Nitric Oxide Concentration: A New Data Set Derived From SABER Measurements

Abstract

Vertical profiles of nitric oxide (NO) concentration are derived between 120 and 250 km using updated NO emission rates measured by Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument on the NASA Thermosphere Ionosphere Mesosphere Energetics and Dynamics satellite. The Naval Research Laboratory Mass Spectrometer Incoherent Scatter Radar (MSIS) 2.1 model is used to provide the required parameters of temperature, atomic oxygen number density, and molecule oxygen number density needed to derive the NO concentrations using a non-local thermodynamic equilibrium (non-LTE) model. The SABER NO concentration shows a significant correlation with solar activity with larger peak NO concentrations and higher altitude extent during solar maximum years compared to those during the solar minimum years. The SABER NO agrees well with the MSIS 2.1 NO at altitudes above 120 km for all latitudes, while the pronounced SABER-MSIS NO discrepancy below 120 km is likely due to the temperature underestimation by MSIS 2.1. A detailed error analysis is presented and considers systematic and random errors in all the terms in the non-LTE model used to derive the NO concentration. Random error in MSIS 2.1 temperature and atomic oxygen dominates the uncertainty in single NO profiles above 120 km. We estimated a systematic error up to ∼36% between 120 and 250 km during solar maximum years.

Introduction

Nitric oxide (NO) is a minor constituent of the Earth's thermosphere and plays a crucial role in regulating the energy budget and facilitating the radiative cooling process at altitudes above 115 km (Kockarts, 1980; Mlynczak et al., 2003, 2005, 2007, 2021; Roble, 1995). The production, transport, and loss of NO depend on the solar radiation intensity, the global circulation, and the temperature of the upper atmosphere (Harvey et al., 2021; Hendrickx et al., 2015, 2018; Siskind et al., 1989, 1990, 1995, 2019).

The NO infrared cooling in the 5.3 μm band regulates the upper atmosphere thermal structure and energy balance (Mlynczak et al., 2003, 2005). NO emissions, as a “natural thermosphere thermostat,” exhibit significant variations on both short timescales (geomagnetic storms and solar eclipses) (Lu et al., 2010; Mlynczak et al., 2003; Wang, Yu, et al., 2022) and long timescales (11-year solar cycle) (Knipp et al., 2017; Mlynczak et al., 2014), and dominates thermospheric radiative cooling processes, particularly above 125 km. While there are extensive studies focused on the NO infrared cooling responses to geomagnetic storms (e.g., Bharti et al., 2018; Dobbin et al., 2006; Knipp et al., 2013, 2017; Lei et al., 2011, 2012; Li et al., 2019; Lu et al., 2010; Mlynczak et al., 2003, 2005; Sheng et al., 2017; Zhang et al., 2014) using both numerical simulations and SABER observations, there have been fewer investigations into the behavior of NO concentration on both short and long timescales, due to limited data availability.

There are several available NO concentration data sets, including the Atmospheric Chemistry Experiment, the Halogen Occultation Experiment, the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS), the Sub-Millimeter Radiometer, the Student Nitric Oxide Explorer, and the Solar Occultation For Ice Experiment. However, studies on NO have been typically limited to specific time periods, locations, altitude ranges, and geophysical conditions, due to the temporal and spatial constraints of these data sets. As a result, trend and climatology analyses of NO concentration are lacking. Additionally, the lack of long-term continuous NO concentration data limits the range of empirical model determinations.

The Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument is on board the NASA Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite and has provided more than 20 years of continuous global monitoring of the upper atmosphere, including measurement of temperature, volume mixing ratios of CO₂, ozone, and water vapor, and infrared radiative cooling rates (from CO₂ and NO). These measurements have been used to investigate the Mesosphere and lower Thermosphere (MLT) temperature responses to different types of geomagnetic storms (Wang et al., 2021), climatology of MLT residual circulations (Wang, Qian, et al., 2022), and long term variability in the infrared radiative cooling (Mlynczak et al., 2010). The NO concentration is related to the NO emission rate, but due to the lack of simultaneous measurements of temperature (T), and atomic oxygen (O) and molecular oxygen (O₂) number densities above 110 km, it cannot be directly derived from the NO infrared emission rate from the SABER 5.3 μm measurements alone. In this work, MSIS 2.1 empirical model estimates of temperature and, O and O₂ number densities at each SABER scan/event will be used together with SABER NO emission rate measurements and a non-local thermodynamic equilibrium (non-LTE) model of NO vibrational populations to derive the first global, long-term (two solar cycle) data set of thermospheric NO concentration with full local time coverage.

The paper is organized as follows: the SABER NO emission data and its recent updates, and MSIS 2.0/2.1 are described in Section 2; the NO concentration retrieval method is discussed in Section 3; the uncertainty analysis of the derived NO concentration is discussed in Section 4; and the results of the SABER NO concentration and comparison with MSIS are presented in Section 5, followed by a brief summary in Section 6.

Data and Models SABER NO Emission Rates

The SABER instrument is on board the NASA TIMED satellite and has been taking measurements since January 2002, with a vertical resolution of approximately 2 km (Esplin et al., 2023; Russell et al., 1999). The latitude coverage of the SABER instrument shifts between 83°N–53°S and 53°N–83°S, due to a ∼60-day yaw cycle of the TIMED satellite.

The SABER instrument scans the Earth's limb vertically from approximately 400 km down to the hard Earth's surface and measures radiance (W/m²/sr) in 10 broadband channels between 1.27 and 17 μm. The NO channel, #6, is centered near 5.255 μm, covering approximately from 1,862 to 1,944 cm⁻¹, including nearly 60%, 48%, and 15% of the band strengths of the NO fundamental (1–0) band, 2 to 1 band, and 3 to 2 band, respectively (Mlynczak et al., 2003, 2021). The SABER radiance measurements are converted to energetics parameters by applying the Abel transform (Mlynczak et al., 2005, 2021). The resulting data product is a vertical profile of energy loss per unit volume/emission rate, I(z), where z is altitude, weighted by the SABER spectral response function (SSRF) of the NO channel. The units are W/m³ and the emission rate profiles generally extend from 100 to 250 km. This is an “in-band” emission rate representing the NO emission that falls within the spectral limits of the bandpass filter. A correction/unfilter factor U(z) is applied to this measured in-band emission rate to yield an estimate, V(z), (which is equivalent to I(z) × U(z)), of the total band emission rate of NO. This factor is the ratio of computed emission from the 3 → 2, 2 → 1, and 1 → 0 bands unweighted by the SSRF to the emission of those bands weighted by the SSRF. We note that the measured emission is typically dominated by the fundamental 1 → 0 band (Mlynczak et al., 2005).

The currently available SABER NO cooling data v2.0 uses a single, global mean unfilter factor (U(z)) for all SABER vertical profiles, because Mlynczak et al. (2005) found it does not vary substantially for different geophysical conditions. In this work, however, we update the unfilter factor for four different conditions. Further, we use an unfilter factor $${U}^{\ast }(z)$$ which considers only the fundamental band, that is, the ratio of the 1 → 0 fundamental band radiance unweighted by the SSRF to the total emission for the 3 → 2, 2 → 1, and 1 → 0 bands weighted by the SSRF. This is nevertheless very accurate since, as shown in Figure 2 of Mlynczak et al. (2021), the NO cooling caused by the first and second bands is less than 0.5% of that caused by the fundamental band during solar maximum conditions, and less than 0.1% during solar minimum conditions. However, Eckermann (2023) has shown that the first hot band (i.e., the 2 → 1) transition may increase the NO cooling by up to 10%–15% during solar maximum conditions based on rate coefficients computed by Caridade et al. (2018). As noted by Mlynczak et al. (2021), these quasi-classical trajectory calculations have not yet been verified by laboratory measurements. Therefore, we do not consider the 2 → 1 cooling process here in the derivation of the NO concentrations. We strongly urge a contemporary laboratory measurement to update the magnitude and temperature dependence of the quenching of vibrationally excited NO by atomic oxygen over the range of thermospheric temperatures. A detailed description of the calculation of the unfilter factor can be found in Mlynczak et al. (2005). The non-LTE populations of the NO levels required to compute the unfilter factor were calculated using the Generic RAdiative traNsfer AnD non-LTE population Algorithm model (Funke et al., 2012).

