Anomaly Detection for GONG Doppler Imagery Using a Binary Classification
Neural Network

Mitchell Creelman, Kiran Jain, Niles Oien and Thomas M. Wentzel

NISP, National Solar Observatory, Boulder, CO 80303, USA

Technical Report No. NSO/NISP-2024-001

###### Abstract

One of the products of the National Solar Observatory’s Integrated Synoptic
Program (NISP) is the farside seismic map which shows the magnetic activity on
the unobserved side of the Sun. The production of these rudimentary maps began
in 2006, and they have since proven to be a valuable tool in tracking solar
activity which cannot be directly observed from the earth’s surface. The
continuous tracking of solar active regions allows space weather forecasters
to monitor critical solar events which may have larger economic and societal
impacts here on Earth. In an effort to improve these maps, several steps are
underway through the Windows on the Universe project (WoU) funded by the NSF.
One of these steps is to improve the quality assurance measures for the images
collected at individual sites throughout the GONG network and is used to
develop the farside maps. To this end, we have designed a binary
classification neural network to determine which of these site images should
and should not be included in the farside pipeline that produces the end
product maps. This convolutional neural network is a highly effective and
computationally efficient method of significantly improving the quality of the
farside maps currently produced by the NISP program.

###### Contents

  1. 1 Background
    1. 1.1 How binned-down images are generated
    2. 1.2 What is the concern?
  2. 2 Image Quality Assurance and Control
    1. 2.1 Current QAQC Filter
    2. 2.2 Proposed QAQC Filter
  3. 3 Training the Network
    1. 3.1 Sampling
    2. 3.2 Network Design
    3. 3.3 Hyperparameters
  4. 4 Performance Validation
    1. 4.1 Test 1: Random Sample
    2. 4.2 Test 2: RMS Rejections
  5. 5 Effects of Implementation
    1. 5.1 Impact on Network Duty Cycle
    2. 5.2 Impact on Site DC
      1. 5.2.1 Learmonth (le)
      2. 5.2.2 Udaipur (ud)
      3. 5.2.3 El Teide (td)
      4. 5.2.4 Cerro Tololo (ct)
      5. 5.2.5 Big Bear (bb)
      6. 5.2.6 Mauna Loa (ml)
  6. 6 Case Studies for Farside Map Effects
    1. 6.1 Noise Reduction in Merged fqi Images
    2. 6.2 Noise Reduction in Farside Maps
  7. 7 Network Updates and Improvements
    1. 7.1 Re-training
    2. 7.2 Network Design Updates
  8. 8 Summary

##  1 Background

The Global Oscillation Network Group (GONG) is a network of ground-based solar
observatories run by the National Solar Observatory’s Integrated Synoptic
Program (NISP) which is aimed at collecting uninterrupted solar observations
(Harvey et al., , 1996; Hill, , 2018). The network, established in 1995, is
comprised of six observatories whose locations were chosen in order to create
a redundant system capable of collecting solar observations with a mean duty
cycle (DC) of over 90%. After a careful survey, observatories were established
at Learmonth, Australia (le), Udaipur, India (ud), El Teide, in the Canary
Islands (td), Cerro Tololo, Chile (ct), Big Bear, California (bb), and Mauna
Loa, Hawaii (ml) (Hill et al., , 1994). The location of these observatories,
shown in Figure 1, were carefully chosen to provide sufficient latitudinal and
longitudinal coverage for consistent observational overlap between adjacent
sites. A recent study by Jain et al., 2021b shows that the network is capable
of collecting observations from as many as four sites simultaneously depending
on the time of year.

Figure 1: Global distribution of all six GONG network observatories.

While multiple data products are derived from the observations of current GONG
network111https://gong2.nso.edu/archive/patch.pl, this report is primarily
focused on the line-of-site low-resolution Dopplergrams which are produced and
used to track the magnetic activity on the farside of the Sun. These
Dopplergrams, or fqi images, are 215 $\times$ 215 pixel images which are
produced from the high-resolution images collected at individual sites. The
individual site minute-resolution Dopplergrams are then merged together to
form a nearly continuous series of images. If there are no images for a given
minute, the produced Dopplergram is left empty. The fraction of 24 hr day for
which the observations are available is known as the duty cycle (DC), with a
range between 0 and 1. The Dopplergrams are then used to determine phase shift
values that are utilized to create helioseismic maps of the farside produced
by the NISP program (Lindsey and Braun, , 2000; Braun and Lindsey, , 2001;
González Hernández et al., , 2007, 2010).

The phase shift maps are employed for a wide variety of space weather
forecasting applications (e.g., Jain et al., , 2023). In particular, they
serve to help monitor the presence of known solar active regions, as well as
the development of new regions on the farside of the Sun. Through developing
improved farside helioseismic maps, we can improve the prediction and warning
times for solar activity events, such as flares, coronal mass ejections
(CMEs), and increase our understanding of the precursors for these events. One
such example can be found in the sudden increase in the irradiance values
during the early phase of the current solar cycle 25. While the frontside
hemisphere saw a reduction in magnetic activity, a large active region which
had emerged on the farside was found responsible for this sudden rise in the
irradiance (Jain et al., 2021a, ). These farside seismic maps have also been
used to create global magnetic index (e.g., González Hernández et al., , 2011,
2014), which is a useful proxy for the magnetic field models.

###  1.1 How binned-down images are generated

To generate single-site binned-down 215 $\times$ 215 pixel fqi images, the
near-real time 860 $\times$ 860 pixel full-resolution vqi images are run
through the Image Reduction and Analysis Facility (IRAF)/GONG data Reduction
and Analysis Software Package (GRASP)’s mkfsi routine to fit a 2-d surface fit
to the image and then subtract the obtained surface from the image to remove
the solar rotation. A Gaussian filter is then applied before the images are
down sampled to their final resolution. These fqi images from sites are
transferred to iQR Keep at the NISP Data Center where they are processed by
qr-filter to place them in the oQR Keep with altered header and added image
statistics. The next step is to merge all oQR single-site images for a given
minute to create merged mrfqi image. During this process, the oQR single-site
fqi images are rotated, flipped, and scaled to a standard radius prior to
merging (see Toner et al., , 2003; Hughes et al., , 2016, for general
description).

Figure 2: Examples of normal (Top) and anomalous site images (Bottom) which
would pass the current RMS site threshold.

