponding view of a few shock parameters that are used as input for SEPMOD, i.e. the difference between shock and ambient speed and the compression ratio. (c) Example results at the STEREO-A spacecraft compared to spacecraft data, from top to bottom: Magnetic field magnitude, solar wind speed, solar wind density, and SEP fluxes at three sample energies. The plot shows results for four different WSA-ENLIL-SEPMOD runs, and the results reported in panels (a) and (b) correspond to Run4 in panel (c). More details on these simulations and comparisons with observations throughout the inner heliosphere can be found in Palmerio et al. (2022).</figcaption></figure>

recent WSA-ENLIL-SEPMOD application is shown in Fig. 13.

When applying and evaluating SEPMOD results, it is important to consider that the underlying MHD modeled ICME shock and heliospheric field line descriptions are just as critical to the performance of SEPMOD as the treatment details within the SEPMOD code itself. In this case, limitations that have particularly important impacts on the SEP-MOD results using ENLIL with cone model CMEs include the location of the ENLIL inner boundary of 21.5 Rs, where below this region (e.g., ~5–10 Rs) the early strong CME shock formation occurs, and the lack of an internal magnetic field description within the cone model CMEs. These limitations affect the modeled SEP time profile onset times and the ICME shock formation and evolution (e.g. timing, shape, strength), respectively. In particular, the current 21.5 Rs inner boundary location affects the modeling of GLE events, which are inferred to originate at heights of a few Rs. Future enhancements to SEPMOD will enable the inclusion of surface sources (e.g., flares) and mappings, as well as coronal mirroring of SEPs below the 21.5 Rs boundary.

In SEPMOD itself, protons are injected into the solar wind on the sequence of observer-connected field lines from the MHD model with a prescribed seed population (energy and angular distribution, and flux) that depends on the MHD model shock properties on the field lines. The energy distribution is currently specified by a standard power law for the diffusive acceleration process based on the shock compression ratio, while the injected flux depends on the shock velocity jump according to an empirical result by Lario et al. (1998). The assumed angular distributions of the injected particles are isotropic. This seed population

is then tracked as it adiabatically propagates along the modeled magnetic field without further scattering to the observer site within the MHD simulation domain. Particle propagation includes any mirroring dictated by the field topology along the particle trajectories. Each time a new magnetic connection to a shock is indicated for either the next field line in the MHD model sampling sequence or the appearance of a new ICME shock connection, SEP-MOD injects a new burst of test particles, diluted by $1/r^2$ due to radial expansion of the volume into which the injection occurs. The particles are transported and the results of these impulsive injections are then integrated at the observer location at each time step to achieve the modeled SEP event time profile. SEPMOD includes two additional optional components that 1) represent particles accelerated by the flare source at the Sun at the start of the event and 2) the ESP increase due to the ICME shock passing Earth. If the observer is located within a few tenths of an AU of the shock source and the shock is moving at greater than 300 km/s, an energy-dependent (softer spectrum) ESP flux enhancement is applied that increases as the shock is approached (Luhmann et al., 2017).

**Inputs:** WSA-ENLIL input parameters:

* Magnetogram

* CME 'cone' cloud parameters (angular width, latitude, longitude, speed at 21.5Rs, time at 21.5Rs)

SEPMOD inputs from post-processing of ENLIL:

* Shock information from ENLIL

* Magnetic field connectivity information from ENLIL
**Outputs:** SEPMOD can produce 1–1000 MeV differen-
tial proton flux and > 10, > 30, > 50, > 60, > 100, > 300,
> 500, > 750 MeV time profiles at any spacecraft/planet
in the ENLIL domain. SEPMOD also outputs pitch angle
distribution (anisotropy) information.

**Free parameters:** Particle injection spectrum parameters.

**Limitations and caveats:** The ENLIL inner boundary starts at 21.5 Rs, so SEPMOD does not necessarily model the onset of a SEP event if the particle acceleration starts within this boundary (i.e., inside the solar corona). SEPMOD performance relies strongly on the performance of the underlying modeling of the solar wind and CME propagation (e.g. by WSA-ENLIL + cone model).

**Access to model output or forecasts:** SEPMOD forecasts are displayed on CCMC's SEP Scoreboard (https://sep.ccmc.gsfc.nasa.gov/intensity/) and archived json files containing forecasts are available for download. SEPMOD may also be run through CCMC's runs-on-request system (https://ccmc.gsfc.nasa.gov/requests/requests.php).

**Model validation:** About 10–15 cases studies have been performed and published, but no systematic validation has been published.

Some preliminary validation work has been carried out
through the ISEP project. An unpublished study (per-
formed by Mays, M. L., Whitman, K., Allison, C. Quinn,
P., and Bain, H., 2021) of 16 SEP events in SC24 was car-
ried out to test the sensitivity of SEPMOD + ENLIL's per-
formance with respect to CME characteristics and
magnetic connectivity to Earth. Nominal CME parameters
were provided by NOAA/SWPC, then the width, speed,
latitude, and longitude were varied by ±30%, ±35%, ±5°,
and ±15°, respectively. One combination of CME parame-
ters was selected to maximize the magnetic connectivity
and CME speed and width (high) and a second combina-
tion of parameters was selected to minimize the magnetic
connectivity and CME speed and width (low). This pro-
duced three separate outcomes for each SEP event—nom-
inal, high, and low. WSA-ENLIL + SEPMOD was run for
each combination and the resulting >10 MeV and
>100 MeV proton time profiles were compared to GOES
observations. The NOAA 10 pfu threshold was applied
to the > 10 MeV fluxes and a threshold of 1 pfu used by
the SRAG was applied to the > 100 MeV fluxes. The study
found that SEPMOD performs best for central and western
CMEs that originate closer to the magnetic footprint of the
observer (within ≈ ±40). The runs with the nominal CME
parameters were found to best reproduce observations
overall. The peak flux predictions resulted in a Mean Log
Error (MLE) of –0.067 and Pearson's correlation coeffi-
cient (R) of 0.71 for > 10 MeV and MLE of 0.53 and R
of –0.27 for the > 100 MeV. The SEPMOD time profiles
were found to start ~6–7 h after the observed proton flux
threshold crossing for both >10 and >100 MeV. These
are preliminary findings and a more comprehensive study
must be carried out to fully assess the performance of
SEPMOD.

The ~6–7 h onset delays can, in part, be attributed to
the ENLIL inner boundary of 21.5 Rs and initial shock
formation time for cone model CMEs, but these known
issues have not yet been examined in detail. The ISEP Pro-
ject analysis found that, in the simulation, CMEs were typ-
ically injected onto the ENLIL inner boundary between
11 h before and 2.5 h after the observed > 10 MeV start
time (median of 40 min after event start). The remaining
~5 to 6 h between the CME injection and the simulated
event start was due to a delay in a magnetic connection
between the shock and the observer, possibly due to the
time for shock formation in the ENLIL simulation. There
are currently no readily available options for addressing
the ENLIL inner boundary limitation.

Similar conclusions were reached in a recent study by
Palmerio et al. (2022), who simulated a sequence of CMEs
and their related SEP enhancements that were observed
between late November and early December 2020 and
compared the results with in situ observations at six well-
separated locations. The authors noted that SEPMOD per-
formed best for well-connected observers located up to sev-
eral tens of degrees away from the corresponding shock
apex and that small differences in the ENLIL shock arrival
time tend to yield larger differences in magnetic connectiv-
ity onset and, thus, in SEP transport. Additionally, the
study reported that in about half of the cases, the SEP
event onset times measured in situ occurred ~6–7 h before
the time of insertion of the modeled CME at the ENLIL
inner boundary of 21.5 Rs. The study of Palmerio et al.
(2022) employed a “mini-ensemble” approach, in which
four different WSA-ENLIL + SEPMOD runs were per-
formed with slightly different CME input parameters.
Among other results, it was noted that the simulation run
for which the ENLIL shock arrival times were adjusted
to match those observed in situ did not perform better than
the one initiated with input parameters derived in real time.

3.26. SEPSTER - SEP prediction derived from STEReo
observations

**Model developers:** Ian G. Richardson (NASA Goddard Space Flight Center and University of Maryland, College Park); M. Leila Mays and Barbara J. Thompson (NASA Goddard Space Flight Center).

**Model description:** Solar Energetic Particle STEReo (SEPSTER) is an empirical model that uses CME speed and direction relative to the observer's magnetic footprint at the Sun to predict the peak intensity of 14–24 MeV protons at the observer's location, assumed to be at 1 AU (Richardson et al., 2018). The peak proton intensity/flux in other energy ranges is predicted through extrapolation.

The basis of SEPSTER is a relationship between the
peak intensity of an SEP event, the speed of the associated
CME, and the observer's connection angle, defined as the
longitudinal angle between the source (e.g., flare) location
and the footpoint at the Sun of the magnetic field line con-
**Outputs:** SEPMOD can produce 1–1000 MeV differential proton flux and > 10, > 30, > 50, > 60, > 100, > 300, > 500, > 750 MeV time profiles at any spacecraft/planet in the ENLIL domain. SEPMOD also outputs pitch angle distribution (anisotropy) information.

**Free parameters:** Particle injection spectrum parameters.

**Limitations and caveats:** The ENLIL inner boundary starts at 21.5 Rs, so SEPMOD does not necessarily model the onset of a SEP event if the particle acceleration starts within this boundary (i.e., inside the solar corona). SEPMOD performance relies strongly on the performance of the underlying modeling of the solar wind and CME propagation (e.g. by WSA-ENLIL + cone model).

**Access to model output or forecasts:** SEPMOD forecasts are displayed on CCMC's SEP Scoreboard (https://sep.ccmc.gsfc.nasa.gov/intensity/) and archived json files containing forecasts are available for download. SEPMOD may also be run through CCMC's runs-on-request system (https://ccmc.gsfc.nasa.gov/requests/requests.php).

**Model validation:** About 10–15 cases studies have been performed and published, but no systematic validation has been published.

Some preliminary validation work has been carried out through the ISEP project. An unpublished study (performed by Mays, M. L., Whitman, K., Allison, C. Quinn, P., and Bain, H., 2021) of 16 SEP events in SC24 was carried out to test the sensitivity of SEPMOD + ENLIL's performance with respect to CME characteristics and magnetic connectivity to Earth. Nominal CME parameters were provided by NOAA/SWPC, then the width, speed, latitude, and longitude were varied by ±30%, ±35%, ±5°, and ±15°, respectively. One combination of CME parameters was selected to maximize the magnetic connectivity and CME speed and width (high) and a second combination of parameters was selected to minimize the magnetic connectivity and CME speed and width (low). This produced three separate outcomes for each SEP event—nominal, high, and low. WSA-ENLIL + SEPMOD was run for each combination and the resulting >10 MeV and >100 MeV proton time profiles were compared to GOES observations. The NOAA 10 pfu threshold was applied to the > 10 MeV fluxes and a threshold of 1 pfu used by the SRAG was applied to the > 100 MeV fluxes. The study found that SEPMOD performs best for central and western CMEs that originate closer to the magnetic footprint of the observer (within ≈ ±40). The runs with the nominal CME parameters were found to best reproduce observations overall. The peak flux predictions resulted in a Mean Log Error (MLE) of –0.067 and Pearson's correlation coefficient (R) of 0.71 for > 10 MeV and MLE of 0.53 and R of –0.27 for the > 100 MeV. The SEPMOD time profiles were found to start ~6–7 h after the observed proton flux threshold crossing for both >10 and >100 MeV. These are preliminary findings and a more comprehensive study must be carried out to fully assess the performance of SEPMOD.

The ~6–7 h onset delays can, in part, be attributed to the ENLIL inner boundary of 21.5 Rs and initial shock formation time for cone model CMEs, but these known issues have not yet been examined in detail. The ISEP Project analysis found that, in the simulation, CMEs were typically injected onto the ENLIL inner boundary between 11 h before and 2.5 h after the observed > 10 MeV start time (median of 40 min after event start). The remaining ~5 to 6 h between the CME injection and the simulated event start was due to a delay in a magnetic connection between the shock and the observer, possibly due to the time for shock formation in the ENLIL simulation. There are currently no readily available options for addressing the ENLIL inner boundary limitation.

Similar conclusions were reached in a recent study by Palmerio et al. (2022), who simulated a sequence of CMEs and their related SEP enhancements that were observed between late November and early December 2020 and compared the results with in situ observations at six well-separated locations. The authors noted that SEPMOD performed best for well-connected observers located up to several tens of degrees away from the corresponding shock apex and that small differences in the ENLIL shock arrival time tend to yield larger differences in magnetic connectivity onset and, thus, in SEP transport. Additionally, the study reported that in about half of the cases, the SEP event onset times measured in situ occurred ~6–7 h before the time of insertion of the modeled CME at the ENLIL inner boundary of 21.5 Rs. The study of Palmerio et al. (2022) employed a “mini-ensemble” approach, in which four different WSA-ENLIL + SEPMOD runs were performed with slightly different CME input parameters. Among other results, it was noted that the simulation run for which the ENLIL shock arrival times were adjusted to match those observed in situ did not perform better than the one initiated with input parameters derived in real time.

### 3.26. SEPSTER - SEP prediction derived from STEREO observations

**Model developers:** Ian G. Richardson (NASA Goddard Space Flight Center and University of Maryland, College Park); M. Leila Mays and Barbara J. Thompson (NASA Goddard Space Flight Center).

**Model description:** Solar Energetic Particle STEREO (SEPSTER) is an empirical model that uses CME speed and direction relative to the observer's magnetic footprint at the Sun to predict the peak intensity of 14–24 MeV protons at the observer's location, assumed to be at 1 AU (Richardson et al., 2018). The peak proton intensity/flux in other energy ranges is predicted through extrapolation.

The basis of SEPSTER is a relationship between the peak intensity of an SEP event, the speed of the associated CME, and the observer's connection angle, defined as the longitudinal angle between the source (e.g., flare) location and the footpoint at the Sun of the magnetic field line con-
nected to the observer (Richardson et al., 2014). This relationship was derived from observations of a sample of 25 SEP events detected by the High Energy Telescopes (von Rosenvinge et al., 2008) on both STEREO spacecraft when widely separated from Earth, and at near-Earth spacecraft, principally by the Energetic and Relativistic Nuclei and Electron (ERNE) (Torsti et al., 1995) and EPHIN (Müller-Mellin et al., 1995) instruments on SOHO. The peak intensities at all three locations for each SEP event were fitted by a Gaussian function of connection angle. The fits are summarized by the relationship:

$$I_p \approx 0.013 \exp \left( 0.0036V - \frac{\phi_{CA}^2}{2\sigma^2} \right). \quad (12)$$

Here, $I_p$ is the peak intensity of 14–24 MeV protons in (MeV s cm² sr)⁻¹, V is the CME speed in km/s, $\phi_{CA}$ is the connection angle in degrees, and σ is the average value of the width of the Gaussian functions fitted to the SEP events (43°).

Because relating flare observations (to give the source longitude) with the associated CME is not always trivial, and in some cases, the flare associated with a CME may be behind the limb, for operational SEP prediction at Earth, SEPSTER uses the CME speed and direction (as a proxy for the source location) taken from the CCMC DONKI database<fnref n="15" />. When available, these CME parameters are inferred from multi-spacecraft coronagraph observations (e.g., from STEREO and SOHO); see Mays et al. (2015) for further details of the derivation of CME parameters by CCMC. The connection angle is then taken to be the longitudinal difference between the direction of the CME and the magnetic field line footpoint. The footpoint location is obtained by using the solar wind speed measured at the observing spacecraft or other nearby spacecraft, at the time of the CME, if available, or otherwise a default speed of 450 km/s, to map a Parker spiral field line back to the Sun. Field line mapping in the corona is not considered in this case because SEP acceleration is believed to occur predominantly at heights above the source surface, often assumed to be at 2.5 R<sub>s</sub>. In addition, the field line connection longitude derived from WSA-ENLIL, which does include coronal field line mapping, is used to give an estimate of the influence of uncertainty in the connection point on the predicted SEP intensity. SEPSTER enters these variables into Eq. 12, then predicts the peak intensity of 14–24 MeV protons at the observing location. For events before April 2010, or other events for which DONKI CME parameters are not available, flare and CME observations may be used to give the source location and CME speed.

The SEPSTER workflow follows the following steps:

1. SEPSTER queries the CCMC DONKI database then copies a list of recent CME parameters to a local file.

2. SEPSTER queries CCMC integrated Space Weather Analysis System (iSWA) for recent solar wind observations from the Deep Space Climate Observatory (DSCOVR) spacecraft and downloads the data for approximately two days before the CME time until the start of the day following the CME, or the end of the available data, if earlier. If no DSCOVR data are available, similar observations from ACE are downloaded, if available. The in situ speed measured closest to CME onset is then selected. If no solar wind data are available, the model assumes a default solar wind speed of 450 km/s.

