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Numerical prediction of sporadic E layer occurrence using GAIA

Abstract

A sporadic E layer has significant influence on radio communications and broadcasting, and predicting the occurrence of sporadic E layers is one of the most important issues in space weather forecast. While sporadic E layer occurrence and the magnitude of the critical sporadic E frequency (foEs) have clear seasonal variations, significant day-to-day variations as well as regional and temporal variations also occur. Because of the highly complex behavior of sporadic E layers, the prediction of sporadic E layer occurrence has been one of the most difficult issues in space weather forecast. To explore the possibility of numerically predicting sporadic E layer occurrence, we employed the whole atmosphere–ionosphere coupled model GAIA, examining parameters related to the formation of sporadic E layer such as vertical ions velocities and vertical ion convergences at different altitudes between 90 and 150 km. Those parameters in GAIA were compared with the observed foEs data obtained by ionosonde observations in Japan. Although the agreement is not very good in the present version of GAIA, the results suggest a possibility that sporadic E layer occurrence can be numerically predicted using the parameters derived from GAIA. We have recently developed a real-time GAIA simulation system that can predict atmosphere–ionosphere conditions for a few days ahead. We present an experimental prediction scheme and a preliminary result for predicting sporadic E layer occurrence.

Introduction

Sporadic E (Es) layers are narrow layers with high electron densities consisting mainly of metallic ions. These layers appear sporadically in the region predominantly at altitudes between 90 and 120 km. Among the many kinds of space weather disturbances, Es layers are one of the most important phenomena because they significantly affect radio communication and broadcast systems with high-frequency (HF) and very high-frequency (VHF) radio waves. In addition, recent studies also suggest that Es layers have a potential impact on air-navigation systems, which use VHF radio waves (Sakai et al. 2019).

At the National Institute of Information and Communications Technology (NICT), Es layers as well as other ionospheric disturbances above Japan are monitored with four ionosonde stations in Japan: Wakkanai (45.16° N, 141.75° E), Kokubunji (35.71° N, 139.49° E), Yamagawa (31.20° N, 130.62° E), and Okinawa (26.68° N, 128.15° E). The critical sporadic E frequency foEs, which is an index of the intensity of Es layers, is derived from the ionosonde data. In the space weather forecast at NICT, a foEs larger than 8 MHz is the criterion for “Es layer occurrence”. On the basis of this criterion, the Space Weather Forecast Center at NICT issues an Es layer forecast along with forecasts of other space weather disturbances (http://swc.nict.go.jp/en/).

The observed ionosonde data are stored in a database that is open to the public and is also utilized for many kinds of research on the ionosphere. Characteristic ionospheric parameters such as foF2, hF2, and foEs derived from the data are categorized into two types of parameters: manually scaled parameters and automatically scaled parameters. The automatically scaled parameters are automatically generated with ionogram scaling algorithms. This system works in real time, but errors occur occasionally owing to the detection of noise signals. The manually scaled parameters are obtained manually and are more accurate than automatically scaled parameters, but are not available in real time. Therefore, in our present study, manually scaled parameters obtained in the past are used for comparisons with GAIA-derived parameters.

The results of a number of studies of Es layers have suggested that a vertical neutral wind shear in the lower thermosphere plays an important role in Es layer formation. The mechanism of ion convergence driven by the neutral wind shear called “wind shear theory” has been confirmed by a number of theoretical and modeling studies (MacLeod 1966; Kato et al. 1972; Mathews and Bekeny 1979; Earle et al. 1998; Arras et al. 2008; Christakis et al. 2009; Chu et al. 2011, 2014; Haldoupis 2012; Yeh et al. 2014; Chu and Yu 2017; Shinagawa et al. 2017). Chu et al. (2014) employed the empirical neutral wind model HWM07 (Drob et al. 2008) to simulate an Es layer. They found that the basic behavior of Es layers is highly coincident with the neutral wind shear, and that the diurnal and seasonal variations in Es layer occurrence can be mainly attributed to variations in the neutral wind shear. While the basic formation processes of Es layers are reproduced by numerical models fairly well, the prediction of Es layer occurrence is still a challenging task, mainly because of the complex behavior of the neutral wind in the lower thermosphere. Therefore, no attempts have been made to numerically predict the occurrence of Es layers.

To explore the possibility of Es layer prediction, we investigated parameters related to Es layer formation such as vertical ions velocities and vertical ion convergences at different altitudes between 90 and 150 km using simulation data obtained from the whole atmosphere–ionosphere coupled model GAIA (Jin et al. 2012; Miyoshi et al. 2012).

