# Modeling of Nitric Oxide Infrared radiative flux in lower thermosphere: a
machine learning perspective

Dayakrishna Nailwal  Indian Institute of Technology Roorkee, Roorkee-247667,
Haridwar,India  M V Sunil Krishna  Correspondence to: M V Sunil Krishna,
<EMAIL_ADDRESS>Indian Institute of Technology Roorkee,
Roorkee-247667, Haridwar,India  Alok Kumar Ranjan  Indian Institute of
Technology Roorkee, Roorkee-247667, Haridwar,India  Jia Yue  NASA’s Goddard
Space Flight Center, 8800 Greenbelt Rd, Greenbelt, 20771, USA  Catholic
University of America, 620 Michigan Avenue, NE, Washington DC, 20064, USA

###### Abstract

Nitric Oxide (NO) significantly impacts energy distribution and chemical
processes in the mesosphere and lower thermosphere (MLT). During geomagnetic
storms, a substantial influx of energy in the thermosphere leads to an
increase in NO infrared emissions. Accurately predicting the radiative flux of
Nitric Oxide is crucial for understanding the thermospheric energy budget,
particularly during extreme space weather events. With advancements in
computational techniques, machine learning (ML) has become a highly effective
tool for space weather forecasting. This effort becomes even more worthwhile
considering the availability of two decades of continuous NO infrared
emissions measurement by TIMED/SABER along with several other key
thermospheric variables. We present the scheme of development of an ML-based
predictive model for Nitric Oxide Infrared Radiative Flux (NOIRF). Various ML
algorithms have been tested for better predictive ability, and an optimized
model (NOEMLM) has been developed for the study of NOIRF. This model is able
to extract the underlying relationships between the input features and
effectively predict the NOIRF. The NOEMLM predictions have very good
agreements with SABER observation during quiet time as well as geomagnetic
storms. In comparison with the existing TIEGCM model, NOEMLM has very good
performance, especially during extreme space weather conditions. The results
of this study suggest that utilizing geomagnetic and space weather indices
with ML/AI can serve as superior parameters for studying the upper atmosphere,
as compared to focusing on specific species having complex chemical processes
and associated uncertainties in constituents. ML techniques can effectively
carry out the analysis with greater ease than traditional chemical studies.

##  1 Introduction

The upper atmosphere of the Earth (mesosphere and thermosphere) is
continuously affected by solar radiation, geomagnetic storms, and other space
weather events like solar flares, Solar Energetic Particle (SEPs), Solar
Proton Events (SPEs), etc (Kutiev et al., 2013; Sinnhuber et al., 2012; Lei et
al., 2008). Direct energy deposition in the MLT region in the form of X-rays
and Extreme Ultra-Violet (EUV) radiation triggers various photochemical
reactions. However, the interaction of highly energetic solar wind plasma
associated with the frozen-in magnetic field to the Earth’s magnetic field
leads to the deposition of a part of the solar wind energy into the upper
atmosphere in the form of energetic particle precipitation and Joule heating.
This energy subsequently results in enhanced auroral activity. The electric
field and energy input through this interaction causes perturbations in
temperature, densities of neutral and charged species, ionospheric electric
fields, and dynamics in the MLT region (Fuller-Rowell et al., 1994; Lu et al.,
1998; Knipp et al., 1998; Richmond and Lu, 2000; Knipp et al., 2004; Turner et
al., 2009; Lu et al., 2016).

The MLT region is mainly composed of the primary atmospheric gas species such
as nitrogen (N2) and oxygen (O, O2) as well as trace gases like carbon dioxide
(CO2), ozone (O3), various oxides of nitrogen (NOx), helium (He) and neon
(Ne). These trace gases significantly contribute to the regulation of long-
term atmospheric compositional changes and also play a crucial role in climate
change. Therefore, there is an overarching need to quantify these trace gases
and understand their mechanistic descriptions so that we can make better
climate change predictions. The role of greenhouse gases (CO2, N2O, and O3) in
climate change is well understood. In addition to these species, there are
several such other trace gases having the potential to change long-term
climatic conditions (methane (CH4), oxides of nitrogen (NO, N2O, NO2), etc.)
(Ramanathan et al., 1985; Hansen et al., 2007). NO is a very important trace
species in the MLT region and plays an essential role in thermospheric
chemistry and energy budget. Due to its low ionization energy, NO is highly
reactive and acts as a terminal ion in many of the charge exchange and ion-
molecule/atom chemical reactions in the thermosphere (Barth, 1992). The
formation of NO in MLT is prominently enhanced by the incoming energetic
particle flux during active auroral periods (Bailey et al., 2002; Baker et
al., 2001). The formation mechanism of NO in the thermosphere is given in the
chemical scheme from R1 to R8 (Bharti et al., 2018; Ballard et al., 1993;
Rusch et al., 1991; Solomon et al., 1982).

N2 \+ $h\nu$ $\rightarrow$ N(4S) + N(4S) (R1-a)

N2 \+ $h\nu$ $\rightarrow$ N(4S) + N(2D) (R1-b)

N2 \+ $h\nu$ $\rightarrow$ N(4S) + N(2P) (R1-c)

$e^{*}$ \+ N2 $\rightarrow$ N(2D) + N(4S) + $e^{*}$ (R2)

N(2D) + O2 $\rightarrow$ NO + O (R3)

N(4S) + O2 $\rightarrow$ NO + O (R4)

NO($\nu$=0) + O $\rightarrow$ NO($\nu$=1) + O (R5)

NO($\nu$=1) $\rightarrow$ NO($\nu$=0) + $h\nu$ (5.3 $\mu m$) (R6)

NO + N(4S) $\rightarrow$ N2 \+ O (R7)

NO($\nu$=1) + O $\rightarrow$ NO + O + Kinetic energy (R8)

Where $h\nu$ represents the photon energy, $e^{*}$ represents an energetic
electron, N(4S), N(2P) and N(2D) are the excited states of atomic nitrogen,
$\nu$=0 and $\nu$=1 are the vibrational ground and first excited states of NO.

