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Automated Solar Activity Prediction: A hybrid computer
platform using machine learning and solar imaging for
automated prediction of solar flares
T. Colak^1 and R. Qahwaji^1
Received 1 April 2008; revised 22 December 2008; accepted 8 January 2009; published 4 June 2009.
[ 1 ] The importance of real-time processing of solar data especially for space weather applications is
increasing continuously. In this paper, we present an automated hybrid computer platform for the short-
term prediction of significant solar flares using SOHO/Michelson Doppler Imager images. This platform
is called the Automated Solar Activity Prediction tool (ASAP). This system integrates image processing
and machine learning to deliver these predictions. A machine learning-based system is designed to
analyze years of sunspot and flare data to create associations that can be represented using computer-
based learning rules. An imaging-based real-time system that provides automated detection, grouping,
and then classification of recent sunspots based on the McIntosh classification is also created and
integrated within this system. The properties of the sunspot regions are extracted automatically by the
imaging system and processed using the machine learning rules to generate the real-time predictions.
Several performance measurement criteria are used and the results are provided in this paper. Also,
quadratic score is used to compare the prediction results of ASAP with NOAA Space Weather Prediction
Center (SWPC) between 1999 and 2002, and it is shown that ASAP generates more accurate predictions
compared to SWPC.
Citation: Colak, T., and R. Qahwaji (2009), Automated Solar Activity Prediction: A hybrid computer platform using machine learning and solar imaging for automated prediction of solar flares, Space Weather, 7 , S06001, doi:10.1029/2008SW000401.
1. Introduction
[ 2 ] Space weather is defined by the U.S. National Space Weather Program (NSWP) as ‘‘conditions on the Sun and in the solar wind, magnetosphere, ionosphere, and thermo- sphere that can influence the performance and reliability of space-borne and ground-based technological systems and can endanger human life or health’’ [Koskinen et al., 2001]. The importance of understanding space weather is increas- ing because extreme solar eruptions could affect our daily life activities. For example, there is a steadily increasing reliance on communications and power systems, both vulnerable to space weather. [ 3 ] The most dramatic solar activity events affecting the terrestrial environment are solar flares and Coronal Mass Ejections (CMEs) [Pick et al., 2001]. Solar flares and CMEs are solar eruptions that can spew vast quantities of radiation and charged particles into space [Lenz, 2004]. The ability to predict major solar storms can give companies sufficient lead time to implement preventive measures [Lenz, 2004]. Satellite operators, space agencies, aviation industry, power generation and distribution
industry, oil and gas industry and railways can benefit from an effective space weather prediction system. [ 4 ] Solar activity is the driver of space weather. An efficient approach for the prediction of solar activities should use real-time, high-quality data and data-processing techniques [Wang et al., 2003]. We designed an automated space weather prediction service that combines solar physics with advanced image processing and machine learning techniques. Warning of eruptions can be initiated if appro- priate instruments to observe the Sun, are combined with efficient data processing techniques. Predicting solar flares is important for space weather applications. These warnings could also provide indirect prediction for some energetic particle events. This could provide useful lead time because some of these events can be seen at Earth within 10--15 min of the occurrence of the flare. Furthermore, if the prediction system generates low flaring probability with a high degree of confidence, one can argue that the probability for an energetic particle event is low. Such prediction could be useful for all those applications affected by energetic particles. [ 5 ] There are various research groups and organizations scattered around the world that are working on solar analysis and forecasting. These analyses and forecasts
(^1) Informatics Research Institute, School of Computing Informatics
and Media, University of Bradford, Bradford, UK.