Then we compared those parameters with foEs data obtained from the ionosonde observations at NICT’s stations. It was found that the vertical ion convergence (VIC), especially VIC at 120 km altitude (VIC120), has the best correlation with foEs so far, suggesting that VIC120 derived from GAIA simulations can be used as practical indices for the prediction of Es layer occurrence. Preliminary results of predictions of Es layer occurrence and values of foEs derived from the GAIA simulation data are presented.

Method of analysis

We analyzed foEs data obtained from the NICT ionosonde observations and simulation data produced by GAIA. An example of observed foEs data (manually scaled foEs), which was derived from ionosonde data obtained at Kokubunji in 2009, is shown in Fig. 1. The day of the year in the plot is in JST (Japan Standard Time = UT + 9 h). The observed foEs exhibits clear seasonal variations: larger in summer and smaller in other seasons with occasional enhancement in winter (Fig. 1a). The seasonal variations in Es layer occurrence and in foEs have been observed in a number of observational studies (e.g., Haldoupis et al. 2007; Christakis et al. 2009; Chu et al. 2014; Yeh et al. 2014). Figure 1b shows foEs between days 160 and 190 in Fig. 1a, indicating that foEs also has significant day-to-day variations as well as hourly variations.

Fig. 1
figure1

Observed foEs data at Kokubunji in 2009. foEs data are obtained by the ionosonde observation at Kokubunji in 2009 for a the entire year and b the days from 160 to 190. The day of year is in Japan Standard Time (UT + 9 h)

The GAIA model used in the present analysis is basically the same as the one used by Shinagawa et al. (2017). For the neutral atmosphere part of GAIA, the horizontal resolutions are 2.8° in longitude and latitude and the vertical resolution is 0.2 scale height. The ionosphere part of GAIA employs a finite difference scheme with a spatial grid of 2.5° longitude by 1° latitude horizontally, and the vertical grid interval is 10 km below 600 km. At altitudes higher than 600 km, the grid size gradually increases up to the upper boundary of 3000 km.

Data from the JRA-55 meteorological reanalysis (Kobayashi et al. 2015; Harada et al. 2016) are incorporated in the lower atmosphere by a nudging method (Jin et al. 2012). The F10.7 index and the geomagnetic field model (IGRF) are taken from the NOAA National Centers for Environmental Information (NCEI) database (https://www.ngdc.noaa.gov). In the present analysis, a quiet magnetospheric condition with a constant cross-polar-cap potential of 30 kV is assumed (Fujiwara and Miyoshi 2006). Thus, effects of magnetic storms are not included in the simulation data. This is a reasonable assumption because Es layers are little affected by magnetic disturbances (Whitehead 1989).

The velocity wi of vertical ion drift driven by vertical shear of horizontal neutral wind can be expressed as follows (Mathews 1998):

$$w_{{\text{i}}} = \frac{{V\cos I\sin I + \left( {\frac{{\nu_{{\text{i}}} }}{{\omega_{{\text{i}}} }}} \right){ }U\cos I}}{{1 + \left( {\frac{{\nu_{{\text{i}}} }}{{\omega_{{\text{i}}} }}} \right)^{2} }},$$
(1)

where νi is the collision frequency of ions relative to neutral species, ωi is the ion gyro frequency, U is the eastward neutral wind velocity, V is the southward neutral wind velocity, and I is the magnetic dip angle. The only ion species-dependent term is (νin/ωi) in Eq. (1), and it has weak dependence on the mass of ion species. The ion used in our analysis is assumed to be NO+ (atomic mass = 30.0), which is a background ion. Using metallic ions such as Fe+ (atomic mass = 55.9) and Mg+ (atomic mass = 24.3) would result in somewhat different number (about 10% difference). This is considered to be insignificant because (νin /ωi) is proportional to the neutral density, which changes rapidly with altitude.

Using Eq. (1), the vertical ion convergence VIC can be obtained from

$$VIC = - \frac{{\partial w_{{\text{i}}} }}{\partial z} .$$
(2)

The values of VIC are compared with the observed foEs obtained by the ionosondes operated at NICT’s stations. In our analyses, we used 1-h foEs data at Kokubunji for the comparisons of the observed foEs and VIC. Note that the “daily” values are those for 0–24 h in JST.