At low and mid-latitudes, primarily the energy input from the sun in the form
of soft X-rays and Extreme Ultra-Violet (EUV) radiation dissociates the
Nitrogen (N2) molecules (represented by (R1-a), (R1-b), (R1-c), which combine
with Oxygen (R3, R4) and form NO (Richards et al., 1981; Bailey et al., 2002;
Barth et al., 2003). At higher latitudes, the energy inputs from particle
precipitation due to auroral and geomagnetic activity lead to the formation of
NO by dissociating nitrogen (N2), as shown in R2. This particle precipitation
also contributes to the enhanced temperature in mesospheric and thermospheric
altitudes. The enhanced temperature, in combination with the available oxygen
density, leads to the production of vibrationally excited NO ($\nu$=1) by
collisional excitation (shown by R3 & R4) (Kockarts, 1980; Rusch et al., 1991;
Sharma et al., 1996). In addition, the joule heating and particle heating
during a geomagnetic storm also contribute to the large-scale production of NO
in polar latitudes by being a major source for the upwelling of N2 rich air
and elevating the temperature. It is important to note that the processes
shown in (R3) and (R4) are the dominant sources of NO near 110 km and above
130 km, respectively. The vibrationally active NO can also be quenched by the
process shown in R7 overall latitude regions (Richards, 2004; Siskind et al.,
1989).

The NO is a vibrationally active molecule, and due to the presence of the 5.3
$\mu$m infrared (IR) active vibrational mode, it plays a vital role in
regulating the thermospheric energy budget (Lu et al., 2010). The rate of
collisional excitation of NO by atomic oxygen into the vibrationally excited
state is given by [k1[O] $exp(-2700/T$) sec-1], where k1 is the collisional
quenching rate coefficient of NO ($\nu$=1) by atomic oxygen (k1 = 4.2 $\times$
10-11cm-3 sec-1) as reported by Hwang et al. (2003). This collisional
excitation rate of NO in the MLT region strongly depends on the temperature
and the concentration O (Sharma et al., 1998; Ranjan et al., 2023). Thus, the
infrared flux of 5.3 $\mu$m emission is highly sensitive to changes in
temperature, [O] and [NO]. The enhanced energy deposition in the lower
thermosphere during geomagnetic storms leads to an increase in temperature and
enhances the production of NO (R3, R4). Due to increased temperature, the
collisional excitation of NO($\nu$=0) with atomic oxygen (O) populates more NO
in its excited vibrational state NO($\nu$=1) (R5). The de-excitation of NO
(R6) leads to the emission of IR radiation at 5.3 µm into the space. A higher
population of NO in the excited state ($\nu$=1) results in enhanced IR
emission of 5.3 µm during the geomagnetic activity and particle precipitation
events. The vibrationally active NO can also be quenched by the process shown
in R7 & R8 overall latitude regions (Richards, 2004; Siskind et al., 1989). A
large part of energy input during intense space weather events into the MLT
region is captured by the NO, and it is re-radiated into space by means of 5.3
$\mu$m infrared flux (IRF). Hence, the NO acts as an effective cooling agent
to control the overall energy and temperature of the MLT region as a natural
thermostat (Mlynczak et al., 2005).

During the geomagnetic storm of April 2002, the zonal mean emission by NO at
5.3 µm, as observed by Sounding of the Atmosphere using Broadband Emission
Radiometry (SABER), suggested an increase of nearly 5-7 times in the total IRF
(Mlynczak et al., 2003). Several other studies (Ranjan et al., 2023; Bharti et
al., 2018; Lu et al., 2010; Mlynczak et al., 2010) have confirmed the role of
NO 5.3 µm infrared flux (IRF) in effectively cooling the upper atmosphere
during extreme space weather events. Further, an investigation of geomagnetic
storms using SABER measurements and TIEGCM simulations found that under the
disturbed condition, about 80% of energy input into the thermosphere is
released back into space through NO 5.3 µm infrared emission (Mlynczak et al.,
2003, 2005; Lu et al., 2010). Thus, the NO species can be a very good
indicator for sensing the changes in the state, structure, and dynamics of MLT
regions during intense geomagnetic storms and particle precipitation events.
Under typical sunlight conditions in the MLT region, the chemical lifetime of
NO is approximately one day. However, during polar winter nights when sunlight
is absent, NO may have a lifetime of several weeks since there is no sunlight
available to initiate photodissociation, and there are no other significant
processes to destroy the NO (Bailey et al., 2022). Due to this prolonged
lifetime in polar regions during the winter nights, NO has sufficient time to
descend into the stratosphere without undergoing photochemical destruction. As
NO descends near the polar region, it is partially converted into nitrogen
dioxide (NO2) and finally reaches into the stratosphere in the form of NO and
NO2, where they react with ozone and destroy it (Pérot et al., 2014; Solomon
et al., 1982).

A significant knowledge about NO and its variability in the MLT region is
based on satellite-based observations. The satellite experiments Solar
Mesosphere Explorer (SME) (Barth et al., 1988) and Halogen Occultation
Experiment (HALOE) (Russell III et al., 1993) have shown that NO in the
thermosphere is highly variable with altitude and time. The observations of NO
volume emission rate (NOVER) by SABER and NO abundance by Student Nitric Oxide
Explorer (SNOE) have found that the radiance and abundance of NO in the
thermosphere are strongly correlated with solar irradiance and geomagnetic
activities (Barth et al., 2003). The emission by NO is highly susceptible to
changes caused by solar and geomagnetic storms and has been reported by
(Bharti et al., 2018, 2019; Tang et al., 2017; Knipp et al., 2017, 2013; Li et
al., 2018, 2019; Mlynczak et al., 2010, 2003, 2005).

