On the Ion Line Calibration by Plasma Line in ISR Measurements

Abstract

The radar constant calibration in incoherent scatter radar ion line processing is essential for the data quality and was not paid enough attention in previous studies. In this investigation, based on several experiments made by the newly built Sanya incoherent scatter radar (SYISR), we made and evaluated the ion line calibration by plasma line both in case study and statistically. The calibration factor had local time and altitude variations, due to the corresponding variations of the transmitted power, the radar gain, and the noise temperature. We obtained a mean calibration factor of 1.35 by the simultaneous measured plasma line and ion line electron density and applied it to a one-month ion line observation calibration. Through a co-located ionosonde measured f_oF₂ evaluation, the calibration decreased the mean deviation from −1.92 MHz (−18%) to −0.33 MHz (−3%), which resulted in much better agreement between the ion line f_oF₂ after calibration and the ionosonde results. The existed deviations between after calibration and ionosonde results were due to the uncertainties either in the used calibration factor or the ionosonde measurements. An empirical T_e/T_i usage in raw electron density estimation and ignoring the seasonal and short-term variations of the effecting factors might influence the calibration performance. Using the to-be-completed SYISR Tristatic System, the performance of plasma line calibration technique is expected to be improved in the future.

1. Introduction

The incoherent scatter radar (ISR) has been one of the most powerful ionospheric monitoring techniques since it was invented [1]. Based on radar equation, the received signal-to-noise ratio (SNR) of monostatic ISR scattered from electrons with respect to the electron number density (N_e) under the condition of ignoring the Debye effect is expressed as follows [2]:

$$SNR=\left(\frac{P_{t}G}{T_s}\right)\left(\frac{c\tau }{2} \frac{r_0^2{\lambda }^2}{K_b{B}_w\left(4\pi \right)R^2}\right)\left(\frac{N_e}{1+T_e/T_i}\right)$$

(1)

where the parameters in the first bracket, including the transmitted power (P_t), the radar gain (G), and the noise temperature (T_s), are the variables that are difficult to accurately determine and, therefore, need calibration; the parameters in the second bracket, including the bandwidth (B_w), the wave length ($\lambda$), effective pulse width ($\tau$), light speed (c), electron radius (r₀), Boltzmann constant (K_b), and range (R), have known values for specific radar and experimental setup; the parameters in the third bracket are related to the ionosphere and need derivation from the received SNR. Using Equation (1), the raw electron density can be derived based on the measured power by ISR and the predetermined ratio T_e/T_i by an empirical model. In this study, the international reference ionosphere (IRI) model was used to predefine the ratio T_e/T_i, regardless which type of waveform was used in the experiment [3]. However, in the actual operation of ISR, the transmitted power (P_t), the radar gain (G), and the noise temperature (T_s) usually have some deviations from the theoretical value, and, therefore, the derived raw electron density is biased to some extent, and needs further calibration for some usage requiring absolute electron density value. For the traditional centralized Klystron ISR, the factors that result in these deviations include the transmitter frequency switch, the antenna scanning, the long-term stability of the transmitter and receiver performance [4], and even external environment such as weather condition. For example, Rietveld et al. reported that during some extreme situations such as wet snow, the calibration factor might change to some extent [5]. For the phased array radar, there exist additional factors such as the stability of usable transmitting/receiving (T/R) units and the beam direction, that can result in such kind of deviation due to its emission mechanism [6,7].

In previous reports, several independent measurements, including ionosonde measured critical frequency and ISR plasma line-derived electron density, were used to calibrate the ISR ion line measurements [4,6,7]. In comparison with ionosonde calibration, the plasma line calibration has the following advantages: (1) the plasma line spectra can be used to derive the absolute electron density profiles with a high accuracy and resolution, which can give more accurate calibration [8,9]; (2) the plasma line could be observed by ISR simultaneously, which enable the calibration independent of an additional radar. However, the amplitude of plasma line spectra is usually several orders lower than that of the ion line; therefore, its detectability depends on the radar sensitivity, local time, and radar geometry very much [10].