To investigate the seasonal and day-to-day variations in the observed foEs and calculated VIC and the relationship between them, we first compare foEs and VIC for (1) daily average values, (2) daily maximum values, and (3) 1-h values. Then, a method of estimating daily maximums of foEs from GAIA data is presented. Finally, we compare “predicted” foEs derived from GAIA with foEs observed at Okinawa in 2019. We used foEs data from Okinawa because the manually scaled data from Kokubunji were not available at the time of this study.

Results

Comparison of daily average foEs and VIC

To study the relationship between daily variations in foEs and VIC in the lower thermosphere, we used ionosonde data obtained by NICT at Kokubunji in 2009. We chose these data simply because of the relatively small number of missing data compared with other years.

Figure 2 shows the daily average foEs (blue line) and the daily average VIC (red line) in 2009 obtained at Kokubunji at four different altitudes: (a) 130 km, (b) 120 km, (c) 110 km, and (d) 100 km. The scale on the axis of the daily average VIC is adjusted so that the values are best fitted to the foEs values. The results indicate that the agreement between foEs and VIC is best at 120 km altitude (Fig. 2b). The agreement is good not only for the seasonal variation, but also for some day-to-day variations. At altitudes of 130 km (Fig. 2a) and 110 km (Fig. 2c) there is less agreement between the two parameters, and no significant correlation is seen at 100 km altitude (Fig. 2d).

Fig. 2
figure2

Daily average foEs and daily average vertical ion convergence. Daily average foEs (blue line) and daily average vertical ion convergence (VIC) (red line) at Kokubunji in 2009 are compared at four different altitudes: a 130 km, b 120 km, c 110 km, and d 100 km. The scales on the daily average VIC are adjusted so that the values are best fitted to the foEs values

Figure 3 shows the correlation coefficients of the daily average foEs and VIC at the four different altitudes obtained at Kokubunji in 2009. The correlation coefficient is highest at 120 km altitude (0.764) (Fig. 3b), while it decreases rapidly away from 120 km altitude: 0.347 at 130 km altitude (Fig. 3a) and 0.357 at 110 km altitude (Fig. 3c). As mentioned before, there is negligible correlation at 100 km altitude (Fig. 3d).

Fig. 3
figure3

Correlations of daily average foEs and VIC. Scatter plots and correlation coefficients of the daily average foEs and VIC are shown at four different altitudes at Kokubunji in 2009

This result implies that VIC around 120 km altitude plays an important role in the development of Es layers. However, the observation that Es layers appear most often in the region between 100 and 110 km altitudes (Wu et al. 2005; Arras et al. 2008). The ionosonde data used in our analysis is also consistent with the result. Figure 4 shows the altitude distribution of Es layers observed by the NICT ionosonde at Kokubunji in 2009.

Fig. 4
figure4

Histogram of the distribution of Es layer altitude for Kokubunji in 2009. The manually scaled 1-h data obtained by the NICT ionosonde were used. The plot indicates that Es layers appear most often in the 100–110 km altitude region.

A possible explanation for this inconsistency is that metallic ions accumulate in the region of about 120 km as a result of the ion convergence driven by a neutral wind shear, and then the metallic ion layers descend and form Es layers in the lower region of 100–110 km altitudes. Recently, Andoh et al. (2020) have studied the formation processes of Es layer using three-dimensional ionospheric simulation model incorporating the neutral density and velocity data produced by GAIA, which are the same as used in our paper. This study demonstrated that the Es layer is initially formed at around 120 km on the average, and that the layer descends to lower altitudes, increasing its electron density. This picture seems consistent with observational result obtained by Haldoupis et al. (2006), Prasad et al. (2012), Yuan et al. (2013), Chu et al. (2014). The Es layer tends to stay at around 100 km because the background bulk neutral wind is weaker. But the wind shear is even stronger at 100 km than at 120 km. It is expected that the Es layer at around 100 km is further strengthened by local smaller-scale wind shear (Larsen et al. 2005), which cannot be reproduced by the present version of GAIA. In this paper, we focus on the possibility of Es prediction using VIC at 120 km altitude (VIC120).