SPACE WEATHER, VOL. 7, S06001, doi:10.1029/2008SW000401, 2009
Copyright 2009 by the American Geophysical Union S06001 1 of 12
are typically subjective and depend mainly on the expert knowledge which may lead to occasional inconsistencies in performance. On the other hand, objective computerized analysis of solar images can provide automated processing and relatively consistent performance by using the large computational capabilities of modern computers to analyze and compare large amounts of recent and historical data. However, the real challenge today is to design high- performance and accurate computer-based systems. [ 6 ] To our knowledge, there has been no fully automated system that can provide real-time prediction of significant solar flares. The accuracies of the previous semiautomated systems that have been designed are generally lower com- pared to the performance provided by subjective analysis. For example, WOLF [Miller, 1988] is an expert system that has been created to analyze active regions and sunspots and then predict the probability of solar flare occurrence. WOLF has a knowledge base consisting of a set of ‘‘if-then’’ rules and an inference engine which applies these rules. Manual user interaction is required to provide a description for the observed active region and sunspots. WOLF would then determine the McIntosh classification for the associated sunspot and hence, the probability of the described group producing a flare of specified X-ray intensity. [ 7 ] THEO [McIntosh, 1990] is another expert system that is also based on the McIntosh classification system, but includes information on spot growth, rotation and shear, and inferred magnetic topology. ARM (Active Region Monitor) is an another solar flare forecasting system that has been developed to estimate the probability for a certain active region to produce C, M, or X class flares. The percentage probabilities are based on the number of flares produced by regions classified by NOAA using the McIntosh classification scheme during cycle 22 [Gallagher et al., 2002]. All these systems are not fully automated as they require user interaction to provide the properties and classifications of active regions as inputs and are not designed to extract data from solar images directly or automatically. [ 8 ] In this paper we introduce our fully automated pilot system called Automated Solar Activity Prediction tool (ASAP), which integrates image processing, machine learning and solar physics to provide automated predic- tion of solar flares based on the characteristics of sunspots. The prediction system is composed of two major stages: an image processing system and a machine learning system. The imaging system processes MDI continuum and magnetogram images in real-time to detect and classify sunspot groups and then determine their properties. The machine learning system is trained using historical sunspot and flare data. Association algorithms are designed to associate flares with the sunspot groups that caused them and to create training sets that are used to train the learning algorithms and produce computerized learning rules. We will demonstrate the reliability of this system by testing it on recent solar images and comparing
the generated predictions with the actual solar flares reported in solar catalogs. [ 9 ] This paper is organized as follows: (1) section 2 describes the imaging system that is responsible for the automated grouping and classification of sunspots, (2) section 3 describes the machine learning system that is trained on historical sunspot and flare data, (3) section 4 discussed the performance and evaluation of the whole system, and (5) section 5 presents the concluding remarks and suggestions for future work.
2. Sunspot Detection and Classification
[ 10 ] A computer system that can automatically detect, group, and classify sunspots on the basis of the McIntosh classification was presented by Colak and Qahwaji [2008]. This system applies imaging techniques to SOHO/ Michelson Doppler Imager (MDI) continuum and magnetogram images to detect sunspot regions and extract their properties including their McIntosh classifications. In this work, this system for the first time is integrated with a machine learning-based system to provide real-time prediction for the possible occurrence of flares, as described in the next section.
2.1. SOHO/MDI Images
[ 11 ] The MDI instrument on SOHO provides routine observations of the Sun in the white light continuum, in the vicinity of the Ni I 6767.8 A˚^ photospheric absorption line. The instrument images the sun with a 1024 1024 CCD camera [Scherrer et al., 1995]. MDI continuum images may be used as a white light equivalent for the purposes of sunspot observations. SOHO provides two to four MDI intensitygram images per day and twice as many magnetogram images with coverage which has been continuous since 1995. [ 12 ] MDI magnetogram images are used to measure the velocity and line-of-sight magnetic flux density in the Sun’s photosphere. The magnetogram images show the magnetic flux density of the solar photosphere, with black and white areas indicating opposite magnetic polar- ities. The dark areas are regions of negative magnetic polarity (pointing toward the Sun) and the white regions have positive magnetic polarity (pointing outward). These images can be used for detecting active regions.
2.2. Summary of Sunspot Detection
and Classification Algorithms
[ 13 ] The detailed description, design, implementation and evaluation of this part of the system was presented by Colak and Qahwaji [2008]. Our automated sunspot detection, grouping and classification algorithm consists of three main stages: preprocessing, sunspot detection and grouping, and sunspot classification. These stages can be summarized as follows:
2.2.1. Preprocessing of MDI Images
[ 14 ] Stage 1 processing, applied to both continuum and magnetogram images, consists of (1) detecting the solar
[ 26 ] The association algorithm has managed to associate a total of 37,515 sunspot groups with solar flares using their NOAA numbers and the 24 hour time difference. These 37,515 sunspot groups are associated with 72,727 C class solar flares, 12,103 M class solar flares, and 1081 X class solar flares. The difference between the total number
of solar flares and the number of associated sunspots is caused by the fact that a sunspot group could produce more than one solar flare within the 24 hour time period. Also, there are multiple observations (three to four obser- vations per day) of the sunspot groups that are included in the NGDC sunspots catalog. Hence, a solar flare can be
Figure 1. The stages and results of sunspot detection and the grouping process. (a and b) The
continuum and magnetogram images, respectively. The (c) detected sunspots and (d) detected
active regions. (e) Figures 1c and 1d are combined using region growing to show the exact locations
of active regions. (f) Using Neural Networks active regions are classified into groups and (g) this
data is also used to detect sunspot groups.
