Improvement of SAMI2 with Comprehensive Photochemistry at Mid-Latitudes and a Preliminary Comparison with Ionosonde Data

Abstract

Photochemistry can significantly affect the ionospheric status. Adopting a comprehensive photochemical scheme with 60 reactions, primarily based on the recent systematic study of ion chemistry by Richards in 2011, we revised the open-source SAMI2 (Sami2 is another model of the ionosphere) model to SAMI2₋ph. The scheme includes both ground state and metastable/vibrational excited compositions (e.g., N(²D), N₂(ν), and O₂(ν)) and associated reactions, which can remarkably affect the ionospheric electron density. The model accuracy is tested using the most widely used ionospheric data foF2 derived from mid-latitude ionosonde stations. The correlation coefficients are larger for SAMI2₋ph than for SAMI2. In addition, the linear slope k is significantly closer to 1 than the default run for the NmF2 comparisons. The smaller RMSE and b indicate that the modified model provides a reasonably good match with the ionosonde NmF2 measurements. The above results demonstrate that the model with the chosen photochemical scheme performs better than the original SAMI2 at mid-latitude.

1. Introduction

Physical models of the ionosphere have played an important role in interpreting observations, understanding the causes of its behavior, and forecasting its status. Many of these models use empirical models to specify neutral atmosphere densities and temperatures, neutral winds, and E × B drift velocities, such as the field line interhemispheric plasma (FLIP) model of Alabama University [1,2], the time-dependent ionospheric model (TDIM) of Utah State University [3], Sheffield University’s plasmasphere–ionosphere model (SUPIM) from the U.K. [4], the global theoretical ionospheric model (GTIM) of Phillips Laboratory [5], the SAMI2 model of the U.S. Navy Research Lab (NRL) [6], the theoretical model of the Earth’s low- and mid-latitude ionosphere and plasmasphere of IZMIRAN [7], and the theoretical ionospheric model of the Earth from the Institute of Geology and Geophysics, Chinese Academy of Sciences (TIME-IGGCAS) [8].

There are also theoretical models that solve the neutral atmosphere equations to determine the neutral atmosphere compositions and dynamics, and self-consistently couple this solution to ionospheric dynamics, such as the global model of the thermosphere–ionosphere–protonsphere system [9], the coupled thermosphere/ionosphere general circulation model (TIGCM) [10], the coupled thermosphere–ionosphere–plasmasphere (CTIP) model [11], and the global ionosphere–thermosphere model (GITM) [12].

Most of the existing models have evolved over many years and each has its advantages. The 2D SAMI2 model includes the ion inertial terms in the ion momentum equations and has been superseded by the SAMI3 model, which is a three-dimensional model of the ionosphere–plasmasphere system [13,14,15,16]. The updated FLIP model uses a flux-preserving method and provides total flexibility in setting up the ionosphere–plasmasphere spatial grid [17]. The CTIP model has evolved into the coupled thermosphere–ionosphere–plasmasphere electrodynamics (CTIPe) model [18]. The ionosphere and plasmasphere part of CTIPe has evolved into the ionosphere–plasmasphere electrodynamics (IPE) model [19]. The TIGCM model has been substituted by the thermosphere–ionosphere–mesosphere electrodynamic general circulation model (TIME-GCM) [20].

In spite of significant advances in ionospheric modeling, some basic chemical reaction rates are still not taken into account in many models of the ionosphere. The physical processes that control the ionosphere can be divided into two broad categories: “photochemical” and “transport” [21]. In addition to gravity, collision forces, winds, and electric and magnetic fields, ionospheric ions are affected by a series of complicated chemical reactions with electrons and neutral constituents. Pavlov reviewed the knowledge of F-region ion chemistry [22]. Richards has systematically studied ion chemistry by comparing densities from a photochemical model with data from the Atmosphere Explorer satellite [1].