Figure 1 shows the vertical profile of the unfilter factor used in the SABER v2.0 data, and the updated global annual average unfilter factors for solar maximum day, solar maximum night, solar minimum day, and solar minimum night from 100 to 200 km. The unfilter factor above 200 km is set constant, taking the value at 200 km. The new factors are generally smaller than the original one, and they vary from solar maximum to solar minimum, but their day-to-day variation (not shown) is insignificant compared to the solar cycle variation which is typically less than 10% over the 100–200 km altitude range. Thus any uncertainty on a daily basis is minimal. The unfilter factors shown in Figure 1 for solar minimum and solar maximum conditions correspond to 2009 and 2014, respectively, and are used as the unfilter factors for 2020 and 2003, respectively. Then the unfilter factors are linearly interpolated between the solar maximum years and the solar minimum years. With that, the annual average unfilter factors as a function of altitude between 100 and 250 km, at 1 km intervals, are computed from 2002 to 2022. Although the new unfilter factors at night are within ∼5% of the daytime values, we use the day and night unfilter factors respectively in deriving the new SABER NO emission rate. The new unfilter factors are of great importance as they not only lead to new radiative cooling values, which reflect a more realistic solar cycle dependence, but also allow the derivation of more accurate NO concentrations, especially above 150 km, where space-based NO measurements are lacking (Marsh et al., 2004).

Figure 1. Vertical profile of unfilter factors between 100 and 200 km. The original unfilter factor used in the currently available Sounding of the Atmosphere using Broadband Emission Radiometry v 2.0 data is shown as black solid line. The updated global annual averaged unfilter factors for the solar maximum year 2014 and solar minimum year 2009 are shown as red lines and blue lines, respectively. The solid-colored lines represent the daytime unfilter factors and the dashed-colored lines are the nighttime unfilter factors.

With the new unfilter factors, we compute the new full band SABER NO emission rate. Figure 2a shows the comparison of the global annual average SABER v2.0 NO emission rate and new NO emission rate for the solar maximum year 2014 and the solar minimum year 2009. The black dashed line denotes the noise equivalent NO emission rate as 5.8 × 10⁻¹¹ W/m³ which is derived from the measured noise equivalent radiance of 1.48 × 10⁻⁶ W/m²/sr (Esplin et al., 2023). The newly derived SABER NO emission rate is smaller than the original NO emission rate for both the solar maximum year and solar minimum year as expected, because the new unfilter factor is smaller than the original one as shown in Figure 1. The ratio between the newly derived NO emission rate and the SABER v2.0 NO emission rate is shown in Figure 2b. The ratio decreases with altitude below 110 km for both 2009 and 2014, then it increases with altitude, peaking at 130 km in 2009 and 140 km in 2014. Above 130 km in 2009 and 140 km in 2014, the ratio decreases with altitude again, while above 195 km, the ratio increases with altitude for both 2009 and 2014. Figure 2b also indicates that the difference between the new and the v2.0 versions is generally (above ∼110 km) larger in 2009 (the solar minimum year) than in 2014 (the solar maximum year), and the difference has changed with altitude.

Figure 2. (a) The global annual average of the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) v2.0 nitric oxide (NO) cooling rate (dashed lines) and the new NO cooling rate (solid lines) for solar maximum year 2014 (blue) and solar minimum year 2009 (red). The black dashed line marks the equivalent noise level of the NO emission rate. (b) The ratio of the newly derived SABER NO cooling rate to SABER v2.0 NO cooling rate.

MSIS 2.1

The Naval Research Laboratory (NRL) Mass Spectrometer Incoherent Scatter Radar (NRLMSIS, herein shortened to MSIS) is an empirical atmospheric model covering altitudes from the ground to the exobase. MSIS version 2.1 (Emmert et al., 2022) is an update to MSIS 2.0 (Emmert et al., 2021); the only change is the addition of NO number density at altitudes from ∼73 km to the exobase (Emmert et al., 2022). The MSIS 2.1 NO density is based on the six data sets listed in Table 1 of Emmert et al. (2022), covering altitudes between 70 and 200 km. MSIS 2.1 utilizes parametric analytic formulation to describe the average observed behavior of temperature and several species' densities and mass density, including atomic oxygen (O), molecular oxygen (O₂), molecular nitrogen (N₂), and NO. The model inputs are longitude, latitude, altitude, day of the year, time of the day, solar activity, and geomagnetic activity (Emmert et al., 2021). The resulting MSIS 2.1 estimates of temperature, O density, and O₂ density are used here to derive the SABER NO concentration. Further, the MSIS 2.1 NO density is used for initial data comparison with the SABER NO derived here. In this work, MSIS 2.1 is evaluated at the SABER measurement times and locations between 100 and 250 km at 1 km steps, from which approximately 10 million vertical profiles of NO concentration are obtained, covering the years 2002 to the present.

Method

The ground state NO concentration (molecules/cm³) for the 20+ years of the SABER record, which is identical to within 1% of the total NO concentration, is derived directly from the new SABER NO 1 → 0 emission rate profiles V(z) (where z is altitude) and the MSIS 2.1 estimates of temperature and of the number densities of atomic and molecular oxygen. Although NO has approximately 28 vibrational levels below its dissociation limit, the radiative emission from NO is primarily from the fundamental vibration-rotation band centered at 5.3 μm(1,887 cm⁻¹) (Mlynczak et al., 2021). Thus, in this work, we only consider the first (υ = 1) and the ground (υ = 0) vibrational levels of NO.

As show in Figure 1 of Mlynczak et al. (2021), the relative population of the NO at energy level 1 n(NO_ν=1) to the ground state n(NO_ν=0) is given by: [Image Omitted. See PDF]where C₀₁ and C₁₀ are the rates of collisional quenching and excitation, and $${\boldsymbol{C}}_{\mathbf{10}}={\boldsymbol{k}}_{\mathbf{O}}\boldsymbol{n}(\mathbf{O})+{\boldsymbol{k}}_{{\mathbf{O}}_{\mathbf{2}}}\boldsymbol{n}\left({\mathbf{O}}_{\mathbf{2}}\right)$$, $${\boldsymbol{C}}_{\mathbf{01}}={\boldsymbol{C}}_{\mathbf{10}}\times \mathbf{exp}\,\left(-\frac{\boldsymbol{h}{\boldsymbol{\nu }}_{\mathbf{0}}}{{\boldsymbol{k}}_{\boldsymbol{B}}{\boldsymbol{T}}_{\boldsymbol{N}}}\right)$$, respectively. n(O) and n(O₂) are number densities of O, O₂, respectively; k_O is set to 4.2 × 10⁻¹¹ cm³ s⁻¹ (Hwang et al., 2003) which is the vibrational relaxation rate of NO(ν = 1) by collisions with O; $${\boldsymbol{k}}_{{\mathbf{O}}_{\mathbf{2}}}$$ is set to 2.4 × 10⁻¹⁴ cm³ s⁻¹ (Murphy et al., 1975), which stands for the vibrational relaxation rate of NO(ν = 1) by collisions with O₂; h is Planck's constant; ν₀ = 1,887 cm⁻¹; k_B is Boltzmann's constant, and T_N is neutral temperature. A₁₀ is the Einstein coefficient for spontaneous emission, representing the transition probability of NO(ν = 1) → NO(ν = 0) + hν_5.3μm, which is approximately 12.85 s⁻¹; R₀₁ is the rate of radiative (solar and terrestrial) excitation. The emission rate V(z) is given by n(NO_ν=1) × A₁₀, then the NO concentration at each altitude z is described as: [Image Omitted. See PDF]