associated with the same sunspot group that is reported more than once within 24 hours.
3.2. Flare Prediction System
[ 27 ] The learning system introduced in this work is inspired by our previous work by Qahwaji and Colak [2007]. Learning algorithms such as Neural Network (NN), Support Vector Machines (SVM) and Radial Bases Functions (RBF) were optimized, trained and then com- pared for flare predictions by Qahwaji and Colak [2007]. In this work, features such as McIntosh classifications and daily sunspot numbers were used as inputs to the learning algorithms. The training and generalization performances of the learning algorithms were evaluated using testing tools such as the jackknife technique [Fukunaga, 1990]. In this paper we are using the area of sunspot groups together with the McIntosh classes as inputs to the learn- ing algorithms in order to generate predictions for the C, M, and X class flares. [ 28 ] Our solar flare prediction algorithm is composed of two Neural Network (NN) systems that are working together as illustrated in Figure 2. The first NN uses the numerical representations of the three parts of the McIntosh classification for the sunspot region under con- sideration together with its sunspot area as inputs. It generates the probability that this sunspot region will produce a C, M, or X class solar flare in the next 24 hours. Hence, this NN has four input nodes and one output node and is trained using sunspot regions and solar flare associations as described in the previous section. The training vector for this NN contains numerical values representing the four inputs and their corresponding target as shown in Figure 3. The target represents the actual ‘‘FLARE’’/‘‘NO FLARE’’ cases. For example, if there is a sunspot region with a McIntosh classification of FKI and an area of 600 in millionths of solar hemisphere that is associated with a C, M, or X class flare then the training vector will be [0.9, 0.9, 0.5, 0.24; 0.9]. [ 29 ] When the first NN predicts that a flare is going to occur, the second NN is activated to determine whether the predicted flare is going to be C, M, and/or X class flare. The second NN is trained using a new training set that contains only the sunspot groups that were associated with C, M, and X class flares. Hence, the second NN consists of four inputs and three outputs. The first, second and third outputs represent the C, M, and X class flares, respectively. These outputs are assigned as follows: (1) If the sunspot group is associated only with a C class flare, then the first output will be 0.9 otherwise it will be 0.1. (2) If the sunspot group is associated only with a M class flare, then the second output will be 0.9 otherwise 0.1. (3) If the sunspot group is associated only with a X class flare, then the third output will be 0.9 otherwise 0.1. (4) If the sunspot group is associated with more than one type of solar flare, all the corresponding outputs (first output for C class, second output for M class, and third output for X class) will be 0.9 otherwise 0.1. For example, if there is a sunspot Table 1.
Some Examples of Wrong McIntosh Classes and/or Missing Data in the NGDC Catalog for the First Months of 1982
Date
a
Time(UT)
Location
MountWilsonClass
RegionNumber
McIntosh
Class
Number of
Spots
Length
Area
Individual Central Meridian
Passage Date
Regional Central Meridian
Passage Date
StationSerialNumber
Observatories
11820101
1249
S19W
B^
3532
CXO
4
4
130
811227
517
3RAMY
11820114
125
N03E
B^
3550
BXX
2
3
820116
22
3LEAR
11820117
55
S08W
B^
3553
HSO
8
7
20
820115
25
4LEAR
11820118
1600
N09E
A
3552
FSX
1
1
50
820121
402
3BOUL
11820118
1600
S11W
BG
3549
DS
10
7
200
820117
399
3BOUL
11820118
1600
S14W
B^
3559
DA
8
7
280
405
3BOUL
11820127
1605
N09E
B^
3573
CKX
9
9
350
820201
418
3BOUL
11820210
1931
S08E
BD
3603
CKC
32
10
450
71
3HOLL
11820215
1500
N13E
B^
3610
CO
3
6
20
79
2HOLL
11820217
1555
N06E
A
3612
BRX
1
10
455
3BOUL
11820304
1400
N13W
B^
3625
DK
7
6
610
820302
82
3RAMY
a^ Date format used here is 11yymmdd. Here 11 is a data code for sunspots.