3. The connection angle is calculated using the equation

$$\phi_{CA} = \frac{1.5 \times 10^8}{u} \frac{360}{86400 \times 27.25} - \phi_{CME} \quad (13)$$

where $\phi_{CA}$ is the connection angle in degrees, 1 AU is ~ 1.5 × 10⁸ km, u is the solar wind speed in km/s, 27.25 days is the Carrington rotation period, and $\phi_{CME}$ is the longitude of the CME direction with respect to the Sun-Earth line.

4. As discussed briefly below and in more detail by Richardson et al. (2018), various types of filtering may be applied to reduce the number of false SEP event predictions, since Eq. 12 can be used to predict the SEP intensity for any CME whereas only a small subset of CMEs are accompanied by SEP events detected at 1 AU. In the operational model, the following simple filters are applied:

* If the CME speed is below 200 km/s, no prediction is made.

* If the CME width is below 10°, no prediction is made.

* If the CME speed × width is less than 50000 km/s. deg., an SEP event “all clear” is predicted.

5. For CMEs that are not filtered by the CME speed/width requirements, Equation 12 is used to estimate the peak intensity of 14–24 MeV protons at Earth.

6. Peak proton fluxes equivalent to the standard GOES integral energy ranges of > 10 MeV, > 30 MeV, > 50 MeV, and > 100 MeV are predicted using scaling factors of ~ 20I<sub>p</sub>, ~ 2I<sub>p</sub>, ~ I<sub>p</sub>, and ~ 0.2I<sub>p</sub>, respectively, where I<sub>p</sub> is given by Eq. 12 and the fluxes obtained are in pfu. These scaling factors are derived from correlating 14–24 MeV proton intensities from SOHO with simultaneous GOES observations over an extended time interval including multiple SEP events.

7. The time of peak intensity (in hours relative to the CME onset time) for 14–24 MeV protons is estimated using a result from Figure 20 of Richardson et al. (2014):

$$T_{\text{peak}}(\text{h}) \approx 7.32 \exp \left( \frac{\phi_{\text{CA}}}{114} \right). \quad (14)$$

<footnote n="15">¹⁵ https://kauai.cmcgsfc.nasa.gov/DONKI/.</footnote>
nected to the observer (Richardson et al., 2014). This relationship was derived from observations of a sample of 25 SEP events detected by the High Energy Telescopes (von Rosenvinge et al., 2008) on both STEREO spacecraft when widely separated from Earth, and at near-Earth spacecraft, principally by the Energetic and Relativistic Nuclei and Electron (ERNE) (Torsti et al., 1995) and EPHIN (Müller-Mellin et al., 1995) instruments on SOHO. The peak intensities at all three locations for each SEP event were fitted by a Gaussian function of connection angle. The fits are summarized by the relationship:

$$I_p \approx 0.013 \exp \left( 0.0036V - \frac{\phi_{CA}^2}{2\sigma^2} \right). \quad (12)$$

Here, $I_p$ is the peak intensity of 14–24 MeV protons in (MeV s cm² sr)⁻¹, V is the CME speed in km/s, $\phi_{CA}$ is the connection angle in degrees, and σ is the average value of the width of the Gaussian functions fitted to the SEP events (43°).

Because relating flare observations (to give the source longitude) with the associated CME is not always trivial, and in some cases, the flare associated with a CME may be behind the limb, for operational SEP prediction at Earth, SEPSTER uses the CME speed and direction (as a proxy for the source location) taken from the CCMC DONKI database<fnref n="15" />. When available, these CME parameters are inferred from multi-spacecraft coronagraph observations (e.g., from STEREO and SOHO); see Mays et al. (2015) for further details of the derivation of CME parameters by CCMC. The connection angle is then taken to be the longitudinal difference between the direction of the CME and the magnetic field line footpoint. The footpoint location is obtained by using the solar wind speed measured at the observing spacecraft or other nearby spacecraft, at the time of the CME, if available, or otherwise a default speed of 450 km/s, to map a Parker spiral field line back to the Sun. Field line mapping in the corona is not considered in this case because SEP acceleration is believed to occur predominantly at heights above the source surface, often assumed to be at 2.5 R<sub>S</sub>. In addition, the field line connection longitude derived from WSA-ENLIL, which does include coronal field line mapping, is used to give an estimate of the influence of uncertainty in the connection point on the predicted SEP intensity. SEPSTER enters these variables into Eq. 12, then predicts the peak intensity of 14–24 MeV protons at the observing location. For events before April 2010, or other events for which DONKI CME parameters are not available, flare and CME observations may be used to give the source location and CME speed.

The SEPSTER workflow follows the following steps:

1. SEPSTER queries the CCMC DONKI database then copies a list of recent CME parameters to a local file.

2. SEPSTER queries CCMC integrated Space Weather Analysis System (iSWA) for recent solar wind observations from the Deep Space Climate Observatory (DSCOVR) spacecraft and downloads the data for approximately two days before the CME time until the start of the day following the CME, or the end of the available data, if earlier. If no DSCOVR data are available, similar observations from ACE are downloaded, if available. The in situ speed measured closest to CME onset is then selected. If no solar wind data are available, the model assumes a default solar wind speed of 450 km/s.

3. The connection angle is calculated using the equation

$$\phi_{CA} = \frac{1.5 \times 10^8}{u} \frac{360}{86400 \times 27.25} - \phi_{CME} \quad (13)$$

where $\phi_{CA}$ is the connection angle in degrees, 1 AU is ~ 1.5 × 10⁸ km, u is the solar wind speed in km/s, 27.25 days is the Carrington rotation period, and $\phi_{CME}$ is the longitude of the CME direction with respect to the Sun-Earth line.

4. As discussed briefly below and in more detail by Richardson et al. (2018), various types of filtering may be applied to reduce the number of false SEP event predictions, since Eq. 12 can be used to predict the SEP intensity for any CME whereas only a small subset of CMEs are accompanied by SEP events detected at 1 AU. In the operational model, the following simple filters are applied:

* If the CME speed is below 200 km/s, no prediction is made.

* If the CME width is below 10°, no prediction is made.

* If the CME speed × width is less than 50000 km/s. deg., an SEP event “all clear” is predicted.

5. For CMEs that are not filtered by the CME speed/width requirements, Equation 12 is used to estimate the peak intensity of 14–24 MeV protons at Earth.

6. Peak proton fluxes equivalent to the standard GOES integral energy ranges of > 10 MeV, > 30 MeV, > 50 MeV, and > 100 MeV are predicted using scaling factors of ~ 20I<sub>p</sub>, ~ 2I<sub>p</sub>, ~ I<sub>p</sub>, and ~ 0.2I<sub>p</sub>, respectively, where I<sub>p</sub> is given by Eq. 12 and the fluxes obtained are in pfu. These scaling factors are derived from correlating 14–24 MeV proton intensities from SOHO with simultaneous GOES observations over an extended time interval including multiple SEP events.

7. The time of peak intensity (in hours relative to the CME onset time) for 14–24 MeV protons is estimated using a result from Figure 20 of Richardson et al. (2014):

$$T_{\text{peak}}(\text{h}) \approx 7.32 \exp \left( \frac{\phi_{\text{CA}}}{114} \right). \quad (14)$$

<footnote n="15">¹⁵ https://kauai.cmcgsfc.nasa.gov/DONKI/.</footnote>
8. The CME parameters, predicted SEP intensity and peak time, and whether or not the predicted intensity meets the criterion for a GOES event “all clear,” are written to a JSON file. This file is overwritten/updated if the file already exists for a CME with the same time and speed.

9. These steps are repeated for the next CME in the list.

10. The DONKI database is re-checked every minute to see if a new CME has been added, and the above steps are repeated for this CME.

11. For “historical” events, SEPSTER options include using the CDAW list of CMEs and flares associated with type II radio emission<fnref n="16" /> or a user-generated CME-source location list in place of the DONKI CME list in step 1.

**Inputs:** The inputs needed for SEPSTER include the CME speed, CME width (optional, used for false-prediction filtering), CME direction longitude or flare/eruption location, SEP-observing spacecraft longitude at ~1 AU, and the solar wind speed at the observing spacecraft, if available, otherwise a default speed is used.

**Outputs:** SEPSTER outputs the peak intensity and peak time of 14–24 MeV protons at the observing location (i.e., Earth) which is extrapolated to give GOES-equivalent >10 MeV, >30 MeV, >50 MeV, and >100 MeV proton fluxes.

**Free parameters:** SEPSTER has no free parameters.

**Limitations and caveats:** SEPSTER predicts an SEP event for every reported CME whereas observationally, only a small subset (~15%) of CMEs are accompanied by SEP events detectable at 1 AU (Richardson et al., 2018). Also, because Eq. 12 is derived from widespread “three-spacecraft” SEP events, it tends to overestimate the intensity of the many small SEP events associated with slow, well-connected CMEs. The filters based on CME speed and width listed above help to mitigate these limitations. Richardson et al. (2018) discuss these and other filtering methods, for example, based on spacecraft observations of type II and III radio emissions accompanying CMEs, and their influence on SEPSTER skill scores (see their Table 1). However, since such radio observations are not currently available in near-real time, they are not considered in the operational version of SEPSTER.

SEPSTER relies on measurements of CME speed and width, requiring coronagraph imagery which currently may be only available hours or even days after the CME has occurred. Estimation of the CME parameters also requires several images to be acquired. Hence, SEPSTER predictions are made later than those from similar flare-triggered models. An SEP event may also commence before the associated CME enters the field of view of a spacecraft coronagraph. On the other hand, since SEPSTER predicts the peak intensity, which may not occur until several hours

following CME onset, a modest delay in estimating the CME parameters may not be a critical concern.

Derivation of Eq. 12 was based on plane-of-the-sky CME speeds from the CDAW LASCO CME catalog<fnref n="17" /> and flare locations, whereas the operational model uses DONKI CME speeds/directions. As discussed by Richardson et al. (2015), the speeds of SEP-associated CMEs reported in different catalogs can differ significantly. Richardson et al. (2018) discuss the use of this Equation for SEP prediction using both CDAW/LASCO and DONKI CME speeds.

**Access to model output or forecasts:** SEPSTER is housed at the CCMC and available for runs-on-request. The model is also running continuously and predictions are displayed on the SEP Scoreboard (https://sep.ccmc.gsfc.nasa.gov/intensity/).

**Model validation:** Richardson et al. (2018) discuss a method of assessing SEPSTER skill scores as a function of a variable (rather than the more usual fixed) SEP event intensity threshold when various filters (as discussed above) are applied. These results clearly show that SEPSTER predictions are most reliable for the larger SEP events that are of space weather interest, while filtering substantially improves the false prediction rate for weaker events. For the larger events, with a peak 14–24 MeV proton intensity exceeding 0.1 (MeV s cm² sr)⁻¹, over 80% of the predictions were within an order of magnitude of the observed intensity. Table 1 of Richardson et al. (2018) shows skill scores for these events assuming different filters. For example, applying the CME speed × width > 50000 km/sDeg. filter used by SEPSTER decreases the false alarm ratio from 0.67 with no filter to 0.31, with the lowest value of 0.21 obtained by requiring the observation of strong type III radio emission accompanying the CME.

## 3.27. SEPSTER2D - SEP prediction derived from STEREO observations 2D

**Model developers:** Alessandro Bruno (Catholic University of America, NASA Goddard Space Flight Center), Ian G. Richardson (University of Maryland, College Park and NASA Goddard Space Flight Center).

**Model description:** SEPSTER2D (Bruno and Richardson, 2021) is an empirical model to predict SEP event-integrated and peak intensity proton spectra between 10 and 130 MeV at 1 AU. Developed from the SEPSTER model, SEPSTER2D similarly assumes that the SEP intensity can be predicted based on the speed and direction of a CME relative to the observing spacecraft using an empirical formula derived from multi-point spacecraft measurements, specifically from GOES-13/15, STEREO A and B, and the PAMELA satellite experiments (Bruno et al., 2018). The GOES data used are based on the *effective* energies derived by Sandberg et al. (2014) for the P2–P5

<footnote n="16">¹⁶ https://cdaw.gsfc.nasa.gov/CME_list/radio/waves_type2.html.</footnote>

<footnote n="17">¹⁷ https://cdaw.gsfc.nasa.gov/CME_list/.</footnote>
8. The CME parameters, predicted SEP intensity and peak time, and whether or not the predicted intensity meets the criterion for a GOES event “all clear,” are written to a JSON file. This file is overwritten/updated if the file already exists for a CME with the same time and speed.

9. These steps are repeated for the next CME in the list.

10. The DONKI database is re-checked every minute to see if a new CME has been added, and the above steps are repeated for this CME.

11. For “historical” events, SEPSTER options include using the CDAW list of CMEs and flares associated with type II radio emission<fnref n="16" /> or a user-generated CME-source location list in place of the DONKI CME list in step 1.

**Inputs:** The inputs needed for SEPSTER include the CME speed, CME width (optional, used for false-prediction filtering), CME direction longitude or flare/eruption location, SEP-observing spacecraft longitude at ~1 AU, and the solar wind speed at the observing spacecraft, if available, otherwise a default speed is used.

**Outputs:** SEPSTER outputs the peak intensity and peak time of 14–24 MeV protons at the observing location (i.e., Earth) which is extrapolated to give GOES-equivalent >10 MeV, >30 MeV, >50 MeV, and >100 MeV proton fluxes.

**Free parameters:** SEPSTER has no free parameters.

**Limitations and caveats:** SEPSTER predicts an SEP event for every reported CME whereas observationally, only a small subset (~15%) of CMEs are accompanied by SEP events detectable at 1 AU (Richardson et al., 2018). Also, because Eq. 12 is derived from widespread “three-spacecraft” SEP events, it tends to overestimate the intensity of the many small SEP events associated with slow, well-connected CMEs. The filters based on CME speed and width listed above help to mitigate these limitations. Richardson et al. (2018) discuss these and other filtering methods, for example, based on spacecraft observations of type II and III radio emissions accompanying CMEs, and their influence on SEPSTER skill scores (see their Table 1). However, since such radio observations are not currently available in near-real time, they are not considered in the operational version of SEPSTER.

SEPSTER relies on measurements of CME speed and width, requiring coronagraph imagery which currently may be only available hours or even days after the CME has occurred. Estimation of the CME parameters also requires several images to be acquired. Hence, SEPSTER predictions are made later than those from similar flare-triggered models. An SEP event may also commence before the associated CME enters the field of view of a spacecraft coronagraph. On the other hand, since SEPSTER predicts the peak intensity, which may not occur until several hours

following CME onset, a modest delay in estimating the CME parameters may not be a critical concern.

Derivation of Eq. 12 was based on plane-of-the-sky CME speeds from the CDAW LASCO CME catalog<fnref n="17" /> and flare locations, whereas the operational model uses DONKI CME speeds/directions. As discussed by Richardson et al. (2015), the speeds of SEP-associated CMEs reported in different catalogs can differ significantly. Richardson et al. (2018) discuss the use of this Equation for SEP prediction using both CDAW/LASCO and DONKI CME speeds.

**Access to model output or forecasts:** SEPSTER is housed at the CCMC and available for runs-on-request. The model is also running continuously and predictions are displayed on the SEP Scoreboard (https://sep.ccmc.gsfc.nasa.gov/intensity/).

**Model validation:** Richardson et al. (2018) discuss a method of assessing SEPSTER skill scores as a function of a variable (rather than the more usual fixed) SEP event intensity threshold when various filters (as discussed above) are applied. These results clearly show that SEPSTER predictions are most reliable for the larger SEP events that are of space weather interest, while filtering substantially improves the false prediction rate for weaker events. For the larger events, with a peak 14–24 MeV proton intensity exceeding 0.1 (MeV s cm² sr)⁻¹, over 80% of the predictions were within an order of magnitude of the observed intensity. Table 1 of Richardson et al. (2018) shows skill scores for these events assuming different filters. For example, applying the CME speed × width > 50000 km/sDeg. filter used by SEPSTER decreases the false alarm ratio from 0.67 with no filter to 0.31, with the lowest value of 0.21 obtained by requiring the observation of strong type III radio emission accompanying the CME.

## 3.27. SEPSTER2D - SEP prediction derived from STEREO observations 2D

**Model developers:** Alessandro Bruno (Catholic University of America, NASA Goddard Space Flight Center), Ian G. Richardson (University of Maryland, College Park and NASA Goddard Space Flight Center).