In EISCAT UHF radar measurement, the ion line data was calibrated through separately determining the transmitted power, the received power, and the radar constant in the radar equation [4]. Specifically, the transmitted power was obtained from a monitor of the applied high voltage given the known transmitter performance. The received power was measured by comparison with a reference noise signal injected into the receiver system before the first preamplifier. The radar constant was derived from the simultaneous ion line and plasma line observations. Through independent evaluation, their absolute accuracy after calibration was ~10%. The newly built Resolute ISR (RISR) tried both the plasma line calibration and independent co-located ionosonde calibration in their multiple beams’ measurements and found reasonably good agreement between both type of observations [6,7]. In addition, Setov et al. and Alsatkin et al. reported that they used the radar measured sky noise to calibrate the ion line data [11,12].

Although there exist several publications mentioned above that involved ISR ion line calibration, this issue was not given enough attention. Especially, there is still a lack of a special articles dedicated to introduce the method and evaluate its effect systematically. In this paper, we attempted to use the simultaneous measured plasma line to calibrate the ion line electron density for the newly built Sanya incoherent scatter radar (SYISR) [13,14]. We used independent measurement to evaluate the performance of the calibration statistically. Such investigation is important and necessary for a newly built radar, which can help to understand and use the produced data product properly. Furthermore, on the basis of SYISR, we are currently developing the SYISR Tristatic System (SYISR-TS) [15]. Specifically, the SYISR-TS will double the current SYISR transmitter antenna array and build two new receivers. Once the SYISR-TS is completed, its performance, especially the plasma line detection capability, will be greatly enhanced given the doubled radar gain and aperture. We are considering to run the plasma line mode as a normal operational mode in the future by SYISR-TS, although this will require much more computational and storage resources. By doing that, we can potentially calibrate the ion line measurements by plasma line in real time. Therefore, this paper could be a necessary demonstration for that purpose. In Section 2, we will briefly describe the experimental data and calibration methodology. The main results will be given in Section 3. We finally present the discussion in Section 4 and conclude the whole investigation in Section 5, respectively.

2. Data and Methodology

The SYISR was a newly developed ISR located in Sanya (18.3°N, 109.6°E), led by the Institute of Geology and Geophysics, Chinese Academy of Sciences, with the main features of an active digital phased array, with all solid-state transmission and digital receiving. The readers can refer to Yue et al. for detailed information regarding the construction process, the hardware composition, radar index and evaluation, signal processing, and preliminary experimental results of SYISR [13,14]. Several detection modes, including zenith stare, perpendicular to the geomagnetic field, meridian scan, and all sky scan, were developed for ionospheric monitoring. The most common waveforms used by ISR, such as Barker code, long pulse, and alternating code, were implemented in SYISR. The detailed ion line processing and evaluation were given by Hao et al. [16]. The hard target, which occurred frequently over Sanya and challenged the data processing significantly, was eliminated by the method described in Wang et al. [17].

The plasma line spectra are induced by the electrostatic Langmuir waves in the plasma [8]. It is usually too weak to be observed by ISR. However, its intensity can be enhanced significantly due to the increased photoelectron flux around sunrise and sunset time or in the aurora region, which enables the detectability of plasma line by ISR. However, it is still much weaker in comparison to that of ion line [18]. Therefore, the detectability of plasma line challenges the sensitivity of ISR [10]. One outstanding feature of SYISR is that it can detect the weak plasma line spectra in addition to the ion line spectra [14]. The maximum bandwidth of SYISR was 4 MHz, which was not sufficient to cover the entire plasma line spectra. To resolve this problem, we used three parallel channels to splice a maximum bandwidth of 12 MHz in one side of ion line to cover the plasma line spectra dynamical range through the optimized configuration of the center frequency for each channel [14]. By our test, SYISR could observe plasma line over Sanya around sunrise and sunset time, and occasionally during the whole daytime. Ignoring the temperature related term, which is insignificant, in the dispersion relation of plasma line, the electron density (N_e) can be calculated from plasma line frequency (${\omega }_{PL}$) using the following formula [8,19]:

$$N_e=e^{-2}{\epsilon }_0{m}_e\left({\omega }_{PL}^2-{\left(\frac{eB}{m_e}\right)}^2{\sin }^2\left(\alpha \right)\right)$$