In addition to the year of 2009, we also analyzed foEs data obtained at Kokubunji for the years from 2010 to 2014, which cover the period from the solar minimum to solar maximum. Although the dependence of Es layer formation on the solar cycle is insignificant compared with the seasonal dependence, some studies indicate that foEs has a weak solar cycle dependence (Maksyutin et al. 2001; Pezzopane et al. 2015, 2016), suggesting the possibility of year-to-year differences in the relationship between foEs and VIC. However, we found that the correlation between foEs and VIC does not change significantly with the year. The correlation coefficients between the daily average foEs and VIC for the years of 2009–2014 are shown in Fig. 5. Although there are small differences in the correlation coefficients among the years, the altitude dependence of the correlation coefficient is almost the same in each year: the correlation coefficient has a peak at about 120 km altitude and is smaller at altitudes above and below 120 km. This result suggests that VIC120 is a key parameter in the formation process of Es layers and that the relationship between VIC120 and foEs does not depend significantly on the year.

Fig. 5
figure5

Correlation coefficients of the daily average foEs and VIC120. Correlation coefficients of the daily average foEs and the vertical ion convergence at 120 km altitude are shown for the years of 2009–2014 at Kokubunji in 2009

Comparison of daily maximum foEs and VIC

The results described in the previous section indicate that there is a strong relationship between the daily average foEs and VIC120. For practical space weather forecast, however, predicting the daily maximum of foEs is more important than predicting the daily average foEs because Es layers with higher electron densities have more influence on communication and broadcast systems.

Figure 6 shows comparisons between the daily maximums of foEs (blue line) and VIC (red line) in 2009 obtained at Kokubunji. The daily maximums of both foEs and VIC show greater variation than the daily average values (Fig. 2). While the daily average foEs is always less than 10 MHz (Fig. 2), the daily maximum foEs is much larger and occasionally exceeds 20 MHz (Fig. 6).

Fig. 6
figure6

Daily maximums of foEs and daily maximums of VIC. The daily maximums of foEs (blue line) and the daily maximums of the vertical ion convergence (VIC) are compared at four different altitudes (red line) in 2009 at Kokubunji

The agreement between the daily maximums of foEs and VIC120 is somewhat less than that of the daily averages (Fig. 2), although the best agreement still occurs at 120 km altitude. The occasional large enhancement of the daily maximum of foEs suggests the existence of a sudden increase in local neutral wind shears, which is probably associated with gravity waves with a large amplitude or shear instabilities (Nygrén et al. 1990; Larsen 2002; Larsen et al. 2005). The daily maximum of VIC also occasionally exhibits sudden enhancement, which does not always match the observed foEs enhancement. Local small-scale wind shears responsible for the large foEs cannot be reproduced by global atmosphere–ionosphere models such as GAIA. This is analogous to the fact in meteorology that the maximum instantaneous wind speed is much more difficult to predict than the average wind speed. Figure 7 shows scatter plots of the daily maximums of foEs and VIC at the four different altitudes obtained at Kokubunji in 2009. The correlation coefficient is highest at 120 km (0.536) (Fig. 7b). This value is less than that for the daily averages (0.764) (Fig. 3b), indicating that the prediction of the daily maximum foEs is more difficult than that of the daily average foEs.

Fig. 7
figure7

Correlation coefficients of the daily maximums of foEs and VIC. Scatter plots and correlation coefficients of the daily maximums of foEs and the daily maximums of the vertical ion convergence (VIC) are shown at four different altitudes at Kokubunji 2009

Comparison of hourly variations between foEs and VIC

Although present numerical models cannot accurately reproduce the temporal variations in foEs, it is meaningful to compare the observed foEs and VIC120. Figure 8 shows 1-h values of foEs (blue line) and VIC120 (red line) obtained at Kokubunji for three different periods in 2009: 13–23 June, 18–28 August, and 17–27 October. Figure 8a corresponds to the most active period of Es layer formation, and Fig. 8b, c are moderate and quiet periods, respectively. The agreement between maximum foEs and maximum VIC120 is not particularly good, but the phases of the variations are in reasonable agreement. For the less active periods (Fig. 8b, c), the overall amplitudes of both foEs and VIC120 decrease in a similar manner.

