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A regional model for the prediction of M(3000)F2 over East Asia
Available online at www.sciencedirect.com
ScienceDirect Advances in Space Research xxx (2020) xxx–xxx www.elsevier.com/locate/asr
A regional model for the prediction of M(3000)F2 over East Asia Jian Wang a,b, Feng Feng c,⇑, Hong-mei Bai a,d, Yue-Bin Cao b,e, Qiang Chen b,e Jian-guo Ma b,f a School of Microelectronics, Tianjin University, Tianjin, China Qingdao Institute for Ocean Technology, Tianjin University, Qingdao, China c Department of Electronics, Carleton University, Canada d School of Mathematics and Statistics, Hulunbuir College, Hulunbuir, China e School of Electrical and Information Engineering, Tianjin University, Tianjin, China f School of Computer, Guangdong University of Technology, Guangzhou, China b
Received 28 July 2019; received in revised form 19 December 2019; accepted 21 January 2020
Abstract Research on empirical or physical models of ionospheric parameters is one of the important topics in the field of space weather and communication support services. To improve the accuracy of predicting the monthly median ionospheric propagating factor at 3000 km of the F2 layer (identified as M(3000)F2) for high frequency radio wave propagation, a model based on modified orthogonal temporal– spatial functions is proposed. The proposed model has three new characteristics: (1) The solar activity parameters of sunspot number and the 10.7-cm solar radio flux are together introduced into temporal reconstruction. (2) Both the geomagnetic dip and its modified value are chosen as features of the geographical spatial variation for spatial reconstruction. (3) A series of harmonic functions are used to represent the M(3000)F2, which reflects seasonal and solar cycle variations. The proposed model is established by combining nonlinear regression for three characteristics with harmonic analysis by using vertical sounding data over East Asia. Statistical results reveal that M(3000)F2 calculated by the proposed model is consistent with the trend of the monthly median observations. The proposed model is better than the International Reference Ionosphere (IRI) model by comparison between predictions and observations of six station, which illustrates that the proposed model outperforms the IRI model over East Asia. The proposed method can be further expanded for potentially providing more accurate predictions for other ionospheric parameters on the global scale. Ó 2020 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Regional modeling; Ionospheric propagating factor at 3000 km of the F2 layer; Reconstruction; Orthogonal temporal-spatial functions; East Asia
1. Introduction Ionosphere is the layer of the atmosphere that lies between 60 and 1000 km above Earth’s surface and comprises three distinct layers, namely the D layer, E layer, and F layer, which is normally divided into F1 and F2
⇑ Corresponding author.
E-mail address: [email protected] (F. Feng).
layers. The propagation factor at a distance of 3000 km of the F2 layer (identified as M(3000)F2) is one of the important high-frequency radio wave propagation parameters defined as the ratio of the Maximum Usable Frequency (MUF) at a distance of 3000 km to the F2layer critical frequency. MUF represents the optimum frequency at which a signal can be received at a distance of 3000 km. Therefore, M(3000)F2 was widely applied in civil and military fields, such as high-frequency communication (Angling et al., 2009; Yan et al., 2011), tracking
https://doi.org/10.1016/j.asr.2020.01.026 0273-1177/Ó 2020 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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J. Wang et al. / Advances in Space Research xxx (2020) xxx–xxx
(Yao et al., 2013), localization (Swamy et al., 2013), and spectrum management (Wang et al., 2013). M(3000)F2 can be estimated from vertical-incidence (Hoque and Jakowski, 2012; Mcnamara and Thompson, 2015; Pezzopane and Scotto, 2007; Pijoan et al., 2014) and oblique ionosonde (Wang et al., 2014). In the absence of observations stations, these parameters (such as M (3000)F2, foF2 and the peak height of F2 layer hmF2) have to be deduced using empirical ionospheric models, which can provide the scientists, engineers, and educators with available empirical values (Bilitza et al., 2011). At present, the most common choice for predicting characteristics of the ionosphere is the International Reference Ionosphere (IRI) model, which mainly describes long-term variations of M(3000)F2 and several additional parameters. The IRI model is well known as the recommended international standard. Researchers have developed and improved empirical ionospheric models through observations. For example, the IRI model has been steadily improved with newer data and better modeling techniques by the joint working group of the Committee on Space Research and the International Union of Radio Science (URSI) (Bilitza et al., 2011). This model has evolved into a number of important editions, including IRI-78 (Rawer et al., 1981), IRI-1990 (Bilitza, 1990), IRI-2000 (Bilitza, 2001), IRI-2007 (Bilitza and Reinisch, 2008), IRI-2012 (Bilitza et al., 2014), and IRI2016 (Bilitza et al., 2017). Oyeyemi et al. (2007), Oronsaye et al. (2014) and Xenos (2002) used a neural network to develop new models of M(3000)F2. Liu et al. (2008) and Zhang et al. (2010) proposed a series of models based on Empirical Orthogonal Function (EOF) analysis method, which are also used to predict foF2 (Ercha et al., 2011), peak height (Zhang et al., 2009; Zhang et al., 2012), total electron content (Ercha et al., 2012; Mao et al., 2008; Wan et al., 2012; Zhao et al., 2005) and other ionospheric parameters. In general, the abovementioned efforts focused on developing global models for predicting M(3000)F2 and other ionospheric parameters. Recently, the scientific community focused on the development of regional models rather than global models because the regional models can provide a more accurate ionospheric representation over restricted areas (Anna et al., 2017; Cao and Sun, 2009; Mao et al., 2008; Nandi and Bandyopadhyay, 2015; Perna et al., 2017; Pietrella, 2014; Xenos, 2002; Zolesi et al., 2004). This paper focuses on the ionosphere over East Asia, which significantly varies due to its coverage of the high, middle, and low-latitude regions. To achieve more accurate prediction of the M (3000)F2 over East Asia, this paper proposes a new longterm prediction model for M(3000)F2 based on orthogonal temporal-spatial reconstruction using ionosonde data. This model is established with orthogonal functions and a series of harmonic parameters, which are determined through reconstructing vertical sounding data over the East Asia region.
2. Methodology 2.1. Fundamental algorithm Previous findings have revealed that variation of ionospheric parameters such as M3000F2 is mainly controlled by some independent processes that can be separated. Therefore, the EOF is an effective way for modeling ionospheric parameters (Pearson 1901; Dvinskikh 1988). Compared with other expansion methods, the EOF not only reduces the computation time but also reduces the number of modeling parameters (Zhang et al., 2009; Zhao, et al. 2005). In particular, the mathematical procedure involved in EOF transforms a dataset into a number of uncorrelated orthogonal principal components (Bai, et al., 2018; Liu et al., 2008), which well suits the prediction of M(3000) F2 and other homologous ionospheric parameters (Zhang et al., 2010). In this study, we use the EOF for the proposed model development. Following the basic idea of EOF, a set of nonlinear functions was developed to describe the dependencies of M(3000)F2 on geographical position, year (including solar activity) , month (or season) and time as Mð3000ÞF2ðk; u; F 10:712 ; R12 ; m; T Þ ¼ F d M ð3000ÞF2ðk; u; F 10:712 ; R12 ; mÞ; T ¼ F d F g k; u; c M ð3000ÞF2ðF 10:712 ; R12 ; mÞ ; T ¼ F d F g ðk; u; F a ðF 10:712 ; R12 ; mÞÞ; T
ð1Þ
where F d , F g and F a are modeling functions including a set of coefficients that respectively describe diurnal, geographical, annual and seasonal dependencies of M(3000) F2; k is geographical latitude; u is geographical longitude; F10.712 is 12-monthly running mean 10.7 cm solar radio flux (expressed in units of 10–22 W m2 Hz1); R12 is 12monthly running mean sunspot number; m is the index of month; T is a scalar representing universal time. Accordingly, the significance of the work in this paper is to determine these functions (F d , F g and F a ) and their relationship with respect to the modeling parameters. Fig. 1 give the flow chart of the model reconstruction and verification. As shown in Fig. 1, we firstly separate M(3000)F2 into temporal and spatial variables. Secondly, we model the temporal and spatial parts: the temporal part is modeling for solar activity and annual dynamic characteristics of M(3000)F2, while the spatial part is modeling for geographical space variation of M(3000)F2. In these two modeling progresses, the modeling parameters are selected, and the relationship between M(3000)F2 and the abovementioned modeling parameters is then derived. For each observed station, we analyze the solar activitybased annual dynamic characteristic of M(3000)F2, and define harmonic functions of M(3000)F2 with respect to the parameters F10.712, R12 and month. We then determine the coefficients of the temporal harmonic functions with observed data. For special solar activity index (F10.712
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
J. Wang et al. / Advances in Space Research xxx (2020) xxx–xxx
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Retain the M(3000)F2 characteristics a numerical mapping technique based on the temporal and spatial empirical orthogonal function.
For every observed station, analyze the solar activitybased, annual dynamic characteristic of M(3000)F2. Define harmonic functions between M(3000)F2 with solar activity and annual index. Determine the coefficient by the least square fitting approach with observed data. Temporal modeling
Observed data
Spatial modeling For special time period, analyze geographical changes of M(3000)F2.
Define M(3000)F2 with the harmonic functions of geographical coordinates
Determine the coefficient by the least square fitting approach with observed data.
Model Verification: (1) Calculate M(3000)F2 of the given predicting time, latitude and longitude by using the reconstruction model (2) Compare the predicted values with IRI predicted values and observed values
Analyze diurnal characteristics of M(3000)F2. Define M(3000)F2 numerical map function is modeled by Fourier time series. Determine the maximum number of harmonics by the least square fitting approach with observed data.