SAMI2 has been widely used (see, e.g., [23,24]). The efficacy of the SAMI2 model for the Indian low-latitude region around 75 °E longitude has been tested for different levels of solar flux [23]. Oh et al. [24] used the model to study the role of vertical E × B drift in the formation of the longitudinal plasma density structure in a low-latitude F region. The most important point is that SAMI2 is open source, and we can easily obtain and modify its source code. Based primarily on those studies [1,22], we revise SAMI2 by adopting the latest photochemical scheme. The major improvement in the model is upgrading the photochemical scheme from 28 to 60 reactions, including the effects of vibrationally excited N₂(ν), O₂(ν), and metastable N(²D).

2. Photochemical Scheme

SAMI2 treats the dynamic and chemical evolutions of the seven major ion species and electrons at mid- and low-latitudes by solving simultaneously the continuity equation, the momentum equation, and the energy equation along the geomagnetic field lines, resulting in two-dimensional structures for the densities of seven ions (H⁺, He⁺, N⁺, O⁺, N₂⁺, NO⁺, and O₂⁺) and the temperatures of three ions (H⁺, He⁺, and O⁺) as well as the density and temperature of the electrons. The solar, the neutral atmosphere, and the ionospheric electrodynamics are specified using several empirical models [6].

In SAMI2, the ion continuity equation is [6]

$$\frac{\partial n_i}{\partial t}+\nabla ·\left(n_i{V}_i\right)=P_i-L_i{n}_i$$

(1)

where t is time, P_i is the ion production term, L_i is the ion loss term, n_i is ion concentration, and V_i is ion vector velocity, respectively. The n_iV_i represents the plasma flux due to transport.

Ionospheric ions are affected by many processes, including chemical reactions between ions and neutral constituents and between ions and electrons. The production of ions comes from photoionization and chemical reactions, and the ions are lost in chemical reactions. A photochemical scheme with 60 reactions is adopted. The main differences compared to SAMI2 are as follows. We calculate the solar EUV production of the ⁴S, ²D, and ²P state divisions of the O⁺. The solar EUV flux is determined from the HEUVAC model developed by [25]. The secondary ionization [26] effect of daytime photoelectrons is considered. The density of N(²D), which the NRLMSISE-00 cannot supply, is calculated self-consistently using a photochemical equilibrium. The loss rate of O₂⁺ ions in the ionospheric E region is closely related to the density of NO. The NO density is calculated using an empirical model that includes reasonable changes in time, season, and solar cycle [27]. The neutral wind is given by the horizontal wind model (HWM14) [28] instead of HWM93. Our scheme includes both ground state and metastable/vibrational excited reactions (e.g., N(²D), N₂(ν), and O₂(ν)). Figure 1 shows a schematic representation of the ionospheric ion chemistry, and the chemical reactions and reaction rates used in the scheme are given in Appendix A.

The metastable/vibrational excited reactions can significantly affect the O⁺ density under certain conditions and cannot be neglected [1,22,29]. Vibrationally excited nitrogen N₂(ν) and oxygen O₂(ν) have significant effects on the F-region ionosphere by increasing the loss rate of the dominant ion O⁺, thereby reducing the electron concentration in the F-region ionosphere, especially during years with high solar activity. The decrease in density leads to an increase in electron temperature, which can further increase the O⁺ loss rate and lead to positive feedback between the density and temperature [1]. In order to determine the effect of N₂(ν), the method developed by Pavlov and Buonsanto [30] for vibrational temperature Tν under steady-state conditions and the rate coefficients derived by Pavlov [31] are used. The effect of O₂(ν) is taken into account implicitly by using the formula given by Hierl et al. [32] (see k₁ and k₂ in Appendix A 

Table A1. Chemical reactions and rates.