###  1.2 What is the concern?

The primary goal of this work is to develop a consistent and reliable
methodology for excluding anomalous site images in the merged fqi images and
thus the downstream farside data products. Figure 2 displays examples of the
normal and erroneous images. The possible causes of anomalous images vary from
malfunctioning calibration sequences, instrumental failures, or processing
issues. The inclusion of anomalous Dopplergrams in the computation of farside
seismic maps can have adverse consequences on the signal-to-noise ratio
without affecting the duty cycle and rendering the final maps ineffective.

##  2 Image Quality Assurance and Quality Control

Implementing an effective quality assurance and quality control (QAQC)
parameters for the site-specific fqi products is the overall focus of this
report. Currently, the only QAQC method in place is a thresholding of Root
Mean Square (RMS) values. As will be covered in more detail later in this
report, this methodology is largely ineffective, allowing many anomalous
images to be included while excluding valuable data. The alternative proposed
here is the implementation of a binary classification neural network for
detection of anomalous fqi images. While not a perfect solution, such networks
have been shown to be highly effective for anomaly identification tasks (Khan
et al., , 2021).

###  2.1 Current QAQC Filter

As mentioned, there is currently only one quality control parameter set on the
fqi images generated at any individual site. This is a RMS filter with a
threshold of 60. An inspection of the source code for the quick_reduce script
shows that this filter was implemented on July 23, 2014. Prior to this date,
all images irrespective of their quality were included in the image-merge
process and sometimes produced poor quality data products. This filter diverts
all images with the RMS exceeding the threshold and stores them in the
Oubliete Keep at sites. These images are then discarded after 41 days without
being transferred to the NISP Data Center. This type of filter fails to
include vital images during the high solar activity periods as well as to
identify many of the anomalous images during the low-activity period. Figure 2
displays examples of four site images with comparable RMS values where two of
these images are erroneous. Such a poor quality control measure has led us to
explore the use of a binary classification neural network as an anomaly
detection measure to replace the current filters.

###  2.2 Proposed QAQC Filter

For this application, we developed a filter using a simple binary
classification network to label an fqi image as normal or anomalous. The
developed filter seeks to prevent anomalous site-fqi images from being
included in the mrfqi products by identifying anomalous site images during the
transition between the iQR and oQR keeps at the NISP Data Center. By excluding
anomalous site-fqi images from the farside pipeline, we seek to improve the
signal-to-noise ratio in the farside maps, thus providing a more reliable data
product to the users relying on the NISP data.

The network was designed using the PyTorch Python package (Ketkar and
Moolayil, , 2021). PyTorch is a machine learning programming package that
allows for a high degree of customization in the design and troubleshooting of
the neural networks.

##  3 Training the Network

###  3.1 Sampling

As mentioned above, the fqi products in the farside pipeline are velocity
images of nearside of the Sun, and the phase shift values are calculated to
determine the location of the active regions which are not directly observed
from the Earth (Lindsey and Braun, , 2000).

The efficacy of machine learning algorithms is highly dependent on the quality
of the datasets that they are trained on. Though imbalanced datasets can be
used to effectively train networks (Korkmaz, , 2020), balanced datasets can
significantly improve the performance of machine learning algorithms (Divovic
et al., , 2021). However, this was complicated by the fact that we wanted to
include a mix of normal and anomalous data within our training dataset. All of
the data used in the training process were manually classified using an in-
house tool developed by Kevin Shuman (Shuman, , 2023).

Figure 3: Number of training dataset images per year.

To find anomalous data, we started with all images in the fqi dataset which
had a variance of over 1600. Additionally, a random sample was taken of the
oQR keep, with 5 random images taken from 20 days for a random 200 months
within the lifespan of the GONG network. This left us with 110,593 high
variance images, and 20,000 randomly sampled images. 21,268 of these images
were then hand-sorted into normal or anomalous classes to be used to train the
machine learning algorithm.

Figure 4: Distribution of individual site contributions to the 17014 images in
the training dataset.

The year-wise distribution of the images used in training the network is shown
in Figure 3. Using a training/testing split of 80 % to 20 %, 17,014 images
were used to train the network while 4,254 images to test the performance of
the classification network. The distribution of individual site images in the
dataset is shown in Figure 4.

A source of imbalance in the training dataset was the rate of site occurrences
between normal and anomalous images. This is illustrated in Figure 5 where ct
is disproportionately represented in the training dataset at a rate nearly
twice the other sites. While ct is the site with the largest sampling, it also
appears as though ct and le produce a disproportionate number of anomalous
images overall.

Figure 5: Distribution of 13098 normal (left) and 3916 anomalous (right)
images by individual site for training dataset.

It appears that le made up nearly half of the anomalous images present in the
training dataset. While improved sampling strategies may result in a more even
distribution of sites among normal images, such discrepancies in the anomalous
images would most likely remain. Such differences in occurrence rate by site
are certainly something to be monitored in the flagged images caught by the
fqi filter during deployment.

Various statistical parameters for these images are plotted in Figure 6.
Although the variance seems to be a good measure for identifying anomalous
images, it becomes less effective during the high activity periods. In
general, the erroneous images have higher variance as well as the RMS values
relative to the normal images. The statistical overlap between the images
during high-activity periods and the anomalous images often was seen in the
database and it became one of the main motivations for the development of this
filter.

Figure 6: Statistics for training dataset highlighting the differences between
normal (green) and anomalous (red) images. Figure 7: Outline of fqi Network
design. This is based on a basic convolutional neural network which reduces
the input image to a binary classification to determine whether the image is
normal or anomalous.

###  3.2 Network Design

The design of the filter, outlined in Figure 7, is based on the neural network
technique of image classification (Wang, , 2022; Yal, , 2023). However, while
most classification algorithms look at a wide variety of classes (Yal, ,
2023), ours reduces the images into two bins: normal images and the anomalous
images (Vailaya et al., , 1998). The network design is simple, consisting of 3
convolutional layers, each followed by a leaky ReLU activation function and a
max pooling. The leaky ReLU activation function was chosen for its better
accuracy when compared to the commonly used ReLU activation function (Dubey
and Jain, , 2019). The network is ended with a sigmoid activation function due
to its compatibility with more shallow networks (Wang, , 2022).

One of the most important choices in designing the network was the ability to
weight the output classes in order to minimize the number of images falsely
classified as anomalous. The reason for this concern is the statistical
similarity between anomalous images and normal images during periods of high
activity. This means that if we allow the network to be more liberal in its
tendency to classify images as anomalies, we run the risk of the network
excluding large time-series of high-activity periods. To help prevent this,
the network was designed to output a 2 $\times$ 1 vector containing scores for
each possible class as discussed by Khan,  (2019). These scores range between
a value of 0 and 1 for each class.