From Mlynczak et al. (2021), it is established that, due to the minimal absorption by NO between 100 km and the tropopause, the source of earthshine excitation of NO is in the troposphere where clouds or absorption by water vapor form an infrared-opaque lower boundary. Thus, the earthshine radiative excitation term can be derived by assuming a blackbody at an appropriate tropospheric temperature. The rate of radiative excitation can be described as: [Image Omitted. See PDF]where S, the 5.3 μm NO fundamental band strength, is 4.6 × 10⁻¹⁸ cm⁻¹/(molecules × cm⁻²) (Mlynczak et al., 2021); T_trop is the appropriate temperature in the troposphere; and J_sun is the solar excitation rate. We estimate the altitude and temperature of this lower boundary using the earthshine excitation rates computed from upwelling infrared radiance measured in the 5.3 μm region by the Infrared Atmospheric Sounding Interferometer (IASI) (Hilton et al., 2012) instrument as reported in Mlynczak et al. (2021). Specifically, we start from the temperature between 4 and 9 km obtained from MSIS 2.1 at the location and time of each SABER observation. Subsequently, the earthshine excitation rates are computed for the temperature between 4 and 9 km according to the first term on the right-hand side of Equation 3 for 15 January and 15 March of 2016. We selected those two particular dates to align with the analysis of Mlynczak et al. (2021). Given that these dates correspond to the solstice and equinox, respectively, the data coverage suffices for deriving the excitation rates. Next, we compute the daily zonal mean of the earthshine excitation rate within the 5° latitude band between 82.5°S and 82.5°N as a function of altitude from 4 to 9 km. The computed daily zonal averaged earthshine excitation rate is compared to the IASI measurement for both 15 January and 15 March 2016, respectively, at each latitude band, to obtain the altitude index, for example, the altitude where the computed earthshine excitation rates match the IASI measurements. The altitude index as a function of latitude is obtained for both 15 January 2016 and 15 March 2016. The former, which represents the index around the solstice, will be used for January, February, June, July, August, and December; and the latter, which stands for the index around the equinox, will be used for March, April, May, September, October, and November for the years from 2002 to 2022. With the identified altitude indices and the MSIS 2.1 temperatures, the earthshine excitation rate at each SABER observation location is determined.

The solar zenith angle is used to distinguish day from night at the SABER observation location. For the SABER observation with a solar zenith angle larger than ∼90°, which is the local night time, the solar excitation rate J_sun is 0, and the radiative excitation rate R₀₁ equals to the earthshine excitation rate. For the SABER observation with a solar zenith angle smaller than 90, which is the local daytime, the solar excitation rate J_sun is 1.09 × 10⁻⁴ s⁻¹ (Mlynczak et al., 2021). The radiative excitation rate R₀₁ is the earthshine excitation rate plus the solar excitation rate.

Figure 3 depicts the process for deriving the NO concentration from the SABER NO emission rate and the MSIS 2.1 parameters. Version 2.0 of the SABER data (including the NO emission rates and the location information e.g., longitude, latitude, altitude, and solar zenith angle of each scan/event) is used in this work. The SABER in-band NO emission rates I(z) are linearly interpolated between 100 and 250 km at 1 km intervals and then multiplied by the updated unfilter factor $${U}^{\ast }(z)$$ to derive the full-band NO emission rate V(z). The SABER location information together with the solar and geomagnetic indices corresponding to the time of the SABER observations are used as inputs to MSIS 2.1 to obtain the temperature, and atomic oxygen and molecular oxygen number densities for each SABER scan between 100 and 250 km. MSIS 2.1 also provides the temperature between 4 and 9 km at each SABER scan to compute the corresponding radiative excitation rate R₀₁. With the full-band NO emission rate, the MSIS 2.1 estimates of temperature, O density, and O₂ density, and the earthshine and solar excitation rate, the NO concentration is derived according to Equation 2.

Figure 3. Road map of deriving the nitric oxide (NO) concentration from the SABER NO emission rate and MSIS 2.1 simulations.

Assessment of Uncertainty in Derived Nitric Oxide

In the region between 110 and 115 km, the collisional and radiative excitation rates of NO are comparable, with the radiative excitation dominating below ∼105 km and the collisional excitation dominating above ∼120 km, as shown in Figures 13 and 14 of Mlynczak et al. (2021). Below 120 km, the collisional excitation is temperature- (highly non-linearly) dependent, because of the low temperatures and the size of the temperature uncertainties, while above 120 km, the uncertainty in temperature is much smaller, reducing the non-linearity (Mlynczak et al., 2021). Thus, the uncertainties are discussed separately for these two regions.

The error terms in the derived SABER NO concentration according to Equation 2 are listed in Table 1. The first 9 items are related to systematic errors and the last three items are random errors. The uncertainty in the NO concentration is assessed by perturbing the parameters listed in Table 1 by the specified amounts (column 4 of Table 1) and then examining the change in the NO concentration from the baseline, unperturbed state. The parameters are assumed to be uncorrelated so that the total uncertainty in NO due to the uncertainty in all parameters is obtained by computing the root-sum-square (RSS) of all of the individual changes in the NO.

Table 1 Error Items in the SABER NO Concentration Derivation

Symbol	Description	Error type	Uncertainty
A10	Einstein coefficient	Systematic error	2%
kO	Vibrational relaxation rate of NO(ν = 1) by collisions with O	Systematic error	17%
kO2	Vibrational relaxation rate of NO(ν = 1) by collisions with O2	Systematic error	60%
R01	Rate of radiative excitation	Systematic error	25%
U	Unfilter factor	Systematic error	3%
Vsys	Bias of the SABER NO 1 → 0 emission rate	Systematic error	3%
n(O)sys	Bias of the atomic oxygen number density simulated by MSIS 2.1	Systematic error	10%
n(O2)sys	Bias of the molecular oxygen number density simulated by MSIS 2.1	Systematic error	10%
Tsys	Bias of the temperature simulated by MSIS 2.1	Systematic error	100–120 km linearly from 5 to 30 Ka
			30 K at 120–250 km
Trnd	Standard deviation of the temperature simulated by MSIS 2.1	Random error	Linearly from 15 K at 100 km to 50 K at 250 km
n(O)rnd	Standard deviation of the atomic oxygen number density simulated by MSIS 2.1	Random error	Linearly from 50% at 100 km to 15% at 250 km
Vrnd	Standard deviation of the SABER NO 1 → 0 emission rate	Random error	5.8e−11 W/m3

^aSee the discussion in Section 4.3.

Uncertainties in MSIS 2.1 Temperature, O Density, and O₂ Density

The estimated systematic uncertainty of the MSIS 2.1 temperature predictions near 100 km is ∼5 K, based on the spread of mean data-minus-MSIS residuals from various data sets (Emmert et al., 2021, Figure 5d, Data Set S2). However, this uncertainty increases to ∼30 K at 120 km (Emmert et al., 2021, Figure 16c). At higher altitudes the MSIS 2.1 temperature is approximately the same as NRLMSISE-00; typical residual biases are similarly ∼30 K (Picone et al., 2002, see Table S2c). We, therefore, adopt a systematic uncertainty profile that linearly increases from 5 K at 100 km to 30 K at 120 km and is a constant 30 K at higher altitudes. Similarly, we estimate the random uncertainty of MSIS 2.1 predictions to be ∼15 K at 100 km (Emmert et al., 2021, Data Set S2) and ∼50 K at 250 km (Picone et al., 2002, Table S2c), based on the standard deviation of data-minus-model residuals, and we linearly interpolate between those two values.