IRI Module Calculate M(3000)F2 of the given predicting time, latitude and longitude by using the IRI model
Fig. 1. Flow chart of the model reconstruction and verification.
and R12), month and universal time, we analyze geographical changes of M(3000)F2 and define the harmonic functions between M(3000)F2 and the geographical parameter. Next, we determine the coefficients of the spatial harmonic functions by the least square fitting approach with observed data. Finally, we model the diurnal dynamic characteristics of M(3000)F2 by using orthogonal Fourier function, and then, we determine the maximum number of harmonics by the least square fitting approach with observed data. As described, the model and relative parameters need to be determined from observations. As shown in Fig. 2 and Table 1, the present study uses ionospheric sounding data for the years from 1949 to 2018 recorded at 15 stations in Asia for modeling (11 out of 15 in years of 1949–2012) and verification (6 out of 15 in years of 2013–2018). Data of M(3000)F2 used in this work can be downloaded from National Oceanic and Atmospheric Administration website (ftp://ftp.swpc.noaa.gov/pub/lists/iono_month), ICSU World Data System (http://wdc.nict.go.jp/IONO/ HP2009/ISDJ/manual_txt-E.html) and Australian government-Bureau of Meteorology Space Weather service (ftp://ftp-out.sws.bom.gov.au/wdc/iondata/medians). As shown in Fig. 3a, the above stations were chosen because the time period covered both ascending and
Fig. 2. Distribution of stations used for modeling and verification.
descending phases of about six solar cycle activities. Not all stations provided data equally distributed over the study period. Some stations (such as Taipei) provided data from 1954 to 1996, some (such as Kokubunji) provided data from 1958 to 2018, and some did not have data for a com-
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Table 1 Geographic coordinates and measured data volume of the ionosonde stations used for modeling and verification. Station Label
Station Name
Geog. L at. (oE)
Geog. Long. (oN)
Years of modeling
Data volume for modeling (entries)
Years of verification
Data volume for verification (entries)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Akita Beijing Chongqing Guangzhou Hainan ICheon Jeju Kokubunji Manila Macau Okinawa Seoul Taipei Wakkanai Yamagawa
39.70 40.00 29.50 23.10 18.30 37.00 33.50 35.70 14.60 22.10 26.30 37.20 25.00 45.40 31.20
140.10 116.30 106.40 113.40 109.3 128.00 126.50 139.50 121.10 113.30 127.80 126.60 121.50 141.70 130.60
1966–1993 1979–2008 1979–2008 1979–2008 – – – 1958–2012 1952–1978 – 1972–2012 1973–1994 1954–1996 1949–2012 1965–2012
6635 6480 6696 6936 – – – 15,984 7104 – 9097 2784 10,512 15,441 10,064
– – – – 2003–2004 2013–2018 2013–2018 – – 1958–1965 2013–2018 – – 2013–2018 –
– – – – 264 1198 1771 – – 720 1680 – – 1614 –
plete solar activity cycle. A station was used in reconstructing the model as long as it could provide at least six years of data within a solar cycle. For the collected data, the following processing is done: (1) the monthly median values of M(3000)F2 for every station were calculated; (2) the sampling interval for 60 min was selected considering the periods of observations include 15, 30, and 60 min; (3) the stations with less than half solar activity period or no recent measurements was verified (e.g., Hainan station only has data for the years of 2003–2004, Jeju station only has data for the years of 2013 and 2018). As shown in Fig. 3b, the solar activity parameters used in this work can be downloaded from Australian government – Bureau of Meteorology Space Weather service (http://www.sws. bom.gov.au/Solar/1/6). To check the model accuracy, the root-mean-square error (RMSE, r) was calculated between model-derived predictions of M(3000)F2 and observations as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u H u1 X 2 r¼t ð2Þ Mð3000ÞF2OBS h Mð3000ÞF2MOD h H h¼1 where M(3000)F2MOD is the model-derived prediction of M(3000)F2; M(3000)F2OBS is the observation of M(3000) F2; H is the number of M(3000)F2 data points. 2.2. Modeling progress 2.2.1. Modeling for solar activity, and annual and seasonal dynamic characteristics The level of solar activity is usually described by two solar indices: (1) the sunspot number and (2) the flux of solar radio waves at a wavelength of 10.7 cm (F10.7). The former is affected by the photosphere and the low layer of the chromosphere, whereas the latter is determined by the corona and high layer of the chromosphere
(Afraimovich, et al., 2008; Zhang et al., 2012). It is well known that these two parameters affect the annual and seasonal dynamic characteristics of M(3000)F2. The correlation coefficients between the M(3000)F2 monthly median values and the twelve-month running mean value of solar indices at sample station (Wakkanai) is fully confirmed in Fig. 4. As shown in Fig. 4, the variation trends of the two types of correlation coefficients are generally similar, but different in some trivial detail. There are superior or inferior between the two types of correlation coefficients during certain hours and months. Especially after noon (from 12:00 to 20:00 clock) in summer, the correlation coefficients between M(3000)F2 and the two solar activity parameters are obviously different. Accordingly, for given specific geographic coordinates and the local time, we can derive a formulation to map the solar cycle variations and the seasonal index (annual, semi-annual, and monthly) to M(3000)F2, which can be written as the harmonic function Mð3000ÞF2ðF 10:712 ; R12 ; mÞ K P J P bk;j F 10:712 j cosð2pkm=12Þ þ ¼ k¼0 j¼0
ck;j F 10:712 j sinð2pkm=12Þ þ b0 k;j R12 j cosð2pkm=12Þþ c0 k;j R12 j sinð2pkm=12Þ ð3Þ where k = 1, 2, 3, 4 harmonics used to represent annual, semi-annual, seasonal and monthly cycles, j is the power exponent of the solar cycle parameter F10.712 or R12. The maximum harmonic orders K and J can be determined by the regression analysis. The coefficients bk,j, ck,j, b0 k,j and c0 k,j can also be derived using observed data of given station and corresponding F10.712 and R12 as follows
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Fig. 3. The time of data collected from ionosonde station and corresponding to different solar activity parameters. (a) The time of data collected from 15 ionosonde station; (b) F10.712 and R12 for the years of 1949–2018.
2 6 6 T 6 6 CC 6 6 6 4
b0;0
3
2
M0 ð3000ÞF21
3
^ ð3000ÞF2ðF 10:712 ; R12 ; mÞ ¼ F a ðF 10:712 ; R12 ; mÞ M
7 7 6 6 M0 ð3000ÞF2 7 b0;1 7 2 7 7 6 7 7 6 ¼ C6 7 .. 7 .. 7 7 6 7 6 . 7 . 5 5 4 0 0 c K;J M ð3000ÞF2O
ð4Þ
where M0 (3000)F2 is observed value of M(3000)F2, O is the maximum number of observed data, and 2 6 6 6 6 C¼6 6 6 6 4
3
1
1
1
ðF 10:712 Þ1
ðF 10:712 Þ2
ðF 10:712 ÞO
.. .
.. .
..
.. .
ðR12 Þ1 J sinJ
2pKm 12
ðR12 Þ1 J sinJ
2pKm 12
.
ðR12 ÞO J sinJ
2pKm
7 7 7 7 7 7 7 7 5
12
Fig. 5 shows the RMSE of M(3000)F2 with different maximum regression orders J and K. It is seen that better convergence and robustness are achieved with J = 2 than with J = 1. Moreover, the regression result using the two solar activity index parameters (F10.712 or R12) is better than that using only a single parameter of F10.712 or R12. As shown in Fig. 5, therefore, we determine the orders of J as 2 and K as 3. Substituting J = 2 and K = 3 into (3), we can derive the formulation as
¼
3 P 2 P k¼0 j¼0
bk;j F 10:712 j cos 2pkm þ 12
ck;j F 10:712 j sin 2pkm þ b0 k;j R12 j cos 2pkm þ 12 12 c0 k;j R12 j sin 2pkm 12 ¼ b0;0 þ b0;1 F 10:712 þ b0;2 F 10:712 2 þ þ b1;2 F 10:712 2 cos 2pm þ b1;0 þ b1;1 F 10:712 cos 2pm 12 12 2pm b2;0 þ b2;1 F 10:712 cos 6 þ b2;2 F 10:712 2 cos 2pm þ 6 2pm b3;0 þ b3;1 F 10:712 cos 3 þ b3;2 F 10:712 2 cos 2pm þ 3 c0 1;0 c0 2;0 c0 3;0
ð5Þ
::: þ c0 1;2 R12 2 sin 2pm þ þ c0 1;1 R12 sin 2pm 12 12 2pm 2pm 2 0 0 þ c 2;1 R12 sin 6 þ c 2;2 R12 sin 6 þ þ c0 3;2 R12 2 sin 2pm þ c0 3;1 R12 sin 2pm 3 3
Based on the determined orders of J = 2 and K = 3, Fig. 6 shows a sample of temporal reconstructed coefficients bk,j, ck,j, b0 k,j and c0 k,j at Wakkanai station. The label numbers from 1 to 48 represent the coefficients b0,0, b0,1, b0,2, c0,0, c0,1, c0,2, b1,0, b1,1, b1,2, c1,0, c1,1, c1,2, b2,0, b2,1, b2,2, c2,0, c2,1, c2,2, b3,0, b3,1, b3,2, c3,0, c3,1, c3,2, b0 0,0, b0 0,1,
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Fig. 4. Correlation coefficients between the monthly median values of M(3000)F2 and (a) the twelve-month running mean value of F10.7, (b) the monthly median values of M(3000)F2 and twelve-month running mean value of sunspot number, at Wakkanai.
b0 0,2, c0 0,0, c0 0,1, c0 0,2, b0 1,0, b0 1,1, b0 1,2, c0 1,0, c0 1,1, c0 1,2, b0 2,0, b0 2,1, b0 2,2, c0 2,0, c0 2,1, c0 2,2, b0 3,0, b0 3,1, b0 3,2, c0 3,0, c0 3,1 and c0 3,2, respectively. As shown in Fig. 6, the c0 0,1 is obviously different from other coefficients. The coefficient b0,0 during 19:00LT–20:00LT is obviously higher than that during other time period. This is because that the influence of solar activity and seasonal variation on M(3000)F2 is different during different time periods. These temporal reconstructed coefficients and two solar activity index parameters (F10.712 or R12) can be substituted into (3) to calculate the predicted values of corresponding ionosonde stations. More details will be further given in Section 2.3.