###  3.3 Hyperparameters

While a variety of hyperparameters were explored for the training regiment,
the final training regiment was set for 150 epochs with a batch size of 32,
and a learning rate of 0.0008. The anomalous images were weighted at 1.6 while
the normal images were weighted at 1.0 in order to minimize the occurrence of
false anomaly classifications.

##  4 Performance Validation

There were two experiments performed in order to validate the efficacy of the
neural network filter. The first of these was a random sampling of 3250 site
fqi images from the keep which were then classified by the filter and also
manually checked. The second experiment was an analysis of 617 images were
rejected at sites due to the RMS values above the threshold as discussed in
Section 2.1 and had been moved to Oubliete.

###  4.1 Test 1: Random Sample

The first experiment was the utilization of the fqi network to classify 3250
randomly sampled images from the storage keep. Of the 3250 randomly sampled
images, 1 was found to be corrupt and unusable, leaving 3249 images to be used
for the experiment. These images were then passed through the fqi network,
which classified the individual site images as either normal or anomalous. We
also manually inspected the 3249 images to ground-truth the dataset. Of the
3249 images, 98.8 % were correctly classified as normal images, and 0.8 % were
correctly classified as anomalous. In addition, the network incorrectly
classified remaining 0.4 % images. Of these 12 images, 10 were anomalous
images which the network labeled as normal and 2 were normal images which the
network misclassified as anomalous (Table 1). Overall, the network correctly
identified normal images with an accuracy of 99.9 % and correctly identified
anomalous images with an accuracy of 71.4 % This is in line with the intended
results, as the network’s training regime was biased towards classifying
images as normal in order to prevent discarding large amounts of good data due
to the statistical similarities between anomalous and high-activity images as
seen in the training dataset statistics (Figure 6).

Table 1: Confusion matrix for random sampling of fqi images from keep to validate the fqi Network. Of the 3250 images selected, one image was found to be corrupt and thus dropped from the overall sample.  | Actual Normal | Actual Anomaly
---|---|---
Predicted Normal | 3212 | 10
Predicted Anomaly | 2 | 25

###  4.2 Test 2: RMS Rejections

The second experiment was comparing the rejection performance of the fqi
network to the current RMS threshold applied at sites before they are
transferred to iQR and merged into mrfqi products. In this threshold, images
are rejected if they have a RMS over 60. As mentioned above, the main drawback
of this technique is that it can result in the rejection of images that are
normal during high activity periods or allowing erroneous images to pass
through during the low-activity periods.

For this experiment, we used 617 discarded site images that were stored in
Oubliete. These images were manually checked to determine whether or not they
had been correctly classified as anomalous by the thresholding methodology. Of
these 617 images, 91.6 % of these images were incorrectly discarded and
contained valuable data, while 8.4 % of the images were correctly discarded
for containing artifacts (Table 2). It should be noted that it did not
determine the performance of the RMS threshold on images which were labeled as
normal and this would have required the manually scanning of all data produced
by the GONG network, which is outside of the current scope of this project.

The next step was to pass all discarded images through the newly developed fqi
network. The network labeled 92.1 % of the images as normal and labeled 7.9 %
of the images as anomalous. The normal image predictions had an accuracy of
99.6 %, while the anomalous predictions had an accuracy of 90.4 %. This gives
the network an overall accuracy of 98.7 % with a false positive rate of 0.4 %,
and a false negative rate of 9.6 % (Table 2).

The comparison is stark. Next to the 8.4 % accuracy of the RMS threshold, the
neural network showed an overall accuracy of 98.9 %. Thus, we can say that
implementing it as a site-based fqi filter would provide a sizable improvement
in the quality of mrfqi images and by extension the farside seismic maps
produced by the GONG network.

Table 2: Test result comparison for RMS filtering (left) and the fqi network (right). The normal predictions for the thresholding method are excluded due to the volume of images, placing the category outside the scope of this study.  Threshold | Actual Normal | Actual Anom. |  | fqi Net | Actual Norm. | Actual Anom.
---|---|---|---|---|---|---
Pred. Norm | N/A | N/A |  | Pred. Norm | 563 | 5
Pred. Anom | 565 | 52 |  | Pred. Anom | 2 | 47

##  5 Effects of Implementation

There are two main areas of concern for implementing the fqi filter. The first
is what is the effect it has on duty cycle. If the filter proves to take large
sections of data, and reduce the duty cycle of the GONG network to below the
generally accepted usability threshold of 0.8 or 80 %, then we would not
consider it adequate as a QAQC measure. The second area of concern is the
effect it has on the farside maps. If the application of the filter results in
significantly lower quality of the farside maps, it would not be considered
adequate as a QAQC measure.

In order to determine the effects of the developed fqi filter on duty cycle,
we examined all images collected between 2010-01-01 and 2014-12-31 for, a
total of 1826 days, or 2,629,440 minutes. It is important to mention that our
data set include only those observations that were transferred to the NISP
Data Center. All rejected site images were lost due to an existing criterion
discussed in Section 2.1 and were unrecoverable. Details of the contributions
from various sites are given in Table 3. It is evident from the table that all
sites provide independent as well as overlapping observations. Though there
are significant overlaps between different sites, the sites observed
independently for about one-third of the total time. The maximum independent
observations came from the le site. It is worth mentioning that erroneous
images during the independent observations can have unfavorable effect on the
duty cycle. Figure 8 illustrates the distribution of multiple-site
observations during the day. One can easily notice that the overlaps between
multiple sites are not random but these follow a specific pattern depending
upon the season and the time during the day. The heatmap, shown in Figure 9,
summarizes the number of overlapping observations between different pairs of
sites. Since the observations are often overlapped, it is important to
quantify the effect, if any, of fqi filter on the overall network duty cycle.
We also discuss the performance of each site during the test period. These
effects are the concentration of the next two subsections of this report.