Figure 1: Variation of (a) NO Volume Emission Rate, and (b) NO abundance as
measured by SABER and SNOE during quiet and storm time.

Figure 1 (a) shows the variability of NO infrared flux at 5.3 µm between a
quiet and disturbed day as observed by SABER. It can be seen that the infrared
flux is enhanced by an order of magnitude during an intense space weather
event in comparison to a quiet control day. This enhancement in the flux is a
result of a combined rise in temperature, NO density, and its collision
through atomic oxygen, as discussed earlier. The NO abundance measured from
SNOE, as shown in Figure 1(b), also supports the role of intense space weather
events in increased NO production. Thus, the role of NO in balancing the
energetics of the mesosphere-thermosphere is very well established.

Understanding NO variation in the thermosphere becomes a key feature of
knowing the thermospheric temperature structure and energy balance. The
enhancement and transport of nitric oxide is part of the global effect that is
generally set up during intense space weather events in terms of large-scale
traveling ionospheric disturbances from the polar region towards the lower
latitudes. In order to completely understand the space weather modulation of
Earth’s atmosphere, NO can be a key parameter. Continuous and simultaneous
global measurements of infrared flux and abundance can help us comprehensively
understand space weather effects on Earth’s atmosphere. However, due to
various limitations (limited orbital geographic sampling and discontinuous
coverage of specific satellite observations), it becomes difficult, expensive,
or sometimes impossible to achieve simultaneous global coverage, even with the
help of advanced observational devices. The orbit’s limitation on geographic
sampling prevents simultaneous real-time global observations. The scope of our
understanding is only limited to the latitude, longitude, and time sectors
where observations are made. The short-time fluctuations and their effects on
the atmosphere are also not captured due to the limited orbital trajectory of
the satellites. It will be a worthwhile effort to fill this gap by developing
advanced mathematical/computational models that can effectively use the
existing data. The information on NO abundance and its change during a
geomagnetic storm is very important to decipher the chemistry, dynamics, and
transport of the MLT region. There have been very limited direct observations
of NO in recent times. To estimate the abundance of NO, especially during
storm time, various theoretical models have been developed (Emmert et al.,
2022; Marsh et al., 2004; Kiviranta et al., 2018). However, in theoretical
models, the reaction rate coefficients of NO and other constituents have
considerable uncertainties. The reaction rate coefficients for NO in the
thermosphere have been investigated theoretically and experimentally by
(Herron, 1999; Duff et al., 2003), but they could not validate the results
completely. There have been reports of discrepancies with the modeled NO
emission in comparison to the measurements of SABER (Chen and Lei, 2018; Li et
al., 2018; Sheng et al., 2017; Qian et al., 2010).

The complex chemical processes and mutual coupling of parameters affected by
the vertical and meridional transport play an essential role in the NO
emissivity from the upper atmosphere. These complex chemical reactions, along
with the associated uncertainties in constituents, make it challenging to
identify the relative importance of various reactions and subsequent
estimation of reaction rates. In recent years, machine-learning modeling
techniques have become effective tools in atmospheric and space science due to
the availability of large amounts of satellite data volume, powerful computing
techniques, and enhanced data processing machines (Ball and Brunner, 2010;
Abadi et al., 2016; Camporeale et al., 2018). The advanced ML/AI models are
based on the measurement of the data from the last several years and have a
distinct advantage over conventional modeling methods such as theoretical or
photochemical models. These models can utilize the vast data sets of multiple
modes of measurement and build a unified understanding of the processes.
Predictive models have the ability to establish even very weak correlations
between several measured parameters against the independent variables and vice
versa. The advanced machine learning methods exploiting SABER measurements can
provide us with a unique opportunity to estimate and predict the NO infrared
flux variation as a function of latitude, longitude, and time. A continuous
and accurate prediction of enhanced NOIRF in the thermosphere with respect to
latitude, longitude, universal time, and local time during different kinds of
geomagnetic activities will definitely improve our understanding of
thermospheric energy budget, and the associated thermospheric density response
(Chen and Lei, 2018; Sheng et al., 2017).

In this paper, we present a machine learning (ML) approach to understanding
the effect of space weather on thermospheric NO infrared emission and
predicting the NOIRF. As we are heading into the active phase of solar cycle
25, this model can be a very valuable tool for the prediction of space weather
fluctuations and their effect on thermospheric chemistry, dynamics, and
energetics. A combined effect of various modes of thermospheric perturbations
has a strong signature on NOIRF, and targeting the NOIRF via very sensitive
information about the overall correlation of several key variables can be
obtained using a machine learning approach. The SABER instrument dataset
provides the measurements of NO IRF for the past two decades, spanning from
2002 to date. In terms of the solar cycle, the measurements hold the
information on thermospheric variability from the solar cycle 23 (descending
phase) and the complete solar cycle 24. It is very important to note that all
possible effects of solar cycle variations on the earth’s MLT region are
recorded in these measurements. This dataset provides a unique opportunity for
us to explore and see the minute correlations by using machine learning
models. In this study, we have developed a machine learning-based model for
NOIRF primarily based on the SABER dataset.

##  2 Data and Model descriptions

###  2.1 SABER Observations

The dataset of 5.3 µm emission by NO is obtained from the SABER instrument,
which is part of NASA’s TIMED (Thermosphere Ionosphere Mesosphere Energetics
Dynamics) satellite. SABER provides data for NO IR emission at 5.3 µm. It
measures the data in selected sets of wavelengths within the spectral range of
1.27 µm to 17 µm, including 5.3 µm NO emission data. The TIMED satellite was
launched into a 625 km near-circular orbit with an inclination of 74 degrees.
Every 60 days, orbit precession provides 24-hour local time coverage, while
TIMED performs a yaw maneuver to avoid SABER from pointing to the Sun,
resulting in few SABER observations around local noon. The SABER observations
cover the latitudes range from 52°S to 83°N or from 83°S to 52°N depending on
the yaw cycle of the satellite (Russell III et al., 1999). The SABER
instrument has been in operation since 25 January 2002. In this study, the
machine learning-based model utilizes the sixteen years of SABER data from
2002 to 2017 as the primary dataset.