Fig. 8
figure8

One-hour values of foEs and VIC120. One-hour values of foEs (blue line) and the vertical ion convergence at 120 km altitude (VIC120) (red line) are plotted for three different periods at Kokubunji in 2009. a corresponds to the most active period, and b, c are moderate and quiet periods, respectively

It appears that diurnal variation is dominant for the observed foEs, while semidiurnal variation is dominant for VIC120. In addition, in some cases, peaks of the foEs and VIC120 appear to occur simultaneously. If variations in VIC120 are related to descending layers associated with tidal variations (Haldoupis et al. 2006; Andoh et al. 2020), peak of foEs should occur a few hours later than the peak of VIC120. These inconsistencies indicate that the present version of GAIA does not have sufficient resolution or accuracy to reproduce the hourly variations in neutral winds in the lower thermosphere, which are likely to be associated with small-scale gravity waves or shear instabilities around 100 km altitude. Although the magnitude and the time of the foEs peak cannot be predicted by GAIA, studies of Andoh et al. (2020) suggest that the basic behavior of Es layer is likely to be reproduced by GAIA.

Prediction of Es layer occurrence using VIC at 120 km

As mentioned before, in space weather forecast it is more practical to predict daily maximum foEs than the daily average foEs. In the previous section, we compared the daily maximums of foEs and VIC120. We found that the correlation between the daily averages of foEs and VIC120 was stronger than the correlation between the daily maximums of foEs and VIC120. This is probably because the daily maximum values of both foEs and VIC120 tend to fluctuate more than the daily average values, which results in lower correlation with the observed foEs.

Figure 9a shows the daily maximum foEs (blue line) and the daily average VIC120 (red line) obtained at Kokubunji in 2009. For this case the correlation coefficient is 0.679, which is somewhat higher than the correlation coefficient (0.536) of the daily maximums of foEs and VIC120 (Fig. 9b). Thus, the daily average VIC120 is a better index for predicting the daily maximums of foEs. Using the relationship between the maximum foEs and the average VIC120, we present an experimental method to deduce the daily maximum of foEs from the daily average VIC120.

Fig. 9
figure9

Daily maximum foEs and daily average VIC120. a Daily maximum foEs (blue line) and the daily average vertical ion convergence at 120 km altitude (VIC120) (red line) at Kokubunji 2009. b Scatter plot and correlation coefficient of the data in a

Strictly speaking, this is not a prediction because the calculated VIC120 is a present value, not a future value, since the present JRA-55 data is incorporated in the model, but in this paper we call it a prediction for convenience. In any prediction, if no information is available, the only way of predicting tomorrow’s condition is to assume that tomorrow will be the same as today, which is called “persistence prediction”. For a prediction method to be useful, its accuracy must be higher than that of the persistence prediction. Therefore, we examined the prediction scheme with daily average VIC120 (VIC120, d-ave) and compared the accuracy with that of the persistence prediction. As mentioned before, the criterion for Es layer occurrence is defined as foEs ≥ 8 MHz. One of the prediction schemes using VIC120, d-ave is to use criteria with threshold values, in which the occurrence and the absence of the Es layer are determined on the basis of the following criteria:

  • If VIC120, d-ave ≥ 6.1 × 10–4, the Es layer is present,

  • If VIC120, d-ave ≤ -2.0 × 10–4, the Es layer is absent,

  • If 6.1 × 10–4 > VIC120, d-ave > -2.0 × 10–4, the persistence prediction applies.

The threshold values in the above criteria were determined to maximize the prediction accuracy, and they might vary with the year or location. Table 1 is the contingency table for the categorical forecast of Es layer occurrence for the ionosonde data obtained at Kokubunji in 2009. “Yes” indicates the occurrence of an Es layer (maximum foEs ≥ 8 MHz), and “No” indicates the absence of an Es layer (maximum foEs < 8 MHz). The numbers in Table 1 are the numbers of days in 2009 for the four categories. The accuracies and the skill scores for the Kokubunji 2009 data obtained by the above prediction method are also included in the table. In this analysis the Heidke skill score described by Hyvärinen (2014) is adopted. In this score, negative values indicate that the random forecast is even better; 0 indicates that the scheme has no skill (same as random forecast); 1 indicates a perfect forecast skill.

Table 1 Contingency table for the categorical forecast of Es layer occurrence

The accuracy and the skill score of the persistence prediction are 0.825 and 0.633, respectively (Table 1a). Since foEs has significant seasonal dependence, even the persistence prediction gives fairly high scores. For the prediction method using VIC120, d-ave (Table 1b), the accuracy and the skill score are 0.860 and 0.711, respectively. This result suggests that using VIC120, d-ave results in better accuracy and skill score of prediction, although the improvement is relatively small.

The small difference between the persistence prediction and the prediction of VIC120, d-ave comes from the fact that even the persistence prediction is able to give a high accuracy or a skill score because in summer Es layer (foEs > 8 MHz) occurs almost every day, while it rarely occurs in winter. The prediction of VIC120, d-ave gives a significantly better prediction of Es occurrence only in spring and fall (mostly in late March–April and September–early October).