**Model description:** SEPSTER2D (Bruno and Richardson, 2021) is an empirical model to predict SEP event-integrated and peak intensity proton spectra between 10 and 130 MeV at 1 AU. Developed from the SEPSTER model, SEPSTER2D similarly assumes that the SEP intensity can be predicted based on the speed and direction of a CME relative to the observing spacecraft using an empirical formula derived from multi-point spacecraft measurements, specifically from GOES-13/15, STEREO A and B, and the PAMELA satellite experiments (Bruno et al., 2018). The GOES data used are based on the *effective* energies derived by Sandberg et al. (2014) for the P2–P5

<footnote n="16">¹⁶ https://cdaw.gsfc.nasa.gov/CME_list/radio/waves_type2.html.</footnote>

<footnote n="17">¹⁷ https://cdaw.gsfc.nasa.gov/CME_list/.</footnote>
($<$80 MeV) proton energy channels, and by Bruno (2017) for the P6–P11 ($>$80 MeV) channels, based on comparison with the IMP-8/GME and PAMELA data, respectively. SEPSTER2D assumes that the SEP intensity distribution, $\Phi$, as a function of energy $E$ and the (energy-dependent) spherical distance $\delta$ from the location of peak SEP intensity, can be estimated as

$$ \Phi(E, \delta) = \Phi_o(E, V_{cme})G(E, \delta), \qquad (15) $$

where

$$ \Phi_o(E, V_{cme}) = \Psi_{cme}(E) \exp [\Lambda_{cme}(E) V_{cme}], \qquad (16) $$

is the SEP maximum intensity spectrum. Here, $V_{cme}$ is the parent CME speed, and the functions $\Psi_{cme}(E)$ and $\Lambda_{cme}(E)$ account for the energy-dependence of the intensity. The SEP angular distribution is modeled with a periodic Gaussian functional form $G(E, \delta) = G(E, \delta \pm 2\pi)$ accounting for both the longitudinal and latitudinal magnetic connectivity. The latitudinal angle of the peak of the SEP distribution is assumed to coincide with the estimated CME latitudinal angle based on coronagraph observations. The model parameters are derived by using the 3-spacecraft (STEREO A, B, and near-Earth) measurements of 32 SEP events occurring between 2010 and 2014. The location of the footpoint of the IMF field lines passing the observer (Earth, STEREO-A and -B) is estimated at the CME first appearance time and at a 2.5 Rs radial distance, based on a simple Parker spiral IMF model using measured solar wind speeds. SEP intensity prediction errors are evaluated by accounting for the uncertainties of the different experimental quantities involved in the calculation. Further details can be found in Bruno and Richardson (2021). Future plans include the implementation of a faster prediction scheme based on X-ray flare data.

**Inputs:** CME speed, direction and first appearance time from DONKI; solar wind speed from ACE/DSCOVR/STEREO.

**Outputs:** SEPSTER2D outputs SEP peak and event-integrated intensities (both differential and energy-integrated) at various proton energies, along with corresponding uncertainties, as well as peak intensity times and event end times.

**Free parameters:** None.

**Limitations and caveats:** Predicted intensities are expected to overestimate those observed for relatively slow ($<$600 km/s) CMEs and narrow SEP events. SEP intensities above 130 MeV are based on spectral extrapolations and are characterized by large uncertainties.

**Access to model output or forecasts:** SEPSTER2D forecasts are available real-time on the SEP Scoreboard (https://sep.ccmc.gsfc.nasa.gov/intensity/).

**Model validation:** The model performance, including its extrapolations to lower/higher energies, was tested by comparing with the spectra of 20 SEP events not used to derive the model parameters, showing a reasonable agreement (Bruno and Richardson, 2021).

## 3.28. SMARP Model

**Model developers:** The model developers are Spiridon Kasapis, Lulu Zhao, Xiantong Wang, Yang Chen and Tamas Gombosi who are members of the Solar Storms and Terrestrial Impacts Center (SOLSTICE) team at the University of Michigan Climate and Space Science Department<fnref n="18" />. Monica Bobra from the Hansen Experimental Physics Laboratory in Stanford University provided the Space-Weather MDI Active Region Patches (SMARP) dataset whose predictive capabilities are being explored in this work.

**Model description:** The SMARP Model from Interpretable Machine Learning to Forecast SEP Events for SC23 is a machine learning-based SEP model developed at the University of Michigan. The developers explore how capable two popular groups of ML algorithms (SVM (Cortes and Vapnik, 1995) and Regression Models) are in predicting whether an AR which produces flares will lead to a SEP event. The SVM models use four different kernels: a linear, two polynomial (second and third degree) and the Gaussian Radial Basis Function (RBF) kernel which has been used in similar studies (Inceoglu et al., 2018). In addition to the above, two Regression models are trained: the Ridge and the Logistic Regression models.

Based on the magnetograms measured by the MDI (Scherrer et al., 1995) onboard SOHO, Bobra et al. (2021) derived a new database called SMARPs, which contains characteristics of the active regions on the solar surface. The developers surveyed the SMARP active regions associated with flares that appear on the solar disk between June 5, 1996 and August 14, 2010, label those that produced SEPs as positive and the rest as negative. Three physical keywords, total unsigned flux, mean gradient of the vertical field, and the logarithm of the total unsigned flux near the polarity inversion line are calculated using the pixels in the active region's magnetogram and are used as inputs to the models. In addition, the SMARP dataset also contains four spatial features specifying the location of the corresponding AR on the solar surface: the minimum and maximum longitude and latitude. Using these spatial features, two more inputs were calculated - the angular distance between the AR and the magnetic foot-point of the earth and the size of the active region.

In this 14-year time span, 65 Solar Energetic Particle events have information adequate to label the 6,510 flare-AR couples, a label is therefore assigned to each couple: positive if it led to an SEP and negative if it did not. Consequently, the output of the binary prediction models is a 0 (negative) or 1 (positive) label.

**Inputs:** SMARP files and derived values.

**Outputs:** Binary yes/no forecast of SEP occurrence ($>$10 MeV), probability of SEP occurrence and quantified uncertainty of the prediction model.

<footnote n="18">¹⁸ https://solstice.engin.umich.edu/</footnote>
($<$80 MeV) proton energy channels, and by Bruno (2017) for the P6–P11 ($>$80 MeV) channels, based on comparison with the IMP-8/GME and PAMELA data, respectively. SEPSTER2D assumes that the SEP intensity distribution, $\Phi$, as a function of energy $E$ and the (energy-dependent) spherical distance $\delta$ from the location of peak SEP intensity, can be estimated as

$$ \Phi(E, \delta) = \Phi_o(E, V_{cme})G(E, \delta), \qquad (15) $$

where

$$ \Phi_o(E, V_{cme}) = \Psi_{cme}(E) \exp[\Lambda_{cme}(E)V_{cme}], \qquad (16) $$

is the SEP maximum intensity spectrum. Here, $V_{cme}$ is the parent CME speed, and the functions $\Psi_{cme}(E)$ and $\Lambda_{cme}(E)$ account for the energy-dependence of the intensity. The SEP angular distribution is modeled with a periodic Gaussian functional form $G(E, \delta) = G(E, \delta \pm 2\pi)$ accounting for both the longitudinal and latitudinal magnetic connectivity. The latitudinal angle of the peak of the SEP distribution is assumed to coincide with the estimated CME latitudinal angle based on coronagraph observations. The model parameters are derived by using the 3-spacecraft (STEREO A, B, and near-Earth) measurements of 32 SEP events occurring between 2010 and 2014. The location of the footpoint of the IMF field lines passing the observer (Earth, STEREO-A and -B) is estimated at the CME first appearance time and at a 2.5 Rs radial distance, based on a simple Parker spiral IMF model using measured solar wind speeds. SEP intensity prediction errors are evaluated by accounting for the uncertainties of the different experimental quantities involved in the calculation. Further details can be found in Bruno and Richardson (2021). Future plans include the implementation of a faster prediction scheme based on X-ray flare data.

**Inputs:** CME speed, direction and first appearance time from DONKI; solar wind speed from ACE/DSCOVR/STEREO.

**Outputs:** SEPSTER2D outputs SEP peak and event-integrated intensities (both differential and energy-integrated) at various proton energies, along with corresponding uncertainties, as well as peak intensity times and event end times.

**Free parameters:** None.

**Limitations and caveats:** Predicted intensities are expected to overestimate those observed for relatively slow ($<$600 km/s) CMEs and narrow SEP events. SEP intensities above 130 MeV are based on spectral extrapolations and are characterized by large uncertainties.

**Access to model output or forecasts:** SEPSTER2D forecasts are available real-time on the SEP Scoreboard (https://sep.ccmc.gsfc.nasa.gov/intensity/).

**Model validation:** The model performance, including its extrapolations to lower/higher energies, was tested by comparing with the spectra of 20 SEP events not used to derive the model parameters, showing a reasonable agreement (Bruno and Richardson, 2021).

### 3.28. SMARP Model

**Model developers:** The model developers are Spiridon Kasapis, Lulu Zhao, Xiantong Wang, Yang Chen and Tamas Gombosi who are members of the Solar Storms and Terrestrial Impacts Center (SOLSTICE) team at the University of Michigan Climate and Space Science Department<fnref n="18" />. Monica Bobra from the Hansen Experimental Physics Laboratory in Stanford University provided the Space-Weather MDI Active Region Patches (SMARP) dataset whose predictive capabilities are being explored in this work.

**Model description:** The SMARP Model from Interpretable Machine Learning to Forecast SEP Events for SC23 is a machine learning-based SEP model developed at the University of Michigan. The developers explore how capable two popular groups of ML algorithms (SVM (Cortes and Vapnik, 1995) and Regression Models) are in predicting whether an AR which produces flares will lead to a SEP event. The SVM models use four different kernels: a linear, two polynomial (second and third degree) and the Gaussian Radial Basis Function (RBF) kernel which has been used in similar studies (Inceoglu et al., 2018). In addition to the above, two Regression models are trained: the Ridge and the Logistic Regression models.

Based on the magnetograms measured by the MDI (Scherrer et al., 1995) onboard SOHO, Bobra et al. (2021) derived a new database called SMARPs, which contains characteristics of the active regions on the solar surface. The developers surveyed the SMARP active regions associated with flares that appear on the solar disk between June 5, 1996 and August 14, 2010, label those that produced SEPs as positive and the rest as negative. Three physical keywords, total unsigned flux, mean gradient of the vertical field, and the logarithm of the total unsigned flux near the polarity inversion line are calculated using the pixels in the active region's magnetogram and are used as inputs to the models. In addition, the SMARP dataset also contains four spatial features specifying the location of the corresponding AR on the solar surface: the minimum and maximum longitude and latitude. Using these spatial features, two more inputs were calculated - the angular distance between the AR and the magnetic foot-point of the earth and the size of the active region.

In this 14-year time span, 65 Solar Energetic Particle events have information adequate to label the 6,510 flare-AR couples, a label is therefore assigned to each couple: positive if it led to an SEP and negative if it did not. Consequently, the output of the binary prediction models is a 0 (negative) or 1 (positive) label.

**Inputs:** SMARP files and derived values.

**Outputs:** Binary yes/no forecast of SEP occurrence ($>$10 MeV), probability of SEP occurrence and quantified uncertainty of the prediction model.

<footnote n="18">¹⁸ https://solstice.engin.umich.edu/</footnote>
**Free parameters:** Both SVM and Linear models are affected by user-defined constants such as the $\alpha$ (complexity parameter) and $C$ (regularization parameter). An embedded grid search using the testing dataset to avoid overfitting is employed varying each free parameter on a range between 0.05 to 20. All the results reported in this work use a probability decision threshold $pt = 0.5$.

**Limitations and caveats:** The task of SEP prediction using SMARPs is subject to a number of limitations such as data uncertainties, a vastly unbalanced dataset which only includes a limited amount of positive events and the inherent limitation of the SMARP dataset which is that compared to other data products it provides lower resolution time series (96-min cadence). It is important to acknowledge that the SMARP dataset could not be used alone to reliably forecast SEP events, therefore the aim of this study is to explore the prediction capabilities of the SMARP dataset and the quality of its different physical parameters rather than propose an operational forecasting apparatus.

**Access to model output or forecasts:** Forecasts from the model are not available, however the source code may be accessed at https://github.com/skasapis/SEP_Prediction_Using_SMARP.

**Model validation:** The mean accuracy we obtain when validating a Third Degree Polynomial SVM trained on the best two SMARP predictors (unsigned flux and active region distance from the magnetic foot-point of the earth) suggests that 72% of the times (±12% for a single run) algorithm can correctly predict whether a flare will lead or not to an SEP. These are the results when training on a balanced data set, however there is a significant reduction in accuracy when training with a more realistic imbalanced data set. These outcomes show that although the SMARP dataset has some ability to make distinctions between flares that produce SEPs and flares that do not, when put in an operational setting where the testing is performed in a vastly imbalanced set of samples, the forecasting model fails to produce meaningful results. This is yet another proof of the initial hypothesis that although the SMARP dataset includes meaningful information which can be proven useful for SEP forecasting if used to augment other existing machine learning models, it cannot be used by itself as a forecasting dataset.

## 3.29. SOLPENCO and SOLPENCO2 - Solar Particle Engineering Code

**Model developers:** SOLPENCO: Angels Aran (main developer, University of Barcelona (UB)), Blai Sanahuja (UB), David Lario (NASA Goddard Space Flight Center). SOLPENCO2: Angels Aran (main developer, UB), Blai Sanahuja (UB), Carla Jacobs (Space Applications Services, Belgium), Stefaan Poedts (KU Leuven).

**Model description:** The original SOLar Particle Engineering Code (SOLPENCO) was an initial step towards developing an operational tool to rapidly predict proton

intensity-time profiles and fluences for gradual SEP events (Aran et al., 2006; Aran et al., 2008). The SOLPENCO predictions are based on database interpolations from synthetic proton intensity-time profiles pre-computed for a range of CME-driven shock scenarios and associated solar-interplanetary conditions.

The SOLPENCO synthetic proton flux database is computed from a physics-based SAP model (Heras et al., 1992; Lario et al., 1998). The conceptual framework of SOLPENCO is based on the assumption that the proton intensity-time profile of a gradual SEP event is mainly the result of particle acceleration by an IP shock, and the subsequent injection of shock-accelerated particles that takes place at the point on the traveling IP shock front that magnetically connects to the observation location (Lario, 2005). This point on the shock front has been given the name Connecting-with-OBserver-POINT (cobpoint) (Heras et al., 1995).

The shock model determines the propagation of an IP shock from the 18 R⊙ inner boundary of a 2.5D (2-dimensions, 3 vector components for the flow velocity and magnetic induction) MHD model to 1.0 AU (Wu et al., 1983). The model numerically solves the ideal adiabatic MHD equations. The shock is introduced into the MHD model at the inner boundary by defining the initial shock speed, the heliolongitude of the origin of the shock disturbance, and the longitudinal width of the shock at the location of origin. The shock perturbation is defined as a finite pulse shape in space and time, and the MHD shock jump conditions are solved separately to determine other state variables (e.g., density and temperature) given the initial shock velocity. The pre-shock IMF is assumed to be a Parker spiral field and homogeneous background solar wind conditions are determined by the pre-shock, steady-state solutions of the MHD equations. The meridional velocity and magnetic field components are adjusted at the inner boundary of the model to maximize agreement with various plasma and field measurements at 1.0 AU.

The particle transport model determines the interplanetary propagation of shock-accelerated energetic particles that are injected at the COBPOINT, by solving the FTE. The physical processes included in the FTE are streaming and convection of energetic particles, adiabatic focusing, pitch-angle scattering, and adiabatic deceleration (Lario et al., 1998). The injection of shock-accelerated energetic protons at the COBPOINT is included as a source term in the FTE. From modeling and analyzing various SEP events, the functional form of the injection rate, $Q$, is described by the following empirical relationship (Lario et al., 1998; Aran et al., 2006; Aran, 2007; Aran et al., 2007):

$$ \log Q(E, t) = \log Q_0(E) + kVR(t), \quad (17) $$

where $VR(t)$ is the ratio of the downstream to upstream normalized radial plasma velocity jump at the COBPOINT, which is derived from the output results of the time-dependent MHD simulations of the shock propaga-
**Free parameters:** Both SVM and Linear models are affected by user-defined constants such as the α (complexity parameter) and C (regularization parameter). An embedded grid search using the testing dataset to avoid overfitting is employed varying each free parameter on a range between 0.05 to 20. All the results reported in this work use a probability decision threshold pt = 0.5.