For the MSIS 2.1 O density, we adopt a systematic uncertainty of ∼10% at 100 km, based on SABER and OSIRIS bias with respect to MSIS 2.0 (Emmert et al., 2021, Figure 10b, Data Set S3). At 250 km, we assume the same value of 10%, based on accelerometer and orbit-derived mass density error (Emmert et al., 2021, Figures 19j and 19k, Data Sets S5 and S6). We further assume that this uncertainty is uniform with height between 100 and 250 km. We estimate the random error of MSIS 2.1 O predictions to be ∼50% at 100 km and ∼15% at 250 km, based on residual standard deviations given in Emmert et al. (2021, Data Sets S3, S6); we linearly interpolate between the values at the two altitudes. For the MSIS 2.1 O₂ density, we arbitrarily assume a systematic uncertainty of 10%.

Uncertainties in NO Above 120 km

Figure 4 shows some examples of the daytime SABER NO concentration and their errors, together with their corresponding MSIS 2.1 NO data. The vertical profiles of the SABER and MSIS 2.1 NO concentrations are shown in Figures 4a–4c; the horizontal bar represents the total error of the SABER NO by computing the RSS of all the error terms listed in Table 1. In Figures 4d–4f, the total error, systematic error, and random error as a function of altitude are shown in black, red, and blue, respectively, and the values of the individual error terms listed in Table 1 are shown in Figures 4g–4i. Note that some of the errors are overlapped as they are very similar. The detailed error terms are provided in Tables 2–4, where the first column is the altitude; the second to the tenth columns show the uncertainties caused by the systematic errors and the eleventh to the thirteenth columns list the uncertainties caused by the random errors; and the last four columns show the accuracy (total uncertainty) of a single event, 10 events, 20 events, and infinite events (the uncertainty without random error).

Figure 4. Single vertical profile of (a–c) the daytime Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) derived nitric oxide (NO) concentration, with horizontal bars representing the total error of the SABER NO concentration, (d–f) Systematic error (red), random error (blue), and total error (black) for this SABER NO concentration, and (h, i) the Error terms listed in Table 1, at 8°, 49°, and 76°N on 4 March 2014 from 120 to 200 km, respectively.

Table 2 Estimated Uncertainty of the Day Time NO Concentration From 120 to 200 km at 8°N on 4 March 2014 Derived From the SABER Observation

	Systematic error									Random error			Accuracy
ALT	A	KO	KO2	R01	U	NO VER	n(O)	n(O2)	T	T	n(O)	NO VER	RSS1	RSS10	RSS20	RSS systematic error
km	2%	17%	60%	25%	3%	3%	10%	10%	5 K/30 K	15 K/50 K	50%/15%	5.80E−11	1 event	10 events	20 events	No random error
120	−0.4	−10.4	0.0	−2.2	3.0	3.0	−6.5	0.0	−36.7	−26.3	−22.8	2.2	52.3	40.5	39.8	39.0
125	−0.3	−11.8	0.0	−1.0	3.0	3.0	−7.4	0.0	−28.3	−20.9	−25.1	1.2	45.6	33.5	32.7	31.8
130	−0.2	−12.5	0.0	−0.7	3.0	3.0	−7.8	0.0	−22.7	−17.4	−26.0	0.8	41.5	29.1	28.2	27.4
135	−0.2	−12.9	0.0	−0.5	3.0	3.0	−8.1	0.0	−18.8	−15.0	−26.3	0.5	39.0	26.3	25.5	24.6
140	−0.1	−13.2	0.0	−0.4	3.0	3.0	−8.2	0.0	−16.0	−13.3	−26.3	0.5	37.2	24.6	23.7	22.7
145	−0.1	−13.4	0.0	−0.4	3.0	3.0	−8.4	0.0	−14.0	−12.1	−26.2	0.4	36.0	23.4	22.5	21.5
150	−0.1	−13.6	0.0	−0.4	3.0	3.0	−8.5	0.0	−12.5	−11.2	−25.9	0.5	35.0	22.6	21.7	20.7
155	−0.1	−13.7	0.0	−0.4	3.0	3.0	−8.6	0.0	−11.3	−10.5	−25.6	0.6	34.2	21.9	21.1	20.1
160	−0.1	−13.8	0.0	−0.4	3.0	3.0	−8.6	0.0	−10.3	−10.0	−25.1	0.6	33.5	21.5	20.6	19.7
165	−0.1	−13.8	0.0	−0.4	3.0	3.0	−8.7	0.0	−9.6	−9.6	−24.7	0.8	32.8	21.1	20.3	19.4
170	−0.1	−13.9	0.0	−0.4	3.0	3.0	−8.7	0.0	−8.9	−9.3	−24.1	0.9	32.2	20.8	20.0	19.1
175	−0.1	−13.9	0.0	−0.4	3.0	3.0	−8.7	0.0	−8.4	−9.1	−23.6	1.1	31.6	20.6	19.8	19.0
180	0.0	−14.0	0.0	−0.4	3.0	3.0	−8.7	0.0	−8.0	−8.9	−23.0	1.3	31.0	20.4	19.6	18.8
185	0.0	−14.0	0.0	−0.4	3.0	3.0	−8.8	0.0	−7.6	−8.8	−22.4	2.2	30.5	20.2	19.4	18.7
190	0.0	−14.0	0.0	−0.5	3.0	3.0	−8.8	0.0	−7.3	−8.7	−21.7	2.4	30.0	20.0	19.3	18.6
195	0.0	−14.0	0.0	−0.5	3.0	3.0	−8.8	0.0	−7.0	−8.6	−21.1	1.8	29.4	19.8	19.2	18.5
200	0.0	−14.0	0.0	−0.5	3.0	3.0	−8.8	0.0	−6.8	−8.5	−20.4	2.8	28.9	19.7	19.1	18.4

Table 3 Estimated Uncertainty of the Day Time NO Concentration From 120 to 200 km at 49°N on 4 March 2014 Derived From the SABER Observation