Reaction	Rate (m−3s−1 or s−1)	Reference
O+ + N2(ν) → NO+ + N	k′10 = 1.533 × 10−18–5.92 × 10−19(Ti/300) + 8.60 × 10−20(Ti/300)2 300 K ≤ Ti ≤ 1700 K k′10 = 2.73 × 10−18–1.155 × 10−18(Ti/300) + 1.483 × 10−19(Ti/300)2 1700 K ≤ Ti ≤ 6000 K k′11 = k′10; k′12 = 38 k′10; k′13 = 85 k′10; k′14 = 220 k′10; k′15 = 270 k′10; [N2(0)] = [N2] (1 − exp(−3353/Tν)); [N2(ν)] = [N2(0)] exp(−3353ν/Tν); [N2] = ∑ [N2(ν)] k1 = ∑ k′1ν [N2(ν)] /[N2]	[31]
O+ + O2(ν) → O2+ + O	k2 = 1.7 × 10−17(300/Tn)0.77 + 8.54 × 10−17 exp(−3467/Tn)	[32]
O+ + H → H+ + O	k3 = 6.4 × 10−16	[41]
O+ + NO → NO+ + O	k4 = 7.0 × 10−19(300/Ti)−0.87	[42]
O+ + N(2D) → N+ + O	k5 = 1.3 × 10−16	[43,44]
O+ + e → O	k6 = 4.43 × 10−18(300/Te)0.7	[6]
O2+ + NO → NO+ + O2	k7 = 4.5 × 10−16	[45]
O2+ + N → NO+ + O	k8 = 1.2 × 10−16	[46]
O2+ + N2 → NO+ + NO	k9 = 5.0 × 10−22	[3]
O2+ + N(2D) → N+ + O2	k10 = 8.65 × 10−17	[47]
O2+ + e → O + O	k11 = 2.0 × 10−13(300/Te)0.70 Te < 1200 K k11 = 1.6 × 10−13(300/Te)0.55 Te ≥ 1200 K	[48]
NO+ + e → N + O	k12 = 0.2 k′ k′ = 4.2 × 10−13(300/Te)0.85	[20]
N2+ + O → NO+ + N	k13 = 1.4 × 10−16(300/Ti)0.44 Ti ≤ 1500 K	[49]
N2+ + O → O+ + N2	k14 = 9.8 × 10−18(300/Ti)0.23 Ti ≤ 1500 K	[50]
N2+ + O2 → O2+ + N2	k15 = 5.1 × 10−17(300/Ti)1.16 Ti ≤ 1000 K k15 = 1.26 × 10−17(1000/Ti)−0.67 Ti > 1000 K	[51]
N2+ + O2 → NO+ + NO	k16 = 1.0 × 10−20	[6]
N2+ + NO → NO+ + N2	k17 = 3.3 × 10−16	[51]
N2+ + N → N+ + N2	k18 = 1.0 × 10−17	[52]
N2+ + e → N + N	k19 = 0.1 k′ k′ = 1.75 × 10−13(300/Te)0.39	[20]
H+ + O → O+ + H	k20 = 2.2 × 10−17 Ti0.5	[53]
H+ + NO → NO+ + H	k21 = 1.9 × 10−15	[54]
H+ + e → H	k22 = 4.43 × 10−18(300/Te)0.7	[6]
He+ + N2 → N2+ + He	k23 = 6.4 × 10−16	[54]
He+ + N2 → N+ + N + He	k24 = 9.6 × 10−16	[54]
He+ + O2 → O+ + O + He	k25 = 1.1 × 10−15	[54]
He+ + O2 → O2+ + O	k26 = 2.0 × 10−16	[6]