processed using the hybrid system and a sunspot catalog was created which we refer to as the Automated Sunspot Catalogue (ASC). Parts of the ASC are shown in Table 2. All the automatically detected and classified sunspot groups, which are taken for 1 April 2001 at 0000 and at 0624, along with their flaring probabilities are provided. It is known that smaller flares occur more frequently than larger flares. However, our hybrid system could generate higher X class flare probability compared to M class probability for some sunspot groups. An example for this can be seen for the FKC sunspot group detected on N17W36 at 0000 and on N17W40 at 0624. These probabil- ities are generated by NNs which are trained with years of historical data representing sunspot groups and their associated solar flares. After convergence in training is reached, the NN accepts new set of inputs and generates outputs on the basis of the learning rules and weights formed during training. From these outputs it can be understood that most of the groups with FKC classification and with an area of around 1500 square degrees are more likely to produce a X class flare than M class flare when
the historical associations are considered. In addition to the ASC, the hybrid system displays its predictions on a web page as shown in Figure 5. The generated images show the detected sunspot groups and their flaring probabilities. [ 35 ] In order to test the hybrid system we compared the solar flare predictions of each sunspot group in ASC to the X-ray solar flares reported in the NGDC solar flare catalogs. Between 1 February 1999 and 31 December 2002 there were 5175 reported C, M, and X class solar flares with location information. Out of these 5175 solar flares 4469 of them were C class, 663 of them were M class and 43 of them were X class flares. [ 36 ] In order to associate the sunspot groups detected by our algorithms with X-ray solar flares reported in the NGDC catalog, we had to modify the association algo- rithm, introduced by Qahwaji and Colak [2007], to compare sunspots and solar flares on the basis of their locations (latitude and longitude) not their NOAA numbers. The new modifications are necessary because the sunspot groups in ASC do not have NOAA numbers. Also, not
Figure 4. The final hybrid system.
Table 2. Automated Sunspot Catalogue
Date Time Location Class
Number of Sunspots
Length of Sunspot Group Area
Flaring Probability C Classa^ M Classa^ X Classa
1 Apr. 2001 0000 N25E28 HKX 1 4 132 0.158 0.136 0.121 0. 1 Apr. 2001 0000 N17W36 FKC 43 37 1440 0.746 0.635 0.203 0. 1 Apr. 2001 0000 N11E27 CSO 6 9 79 0.084 0.076 0.064 0. 1 Apr. 2001 0000 N08W04 HRX 1 1 1 0.113 0.102 0.030 0. 1 Apr. 2001 0000 S05E08 DSO 18 6 74 0.099 0.091 0.073 0. 1 Apr. 2001 0000 S10W16 FKC 35 35 450 0.648 0.578 0.516 0. 1 Apr. 2001 0000 S11W72 BXO 6 8 49 0.108 0.095 0.076 0. 1 Apr. 2001 0000 S13E64 AXX 1 1 153 0.103 0.092 0.014 0. 1 Apr. 2001 0000 S24E23 BXO 2 1 3 0.108 0.095 0.082 0. 1 Apr. 2001 0000 S36E30 AXX 1 1 4 0.116 0.103 0.027 0. 1 Apr. 2001 0624 N25E25 HKX 1 4 134 0.158 0.136 0.121 0. 1 Apr. 2001 0624 N17W40 FKC 41 37 1558 0.750 0.624 0.036 0. 1 Apr. 2001 0624 N11E24 CSO 5 9 65 0.080 0.073 0.062 0. 1 Apr. 2001 0624 N10W07 CAO 3 3 28 0.078 0.070 0.058 0. 1 Apr. 2001 0624 S01W30 BXO 2 1 9 0.108 0.095 0.082 0. 1 Apr. 2001 0624 S05E04 DSO 17 6 128 0.119 0.109 0.091 0. 1 Apr. 2001 0624 S09W19 FKO 29 35 533 0.593 0.509 0.543 0. 1 Apr. 2001 0624 S12W75 BXO 2 6 68 0.108 0.095 0.073 0. 1 Apr. 2001 0624 S13E60 AXX 1 1 151 0.103 0.092 0.014 0. a (^) Probability of the flare to be C, M, or X class, respectively.