	Systematic error									Random error			Accuracy
ALT	A	KO	KO2	R01	U	NO VER	n(O)	n(O2)	T	T	n(O)	NO VER	RSS1	RSS10	RSS20	RSS systematic error
km	2%	17%	60%	25%	3%	3%	10%	10%	5 K/30 K	15 K/50 K	50%/15%	5.80E−11	1 event	10 events	20 events	No random error
120	−0.4	−10.5	0.0	−1.8	3.0	3.0	−6.6	0.0	−38.5	−27.8	−22.9	1.6	54.4	42.3	41.5	40.7
125	−0.3	−11.9	0.0	−0.8	3.0	3.0	−7.4	0.0	−29.5	−21.9	−25.1	0.7	46.9	34.6	33.8	33.0
130	−0.2	−12.5	0.0	−0.5	3.0	3.0	−7.8	0.0	−23.5	−18.1	−26.0	0.6	42.4	29.9	29.0	28.1
135	−0.2	−12.9	0.0	−0.4	3.0	3.0	−8.1	0.0	−19.5	−15.6	−26.3	0.6	39.6	26.9	26.0	25.1
140	−0.2	−13.2	0.0	−0.3	3.0	3.0	−8.3	0.0	−16.6	−13.8	−26.4	0.5	37.8	25.0	24.1	23.2
145	−0.1	−13.4	0.0	−0.3	3.0	3.0	−8.4	0.0	−14.5	−12.6	−26.2	0.5	36.4	23.8	22.9	21.9
150	−0.1	−13.6	0.0	−0.3	3.0	3.0	−8.5	0.0	−13.0	−11.7	−26.0	0.6	35.4	22.9	22.0	21.1
155	−0.1	−13.7	0.0	−0.3	3.0	3.0	−8.6	0.0	−11.8	−11.0	−25.6	0.8	34.6	22.3	21.4	20.4
160	−0.1	−13.8	0.0	−0.3	3.0	3.0	−8.6	0.0	−10.8	−10.5	−25.2	0.8	33.8	21.8	20.9	20.0
165	−0.1	−13.9	0.0	−0.3	3.0	3.0	−8.7	0.0	−10.0	−10.1	−24.7	1.0	33.2	21.4	20.6	19.7
170	−0.1	−13.9	0.0	−0.3	3.0	3.0	−8.7	0.0	−9.4	−9.8	−24.2	1.1	32.6	21.1	20.3	19.4
175	−0.1	−14.0	0.0	−0.3	3.0	3.0	−8.7	0.0	−8.9	−9.6	−23.6	1.4	32.0	20.8	20.0	19.2
180	0.0	−14.0	0.0	−0.3	3.0	3.0	−8.8	0.0	−8.5	−9.4	−23.1	1.8	31.4	20.6	19.9	19.1
185	0.0	−14.1	0.0	−0.3	3.0	3.0	−8.8	0.0	−8.1	−9.3	−22.4	1.9	30.9	20.4	19.7	18.9
190	0.0	−14.1	0.0	−0.4	3.0	3.0	−8.8	0.0	−7.8	−9.2	−21.8	1.9	30.3	20.3	19.6	18.8
195	0.0	−14.1	0.0	−0.4	3.0	3.0	−8.8	0.0	−7.5	−9.2	−21.1	2.4	29.8	20.1	19.4	18.7
200	0.0	−14.1	0.0	−0.4	3.0	3.0	−8.8	0.0	−7.3	−9.2	−20.5	2.8	29.3	20.0	19.3	18.7

Table 4 Estimated Uncertainty of the Day Time NO Concentration From 120 to 200 km at 76°N on 4 March 2014 Derived From the SABER Observation

	Systematic error									Random error			Accuracy
ALT	A	KO	KO2	R01	U	NO VER	n(O)	n(O2)	T	T	n(O)	NO VER	RSS1	RSS10	RSS20	RSS systematic error
km	2%	17%	60%	25%	3%	3%	10%	10%	5 K/30 K	15 K/50 K	50%/15%	5.80E−11	1 event	10 events	20 events	No random error
120	−0.4	−10.5	0.0	−2.2	3.0	3.0	−6.6	0.0	−40.0	−29.0	−23.0	1.1	56.1	43.8	43.0	42.2
125	−0.3	−12.0	0.0	−0.9	3.0	3.0	−7.5	0.0	−30.6	−22.7	−25.4	0.7	48.2	35.6	34.8	34.0
130	−0.2	−12.7	0.0	−0.6	3.0	3.0	−7.9	0.0	−24.2	−18.6	−26.3	1.0	43.2	30.5	29.7	28.8
135	−0.2	−13.1	0.0	−0.4	3.0	3.0	−8.2	0.0	−19.9	−15.9	−26.6	1.1	40.2	27.4	26.5	25.6
140	−0.1	−13.4	0.0	−0.4	3.0	3.0	−8.4	0.0	−17.0	−14.1	−26.6	1.3	38.3	25.4	24.5	23.5
145	−0.1	−13.5	0.0	−0.3	3.0	3.0	−8.5	0.0	−14.8	−12.8	−26.4	1.4	36.9	24.1	23.2	22.2
150	−0.1	−13.7	0.0	−0.3	3.0	3.0	−8.6	0.0	−13.3	−11.9	−26.1	1.5	35.8	23.2	22.3	21.3
155	−0.1	−13.8	0.0	−0.3	3.0	3.0	−8.6	0.0	−12.0	−11.2	−25.8	3.0	35.0	22.5	21.6	20.7
160	−0.1	−13.9	0.0	−0.3	3.0	3.0	−8.7	0.0	−11.1	−10.8	−25.3	3.2	34.3	22.0	21.1	20.2
165	−0.1	−13.9	0.0	−0.3	3.0	3.0	−8.7	0.0	−10.3	−10.4	−24.8	2.1	33.5	21.6	20.8	19.9
170	−0.1	−14.0	0.0	−0.3	3.0	3.0	−8.7	0.0	−9.7	−10.1	−24.3	2.3	32.9	21.3	20.5	19.6
175	0.0	−14.0	0.0	−0.3	3.0	3.0	−8.8	0.0	−9.2	−9.9	−23.7	2.3	32.3	21.1	20.2	19.4
180	0.0	−14.1	0.0	−0.3	3.0	3.0	−8.8	0.0	−8.8	−9.8	−23.1	2.8	31.8	20.8	20.1	19.2
185	0.0	−14.1	0.0	−0.4	3.0	3.0	−8.8	0.0	−8.5	−9.7	−22.5	3.8	31.3	20.7	19.9	19.1
190	0.0	−14.1	0.0	−0.4	3.0	3.0	−8.8	0.0	−8.2	−9.7	−21.8	14.7	33.9	21.0	20.0	19.0
195	0.0	−14.1	0.0	−0.4	3.0	3.0	−8.8	0.0	−7.9	−9.6	−21.2	4.3	30.3	20.3	19.6	18.9
200	0.0	−14.1	0.0	−0.4	3.0	3.0	−8.8	0.0	−7.7	−9.6	−20.5	14.2	32.7	20.6	19.7	18.8

At 49°N, SABER NO is larger than the MSIS 2.1 NO above 120 km, while at 76°N, the SABER NO is larger than MSIS 2.1 NO above ∼170 km but smaller than the MSIS 2.1 from 120 to 170 km. At 8°N, SABER NO is close to MSIS 2.1 NO above ∼140 km, while is smaller than MSIS 2.1 NO between 120 and 140 km. Overall, the SABER NO agrees well with MSIS 2.1 NO above 120 km, as the difference between SABER NO and MSIS 2.1 NO is smaller than the total uncertainty of the SABER NO. The SABER NO errors (both the systematic and random errors) decrease with increasing altitude from 120 to 200 km. The errors caused by both the temperature systematic uncertainty and random uncertainty decrease with the increasing altitude. The NO concentration depends non-linearly on the temperature due to the exponential term in Equation 2, so that the error in NO due to the temperature increases exponentially with the increasing altitude. For example, at middle latitude (see Figure 4e), the systematic error decreases from 40% at 120 km to 19% at 200 km, and below ∼150 km, the systematic uncertainty in the temperature is the major contributor to the total systematic error while above 150 km the error caused by the k_O uncertainty is dominated. The systematic uncertainty in the n(O) is the third large contributor of the total systematic error varying from 6.5% at 120 km to 8.8% at 200 km. Thus, a more accurate temperature determination together with the n(O) and k_O could improve the systematic accuracy of the SABER NO concentration. The random error quasi-linearly decreases from 35% at 120 km to 24% at 200 km, as shown in Figure 4e. The decrease of the total random error is due to the decrease of the random uncertainty of temperature. The random uncertainty in the temperature and n(O) dominate the random error at altitudes below ∼170 km.