###  2.2 Model Descriptions

This paper presents the implementation of machine learning algorithms to
predict the NOIRF based on earlier observations. The SABER-measured NO volume
emission rate altitude profiles, along with its trajectory, are integrated to
calculate the NOIRF. The machine learning model referred to as the Nitric
Oxide Emission Machine Learning Model (NOEMLM) is constructed for the target
variable NOIRF. The observed values of infrared flux based on current
understanding depend on several global variables such as geographic
coordinates, geomagnetic indices, solar flux, and local time of measurement.
These parameters along the trajectory are obtained from the OMNIWeb datasets
and SABER measurements (Esplin et al., 2023). The selection of various
features of the machine learning algorithm is entirely based on the current
understanding of NO radiative emissions and their variability throughout.
Machine learning techniques have the ability to recognize the subtle
underlying correlation present between features in addition to the correlation
of features with the target variable. The OMNIWeb datasets for the respective
conditions are merged with the SABER dataset.

To include all possibilities of correlations between features and target and
cross-correlations between features, we have exposed the entire SABER-OMNIWeb
dataset corresponding to the observation period of 2002-2014. The selection of
this range of data from 2002 to 2014 is based on that this time period
includes the descending phase of solar cycle 23 and the ascending phase of
solar cycle 24. So, it provides a complete dataset of NOIRF variability during
the solar cycle. This dataset can be considered the training dataset.
Different machine learning algorithms have been implemented on this dataset,
and their performance is evaluated using the ML model output against the
actual observations made by SABER from 2015 to 2017. The period from 2015 to
2017 spans the descending phase of solar cycle-24 (2009-2021), which achieved
its maximum during 2014. This period includes major solar prominences, which
can have a significant impact on the thermosphere radiative cooling like
geomagnetic storms, solar flares, and other extreme space weather events. This
makes the dataset ideal for the evaluation of NOEMLM’s performance. The target
variable (NOIRF) is the integrated NOVER in the altitude range of 115 - 250
km. It is very well established by (Mlynczak et al., 2003; Bharti et al.,
2018) that NO IR emission in this altitude region is highly sensitive to the
space weather modulation, and Figure 1 (a) also shows the very strong
enhancement in NO IR emission during geomagnetically disturbed periods.

Table 1: List of input parameters, their description, unit, and sources. Input parameter | Description | Unit | Source
---|---|---|---
Bz | Z- component of interplanetary magnetic field | nT | OMNIWeb
Dst index | Disturbance storm time index | nT | OMNIWeb
AE index | Auroral electrojet index | nT | OMNIWeb
S spot | Sunspot number |  | OMNIWeb
SZA | Solar zenith angle | Rad | SABER
Kp | Geomagnetic planetary K-index |  | SABER
F10.7 | Solar radio flux at (10.7 cm) | SFU | SABER
Ktemp | Kinetic temperature | K | SABER
Latitude | Latitude | Deg | SABER
Longitude | Longitude | Deg | SABER
NOIRF | NO Infrared Radiative Flux | mW.m-2 | SABER

The complete list of features and their respective sources being used for this
study are listed in Table 1. In all likelihood, the total variability of NOIRF
may also depend on parameters out of this list, such as atmospheric tidal
effects (Nischal et al., 2019; Oberheide et al., 2013).

Figure 2: Correlation of measured NOIRF by SABER with (a) Dst index, (b)
F10.7, and (c) AE-index.

Due to a lack of data, such parameters have been excluded from our list. Some
of the investigated parameters/features mentioned in Table 1 have a
significant correlation with the target parameter (NOIRF) and are the primary
cause of its variation. Among the various features, the Dst index has been
found to be strongly anti-correlated (-0.46) to the NOIRF, and the maximum
correlation is (0.44), which is obtained with the F10.7 flux. The AE index
known to be directly related to the NOIRF in the thermosphere is positively
correlated with a factor of 0.33. The correlation of NOIRF with these
parameters based on the SABER observations (2002-2017) is shown in Figure 2.

##  3 Algorithm and implementation

In the present work, we have used regression algorithms based on supervised
learning, a subset of machine learning and artificial intelligence approach
that can be used for building highly accurate machine learning models (Mahesh,
2020). Based on our tasks and data structure, we used supervised ensemble
machine learning algorithms like Decision Tree, Extreme Gradient Boosting
(XGBoost) (Chen and Guestrin, 2016), and Random Forest (Ho, 1998; Breiman,
2001) to train our model. These three ML models have been used, and their
performance is evaluated based on the actual data. The model with the highest
R-value has been chosen for predictive modeling. The R-value is a statistical
measure that represents the goodness of fit of a regression model. It is also
known as the linear correlation coefficient, which has a value between -1 and
1. A higher R-value represents the more accurate model. R-value equals 1 when
the model perfectly fits the data, and there is no difference between the
predicted and actual values. The Decision Tree algorithm is a supervised non-
parametric learning method that can be used for regression as well as
classification tasks (Pathak et al., 2018). It requires little data
preparation and can handle multi-output problems for both numerical and
categorical data types. It is also possible to validate this method using
statistical tests, which makes the model reliable. The Random Forest (RF)
technique (Ho, 1998; Breiman, 2001) is a combination of several decision
trees. To obtain a minimal variance, RF takes an average of numerous decision
trees. In this study, an RF regressor with 150 decision trees is used for
training the model. The third machine learning algorithm used in this study is
known as XGBoost (Chen and Guestrin, 2016). It is based on decision trees and
is an ensemble method developed to prevent overfitting and for effective
parallel processing. It uses the gradient descent algorithm to minimize the
loss and thus creates a model with good accuracy. Here, we used XGBoost at a
learning rate of 0.3 with 300 estimators and a maximum depth of 15. We apply
these three algorithms to the same training and testing datasets. The
comparison and performance results for the three algorithms with their
R-values are shown in Table 2. The Higher R-value indicates the higher
reliability and accuracy of the respective model.