**Limitations and caveats:** The task of SEP prediction using SMARPs is subject to a number of limitations such as data uncertainties, a vastly unbalanced dataset which only includes a limited amount of positive events and the inherent limitation of the SMARP dataset which is that compared to other data products it provides lower resolution time series (96-min cadence). It is important to acknowledge that the SMARP dataset could not be used alone to reliably forecast SEP events, therefore the aim of this study is to explore the prediction capabilities of the SMARP dataset and the quality of its different physical parameters rather than propose an operational forecasting apparatus.

**Access to model output or forecasts:** Forecasts from the model are not available, however the source code may be accessed at https://github.com/skasapis/SEP_Prediction_Using_SMARP.

**Model validation:** The mean accuracy we obtain when validating a Third Degree Polynomial SVM trained on the best two SMARP predictors (unsigned flux and active region distance from the magnetic foot-point of the earth) suggests that 72% of the times (±12% for a single run) algorithm can correctly predict whether a flare will lead or not to an SEP. These are the results when training on a balanced data set, however there is a significant reduction in accuracy when training with a more realistic imbalanced data set. These outcomes show that although the SMARP dataset has some ability to make distinctions between flares that produce SEPs and flares that do not, when put in an operational setting where the testing is performed in a vastly imbalanced set of samples, the forecasting model fails to produce meaningful results. This is yet another proof of the initial hypothesis that although the SMARP dataset includes meaningful information which can be proven useful for SEP forecasting if used to augment other existing machine learning models, it cannot be used by itself as a forecasting dataset.

## 3.29. SOLPENCO and SOLPENCO2 - Solar Particle Engineering Code

**Model developers:** SOLPENCO: Angels Aran (main developer, University of Barcelona (UB)), Blai Sanahuja (UB), David Lario (NASA Goddard Space Flight Center). SOLPENCO2: Angels Aran (main developer, UB), Blai Sanahuja (UB), Carla Jacobs (Space Applications Services, Belgium), Stefaan Poedts (KU Leuven).

**Model description:** The original SOLar Particle Engineering Code (SOLPENCO) was an initial step towards developing an operational tool to rapidly predict proton

intensity-time profiles and fluences for gradual SEP events (Aran et al., 2006; Aran et al., 2008). The SOLPENCO predictions are based on database interpolations from synthetic proton intensity-time profiles pre-computed for a range of CME-driven shock scenarios and associated solar-interplanetary conditions.

The SOLPENCO synthetic proton flux database is computed from a physics-based SAP model (Heras et al., 1992; Lario et al., 1998). The conceptual framework of SOLPENCO is based on the assumption that the proton intensity-time profile of a gradual SEP event is mainly the result of particle acceleration by an IP shock, and the subsequent injection of shock-accelerated particles that takes place at the point on the traveling IP shock front that magnetically connects to the observation location (Lario, 2005). This point on the shock front has been given the name Connecting-with-OBserver-POINT (cobpoint) (Heras et al., 1995).

The shock model determines the propagation of an IP shock from the 18 R⊙ inner boundary of a 2.5D (2-dimensions, 3 vector components for the flow velocity and magnetic induction) MHD model to 1.0 AU (Wu et al., 1983). The model numerically solves the ideal adiabatic MHD equations. The shock is introduced into the MHD model at the inner boundary by defining the initial shock speed, the heliolongitude of the origin of the shock disturbance, and the longitudinal width of the shock at the location of origin. The shock perturbation is defined as a finite pulse shape in space and time, and the MHD shock jump conditions are solved separately to determine other state variables (e.g., density and temperature) given the initial shock velocity. The pre-shock IMF is assumed to be a Parker spiral field and homogeneous background solar wind conditions are determined by the pre-shock, steady-state solutions of the MHD equations. The meridional velocity and magnetic field components are adjusted at the inner boundary of the model to maximize agreement with various plasma and field measurements at 1.0 AU.

The particle transport model determines the interplanetary propagation of shock-accelerated energetic particles that are injected at the COBPOINT, by solving the FTE. The physical processes included in the FTE are streaming and convection of energetic particles, adiabatic focusing, pitch-angle scattering, and adiabatic deceleration (Lario et al., 1998). The injection of shock-accelerated energetic protons at the COBPOINT is included as a source term in the FTE. From modeling and analyzing various SEP events, the functional form of the injection rate, Q, is described by the following empirical relationship (Lario et al., 1998; Aran et al., 2006; Aran, 2007; Aran et al., 2007):

$$ \log Q(E, t) = \log Q_0(E) + kVR(t), \quad (17) $$

where VR(t) is the ratio of the downstream to upstream normalized radial plasma velocity jump at the COBPOINT, which is derived from the output results of the time-dependent MHD simulations of the shock propaga-
tion. Thus, the rate at which shock-accelerated particles are
injected into interplanetary space is directly related to the
dynamical evolution of the shock strength at the COB-
POINT. The parameters *k* and *Q*₀ are determined by fitting
the shock-and-particle model simulations to proton flux
measurements at 1.0 AU at a reference energy for several
SEP events. The slope parameter (*k*) is taken as the average
value derived from the different SEP events analyzed, and
other energies are fit to the proton flux measurements by
assuming *Q*₀ varies as a power-law in energy, i.e.,
*Q*₀(*E*) = *Q*₀(*E*₀) (*E*/*E*₀)⁻⁷ (Aran et al., 2006; Aran et al.,
2008).

The remaining parameter in the interplanetary transport
of the shock-accelerated particles is the parallel proton
mean free path (perpendicular diffusion across field lines
is not included). Along with the parameters *k* and *Q*₀, the
parallel mean free path for 0.5 MeV protons (λ∥₀) was
determined by fits to proton flux and first-order anisotropy
measurements at 1.0 AU. From the analysis and fits to the
SEP events, two values for λ∥₀ were adopted: 0.2 AU and
0.8 AU (Aran et al., 2006). The parallel scattering lengths
at other energies were assumed to scale with rigidity
according to a power-law: λ∥ = λ∥₀(R/R₀)⁰.⁵, where R is
the proton rigidity. To mimic the ESP component of SEP
events, a turbulent foreshock is modelled by taking a 0.01
AU region in front of the shock where the proton mean
free path scales as λ∥c = 0.01(R/R₀)⁻⁰.⁶ AU, where
R₀ = 30.635 MV. Such foreshock region starts acting
20 h prior the shock arrival to the observer. The values
of the parameters defining this foreshock are average val-
ues from modelled events (Aran et al., 2006).

The SOLPENCO database of synthetic proton
intensity-time profiles contains 448 combined shock-and-
particle scenarios (Aran et al., 2005b; Aran et al., 2006).
There are eight IP shocks with initial velocities ranging
from 750 kms⁻¹ to 1800 kms⁻¹, which translate to shock
transit times at 1.0 AU that range from roughly 25 h to
100 h (Aran et al., 2008). The model calculations were also
run for 14 heliolongitudes of the associated parent solar
event with respect to the observer, from E75 to W90 for
observers at 1.0 AU. In addition, for each database
shock/heliolongitude combination there are four IP parti-
cle transport conditions: parallel scattering lengths of λ∥₀
= 0.2 AU and 0.8 AU, and simulations with and without
a turbulent foreshock region. Furthermore, the output
results for the shock-and-particle model scenarios are pro-
vided at heliocentric radial distances of 0.4 AU and 1.0 AU
and at 10 proton energies ranging from 0.125 MeV to
64 MeV, equally distributed in logarithmic space. The soft-
ware interface allows the user to retrieve the upstream
intensity-time profiles at the selected input parameters
(among those for the scenarios depicted above) as well as
the integral cumulative fluence profiles above the low-
energy bound of each differential channel (labelled by using
the mean energy of each energy channel). The code also
gives the transit time and velocity of the shock from the

Sun to the observer, the maximum proton intensity (peak
flux), and the total fluence of the SEP event computed from
the onset of the event up to the arrival of the associated
transient CME-driven shock. SOLPENCO and its valida-
tion are fully documented in Aran (2007).

SOLPENCO2 is based on a version of the University of
Barcelona’s SAP model that was built in collaboration with
the KU Leuven (Aran et al., 2011; Pomoell et al., 2015).

SOLPENCO2¹⁹ furnishes the SEPEM statistical SEP
model (e.g., Jiggens et al., 2012) with 5–300 MeV proton
peak flux and event differential-fluence heliocentric radial
power-law dependences, derived from the modeling of ten
reference gradual proton events: 6 March 1989, 4 April
2000, 6 and 10 June 2000, 29 March 2001, 24 September
2001, 29 October 2003, 13 and 14 December 2006 and 13
March 2012. These events were selected as representative
of the 243 SEP events in the SEPEM Reference Event List
(REL) at 1.0 AU, spanning the period from January 1988
to March 2013. The synthetic proton peak flux and event
differential fluence quantities from these ten events were
scaled to the observed values at 1.0 AU in order to ensure
that the synthetic quantities match the reference data uti-
lized by the SEPEM statistical tools. The scaling is done
for each of the eleven energy channels of the SEPEM Ref-
erence Data Set (RDS v2.0) (e.g., Jiggens et al., 2018). For
each of the ten SEP events, and for each energy channel,
the peak proton flux and event fluence quantities are
extracted from the simulations at the seven SEPEM refer-
ence heliocentric radial distances that lie along the same
IMF Parker spiral field line that passes through 1.0 AU
(i.e. the Earth’s nominal magnetic field line connecting with
the Sun). These quantities are then fit to a power-law with
the heliocentric radial distance, which provides the means
by which the SEPEM tool extends the proton peak flux
and event fluence quantities away from 1.0 AU. The events
in REL are classified into one of the ten event categories
and the corresponding radial scales are applied. The classi-
fication depends on the detection of an interplanetary
shock at 1.0 AU, the level reached in the proton intensity
for E > 66 MeV, the heliolongitude of the parent solar
activity, and for the largest events, the peak intensity level
reached 8.7 MeV and 79.5 MeV protons (Crosby et al.,
2015; Aran et al., 2017). The design of this classification
was performed in collaboration with P. Jiggens from
ESA. Currently, SOLPENCO2 provides SEPEM with
scaled-to-observed (1AU) peak intensity and event fluence
ratios for each of the 249 SEP events and for virtual obser-
vers located at 0.2, 0.4, 0.6, 0.8, 1.0, 1.3 and 1.6 AU. This
allows the inclusion of interplanetary missions in the
SEPEM statistical SEP model. (http://sepem.eu/help/sat_
radial.html).

SOLPENCO2 is designed for the description of grad-
ual solar proton events, originating from the solar west-
ern limb to far eastern heliolongitudes, as seen from

<footnote n="19">¹⁹ http://sepem.eu/help/solpenco2_intro.html.</footnote>
tion. Thus, the rate at which shock-accelerated particles are
injected into interplanetary space is directly related to the
dynamical evolution of the shock strength at the COB-
POINT. The parameters *k* and *Q*₀ are determined by fitting
the shock-and-particle model simulations to proton flux
measurements at 1.0 AU at a reference energy for several
SEP events. The slope parameter (*k*) is taken as the average
value derived from the different SEP events analyzed, and
other energies are fit to the proton flux measurements by
assuming *Q*₀ varies as a power-law in energy, i.e.,
*Q*₀(*E*) = *Q*₀(*E*₀) (*E*/*E*₀*)⁻⁷ (Aran et al., 2006; Aran et al.,
2008).

The remaining parameter in the interplanetary transport
of the shock-accelerated particles is the parallel proton
mean free path (perpendicular diffusion across field lines
is not included). Along with the parameters *k* and *Q*₀, the
parallel mean free path for 0.5 MeV protons (λ∥₀) was
determined by fits to proton flux and first-order anisotropy
measurements at 1.0 AU. From the analysis and fits to the
SEP events, two values for λ∥₀ were adopted: 0.2 AU and
0.8 AU (Aran et al., 2006). The parallel scattering lengths
at other energies were assumed to scale with rigidity
according to a power-law: λ∥ = λ∥₀(R/R₀)⁰.⁵, where R is
the proton rigidity. To mimic the ESP component of SEP
events, a turbulent foreshock is modelled by taking a 0.01
AU region in front of the shock where the proton mean
free path scales as λ|c = 0.01(R/R₀)⁻⁰.⁶ AU, where
R₀ = 30.635 MV. Such foreshock region starts acting
20 h prior the shock arrival to the observer. The values
of the parameters defining this foreshock are average val-
ues from modelled events (Aran et al., 2006).

The SOLPENCO database of synthetic proton
intensity-time profiles contains 448 combined shock-and-
particle scenarios (Aran et al., 2005b; Aran et al., 2006).
There are eight IP shocks with initial velocities ranging
from 750 kms⁻¹ to 1800 kms⁻¹, which translate to shock
transit times at 1.0 AU that range from roughly 25 h to
100 h (Aran et al., 2008). The model calculations were also
run for 14 heliolongitudes of the associated parent solar
event with respect to the observer, from E75 to W90 for
observers at 1.0 AU. In addition, for each database
shock/heliolongitude combination there are four IP parti-
cle transport conditions: parallel scattering lengths of λ∥₀
= 0.2 AU and 0.8 AU, and simulations with and without
a turbulent foreshock region. Furthermore, the output
results for the shock-and-particle model scenarios are pro-
vided at heliocentric radial distances of 0.4 AU and 1.0 AU
and at 10 proton energies ranging from 0.125 MeV to
64 MeV, equally distributed in logarithmic space. The soft-
ware interface allows the user to retrieve the upstream
intensity-time profiles at the selected input parameters
(among those for the scenarios depicted above) as well as
the integral cumulative fluence profiles above the low-
energy bound of each differential channel (labelled by using
the mean energy of each energy channel). The code also
gives the transit time and velocity of the shock from the

Sun to the observer, the maximum proton intensity (peak
flux), and the total fluence of the SEP event computed from
the onset of the event up to the arrival of the associated
transient CME-driven shock. SOLPENCO and its valida-
tion are fully documented in Aran (2007).

SOLPENCO2 is based on a version of the University of
Barcelona’s SAP model that was built in collaboration with
the KU Leuven (Aran et al., 2011; Pomoell et al., 2015).

SOLPENCO2¹⁹ furnishes the SEPEM statistical SEP
model (e.g., Jiggens et al., 2012) with 5–300 MeV proton
peak flux and event differential-fluence heliocentric radial
power-law dependences, derived from the modeling of ten
reference gradual proton events: 6 March 1989, 4 April
2000, 6 and 10 June 2000, 29 March 2001, 24 September
2001, 29 October 2003, 13 and 14 December 2006 and 13
March 2012. These events were selected as representative
of the 243 SEP events in the SEPEM Reference Event List
(REL) at 1.0 AU, spanning the period from January 1988
to March 2013. The synthetic proton peak flux and event
differential fluence quantities from these ten events were
scaled to the observed values at 1.0 AU in order to ensure
that the synthetic quantities match the reference data uti-
lized by the SEPEM statistical tools. The scaling is done
for each of the eleven energy channels of the SEPEM Ref-
erence Data Set (RDS v2.0) (e.g., Jiggens et al., 2018). For
each of the ten SEP events, and for each energy channel,
the peak proton flux and event fluence quantities are
extracted from the simulations at the seven SEPEM refer-
ence heliocentric radial distances that lie along the same
IMF Parker spiral field line that passes through 1.0 AU
(i.e. the Earth’s nominal magnetic field line connecting with
the Sun). These quantities are then fit to a power-law with
the heliocentric radial distance, which provides the means
by which the SEPEM tool extends the proton peak flux
and event fluence quantities away from 1.0 AU. The events
in REL are classified into one of the ten event categories
and the corresponding radial scales are applied. The classi-
fication depends on the detection of an interplanetary
shock at 1.0 AU, the level reached in the proton intensity
for E > 66 MeV, the heliolongitude of the parent solar
activity, and for the largest events, the peak intensity level
reached 8.7 MeV and 79.5 MeV protons (Crosby et al.,
2015; Aran et al., 2017). The design of this classification
was performed in collaboration with P. Jiggens from
ESA. Currently, SOLPENCO2 provides SEPEM with
scaled-to-observed (1AU) peak intensity and event fluence
ratios for each of the 249 SEP events and for virtual obser-
vers located at 0.2, 0.4, 0.6, 0.8, 1.0, 1.3 and 1.6 AU. This
allows the inclusion of interplanetary missions in the
SEPEM statistical SEP model. (http://sepem.eu/help/sat_
radial.html).