The uncertainty (random and systematic) arising from the MSIS temperature estimate can result in an uncertainty of up to 46% (in NO concentration), while the uncertainty stemming from the MSIS atomic oxygen density uncertainty (both random and systematic) can lead to an uncertainty of up to 27% (in NO concentration). Additionally, the uncertainty in NO due to measurement noise can be substantial at very low and at very high altitudes. In both cases the SABER NO emission rate is close to its equivalent noise level as shown in Figure 2, thus, the perturbation in the NO emission rate will cause a huge variation in the derived NO concentration for a single profile. At altitudes between 120 and 200 km, the NO uncertainty related to radiometric noise in the measured NO emission rate is as small as 0.5%.

Averaging NO concentrations from different events will not alter the systematic error but will decrease the random error. For instance, at 130 km, the total uncertainty for a single event at 49°N is 42%. However, the uncertainty decreases to 30% for an average of 10 events/profiles and to 29% for an average of 20 events/profiles. The last column (of each table) shows the uncertainty without the random error, which is 28% at 130 km, indicating the minimum uncertainty of the SABER NO concentration. Furthermore, the uncertainty caused by the systematic error is ∼1% less than the total uncertainty of the average of 20 events. Hence, the random error of a mean profile calculation is reduced by using a greater number of measurements. For example, using an average of 20 events, which will reduce the random error by a factor of 4.5, would provide better accuracy in the SABER NO results than can be obtained from a single profile alone.

Uncertainty results for years with different solar activity (2009, a solar minimum year, and 2016, a moderate solar activity year) and local times (day and night) can be found in Supporting Information S1. For instance, at middle latitudes during the daytime, the systematic uncertainty does not change much (only up to 3%) across different solar conditions. The uncertainty is slightly larger during the solar quiet condition in 2009 while it is relatively smaller during the solar active condition in 2014. Since the absolute systematic error of the MSIS 2.1 temperature is identical across different solar conditions but the temperature is higher during the solar maximum, the contribution of the T systematic error to the NO absolute systematic error is smaller during the solar maximum conditions. The random uncertainty in the SABER NO emission rate has a strong solar cycle dependence, with smaller values during a solar active year. The SABER NO emission rate during the solar maximum year is significantly greater than the equivalent noise level of 5.8 × 10⁻¹¹ W/m³, as shown in Figure 2a, compared to the NO emission rate during the solar minimum year. Consequently, perturbing the NO emission rate by the same noise value leads to a more substantial variation during the solar minimum year than during the solar maximum year.

Uncertainties in NO From 100 to 120 km

In the altitudes between 100 and 120 km, the NO concentration is highly variable with large uncertainties as shown in Figure 5 which is similar to Figure 4, but for the altitude from 100 to 120 km. The difference between SABER NO and MSIS 2.1 NO is larger at both high latitudes and equatorial regions, where SABER NO is up to a factor of 3–5 larger than the MSIS 2.1 NO and the MSIS 2.1 NO is well outside of the SABER NO error bars.

Figure 5. Same as Figure 4 for the altitude from 100 to 120 km.

At altitudes below ∼110 km, the collisional excitation is small relative to radiative excitation, thus the NO concentration depends on the solar and earthshine rates. Consequently, the uncertainty of the R₀₁ up to 20% dominates the systematic error. As the altitude increases, the collisional excitation becomes comparable to radiative excitation between 110 and 115 km and dominates over it above 115 km due to the rapid increase of neutral kinetic temperature. At this altitude, the uncertainties in the temperature (both systematic and random) are significant. Moreover, the collisional excitation rate is highly non-linearly dependent on the temperature between 110 and 120 km because of the low temperatures and the size of the temperature uncertainties. Thus, the derived NO concentration is highly uncertain in this region. For example, at ∼115 km, with the temperature of 270 K, a ∼20 K change in temperature will result in up to a factor of 2 change in the NO concentration.

Furthermore, the recent MIPAS-MSIS comparison indicates that the MSIS 2.1 temperature is up to 80 K colder at ∼115 km (Funke et al., 2023) than the MIPAS v8 results. The large discrepancy between SABER NO and MSIS 2.1 NO can readily be explained if MSIS 2.1 temperatures are up to 80 K colder than actual atmospheric temperatures. As shown in the second column of Figure 20 in Funke et al. (2023), the MIPAS-MSIS temperature difference is up to 80 K in the equator and high-latitude regions, while the difference is smaller in the middle-latitude region which is up to ∼50 K at 115 km. A similar discrepancy in temperature between MSIS 2.1 and the Michelson Interferometer for Global High-Resolution Thermospheric Imaging (MIGHTI) is reported by Stevens et al. (2022). These temperature differences also can explain the SABER-MSIS NO concentration difference as shown in Figure 5: The SABER-MSIS NO difference is larger at high-latitudes than that at mid-latitudes. At ∼115 km the global average temperature for March 2014 is ∼387 K; a 30 K (the uncertainty of the MSIS 2.1 T applied in this work) increase in temperature would cause a factor of ∼1.6 decrease (i.e., −38%) in the derived NO concentration according to Equation 2, while an 80 K increase in temperature would result in a factor of ∼3.3 decrease (−70%) in NO concentration. Substantially warmer MSIS 2.1 temperatures would significantly reduce the large discrepancy that currently exists between SABER and MSIS 2.1 NO below 120 km. Furthermore, Figure 5c shows that the MSIS 2.1 NO is well outside of the errors of the SABER NO profile, suggesting that the uncertainty in MSIS 2.1 temperature is likely underestimated below 120 km. Assuming that the systematic uncertainty of the MSIS 2.1 temperature is 80 K in this altitude region, we re-calculated SABER NO total uncertainties as shown in Figure 6. With larger temperature uncertainty, the SABER NO total uncertainty becomes larger and the MSIS 2.1 NO falls within the SABER NO error bars.

Figure 6. Single vertical profile of the daytime Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) derived nitric oxide (NO) concentration (red) and the Mass Spectrometer Incoherent Scatter Radar (MSIS) 2.1 NO (black) at (a) 8°N, (b) 49°N, and (c) 76°N, respectively. The horizontal bars are the new total error of the SABER NO concentration with 80 K systematic uncertainty in MSIS 2.1 Temperature.

Given the potentially large uncertainty in the MSIS 2.1 temperature determinations in this region, it is very challenging to retrieve accurate NO concentrations from SABER NO emission rates. Conversely, much more accurate temperature measurements are required and these would be a critical component of closing the “thermospheric gap” (Jones et al., 2022; Oberheide et al., 2011). Due to the large SABER NO uncertainty and the discrepancy with the MSIS 2.1 NO between 100 and 120 km, the SABER NO data below 120 km will not be publicly available in the current version.

Results and Discussions SABER NO Concentration

Figure 7 illustrates the yearly distribution of the global annual averaged SABER NO concentration from 2003 to 2020 between 120 and 250 km. The NO concentration decreases with increasing altitude. The result indicates a significant dependence on solar activity. At 120 km, the NO concentration is ∼10⁸ molecules/cm³ during the solar maximum years (e.g., 2003, 2014), and ∼3.5 × 10⁷ molecules/cm³ during the solar minimum years (e.g., 2009, 2020). Moreover, the uppermost altitude of the NO concentration retrieved here depends on the solar activity, being higher (up to ∼275 km) during solar active years and lower (230 km) during solar minimum years. The lower altitude limit of the SABER NO concentration during the solar quiet period is due to the lower signal-to-noise (S/N) ratio associated with lower NO concentrations at that time.

Figure 7. Contours of the global annual mean nitric oxide (NO) concentration derived from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) measurements for the years 2003–2020, in the altitude between 120 and 250 km. Each pixel color represents the NO concentration in the logarithm scale.