(2)

where e, ${\epsilon }_0$, m_e, B, and $\alpha$ are charge constant, electrical constant, electron static mass, geomagnetic field intensity, and the angle between scattered beam direction and geomagnetic field, respectively. For SYISR, the $\alpha$ is ~65° when the beam points to the zenith direction.

In this study, five different experimental data were used based on SYISR, the configurations of which are summarized in

Table 1. Experimental setup of SYISR observations used in the figures. LP: long pulse; AC: alternating code; BC: Barker code.

#	Waveform	Sampling Rate	Time Interval	Figures
1	LP, 100 μs	4 MHz (3 channels)	28 December 2021	1–3
2	16-bit AC, 480 μs	0.1 MHz (1 channel)	6 May 2022	4
3	13-bit BC, 390 μs	0.1 MHz (1 channel)	12 March 2022 to 10 April 2022	5–7
4	32-bit AC, 100 μs LP	4 MHz (3 channels)	6 January 2022	8
5	N/A	0.1 MHz	26 November 2022	9

. Using experimental #1, we obtained simultaneous ion line and plasma line, which were used to calculate the calibration factor. A 100 μs long pulse waveform selected here was a balanced choice of range resolution and spectra intensity of plasma line. The experimental #2 data was used to evaluate the effect of calibration on multiple parameters of alternating code measured ion line. In experimental #3, a one-month long experimental data were used to statistically analyze the effect of calibration. The experimental #4–5 were used in the Section 4. In all five experiments, the radar was run with a single beam pointing to the zenith direction over Sanya to ensure maximized gain and SNR.

As an example, Figure 1 shows a simultaneously observed ion line spectra and plasma line spectra by SYISR at 28 December 2021 10:14:17 local time. The ion line spectra shows enhanced intensity around E and F2 layers, which is very common in ISR measurements [14]. However, the usual double crests structure of ion line spectra was not identified. This was due to the relatively lower frequency resolution of 100 μs long pulse waveform used in the experiment. However, this did not influence the calibration effect because the calibration factor was calculated using the raw electron density derived from received power using Formula (1) and the plasma line-derived electron density using Formula (2). In the plasma line spectra, although its intensity was not very significant, it still showed obvious altitude variation of the ionosphere. Furthermore, according to Formula (1), the altitude variation of the signal power was determined by both range and ionosphere status (electron density and T_e/T_i). We can see that the plasma line intensity shown in Figure 1b had obvious enhancement in the F₂ peak altitude, corresponding to the highest ionospheric electron density. However, the effect of range variation was not very obvious, which was probably due to the relative narrow altitude interval in this experiment. We also investigated other experiments with higher altitude coverage and found that the plasma line spectra intensity evidently decreased with altitude increase. Before using Formula (2) to calculate the electron density profile from the spectra, we first denoised the spectra image and identified the plasma line profile. In the bottom panel of Figure 1, the corresponding ion line raw electron density and the plasma line-derived electron density are also displayed. We can see that the plasma line-derived electron density was generally larger than that of the ion line. This is understandable since Formula (1) assumed a 100% radiation efficiency, which is usually lower than 100%. This was expected to result in underestimation of electron density. In addition, the profile shape especially in the lower altitude showed difference between two results. This might be due to the uncertainty of the used empirical T_e/T_i in Formula (1).