SOLPENCO2 is designed for the description of grad-
ual solar proton events, originating from the solar west-
ern limb to far eastern heliolongitudes, as seen from

<footnote n="19">¹⁹ http://sepem.eu/help/solpenco2_intro.html.</footnote>
virtual observers located within 0.2 AU and 1.6 AU. For any modeled event, the tool provides the 5–300 MeV proton differential intensity-time profiles for the eleven energy channels of RDS v2.0. SOLPENCO2 consists of two main parts: (i) A database of simulated interplanetary shocks and (ii) a database of ten modeled SEP events. These data bases are generated from the physics-based SAP model (Aran et al., 2011; Pomoell et al., 2015). The underlying 2D MHD component of the SAP model used in SOLPENCO2 was significantly updated with respect to the original SOLPENCO version (Aran et al., 2006; Aran et al., 2011; Jacobs and Poedts, 2011; Pomoell et al., 2015). Its inner boundary is now low in the solar corona at $1.03 R_⊙$ (Aran et al., 2011), enabling the modeling of shock-accelerated proton spectra to be extended from 64 MeV to 300 MeV. The approach taken to specify the pre-shock, background solar wind plasma is to adopt a polytropic solar wind model which is a 1.5D extension to the Parker model that includes both solar rotation and the magnetic field (Aran et al., 2011; Jacobs and Poedts, 2011). Advantages and drawbacks in the use of the polytropic wind with interplanetary shock simulations are discussed by Jacobs and Poedts (2011) and (Pomoell et al., 2015). The propagation of an IP shock is performed by numerically solving the ideal MHD equations with a perturbation in solar wind radial velocity and density superimposed onto the background solar wind plasma state (Aran et al., 2011). The functional form of the radial velocity and density perturbations are exponential pulse profiles, with additional parameters introduced to control the pulse shape and the angular width and radial thickness of the initial shock disturbance (Aran et al., 2011; Pomoell et al., 2015). The functional form and shape parameters of the IP shock were selected to reproduce IP shock transit times and solar wind plasma measurements for various gradual SEP events observed at 1.0 AU. The 2D MHD equations are solved using the Versatile Advection Code (VAC) (Toth, 1996). The more reduced grid spacing of the MHD model has led to noticeable improvements in the numerical representation of IP shock propagation with respect to the MHD model used in SOLPENCO. The database of 2D MHD shocks includes the evolution of the COBPOINT for virtual observers located at different heliolongitudes with respect to the incoming shocks (Aran et al., 2011). Specifically, the simulated shocks and cobpoints are computed for:

* Solar winds extending from $1.03 R_⊙$ to 1.6 AU: a slow wind of $365 \text{ km s}^{-1}$, and a fast wind of $595 \text{ km s}^{-1}$.

* Eight initial shock conditions (different values in speed and density), centered at $1.75 R_⊙$, that yield to shocks arriving to 1 AU between 25 h and 66 h, for the shocks evolving in the slow solar wind, and between 17 h and 48 h, for the shocks in the fast solar wind.

* Two longitudinal widths for the initial shocks: narrow and wide.

* 14 virtual observers located at 1.0 AU, at longitudinal positions between W85 and E65.

The shock-finder procedure, to extract the evolution of the COBPOINT and the shock plasma jumps at the COBPOINT was also automated and significantly improved with respect to the previous version used in SOLPENCO (Aran et al., 2011). A adaptation for a 3D geometry is described in (Rodríguez-Gasén et al., 2011). For each modelled shock, SOLPENCO2 provides the COBPOINT position as well as density, magnetic field ratios and normalized speed ratio, VR, in the lab's frame, for the 14 (longitudes) x 7 (radial distances) virtual observers.

The database of intensity-time profiles are generated with the SAP's transport model (Lario et al., 1998). For the 10 reference events SOLPENCO2 provides:

* The particle source at the COBPOINT, Q, which is obtained by means of a Q(VR) relation based on the parameters derived from the modeling of the April 4, 2000 and December 13, 2006 SEP events (Aran et al., 2011; Pomoell et al., 2015).

* The proton intensity-time profiles for the 11 SEPEM reference energies, for the virtual observers located between 0.2 AU and 1.6 AU. The profiles are obtained by setting constant proton mean free path values (0.35 AU or 1.17 AU for 8.7 MeV protons) and the presence of a turbulent foreshock as in SOLPENCO (Aran et al., 2011). The choice of these transport parameters that leads a better comparison with data is selected.

* The peak intensity and the upstream differential fluence [$MeV^{-1} cm^{-2}$] as a function of the observer's radial distance, and the derived power-law indices.

To account for the post-shock portion of the fluence (i.e., the downstream fluence) of the events time-profiles in the REL list, an observational analysis (including SEPEM, STEREO and Helios data) of the fluence in the downstream region of the proton intensity-time profiles of gradual SEP events was performed (Aran et al., 2017; Pacheco, 2019). In SOLPENCO2, all fluences are differential fluences. For each event in REL with an IP shock detected, the total fluence at the different radial distances is obtained by adding the scaled upstream fluence and a scaled downstream fluence (values at 1 AU match the observations). The scaling of the downstream fluence is based on an empirical relation found between the downstream-to-total fluence ratio and the longitudinal separation of the observer with respect to the nose of the shock, for each energy channel (Pacheco, 2019). Therefore, in contrast to SOLPENCO, SOLPENCO2 can include a prediction for the downstream fluence of the synthetic events.

The main difference between SOLPENCO and SOLPENCO2 lies in the purpose of the two tools. SOLPENCO is a stand-alone tool ready to be operated by any user with some knowledge of SEP events; and SOLPENCO2 is
virtual observers located within 0.2 AU and 1.6 AU. For any modeled event, the tool provides the 5–300 MeV proton differential intensity-time profiles for the eleven energy channels of RDS v2.0. SOLPENCO2 consists of two main parts: (i) A database of simulated interplanetary shocks and (ii) a database of ten modeled SEP events. These data bases are generated from the physics-based SAP model (Aran et al., 2011; Pomoell et al., 2015). The underlying 2D MHD component of the SAP model used in SOLPENCO2 was significantly updated with respect to the original SOLPENCO version (Aran et al., 2006; Aran et al., 2011; Jacobs and Poedts, 2011; Pomoell et al., 2015). Its inner boundary is now low in the solar corona at 1.03 R⊙ (Aran et al., 2011), enabling the modeling of shock-accelerated proton spectra to be extended from 64 MeV to 300 MeV. The approach taken to specify the pre-shock, background solar wind plasma is to adopt a polytropic solar wind model which is a 1.5D extension to the Parker model that includes both solar rotation and the magnetic field (Aran et al., 2011; Jacobs and Poedts, 2011). Advantages and drawbacks in the use of the polytropic wind with interplanetary shock simulations are discussed by Jacobs and Poedts (2011) and (Pomoell et al., 2015). The propagation of an IP shock is performed by numerically solving the ideal MHD equations with a perturbation in solar wind radial velocity and density superimposed onto the background solar wind plasma state (Aran et al., 2011). The functional form of the radial velocity and density perturbations are exponential pulse profiles, with additional parameters introduced to control the pulse shape and the angular width and radial thickness of the initial shock disturbance (Aran et al., 2011; Pomoell et al., 2015). The functional form and shape parameters of the IP shock were selected to reproduce IP shock transit times and solar wind plasma measurements for various gradual SEP events observed at 1.0 AU. The 2D MHD equations are solved using the Versatile Advection Code (VAC) (Toth, 1996). The more reduced grid spacing of the MHD model has led to noticeable improvements in the numerical representation of IP shock propagation with respect to the MHD model used in SOLPENCO. The database of 2D MHD shocks includes the evolution of the COBPOINT for virtual observers located at different heliolongitudes with respect to the incoming shocks (Aran et al., 2011). Specifically, the simulated shocks and cobpoints are computed for:

* Solar winds extending from 1.03 R⊙ to 1.6 AU: a slow wind of 365 km s⁻¹, and a fast wind of 595 km s⁻¹.

* Eight initial shock conditions (different values in speed and density), centered at 1.75 R⊙, that yield to shocks arriving to 1 AU between 25 h and 66 h, for the shocks evolving in the slow solar wind, and between 17 h and 48 h, for the shocks in the fast solar wind.

* Two longitudinal widths for the initial shocks: narrow and wide.

* 14 virtual observers located at 1.0 AU, at longitudinal positions between W85 and E65.

The shock-finder procedure, to extract the evolution of the COBPOINT and the shock plasma jumps at the COBPOINT was also automated and significantly improved with respect to the previous version used in SOLPENCO (Aran et al., 2011). A adaptation for a 3D geometry is described in (Rodríguez-Gasén et al., 2011). For each modelled shock, SOLPENCO2 provides the COBPOINT position as well as density, magnetic field ratios and normalized speed ratio, VR, in the lab's frame, for the 14 (longitudes) x 7 (radial distances) virtual observers.

The database of intensity-time profiles are generated with the SAP's transport model (Lario et al., 1998). For the 10 reference events SOLPENCO2 provides:

* The particle source at the COBPOINT, Q, which is obtained by means of a Q(VR) relation based on the parameters derived from the modeling of the April 4, 2000 and December 13, 2006 SEP events (Aran et al., 2011; Pomoell et al., 2015).

* The proton intensity-time profiles for the 11 SEPEM reference energies, for the virtual observers located between 0.2 AU and 1.6 AU. The profiles are obtained by setting constant proton mean free path values (0.35 AU or 1.17 AU for 8.7 MeV protons) and the presence of a turbulent foreshock as in SOLPENCO (Aran et al., 2011). The choice of these transport parameters that leads a better comparison with data is selected.

* The peak intensity and the upstream differential fluence [MeV⁻¹ cm⁻²] as a function of the observer's radial distance, and the derived power-law indices.

To account for the post-shock portion of the fluence (i.e., the downstream fluence) of the events time-profiles in the REL list, an observational analysis (including SEPEM, STEREO and Helios data) of the fluence in the downstream region of the proton intensity-time profiles of gradual SEP events was performed (Aran et al., 2017; Pacheco, 2019). In SOLPENCO2, all fluences are differential fluences. For each event in REL with an IP shock detected, the total fluence at the different radial distances is obtained by adding the scaled upstream fluence and a scaled downstream fluence (values at 1 AU match the observations). The scaling of the downstream fluence is based on an empirical relation found between the downstream-to-total fluence ratio and the longitudinal separation of the observer with respect to the nose of the shock, for each energy channel (Pacheco, 2019). Therefore, in contrast to SOLPENCO, SOLPENCO2 can include a prediction for the downstream fluence of the synthetic events.

The main difference between SOLPENCO and SOLPENCO2 lies in the purpose of the two tools. SOLPENCO is a stand-alone tool ready to be operated by any user with some knowledge of SEP events; and SOLPENCO2 is
designed for providing inputs to the SEPEM interplanetary
statistical SEP model. SOLPENCO2 uses scaling factors
that are specific for the reference events, in order to match
1.0 AU data, whereas SOLPENCO used a universal scaling
factor for its SEP events database. Both, however, share
the same modular approach, which would enable the pos-
sibility of developing another tool more similar to the first
SOLPENCO, using the simulations available in SOL-
PENCO2. The first attempt for this is the inclusion of
SOLPENCO2 outputs in SAWS-ASPECS.

**Inputs:**

For the SOLPENCO tool, the user needs to specify the
following parameters:

* Radial distance from the Sun (0.4 AU or 1.0 AU).

* Angular position of the observer from the CME eruption (any value from E75 to W90).

* Shock initial speed at $18R_⊙$ (any value from $750 \text{ km s}^{-1}$ to $1800 \text{ km s}^{-1}$).

* Proton energy in MeV (0.125, 0.25, 0.5, 1, 2, 4, 8, 16, 32, or 64).

* The proton mean free path of 0.5 MeV protons (0.2 AU or 0.8 AU).

* Turbulent foreshock region (Yes or No).

For SOLPENCO2, in order to model an event, the tran-
sit time of the shock to 1 AU, the longitude of the parent
event (the CME or the flare if the first is not known) and
the pre-event solar wind speed are needed. To scale the
data, the observed peak flux or the upstream fluence is
needed, at least for one energy channel.

**Outputs:** For the user's selected input values the SOLPENCO tool gives: the proton flux time profile, the cumulative fluence profile and the shock transit time and speed to the observer's location and total upstream fluence. For a particular event, SOLPENCO2 provides proton differential intensity-time profiles for the 11 energy channels of SEPEM RDS v2.0 data set, with prescribed values for the transport and source function parameters, as described above.

**Free parameters:** For the SOLPENCO tool all param-
eter values are fixed. For the SOLPENCO2 tool, the val-
ues of the parameters describing the particle source
function, Eq. 17, change for each reference event. With
respect to the FTE of the SAP model (Lario et al.,
1998), the free parameters are the parallel proton mean
free path, the turbulent foreshock region characteristics
which are determined by fitting the observed intensity-
time profiles, as well as the particle source function. The
solar wind speed is also determined by observations, or
by the simulated solar wind. The free parameters of the
shock propagation models used to describe the initial per-
turbation: initial speed, width and duration for (Wu et al.,
1983) and density (Aran et al., 2011), which are fixed in
the databases of the SOLPENCO tools to obtain different
shock transit times to the virtual observers. The solar
wind model of SOLPENCO2 has also the polytropic

index as a free parameter to match observations (Jacobs
and Poedts, 2011).

**Limitations and caveats:** SOLPENCO and SOLPENCO2 generated databases of SEP time profiles for use in forecasting. The models themselves are not run in real time. The main difficulty for that is to find an appropriate proxy for the initial shock speed. The transport model used assumes an Archimedean IMF, perpendicular diffusion is not included, and transport is simulated only up to the shock arrival to the observer. Another limitation for SOLPENCO is the inner boundary location of the shock propagation model, that prevents the simulation of the particle source function at coronal heights. The two tools depend on 1-D particle transport simulations, and hence perpendicular transport is not considered. In addition, the particle source function depends only on the plasma shock-jump in speed at the COBPOINT, and hence does not consider explicitly other parameters that may be relevant for particle acceleration such as the shock obliquity (Lario et al., 1998; Pomoell et al., 2015). Given the underlying assumption of an Archimedean IMF field in the model, non nominal conditions for the solar wind are not taken into account.

**Access to model output or forecasts:** SOLPENCO is available by request to the main author. SOLPENCO2 time profiles are one of the outputs of the SAWS-ASPECS (Section 3.23) real time forecasting tool. Peak flux and total fluence energy spectra for the 172 events in the SEPEM radial event list (1988–2013) are available for seven heliocentric distances (0.2 AU to 1.6 AU) at the SEPEM application server (sepem.eu).

**Model validation:** SOLPENCO's proton intensity-time profiles outputs have been compared with actual large SEP events (Aran et al., 2005a; Aran et al., 2006; Aran, 2007; Aran et al., 2008). The validation shows good results for $E < 2$ MeV protons, and SOLPENCO fails in predicting the peak intensity for $E > 5$ MeV for events showing a strong prompt component (e.g., Aran et al., 2008). The two main reasons for the mismatch are the impossibility of tracking the COBPOINT (and hence of modelling the source function at the shock) below 0.1 au, and the value of *k* in Eq. 17 for high energies. Both are taken into account in the development of SOLPENCO2. SOLPENCO2 time profiles have recently been validated as part of the SAWS-ASPECS system (Section 3.23), however the work is ongoing and has not yet been published.

3.30. *South African Model*

**Model developers:** Du Toit Strauss (principal developer, North-West University), Ruhann Steyn (North-West University), Jabus van den Berg (North-West University, South African National Space Agency).

**Model description:** The South African SEP transport model is a physics-based model aimed at simulating the transport of solar energetic particles, on the pitch-angle level, through the turbulent interplanetary plasma. The
designed for providing inputs to the SEPEM interplanetary
statistical SEP model. SOLPENCO2 uses scaling factors
that are specific for the reference events, in order to match
1.0 AU data, whereas SOLPENCO used a universal scaling
factor for its SEP events database. Both, however, share
the same modular approach, which would enable the pos-
sibility of developing another tool more similar to the first
SOLPENCO, using the simulations available in SOL-
PENCO2. The first attempt for this is the inclusion of
SOLPENCO2 outputs in SAWS-ASPECS.

**Inputs:**

For the SOLPENCO tool, the user needs to specify the
following parameters:

* Radial distance from the Sun (0.4 AU or 1.0 AU).

* Angular position of the observer from the CME eruption (any value from E75 to W90).

* Shock initial speed at $18R_⊙$ (any value from $750 \text{ km s}^{-1}$ to $1800 \text{ km s}^{-1}$).