He+ + NO → N+ + He + O	k27 = 1.25 × 10−15	[54]
He+ + e → He	k28 = 4.43 × 10−18(300/Te)0.7	[6]
N+ + O → O+ + N	k29 = 2.2 × 10−18	[43,44]
N+ + NO → NO+ + N	k30 = 2.0 × 10−17	[6]
N+ + NO → N2+ + O	k31 = 8.33 × 10−17(300/Ti)0.24	[55]
N+ + O2 → O2+ + N	k32 = 3.1 × 10−16	[56]
N+ + O2 → NO+ + O	k33 = 2.6 × 10−16	[56]
N+ + e → N	k34 = 4.43 × 10−18(300/Te)0.7	[6]
O+(2D) + N2 → N2+ + O	k35 = 1.5 × 10−16(Ti/300)0.5	[57]
O+(2D) + N2 → NO+ + N	k36 = 2.5 × 10−17	[57]
O+(2D) + O2 → O2+ + O	k37 = 1.3 × 10−16(Ti/300)0.5	[7]
O+(2D) + N → N+ + O	k38 = 1.5 × 10−16	[58]
O+(2D) + NO → NO+ + O	k39 = 1.2 × 10−15	[59]
O+(2D) + O → O+(4S) + O	k40 = 1.0 × 10−16	[60]
O+(2D) + e → O+(4S) + e	k41 = 4.0 × 10−14(300/Te)0.5	[7]
O+(2P) + N2 → N2+ + O	k42 = 2.0 × 10−16(Ti/300)0.5	[7,57]
O+(2P) + N2 → N+ + NO	k43 = 1.0 × 10−17	[61]
O+(2P)+O2 → O2++O	k44 = 1.3 × 10−16	[59]
O+(2P) + O2 → O+(4S) + O2	k45 = 1.3 × 10−16	[59]
O+(2P) + O → O+(4S) + O	k46 = 4.0 × 10−16	[62]
O+(2P) + e → O+(4S) + e	k47 = 2.5 × 10−14(300/Te)0.5	[63]
O+(2P) + e → O+(2D) + e	k48 = 7.0 × 10−14(300/Te)0.5	[63]
O+(2P) → O+(4S) + hv	k49 = 0.0833 s−1	[64]
O+(2P) → O+(2D) + hv	k50 = 0.277 s−1	[64]
NO+ + e → N(2D) + O	k51 = 0.8 k′ k′ = 4.2 × 10−13(300/Te)0.85	[20]
N2+ + e → N(2D) + N	k52 = 0.9 k′ k′ = 1.8 × 10−13(300/Te)0.39	[20]
N2+ + O → N(2D) + NO+	k53 = 1.4 × 10−16(300/TR)0.44 TR ≤ 1500 K k53 = 5.2 × 10−17(TR/300)0.2 TR > 1500 K TR = (Ti + Tn)/2	[20]
N+ + O2 → N(2D) + O2+	k54 = 0.15 k′ k′ = 5.5 × 10−16(Ti/300)0.45 Ti ≤ 1000 K k′ = 9.5 × 10−16 Ti > 1000 K	[47,65]
N(2D) → N(4S) + hv	k55 = 1.06 × 10−5 s−1	[20]
N(2D) + e → N(4S) + e	k56 = 5.0 × 10−16(Te/300)0.5	[66]
N(2D) + O → N(4S) + O	k57 = 7.0 × 10−19	[67]
N(2D) + O2+ → NO+ + O	k58 = 1.8 × 10−16	[68]
N(2D) + NO → N2 + O	k59 = 7 × 10−17	[20]
N(2D) + O2 → NO + O	k60 = 6 × 10−18	[69]