Table 3: Rate of simultaneous observations from 2010-01-01 to 2014-12-31. This covered a period of 1826 days, or 2,629,400 minutes. The image counts for the individual sites show how often each site observed as a group of 0, 1, 2, 3, or 4 sites with the % of time as part of a group in parentheses. # of Sites | minutes | le | ud | td | ct | bb | ml
---|---|---|---|---|---|---|---
0 | 153309 | 0 | 0 | 0 | 0 | 0 | 0
| (5.83 %) |  |  |  |  |  |
1 | 880548 | 288664 | 99175 | 192205 | 137100 | 81304 | 82100
| (33.49 %) | (33.81 %) | (19.05 %) | (24.05 %) | (15.57 %) | (10.14 %) | (11.07 %)
2 | 1116679 | 452873 | 347749 | 374118 | 391754 | 326827 | 340037
| (42.47 %) | (53.05 %) | (66.80 %) | (46.81 %) | (44.50 %) | (40.78 %) | (45.85 %)
3 | 432654 | 111027 | 73256 | 187757 | 305556 | 347117 | 273249
| (16.45 %) | (13.00 %) | (14.07 %) | (23.49 %) | (34.71 %) | (43.31 %) | (36.84 %)
4 | 46250 | 1170 | 402 | 45080 | 45848 | 46250 | 46250
| (1.76 %) | (0.14 %) | (0.08 %) | (5.64 %) | (5.21 %) | (5.77 %) | (6.24 %)

In the next section, we look at the effects of filtering out anomalous fqi
images on the farside maps. There, we show multiple examples of farside maps
where the duty cycle either remained unchanged, or only slightly reduced with
the application of fqi filter, and examine the effect excluding anomalous
images has on the signal-to-noise ratio of these developed maps.

###  5.1 Impact on Network Duty Cycle

The impact of the fqi filter on the network duty cycle is an important concern
for the implementation of this newly developed quality assurance tool as well
as for the performance of the GONG network. If the network is too aggressive
in its labeling of anomalous images, we risk losing large time series of good
data. This is particularly difficult due to the overlap in statistical
similarities between anomalous and high-activity images (Figure 6). However,
if the network lets too many images pass through, then it will be ineffective
as a QAQC measure. An analysis of the impacts of the fqi filter during our
study period shows that it has been able to remove a significant number of
anomalous images from the test dataset without seriously impacting the overall
duty cycle of the GONG network. We summarize total number of rejected images
at each site in Table 4 and Figure 10 displays the daily distribution of these
rejected site images. We discuss two types of images in the following
sections; the unfiltered and filtered images are the images prior and after
passing through the proposed fqi filter, respectively.

Figure 8: Minute-resolution figure showing the number of sites observed simultaneously during the day for the entire study period. Note that the temporal and seasonal patterns are clearly visible through density fluctuations. Figure 9: Heatmap showing the frequency of simultaneous observations for all site combinations for the testing period. Table 4: Total number of images contributed by each site and the number of rejected images by the fqi filter. The % values indicate the percentage of all rejected images contributed from each site. Site | Total Images (Unfiltered) |  | Rejected Images (Filtered)
---|---|---|---
| Total # | % |  | Total # | % of site Images | % of All Rejections
le | 853734 | 18.50 |  | 624 | 0.07 | 4.10
ud | 520582 | 11.30 |  | 1454 | 0.28 | 9.50
td | 799160 | 17.40 |  | 6510 | 0.81 | 42.50
ct | 880258 | 19.10 |  | 328 | 0.04 | 2.10
bb | 801498 | 17.40 |  | 5974 | 0.75 | 39.00
ml | 741636 | 16.10 |  | 425 | 0.06 | 2.80
Total: | 4596868 | 100.00 |  | 15315 | 0.33 | 100.00

Figure 10: Number of images rejected each day of the sample period. Note the
high volume events for each year which make up periods of consistent anomaly
production. Figure 11: Changes in network duty cycle due to fqi network
implementation on the test dataset. The dashed lines show mean duty cycles for
filtered and unfiltered images.

In short, we find that the overall impacts on the GONG network’s duty cycle
were minimal after passing all site images through the fqi filter. From Table
4, it can be seen that of the 4,596,868 images in the test dataset, the
network excluded only 0.33 % of the total dataset. The daily distribution of
rejected site images and the yearly total rejections for the testing period,
exhibited in Figure 10, clearly suggests the sporadic nature of these
rejections and the occurrence of these anomalous events is unpredictable. We
notice that the maximum rejections happened during 2014. This resulted in the
slight reduction of mean duty cycle from 94.17 % to 94.12 %, and the median
duty cycle from 97.70 % to 97.65 % (Figure 11). Due to significant overlaps
between different sites, there were only 145 days when the network duty cycle
was affected by the exclusion of erroneous images. Of these days, as shown in
Figure 12, the duty cycles were reduced by 0 – 1 %, 1 – 2 %, 2 – 4 % and 4 – 5
%, for 126, 7, 8 and 3 days, respectively. It is visible from Figure 13 that
there was only one day when the duty cycle for the GONG network reduced by 10
%.

Figure 12: Drops in duty cycle due to application of the fqi filter excluded
15,315 of the 4,596,868 images, affecting 145 days.  Figure 13: Daily duty
cycle for the network-merged images during the testing period from 2010
through 2014. The effects of the fqi filter are shown in red and the lower y
limit shown is 0.45.

The relatively minimal impact of the exclusion of bad site images on the
network duty cycle is attributed to the distributed and redundant nature of
the GONG network (Hill et al., , 1994). While there are temporal coverage
patterns of the overall network as shown in Figure 8 and also discussed in
detail by Jain et al., 2021b , the network did not collect any observations
for 5.7 % of the total minutes during our study period. Overall, total
independent observations from all individual sites in the network were 33.4 %
of the total examined minutes, the simultaneous observations by two, three and
four sites were 42.7 %, 16.5 % and 1.6 %, respectively. It is worth mentioning
that the network’s duty cycle is most vulnerable to impact from the exclusion
of site-images during the independent observing periods. These opportunities
are especially prevalent during the period between July and October when the
ud site is prone to be down due to the Indian monsoon or any other site being
down due to instrument failures or other reasons (Jain et al., 2021b, ). The
specifics of which sites often observe at the same time will be covered in the
site-by-site analysis in the next section.

###  5.2 Impact on Site DC

While the potential impact of the fqi filter on the duty cycle of entire
network is of obvious importance, we also investigate its effects on the duty
cycles for individual sites. We display distribution of duty cycle at each
site in Figure 14. Aside from the obvious concern, that the overall resiliency
of the network is dependent on its component sites, we also want to explore
when and which sites produced anomalous images and what could be the probable
reason. For reliably identifying anomalous image occurrences at each site in
near-real time, this fqi filter may be proven useful for setting up a flag for
an instrument malfunctioning if a large number of images are rejected. This
information may be useful for the NISP operations team who may be able to
identify and troubleshoot the regularly occurring problems in a timely manner.
It should be noted that, due to the time discrepancy between data collection
and when this test was conducted, any site images which have been excluded at
the sites were not included for the purpose of DC analysis. However, as the
prior performance comparison showed, we can expect the results to be
comparably favorable.