The method shown here is only one of ways of predicting Es layer occurrence, and there might be a better method of prediction. We will investigate various schemes to improve the accuracy of prediction (Table 2).

Table 2 Contingency table for the 24–48 h categorical forecast of Es layer occurrence

Experimental prediction of foEs using real-time GAIA

In actual space weather forecast, it is necessary to predict a future state of the upper atmosphere. We have recently developed a real-time and forecasting version of GAIA (GAIA-RF), which started to run in June 2019 (Tao et al. 2020). In the present GAIA-RF, meteorological reanalysis data (JRA-55) are incorporated in the lower atmosphere until about one day before the present, but magnetospheric inputs are not included. Since the effect of the magnetospheric activities on Es layer formation is thought to be insignificant (Whitehead 1989), it is adequate to use the data obtained by GAIA-RF for Es layer prediction.

After about one day before the present, the model is run without JRA-55 and produces 4-day prediction data once a day. We found that even without JRA data, the model could produce almost the same data for about 3 or 4 days ahead. Figure 10 shows comparisons of the eastward neutral wind velocity at 120 km for five different periods, obtained at Okinawa, starting from the same initial values at 0 UT on the first day of 5 months in 2019: (a) July, (b) August, (c) September, (d) October, and (e) November. The black line and the red line indicate neutral wind velocities obtained with and without JRA-55 data, respectively. Correlation coefficients for each day are calculated and shown in Fig. 10. In most cases, the difference between the two is very small at least for about 3 days ahead. After 4 days, the correlation coefficient decreases significantly. The results suggest that even without JRA-55 data GAIA is able to produce almost the same neutral winds as those with JRA-55 for about 3 days ahead.

Fig. 10
figure10

Comparisons of neutral wind velocities with and without JRA-55. The eastward neutral wind velocities at 120 km with and without JRA-55 for five different periods in Okinawa 2019 are compared, starting from the same initial values at 0 UT of the first day of the 5 months in 2019: a July, b August, c September, d October, and e November. The black line and the red line indicate neutral wind velocities with and without JRA-55, respectively

Figure 11 shows comparisons of VIC120 obtained with JRA-55 data (black line) and without JRA-55 data (red line) for the same periods as in Fig. 10, starting from the same initial conditions. Correlation coefficients for each day are also shown in Fig. 11. It is clear that the difference between VIC120 with and without JRA-55 data is insignificant for two ahead. Beyond 3 days ahead, the correlation between the two values becomes worse, but the daily maximum values of VIC120 still seem to be relatively small, indicating that as long as the foEs derived from VIC120 agrees with the observed foEs of the present day, it is possible to make a forecast for foEs for 1 or 2 days ahead.

Fig. 11
figure11

Comparisons of VIC120 with and without JRA-55. The vertical ion convergence values at 120 km (VIC120) with and without JRA-55 are compared for the same periods as Fig. 10, starting from the same initial values. The black line and the red line indicate VIC with and without JRA-55, respectively. Numbers for each day are correlation coefficients of VIC120 with and without JRA-55

There are several possible ways to derive foEs from VIC120. At the moment, we convert VIC120 to predicted foEs by using the following simple linear formula:

$$ foEs = 1.25 \times 10^{3} \overline{VIC} + 4.75 \left[ {{\text{MHz}}} \right],$$
(3)

where \( \overline{VIC}\) [s−1] is a 2-h average of VIC120.

The formula to convert from VIC120 to foEs is determined by eye so that the predicted values agree best with the observed foEs. This is a tentative fitting formula, and there is likely to be a better formula or method for predicting foEs. To compare the observed and predicted foEs, we adopted manually scaled foEs data obtained at Okinawa in 2019 instead of at Kokubunji in 2019 because manually scaled foEs data obtained at Kokubunji from late 2019 were not available at the time of this analysis.

Figure 12 shows comparisons between the predicted foEs and the observed foEs for three different periods obtained at Okinawa in late 2019. Figure 12a schematically illustrates the relationship between the prediction time and the predicted period of foEs. It is assumed that the prediction is made at 0 JST on Day N for the period of 24–48 h later (Day N + 1). Figure 12b–d shows the hourly values of predicted foEs for which each day corresponds to the “predicted period” of Fig. 12a. The red line indicates a series of predicted foEs for 24–48 h, and the black line indicates the observed foEs obtained by the ionosonde at Okinawa.