).

3. Influence of the Photochemical Scheme

To evaluate the role of the metastable and vibrational excited species in the ionosphere, we compare the modeled O⁺ loss rate (β₋O⁺) and electron concentration (Ne) obtained from the model simulations with the new photochemical scheme (i.e., SAMI2₋ph) using the open-source model SAMI2 by relative deviation (Dev). The deviation of the current result from the original result is obtained as

$$\mathrm{D}\mathrm{e}\mathrm{v}\left(\%\right)=\frac{p-p_0}{p_0}\times 100\%$$

(2)

where p is the modeled β₋O⁺ or Ne obtained from SAMI2₋ph, correspondingly, p₀ is the modeled β₋O⁺ or Ne obtained from the original SAMI2.

Figure 2 shows the altitude variations in the Dev. One can note that the new scheme brings a foreseeable increase in the loss rate of O⁺ and a decrease in the electron concentration Ne. The variation in electron concentration has the same amplitude as in the O⁺ loss rate (20%), and it is more pronounced at 18:00 LT. The affected height of the ionosphere is around ~200 km and the latitude is around ~20°. The altitude profiles of electron concentration are shown in Figure 3. The increase in the loss rate of O⁺ due to N₂(ν) and O₂(ν) causes an obvious decrease in F2-layer Ne. In another part of the ionosphere, the dominant ion is no longer O⁺, hence the electron density is almost the same. In Ref. [23], the vertical electron density profile over an equator at the geographic latitude of 5 °N was provided by SAMI2. The electron density maximizes around 500 km, while the maximum appears at about 350 km in Figure 3. This is a characteristic of the EIA, that is, the peak height of the ionosphere in the equatorial region is slightly higher.

If we scrutinize Figure 2, we will find pronounced north–south asymmetry, both in β₋O⁺ and Ne. This asymmetry is due to the effect of daytime transequatorial neutral wind blowing from the south to the Northern Hemisphere [33,34]. Figure 4 gives the distribution of the neutral wind and the neutral N₂ density. One can find transequatorial northward wind prevails at low and equatorial latitudes, which lifts the plasma to higher altitudes along magnetic field lines in the Southern Hemisphere and brings the plasma downward in the Northern Hemisphere, leading to the asymmetric EIA (equatorial ionization anomaly) and asymmetric neutral composition distribution in N₂ (as shown in Figure 4) by the drag force of the northward wind.

4. Comparison with Ionosonde Data

The accuracy of the ionosonde observations is widely accepted, and the data are usually applied to validate the model’s accuracy [36,37,38]. To examine the effect of the photochemical scheme on ionospheric status, here we compare the modeled NmF2–obtained from the model simulations when the scheme is substituted (SAMI2₋ph) and not substituted (open-source model, SAMI2) in the model–with actual ionosonde observations. The selected data are derived from two mid-latitude ionosonde stations located in Beijing (30.22 °N, 187.51 °E geomagnetic) and Xinxiang (25.33 °N, 185.56 °E geomagnetic). The ionogram provides the critical frequency of the F2 layer, foF2. The formula [39]

$$\mathrm{N}\mathrm{m}\mathrm{F}2\left({\mathrm{m}}^{-3}\right)=1.24\times {10}^{10}\times {\left(\mathrm{f}\mathrm{o}\mathrm{F}2\left(\mathrm{M}\mathrm{H}\mathrm{z}\right)\right)}^2$$

(3)

is used to convert foF2 to the F2 peak electron density, NmF2. We chose March, June, September, and December of 2009–2019 as the times for comparison to have good seasonal and solar activity coverage. The days with a Dst index larger than −15 nT are selected to avoid magnetic storm effects.

Table 1. Ionosonde data sets.

Date	Daily Ap	F107d	F107_81
20 March 2009	4	68.2	69.1
19 June 2009	2	69.2	71.2
24 September 2009	1	75.0	71.0
21 December 2009	3	80.0	75.6
21 March 2010	1	84.1	80.7
21 June 2010	4	74.3	77.3
22 September 2010	2	85.4	80.9
19 December 2010	2	78.3	81.2
19 March 2011	4	88.0	109.3
21 June 2011	9	98.2	97.0
25 September 2011	4	169.8	130.6
25 December 2011	3	139.6	133.0
10 June 2012	5	132.3	131.5
23 September 2012	0	134.4	119.2
20 December 2012	8	110.4	117.8
11 March 2013	5	118.2	110.7
20 June 2013	11	130.5	120.5
23 September 2013	4	108.5	119.7
22 December 2013	1	133.4	148.0
19 March 2014	4	147.9	151.4
17 June 2014	8	118.0	132.6
6 October 2014	6	129.9	147.3
4 June 2015	2	121.4	125.0
28 September 2015	3	124.5	106.0
24 March 2016	6	86.0	92.8
20 June 2016	4	87.1	89.7
23 September 2016	3	86.1	86.6
17 December 2016	5	69.8	74.8
20 March 2017	1	72.1	77.3
28 June 2017	3	74.5	78.3
23 September 2017	4	81.7	84.4
23 December 2017	5	73.7	69.3
13 March 2018	3	67.7	69.2
22 June 2018	3	83.0	73.5
20 September 2018	1	67.2	69.4
21 December 2018	4	68.8	68.3
22 March 2019	1	81.8	71.1
18 June 2019	3	69.2	70.6
23 September 2019	3	66.6	68.0
23 December 2019	3	70.2	69.1

gives the selected dates and corresponding model inputs.