Furthermore, observations made by a co-located ionosonde over Sanya, named portable digital ionosonde (PDI), was also used for evaluation purpose in the study. The readers can refer to Lan et al. for detailed information regarding PDI [20]. In experiment #1, the corresponding original ionograms were manually scaled, while in experiment #3, the automatically scaled peak density and height were used.

3. Results

3.1. The Calibration Factor

The calibration factor was defined as the ratio between plasma line derived electron density to the ion line raw electron density in this study. In the actual operation of SYISR, the plasma line was not a regular monitoring mode. In the occasional experiment, the plasma line spectra were only obvious around sunrise and sunset time over Sanya. During the experiment on 28 December 2021, we fortunately measured clear plasma line spectra during 09:00–16:30 local time, the data of which, therefore, were used to determine the calibration factor in this study. Figure 2 shows the local time and altitude variation of electron density derived from the SYISR plasma line (a), ion line (b), and the co-located PDI (c). Three observations showed generally similar time variations. The plasma line electron density was systematically larger than that of the ion line. The PDI electron density profiles showed obvious fluctuations above the peak height. This was probably because the profiles by ionosondes were extrapolated under the assumption of constant scale height in the topside ionosphere rather than directly measured [21].

Figure 3 further shows the electron density ratio between the plasma line and ion line (a) and between the plasma line and PDI (b) during the same day as Figure 2. Regarding the ratio of plasma line to ion line, its value ranged from ~0.8 to ~2.5, with obvious local time and altitude variations, which might be explained by the corresponding variations of the uncertain terms in Formula (1). The altitudinal mean value showed no significant local time variation, with the values oscillating around ~1. The local time mean value had evident altitude variation, with values ranging from ~1 to ~2. For the ratio of plasma line to ionosonde, the main feature was the relatively larger value above the peak height region. Again, this was due to the extrapolated density profile in ionosonde inversion under the assumption of constant scale height in the topside ionosphere, which deviated from the real condition. During the altitude range of ~200 km to the peak height, the mean value of this ratio was around ~1, which indicated good consistency between the plasma line and ionosonde in this altitude interval.

Since few plasma line experimental data were available, it was difficult to derive accurate altitude and local time variations of the calibration factor statistically. Therefore, we calculated the mean value of plasma line to ion line ratio around peak height in Figure 3a, whose value was 1.35, to represent the calibration factor in the experiment hereafter. The corresponding uncertainty of this factor, represented by the standard deviation in the mean value calculation, was ~0.24.

3.2. Calibration Effect on Multiple Ionospheric Parameters

Theoretically, power calibration will not influence the temperature and ion velocity determination. However, in the least square fitting of the auto correlation function (ACF), the electron density, temperature, and ion velocity were derived simultaneously numerically. To determine the calibration effect on other parameters, Figure 4 shows the retrieved multiple ionospheric parameters using alternating code waveform during 6 May 2022 and the difference between before and after calibration. We observed that, in this experiment, the raw ion line value underestimated the electron density up to ~0.5 × 10¹² m⁻³, depending on the amplitude of the background ionosphere. However, the difference of electron temperature, ion temperature, and line of sight ion bulk velocity, between before and after calibration value, was negligible, which meant that the calibration had no effect on those parameters. Some occasional relatively larger value around lower altitude of nighttime might have been due to the retrieval noise because of the low SNR.

3.3. Statistical Effect of the Calibration on Ionospheric F₂ Peak Results

To observe the calibration effect statically, we further used the above calibration factor to calibrate the continuously SYISR measurements for one whole month. Then, the co-located ionosonde critical frequency (f_oF₂, in MHz) and peak height (h_mF₂, in km) were used to make an independent evaluation.

Figure 5 shows the statistical comparison of ionosonde f_oF₂ and SYISR ion line-derived f_oF₂ before and after calibration during the whole month. Before calibration, the ion line f_oF₂ underestimated the ionosonde f_oF₂ systematically with a mean deviation of −1.92 MHz. While after calibration, this value decreased to −0.33 MHz, although underestimation still existed.