2.2.2. Modeling for geographical space variation Ionospheric parameters including M(3000)F2 have an irregular non-homogeneous spatial distribution. Therefore, the spatial characteristics of M(3000)F2 and other ionospheric parameter have been modeled and improved without interruption over several years. At present, numerous techniques based on different empirical or mathematical methods have been discussed to describe ionospheric spatial characteristics, including inverse distance weighted interpolation (Pradipta et al., 2016), moving surface interpolation (Deng and Tang, 2011), spherical harmonic (Legendre) functions depending on latitude and longitude (Jones and Gallet, 1962), along with statistical approaches such as kriging (Huang et al., 2017; Stanislawska et al., 1996). Considering that variations of ionospheric parame-
ters are controlled by both the orientation of the Earth’s rotational axis and the configuration of the geomagnetic field, Rawer presented a coordinate system expressed by the modified dip latitude (Rawer, 1984; Zhang et al., 2009). Therefore, such a coordinate system (Ercha et al., 2011; Kitanidis, 1997; Swamy, et al., 2013) has been adopted in many studies, showing that the global features and variability within the ionosphere can be well captured. We therefore propose to represent M(3000)F2 with the harmonic functions of the magnetic dip latitude and its
Fig. 5. RMSE of different regression parameters and analysis orders. K is the maximum harmonic order that represents the upper bound of annual, semi-annual, seasonal and monthly cycle, and J is the maximum harmonic order that represents the upper bound of the solar cycle.
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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modified value instead of simple geographic coordinates. The numerical mapping function is derived as Mð3000ÞF2ðk; uÞ ¼
L n X
gl ½Gðmðk;uÞÞl þ gl 0 ½Gðlðk;uÞÞl
o
ð6Þ
l¼0
where m(k,u) is magnetic dip latitude which is the function of latitude and longitude; l(k,u) is modified magnetic dip latitude which is the function of latitude and longitude; ‘G()’ is sine or the other type function of m or l; l is power exponent of G(m) and G(l); L is the maximum harmonic order number. The magnetic dip latitude is defined by the downward and horizontal components of the geomagnetic field (VanZandt et al., 1972), and the modified magnetic dip latitude is defined by arctan [m(k, u)/cos(u)0.5] (Rawer, 1984). The maximum harmonic order number L and the functional form of ‘G()’ can be determined by the regression analysis. The coefficients gl and g0l can be derived using M(3000)F2 of 11 modeling station and corresponding m(k,u) and l(k,u) as follows: 3 2 3 2 Mð3000ÞF21 g0 6 7 6 Mð3000ÞF22 7 7 6 T 6 g 1 7 7 7 6 ð7Þ CC 6 . 7 ¼ C6 . 7 6 .. 5 4 .. 5 4 g0 L where 2
7
Fig. 7 shows a bar chart for the RMSE of M(3000)F2 for different regression parameters and order. Fig. 7 shows that (1) the RMSE of twofold regression using the m and l is obviously lower than that of regression using only one of these parameters and (2) the accuracy using a sinusoidal function is better than that directly using the m or l. We therefore choose twofold regression with m and l to determine a third-order sinusoidal harmonic function. Substituting L = 3 into (6), we can simplify the formulation as
Mð3000ÞF211
1
6 Gðmðk1 ; u ÞÞ 1 6 C¼6 .. 6 4 . Gðlðk1 ; u1 ÞÞ
L
3
1
1
Gðmðk2 ; u2 ÞÞ .. .
.. .
Gðmðk2 ; u2 ÞÞ .. .
Gðlðk2 ; u2 ÞÞ
L
Gðlðk2 ; u2 ÞÞ
L
7 7 7 7 5
Fig. 7. The RMSE distribution of M(3000)F2 with different parameters and maximum harmonic order.
Fig. 6. Sample of temporal reconstructed coefficients at Wakkanai station. The label numbers represent the coefficientsb0,0, b0,1, b0,2, c0,0, c0,1, c0,2, b1,0, b1,1, b1,2, c1,0, c1,1, c1,2, b2,0, b2,1, b2,2, c2,0, c2,1, c2,2, b3,0, b3,1, b3,2, c3,0, c3,1, c3,2, b0 0,0, b0 0,1, b0 0,2, c0 0,0, c0 0,1, c0 0,2, b0 1,0, b0 1,1, b0 1,2, c0 1,0, c0 1,1, c0 1,2, b0 2,0, b0 2,1, b0 2,2, c0 2,0, c0 2,1, c0 2,2, b0 3,0, b0 3,1, b0 3,2, c0 3,0, c0 3,1 and c0 3,2, respectively.
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Fig. 8. Sample contours of spatial reconstructed coefficients gl and g0l against months and universal time during low and high solar activities. The label a, b, c, d, e f, and g represent the min-max normalization of spatial reconstructed coefficients g0, g1, g2, g3, g0 1, g0 2, and g0 3 during high solar activity epoch respectively. The label h, i, j, k, l, m, and n represent the min-max normalization of spatial reconstructed coefficients g0, g1, g2, g3, g0 1, g0 2, and g0 3 low solar activity epoch respectively.
M ð3000ÞF2ðk; uÞ ¼ F g ðk; uÞ 3
P ¼ g0 þ gl sinl ðmÞ þ gl 0 sinl ðlÞ
ð8Þ
l¼1
¼ g0 þ g1 sinðmÞ þ g2 sin ðmÞ þ g3 sin ðmÞþ g1 0 sinðlÞ þ g2 0 sin2 ðlÞ þ g3 0 sin3 ðlÞ 2
3
Based on the determined orders L = 3, sinusoidal function of magnetic dip latitude and modified value, Fig. 8 shows samples of spatial reconstructed coefficients gl and g0l against months and universal time during low and high solar activities. In Fig. 8, the min–max normalization of spatial reconstructed coefficients is calculated for better viewing.
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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2.2.3. Modeling for diurnal dynamic characteristics There are numerous approaches for ionospheric modeling for diurnal dynamic characteristics of ionospheric parameters, such as Fourier analysis (ITU, 2012) and spline methods (Deng and Tang, 2011; Hardy and Nelson, 1986; Sandwell, 1987; Scherliess and Fejer, 1999). Fourier expansion is known to be useful in characterizing periodic waveforms. Because M(3000)F2 inherently has diurnal periodicities, Fourier analysis outperforms other ionospheric modeling methods in constructing empirical models for M(3000)F2 prediction. In particular, M(3000) F2 numerical map of diurnal variations has been modeled using a Fourier function (Liu et al., 2008) with a period of 24 h as Mð3000ÞF2ðT Þ ¼
N h p p i X nT þbn sin nT an cos 12 12 n¼0
ð9Þ
where T is the given universal time; N is the maximum number of harmonics used to represent the diurnal variation and can be determined by the statistics analysis; n is the harmonic number expressed as (0, 1, . . ., N); an and bn are Fourier coefficients relevant to geographical coordinates and solar activity parameters. Combined with Sections 2.2.1 and 2.2.2, the coefficients an, and bn in (10) are determined by Fourier series decompositions (Jones and Gallet, 1962), i.e., 9 11 P > > > a0 ¼ 241 M ð3000ÞF2ðk; uÞ; > > > i¼12 > > = 11 P ð10Þ an ¼ 121 M ð3000ÞF2ðk; uÞ cosðn iT Þ; > i¼12 > > > > 11 > P > 1 bn ¼ M ð3000ÞF2ðk; uÞ sinðn iT Þ; > ; 12
i¼12
where M ð3000ÞF2ðk; uÞ is derived from spatial reconstructed coefficients (gl and g0l ) by using (9)
Fig. 9. The prediction example of M(3000)F2 against the maximum harmonic number N at Wakkanai station in May 2013.
9
h i M ð3000ÞF2ðk; uÞ ¼ g0 c M ð3000ÞF2ðF 10:712 ; R12 ; mÞ; s ¼ 1; 2;:::11 þ i 3 n h P gl c M ð3000ÞF2ðF 10:712 ; R12 ; mÞ; s ¼ 1; 2;:::11 sinl ðmÞþ l¼1 h i o gl 0 c M ð3000ÞF2ðF 10:712 ; R12 ; mÞ; s ¼ 1; 2;:::11 sinl ðlÞ
ð11Þ
where s = 1, 2,. . ., 11 corresponds to 11 modeling stations, and c M ð3000ÞF2 can be derived from temporal reconstructed coefficients (bk,j, ck,j, b0 k,j and c0 k,j) by using (5). In terms of (9), we analyzed the relationship between the prediction result of M(3000)F2 and the maximum harmonic number N. Fig. 9 shows a prediction example of M(3000)F2 against the maximum harmonic number N at Wakkanai station in May 2013. Fig. 10 shows the RMSE statistics result of 11 stations. As observed in Figs. 9 and 10, the maximum harmonic number N, is up to 11 in the above model to ensure the highest precision and robustness. Therefore, the maximum number of harmonics used to represent the diurnal variation is determined to be 11. Substituting N = 11 into (9), we can revise the formulation as Mð3000ÞF2ðk; u; F 10:712 ; R12 ; m; T Þ ¼ F d ðT Þ ¼ a0 ðk; u; F 10:712 ; R12 ; m;Þþ 11 p P an ðk; u; F 10:712 ; R12 ; mÞ cos 12 nT þ
n¼1
bn ðk; u; F 10:712 ; R12 ; mÞ sin
p 12
nT
ð12Þ
2.3. Prediction procedure With the aforementioned parameters reconstructed from least-square fitting regression, by given geographic coordinates (k, u), year, month, universal time, and solar activity factors F10.712 and R12, we can use the following steps for predicting M(3000)F2 as Fig. 11.
Fig. 10. The prediction RMSE with different maximum harmonic number.
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Fig. 11. The flow chart for calculating M(3000)F2 by using the proposed model.