Figure 14: Histogram of the distributions of duty cycles for each site before
the fqi filter is applied.  Figure 15: Images rejected by month for the sample
period. Site contributions are shown in different colors.

####  5.2.1 Learmonth (le)

Learmonth (le) had a mean daily duty cycle of 32.47 % for the testing period
and as exhibited in Figure 14, for the majority of its days, the duty cycle
was between 0.30 and 0.50. The details of total observations and the rejected
images are given in Table 4. Overall it collected 853,734 minutes worth of
observations, which makes 18.50 % of the total observations for the testing
period. Of these total minutes observed by le, about one-third observation had
no overlap with any other site and more than half were overlapped by one other
site. Rest of the observations were gathered with two or three other sites
(see Table 3). It is further evident from Figure 9 that the maximum overlap of
le was with ud, followed by ml, td, bb, and ct, respectively.

From Table 4, it can be seen that of all the images collected by le, 624 (0.07
%) images were rejected by the fqi filter for being anomalous. This comprises
4.1 % of all the anomalous images found by the fqi network. Figure 15 provides
number of the monthly rejections each year. We did not find any outstanding
events contributing to anomalous images from the le site. This is also
confirmed by a lack of visible drops in the daily duty cycle plotted in Figure
16. Overall, the application of the fqi filter reduced the mean duty cycle of
the le site from 32.47 % to 32.45 % (Table 5) and did not discard all the
observations for a given day.

Figure 16: Daily duty cycle for the le site for the testing period from 2010
through 2014. The effects of the filter on duty cycle are shown in green. The
major drops in duty cycles are seen on one day in February 2012 and several
days in June 2014.

####  5.2.2 Udaipur (ud)

As illustrated in Figure 14, while a majority of the non-zero days for the ud
site had a duty cycle between 0.3 and 0.5, there are a disproportionate number
of days when it did not contribute any observation to the GONG network. This
is due to the annual monsoon season, which forces ud site to shutdown for a
couple of months every year. These periods are clearly visible in Figure 17.
In addition, there was a disruption which lasted for several months from mid
2010 to the beginning of 2011 due to a fire near the ud site. These long
outages adversely affected the mean and median duty cycles of ud for the
testing period of five years and the mean and median daily duty cycles were
19.80% and 23.85 %, respectively, as summarized in Table 5. Of the 520,582
minutes that the ud site observed (Table 4), 19.05 % were independent without
overlapping with any other site. About two-third of ud observations were
collected simultaneously with only one other site. There were relatively
smaller number of observations that had overlaps with two or more other sites.
Details of these overlapping observations are given in Table 3. As illustrated
in Figure 9, the ud site most often observed in conjunction with two
neighboring sites, i.e. le and td sites.

Table 5: Duty cycle statistics for filtered vs. unfiltered images for each of the GONG sites during the testing period of five years. The percentage statistics are taken to 2 decimals places as many of the changes are too minute to be seen otherwise. Site | Filter | Mean | Median | Standard | Maximum | Minimum | # of Days Dropped
---|---|---|---|---|---|---|---
|  | DC [%] | DC [%] | Deviation [%] | DC [%] | DC [%] | to 0 % DC
le | Unfiltered | 32.47 | 38.20 | 14.86 | 48.50 | 0 |
| Filtered | 32.45 | 38.20 | 14.87 | 48.50 | 0 | 0
ud | Unfiltered | 19.80 | 23.85 | 17.27 | 48.30 | 0 |
| Filtered | 19.74 | 23.85 | 17.29 | 48.30 | 0 | 6
td | Unfiltered | 30.39 | 35.50 | 17.12 | 49.90 | 0 |
| Filtered | 30.15 | 35.45 | 17.30 | 49.90 | 0 | 6
ct | Unfiltered | 33.48 | 37.60 | 15.37 | 50.30 | 0 |
| Filtered | 33.46 | 37.60 | 15.37 | 50.30 | 0 | 1
bb | Unfiltered | 30.48 | 34.00 | 15.81 | 50.50 | 0 |
| Filtered | 30.25 | 33.80 | 15.88 | 50.50 | 0 | 3
ml | Unfiltered | 28.20 | 31.00 | 15.00 | 50.00 | 0 |
| Filtered | 28.19 | 31.00 | 15.00 | 50.00 | 0 | 0
Figure 17: Daily duty cycle for the ud site for the testing period from 2010
through 2014. The effects of the fqi filter on duty cycle are shown in cyan.
The major drops in duty cycles are apparent in August 2014 and November 2014.

A total of 1,545 (0.30 %) out of 520,582 images were identified as anomalous
by the fqi filter. These made up 9.50 % of the total anomalous images found
for the testing period. Figure 15 shows that there were two major periods in
August and November in 2014 when most rejections happened. In addition, the
filter brought down the duty cycle to zero only for 5 days. While one of these
days was during an expected operational period, many of these days were during
a low-performance period during the month of August 2014. This is clearly
visible in Figure 17 where we display the daily duty cycle for the entire test
period. Also, the fqi filter reduced the mean duty cycle of the ud from 19.80
% to 19.74 % but did not affect the median DC. A comparison between the
statistics of filtered and unfiltered images is given in Table 5.

####  5.2.3 El Teide (td)

The El Teide (td) site had a mean and median daily duty cycles of 30.39 % and
17.12 %, respectively, for the testing period. As exhibited in Figure 14, the
non-zero duty cycle days for the td site were disproportionately distributed
towards 0.50 with most of the observing days being reported as above a duty
cycle of 0.30 and nearly 25 % of reported days being between 0.45 and 0.50.
While td does not experience the seasonal drops in observations similar to ud,
it provided good coverage during the months of April to September (Figure 18).
As summarized in Table 3, the statistical analysis of the total observations
for 799,160 minutes at td suggests that it collected independent observations
for 24.05 % of those minutes, and the simultaneous observations with one, two
and three other sites for 46.81 %, 23.49 % and 5.64 %, respectively. From
Figure 9, we notice that the td site was most often observed with the ct and
bb sites.

Figure 18: Daily duty cycle for the td site for the testing period from 2010
through 2014. The effects of the fqi filter are shown in red. The significant
drop in duty cycles are apparent in December 2013 and January 2014.