To demonstrate the local time variation of the calibration effect, Figure 6 shows the mean local time variation of f_oF₂ before and after calibration from SYISR ion line, and that from the ionosonde. We clearly observed that the after calibration f_oF₂ showed much better agreement with the ionosonde result than before calibration. Before calibration, the relative deviation ranged from ~−25% to ~−4%, with the mean value of −18%. After calibration, the mean deviation decreased to −3%, ranging from ~−11% to ~+13%. The overall agreement after calibration between SYISR and PDI appeared better during the interval of 04:00 to 16:00. This was probably because the calibration factor was calculated based on the observations during the similar time interval. Furthermore, in both Figure 5 and Figure 6, the shown results were derived in the interval of March to April of 2022, during which the mean F10.7 index was ~112 sfu (solar flux unit, 1 sfu = 10⁻²² W m⁻² Hz⁻¹), which represented a middle-low solar activity level. Therefore, the absolute deviation between the after calibration and ionosonde measurement should be larger in higher solar activity since the corresponding background ionospheric electron density was higher. However, in terms of relative deviation, the results should be similar, given a single calibration factor was used in our calibration processing.

4. Discussions

4.1. Potential Reason of the Residuals after Calibration

As indicated in Figure 5 and Figure 6, the calibration improved the ion line raw f_oF₂ significantly. However, deviations between calibrated f_oF₂ and ionosonde f_oF₂ results, including a mean deviation of −0.33 MHz and the local time variation of the calibration performance, still existed. We think the probable reasons for this include:

(1) The current used calibration factor was calculated from one experiment, which might not represent the radar status statistically. In addition, we used one single calibration factor rather than considering its altitude and local time variation. This will also result in deviation to some extent. Furthermore, we used the calculated calibration factor from the measurements in 2021 to calibrate the results in 2022. Since the radar circumstance might change versus times, this will also result in deviations. For example, the radar noise temperature might change with seasons; the usable T/R units might be different between two experiments; the radar stability might also change in a longer time period [5]. In the future, more plasma line experiments are needed to consider the altitude and local time variation of the calibration factor with statistical significance. In addition, an operational mode with observing both ion line and plasma line simultaneously might be very useful for the ion line calibration, although realizing this is very challenging from the perspective of radar resources and computation resources.

(2) In the evaluation, we used a co-located ionosonde measured f_oF₂ and h_mF₂, both of which were direct measurements and were believed to be accurate enough. Scotto and Sabbagh used to compare the MillStone Hill ISR measured h_mF₂ with that from a co-located ionosonde during ~20 years [22]. They found that the ionosonde h_mF₂ tended to underestimate the ISR h_mF₂ with ~10 km, regardless of which kind of inversion was used in the ionogram processing. This indicated that the deviations in Figure 5 and Figure 6 might also have been due to the bias of ionosonde measurements. To confirm this issue, we also made a statistical comparison between the SYISR ion line h_mF₂ and ionosonde h_mF₂, as shown in Figure 7. The ion line h_mF₂ were derived from the original power profile and were not influenced by the calibration, therefore, should be accurate. As indicated, the ionosonde h_mF₂ underestimated the SYISR h_mF₂ by ~25.4 km on average, although both had a high correlation coefficient of 0.97. The larger underestimation in our results than that of Scotto and Sabbagh might have been due to different seasons and locations [22]. Furthermore, the deviation of ionosonde h_mF₂ from that of SYISR was most significant around the middle noon time, with the mean deviation potentially reaching up to ~80 km.