Table 2 Verification stations, time and other corresponding characteristics. Label
Station
Year
Solar activity epoch
Month
Season
Geomagnetic Strom
Included in modeling
RMSEs of IRI model
RMSEs of PRM
a b c d e f
Hainan ICheon Jeju Macau Okinawa Wakkanai
2003 2015 2016 1961 2014 2017
Middle High Middle Low High Low
Jan. Mar. Jun. Aug. Feb. Oct.
Winter Equinox (spring) Summer Summer Winter Equinox (autumn)
No Yes No No No No
No No No No Yes Yes
0.12 0.13 0.21 0.40 0.18 0.12
0.11 0.10 0.11 0.34 0.10 0.08
3. Results and discussions To test the accuracy of the proposed reconstruction model (PRM), the performance of the PRM was compared with that of IRI-2016 (http://irimodel.org/IRI-2016) in terms of differences between model-derived predictions of M(3000)F2 and observations collected from Hainan, ICheon, Jeju, Macau, Okinawa, and Wakkanai stations. As shown in Table 2, the ionosonde data for 6 stations in high, middle and low solar activity years are selected. The abovementioned ionosonde data for 6 stations were used for verification because they cover four seasons of spring, summer, autumn and winter. Among these 6 sta-
tions, Hainan, ICheon, Jeju and Macau station are only for verification because their usable data mainly cover a few years less than half of the solar activity period. The other 2 stations (Okinawa and Wakkanai) have been both used in modeling and verification. The high solar activity years include 2014 and 2015. The middle activity years include 2003 and 2016. The low solar activity years include 1961 and 2017. Hainan and Okinawa stations are in winter. Jeju and Macau stations are in summer. ICheon and Wakkanai stations are in equinox that correspond to spring and autumn, respectively. Fig. 12 show examples of the diurnal variation in M (3000)F2 predicted using PRM, in comparison with the
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Fig. 12. Sample comparison of the diurnal behavior of monthly median M(3000)F2 predicted by IRI model and PRM.
IRI model and observations (OBS) collected at Hainan, ICheon, Jeju, Macau, Okinawa, and Wakkanai stations in Table 2. It can be seen that the prediction curves for M(3000)F2 obtained using both IRI model and PRM reflect the tendency of the diurnal variation characteristics whenever geomagnetic quiet and storm periods. The geomagnetic storm appeared in March 2015 (shown in Fig. 12b), and the maximum Dst index reached 223 nT (Zolotukhina et al., 2017). To estimate the accuracy of the proposed model, a statistical analysis of the differences between the predicted monthly mean values of M(3000)F2 from PRM and measured values is made by calculating average RMSE as follows (Oronsaye et al. 2014) rave ¼
W 1 X rw w w
ð13Þ
where w represents the number of statistical parameters such as ionosonde stations, years, seasons, months or others. As shown in Fig. 12 and Table 2, the average RMSEs of IRI and PRM are 0.20 and 0.12. The percentage error improvement between IRI and PRM is evaluated using the relations (Oronsaye et al. 2014):
d¼
rIRI rPRM rIRI
100%
ð14Þ
where rIRI and rPRM are the RMSEs of the predicted values of IRI model and PRM with respect to the measured values of M(3000)F2, respectively. From (14), the percentage error improvements between IRI and PRM of Hainan, ICheon, Jeju, Macau, Okinawa, and Wakkanai stations are 8.22%, 27.21%, 46.35%, 16.35%, 42.66%, and 30.24%. The average value of the percentage error improvements of the abovementioned six stations is 28.51%. Fig. 13 shows three sample plots for the comparisons of the monthly mean values of M(3000)F2 predicted values from the PRM and the IRI model and measured values obtained from ionosonde stations for the years of high solar activity (2013), middle solar activity (2015) and low solar activity (2017). All three stations cover 4 seasons and 12 months of the whole year. As shown in Fig. 13, these graphs serve to illustrate that IRI model and PRM successfully predict the general yearly variation shape of behavior of M(3000) F2. At the same time, it is found that the results also reflect the annual, semi-annual, seasonal, and monthly variation characteristics and the solar cycle variations of M(3000)F2.
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Fig. 13. Sample plots of different model predicted values and measured value of M(3000)F2 at Wakkanai, Jeju and Okinawa station for the years of 2013 (high solar activity year), 2015 (middle solar activity year) and 2017 (low solar activity year). Table 3 The RMSE between measured values of M(3000)F2 and predicted values of IRI model and PRM for three solar activity epochs, four seasons, four local time periods and six stations. Statistical analysis item
RMSE
Percentage error improvement between IRI and PRM (%)
IRI
PRM
Solar activity epochs
High Middle Low
0.18 0.17 0.24
0.15 0.11 0.14
20.75 38.47 40.78
Seasons
Spring (Mar., Apr., May) Summer (June, July, Aug.) Autumn (Sep., Oct., Nov.) Winter (Jan., Feb., Dec.)
0.20 0.20 0.16 0.22
0.12 0.12 0.12 0.12
43.82 42.42 22.24 45.56
Local time periods
Midnight (22:00–2:00) Sunrise (5:00–9:00) Noon (10:00–14:00) Sunset (16:00–20:00)
0.18 0.19 0.23 0.16
0.13 0.14 0.12 0.11
29.59 28.15 45.99 28.98
Stations
Jeju Okinawa ICheon Kokubunji Wakkanai Yamagawa
0.22 0.19 0.21 0.18 0.18 0.20
0.19 0.10 0.14 0.11 0.10 0.10
15.60 46.65 33.65 41.79 44.62 48.84
0.20
0.12
36.66
Average
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Fig. 14. Statistical average RMSE of IRI model and PRM. (a) average RMSE for the years of 2013–2018; (b) average RMSE for 12 months of the whole year; (c) average RMSE for the local time from 0:00 to 23:00.
In addition, we respectively analyzed the average RMSEs of six-years (2013–2018), 12-months (1–12) and 24-hours (local time 0:00–23:00) using (13). Fig. 14 shows that statistical RMSEs of the monthly mean values of M (3000)F2 predicted values from PRM are compared with those determined by the IRI model, which correspond to 6-years, 12-months and 24-hours by (13). It can be seen that the predicted average RMSE of PRM is lower than that of the IRI model. As shown in Fig. 14a, the yearly trend of average RMSE of PRM is consistent with that of IRI model, and there is a rising trend for the years from 2015 to 2018. As shown in Fig. 14b, the average RMSEs of IRI model during September to December are lower than those during other months. The average RMSEs of PRM during January, May, June, July and September are lower than those during other months. As shown in Fig. 14c, the diurnal average RMSEs of PRM are more flat than those of IRI model. Table 3 presents the average RMSEs between measured values of M(3000)F2 and predicted values of two models (IRI model and PRM) under different conditions, which correspond to three solar activity epochs (high, middle and low), four seasons (Spring, Summer, Autumn, and Winter) of the whole year, four time periods (midnight, sunrise, noon, and sunset) of the whole day. The percentage error improvement between IRI and PRM is calculated as listed in Table 3. The average RMSEs and percentage error improvement are based on measured data of M (3000)F2 and predicted values for the years of 2013– 2018. For different statistical conditionS, the iterative computation would be done by (13) and (14). These conclusions are drawn from Fig. 14 and Table 3: (a) the predicted results from PRM perform better than
those from the IRI model; (b) the percent error improvement of the PRM over the IRI model during low solar activity year is the highest among all the years; (c) the percentage error improvement of the PRM over the IRI model during winter is the highest among all the seasons; (d) the percent error improvements of the PRM over the IRI model during noon are higher than other time periods; and (e) the percent error improvements of the PRM over the IRI model at Yamagawa stations are maximum. Fig. 15 shows the spatial distribution (with intervals of 5° for both geographic longitude and latitude) of monthly median values of M(3000)F2 predicted using PRM and IRI model for June 2013 at 4:00 UT (corresponding to local time 10:00–14:00 in approximate noon) and December 2017 at 16:00 UT (corresponding to local time 22:00– 02:00 in approximate nighttime). The reason for this choice is that we want to analyse the recent years during high, middle and low solar activity epochs. Fig. 15(a) and (b) shows that the spatial distribution maps have similar shape. A similar situation also appears in (c) and (d). In conclusion, the spatial validity can be confirmed for PRM. 4. Summary and conclusions This paper proposed a model for predicting M(3000)F2, in which a series of harmonic functions used to represent the geographical spatial variation and reflects seasonal and solar cycle variations have been rebuild. The three main important features of the proposed model are (a) the ionospheric index F10.7 and sunspot number have been introduced together in the model to assist in the temporal reconstruction; (b) this model has expressed M(3000)F2
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Fig. 15. Sample contour of different model predicted values of M(3000)F2 during high and low solar activity years: (a) derived from IRI model at 04:00 UT (approximate noon in summer) June 2013; (b) derived from PRM at 04:00 UT (approximate noon in summer) June 2013; (c) derived from IRI model at 16:00 UT (approximate midnight in winter) December 2017; derived from PRM at 16:00 UT (approximate midnight in winter) December 2017.
with harmonic functions representing the annual, semiannual, seasonal, monthly and solar cycle variations; and (c) the geomagnetic dip latitudes and modified value have been introduced together in the model to assist the proposed model in the spatial reconstruction. Prediction results of the proposed model agree well with observations. Both the accuracy of the predictions of the IRI model and our proposed model have been analyzed by comparisons with the observations. It was concluded that our proposed model is more accurate than the IRI model over the East Asia region. To use our proposed model, the following inputs are required: latitude, longitude, month, hour, the twelvemonth running mean value of the monthly flux of solar radio waves at 10.7 cm, and the twelve-month running mean value of the monthly sunspot number. Future research is expected to extend the suitability of the proposed model to wider regions and even the globe. Moreover, this modeling approach is expected to be used in
predicting other ionospheric parameters such as peak height and total electron content. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research was funded by the National 973 Program of China (No. 61331901) and Qingdao National Laboratory for Marine Science and Technology of China (No. QNLM2016ORP0411). The Leading Talents of Guangdong Province Program (No. 2016LJ06D557), AoShan Talents Outstanding Scientist Program Supported by Pilot National Laboratory for Marine Science and Technology (Qingdao) (No. 2017ASTCP-OS03)".