* Proton energy in MeV (0.125, 0.25, 0.5, 1, 2, 4, 8, 16, 32, or 64).

* The proton mean free path of 0.5 MeV protons (0.2 AU or 0.8 AU).

* Turbulent foreshock region (Yes or No).

For SOLPENCO2, in order to model an event, the tran-
sit time of the shock to 1 AU, the longitude of the parent
event (the CME or the flare if the first is not known) and
the pre-event solar wind speed are needed. To scale the
data, the observed peak flux or the upstream fluence is
needed, at least for one energy channel.

**Outputs:** For the user's selected input values the SOLPENCO tool gives: the proton flux time profile, the cumulative fluence profile and the shock transit time and speed to the observer's location and total upstream fluence. For a particular event, SOLPENCO2 provides proton differential intensity-time profiles for the 11 energy channels of SEPEM RDS v2.0 data set, with prescribed values for the transport and source function parameters, as described above.

**Free parameters:** For the SOLPENCO tool all param-
eter values are fixed. For the SOLPENCO2 tool, the val-
ues of the parameters describing the particle source
function, Eq. 17, change for each reference event. With
respect to the FTE of the SAP model (Lario et al.,
1998), the free parameters are the parallel proton mean
free path, the turbulent foreshock region characteristics
which are determined by fitting the observed intensity-
time profiles, as well as the particle source function. The
solar wind speed is also determined by observations, or
by the simulated solar wind. The free parameters of the
shock propagation models used to describe the initial per-
turbation: initial speed, width and duration for (Wu et al.,
1983) and density (Aran et al., 2011), which are fixed in
the databases of the SOLPENCO tools to obtain different
shock transit times to the virtual observers. The solar
wind model of SOLPENCO2 has also the polytropic

index as a free parameter to match observations (Jacobs
and Poedts, 2011).

**Limitations and caveats:** SOLPENCO and SOLPENCO2 generated databases of SEP time profiles for use in forecasting. The models themselves are not run in real time. The main difficulty for that is to find an appropriate proxy for the initial shock speed. The transport model used assumes an Archimedean IMF, perpendicular diffusion is not included, and transport is simulated only up to the shock arrival to the observer. Another limitation for SOLPENCO is the inner boundary location of the shock propagation model, that prevents the simulation of the particle source function at coronal heights. The two tools depend on 1-D particle transport simulations, and hence perpendicular transport is not considered. In addition, the particle source function depends only on the plasma shock-jump in speed at the COBPOINT, and hence does not consider explicitly other parameters that may be relevant for particle acceleration such as the shock obliquity (Lario et al., 1998; Pomoell et al., 2015). Given the underlying assumption of an Archimedean IMF field in the model, non nominal conditions for the solar wind are not taken into account.

**Access to model output or forecasts:** SOLPENCO is available by request to the main author. SOLPENCO2 time profiles are one of the outputs of the SAWS-ASPECS (Section 3.23) real time forecasting tool. Peak flux and total fluence energy spectra for the 172 events in the SEPEM radial event list (1988–2013) are available for seven heliocentric distances (0.2 AU to 1.6 AU) at the SEPEM application server (sepem.eu).

**Model validation:** SOLPENCO's proton intensity-time profiles outputs have been compared with actual large SEP events (Aran et al., 2005a; Aran et al., 2006; Aran, 2007; Aran et al., 2008). The validation shows good results for $E < 2$ MeV protons, and SOLPENCO fails in predicting the peak intensity for $E > 5$ MeV for events showing a strong prompt component (e.g., Aran et al., 2008). The two main reasons for the mismatch are the impossibility of tracking the COBPOINT (and hence of modelling the source function at the shock) below 0.1 au, and the value of *k* in Eq. 17 for high energies. Both are taken into account in the development of SOLPENCO2. SOLPENCO2 time profiles have recently been validated as part of the SAWS-ASPECS system (Section 3.23), however the work is ongoing and has not yet been published.

3.30. *South African Model*

**Model developers:** Du Toit Strauss (principal developer, North-West University), Ruhann Steyn (North-West University), Jabus van den Berg (North-West University, South African National Space Agency).

**Model description:** The South African SEP transport model is a physics-based model aimed at simulating the transport of solar energetic particles, on the pitch-angle level, through the turbulent interplanetary plasma. The
model implements a Parker (1958) magnetic field geometry and focuses on applying transport coefficients that are derived from first principles, also including the perpendicular diffusion of SEPs. The model implements a finite differences numerical scheme, with special flux conservative boundary conditions, that solves the focused transport equations in a reduced geometry (neglecting adiabatic energy losses and only performing simulations in the equatorial plane) in order to speed up computations so that the model can be executed in a real-time operational setting (Strauss and Fichtner, 2015; Heita, 2018).

Previously, the focus of the model was on simulating SEP electrons (Strauss et al., 2017; Strauss and le Roux, 2019; Strauss et al., 2020), including the effects of wave generation. The model was also tested for an operational setting by Steyn et al. (2020) where the model was driven using an observationally constrained inner boundary condition in order to simulate historical SEP electron events. As the acceleration of SEP is not simulated self-consistently in this transport model, the time and spatial profile of the accelerated SEP distribution must be specified at the inner numerical boundary (assumed to be the solar source surface). We refer to this as the injection function. Work continues to constrain this function, especially for protons, using historical SEP events. The model is currently being tested and optimized to simulate SEP proton transport, where after it will be moved into a predictive setting.

**Inputs:** The model requires the following inputs:

1. The injection function, i.e., the time and spatial dependence of the accelerated SEP source that propagates into the inner heliosphere. The time dependence can be derived from different proxies, e.g. the SXR flux or the CME speed, and is directly read into the model. The spatial dependence of the injection function, most importantly the width/broadness of the SEP source, also needs to be specified. We generally assume the SEP source to have a Gaussian shape in terms of longitude and only specify the broadness of this Gaussian function.

2. The position of active region that produced the SEP event and the position of the virtual observers where the predicted SEP intensity is required.

**Outputs:** The model provides the pitch-angle dependent particle distribution function as a function of time at all spatial grid points in the equatorial plane. From this the omni-directional SEP intensity and first-order anisotropy, amongst other quantities, can be calculated. Fig. 14 shows an example of a simulated multi-spacecraft event.

**Free parameters:** In the present iteration of the model, the level of perpendicular diffusion is a free parameter. However, work is underway in order to constrain this parameter using historical SEP measurements. The level of pitch-angle scattering is fixed but can be varied if required.

**Limitations and caveats:** When using this SEP model, the following limitations should be taken into account:

1. The model neglects adiabatic energy losses.

2. The model only solves the focused transport equation in the equatorial plane and therefore adopts a 2D spatial geometry. However, a comparison between 2D and 3D models show very good agreement (Steyn et al., 2020).

**Access to model output or forecasts:** A 1D (i.e. neglecting the cross-field coordinate) version of the model is described in detail by van den Berg et al. (2020) and available at https://github.com/RDStrauss/SEPPropagator. Once the real-time implementation of 2D model is complete, it will be included in the same repository. Interested users can contact the model developers for access to a preliminary version of the model.

**Model validation:** The validation of the model is an actively ongoing process. The model is primarily a research tool and the emphasis in the past was on comparing model results with SEP measurements in order to understand the underlying processes in more detail. The validation of the model's predictive capability is currently underway and we hope to present this to the community in the very near future.

### 3.31. SPARX - Solar Particle Radiation swX

**Model developers:** Michael S. Marsh (Met Office), Silvia Dalla (University of Central Lancashire), Bill Swalwell (University of Central Lancashire), Charlotte Waterfall (University of Central Lancashire).

**Model description:** Solar Particle Radiation SWx (SPARX) is a forecasting system based on a full 3-D physics-based model for simulating SEP propagation for Space Weather forecasting purposes (Marsh et al., 2015). As SPARX was initially developed as part of the European Union-funded Seventh Framework Programme (FP7) COMESEP project (Crosby et al., 2012), a version of the SPARX output is operational within its SEP forecasting component which produces alerts at https://swe.ssa.esa.int/bira-comesep-federated. As described in Figure 1 of Marsh et al. (2015), results of earlier runs of a 3D test particle code are used by SPARX in real time to produce a forecast.

The 3D test particle code naturally describes propagation across the magnetic field. High energy SEPs have a strong influence on radiation dose and these particles are affected by drifts due to the gradient and curvature of the Parker spiral, requiring a 3D description (Dalla et al., 2013). The latter effects are included in the current version (v1.0) of SPARX, while neither drift along the heliospheric current sheet nor magnetic field line meandering are considered at present. SPARX simulates a large number of independent test particles that follow the equation of motion in 3D:
model implements a Parker (1958) magnetic field geometry and focuses on applying transport coefficients that are derived from first principles, also including the perpendicular diffusion of SEPs. The model implements a finite differences numerical scheme, with special flux conservative boundary conditions, that solves the focused transport equations in a reduced geometry (neglecting adiabatic energy losses and only performing simulations in the equatorial plane) in order to speed up computations so that the model can be executed in a real-time operational setting (Strauss and Fichtner, 2015; Heita, 2018).

Previously, the focus of the model was on simulating SEP electrons (Strauss et al., 2017; Strauss and le Roux, 2019; Strauss et al., 2020), including the effects of wave generation. The model was also tested for an operational setting by Steyn et al. (2020) where the model was driven using an observationally constrained inner boundary condition in order to simulate historical SEP electron events. As the acceleration of SEP is not simulated self-consistently in this transport model, the time and spatial profile of the accelerated SEP distribution must be specified at the inner numerical boundary (assumed to be the solar source surface). We refer to this as the injection function. Work continues to constrain this function, especially for protons, using historical SEP events. The model is currently being tested and optimized to simulate SEP proton transport, where after it will be moved into a predictive setting.

**Inputs:** The model requires the following inputs:

1. The injection function, i.e., the time and spatial dependence of the accelerated SEP source that propagates into the inner heliosphere. The time dependence can be derived from different proxies, e.g. the SXR flux or the CME speed, and is directly read into the model. The spatial dependence of the injection function, most importantly the width/broadness of the SEP source, also needs to be specified. We generally assume the SEP source to have a Gaussian shape in terms of longitude and only specify the broadness of this Gaussian function.

2. The position of active region that produced the SEP event and the position of the virtual observers where the predicted SEP intensity is required.

**Outputs:** The model provides the pitch-angle dependent particle distribution function as a function of time at all spatial grid points in the equatorial plane. From this the omni-directional SEP intensity and first-order anisotropy, amongst other quantities, can be calculated. Fig. 14 shows an example of a simulated multi-spacecraft event.

**Free parameters:** In the present iteration of the model, the level of perpendicular diffusion is a free parameter. However, work is underway in order to constrain this parameter using historical SEP measurements. The level of pitch-angle scattering is fixed but can be varied if required.

**Limitations and caveats:** When using this SEP model, the following limitations should be taken into account:

1. The model neglects adiabatic energy losses.

2. The model only solves the focused transport equation in the equatorial plane and therefore adopts a 2D spatial geometry. However, a comparison between 2D and 3D models show very good agreement (Steyn et al., 2020).

**Access to model output or forecasts:** A 1D (i.e. neglecting the cross-field coordinate) version of the model is described in detail by van den Berg et al. (2020) and available at https://github.com/RDStrauss/SEPPropagator. Once the real-time implementation of 2D model is complete, it will be included in the same repository. Interested users can contact the model developers for access to a preliminary version of the model.

**Model validation:** The validation of the model is an actively ongoing process. The model is primarily a research tool and the emphasis in the past was on comparing model results with SEP measurements in order to understand the underlying processes in more detail. The validation of the model's predictive capability is currently underway and we hope to present this to the community in the very near future.

### 3.31. SPARX - Solar Particle Radiation swX

**Model developers:** Michael S. Marsh (Met Office), Silvia Dalla (University of Central Lancashire), Bill Swalwell (University of Central Lancashire), Charlotte Waterfall (University of Central Lancashire).

**Model description:** Solar Particle Radiation SWx (SPARX) is a forecasting system based on a full 3-D physics-based model for simulating SEP propagation for Space Weather forecasting purposes (Marsh et al., 2015). As SPARX was initially developed as part of the European Union-funded Seventh Framework Programme (FP7) COMESEP project (Crosby et al., 2012), a version of the SPARX output is operational within its SEP forecasting component which produces alerts at https://swe.ssa.esa.int/bira-comesep-federated. As described in Figure 1 of Marsh et al. (2015), results of earlier runs of a 3D test particle code are used by SPARX in real time to produce a forecast.

The 3D test particle code naturally describes propagation across the magnetic field. High energy SEPs have a strong influence on radiation dose and these particles are affected by drifts due to the gradient and curvature of the Parker spiral, requiring a 3D description (Dalla et al., 2013). The latter effects are included in the current version (v1.0) of SPARX, while neither drift along the heliospheric current sheet nor magnetic field line meandering are considered at present. SPARX simulates a large number of independent test particles that follow the equation of motion in 3D:
<figure><img src="image_15.png" /><figcaption>Fig. 14. An example of the South African SEP model applied to a multi-spacecraft event. The left panel shows a contour plot of 25 MeV proton intensities and the position of a number of spacecraft. The right panel shows the simulated differential intensity and anisotropy levels at the position of these spacecraft.</figcaption></figure>

$$ \frac{d\mathbf{p}}{dt} = q \left( \mathbf{E} + \frac{1}{c} \frac{\mathbf{p}}{m_0 \gamma} \times \mathbf{B} \right) \qquad (18) $$

where **p** is the particle's momentum, *q* is the particle charge, *m*₀ is its rest mass, *γ* is its Lorentz factor, and *c* is the speed of light. The magnetic field **B** is defined by a unipolar Parker Spiral and **E** is the solar wind electric field in a fixed reference frame (Marsh et al., 2015). The field polarity of the IMF used in the SPARX forecast is determined by the hemisphere in which the eruptive event occurs and the A⁺ or A⁻ phase of the global solar magnetic field, which changes throughout the solar cycle. The particle motion is calculated in a fixed reference frame that sees the solar wind move radially outward and the effects of corotation of magnetic flux tubes anchored at the Sun are included. Turbulence is simulated by introducing isotropic scattering of each particle's pitch angle and gyrophase in the reference frame of the solar wind with a prescribed value of the mean free path. Particle drifts are naturally described by SPARX's approach and play an important role in longitudinal spreading and particle deceleration (Marsh et al., 2013; Dalla et al., 2013).

In the test particle simulations particles are injected instantaneously at 2*R*<sub>sun</sub> across a spatially extended source region that represents a CME-driven shock in the corona. The input particle spectrum is assumed to be a power law E⁻⁷. Particles are propagated and every time they cross a

spherical boundary at 1 AU, their parameters are output and used to generate a synthetic particle spectrum.

SPARX is part of the COMESEP Alert System and its implementation within that system is described in detail in Section 3.6. Running of the 3D test particle code is too time consuming for operational usage, therefore the real-time forecasting tool, SPARX, uses a pre-generated database of outputs of runs with varying proton injection locations. The database contains 30 model runs for each IMF polarity, each run describing a specific 6° × 6° injection tile at a given central latitude, following the particles for 100 h. In each tile 100,000 protons are injected with energies in the range 10–400 MeV. An extended CME-shock-like injection region is simulated by summing up the outputs of multiple 6° × 6° tiles. In SPARX v1.0 a default fixed injection width of 48° × 48° is used. The centre of the shock-like region is the location of the flare associated to the event. A constant particle injection density over the shock is maintained, i.e. it is assumed that the acceleration efficiency is constant across the full injection region. In v1.0 the spectral index of the injection energy spectrum is taken to be γ = 1.1 and the mean free path λ = 0.3 AU. Because of the symmetric nature of the assumed IMF, only a single strip of injection tiles are required to build up the 48° × 48° injection region by utilising the rotational symmetry and relative longitude difference between the observer and the detected flare (Marsh et al., 2015). A synthetic particle spectrum is produced at
<figure><img src="image_15.png" /><figcaption>Fig. 14. An example of the South African SEP model applied to a multi-spacecraft event. The left panel shows a contour plot of 25 MeV proton intensities and the position of a number of spacecraft. The right panel shows the simulated differential intensity and anisotropy levels at the position of these spacecraft.</figcaption></figure>

<figure><img src="image_16.png" /></figure>

$$ \frac{d\mathbf{p}}{dt} = q \left( \mathbf{E} + \frac{1}{c} \frac{\mathbf{p}}{m_0 \gamma} \times \mathbf{B} \right) \qquad (18) $$

where **p** is the particle's momentum, *q* is the particle charge, *m*₀ is its rest mass, *γ* is its Lorentz factor, and *c* is the speed of light. The magnetic field **B** is defined by a unipolar Parker Spiral and **E** is the solar wind electric field in a fixed reference frame (Marsh et al., 2015). The field polarity of the IMF used in the SPARX forecast is determined by the hemisphere in which the eruptive event occurs and the A⁺ or A⁻ phase of the global solar magnetic field, which changes throughout the solar cycle. The particle motion is calculated in a fixed reference frame that sees the solar wind move radially outward and the effects of corotation of magnetic flux tubes anchored at the Sun are included. Turbulence is simulated by introducing isotropic scattering of each particle's pitch angle and gyrophase in the reference frame of the solar wind with a prescribed value of the mean free path. Particle drifts are naturally described by SPARX's approach and play an important role in longitudinal spreading and particle deceleration (Marsh et al., 2013; Dalla et al., 2013).