Table 2: R-value of various ML algorithms for training and test dataset. ML/AI Algorithm | R-value
---|---
| Training | Testing
Decision Tree | 0.99 | 0.93
XGBoost | 0.99 | 0.95
Random Forest | 0.99 | 0.96

All the above-mentioned work has been implemented in Python programming
language (Van Rossum et al., 1995) using Scikit-learn(Pedregosa et al., 2011)
and Keras (Chollet et al., 2015) libraries.

##  4 Model performance:

The objective of the present work is to develop an ML-based model to estimate
and predict the value of NOIRF using the SABER data for a period of 16 years
(2002-2017). For this purpose, we have merged the SABER and OMNIWeb data and
applied various machine learning algorithms, as discussed in section 2. The
entire dataset has been split into two subsets. One subset from 2002-2014 is
used for the model training and testing. The other subset from 2015-2017 is
used to evaluate the performance of the model. It is very important to note
that the second subset of the data is never exposed to the model. This is the
key feature of this study, and this approach helps develop a functional
predictive model with the algorithm chosen with the given efficiency. To train
and test the model we used the main dataset 2002-2014 and split this again
into two subsets known as the training set and testing set. The subsets for
training and testing contain 90% and 10% of data, respectively, from the main
dataset. The subset with 90% data is used for training, and the remaining 10%
subset is used to test the model. The data for training and testing subsets
were selected randomly from the main dataset (2002-2014) without any bias to
the prevalent geophysical conditions. This allows the ML model to develop
finer connections between the features and the target parameter. For all ML
algorithms discussed earlier, the same training dataset has been used so that
the accuracy of the model can be compared on an equal footing. Amongst the
three algorithms, Random Forest produces a better accuracy in terms of
R-value. Hence, this algorithm is further used to develop the model, make
predictions, and compare the predictions with actual measurements. The NOIRF
obtained from SABER measurements against the input features, such as latitude,
longitude, time, etc, is compared with the ML model (NOEMLM) derived IRF for
the same set of features. The correlation between the predicted and the actual
value of log10(NOIRF) for training and testing datasets is shown in Figure 3.

Figure 3: The correlation between NOEMLM predicted and SABER observed NOIRF
for the (a) training and (b) test datasets. The unit of NOIRF is mW.m-2.

The green line in Figure 3 corresponds to the absolute agreement between the
predicted NOIRF by NOEMLM and the measurements of SABER. This line is the
best-fit line, for which we have zero deviation from the true values of NOIRF.
The deviation from the green line measures the difference between the model
prediction vs the actual value of NOIRF. The accuracy of the model for the
training and testing set is presented by the R-value. A higher value of R
means a higher accuracy of prediction. It can be seen from Figures 3(a) and
3(b) that the slope of log10(NOIRF) stands at 0.994 for the training dataset
and 0.957 for the testing dataset. The modeled NOIRF is correlated positively
with a coefficient of 0.988 and 0.918 for the training and testing datasets,
respectively. These coefficients indicate that the ML model is able to
accurately predict 98.8% of the variability in NOIRF within the training
dataset and 91.8% in the testing dataset. The absolute value of the
correlation coefficient indicates the better-performing ability of the ML
model for the given dataset. To quantify the prediction accuracy of the
current ML model, the root mean square error (RMSE) has been calculated for
the predicted NOIRF against SABER observations during 2015-2017. The RMSE is
calculated as follows.

Root Mean Square Error (RMSE) =
$\sqrt{\frac{(\Sigma^{N}_{i=1}(y-y^{\prime})^{2}}{N}}$

Root Mean Square percentage Error (RMSE%) =
$\frac{1}{N}\sqrt{\frac{(\Sigma^{N}_{i=1}(y-y^{\prime})^{2}}{y}}\times 100$

Where, i = variable

y = SABER measured actual values of NOIRF

y’ = NOEMLM predicted value of NOIRF

N = Total number of data points

With respect to the testing dataset, An RMSE of 0.0468 mW.m-2 has been
obtained. The low magnitude of RMSE indicates the better prediction ability of
NOEMLM, which also complements the earlier discussion based on correlation
coefficients. A set of all input features (listed in Table 1) for a single
event in the observational dataset (between 2015 and 2017) is defined as an
Index. The NOIRF measured against this Index by SABER and the NOEMLM
prediction for the same Index is shown in Figure 4.

Figure 4: The NOIRF values predicted by NOEMLM in comparison to the
observations of SABER. The test samples were selected randomly from the
dataset (2015-2017)

It can be seen from the figure that the model predictions match the
observational dataset quite well at all Index values. The daily averaged NOIRF
predicted by the NOEMLM for the observational period of three years
(2015-2017), along with the actual SABER measurements, are shown in Figure 5.

Figure 5: Daily averaged NOIRF as predicted by NOEMLM, in comparison to SABER
observations.

As established from the discussion in the earlier sections, it is evident that
the NOEMLM is able to make finer connections between the target variables and
input features and is also able to weigh in the subtle relations among the
features for the observed fluctuation in NOIRF. The period 2015-2017
corresponds to the descending phase of solar cycle 24, which has witnessed a
few very intense geomagnetic storms. The large-scale geomagnetic fluctuations
affect various input features simultaneously, and hence, it is a challenging
task to estimate the combined effect of these events on the target variable.
It would be a worthwhile effort to test the NOEMLM for the understanding and
estimation of the geomagnetic forcing on the NOIRF. The testing of the ML
model for selected intense space weather fluctuations during the period
2015-2017 is discussed in the sections ahead.