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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A regional model for the prediction of M(3000)F2 over East Asia Jian Wang a,b, Feng Feng c,⇑, Hong-mei Bai a,d, Yue-Bin Cao b,e, Qiang Chen b,e Jian-guo Ma b,f a School of Microelectronics, Tianjin University, Tianjin, China Qingdao Institute for Ocean Technology, Tianjin University, Qingdao, China c Department of Electronics, Carleton University, Canada d School of Mathematics and Statistics, Hulunbuir College, Hulunbuir, China e School of Electrical and Information Engineering, Tianjin University, Tianjin, China f School of Computer, Guangdong University of Technology, Guangzhou, China b
Received 28 July 2019; received in revised form 19 December 2019; accepted 21 January 2020
Abstract Research on empirical or physical models of ionospheric parameters is one of the important topics in the field of space weather and communication support services. To improve the accuracy of predicting the monthly median ionospheric propagating factor at 3000 km of the F2 layer (identified as M(3000)F2) for high frequency radio wave propagation, a model based on modified orthogonal temporal– spatial functions is proposed. The proposed model has three new characteristics: (1) The solar activity parameters of sunspot number and the 10.7-cm solar radio flux are together introduced into temporal reconstruction. (2) Both the geomagnetic dip and its modified value are chosen as features of the geographical spatial variation for spatial reconstruction. (3) A series of harmonic functions are used to represent the M(3000)F2, which reflects seasonal and solar cycle variations. The proposed model is established by combining nonlinear regression for three characteristics with harmonic analysis by using vertical sounding data over East Asia. Statistical results reveal that M(3000)F2 calculated by the proposed model is consistent with the trend of the monthly median observations. The proposed model is better than the International Reference Ionosphere (IRI) model by comparison between predictions and observations of six station, which illustrates that the proposed model outperforms the IRI model over East Asia. The proposed method can be further expanded for potentially providing more accurate predictions for other ionospheric parameters on the global scale. Ó 2020 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Regional modeling; Ionospheric propagating factor at 3000 km of the F2 layer; Reconstruction; Orthogonal temporal-spatial functions; East Asia
1. Introduction Ionosphere is the layer of the atmosphere that lies between 60 and 1000 km above Earth’s surface and comprises three distinct layers, namely the D layer, E layer, and F layer, which is normally divided into F1 and F2
⇑ Corresponding author.
E-mail address: [email protected] (F. Feng).
layers. The propagation factor at a distance of 3000 km of the F2 layer (identified as M(3000)F2) is one of the important high-frequency radio wave propagation parameters defined as the ratio of the Maximum Usable Frequency (MUF) at a distance of 3000 km to the F2layer critical frequency. MUF represents the optimum frequency at which a signal can be received at a distance of 3000 km. Therefore, M(3000)F2 was widely applied in civil and military fields, such as high-frequency communication (Angling et al., 2009; Yan et al., 2011), tracking
https://doi.org/10.1016/j.asr.2020.01.026 0273-1177/Ó 2020 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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J. Wang et al. / Advances in Space Research xxx (2020) xxx–xxx
(Yao et al., 2013), localization (Swamy et al., 2013), and spectrum management (Wang et al., 2013). M(3000)F2 can be estimated from vertical-incidence (Hoque and Jakowski, 2012; Mcnamara and Thompson, 2015; Pezzopane and Scotto, 2007; Pijoan et al., 2014) and oblique ionosonde (Wang et al., 2014). In the absence of observations stations, these parameters (such as M (3000)F2, foF2 and the peak height of F2 layer hmF2) have to be deduced using empirical ionospheric models, which can provide the scientists, engineers, and educators with available empirical values (Bilitza et al., 2011). At present, the most common choice for predicting characteristics of the ionosphere is the International Reference Ionosphere (IRI) model, which mainly describes long-term variations of M(3000)F2 and several additional parameters. The IRI model is well known as the recommended international standard. Researchers have developed and improved empirical ionospheric models through observations. For example, the IRI model has been steadily improved with newer data and better modeling techniques by the joint working group of the Committee on Space Research and the International Union of Radio Science (URSI) (Bilitza et al., 2011). This model has evolved into a number of important editions, including IRI-78 (Rawer et al., 1981), IRI-1990 (Bilitza, 1990), IRI-2000 (Bilitza, 2001), IRI-2007 (Bilitza and Reinisch, 2008), IRI-2012 (Bilitza et al., 2014), and IRI2016 (Bilitza et al., 2017). Oyeyemi et al. (2007), Oronsaye et al. (2014) and Xenos (2002) used a neural network to develop new models of M(3000)F2. Liu et al. (2008) and Zhang et al. (2010) proposed a series of models based on Empirical Orthogonal Function (EOF) analysis method, which are also used to predict foF2 (Ercha et al., 2011), peak height (Zhang et al., 2009; Zhang et al., 2012), total electron content (Ercha et al., 2012; Mao et al., 2008; Wan et al., 2012; Zhao et al., 2005) and other ionospheric parameters. In general, the abovementioned efforts focused on developing global models for predicting M(3000)F2 and other ionospheric parameters. Recently, the scientific community focused on the development of regional models rather than global models because the regional models can provide a more accurate ionospheric representation over restricted areas (Anna et al., 2017; Cao and Sun, 2009; Mao et al., 2008; Nandi and Bandyopadhyay, 2015; Perna et al., 2017; Pietrella, 2014; Xenos, 2002; Zolesi et al., 2004). This paper focuses on the ionosphere over East Asia, which significantly varies due to its coverage of the high, middle, and low-latitude regions. To achieve more accurate prediction of the M (3000)F2 over East Asia, this paper proposes a new longterm prediction model for M(3000)F2 based on orthogonal temporal-spatial reconstruction using ionosonde data. This model is established with orthogonal functions and a series of harmonic parameters, which are determined through reconstructing vertical sounding data over the East Asia region.
2. Methodology 2.1. Fundamental algorithm Previous findings have revealed that variation of ionospheric parameters such as M3000F2 is mainly controlled by some independent processes that can be separated. Therefore, the EOF is an effective way for modeling ionospheric parameters (Pearson 1901; Dvinskikh 1988). Compared with other expansion methods, the EOF not only reduces the computation time but also reduces the number of modeling parameters (Zhang et al., 2009; Zhao, et al. 2005). In particular, the mathematical procedure involved in EOF transforms a dataset into a number of uncorrelated orthogonal principal components (Bai, et al., 2018; Liu et al., 2008), which well suits the prediction of M(3000) F2 and other homologous ionospheric parameters (Zhang et al., 2010). In this study, we use the EOF for the proposed model development. Following the basic idea of EOF, a set of nonlinear functions was developed to describe the dependencies of M(3000)F2 on geographical position, year (including solar activity) , month (or season) and time as Mð3000ÞF2ðk; u; F 10:712 ; R12 ; m; T Þ ¼ F d M ð3000ÞF2ðk; u; F 10:712 ; R12 ; mÞ; T ¼ F d F g k; u; c M ð3000ÞF2ðF 10:712 ; R12 ; mÞ ; T ¼ F d F g ðk; u; F a ðF 10:712 ; R12 ; mÞÞ; T
ð1Þ
where F d , F g and F a are modeling functions including a set of coefficients that respectively describe diurnal, geographical, annual and seasonal dependencies of M(3000) F2; k is geographical latitude; u is geographical longitude; F10.712 is 12-monthly running mean 10.7 cm solar radio flux (expressed in units of 10–22 W m2 Hz1); R12 is 12monthly running mean sunspot number; m is the index of month; T is a scalar representing universal time. Accordingly, the significance of the work in this paper is to determine these functions (F d , F g and F a ) and their relationship with respect to the modeling parameters. Fig. 1 give the flow chart of the model reconstruction and verification. As shown in Fig. 1, we firstly separate M(3000)F2 into temporal and spatial variables. Secondly, we model the temporal and spatial parts: the temporal part is modeling for solar activity and annual dynamic characteristics of M(3000)F2, while the spatial part is modeling for geographical space variation of M(3000)F2. In these two modeling progresses, the modeling parameters are selected, and the relationship between M(3000)F2 and the abovementioned modeling parameters is then derived. For each observed station, we analyze the solar activitybased annual dynamic characteristic of M(3000)F2, and define harmonic functions of M(3000)F2 with respect to the parameters F10.712, R12 and month. We then determine the coefficients of the temporal harmonic functions with observed data. For special solar activity index (F10.712
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Retain the M(3000)F2 characteristics a numerical mapping technique based on the temporal and spatial empirical orthogonal function.
For every observed station, analyze the solar activitybased, annual dynamic characteristic of M(3000)F2. Define harmonic functions between M(3000)F2 with solar activity and annual index. Determine the coefficient by the least square fitting approach with observed data. Temporal modeling
Observed data
Spatial modeling For special time period, analyze geographical changes of M(3000)F2.
Define M(3000)F2 with the harmonic functions of geographical coordinates
Determine the coefficient by the least square fitting approach with observed data.
Model Verification: (1) Calculate M(3000)F2 of the given predicting time, latitude and longitude by using the reconstruction model (2) Compare the predicted values with IRI predicted values and observed values
Analyze diurnal characteristics of M(3000)F2. Define M(3000)F2 numerical map function is modeled by Fourier time series. Determine the maximum number of harmonics by the least square fitting approach with observed data.