4.2. The Effect of the Used T_e/T_i in the Formula (1)

When deriving the raw electron density using Formula (1), we used the empirical IRI model to provide the T_e/T_i ratio [3]. However, this was a climatological model, which might have deviated from the realistic situation; therefore, this resulted in the uncertainty of the calculated calibration factor. Especially, the derived calibration factor shown in Figure 3 had altitude dependency, which might be related to the IRI T_e/T_i error. To clarify this point, we made another simultaneous plasma line and ion line experiment with combined 100 μs LP waveform and 32-bit AC waveform during 6 January 2022. Therefore, the AC measurements could be used to derive the T_e/T_i self-consistently through the ACF fitting [16]. Unfortunately, the visible PL spectra, that can be used to derive electron density profile successfully, only lasted for ~2 h in this experiment. However, it was enough for our clarification purpose here, especially because this valid time interval covered the typical T_e/T_i enhancement around the dawn sector. Figure 8 shows the comparison of T_e/T_i and the corresponding ratio of PL electron density to LP electron density between IRI model calculation and SYISR AC measurements.

We observed that the overall local time and altitude variation of T_e/T_i between IRI model and SYISR AC measurement appeared similar. For example, both T_e/T_i peaked around ~200–300 km, and had higher value around 07:00 due to the photoelectron heating of the low-density thermal electrons [23]. However, the AC measured T_e/T_i value and its peak height was more or less lower than that of IRI model after 07:30 local time. This is understandable since the IRI model was a climatological model, while the realistic ionosphere showed significant day-to-day variability, whose effect was most significant around morning hours [24]. In addition, the AC measured T_e/T_i was much nosier than the model result because the electron density was much lower around the dawn sector, which resulted in lower measured SNR and, therefore, larger retrieval uncertainty of T_e/T_i [14].

After replacing the IRI T_e/T_i with the AC-measured T_e/T_i in deriving the LP electron density using the radar equation, the electron density ratio of PL to LP measurements showed some differences. The variability among different local times became smaller, especially in the higher altitudes, which can be indicated from the degree of dispersion among different color lines. The mean ratio with AC-measured T_e/T_i generally increased with the altitude increase, while for the IRI T_e/T_i, it showed a decreasing trend during the 250–300 km altitude interval. However, the altitude dependency of the ratio still existed with AC measured T_e/T_i, which implied that the altitude variation of the calibration factor not only resulted from the T_e/T_i factor. Furthermore, in terms of mean profile of the ratio, the difference between both was insignificant, with IRI T_e/T_i based ranges from 1.13 to 2.26 and AC T_e/T_i ranges from 1.35 to 2.72. The corresponding mean value was ~1.5 and ~1.6, respectively. Please note that the mean altitude dependency here was slightly different from that shown in Figure 3, which was probably due to local time coverage difference in both experiments. In summary, replacing the empirical T_e/T_i ratio with the AC measured T_e/T_i ratio, the calibration factor will be slightly different in terms of both mean value and altitude variation. However, the altitude dependency still exists.

4.3. Shortcomings of the Current Calibration Method

Most other ISRs, especially those equipped with parabolic antenna, such as the EISCAT radar [25], usually employ a noise injection technique to monitor the noise temperature. In addition, they can measure the transmitted power by a separate channel. Therefore, they can separate the effect of transmitter power and noise temperature in their calibration process. However, in our phased array SYISR radar, we did not design a mechanism to monitor the noise temperature and the transmitted power, given that we had 4096 channels in total and a limited budget [14]. Therefore, our calibration accuracy was determined by a mixed effect of the variations of the transmitted power, the noise temperature, and radar constant.