Figure 8 shows the monthly latitudinal distribution of the NO concentration during equinoxes (Figures 8a and 8c) and solstices (Figures 8b and 8d) for 2009. The NO concentration varies with latitude and is larger at high latitudes. During March and September equinoxes, the NO concentration behaviors are similar for both northern and southern polar areas with the NO concentration being over 3.5 × 10⁷ molecules/cm³. There is also a local maximum NO concentration at 120 km in the equatorial region with the NO concentration up to 2 × 10⁷ molecules/cm³. The decreasing of the NO concentration with altitude is larger at high latitudes than at low latitudes. Note that the full latitudinal coverage (80°S–80°N) in Figures 8a and 8c is due to a yaw maneuver of the TIMED spacecraft in the middle of the time period observed in March and September 2009. During June and December solstices, the NO concentration is up to a factor of ∼3 greater in the summer hemisphere (northern hemisphere in June and southern hemisphere in December) than in the winter hemisphere. The larger NO concentration at high latitudes summer hemisphere is due to both chemical and dynamical processes, as demonstrated by Funke et al. (2023, Figure 13). During the summer solstice, the prolonged exposure to the sunlight increases the production of the NO (Barth, 1992), and the winter-to-summer lower thermospheric and the summer-to-winter thermospheric circulations can result in a larger NO concentration. In the upper thermosphere, higher summer temperatures produce a more expanded column, leading to higher density at a given altitude.

Figure 8. Monthly zonal average of nitric oxide (NO) concentration for 2009 (a) March, (b) June, (c) September, and (d) December. Each pixel color represents the NO concentration in the logarithm scale.

In 2014 as shown in Figure 9, the NO concentration distribution is similar to that in 2009, except that the magnitude of the NO concentration in 2014 is up to a factor of 3 larger. During equinoxes, the NO concentration in 2014 at ∼125 km has also a peak in the equatorial region, which is over 10⁸ molecules/cm³, a factor of 5 larger than that in 2009. A similar feature has been found in MIPAS data but at ∼100 km (Funke et al., 2023). The latitudinal distribution of the NO concentration varies from the equinox to the solstice, indicating the change in the photochemical process from the equinox to the solstice. During the winter polar night (poleward of 60° for both January and July, not shown), the SABER NO and MSIS 2.1 NO have a better agreement in 2014 than in 2009. The SABER NO during polar winter night matches the observation by Bailey et al. (2022) in magnitude, but at higher altitudes.

Figure 9. Monthly zonal average of nitric oxide (NO) concentration for 2014 (a) March, (b) June, (c) September, and (d) December. Each pixel color represents the NO concentration in the logarithm scale.

As the thermostat of the Earth's upper atmosphere (Mlynczak et al., 2005), the NO emission, which linearly depends on the NO concentration, is sensitive to variations in the energy budget of the Earth's atmosphere. During geomagnetic storms, energetic particles precipitate into the Earth's upper atmosphere from the solar wind and perturb the atmosphere, leading to NO concentration fluctuations (Barth, 2010; Siskind et al., 1989). Recent work revealed that the MLT temperature measured by SABER responds to both coronal mass ejections (CMEs) and corotating interaction regions (CIRs) events (Wang et al., 2021). The NO concentration in the upper atmosphere is anticipated to exhibit analogous behavior as the MLT temperature during these two different types of geomagnetic activities. The NO cooling responses to the CME and CIR events have been investigated using both measurements and model simulations (Verkhoglyadova et al., 2016, 2017). However, few studies have examined the NO concentration variation during transient solar events. In this work, we investigate the SABER NO concentration behavior during two single geomagnetic storms, the 17 March 2015 CME storm, and the 31 March 2007 CIR storm.

The vertical profile of high-latitude (poleward of 60°) NO concentration as a function of time from 15 March to 27 March 2015 is shown in Figure 10a. The NO concentration is enhanced at all altitudes between 120 and 250 km. Specifically, at ∼125 km, the NO concentration rose to ∼10⁸ from ∼3.5 × 10⁸ molecules/cm³ on 17 March 2015 and then returned to its pre-storm state on 21 March. The storm effect is strong and lasted around 4 days at altitudes below ∼130 km. The length of the storm time NO concentration enhancement decreases with increasing altitude. At 180 km, the storm effect lasts ∼2 days as the “7” contour line returns to its pre-storm altitude on 19 March.

Figure 10. High latitudes (poleward of 60°) vertical profiles of the Sounding of the Atmosphere using Broadband Emission Radiometry derived nitric oxide (NO) concentration as a function of time during the (a) coronal mass ejection (CME) storm on 17 March 2015 and (b) corotating interaction region (CIR) storm on 31 March 2007. Each pixel color represents the NO concentration in the logarithm scale.

The storm time NO concentration change during the 31 March 2007 CIR storm is shown in Figure 10b. The behavior of the NO concentration is comparable to that of the 17 March 2015 storm, but with a smaller enhancement in NO concentration and a more prolonged duration of the enhancement. During the 31 March 2007 storm, the NO concentration at 120 km increased from 3.5 × 10⁷ to 10⁸ molecules/cm³ on 31 March and did not resume to its pre-storm state until 8 April 2007. The storm-induced NO enhancement lasts ∼8 days. Similar to the 17 March 2015 CME storm, the CIR storm-induced NO enhancement duration decreases with increasing altitude, but occurs from 120 to ∼210 km, which is lower than the height extent of the CME storm response. As CME storms are more intense but of shorter duration than CIR storms, the energy deposited into the Earth's atmosphere is strong but brief during the CME events. As the NO is related to the energy budget in the Earth's upper atmosphere, the NO concentration enhancement is larger with a shorter duration during the CME storms compared to that during CIR storms. The storm time NO concentration variation matches the MLT temperature variations discussed in (Wang et al., 2021). Moreover, since the NO concentration is quasi-linearly related to the NO cooling (Wang, Yu, et al., 2022), understanding the storm-time NO concentration behavior can provide insight into the NO cooling variation during geomagnetic storms.

Data and Model Comparison

The MSIS 2.1 NO number density is based on six NO data sets listed in Table 1 of Emmert et al. (2022), and is possibly coupled to the MSIS 2.1 temperature at high altitudes where MSIS 2.1 NO scale height is controlled by the MSIS 2.1 temperature. Although the derived SABER NO concentration depends on the MSIS 2.1 values of temperature, atomic oxygen, and molecule oxygen, and to a lesser extent on the various rate coefficients used in the non-LTE modeling, the derived SABER NO concentration is independent of the MSIS 2.1 NO estimations. Thus, the SABER-MSIS comparison is effectively a comparison of SABER NO with the best estimation of NO from six currently available satellite measurement data sets.

Figure 11 shows the monthly zonal average of SABER and MSIS 2.1 NO vertical profiles (left column) and the SABER NO to MSIS 2.1 NO ratio (right column) in March for both 2009 (blue) and 2014 (red) at low, middle, and high latitudes, respectively. The SABER NO agrees well with the MSIS 2.1 NO for all three latitude regions. The SABER to MSIS 2.1 ratio ranges from 0.7 to 2, and SABER NO matches MSIS 2.1 NO better at equatorial regions above ∼125 km during the solar minimum year than during the solar maximum year. At middle to high latitudes, SABER NO agrees better with MSIS 2.1 NO during the solar minimum year 2009 than during the solar maximum year 2014 between 130 and 160 km. This alignment reverses above 160 km and below 125 km.

Figure 11. Vertical profiles of the monthly zonal average in March for Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) and Mass Spectrometer Incoherent Scatter Radar (MSIS) 2.1 nitric oxide (NO) (left column) and the corresponding SABER to MSIS 2.1 ratio (right column), at (a, b) equator, (c, d) middle latitudes, and (e, f) high latitudes, respectively. In each panel on the left, the solid lines represent the SABER NO vertical profiles, and the dashed lines represent the MSIS 2.1 NO vertical profiles, respectively. In each panel, the blue line(s) is/are for the results of 2009 and the red line(s) is/are for the results of 2014, respectively.