Fig. 12
figure12

Comparisons between predicted foEs and observed foEs. a Schematic figure showing the prediction time and the predicted period. Prediction for the 24–48 h later is made at 0 JST. The predicted foEs and the observed foEs for three different periods at Okinawa in late 2019 are compared: b DOY 184–200, c DOY 221–236, and d DOY 260–276. The red line indicates a series of predicted foEs of 24–48 h after the start of “free run” (without JRA-55 data). The black line indicates the observed foEs obtained by the ionosonde at Okinawa

Although the daily variations in the predicted foEs are similar to the observed foEs, the agreement is not very good. In particular, a large enhancement of foEs over 15 MHz occasionally observed in summer could not be reproduced. It appears that the present version of GAIA is not able to reproduce a magnitude of foEs especially large enhancements of foEs. In fact, the correlation between the observed foEs and the predicted foEs is rather small (~ 0.213) (Fig. 13). However, it is still possible to predict Es occurrence (foEs > 8 MHz) if we choose an adequate scheme.

Fig. 13
figure13

Correlation coefficients of the observed foEs and predicted foEs. Scatter plots and correlation coefficients of 1-h data of the observed foEs and the predicted foEs are shown using the data from DOY 179 to DOY 299 at Okinawa in 2019

The following is the scheme, in which the occurrence and the absence of the Es layer for “the day after tomorrow” are determined using the predicted foEs and the daily maximum of foEs for today (foEsdmax).

  • If foEsdmax ≥ 15 MHz, the Es layer will occur regardless of VIC prediction,

  • If 15 MHz > foEsdmax > 6.2 MHz, the VIC-predicted foEs applies,

  • If foEsdmax < 6.2 MHz, the Es layer will be absent regardless of VIC prediction.

This is based on the idea that when the Es is very active or inactive today, it is better to trust the persistence prediction rather than the prediction with VIC.

Both the persistence prediction and the prediction using VIC have less accuracies and skill scores partly because the prediction is for the day after tomorrow and partly because foEs in late 2019 at Okinawa shows more complicated variations than foEs in 2009 at Kokubunji shown in Table 1. It is found that the prediction using VIC slightly improves the accuracy and score.

Further analysis of the observed and predicted foEs for a much longer period is necessary to evaluate the prediction accuracy and to develop a better prediction scheme. We plan to construct a system for Es layer forecast that displays the predicted foEs and the observed foEs in real time.

Discussion and conclusions

The development of a system for numerically predicting space weather disturbances is an important issue. To simulate ionospheric disturbances, a number of global ionosphere–atmosphere models have been constructed (e.g., Codrescu et al. 2012; Qian et al. 2014; Liu et al. 2018), which are successful in reproducing large-scale structures and variations of the ionosphere. The formation processes of Es layers have also been studied using various types of numerical models (MacLeod 1966; Kato et al. 1972; Mathews and Bekeny 1979; Earle et al. 1998; Arras et al. 2008; Christakis et al. 2009; Chu et al. 2011, 2014; Yeh et al. 2014; Chu and Yu 2017). However, it is still difficult to numerically reproduce the structures and variations of the observed foEs of Es layers.

In our study, instead of reproducing the structure of Es layers, we searched for ionospheric parameters that have strong correlations with the observed foEs. Although the agreement between VIC120 and foEs is not very good in the present version of GAIA, the results suggest a possibility that VIC120 can be used as an index to predict the daily occurrence of Es layers. The fact that VIC120 is in better agreement with foEs than VIC at other altitudes also suggests that the accumulation of metallic ions around 120 km altitude plays an important role in Es layer formation.

Es layer prediction requires the prediction of thermospheric winds, which must be accomplished without using the meteorological reanalysis data in GAIA. To test the predictivity of neutral winds in the lower thermosphere, we compared two simulations: one with JRA-55 data and one without JRA-55 data. The simulated eastward neutral winds at 120 km in Fig. 10 demonstrate that even without meteorological reanalysis data, almost the same neutral wind in the lower thermosphere can be produced as that with JRA-55 data for about 3 or 4 days ahead, indicating that GAIA is able to reproduce meteorological processes in the lower atmosphere fairly realistically. To further improve the accuracy of neutral wind prediction in the thermosphere, it is possible to incorporate weather forecast data of the lower atmosphere into GAIA. This method may enable us to make 1-week forecasts of Es layer occurrence.