all the solar flares reported in NGDC flare catalog have location information and these solar flares are not included in this study. The association algorithm that we have used here is explained as follows: [ 37 ] 1. Read all the sunspot groups and their solar flare predictions as reported in ASC. [ 38 ] 2. Read the actual M and X class flares with location information as reported in the NGDC solar flare catalog. [ 39 ] 3. Carry out extensive search to associate each actual flare with its corresponding sunspot group by comparing their longitude, latitude, and time information. In order to confirm that a sunspot group and a solar flare are associated the following criteria must be met: (1) The difference in time between the detected sunspot group and its associated flare must be less than 6, 12, 24, 48, and 72 hours, depending on the forecast lead time objective. (2) Sunspot group locations must be corrected for solar rotation (the new coordinates are calculated using Carrington Heliographic coordinates) depending on the time difference between sunspot group and solar flare under consideration. (3) The solar flare must be within the 10 ° radius of corrected sunspot location. [ 40 ] 4. If all the criteria are satisfied then this sunspot group is highlighted as being associated with a solar flare, otherwise it is considered not to be associated. [ 41 ] After the completion of the association process the prediction performance is evaluated using various verifi- cation measures as explained below.
4.2. Verification Results
[ 42 ] The hybrid system generates predictions in numer- ical format, between 0.0 and 1.0, as shown in Table 2. In order to evaluate the predictions of the hybrid system several measures are used. Some of these measures require forecast probabilities and some of them require categorical forecasts (Yes/No) as inputs for assessing the outputs of the hybrid system. For the measures that require forecast probabilities the outputs of the hybrid system are used by directly converting them to percen- tages. For example, if the flaring output of the system is 0.23, it is assumed that the sunspot group under consid- eration has a 23% flaring probability. As for categorical forecasts (Yes/No); a threshold value of 0.5 (50%) is used for determining the final predictions. Our training data includes output values 0.1 (10%) and 0.9 (90%) for nonflaring and flaring sunspot groups respectively and therefore if the output generated by the hybrid system is above this threshold value then it is assumed that a flare is predicted to occur. On the other hand, if the generated output is less than the threshold value then no flare is expected. [ 43 ] In order to calculate the success of the generated predictions the association results are investigated using the following four criteria: (1) If a sunspot group is associated with an actual flare, as explained previously, and a flare prediction is generated then this prediction is successful. (2) If a sunspot group is associated with an
Figure 5. Two images generated by the hybrid system. (left) The detected sunspot groups and
(right) the classification and flare probabilities of the detected sunspot groups. Figure 4 (right) is
updated automatically on http://spaceweather.inf.brad.ac.uk/index.html every time a new MDI
continuum image is available on SOHO’s website.
verification of the systems especially when occurrences of the events to be predicted are very rare. As mentioned above, even if our systems outputs would have been set to be no flare all the time, our predictions would be correct by more than 90%. Therefore, HSS is a very important measure for evaluating our prediction performance. HSS results show that ASAP predictions are much more than chance especially for flaring and C and M class flare predictions. HSS can also be used to optimize the system by changing the threshold value (0.5 was used for our calculations as described earlier) and achieve better prediction results. [ 49 ] To provide further evaluation for the system we created a forecast reliability diagram. The reliability diagram plots the observed frequency against the forecast probability, where the range of forecast probabilities is divided into bins. Figure 6 plots the observed frequency of all the flaring sunspot groups against their corresponding prediction probabilities, grouped in 5% (0.05) bins (0 -- 5% (0 -- 0.05), 5 -- 10% (0.05 -- 0.1), 10-- 15% (0.1 --0.15),.. .). The dashed diagonal line represents perfect correspondence. This reliability chart is produced by comparing the pre- dictions of ASAP for 24 hour time window and includes the output from the main Neural network of the system
that decides if the sunspot group is going to produce a flare or not. The reliability diagram is similar to a scattered plot, where the sunspot groups are stratified by their flaring forecast into probability bins and the observed flaring frequency of these sunspot groups are calculated. For example, if there are 10 sunspot groups with calculated flaring probabilities that varies between 5% and 10%, and in reality 3 (30%) of them produced flares, then this means that the calculated flaring probabilities are lower than it should be and it is not a very reliable system. As it can be seen from Figure 6, our results are showing good correspondence and are highly reliable. Also this diagram shows that there are no flare prediction probabilities produced by our system that are higher than 80% and therefore the forecast bins after 75-- 80% bin are empty.