###  4.1 NOIRF prediction during space weather events:

For the purpose of testing the NOEMLM’s prediction ability of NOIRF during
intense space weather events, two severe geomagnetic storms, which occurred
during 22-25 June 2015 (Storm 1) and 7-9 September 2017 (Storm 2), have been
chosen. A geoeffective coronal mass ejection associated with an M-class flare
on the Sun resulted in a moderately severe G4-class geomagnetic storm on 22
June 2015 (Augusto et al., 2018). This geomagnetic storm was the second most
intense storm in the solar cycle 24. The main phase of the storm lasted for
two days, followed by the recovery phase. The impact of CME on the
magnetosphere and subsequent changes in the earth’s magnetic field is
quantified by the Dst index (Gonzalez et al., 1994). It essentially indicates
the decrease in the horizontal component of the earth’s magnetic field during
the time of enhanced ring current result of gradient and curvature drifts of
highly energetic electrons and protons injected in the inner magnetosphere due
to multiple magnetic reconnections into the nightside during geomagnetic
storms. The Auroral Electrojet Index (AE) is a quantitative measure of auroral
zone magnetic activity produced by the enhanced ionospheric currents flowing
within and below the auroral oval (Davis and Sugiura, 1966).

Figure 6: Variation of (a) AE-index, (b) Dst index, (c) SABER observed global
NOIRF, (d) NOEMLM predicted global NOIRF, (e) TIEGCM calculated NOIRF, and (f,
g) time series evolution of NOIRF during Storm 1 (22-25 June 2015).

The variation in Dst and AE-index during Storm 1 (22-25 June 2015) is shown in
Figure 6 (a & b). As the storm time energy enters the Earth’s atmosphere at
the polar latitudes, there is a substantial enhancement in the total NOIRF,
which can be seen from SABER measurements (Figure 6(c)). The enhancement is
centered at the high latitudes and is spread towards the mid and low latitudes
due to the transport of depleted O/N2 by means of strong meridional wind at
high velocities (Zhang et al., 2004). The enhancement in NOIRF persists over
several days during the recovery phase before it reaches normal values towards
25 June 2015. The enhancement in the southern polar region cannot be clearly
seen as the SABER instrument was in the north viewing mode at that time.

In order to evaluate the performance of NOEMLM, it has been implemented to
predict the storm time variation of NOIRF during Storm 1. The predicted NOIRF
for Storm 1 is shown in Figure 6(d). Although the observational period of
2015-2017 is completely new to the NOEMLM, the figure shows that the model
captures the variability of NOIRF with respect to the Dst and AE- index very
well. The penetration of NO cooling emissions during Storm 1 is larger in the
northern hemisphere, as expected due to the background summer to winter wind
in addition to the joule heating induced meridional wind; this wind brings the
nitrogen (N2) and NO abundant air towards lower latitude, which ultimately
results in higher NOIRF in low to mid-latitude of the summer hemisphere in
comparison to the winter hemisphere. It can be seen from Figure 6 (d) that
NOEMLM is able to capture the latitudinal variability of NOIRF for quiet as
well as storm time which can be considered a great achievement for NOEMLM to
be able to predict this effect.

The NOEMLM predictions during Storm 1 are compared with the existing
Thermosphere-Ionosphere- Electrodynamics General Circulation Model (TIEGCM)
shown in Figure 6 (e). By observing Figure 6 (e), it is clearly seen that the
TIEGCM overestimates the NOIRF compared to SABER, and its predictions are far
ahead of the actual measurements. For TIEGCM, an RMSE of 0.522 mW.m-2 is
calculated, which shows a higher deviation from the actual values of NOIRF.
The comparison results show that the NOEMLM predictions have much better
accuracy than the TIEGCM and hence can be considered a better tool for
predicting the space weather fluctuations induced in the radiative cooling
emissions. The time series comparison of NOIRF predictions by NOEMLM and
TIEGCM compared to SABER is shown in Figure 6 (f). For better visualization,
the comparison results of NOEMLM prediction and SABER with the time are shown
in Figure 6 (g).

The NOEMLM effectively captures the variability and the enhancement of NOIRF
very well, but it can also be seen that the model predictions are slightly off
in comparison to the SABER observations in terms of numerical values. To
quantify this, an RMSE of 0.129 mW.m-2 calculated during Storm 1 assures the
reliability of the NOEMLM to predict the storm-time variation of NOIRF. This
low RMSE also suggests that the model can further be used to know the possible
effect of geomagnetic storms on the Earth’s atmosphere in the context of
radiative cooling processes. The differences in measured and predicted values
may be attributed to several factors; the lack of a complete set of dependent
variables against the NOIRF in the measurement dataset could be the major one.
The day/night asymmetry in terms of SABER coverage could also bring some
uncertainty to the agreement. Including these parameters may further enhance
the model’s prediction accuracy.

During the descending phase of solar cycle 24, a coronal mass ejection
associated with an X-9 flare resulted in a G3 class geomagnetic storm on 7
September 2017. The peculiarity of this storm is that the total duration of
the storm is associated with two depletion phases with minimum Dst indices of
-142 and -122 nT. The entire storm duration has two main phases with high
intensity separated by nearly 14 hours (Sun et al., 2022). The variability of
NOIRF during double storms has been observed to be quite different with
respect to a normal geomagnetic storm (Bharti et al., 2018; Ranjan et al.,
2023). Thus, this storm provides a unique case for understanding the NOIRF
variability when there is not sufficient time for the entire atmosphere to
recover from a storm before another intense geomagnetic storm occurs.