The comparisons using actual values of F10.7 and Ap as inputs and observations are given in Figure 5. Ideally, a perfect one-to-one correlation occurs when the correlation coefficient r = 1, and the magnitudes of the two variables are equal to each other when the slope is k = 1 and the intercept is b = 0. We find that the linearity is quite obvious, and all correlation coefficients between model results and observations are bigger than 0.8. The correlation coefficients (r) of Beijing and Xinxiang are both larger for SAMI2₋ph than for SAMI2, implying that the revised model SAMI₋ph simulates the ionosphere better than the original SAMI2 does. With a linear correlation analysis between the modeled and the observed data, we derive the linear slope k and intercept b. When the photochemical scheme in SAMI2 is substituted, the slope is significantly larger than the default run for the NmF2 comparisons at Beijing and Xinxiang. Before the scheme is replaced, the slopes are significantly smaller than 1. This means that the electron densities obtained from SAMI2 are larger than the ionosonde data. The increase in the O⁺ loss rate leads to a decrease in the dominant ion O⁺ concentration, which reduces the electron concentration in the F region as expected, and makes the slope larger than 1, implying that the modeled NmF2 data are smaller than the ionosonde data. Nevertheless, the smaller RMSE and b can indicate that the modified model provides a reasonably good match with the ionosonde NmF2 measurements.

Figure 6 provides the comparison with the low-latitude ionosonde station Guangzhou (12.48 °N, 184.58 °E geomagnetic). The correlation coefficient r for SAMI₋ph is smaller than SAMI2, and the slope k is further away from 1, which implies that the revised model severely underestimates the ionosphere at the low-latitude ionosonde station. It is well-known that the low-latitude ionosphere is strongly affected by several highly variable electrodynamic processes, producing large ranges of temporal and spatial variations in the equatorial ionization anomaly (EIA) [40]. Guangzhou is located at the northern crest of the EIA. It is not difficult to envisage that SAMI₋ph might not perform well at low latitudes as at mid-latitudes. To improve the performance of ionosphere physical models at low latitudes, one reasonable and effective attempt should be made by seeking more accurate methods to represent the ionospheric electrodynamic processes. Hence, we can conclude that the new photochemical scheme significantly improves the performance of SAMI2 at mid-latitudes but not low latitudes.

In addition, SAMI2 is a physics-based ionosphere model, and not coupled with the thermosphere; hence, the modeled results are susceptible to several drivers, including thermospheric composition, winds, and electric fields. These drivers are obtained using empirical models. The uncertainties associated with these models may cause inaccurate representations of the ionospheric state. The accurate specification of the temporal and spatial variability in the ionospheric plasma transport and thermospheric constitutes can strongly affect the performance of the ionosphere model. The most promising approach to improve the performance of physics-based ionosphere models is data assimilation, which is implemented by using certain optimization schemes to incorporate the measurements into the background models.

5. Summary

Concentrating on the significant role of physical models of the ionosphere, a complicated photochemical scheme with 60 reactions—taking the effects of vibrationally excited N₂(ν) and O₂(ν), and metastable O⁺(²D), O⁺(²P), and N(²D) into account—is developed primarily based on the recently developed photochemistry by Richards [1]. We revise the open-source SAMI2 model using this photochemical scheme. By comparing the modeled NmF2 with the ionosonde data from 2009 to 2019, one can find that the revised model performance is better than the original at mid-latitudes. In other words, the photochemical scheme plays a fundamental role in the ionosphere model, and the effects of metastable and vibrationally excited constituents on the ionosphere cannot be ignored. In future work, we will validate the model’s performance by using multiple data from ISR (Incoherent Scatter Radar), GNSS, and satellites.