From Table 4, we note that the implementation of fqi filter rejected 6510
observations. These rejected images accounted for 0.81 % of the total
observations at td and 42.51 % of the all anomalous images identified by the
fqi network, making the td site the largest contributor of anomalous images
for the testing period. As a result of the filter’s application, the duty
cycles for 6 days completely reduced to 0 (Table 5). It is also observed from
Figure 15 that the vast majority of the anomalous images were generated during
December 2013 through February 2014. The application of the fqi filter reduced
the mean duty cycle of the td site from 30.39 % to 30.15 %, however increased
the median duty cycle from 17.12 % to 17.30 %.

Figure 19: Daily duty cycle for the ct site for the testing period from 2010
through 2014. The effects of the fqi filter are shown in red. The drop in the
duty cycle is apparent in on one day September 2011 where the duty cycle
dropped to 0.

####  5.2.4 Cerro Tololo (ct)

The Cerro Tololo (ct) site had an average daily duty cycle of 33.76 % and a
median duty cycle of 37.60 % for the testing period. It is demonstrated in
Figure 14 that the non-zero duty cycle days for the ct site were largely above
0.30 with the majority of days reporting a duty cycle between 0.45 and 0.50.
During the testing period, the ct site produced consistent observations but
with some notable lapses in September of 2010 and 2011, and February and April
of 2012. These gaps are clearly visible in Figure 19. The application of the
fqi filter resulted in one day only having its duty cycle reduced entirely to
zero. Of the 880,258 images collected at ct, 328 (0.04 %) of those images were
identified as anomalous by the neural network (Table 4), making it the lowest
contributing site to the anomalous images and accounted for 2.14 % of the
total anomalous images found during the testing period.

Of the 880,258 minutes observed by ct during the testing period, it observed
independently for 15.57 % of the total minutes. In addition, its observations
were overlapped with one, two and three other sites for 44.50 %, 34.71 %, and
5.21%̇ of the total minutes, respectively. It is also seen from Figure 9 that
the ct site observed most frequently with the td and bb sites. The application
of the fqi filter reduced the mean duty cycle for ct from 33.48 % to 33.46 %
and did not affect the median duty cycle.

Figure 20: Daily duty cycle for the bb site for the testing period from 2010
through 2014. The effects of the fqi filter are shown in red. The drops in
duty cycles are apparent in July 2010, July – September 2011, August –
September 2013 and July – December 2014.

####  5.2.5 Big Bear (bb)

The average daily duty cycle of Big Bear (bb) site was 30.48 % with a median
duty cycle of 34.00 %. As shown in Figure 14, a little over 10 % of the
reported days for the testing period were reported as having a duty cycle of
0, while 20 % of the reported days had a duty cycle between 0.45 and 0.50 for
the bb site. From Figure 20, we find that the bb site provided relatively good
coverage in the months of May and June. Of the 801,498 images from bb, 5974
(0.75 %) of them were rejected for being anomalous (Table 4). This comprised
39.01 % of all anomalous images found for the testing period, making the bb
site the second largest contributor of the erroneous images in the network.
There were two major events, as shown in Figure 15, which accounted for the
majority of the rejected images from the bb site, the first occurring between
July and September of 2012, and the second occurring between July and November
of 2014. It is important to mention that the RMS filter became operational in
July 2014 as discussed in Section 2.1, but it did not exclude all the
anomalous images after its implementation and allowed these images to get
ingested in downstream pipelines and related data products. The application of
the fqi filter on the bb site images resulted in reducing the duty cycle to 0
for 3 days as listed in Table 5.

Figure 21: Daily duty cycle for the ml site for the testing period from 2010
through 2014. The effects of the filter are shown in green. There were no
major drops in the duty cycle due to the applications of fqi filter, however
one can notice changes in August 2010 and January 2013.

Of the 801,498 minutes observed at the bb site during the testing period, it
provided independent observations for 10.14 % of those minutes, and was one of
two, three and four sites observed at the same time for 40.78 %, 43.31 % and
5.77 % of the total minutes, respectively (Table 3). It is noticed from Figure
9 that the bb site most often observed with the ml and ct sites. Due to the
implementation of the fqi filter, the mean daily and median duty cycles were
reduced from 30.48 % to 30.25 %, and 34.00 % to 33.80 %, respectively.

####  5.2.6 Mauna Loa (ml)

The last site to be considered is Mauna Loa (ml). The daily duty cycles for
the testing period are shown in Figure 21. It had an average daily duty cycle
of 28.20 % with a median duty cycle of 31.00 %. As presented in Figure 14, the
ml site had a DC of 0 for a little over 10 % of the reported days with the
majority of its days being reported above 0.30. For the testing period, ml had
relatively consistent performance except for two large outages occurring in
May of 2011, and February/March of 2014. Additionally, observations collected
during October through December were relatively less due to its geographic
location. Nevertheless, this site has crucial importance because of its
location in the middle of the Pacific ocean and provides vital support for
overlapping observations to its neighboring sites. Of the 741,636 images
collected by the ml site, 425 (0.06 %) of these images were identified as
anomalous by the network (Table 4). These comprised 2.78 % of all the
anomalous images found during the testing period. These images were rejected
during multiple small epochs as seen in Figure 15 and the implementation of
the fqi filter did not result in the duty cycle of any day being brought down
to zero for this site (Table 5).

The ml site collected observations for 741,636 minutes in total and 11.07 % of
them were independent observations. As given in Table 3, 45.9 % of its
observations were overlapped by one other site, 36.8 % and 6.2 % were
overlapped with two and three other sites, respectively. An examinations of
Figure 9 reveals that the ml site had maximum overlap with bb and then with ct
sites. Due to the implementation of the fqi filter on ml site images, the mean
daily duty cycle reduced from 28.20 % to 28.19 %, and the median duty cycle
remained unchanged at 31.00 %.

##  6 Case Studies for Farside Map Effects

###  6.1 Noise Reduction in Merged fqi Images

In order to illustrate the impact of single image exclusions on merged fqi
images, we have selected three examples from the database where fqi filter
identified erroneous site images. These were taken at 20100805t2005,
20141031t1742, and 20140625t0502, representing examples of some of the common
types of anomalies seen in the site fqi images.

  1. 1.