Figure 7: Variation of (a) AE-index, (b) Dst index, (c) SABER observed global
NOIRF, (d) NOEMLM predicted global NOIRF, (e) TIEGCM calculated NOIRF, and
(f,g) time series evolution of NOIRF during Storm 2 (7-9 September 2017).

The storm time variation of the AE index and Dst index is shown in Figure 7
(a) and (b), respectively. The SABER retrieved NOIRF obtained using the
procedure explained in earlier sections is shown in Figure 7 (c). The effect
of a double storm on radiative cooling can be clearly seen in Figure 7 (c). It
can be noticed that the enhancement in the NOIRF is more pronounced during the
second main phase (14:00 UT on 8 September 2017) in comparison to the first
main phase (01:00 UT on 8 September 2017), although the first main phase is
more intense in magnitude (Sun et al., 2022). This can be due to the pre-
conditioning of the upper atmosphere by the first main phase. More
importantly, the equatorward spread of enhanced NOIRF can be very clearly
seen. The NOEMLM is used to predict the global variation in the NOIRF during
the entire duration of the double storm. The predicted value of NOIRF is
completely based on the training dataset. It can be seen that the predicted
NOIRF with an RMSE of 0.110 mW.m-2 agrees very closely with the actual SABER
measurements. The basic nature of the fluctuation in NOIRF during the double
storm is successfully captured by the NOEMLM. As it was seen in the
correlation investigation of NOIRF emissions with various solar activity
indices, the NOIRF has a larger negative correlation with Dst (-0.46) and a
positive correlation of 0.33 with the AE index. However, NOEMLM is able to
predict comparatively higher NOIRF during the second phase of Storm 2 (Figure
7 (d)), where the AE index is higher and the Dst index is lower compared to
the first main phase. The same results are also observed by SABER during the
second phase of Storm 2, as seen in Figure 7 (c). The AE index is a proxy of
joule heating during geomagnetic storm (Ahn et al., 1983; Baumjohann and
Kamide, 1984). During the second main phase of Storm 2, the higher AE index
represents the higher amount of joule heating, which results in the higher
NOIRF as observed by SABER and predicted by NOEMLM. This also shows the
accuracy of NOEMLM in effectively capturing and predicting variation in NOIRF
in extreme space weather events and quiet time. The NOEMLM’s predictions
during Storm 2 (7-9 September 2017) were also compared with the existing
chemistry-based model TIEGCM, and comparison results are shown in Figure 7. By
observing Figure 7 (e), it is clearly visible that the TIEGCM predictions
significantly overestimated the actual SABER observations and NOEMLM
predictions. The root mean square error (RMSE) was calculated to quantify the
performance of both models. The calculated RMSE values for NOEMLM and TIEGCM
are 0.110 mW.m-2 and 0.380 mW.m-2, respectively. These results indicate that
NOEMLM demonstrates better capability in predicting NOIRF as compared to
TIEGCM. This also suggests that the machine learning (ML) technique presented
in this paper is much more effective in capturing complex atmospheric dynamics
and processes compared to traditional chemistry-based climatological models.
Figure 7 (f) shows the time-series variation of NOIRF during the entire
duration of the storm. For better visualization of the temporal variation in
NOIRF, the comparison results of NOEMLM prediction with SABER observation are
shown in Figure 7 (g).

However, the RMSE values calculated for both storms represent the all-over
performance of the model at all latitudes during the geomagnetic storms.
During the geomagnetic storm, the higher latitudes show complex behavior
compared to lower, so it would be better to test the ability of NOEMLM to
capture NOIRF variation over higher as well as lower latitudes. To do this, we
consider a range of latitudes listed in Table 3 and test the prediction
accuracy of NOEMLM compared to the SABER observations. To quantify the
performance of NOEMLM at each latitude range, we calculate the error in terms
of RMSE for both storms (Storm 1 and Storm 2) listed in Table 3. It can be
clearly seen from Table 3 that the accuracy of the model prediction varies
with the latitude range. For lower latitudes, the predictions are closer to
the measurements, and for mid to higher latitudes, the accuracy becomes lower.
As it is known, the nature of physical and electrodynamical interactions that
occur over the high latitude thermosphere are highly complex, and there is a
need to identify and include other drivers to achieve better prediction
accuracy.

Table 3: The error in prediction accuracy of NOEMLM in terms of RMSE for various latitude ranges. Latitude (in Degree) | RMSE (in %)
---|---
| Storm 1 | Storm 2
70-83 | 12.60 | 12.45
60-70 | 14.33 | 14.56
50-60 | 13.79 | 12.58
-40 to -50 & 40 to 50 | 17.89 | 13.07
-30 to -40 & 30 to 40 | 12.68 | 12.55
-20 to -30 & 20 to 30 | 09.14 | 09.40
-10 to -20 & 10 to 20 | 06.98 | 07.12
-10 to 10 | 07.59 | 06.11

The time series variation from Figures 6 (g) & 7 (g) shows that the NOEMLM has
a good agreement to capture the variation with time and the progression of the
storm. The predicted value of NOIRF by NOEMLM corresponds to the same time for
each value observed by SABER. To test the ability of NOEMLM to capture the
temporal variation of NOIRF during the initial, main, and recovery phases of
geomagnetic storms, we consider Storm 2. The recovery phase of Storm 1 is more
than ten days, and it overlaps with other geomagnetic activity during its
recovery phase. Due to this, Storm 1 could not recover completely and could
not achieve its pre-storm value of NOIRF. However, in the case of Storm 2,
having a time period of nearly three days, it recovered within this window of
three days and achieved its pre-storm value of NOIRF about 0.158 mW.m-2 (less
than 0.2 mW.m-2, shown by horizontal line) after 42.66 hours as marked by
vertical line nearly 62.66 UT in Figure 7 (g). The predicted value of NOIRF at
the same time by NOEMLM is 0.186 mW.m-2, and the TIEGCM estimated value is
0.504 mW.m-2. It can be concluded that the NOEMLM predicted value is closer to
the actual measurement of SABER. The findings indicate that the NOEMLM
demonstrates good latitudinal and temporal predictive capability for NOIRF
during various geophysical conditions.