We adopted VIC120 obtained by GAIA as an index for foEs prediction, but other parameters or their combination might give a better result than those in the present study. Since our present analysis is only for the period of July–December 2019, further analysis of data of extended periods is necessary to obtain more suitable parameters that improve the prediction accuracy.

As mentioned before, it is possible to simulate Es layers by including metallic ion species in GAIA. We are currently developing a simulation model that self-consistently reproduces an Es layer in the neutral wind in GAIA. This approach, however, has some uncertainties in the initial distribution of metallic ions, which originate from meteor influx into the upper atmosphere. Since the rate of meteor influx has been roughly estimated (Singer et al. 2004; Campbell-Brown and Jones 2006; Fentzke and Janches 2008), empirical models of the meteor influx rate can be used in upper atmosphere models (Feng et al. 2013).

There is also a significant uncertainty in the thermospheric wind in numerical models, which is critical to modeling Es layer formation. Unfortunately, there are not enough observations of the neutral wind in the lower thermosphere, and it is practically impossible to validate the modeled neutral winds in the lower thermosphere. We incorporate the JRA-55 meteorological reanalysis data in GAIA in the lower atmosphere below about 30 km altitude, but there are some limitations to the accuracy of the lower-atmospheric parameters. Despite some uncertainties with the parameters in models, numerical modeling of the Es layer is a promising approach to the practical prediction of Es layer occurrence.

At the Space Weather Forecast Center of NICT, a real-time forecasting system for the ionosphere has recently been developed. The system can predict atmosphere–ionosphere conditions for 3 or 4 days ahead. Using the forecast data obtained by the system, we have developed a tentative prediction scheme and given preliminary results for the prediction of Es layer occurrence. The results indicate that VIC or other ionospheric parameters derived from a numerical model can be used as a practical index for the prediction of Es layer occurrence.

Availability of data and materials

All the ionosonde data used in this study are available from website (http://wdc.nict.go.jp/IONO/index_E.html). GAIA simulation data are available upon request to H. Jin (jin@nict.go.jp).

Abbreviations

DOY:

Day of year

Es:

Sporadic E

GAIA:

Ground-to-topside model of Atmosphere and Ionosphere for Aeronomy

GAIA-RF:

Real-time and forecast version of GAIA

HF:

High-frequency

IGRF:

International Geomagnetic Reference Field

JRA-55:

Japanese 55-year reanalysis

JST:

Japan Standard Time

NCEI:

National Centers for Environmental Information

NICT:

National Institute of Information and Communications Technology

NOAA:

National Oceanic and Atmospheric Administration

UT:

Universal time

VHF:

Very high-frequency

VIC:

Vertical ion convergence

VIC120 :

Vertical ion convergence at 120 km altitude

VIC120, d-ave :

Daily average of vertical ion convergence at 120 km altitude

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Acknowledgements

This work was carried out with support from the Project for Solar-Terrestrial Environment Prediction (PSTEP) in Grant-in-Aid for Scientific Research on Innovative Areas from MEXT/Japan. The meteorological reanalysis data are obtained from the cooperative research project of the JRA-55 long-term reanalysis by the Japan Meteorological Agency (JMA) and the Central Research Institute of Electric Power Industry (CRIEPI). Part of this work was carried out as the commissioned work (0155-0133 Promotion of observation and analysis of radio wave propagation) of the Ministry of Internal Affairs and Communications, Japan.

Funding

This work was supported by JSPS KAKENHI Grant Numbers JP15H03733 and JP15H05815. Part of this work was also supported by the commissioned work (0155-0133 Promotion of observation and analysis of radio wave propagation) of the Ministry of Internal Affairs and Communications, Japan.

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HS proposed the topic and analyzed the data of GAIA simulation and foEs data. HS, HJ, YM, and HF developed the GAIA model. HJ and YM carried out simulation and created the simulation database. CT developed the real-time GAIA system and constructed the database. All authors read and approved the final manuscript.

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Correspondence to Hiroyuki Shinagawa.

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Shinagawa, H., Tao, C., Jin, H. et al. Numerical prediction of sporadic E layer occurrence using GAIA. Earth Planets Space 73, 28 (2021). https://doi.org/10.1186/s40623-020-01330-y

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Keywords

  • Sporadic E layer
  • Wind shear
  • Occurrence
  • Prediction
  • GAIA
  • Model
  • Vertical ion convergence