IRI Module Calculate M(3000)F2 of the given predicting time, latitude and longitude by using the IRI model
Fig. 1. Flow chart of the model reconstruction and verification.
and R12), month and universal time, we analyze geographical changes of M(3000)F2 and define the harmonic functions between M(3000)F2 and the geographical parameter. Next, we determine the coefficients of the spatial harmonic functions by the least square fitting approach with observed data. Finally, we model the diurnal dynamic characteristics of M(3000)F2 by using orthogonal Fourier function, and then, we determine the maximum number of harmonics by the least square fitting approach with observed data. As described, the model and relative parameters need to be determined from observations. As shown in Fig. 2 and Table 1, the present study uses ionospheric sounding data for the years from 1949 to 2018 recorded at 15 stations in Asia for modeling (11 out of 15 in years of 1949–2012) and verification (6 out of 15 in years of 2013–2018). Data of M(3000)F2 used in this work can be downloaded from National Oceanic and Atmospheric Administration website (ftp://ftp.swpc.noaa.gov/pub/lists/iono_month), ICSU World Data System (http://wdc.nict.go.jp/IONO/ HP2009/ISDJ/manual_txt-E.html) and Australian government-Bureau of Meteorology Space Weather service (ftp://ftp-out.sws.bom.gov.au/wdc/iondata/medians). As shown in Fig. 3a, the above stations were chosen because the time period covered both ascending and
Fig. 2. Distribution of stations used for modeling and verification.
descending phases of about six solar cycle activities. Not all stations provided data equally distributed over the study period. Some stations (such as Taipei) provided data from 1954 to 1996, some (such as Kokubunji) provided data from 1958 to 2018, and some did not have data for a com-
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Table 1 Geographic coordinates and measured data volume of the ionosonde stations used for modeling and verification. Station Label
Station Name
Geog. L at. (oE)
Geog. Long. (oN)
Years of modeling
Data volume for modeling (entries)
Years of verification
Data volume for verification (entries)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Akita Beijing Chongqing Guangzhou Hainan ICheon Jeju Kokubunji Manila Macau Okinawa Seoul Taipei Wakkanai Yamagawa
39.70 40.00 29.50 23.10 18.30 37.00 33.50 35.70 14.60 22.10 26.30 37.20 25.00 45.40 31.20
140.10 116.30 106.40 113.40 109.3 128.00 126.50 139.50 121.10 113.30 127.80 126.60 121.50 141.70 130.60
1966–1993 1979–2008 1979–2008 1979–2008 – – – 1958–2012 1952–1978 – 1972–2012 1973–1994 1954–1996 1949–2012 1965–2012
6635 6480 6696 6936 – – – 15,984 7104 – 9097 2784 10,512 15,441 10,064
– – – – 2003–2004 2013–2018 2013–2018 – – 1958–1965 2013–2018 – – 2013–2018 –
– – – – 264 1198 1771 – – 720 1680 – – 1614 –
plete solar activity cycle. A station was used in reconstructing the model as long as it could provide at least six years of data within a solar cycle. For the collected data, the following processing is done: (1) the monthly median values of M(3000)F2 for every station were calculated; (2) the sampling interval for 60 min was selected considering the periods of observations include 15, 30, and 60 min; (3) the stations with less than half solar activity period or no recent measurements was verified (e.g., Hainan station only has data for the years of 2003–2004, Jeju station only has data for the years of 2013 and 2018). As shown in Fig. 3b, the solar activity parameters used in this work can be downloaded from Australian government – Bureau of Meteorology Space Weather service (http://www.sws. bom.gov.au/Solar/1/6). To check the model accuracy, the root-mean-square error (RMSE, r) was calculated between model-derived predictions of M(3000)F2 and observations as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u H u1 X 2 r¼t ð2Þ Mð3000ÞF2OBS h Mð3000ÞF2MOD h H h¼1 where M(3000)F2MOD is the model-derived prediction of M(3000)F2; M(3000)F2OBS is the observation of M(3000) F2; H is the number of M(3000)F2 data points. 2.2. Modeling progress 2.2.1. Modeling for solar activity, and annual and seasonal dynamic characteristics The level of solar activity is usually described by two solar indices: (1) the sunspot number and (2) the flux of solar radio waves at a wavelength of 10.7 cm (F10.7). The former is affected by the photosphere and the low layer of the chromosphere, whereas the latter is determined by the corona and high layer of the chromosphere
(Afraimovich, et al., 2008; Zhang et al., 2012). It is well known that these two parameters affect the annual and seasonal dynamic characteristics of M(3000)F2. The correlation coefficients between the M(3000)F2 monthly median values and the twelve-month running mean value of solar indices at sample station (Wakkanai) is fully confirmed in Fig. 4. As shown in Fig. 4, the variation trends of the two types of correlation coefficients are generally similar, but different in some trivial detail. There are superior or inferior between the two types of correlation coefficients during certain hours and months. Especially after noon (from 12:00 to 20:00 clock) in summer, the correlation coefficients between M(3000)F2 and the two solar activity parameters are obviously different. Accordingly, for given specific geographic coordinates and the local time, we can derive a formulation to map the solar cycle variations and the seasonal index (annual, semi-annual, and monthly) to M(3000)F2, which can be written as the harmonic function Mð3000ÞF2ðF 10:712 ; R12 ; mÞ K P J P bk;j F 10:712 j cosð2pkm=12Þ þ ¼ k¼0 j¼0
ck;j F 10:712 j sinð2pkm=12Þ þ b0 k;j R12 j cosð2pkm=12Þþ c0 k;j R12 j sinð2pkm=12Þ ð3Þ where k = 1, 2, 3, 4 harmonics used to represent annual, semi-annual, seasonal and monthly cycles, j is the power exponent of the solar cycle parameter F10.712 or R12. The maximum harmonic orders K and J can be determined by the regression analysis. The coefficients bk,j, ck,j, b0 k,j and c0 k,j can also be derived using observed data of given station and corresponding F10.712 and R12 as follows
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Fig. 3. The time of data collected from ionosonde station and corresponding to different solar activity parameters. (a) The time of data collected from 15 ionosonde station; (b) F10.712 and R12 for the years of 1949–2018.
2 6 6 T 6 6 CC 6 6 6 4
b0;0
3
2
M0 ð3000ÞF21
3
^ ð3000ÞF2ðF 10:712 ; R12 ; mÞ ¼ F a ðF 10:712 ; R12 ; mÞ M
7 7 6 6 M0 ð3000ÞF2 7 b0;1 7 2 7 7 6 7 7 6 ¼ C6 7 .. 7 .. 7 7 6 7 6 . 7 . 5 5 4 0 0 c K;J M ð3000ÞF2O
ð4Þ
where M0 (3000)F2 is observed value of M(3000)F2, O is the maximum number of observed data, and 2 6 6 6 6 C¼6 6 6 6 4
3
1
1
1
ðF 10:712 Þ1
ðF 10:712 Þ2
ðF 10:712 ÞO
.. .
.. .
..
.. .
ðR12 Þ1 J sinJ
2pKm 12
ðR12 Þ1 J sinJ
2pKm 12
.
ðR12 ÞO J sinJ
2pKm
7 7 7 7 7 7 7 7 5
12
Fig. 5 shows the RMSE of M(3000)F2 with different maximum regression orders J and K. It is seen that better convergence and robustness are achieved with J = 2 than with J = 1. Moreover, the regression result using the two solar activity index parameters (F10.712 or R12) is better than that using only a single parameter of F10.712 or R12. As shown in Fig. 5, therefore, we determine the orders of J as 2 and K as 3. Substituting J = 2 and K = 3 into (3), we can derive the formulation as
¼
3 P 2 P k¼0 j¼0
bk;j F 10:712 j cos 2pkm þ 12
ck;j F 10:712 j sin 2pkm þ b0 k;j R12 j cos 2pkm þ 12 12 c0 k;j R12 j sin 2pkm 12 ¼ b0;0 þ b0;1 F 10:712 þ b0;2 F 10:712 2 þ þ b1;2 F 10:712 2 cos 2pm þ b1;0 þ b1;1 F 10:712 cos 2pm 12 12 2pm b2;0 þ b2;1 F 10:712 cos 6 þ b2;2 F 10:712 2 cos 2pm þ 6 2pm b3;0 þ b3;1 F 10:712 cos 3 þ b3;2 F 10:712 2 cos 2pm þ 3 c0 1;0 c0 2;0 c0 3;0
ð5Þ
::: þ c0 1;2 R12 2 sin 2pm þ þ c0 1;1 R12 sin 2pm 12 12 2pm 2pm 2 0 0 þ c 2;1 R12 sin 6 þ c 2;2 R12 sin 6 þ þ c0 3;2 R12 2 sin 2pm þ c0 3;1 R12 sin 2pm 3 3
Based on the determined orders of J = 2 and K = 3, Fig. 6 shows a sample of temporal reconstructed coefficients bk,j, ck,j, b0 k,j and c0 k,j at Wakkanai station. The label numbers from 1 to 48 represent the coefficients b0,0, b0,1, b0,2, c0,0, c0,1, c0,2, b1,0, b1,1, b1,2, c1,0, c1,1, c1,2, b2,0, b2,1, b2,2, c2,0, c2,1, c2,2, b3,0, b3,1, b3,2, c3,0, c3,1, c3,2, b0 0,0, b0 0,1,
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Fig. 4. Correlation coefficients between the monthly median values of M(3000)F2 and (a) the twelve-month running mean value of F10.7, (b) the monthly median values of M(3000)F2 and twelve-month running mean value of sunspot number, at Wakkanai.
b0 0,2, c0 0,0, c0 0,1, c0 0,2, b0 1,0, b0 1,1, b0 1,2, c0 1,0, c0 1,1, c0 1,2, b0 2,0, b0 2,1, b0 2,2, c0 2,0, c0 2,1, c0 2,2, b0 3,0, b0 3,1, b0 3,2, c0 3,0, c0 3,1 and c0 3,2, respectively. As shown in Fig. 6, the c0 0,1 is obviously different from other coefficients. The coefficient b0,0 during 19:00LT–20:00LT is obviously higher than that during other time period. This is because that the influence of solar activity and seasonal variation on M(3000)F2 is different during different time periods. These temporal reconstructed coefficients and two solar activity index parameters (F10.712 or R12) can be substituted into (3) to calculate the predicted values of corresponding ionosonde stations. More details will be further given in Section 2.3.