##  5 Discussion and Summary

This research examines how space weather primarily affects the Earth’s upper
atmosphere in terms of radiative cooling by NO. The variation of NO during
space weather events has been attempted in many earlier studies. The observed
variation of several chemical species and their overall effect on radiative
cooling is mentioned in the introduction. The central objective of this study
is to develop a working machine-learning model that can capture the
climatological observations of NOIRF by SABER and produce good accuracy in
predicting the fluctuations. This study, however, does not delve into the
chemistry and physics of a specific species. Instead, it describes the
behavior of the upper atmosphere during quiet and storm times based on the
NOIRF as an indicator of higher solar electron and proton precipitation in the
upper atmosphere of Earth. In this study, random forest machine learning
algorithms are used to develop a predictive model for the NOIRF. The choice of
algorithm is based on the model’s performance on the test dataset. The model
is trained with thirteen years of SABER observations of NOIRF in the altitude
range of 115-250 km of Earth’s atmosphere. The satellite data is successfully
merged with other magnetic indices and solar proxies, which are representative
of the various geophysical conditions prevalent during the observation period
of SABER. The objective of the model is to successfully predict the
variability of NOIRF with respect to latitude, longitude, and time during
various space weather events and also with respect to the progression of the
solar cycle. The NOIRF can be considered an essential tracer to understand the
energetics and structure of the upper atmosphere, mainly the thermosphere
during space weather fluctuations. The NOEMLM tested with actual measurements
and is able to capture 91.8% accurate variations in NOIRF for the testing
dataset. This indicates that the NOEMLM has successfully been able to capture
the very nature of fluctuations in NOIRF with respect to several other
independent variables. The model once validated with good R-values has been
further used to predict NOIRF during intense geomagnetic storms which occurred
in the years 2015 and 2017. The global predicted NOIRF is compared with the
actual measurements, and it has been found that the model demonstrates very
good prediction accuracy. A few very important connections between space
weather and radiative flux are very well represented in the model output. The
model performed very well during extreme space weather events, specifically
Storm 1 and Storm 2. For both geomagnetic storms, the NOIRF pattern and upper
atmospheric dynamics were very well captured by the NOEMLM with the time and
latitudes.

For both measured and predicted NOIRF, the intensity is found to have an
inverse relationship with the Dst index, while the latitudinal penetration
strongly correlates with the AE index during geomagnetic storms. This
demonstrates that Dst and AE indices are useful parameters for understanding
atmospheric behavior during such events, and the model successfully accounts
for their effects on the upper atmosphere of Earth. The model indicates that
for higher AE indices, there is greater penetration towards lower latitudes,
which can be explained by the general physics of the AE index, whereby
stronger AE indices generate stronger currents in the ionosphere that interact
with the Earth’s magnetic field at lower latitudes. During geomagnetic storms,
the density, temperature, and composition of the thermosphere undergo rapid
and non-uniform changes, leading to variable densities and temperature
distributions. This may be the major cause for the overestimation of NOIRF by
TIEGCM. These changes are primarily caused by solar radiation, magnetic
fields, and particle precipitation. To proxy these changes in NOEMLM, the
F10.7, Dst, and AE indices have been used to estimate changes in temperature,
density, and chemical composition. The learning algorithm calculates the
correlation factor for each input using training data and is optimized to
estimate the NOIRF based on these controlling factors (Dst, AE, F10.7, etc.).
A small deviation in the predicted value of NOIRF by NOEMLM could be due to
the absence of concurrent measurements of real-time data for various
controlling factors (AE, Dst, etc.), which were considered uniform for a
small-time range due to lack of real-time data. This could be a significant
reason for the deviation of predicted values compared with the SABER,
especially during the geomagnetic storm. Additionally, day/night asymmetry in
SABER coverage may also contribute to uncertainty in the agreement.

However, in comparison to the existing TIEGCM model, NOEMLM has excellent
performance, especially during storm time, when the behavior of the atmosphere
became very complex. From Figure 6 (d, e) & 7 (d, e) it is clear that the
predictions of TIEGCM are much higher than the actual measurements. The
findings of this study suggest that utilizing geomagnetic and space weather
indices can serve as superior parameters for studying the upper atmosphere, as
compared to focusing on specific species having complex chemical processes and
associated uncertainties in constituents. Additionally, machine learning
techniques can effectively carry out this analysis with greater ease than
traditional chemical studies. This study presents a working machine learning
model which can be used as an effective tool in predicting space weather
influence on the thermosphere. This work also establishes the ML methodology
as an effective tool for understanding the complex and dynamic behavior of
Earth’s atmosphere when the chemistry of the atmosphere changes dramatically.

##  6 Acknowledgments

We acknowledge the SABER, OMNIWeb, SNOE, and Community Coordinated Modeling
Center (CCMC) for providing all necessary data for developing this NOIRF
model. The OMNIWeb data is available at
https://omniweb.gsfc.nasa.gov/form/dx1.html, and SABER data is available at:
http://saber.gats-inc.com/data.php. The SNOE data can be accessed from
https://lasp.colorado.edu/snoe/data/download-data/. The TIEGCM simulation
results have been provided by CCMC at Goddard Space Flight Center through
their publicly available simulation services https://ccmc.gsfc.nasa.gov. One
of the authors D.Nailwal thanks the Ministry of Human Resource Development
(MHRD), Government of India for financial support as a graduate assistantship.

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