In the current calibration investigation, we used a constant calibration factor to make the correction. However, most effecting factors, including the transmitted power, the gain and the noise temperature, might have time variations. Generally, some components, especially the T/R unit, might break down during the operation for a phased radar. By our monitoring, this was a very small probability event primarily because SYISR is a brand new developed radar. So, the breakdown of the T/R unit resulted variations of the transmitted power and gain could be ignored in the short term. The noise temperature roughly included the system noise temperature and the external noise temperature [14]. In the factory test stage, we measured the system noise coefficient and gain for each T/R unit, amplifier, digital receiver, and the SNR loss of the feeder network and cable. Then, we calculated the noise temperature of the system using those measured value [14]. In the field test stage, we re-tested the noise coefficient of the sampled 1% T/R units and found that it was relatively stable. The external noise temperature was determined by many factors, such as atmospheric absorption, cosmic noise, and even anthropogenic noise. Most of these factors can vary from time to time and, therefore, result in the short-term variability of external noise temperature [26]. Using one constant calibration factor definitely cannot indicate this short-term variability. To demonstrate the short-term time variation of the noise, we made a sampling experiment without transmitting power using SYISR on 26 November 2022. As shown in Figure 9, the measured noise showed short-time variation, with peaks around 07:00 and 17:30. The variability (maximum minus minimum) was ~6% relatively to the mean value. In real signal processing, we usually prepared the range gate as high as possible (~1200 km in this article). Then, the echo from highest altitude was considered as the background noise. Doing this would produce the defect of non-noise injection mechanism in the radar to some extent.

4.4. Applicability to Multiple Beams Experiment

In this article, we only calculated the calibration factor and evaluated its performance in single vertical beam experiments. Actually, the SYISR can be configured to make measurements in arbitrary beam direction within its effective detection area [14]. In realistic operation, we also ran the radar in multiple beams mode for the purpose of monitoring the regional variation of the ionosphere. For those beams that deviated from the vertical direction, the current calibration factor was not valid anymore, since the corresponding beam width, radar gain, and the environmental noise were different. However, the current method could also be used to calculate the corresponding calibration factor if simultaneous plasma line measurements are available. We actually made some multiple beams experiments with simultaneous ion line and plasma line measurements. However, due to the decreased gain and, therefore, SNR in non-vertical direction, the effect, especially the visibility of the plasma line spectra in comparison with that of the vertical direction under the same waveforms, was not good enough. As stated previously, once the SYISR-TS is completed, we will conduct another experiment to carry out the multiple beam’s calibration investigation using the plasma line. Considering that both the transmitted power and gain will be increased, we expect this plasma line calibration to work well.

5. Conclusions

In this study, based on the plasma line experiment by the newly built SYISR, we calculated the calibration factor by the simultaneous plasma line and ion line electron density. We then applied this calibration factor to several SYISR ion line experiments and made a statistical evaluation on the calibration effect. The main conclusions are summarized as follows:

(1) The calibration factor had local time and altitude variations, which might be due to the corresponding variations of the transmitted power, the radar gain, and the noise temperature in the soft target radar equation. Then, a mean calibration factor of 1.35 was obtained by averaging the corresponding value around peak height during one specific plasma line experiment.

(2) We then applied this calibration factor to calibrate one-month SYISR measurements and made a statistical comparison between SYISR result and a co-located ionosonde measured f_oF₂ and h_mF₂. The results showed that the calibration decreased the mean deviation from −1.92 MHz (−18%) to −0.33 MHz (−3%), which resulted in much better agreement between the ion line f_oF₂ after calibration and the ionosonde results. The existed deviations between after calibration and ionosonde results were due to the uncertainties either in the used calibration factor or the ionosonde measurements.

(3) Considering that the SYISR had no noise injection mechanism to monitor the radar’s noise temperature and no additional channel to measure the transmitted power in operation, the current calibration cannot distinguish the effects of those factors. We used an empirical T_e/T_i in the raw electron density estimation using the radar equation, which might deviate from the real situation to some extent. In addition, we did not consider the seasonal and short-term variations of those effecting factors such as noise temperature and transmitted power in this calibration. All the above facts should influence the calibration performance. Furthermore, the current calculated calibration factor is inapplicable to other non-vertical beam experiments, given that the corresponding beam width, radar gain, and the environmental noise were different. Considering that the developing SYISR-TS will have higher gain and power, we can use AC code to measure more obvious plasma line and self-consistently determine T_e/T_i. More accurate calibration using plasma line is expected for both single vertical beam and multiple beams experiments.