In the test particle simulations particles are injected instantaneously at 2*R*<sub>sun</sub> across a spatially extended source region that represents a CME-driven shock in the corona. The input particle spectrum is assumed to be a power law E⁻⁷. Particles are propagated and every time they cross a

spherical boundary at 1 AU, their parameters are output and used to generate a synthetic particle spectrum.

SPARX is part of the COMESEP Alert System and its implementation within that system is described in detail in Section 3.6. Running of the 3D test particle code is too time consuming for operational usage, therefore the real-time forecasting tool, SPARX, uses a pre-generated database of outputs of runs with varying proton injection locations. The database contains 30 model runs for each IMF polarity, each run describing a specific 6° × 6° injection tile at a given central latitude, following the particles for 100 h. In each tile 100,000 protons are injected with energies in the range 10–400 MeV. An extended CME-shock-like injection region is simulated by summing up the outputs of multiple 6° × 6° tiles. In SPARX v1.0 a default fixed injection width of 48° × 48° is used. The centre of the shock-like region is the location of the flare associated to the event. A constant particle injection density over the shock is maintained, i.e. it is assumed that the acceleration efficiency is constant across the full injection region. In v1.0 the spectral index of the injection energy spectrum is taken to be γ = 1.1 and the mean free path λ = 0.3 AU. Because of the symmetric nature of the assumed IMF, only a single strip of injection tiles are required to build up the 48° × 48° injection region by utilising the rotational symmetry and relative longitude difference between the observer and the detected flare (Marsh et al., 2015). A synthetic particle spectrum is produced at
the observer by integrating over a 2° × 2° surface area element at 1 AU for a selected period of time. The flux spectrum is normalized by applying the statistical relationships between proton peak flux and flare X-ray peak flux derived by (Dierckxsens et al., 2015), described in detail in Section 3.6.

**Inputs:**

SPARX inputs:

* Flare location

* Flare peak time

* Flare X-ray peak value (input into SPARX as a magnitude, i.e., ~-4.0' for M1.0 flare)

3D test particle code inputs: (fixed in current implementation but could be varied in future)

* Solar magnetic field polarity

* Particle species (in v1.0: protons)

* Output flux energy range (in v1.0: >10 MeV, >60 MeV)

* Injection energy spectrum (in v1.0: power law with index 1.1)

* Location in the heliosphere where to generate flux profiles (in v1.0: 1 AU)

* Mean free path

**Outputs:** SPARX v1.0 produces as outputs SEP flux time profiles for E >10 MeV and E >60 MeV (see Fig. 15 for an example). Threshold crossing times, proton peak flux and peak time, and SEP event duration are calculated from the time profile. The 3D test particle model can be used to produce new versions of SPARX that output profiles in other energy ranges and a version for >300 MeV protons is currently being developed (Waterfall et al. 2022, in preparation).

**Free parameters:**

* Power law index of input energy spectrum

* Mean free path

* Solar wind speed (which affects the shape of the unipolar Parker Spiral)

* Width of injection region

**Limitations and caveats:** Only flares >M1.0 can be taken as input by SPARX. The analysis that led to this selection (Dierckxsens et al., 2015) was carried out for 5 flare bins, where the last bin is for >X5.0 flares. Any flares >X5.0 will result in the same scaling/normalisation factors in SPARX.

The SPARX 3D test particle code model accounts for the initial acceleration and transport of the particles at the start of an event low in the corona. No evolution of the acceleration region, such as the propagation of a CME out into the inner heliosphere, is considered. Through this approach, this model can predict event onset and evolution of the initially accelerated particles, but does not include the particle populations that are continuously accelerated at a CME shock front following the initial eruption.

**Access to model output or forecasts:** An initial SPARX version is implemented in COMESEP at https://swe.ssa.esa.int/bira-comesep-federated. SPARX is planned to be run operationally at the UK Met Office in future, using the GOES-R XRS flare magnitude and location products as inputs. It will also be possible to run SPARX via the ESA VSWMC (https://esa-vswmc.eu/).

**Model validation:** Dalla et al. (2018) assessed model performance using a list of 125 X-class flares between 1 September 1997 and 30 April 2017. For each flare, SPARX was run in forecast mode with a fixed set of model parameters for all events. The output >10 MeV fluxes were

<figure><img src="image_16.png" /><figcaption>Fig. 15. Example of a SPARX output. Flux profiles of >10 MeV and >60 MeV protons for an X1.0 flare at N10W20 are shown. The legend displays calculated parameters of the flux profiles.</figcaption></figure>
the observer by integrating over a 2° × 2° surface area element at 1 AU for a selected period of time. The flux spectrum is normalized by applying the statistical relationships between proton peak flux and flare X-ray peak flux derived by (Dierckxsens et al., 2015), described in detail in Section 3.6.

**Inputs:**

SPARX inputs:

* Flare location

* Flare peak time

* Flare X-ray peak value (input into SPARX as a magnitude, i.e., ~-4.0~ for M1.0 flare)

3D test particle code inputs: (fixed in current implementation but could be varied in future)

* Solar magnetic field polarity

* Particle species (in v1.0: protons)

* Output flux energy range (in v1.0: >10 MeV, >60 MeV)

* Injection energy spectrum (in v1.0: power law with index 1.1)

* Location in the heliosphere where to generate flux profiles (in v1.0: 1 AU)

* Mean free path

**Outputs:** SPARX v1.0 produces as outputs SEP flux time profiles for E >10 MeV and E >60 MeV (see Fig. 15 for an example). Threshold crossing times, proton peak flux and peak time, and SEP event duration are calculated from the time profile. The 3D test particle model can be used to produce new versions of SPARX that output profiles in other energy ranges and a version for >300 MeV protons is currently being developed (Waterfall et al. 2022, in preparation).

**Free parameters:**

* Power law index of input energy spectrum

* Mean free path

* Solar wind speed (which affects the shape of the unipolar Parker Spiral)

* Width of injection region

**Limitations and caveats:** Only flares >M1.0 can be taken as input by SPARX. The analysis that led to this selection (Dierckxsens et al., 2015) was carried out for 5 flare bins, where the last bin is for >X5.0 flares. Any flares >X5.0 will result in the same scaling/normalisation factors in SPARX.

The SPARX 3D test particle code model accounts for the initial acceleration and transport of the particles at the start of an event low in the corona. No evolution of the acceleration region, such as the propagation of a CME out into the inner heliosphere, is considered. Through this approach, this model can predict event onset and evolution of the initially accelerated particles, but does not include the particle populations that are continuously accelerated at a CME shock front following the initial eruption.

**Access to model output or forecasts:** An initial SPARX version is implemented in COMESEP at https://swe.ssa.esa.int/bira-comesep-federated. SPARX is planned to be run operationally at the UK Met Office in future, using the GOES-R XRS flare magnitude and location products as inputs. It will also be possible to run SPARX via the ESA VSWMC (https://esa-vswmc.eu/).

**Model validation:** Dalla et al. (2018) assessed model performance using a list of 125 X-class flares between 1 September 1997 and 30 April 2017. For each flare, SPARX was run in forecast mode with a fixed set of model parameters for all events. The output >10 MeV fluxes were

<figure><img src="image_17.png" /><figcaption>Fig. 15. Example of a SPARX output. Flux profiles of >10 MeV and >60 MeV protons for an X1.0 flare at N10W20 are shown. The legend displays calculated parameters of the flux profiles.</figcaption></figure>
<table><caption>Table 8
Validation of the SPARX model by Dalla et al. (2018). Bias = tendency to under/over forecast; POD = Probability of Detection; FAR = False Alarm Rate; POFD = Probability of False Detection; CSI = Critical Success Index.</caption><thead><tr><th></th><th><i>F</i><sub>10</sub></th><th><i>F</i><sub>1</sub></th></tr></thead><tbody><tr><td>Bias</td><td>1.18</td><td>1.37</td></tr><tr><td>POD</td><td>0.5</td><td>0.77</td></tr><tr><td>FAR</td><td>0.57</td><td>0.44</td></tr><tr><td>POFD</td><td>0.32</td><td>0.43</td></tr><tr><td>CSI</td><td>0.30</td><td>0.48</td></tr></tbody></table>

assessed for event/no event predictions by applying the standard NOAA threshold of 10 pfu ($F_{10}$) and additional lower threshold of 1 pfu ($F_1$). The forecasts were compared to GOES >10 MeV observations with the same thresholds applied.

SPARX performance when applying the 10 pfu threshold resulted in 20 hits, 27 false alarms, 20 misses, and 58 correct negatives. Application of the 1 pfu threshold resulted in 40 hits, 31 false alarms, 12 misses, and 42 correct negatives. The corresponding metrics and skill scores are reported in Table 8.

### 3.32. SPREADFAST - Solar Particle Radiation
*Environment Analysis and Forecasting - Acceleration and Scattering Transport*

**Model developers:** Kamen Kozarev (Institute of Astronomy, Bulgarian Academy of Sciences (IA-BAS)), Mohamed Nedal (IABAS), Rositsa Miteva (IABAS), Momchil Dechev (IABAS), Pietro Zucca (Netherlands Institute for Radio Astronomy (ASTRON)).

**Model description:** Over the last fifteen years, observations and numerical models have confirmed that in their early stages (below 5–10 $R_{Sun}$), CMEs often drive shocks (Ontiveros and Vourlidas, 2009; Gopalswamy and Yashiro, 2011), and those shocks may accelerate SEPs to energies up to and beyond 100 MeV/n (Battarbee et al., 2013; Kozarev et al., 2013; Schwadron et al., 2014; Kong et al., 2017). To investigate the particle acceleration and transport in these very early stages of solar eruptions, we have developed a prototype and various scientific aspects of an end-to-end, physics-based, heliospheric SEP modeling and forecasting system —Acceleration and Scattering Transport (SPREADFAST). It allows for producing predictions of SEP fluxes in the inner heliosphere, by modeling the acceleration of protons at CME-driven shocks near the Sun, and their subsequent interplanetary transport. The system prototype incorporates results from our scientific investigations, the modification and linking of existing open-source scientific software, and its adaptation to the goals of the proposed work. SPREADFAST helps fulfill a vital component of ESA’s Space Situational Awareness program by contributing to the capability to protect space assets from solar activity space radiation. A description of the project is available at https://spreadfast.astro.bas.bg/.

The modeling framework combines detailed EUV observations of Coronal Bright Front (CBF) events with modeling of the interacting coronal plasma and the resulting SEP production and interplanetary transport. It is a chain of data-driven analytic and numerical models for estimating: coronal plasma conditions, dynamics of large-scale coronal (CME-driven) shock waves; energetic particle acceleration; scatter-based, time-dependent SEP propagation in the heliosphere to specific positions.

To characterize the kinematics of CBFs, we applied to the AIA observations the methodology of the Coronal Analysis of SHocks and Wave (CASHeW) framework (Kozarev et al., 2017), updated and implemented in SPREADFAST. Our framework estimates the CBF kinematics in a similar way to Long et al. (2021) and Downs et al. (2021), by following the leading edge of the front on consecutive images. We explicitly measure the kinematics of the front in both the radial and lateral (parallel to the limb) directions, in order to model the CBF shape more realistically. In addition, we calculate the kinematics of the peak and back edge of the CBFs over time, which allows us to estimate their time-dependent mean intensity and thickness. The front observations may be extrapolated to 10–30 solar radii based on some model (Gallagher et al., 2003; Byrne et al., 2013).

Based on the radial and lateral measured front positions over time, a three-dimensional, time-dependent geometric spheroid model - Synthetic Shock Model (S2M) - is developed for all compressive fronts, consisting of a large number of points (>1000), used for the estimation of the dynamic shock upstream coronal parameters. The spheroid remains centered on the eruption source throughout the event, while its aspect ratio varies based on the radial and lateral CBF position measurements and extrapolations. The three-dimensional geometric model describes the shock surface evolution at 24-s intervals from the onset of the CBF to the time when its nose (leading direction’s front position) reaches $10 R_{Sun}$. This model shock surface is then propagated through a model solar corona, represented by results of a Magnetohydrodynamic Algorithm outside a Sphere (MAS Mikić et al., 1999) synoptic coronal MHD model run for the Carrington rotation of each simulated event. The shock surface thus samples at discrete points the relevant parameters for coronal shock acceleration of SEPs, determined by the magnetic field lines crossing it consecutively at each point.

After the plasma parameters along the individual shock-crossing field lines have been established, they are fed in a time-dependent manner into the coronal DSA model (Kozarev and Schwadron, 2016; Kozarev et al., 2019) for calculation of the proton acceleration between the low corona and $10 R_{Sun}$. The model was specifically developed to take as input remote solar observations and data-driven model output from the CASHEW framework. The model solves for the coronal charged particle acceleration by large-scale CME-driven shocks. The model calculates the minimum shock injection momenta for the particles. It
<table><caption>Table 8
Validation of the SPARX model by Dalla et al. (2018). Bias = tendency to under/over forecast; POD = Probability of Detection; FAR = False Alarm Rate; POFD = Probability of False Detection; CSI = Critical Success Index.</caption><thead><tr><th></th><th><i>F</i><sub>10</sub></th><th><i>F</i><sub>1</sub></th></tr></thead><tbody><tr><td>Bias</td><td>1.18</td><td>1.37</td></tr><tr><td>POD</td><td>0.5</td><td>0.77</td></tr><tr><td>FAR</td><td>0.57</td><td>0.44</td></tr><tr><td>POFD</td><td>0.32</td><td>0.43</td></tr><tr><td>CSI</td><td>0.30</td><td>0.48</td></tr></tbody></table>

assessed for event/no event predictions by applying the standard NOAA threshold of 10 pfu ($F_{10}$) and additional lower threshold of 1 pfu ($F_1$). The forecasts were compared to GOES >10 MeV observations with the same thresholds applied.

SPARX performance when applying the 10 pfu threshold resulted in 20 hits, 27 false alarms, 20 misses, and 58 correct negatives. Application of the 1 pfu threshold resulted in 40 hits, 31 false alarms, 12 misses, and 42 correct negatives. The corresponding metrics and skill scores are reported in Table 8.

### 3.32. SPREADFAST - Solar Particle Radiation
*Environment Analysis and Forecasting - Acceleration and Scattering Transport*

**Model developers:** Kamen Kozarev (Institute of Astronomy, Bulgarian Academy of Sciences (IA-BAS)), Mohamed Nedal (IABAS), Rositsa Miteva (IABAS), Momchil Dechev (IABAS), Pietro Zucca (Netherlands Institute for Radio Astronomy (ASTRON)).

**Model description:** Over the last fifteen years, observations and numerical models have confirmed that in their early stages (below 5–10 $R_{Sun}$), CMEs often drive shocks (Ontiveros and Vourlidas, 2009; Gopalswamy and Yashiro, 2011), and those shocks may accelerate SEPs to energies up to and beyond 100 MeV/n (Battarbee et al., 2013; Kozarev et al., 2013; Schwadron et al., 2014; Kong et al., 2017). To investigate the particle acceleration and transport in these very early stages of solar eruptions, we have developed a prototype and various scientific aspects of an end-to-end, physics-based, heliospheric SEP modeling and forecasting system —Acceleration and Scattering Transport (SPREADFAST). It allows for producing predictions of SEP fluxes in the inner heliosphere, by modeling the acceleration of protons at CME-driven shocks near the Sun, and their subsequent interplanetary transport. The system prototype incorporates results from our scientific investigations, the modification and linking of existing open-source scientific software, and its adaptation to the goals of the proposed work. SPREADFAST helps fulfill a vital component of ESA’s Space Situational Awareness program by contributing to the capability to protect space assets from solar activity space radiation. A description of the project is available at https://spreadfast.astro.bas.bg/.