20100805t2005 The first example includes a fully contaminated site image from
ml shown in the top left panel of Figure 22. These types of artifacts often
start at one corner of the site images and progress until they cover the
entire observed hemisphere. There were two more sites, ct and bb, that
provided observations at the same time. When anomalous ml image was combined
with good ct and bb images, it contaminated the merged product (mrfqi) shown
in the top right panel of the same figure, completely erasing the valuable
Doppler signals. The application of fqi filter correctly identified ml image
as anomalous and rejected its inclusion in the merged image. By eliminating
the anomalous image, shown in the bottom row, we obtained a good quality
merged mrf6i image that can be reliably used in the farside pipeline or any
other scientific study.

Figure 22: Effects of including (top row) and excluding (bottom row) anomalous
site data in merged fqi image for 20100805t2005. The ml image was identified
by the fqi filter network. The merged images without contaminated data are
labeled F6I instead of FQI for the traditional pipeline.

  2. 2.

20141031t1742 Another example shows a corrupted image with the so-called
dinner plate artifacts. These artifacts are a ring pattern which often appear
from time to time and disappear suddenly. This is a more common type of
artifact seen in the site images that may affect either full or half disk. Its
origin is not yet fully understood, however it adversely affects the quality
of the merged images. As visible in Figure 23, the rings in bb image
translated to the final merged image, introducing subdued noise in the ring
pattern. The fqi filter eliminated the bb image from the list of images to be
merged for this timestamp, thus allowed us to produce a merged image without
any artifact.

Figure 23:  Same as Figure 22, but for the merged image at 20141031t1742
excluding the bb image.

  3. 3.

20140625t0502 The third example of the contaminated site fqi image includes a
pressed plate artifact. These often appear suddenly and can completely erase
the data from good images when included in merged (mrfqi) images. Due to their
significant impact, it is important for the network to identify and exclude
these images, as they can introduce significant noise from a single point. By
excluding such artifacts, we are able to produce clean mrfqi images. Figure 24
shows an image from le with this type of artifact. Although ud image at the
same time was absolutely normal, the inclusion of abnormal le produced
corrupted merged image. The result of using the fqi filter for this timestamp
as shown in the bottom row.

Figure 24: Same as Figure 22, but for the merged image at 20140625t0502
excluding the le image.

###  6.2 Noise Reduction in Farside Maps

While the effects of the fqi network are not visible in every farside map, it
is more prominent during the periods when the fqi filter identified several
anomalous images and the seismic maps were extremely noisy. The network filter
significantly reduced the noise in exchange of a small drop in duty cycle. In
order to demonstrate the efficacy of the small number of images excluded by
the fqi filter, we discuss three examples of the farside seismic maps at 1200
UT on 20111126, 20111202, and 20120206. These maps are calculated using 1440
merged images. The statistical effects of the implementation of the filter on
farside maps are summarised in Table 6.

Table 6: Summary statistics for production (fqm) and cleaned (f6m) sample phase shift maps.  Date | Map | Number of | Duty | Phase Shift (radians) | Standard | Signal-to-noise
---|---|---|---|---|---|---
| Type | Input Images | Cycle | Min | Max | Mean | Deviation | Ratio
20111126t1200 | fqm | 1395 | 0.97 |  $-$3.34 | 2.738 | 0.025 | 0.401 | 0.063
| f6m | 1383 | 0.96 |  $-$0.206 | 0.133 |  $-$0.017 | 0.051 | 0.338
20111202t1200 | fqm | 1430 | 0.99 |  $-$0.691 | 0.973 | 0.027 | 0.173 | 0.155
| f6m | 1430 | 0.99 |  $-$0.2 | 0.134 |  $-$0.015 | 0.050 | 0.307
20120206t1200 | fqm | 1239 | 0.86 |  $-$0.594 | 1.064 | 0.049 | 0.155 | 0.318
| f6m | 1235 | 0.86 |  $-$0.241 | 0.185 |  $-$0.003 | 0.055 | 0.054

  1. 1.

20111126t1200 The first example is the farside seismic map with the timestamp
of 20111126t1200. This map was initially computed with 44 contaminated site
fqi images from the td site and the exclusion of these images resulted in the
loss of 12 merged fqi images. The unfiltered images introduced significant
noise in the farside as displayed in the left panel of Figure 25, however the
barring these images not only resulted in a striking visual improvement in
clarity (right panel in the same figure), but also a statistically noticeable
improvement. From Table 6, it can be seen that the standard deviation dropped
from 0.401 to 0.051 radians, indicating a far more narrow band of readings.
Additionally, the minimum and maximum values changed from $-$3.34 to $-$0.206
radians and 2.738 to 0.133 radians, respectively. The values with unfiltered
images were excessive and had no physical significance. The mean being reduced
from 0.025 to $-$0.017 radians is more in line with the predominantly negative
phase shift values that we expect to see from the helioseismic maps. The
signal-to-noise ratio also increased significantly from 0.063 to 0.338.

Figure 25: Farside phase-shift maps using contaminated (fqm) and cleaned (f6m)
merged site images for 20111126t1200. This fqm map was contaminated by
anomalous site images which were identified by the fqi network. The scale
depicts the phase-shift values in radians with the frontside of the sun masked
out in green.

  2. 2.

20111202t1200 The second example is the farside seismic map at 20111202t1200.
This map, displayed in Figure 26, also has visible and statistical
improvements when filtered images are used. The contaminated 83 images from
the le and ml sites produced a noisy map as shown in the left panel and the
exclusion of which did not reduce the number to good merged fqi images.
Similar to previous case, the exclusion of erroneous images dropped the
standard deviation from 0.173 to 0.050 radians, indicating a more accuracy in
the farside map. The minimum and maximum values also modified from $-$0.691 to
$-$0.200 radians and from 0.973 to 0.134 radians, respectively. The modified
values are within the expected range of phase shifts and the mean changed from
0.027 to $-$0.015 radians. Again, this shows the predominantly negative phase
shift values that we expect from the helioseismic maps. The signal-to-noise
ratio again doubled from 0.155 to 0.307 (Table 6).

Figure 26: Same as Figure 25, but for 20111102t1200.

  3. 3.