5. Conclusions
[ 50 ] In this paper we have introduced, for the first time, a fully automated hybrid system called ASAP that integrates advanced machine learning and image process- ing techniques with solar physics to predict automatically whether a sunspot group is going to produce a solar flare and whether the predicted flare is going to be a C, M, or X class flare.
Figure 6. The observed relative frequency of all the flaring sunspot groups against their
559 corresponding predictions, grouped in 5% (0.05) bins.
[ 51 ] The performance of the hybrid system depends on the generalization capabilities of the machine learning system and the grouping and classification performance of the image processing system. For our hybrid system the HSS, POD, PC, and QR measures are quite good particularly when predicting that a solar flare is going to erupt. Especially HSS is very promising which shows that ASAP predictions are much better than chance. However, the same thing cannot be said for the FAR measure. This is a problem that has to be tackled especially for X class flare predictions which we are planning to solve in the near future. Also comparison of QR results of ASAP and SWPC showed that ASAP provides better prediction results than SWPC especially for M class flares. [ 52 ] The prediction rates for the hybrid systems can be improved by exploiting the generalization capability of machine learning system. Better generalization is obtained when more training data are used. Hence, we believe that it is important to monitor the performance of the hybrid system during its initial stages which includes comparing the prediction performance with the actual flares reported by NOAA. Evolutionary algorithms may be used to allow the learning algorithms to evolve and provide better optimization and generalization. [ 53 ] The geometric effect on MDI images close to the limb also affects the classification of sunspot groups which would lead to wrong prediction results. Although, most of the calculations needed for classification are carried out in heliographic coordinates, the lack of graphical information toward the limb is the main problem preventing us from obtaining more accurate classifications. For example, large sunspot groups just starting to appear from the limb are more likely to be classified incorrectly [Colak and Qahwaji, 2008]. [ 54 ] An automated and real-time version of ASAP is running on our website at http://spaceweather.inf.brad. ac.uk/index.html since March 2007. This system connects automatically to SOHO’s website (http://sohowww. nascom.nasa.gov/data/realtime/, last access in 2008) to download the latest MDI continuum and magnetogram images. After automatically running the algorithms described in this paper the results are displayed on our website as shown in Figure 5 and are updated automatically. ASAP is available publicly for download at http:// spaceweather.inf.brad.ac.uk/downloads.html. [ 55 ] The processing time for our system is approximately 15 s to process the two MDI images and to generate the predictions on an Intel Centrino machine with 2 GB memory. This enables our system to provide near-real- time classifications and predictions. The system can be modified to accept other types of solar images. Sometimes the characteristics of a sunspot group can change rapidly in hours and cause flares, it is almost impossible for a human observer to determine what triggers this process without having the appropriate tools. We believe that the system introduced here can help researchers or observers investigate and understand solar features and activity and
identify patterns that could be useful for space weather predictions. [ 56 ] In our previous work [Qahwaji et al., 2007; Qahwaji and Colak, 2007], we have shown that SVM provides better generalization performance compared to NN. In the near future we will integrate these findings and use SVM networks to enhance the predictions. We also believe designing a sunspot group tracking system that studies the evolution of the sunspot groups can improve the overall performance. Moreover, we believe that we need to take into consideration the magnetic properties and energies of the sunspot regions under investigation. Very recently, we designed an algorithm [Ahmed et al., 2008] that would analyze magnetogram images to estimate the mag- netic energy of an active region on the basis of the Ising model. In the future we are planning to implement this magnetic energy parameter to the flare prediction part of the system to improve the reliability of the predictions.
[ 57 ] Acknowledgments. This work is supported by EPSRC (GR/T17588/01) and (EP/F022948/1) grants, which are entitled ‘‘Image Processing and Machine Learning Techniques for Short-Term Prediction of Solar Activity’’ and ‘‘Image Processing, Machine Learning and Geometric Modeling for the 3D Representation of Solar Features,’’ respectively.
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