Figures 12–15 show the monthly and yearly latitudinal distribution of the SABER NO and MSIS 2.1 NO during the solar minimum and the solar maximum years, and the SABER NO to MSIS 2.1 NO ratio, respectively. The SABER NO agrees well with the MSIS 2.1 NO for all latitudes in the altitudes between ∼130 and 180 km; both data sets indicate greater NO concentration at high latitudes than at middle-to-low latitudes. The NO concentration is nearly constant at the middle-to-low latitude region as the NO contour lines are horizontal for both SABER and MSIS 2.1 NO. Further, the vertical gradient is larger in the MSIS 2.1 NO than in the SABER NO above ∼150 km. Daily average comparisons are shown in Figures 16 and 17. Again, SABER NO agrees well with MSIS 2.1 NO between ∼130 and 180 km. The SABER-MSIS difference is smaller during solar maximum conditions than during solar minimum. Although the SABER and MSIS 2.1 NO do not match in magnitude below 130 km and above 180 km, their day-to-day variations agree with each other during both 2009 and 2014. During geomagnetically active periods, such as 13–16 March 2009 and 20–29 March 2009, the SABER to MSIS 2.1 ratio below 130 km becomes larger (up to 2.5) indicating a large difference between SABER NO and MSIS 2.1 NO in this region. As the SABER NO is derived from the MSIS 2.1 T and O, the SABER-MSIS NO difference suggests that MSIS 2.1 O and T may be inaccurate in these regions.

Figure 12. Latitudinal distributions of the (a) Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) and (b) Mass Spectrometer Incoherent Scatter Radar (MSIS) 2.1 monthly mean nitric oxide (NO) concentration in March 2009. Each pixel color represents the NO concentration in the logarithm scale ranging from 5 to 8. (c) The SABER NO to MSIS 2.1 NO ratio. The pixel color represents the ratio ranging from 0 to 3.

Figure 13. Same as Figure 12, but for March 2014.

Figure 14. Latitudinal distributions of the (a) Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) and (b) Mass Spectrometer Incoherent Scatter Radar (MSIS) 2.1 annual mean nitric oxide (NO) concentration in 2009. Each pixel color represents the NO concentration in the logarithm scale ranging from 5 to 8. (c) The SABER NO to MSIS 2.1 NO ratio. The pixel color represents the ratio ranging from 0 to 3.

Figure 15. Same as Figure 14, but for 2014.

Figure 16. Daily global average of (a) Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) and (b) Mass Spectrometer Incoherent Scatter Radar (MSIS) 2.1 nitric oxide (NO) concentration in March 2009. Each pixel color represents the NO concentration in the logarithm scale ranging from 5 to 8. (c) The SABER NO to MSIS NO ratio with pixel color representing the ratio ranging from 0 to 3.

Figure 17. Same as Figure 16, but for 2014.

Despite some differences between SABER NO and MSIS 2.1 NO, they are in good agreement with respect to monthly, yearly, and daily variations above 130 km. As an empirical model, the MSIS 2.1 NO estimation is computed by assimilating several data sets. Thus, the accuracy and coverage of the assimilated data can affect the estimated results. As shown in Table 1 of Emmert et al. (2022), the number of data sets used in MSIS 2.1 decreases with altitude, and only MIPAS data (with 10 km vertical resolution) is considered in MSIS 2.1 above 150 km. Since SABER measurements have different data coverage and span, as well as different systematic errors, the data-model differences are as expected. Further comparisons of the SABER NO to the individual data sets assimilated into MSIS, and to a physical model such as WACCM-X, will be conducted in future work.

Summary

Nitric oxide concentration profiles between 120 and 250 km are derived from updated NO emission rate measurements made by the SABER instrument on the TIMED satellite, using temperature and number densities of atomic oxygen and molecular oxygen provided by the MSIS 2.1 model.

The updated SABER NO emission rates are derived by using updated “unfilter” factors for different solar activity conditions, and different local times (day or night). With the updated SABER NO emission rate, the NO concentration data from 2002 until the present are derived. The global annual average NO concentration shows a strong correlation with the solar cycle with the NO peak concentration as large as 10⁸ molecules/cm³, while during solar minimum the global annual average peak concentration is ∼3. 5 × 10⁷ molecules/cm³. SABER measures NO emission up to higher altitudes during solar maximum than during solar minimum.

The uncertainty analysis shows that the SABER NO concentration systematic uncertainty is 33%–36% above 120 km and largely independent of location, local time, and solar activity. Above 120 km, the most significant contributors to the total uncertainty are the uncertainties in the vibrational relaxation rate of NO(ν = 1) by collisions with O, k_O, and MSIS 2.1 estimations of O density and temperature. Radiometric calibration of SABER has a minor impact on the total uncertainty. A more accurate temperature is important to understand NO distribution derived from infrared emission measurements and to provide further enhancements of empirical models such as MSIS. The random error resulting from radiance noise is smaller in percentage during solar maximum when the signal is larger, while errors resulting from the MSIS 2.1 estimates of n(O) and T do not vary significantly under different conditions. Random errors can be rapidly reduced through averaging to zonal or global means on daily or longer time scales.

The SABER NO concentration is enhanced during both the 17 March 2015 CME and the 31 March 2007 CIR geomagnetic storms. The storm time NO concentration behavior is similar to the temperature variation in the MLT region. The NO concentration enhancement is more pronounced but shorter-lived during the CME event compared to the CIR event.

The SABER NO concentration shows a good relative agreement with the MSIS 2.1 NO, but is ∼50%–100% larger than the MSIS 2.1 NO below 130 km and above 180 km in the monthly and annual zonal averages for both 2009 and 2014. The vertical gradient is larger in MSIS 2.1 data than in SABER NO above ∼150 km. Moreover, the discrepancy of NO zonal average between SABER and MSIS increases with solar activity between 130 and 180 km, while the discrepancy decreases with the solar activity below 130 km and above 180 km. The NO daily average SABER-MSIS differences are smaller during the solar maximum year than during the solar minimum year. More comparisons of SABER NO to physics-based numerical simulations are needed and will be done in future work.

The significant SABER-MSIS NO discrepancy in the lower thermosphere is likely due to the temperature underestimation in this region, as both MIPAS-MSIS (Funke et al., 2023) and MIGHTI-MSIS (Stevens et al., 2022) comparisons indicate a warmer lower thermospheric compared to the MSIS 2.1 estimation. These discrepancies highlight the critical need for accurate new temperature and composition measurements to help fill the 100–200 km thermospheric observation gap.

The SABER NO concentration data set spans ∼22 years with over 10 million individual vertical profiles of NO concentration. The SABER NO data set will eventually be assimilated into MSIS to potentially improve the accuracy of the model's estimation of the NO number density. The data are available on the SABER project website at the https://saber.gats-inc.com/data.php listed in the Data Availability Statement below.

Acknowledgments

This work is supported by NASA Postdoctoral Program fellowship, NASA TIMED/SABER missions, NASA HGIO Grant 21-HGIO_2-0040. Research was sponsored by the National Aeronautics and Space Administration (NASA) through a contract with ORAU. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the National Aeronautics and Space Administration (NASA) or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. The IAA team acknowledges financial support from the Agencia Estatal de Investigación, MCIN/AEI/10.13039/501100011033, through Grants PID2022-141216NB-I00 and CEX2021-001131-S.

Data Availability Statement

Version 2.0 of the SABER data used in this work is downloaded from https://data.gats-inc.com/saber/Version2_0/. The updated unfilter SABER NO cooling rate data, SABER NO concentration data, and MSIS 2.1 NO shown in the paper are available at https://data.gats-inc.com/saber/Version2_0/SABER_NO/.