20120206t1200 The last illustration is the map from 20120206t1200 shown in
Figure 27. This is the most interesting map because it appears to be a seismic
maps for the abnormally high-activity period at first glance. However, a close
inspection of the images used to produce this map reveals that the fqm map was
contaminated by 44 anomalous images from the td site and the exclusion of
these images resulted in the loss of four merged fqi images. The result of the
exclusion of these images produced a map with far more consistency that lost
large phase-shift values which it initially displayed. The maximum phase-shift
value was reduced from 1.064 to 0.185 radians, while it’s minimum was also
brought in from $-$0.594 to $-$0.241 radians. This also reduced the standard
deviation from 0.155 to 0.055 radians. However, the signal-to-noise ratio
reduced from 0.318 to 0.54 (see Table 6). This map is an excellent example of
the necessity of the fqi neural network filter. While it clearly had anomalous
images as its components, statistical analysis of the map itself would not
have revealed it to be faulty.

Figure 27: Same as Figure 25, but for 20120206t1200.

These examples show the adaptability of the discriminatory network and its
ability to provide quality assurance and control measures in a variety of
statistically novel situations. We further checked the credibility of f6m maps
by comparing them with those produced by both Helioseismic and Magnetic Imager
farside pipelines based on the helioseismic holography (a similar technique
used by the NISP farside pipeline) and the time-distance techniques, and found
a close correspondence between them. It should be noted that HMI has several
advantages being in space and the images are less prone to any artifacts.

##  7 Network Updates and Improvements

There are two methods through which the performance of the current fqi network
can be improved. The first of these is re-training, during which the network
weights would be updated through training on newly labeled data. The second of
these methods is a network re-design, in which the current network
architecture would be replaced by an updated architecture design.

###  7.1 Re-Training

In order to make network re-training and updates as easy as possible, a
Jupyter notebook has been created and uploaded to the NISP Data Center’s
GitLab under the name fqi_Network_Retraining. While the README file in the
repository contains specific step-by-step instructions, the seven steps of
implementing new weights are also outlined in this document. This explanation
will assume that the user has already locally cloned the retraining repository
and has the appropriate environmental packages installed.

  1. 1.

Load the newly labeled data: Load the newly labeled normal and anomalous data
into .lst files so that it can be included in the training regime. The
notebook assumes that a number of images which have not been previously used
in training the network have been manually labeled into Normal and Anomalous
classifications. Directories to the new anomalous and normal data should be
collected and stored in two files named anom_new.lst and norm_new.lst
respectively. These should be stored in the data/new_data/ subdirectory of the
retraining regime. The re-training regime is designed to take directories from
the oQR directory. These files will be combined with old training data in
order to update the fqi network weights. At the end of the re-training
process, there is an opportunity to combine the new and old datasets so that
the process can be repeated as many times as possible. The more data that is
added to the re-training data, the better the updated results will be. It is
recommended that re-training be conducted with at least a 1 % expansion on the
current dataset, but more is always better.

  2. 2.

Ensure old network weights are available: Ensure that the old network weights
are available. These are stored as the .pt file from which the fqi Network
loads its weights in deployment. This file needs to be stored in the
params/old_params directory, and does not need to have a specific name as the
re-training regime will pick up any file stored in this directory.

  3. 3.

Run the training regime: Run the training regime. So long as the environment
is properly set up, this should only entail running the Jupyter notebook. All
of the required packages are stored in the first cell of the notebook.

  4. 4.

Evaluate the network performance: Evaluate the network performance. New
network performance can be seen at the bottom of the Jupyter notebook, where
the network statistics, confusion matrix, and a visual sample of said matrix
results can be seen. If there are patterns of images which the network has
trouble identifying, then the suggestion is to add more of those images to the
new dataset and re-run the program before re-deploying. It should be noted
that the goal is not absolute perfection, as this would be indicative of over-
training and may, counter-intuitively, lead to poor performance in deployment,
but rather the minimization of false-negative results so as to avoid the
taking of large sections of high-activity periods.

  5. 5.

Make adjustments to the network: If network performance is not sufficiently
improved, make adjustments. These include gathering more data, adjusting
hyperparameters such as learning rate, batch size, or number of epochs, and
double-checking the sample for incorrectly labeled images.

  6. 6.

Update the network weights: Update the network weights. The new weights will
be stored in params/new_params/Spotty_Net_Update.pt. This file can be renamed
in accordance with the decided naming conventions for the fqi Network weights
and replaced in the appropriate file.

  7. 7.

Merge the new and old data: Once the network performance is satisfactory,
merge the new and old data to prepare the re-training regime for future
updates. Replace the files anom_new.lst, anom_old.lst, norm_new.lst,
norm_old.lst with the files found under new_data of the same name. After this
is done, you may delete the new_data directory.

###  7.2 Network Design Updates

The second option for improving the performance of the fqi network would be a
fundamental re-design. While the specifics of a network re-design are outside
the scope of this discussion, it would broadly entail re-training on the
existent dataset with an updated network architecture. Such a campaign would
be more intensive than a simple weight update and thus should be considered
carefully. However, given the rapid pace of improvement in the field of
machine learning, new network designs may provide significant performance
improvements. New strategies such as GANs or other fundamental improvements in
architectures should be considered for performance improvements (Di Mattia and
et al., , 2021; Xia and et al., , 2022).

In the event the the network is re-designed, both the weights file and the
network architecture files should be replaced. Once these are replaced and the
associated calls in the code have been updated, that should be sufficient to
run the network on the new architectures.

##  8 Summary

The binary classification network developed and analyzed in this report has
proven to be a highly effective method for reducing the impact of anomalous
site-images on the noise of NISP’s farside helioseismic maps. This neural
network-based classification methodology is resilient enough to accurately
identify anomalous images despite their statistical variability. It is also
more selective than the current thresholding technique, preventing the
exclusion of large amounts of valuable high-activity data. The spacial
variability of the GONG network’s observational sites also provide adequate
resiliency to compensate for the majority of anomaly production events at any
single site. When we also consider the potential for re-training and redesign,
the fqi network has proven to be invaluable and adaptable QAQC methodology for
the NISP farside program. We hope that the performance and adaptability of
this new methodology serves as a proof of concept for the implementation of
similar measures for other NISP data products in the future.

Acknowledgements: This work utilises GONG data obtained by the NSO Integrated
Synoptic Program, managed by the National Solar Observatory, which is operated
by the Association of Universities for Research in Astronomy (AURA), Inc.
under a cooperative agreement with the National Science Foundation (NSF) and
with contribution from the National Oceanic and Atmospheric Administration
(NOAA). The GONG network of instruments is hosted by the Big Bear Solar
Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur
Solar Observatory, Instituto de Astrofísica de Canarias, and Cerro Tololo
Interamerican Observatory. This work is partially supported by the Windows On
the Universe (WoU) grant funded by NSF.

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