The modeling framework combines detailed EUV observations of Coronal Bright Front (CBF) events with modeling of the interacting coronal plasma and the resulting SEP production and interplanetary transport. It is a chain of data-driven analytic and numerical models for estimating: coronal plasma conditions, dynamics of large-scale coronal (CME-driven) shock waves; energetic particle acceleration; scatter-based, time-dependent SEP propagation in the heliosphere to specific positions.

To characterize the kinematics of CBFs, we applied to the AIA observations the methodology of the Coronal Analysis of SHocks and Wave (CASHeW) framework (Kozarev et al., 2017), updated and implemented in SPREADFAST. Our framework estimates the CBF kinematics in a similar way to Long et al. (2021) and Downs et al. (2021), by following the leading edge of the front on consecutive images. We explicitly measure the kinematics of the front in both the radial and lateral (parallel to the limb) directions, in order to model the CBF shape more realistically. In addition, we calculate the kinematics of the peak and back edge of the CBFs over time, which allows us to estimate their time-dependent mean intensity and thickness. The front observations may be extrapolated to 10–30 solar radii based on some model (Gallagher et al., 2003; Byrne et al., 2013).

Based on the radial and lateral measured front positions over time, a three-dimensional, time-dependent geometric spheroid model - Synthetic Shock Model (S2M) - is developed for all compressive fronts, consisting of a large number of points (>1000), used for the estimation of the dynamic shock upstream coronal parameters. The spheroid remains centered on the eruption source throughout the event, while its aspect ratio varies based on the radial and lateral CBF position measurements and extrapolations. The three-dimensional geometric model describes the shock surface evolution at 24-s intervals from the onset of the CBF to the time when its nose (leading direction’s front position) reaches $10 R_{Sun}$. This model shock surface is then propagated through a model solar corona, represented by results of a Magnetohydrodynamic Algorithm outside a Sphere (MAS Mikić et al., 1999) synoptic coronal MHD model run for the Carrington rotation of each simulated event. The shock surface thus samples at discrete points the relevant parameters for coronal shock acceleration of SEPs, determined by the magnetic field lines crossing it consecutively at each point.

After the plasma parameters along the individual shock-crossing field lines have been established, they are fed in a time-dependent manner into the coronal DSA model (Kozarev and Schwadron, 2016; Kozarev et al., 2019) for calculation of the proton acceleration between the low corona and $10 R_{Sun}$. The model was specifically developed to take as input remote solar observations and data-driven model output from the CASHEW framework. The model solves for the coronal charged particle acceleration by large-scale CME-driven shocks. The model calculates the minimum shock injection momenta for the particles. It
takes as input a particle distribution function, and provides time-dependent distribution function spectra or fluxes, as output. We use as input to the model averaged and rescaled suprathermal proton spectra from the SOHO/ERNE instrument (Torsti et al., 1995), observed during the 24 h of quiet time preceding each SEP event. We fit power laws to each suprathermal spectrum in the energy range 0.056 – 3.0MeV, and scale them to 1.05$R_{Sun}$, assuming a simple inverse square dependence on radial distance (implying flux conservation).

The final step of the modeling chain is the transport of the accelerated SEPs to 1 AU, and subsequent comparison with particle observations with the ERNE instrument. This is achieved by taking the resulting averaged fluxes from the coronal acceleration model for the entire event as input to a modified version of the EPREM focused transport model (Schwadron et al., 2010), and transporting them through a Parker-type static interplanetary medium.

We have so far modeled a set of 62 historical events with typical coronal and interplanetary conditions, with results available at https://spreadfast.astro.bas.bg/catalog/. The SPREADFAST system also has a real-time version, which is under development.

**Inputs:**

* SDO/AIA Level 1 full-cadence and full resolution data (EUV channels 94,131,171,193,211,335)

* SOHO/ERNE observations (LEMS120 P1-P8 channels)

* ACE/EPAM hourly observations (channels p1, p3, p5, fp6p, p7)

* Synoptic MAS MHD model results (datacubes freely available from Predictive Science's website https://www Predsci com/mhdweb/home.php

**Outputs:**

* 3D models of EUV wave eruptions in the corona (below 10 Rs)

* Modeled shock front plasma parameters below 10 Rs

* Proton fluxes and fluences below 10 Rs for ~4 h of events

* Proton fluxes and fluences at 1 au for the first ~10 h of events

**Free parameters:**

* Coronal acceleration (DSA) scattering mean free path

* Interplanetary transport parallel scattering mean free path

* Interplanetary transport ratio of perpendicular to parallel diffusion (for model runs with perpendicular transport)

**Limitations and caveats:**

* SPREADFAST is currently set up to run only for protons;

* The model assumes a source spectrum based on quiet-time suprathermal observations (no flare particles);

* Currently, only parallel interplanetary transport is implemented

* No lat/lon dependence of coronal DSA fluxes for interplanetary transport - to be implemented in next version;

**Access to model output or forecasts:**

Results for modeled historical events are available in the SPREADFAST catalog at https://spreadfast.astro.bas.bg/catalog/. The near-real time forecasting service is under development. It will be available at https://spreadfast.astro.bas.bg/

**Model validation:** Kozarev et al. (2022) modeled 62 events with the SPREADFAST model framework. The modeled time profiles were calculated for the geometric mean of the ERNE energy channels between 3 and 115 MeV and the ERNE pre-event background was added for better comparison with data. The modeled results were plotted on top of ERNE data for May 11, 2011, and were found to have good agreement. The event-integrated fluence was also compared. Similar plots for all 62 events are available in the SPREADFAST catalog.

Kozarev et al., 2022 presented correlation plots between the modeled and observed power-law indices of the fluence spectra as well as the modeled and observed onset times for all 62 events. The power law indices showed significant scatter, but clustered around an index of −2.5 for both SPREADFAST and ERNE. The onset times were strongly correlated for multiple energies, with the modeled times typically within ~5 h of the observed onsets.

The paper reports that 2/3 of the modeled events showed good agreement with observations, but there was a discrepancy in the remaining events. It is hypothesized that this is likely due to the existence of additional seed population beyond the quiet-time suprathermal spectra, possibly from flare-accelerated protons.

### 3.33. SPRINTS - Space Radiation Intelligence System

**Model developers:** Alec Engell (NextGen), Brianna Maze (NextGen), Harold Farmer (NextGen), Thuha Kerber (NextGen), Ben Barnett (NextGen), Jeremy Loomis (NextGen), David Falconer (University of Alabama Huntsville), Ian Richardson (University of Maryland/Goddard Space Flight Center (GSFC)), Maher Dayeh (SWRI), Barbara Thompson (GSFC), Tilaye Tadesse (JSC), Ian Fernandez (JSC, Princeton), Kerry Lee (JSC).

**Model description:** The Space Radiation Intelligence System (SPRINTS) is an empirical and machine-learned forecasting tool that is capable of giving forecasts for solar-driven events covering solar flares, solar particle events (SPEs), and coronal mass ejections (CMEs). SPRINTS uses and independently runs MAG4 (3.13) and extends MAG4 capabilities to make predictions of solar flares out to 48 h, with additional forecast probabilities of the GOES X-ray flare fluence and the peak flare ratio
takes as input a particle distribution function, and provides time-dependent distribution function spectra or fluxes, as output. We use as input to the model averaged and rescaled suprathermal proton spectra from the SOHO/ERNE instrument (Torsti et al., 1995), observed during the 24 h of quiet time preceding each SEP event. We fit power laws to each suprathermal spectrum in the energy range $0.056 – 3.0MeV$, and scale them to $1.05R_{Sun}$, assuming a simple inverse square dependence on radial distance (implying flux conservation).

The final step of the modeling chain is the transport of the accelerated SEPs to 1 AU, and subsequent comparison with particle observations with the ERNE instrument. This is achieved by taking the resulting averaged fluxes from the coronal acceleration model for the entire event as input to a modified version of the EPREM focused transport model (Schwadron et al., 2010), and transporting them through a Parker-type static interplanetary medium.

We have so far modeled a set of 62 historical events with typical coronal and interplanetary conditions, with results available at https://spreadfast.astro.bas.bg/catalog/. The SPREADFAST system also has a real-time version, which is under development.

### Inputs:

* SDO/AIA Level 1 full-cadence and full resolution data (EUV channels 94,131,171,193,211,335)

* SOHO/ERNE observations (LEMS120 P1-P8 channels)

* ACE/EPAM hourly observations (channels p1, p3, p5, fp6p, p7)

* Synoptic MAS MHD model results (datacubes freely available from Predictive Science's website https://www Predsci com/mhdweb/home.php

### Outputs:

* 3D models of EUV wave eruptions in the corona (below 10 Rs)

* Modeled shock front plasma parameters below 10 Rs

* Proton fluxes and fluences below 10 Rs for ~4 h of events

* Proton fluxes and fluences at 1 au for the first ~10 h of events

### Free parameters:

* Coronal acceleration (DSA) scattering mean free path

* Interplanetary transport parallel scattering mean free path

* Interplanetary transport ratio of perpendicular to parallel diffusion (for model runs with perpendicular transport)

### Limitations and caveats:

* SPREADFAST is currently set up to run only for protons;

* The model assumes a source spectrum based on quiet-time suprathermal observations (no flare particles);

* Currently, only parallel interplanetary transport is implemented

* No lat/lon dependence of coronal DSA fluxes for interplanetary transport - to be implemented in next version;

### Access to model output or forecasts:

Results for modeled historical events are available in the SPREADFAST catalog at https://spreadfast.astro.bas.bg/catalog/. The near-real time forecasting service is under development. It will be available at https://spreadfast.astro.bas.bg/

**Model validation:** Kozarev et al. (2022) modeled 62 events with the SPREADFAST model framework. The modeled time profiles were calculated for the geometric mean of the ERNE energy channels between 3 and 115 MeV and the ERNE pre-event background was added for better comparison with data. The modeled results were plotted on top of ERNE data for May 11, 2011, and were found to have good agreement. The event-integrated fluence was also compared. Similar plots for all 62 events are available in the SPREADFAST catalog.

Kozarev et al., 2022 presented correlation plots between the modeled and observed power-law indices of the fluence spectra as well as the modeled and observed onset times for all 62 events. The power law indices showed significant scatter, but clustered around an index of −2.5 for both SPREADFAST and ERNE. The onset times were strongly correlated for multiple energies, with the modeled times typically within ~5 h of the observed onsets.

The paper reports that 2/3 of the modeled events showed good agreement with observations, but there was a discrepancy in the remaining events. It is hypothesized that this is likely due to the existence of additional seed population beyond the quiet-time suprathermal spectra, possibly from flare-accelerated protons.

## 3.33. SPRINTS - Space Radiation Intelligence System

**Model developers:** Alec Engell (NextGen), Brianna Maze (NextGen), Harold Farmer (NextGen), Thuha Kerber (NextGen), Ben Barnett (NextGen), Jeremy Loomis (NextGen), David Falconer (University of Alabama Huntsville), Ian Richardson (University of Maryland/Goddard Space Flight Center (GSFC)), Maher Dayeh (SWRI), Barbara Thompson (GSFC), Tilaye Tadesse (JSC), Ian Fernandez (JSC, Princeton), Kerry Lee (JSC).

**Model description:** The Space Radiation Intelligence System (SPRINTS) is an empirical and machine-learned forecasting tool that is capable of giving forecasts for solar-driven events covering solar flares, solar particle events (SPEs), and coronal mass ejections (CMEs). SPRINTS uses and independently runs MAG4 (3.13) and extends MAG4 capabilities to make predictions of solar flares out to 48 h, with additional forecast probabilities of the GOES X-ray flare fluence and the peak flare ratio
of the long and short wavelength channels. SPRINTS combines the pre-eruptive forecast probabilities of MAG4 with SPRINTS post-eruptive forecast probabilities to provide continuously-updated and coupled forecast probabilities of SPEs as new phenomena and events are observed. It is designed as an extensible forecast application, where new datasets and new models can be integrated into the system's database and forecast modeling processes. The model currently runs automatically and in real-time on an Amazon Web Services GovCloud environment.

For its SPE primary forecast model, SPRINTS uses MAG4's X-ray flare forecast probabilities and feeds them into a user-defined ML model. The currently running ML model is the Multi-Layer Perceptron (MLP) model but has options to run other models including random forecasts and SVM. The MLP model is trained to predict SPEs at user-defined proton energy channels (e.g., 1, 5, 10, 30, 50, 100 MeV), fluxes, and time resolution (e.g., 12-h) out to 96 h.

To train the SPRINTS models, the data first needed to be labeled. Flare-only events were all labeled as a “zero”, while the flare events that led to an SPE were labeled as a “one”. The labeling was done per the desired temporal resolution, i.e., if the SPE occurred in the first 24 h after the flare onset, the 24-h bin was labeled as a one, while all other temporal resolutions were labeled as a zero.

As expected, the labeled data was unbalanced and heavily weighted towards flare-only events. For example, the maximum number of flares with SPEs was 152 for the proton events reaching 10 pfu at 50 MeV in a 96-h bin, whereas the number of flare-only events was 19,959. Because the problem of detecting SPEs suffers from the issue of unbalanced data, the selection of the training data is important to ensure the accuracy of the models.

To select the training data, the flares were first subsampled down to only include those flares with an SPE fluence above the minimum threshold for SPEs. This left 10,084 flare-only events. It was also empirically found that a 1 to 3 ratio of SPE to flare events resulted in the best models. For training the models, the SPEs were up sampled to a 1 to 3 ratio. The models were then trained through cross-validation using 4-folds. Results are reported for all flare and SPEs within the catalog.

Prior to an eruption of a flare, SPRINTS takes the MAG4 flare probabilities and feeds them into the MLP model where it then provides the probabilities of the user defined SPEs. As a flare is detected, the forecast transitions from the pre-eruptive forecast mode to the post- (or ongoing) eruptive mode. The flare metadata parameters are captured on-the-fly throughout the course of the flare and feed into the model every 5 min. Once the flare has ended, those parameters are “locked” in and the post-eruptive forecast is final. SPRINTS provides the pre-eruptive (MAG4), post-eruptive, and coupled forecasts through its REST API.

**Inputs:** SPRINTS ingests everything MAG4 needs and GOES X-ray and proton data. An automatic flare event

detection script Aschwanden and Freeland (2012) identifies flare start, peak, and end times. SPE predictions are made by the MLP model based on the metadata from the MAG4 predicted or observed X-ray flare events (peak flux, fluence, peak ratio) and eruptive location provided by the Latest Events Pipeline from Lockheed Martin Solar and Astrophysics Laboratory (LMSAL)) or, optionally, NOAA SWPC.

**Outputs:**

* Pre-eruptive (updated MAG4)

- M- and X-Class Flares (24 and 48 h)

- X-class Flares (24 and 48 h)

- X-ray fluences (24 and 48 h)

- X-ray peak ratio (24 and 48 h)

- CMEs (24 and 48 h)

- Fast CMEs (24 and 48 h)

* Post-eruptive and coupled

- SPEs (96 h at 12-h temporal resolution)

* Currently deployed in real-time for: 10 MeV @ 10 pfu, 10 @ 40, 30 @ 10, 50 @ 10, 100 @ 1

* Configurable to any desired GOES energy channel and flux threshold

**Free parameters:** None.

**Limitations and caveats:** Fig. 16 shows the SPRINTS primary forecast dashboard. X-ray, proton, and solar wind observations are displayed for the past 8 days with 4-day forecast panels directly to the right. For the observed SPE for this time-period you can see what the forecast probabilities were for the five SPE criteria at a 12-h resolution out to 96 h from the peak of the flare.

We note that the red forecast bar in the first 12-h bin is for the 30 MeV channel at 10 pfu and is a higher probability than the 10 MeV channel at 10 pfu. This is because the forecast capability is comprised of multiple MLP models – one for each temporal bin and energy/flux. Therefore, this results in 20 MLP independent models.

As with many ML models the unbalanced nature of the number of flares to SPEs leads to problems during the training of the model. The SPRINTS team is currently developing a time-series ML model to address this issue.

For the forecast example shown for the May 2012 event, the flare occurred close to the western limb. This was well outside of MAG4's optimal active region observation window of 45 heliocentric degrees. This highlights the benefit of combining the MAG4 pre-eruptive capability with a post-eruptive capability within SPRINTS.

**Access to model output or forecasts:** Access to model outputs and supporting dashboards can be obtained by becoming IP whitelisted to NextGen's REST API. Email aengell@nextgenfed.com to be whitelisted. NextGen is currently deploying the real-time dashboard on a public website and will be available in 2022. Additionally, SPRINTS will be providing forecasts on the SEP Scoreboard.