2.2.2. Modeling for geographical space variation Ionospheric parameters including M(3000)F2 have an irregular non-homogeneous spatial distribution. Therefore, the spatial characteristics of M(3000)F2 and other ionospheric parameter have been modeled and improved without interruption over several years. At present, numerous techniques based on different empirical or mathematical methods have been discussed to describe ionospheric spatial characteristics, including inverse distance weighted interpolation (Pradipta et al., 2016), moving surface interpolation (Deng and Tang, 2011), spherical harmonic (Legendre) functions depending on latitude and longitude (Jones and Gallet, 1962), along with statistical approaches such as kriging (Huang et al., 2017; Stanislawska et al., 1996). Considering that variations of ionospheric parame-
ters are controlled by both the orientation of the Earth’s rotational axis and the configuration of the geomagnetic field, Rawer presented a coordinate system expressed by the modified dip latitude (Rawer, 1984; Zhang et al., 2009). Therefore, such a coordinate system (Ercha et al., 2011; Kitanidis, 1997; Swamy, et al., 2013) has been adopted in many studies, showing that the global features and variability within the ionosphere can be well captured. We therefore propose to represent M(3000)F2 with the harmonic functions of the magnetic dip latitude and its
Fig. 5. RMSE of different regression parameters and analysis orders. K is the maximum harmonic order that represents the upper bound of annual, semi-annual, seasonal and monthly cycle, and J is the maximum harmonic order that represents the upper bound of the solar cycle.
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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modified value instead of simple geographic coordinates. The numerical mapping function is derived as Mð3000ÞF2ðk; uÞ ¼
L n X
gl ½Gðmðk;uÞÞl þ gl 0 ½Gðlðk;uÞÞl
o
ð6Þ
l¼0
where m(k,u) is magnetic dip latitude which is the function of latitude and longitude; l(k,u) is modified magnetic dip latitude which is the function of latitude and longitude; ‘G()’ is sine or the other type function of m or l; l is power exponent of G(m) and G(l); L is the maximum harmonic order number. The magnetic dip latitude is defined by the downward and horizontal components of the geomagnetic field (VanZandt et al., 1972), and the modified magnetic dip latitude is defined by arctan [m(k, u)/cos(u)0.5] (Rawer, 1984). The maximum harmonic order number L and the functional form of ‘G()’ can be determined by the regression analysis. The coefficients gl and g0l can be derived using M(3000)F2 of 11 modeling station and corresponding m(k,u) and l(k,u) as follows: 3 2 3 2 Mð3000ÞF21 g0 6 7 6 Mð3000ÞF22 7 7 6 T 6 g 1 7 7 7 6 ð7Þ CC 6 . 7 ¼ C6 . 7 6 .. 5 4 .. 5 4 g0 L where 2
7
Fig. 7 shows a bar chart for the RMSE of M(3000)F2 for different regression parameters and order. Fig. 7 shows that (1) the RMSE of twofold regression using the m and l is obviously lower than that of regression using only one of these parameters and (2) the accuracy using a sinusoidal function is better than that directly using the m or l. We therefore choose twofold regression with m and l to determine a third-order sinusoidal harmonic function. Substituting L = 3 into (6), we can simplify the formulation as
Mð3000ÞF211
1
6 Gðmðk1 ; u ÞÞ 1 6 C¼6 .. 6 4 . Gðlðk1 ; u1 ÞÞ
L
3
1
1
Gðmðk2 ; u2 ÞÞ .. .
.. .
Gðmðk2 ; u2 ÞÞ .. .
Gðlðk2 ; u2 ÞÞ
L
Gðlðk2 ; u2 ÞÞ
L
7 7 7 7 5
Fig. 7. The RMSE distribution of M(3000)F2 with different parameters and maximum harmonic order.
Fig. 6. Sample of temporal reconstructed coefficients at Wakkanai station. The label numbers represent the coefficientsb0,0, b0,1, b0,2, c0,0, c0,1, c0,2, b1,0, b1,1, b1,2, c1,0, c1,1, c1,2, b2,0, b2,1, b2,2, c2,0, c2,1, c2,2, b3,0, b3,1, b3,2, c3,0, c3,1, c3,2, b0 0,0, b0 0,1, b0 0,2, c0 0,0, c0 0,1, c0 0,2, b0 1,0, b0 1,1, b0 1,2, c0 1,0, c0 1,1, c0 1,2, b0 2,0, b0 2,1, b0 2,2, c0 2,0, c0 2,1, c0 2,2, b0 3,0, b0 3,1, b0 3,2, c0 3,0, c0 3,1 and c0 3,2, respectively.
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Fig. 8. Sample contours of spatial reconstructed coefficients gl and g0l against months and universal time during low and high solar activities. The label a, b, c, d, e f, and g represent the min-max normalization of spatial reconstructed coefficients g0, g1, g2, g3, g0 1, g0 2, and g0 3 during high solar activity epoch respectively. The label h, i, j, k, l, m, and n represent the min-max normalization of spatial reconstructed coefficients g0, g1, g2, g3, g0 1, g0 2, and g0 3 low solar activity epoch respectively.
M ð3000ÞF2ðk; uÞ ¼ F g ðk; uÞ 3
P ¼ g0 þ gl sinl ðmÞ þ gl 0 sinl ðlÞ
ð8Þ
l¼1
¼ g0 þ g1 sinðmÞ þ g2 sin ðmÞ þ g3 sin ðmÞþ g1 0 sinðlÞ þ g2 0 sin2 ðlÞ þ g3 0 sin3 ðlÞ 2
3
Based on the determined orders L = 3, sinusoidal function of magnetic dip latitude and modified value, Fig. 8 shows samples of spatial reconstructed coefficients gl and g0l against months and universal time during low and high solar activities. In Fig. 8, the min–max normalization of spatial reconstructed coefficients is calculated for better viewing.
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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2.2.3. Modeling for diurnal dynamic characteristics There are numerous approaches for ionospheric modeling for diurnal dynamic characteristics of ionospheric parameters, such as Fourier analysis (ITU, 2012) and spline methods (Deng and Tang, 2011; Hardy and Nelson, 1986; Sandwell, 1987; Scherliess and Fejer, 1999). Fourier expansion is known to be useful in characterizing periodic waveforms. Because M(3000)F2 inherently has diurnal periodicities, Fourier analysis outperforms other ionospheric modeling methods in constructing empirical models for M(3000)F2 prediction. In particular, M(3000) F2 numerical map of diurnal variations has been modeled using a Fourier function (Liu et al., 2008) with a period of 24 h as Mð3000ÞF2ðT Þ ¼
N h p p i X nT þbn sin nT an cos 12 12 n¼0
ð9Þ
where T is the given universal time; N is the maximum number of harmonics used to represent the diurnal variation and can be determined by the statistics analysis; n is the harmonic number expressed as (0, 1, . . ., N); an and bn are Fourier coefficients relevant to geographical coordinates and solar activity parameters. Combined with Sections 2.2.1 and 2.2.2, the coefficients an, and bn in (10) are determined by Fourier series decompositions (Jones and Gallet, 1962), i.e., 9 11 P > > > a0 ¼ 241 M ð3000ÞF2ðk; uÞ; > > > i¼12 > > = 11 P ð10Þ an ¼ 121 M ð3000ÞF2ðk; uÞ cosðn iT Þ; > i¼12 > > > > 11 > P > 1 bn ¼ M ð3000ÞF2ðk; uÞ sinðn iT Þ; > ; 12
i¼12
where M ð3000ÞF2ðk; uÞ is derived from spatial reconstructed coefficients (gl and g0l ) by using (9)
Fig. 9. The prediction example of M(3000)F2 against the maximum harmonic number N at Wakkanai station in May 2013.
9
h i M ð3000ÞF2ðk; uÞ ¼ g0 c M ð3000ÞF2ðF 10:712 ; R12 ; mÞ; s ¼ 1; 2;:::11 þ i 3 n h P gl c M ð3000ÞF2ðF 10:712 ; R12 ; mÞ; s ¼ 1; 2;:::11 sinl ðmÞþ l¼1 h i o gl 0 c M ð3000ÞF2ðF 10:712 ; R12 ; mÞ; s ¼ 1; 2;:::11 sinl ðlÞ
ð11Þ
where s = 1, 2,. . ., 11 corresponds to 11 modeling stations, and c M ð3000ÞF2 can be derived from temporal reconstructed coefficients (bk,j, ck,j, b0 k,j and c0 k,j) by using (5). In terms of (9), we analyzed the relationship between the prediction result of M(3000)F2 and the maximum harmonic number N. Fig. 9 shows a prediction example of M(3000)F2 against the maximum harmonic number N at Wakkanai station in May 2013. Fig. 10 shows the RMSE statistics result of 11 stations. As observed in Figs. 9 and 10, the maximum harmonic number N, is up to 11 in the above model to ensure the highest precision and robustness. Therefore, the maximum number of harmonics used to represent the diurnal variation is determined to be 11. Substituting N = 11 into (9), we can revise the formulation as Mð3000ÞF2ðk; u; F 10:712 ; R12 ; m; T Þ ¼ F d ðT Þ ¼ a0 ðk; u; F 10:712 ; R12 ; m;Þþ 11 p P an ðk; u; F 10:712 ; R12 ; mÞ cos 12 nT þ
n¼1
bn ðk; u; F 10:712 ; R12 ; mÞ sin
p 12
nT
ð12Þ
2.3. Prediction procedure With the aforementioned parameters reconstructed from least-square fitting regression, by given geographic coordinates (k, u), year, month, universal time, and solar activity factors F10.712 and R12, we can use the following steps for predicting M(3000)F2 as Fig. 11.
Fig. 10. The prediction RMSE with different maximum harmonic number.
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Fig. 11. The flow chart for calculating M(3000)F2 by using the proposed model.
Table 2 Verification stations, time and other corresponding characteristics. Label
Station
Year
Solar activity epoch
Month
Season
Geomagnetic Strom
Included in modeling
RMSEs of IRI model
RMSEs of PRM
a b c d e f
Hainan ICheon Jeju Macau Okinawa Wakkanai
2003 2015 2016 1961 2014 2017
Middle High Middle Low High Low
Jan. Mar. Jun. Aug. Feb. Oct.
Winter Equinox (spring) Summer Summer Winter Equinox (autumn)
No Yes No No No No
No No No No Yes Yes
0.12 0.13 0.21 0.40 0.18 0.12
0.11 0.10 0.11 0.34 0.10 0.08
3. Results and discussions To test the accuracy of the proposed reconstruction model (PRM), the performance of the PRM was compared with that of IRI-2016 (http://irimodel.org/IRI-2016) in terms of differences between model-derived predictions of M(3000)F2 and observations collected from Hainan, ICheon, Jeju, Macau, Okinawa, and Wakkanai stations. As shown in Table 2, the ionosonde data for 6 stations in high, middle and low solar activity years are selected. The abovementioned ionosonde data for 6 stations were used for verification because they cover four seasons of spring, summer, autumn and winter. Among these 6 sta-
tions, Hainan, ICheon, Jeju and Macau station are only for verification because their usable data mainly cover a few years less than half of the solar activity period. The other 2 stations (Okinawa and Wakkanai) have been both used in modeling and verification. The high solar activity years include 2014 and 2015. The middle activity years include 2003 and 2016. The low solar activity years include 1961 and 2017. Hainan and Okinawa stations are in winter. Jeju and Macau stations are in summer. ICheon and Wakkanai stations are in equinox that correspond to spring and autumn, respectively. Fig. 12 show examples of the diurnal variation in M (3000)F2 predicted using PRM, in comparison with the
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Fig. 12. Sample comparison of the diurnal behavior of monthly median M(3000)F2 predicted by IRI model and PRM.
IRI model and observations (OBS) collected at Hainan, ICheon, Jeju, Macau, Okinawa, and Wakkanai stations in Table 2. It can be seen that the prediction curves for M(3000)F2 obtained using both IRI model and PRM reflect the tendency of the diurnal variation characteristics whenever geomagnetic quiet and storm periods. The geomagnetic storm appeared in March 2015 (shown in Fig. 12b), and the maximum Dst index reached 223 nT (Zolotukhina et al., 2017). To estimate the accuracy of the proposed model, a statistical analysis of the differences between the predicted monthly mean values of M(3000)F2 from PRM and measured values is made by calculating average RMSE as follows (Oronsaye et al. 2014) rave ¼
W 1 X rw w w
ð13Þ
where w represents the number of statistical parameters such as ionosonde stations, years, seasons, months or others. As shown in Fig. 12 and Table 2, the average RMSEs of IRI and PRM are 0.20 and 0.12. The percentage error improvement between IRI and PRM is evaluated using the relations (Oronsaye et al. 2014):
d¼
rIRI rPRM rIRI
100%
ð14Þ
where rIRI and rPRM are the RMSEs of the predicted values of IRI model and PRM with respect to the measured values of M(3000)F2, respectively. From (14), the percentage error improvements between IRI and PRM of Hainan, ICheon, Jeju, Macau, Okinawa, and Wakkanai stations are 8.22%, 27.21%, 46.35%, 16.35%, 42.66%, and 30.24%. The average value of the percentage error improvements of the abovementioned six stations is 28.51%. Fig. 13 shows three sample plots for the comparisons of the monthly mean values of M(3000)F2 predicted values from the PRM and the IRI model and measured values obtained from ionosonde stations for the years of high solar activity (2013), middle solar activity (2015) and low solar activity (2017). All three stations cover 4 seasons and 12 months of the whole year. As shown in Fig. 13, these graphs serve to illustrate that IRI model and PRM successfully predict the general yearly variation shape of behavior of M(3000) F2. At the same time, it is found that the results also reflect the annual, semi-annual, seasonal, and monthly variation characteristics and the solar cycle variations of M(3000)F2.
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Fig. 13. Sample plots of different model predicted values and measured value of M(3000)F2 at Wakkanai, Jeju and Okinawa station for the years of 2013 (high solar activity year), 2015 (middle solar activity year) and 2017 (low solar activity year). Table 3 The RMSE between measured values of M(3000)F2 and predicted values of IRI model and PRM for three solar activity epochs, four seasons, four local time periods and six stations. Statistical analysis item
RMSE
Percentage error improvement between IRI and PRM (%)
IRI
PRM
Solar activity epochs
High Middle Low
0.18 0.17 0.24
0.15 0.11 0.14
20.75 38.47 40.78
Seasons
Spring (Mar., Apr., May) Summer (June, July, Aug.) Autumn (Sep., Oct., Nov.) Winter (Jan., Feb., Dec.)
0.20 0.20 0.16 0.22
0.12 0.12 0.12 0.12
43.82 42.42 22.24 45.56
Local time periods
Midnight (22:00–2:00) Sunrise (5:00–9:00) Noon (10:00–14:00) Sunset (16:00–20:00)
0.18 0.19 0.23 0.16
0.13 0.14 0.12 0.11
29.59 28.15 45.99 28.98
Stations
Jeju Okinawa ICheon Kokubunji Wakkanai Yamagawa
0.22 0.19 0.21 0.18 0.18 0.20
0.19 0.10 0.14 0.11 0.10 0.10
15.60 46.65 33.65 41.79 44.62 48.84
0.20
0.12
36.66
Average
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Fig. 14. Statistical average RMSE of IRI model and PRM. (a) average RMSE for the years of 2013–2018; (b) average RMSE for 12 months of the whole year; (c) average RMSE for the local time from 0:00 to 23:00.
In addition, we respectively analyzed the average RMSEs of six-years (2013–2018), 12-months (1–12) and 24-hours (local time 0:00–23:00) using (13). Fig. 14 shows that statistical RMSEs of the monthly mean values of M (3000)F2 predicted values from PRM are compared with those determined by the IRI model, which correspond to 6-years, 12-months and 24-hours by (13). It can be seen that the predicted average RMSE of PRM is lower than that of the IRI model. As shown in Fig. 14a, the yearly trend of average RMSE of PRM is consistent with that of IRI model, and there is a rising trend for the years from 2015 to 2018. As shown in Fig. 14b, the average RMSEs of IRI model during September to December are lower than those during other months. The average RMSEs of PRM during January, May, June, July and September are lower than those during other months. As shown in Fig. 14c, the diurnal average RMSEs of PRM are more flat than those of IRI model. Table 3 presents the average RMSEs between measured values of M(3000)F2 and predicted values of two models (IRI model and PRM) under different conditions, which correspond to three solar activity epochs (high, middle and low), four seasons (Spring, Summer, Autumn, and Winter) of the whole year, four time periods (midnight, sunrise, noon, and sunset) of the whole day. The percentage error improvement between IRI and PRM is calculated as listed in Table 3. The average RMSEs and percentage error improvement are based on measured data of M (3000)F2 and predicted values for the years of 2013– 2018. For different statistical conditionS, the iterative computation would be done by (13) and (14). These conclusions are drawn from Fig. 14 and Table 3: (a) the predicted results from PRM perform better than
those from the IRI model; (b) the percent error improvement of the PRM over the IRI model during low solar activity year is the highest among all the years; (c) the percentage error improvement of the PRM over the IRI model during winter is the highest among all the seasons; (d) the percent error improvements of the PRM over the IRI model during noon are higher than other time periods; and (e) the percent error improvements of the PRM over the IRI model at Yamagawa stations are maximum. Fig. 15 shows the spatial distribution (with intervals of 5° for both geographic longitude and latitude) of monthly median values of M(3000)F2 predicted using PRM and IRI model for June 2013 at 4:00 UT (corresponding to local time 10:00–14:00 in approximate noon) and December 2017 at 16:00 UT (corresponding to local time 22:00– 02:00 in approximate nighttime). The reason for this choice is that we want to analyse the recent years during high, middle and low solar activity epochs. Fig. 15(a) and (b) shows that the spatial distribution maps have similar shape. A similar situation also appears in (c) and (d). In conclusion, the spatial validity can be confirmed for PRM. 4. Summary and conclusions This paper proposed a model for predicting M(3000)F2, in which a series of harmonic functions used to represent the geographical spatial variation and reflects seasonal and solar cycle variations have been rebuild. The three main important features of the proposed model are (a) the ionospheric index F10.7 and sunspot number have been introduced together in the model to assist in the temporal reconstruction; (b) this model has expressed M(3000)F2
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Fig. 15. Sample contour of different model predicted values of M(3000)F2 during high and low solar activity years: (a) derived from IRI model at 04:00 UT (approximate noon in summer) June 2013; (b) derived from PRM at 04:00 UT (approximate noon in summer) June 2013; (c) derived from IRI model at 16:00 UT (approximate midnight in winter) December 2017; derived from PRM at 16:00 UT (approximate midnight in winter) December 2017.
with harmonic functions representing the annual, semiannual, seasonal, monthly and solar cycle variations; and (c) the geomagnetic dip latitudes and modified value have been introduced together in the model to assist the proposed model in the spatial reconstruction. Prediction results of the proposed model agree well with observations. Both the accuracy of the predictions of the IRI model and our proposed model have been analyzed by comparisons with the observations. It was concluded that our proposed model is more accurate than the IRI model over the East Asia region. To use our proposed model, the following inputs are required: latitude, longitude, month, hour, the twelvemonth running mean value of the monthly flux of solar radio waves at 10.7 cm, and the twelve-month running mean value of the monthly sunspot number. Future research is expected to extend the suitability of the proposed model to wider regions and even the globe. Moreover, this modeling approach is expected to be used in
predicting other ionospheric parameters such as peak height and total electron content. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research was funded by the National 973 Program of China (No. 61331901) and Qingdao National Laboratory for Marine Science and Technology of China (No. QNLM2016ORP0411). The Leading Talents of Guangdong Province Program (No. 2016LJ06D557), AoShan Talents Outstanding Scientist Program Supported by Pilot National Laboratory for Marine Science and Technology (Qingdao) (No. 2017ASTCP-OS03)".
Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026
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Please cite this article as: J. Wang, F. Feng, H. m. Bai et al., A regional model for the prediction of M(3000)F2 over East Asia, Advances in Space Research, https://doi.org/10.1016/j.asr.2020.01.026