Recent advances in computing technologies have renewed interest in the intelligent systems for automatic interpretation of ionograms, images obtained by remote sensing of the ionospheric plasma. The ionogram “autoscaling” techniques based on the template matching method, previously rendered unrealistic for their computing complexity, have now become feasible. This work presents an automatic scaling technique for extracting the main features of the F1 and F2 layers of the ionosphere, such as critical frequency and virtual height, from vertical incidence ionograms that do not distinguish O/X polarization of the echoes. The proposed technique uses the quasi-parabolic segments (QPS) to model the electron density profile shapes that are used to synthesize a pool of candidate traces. Moreover, the empirical orthogonal functions and image technique are applied to reduce the size of the candidate traces so that the auto-scaling algorithm can run in realistic time. With the template matching algorithm, the technique will provide the initial parameters of the QPS model for the F1 and F2 layers, which are then fine-tuned to obtain the better fitting parameters. In order to evaluate the performance of this technique, a large data set of ionograms recorded in Wuhan at daytime and nighttime in winter, summer, and equinoctial months, are analyzed and investigated. The automatic scaling results are compared with manually scaling results. Our results indicate that the proposed technique described in this paper is reliable and efficient and will facilitate the statistical study of temporal and spatial ionospheric characteristics over Wuhan.
 The region of the ionosphere ionized by solar radiation extends from approximately 70 km to 1000 km above the Earth and includes the thermosphere and parts of the mesosphere and exosphere. Because of the effect of the ionization, the ionosphere contains plasma and is made up of three layers. The lowest layer is called the D layer and extends from approximately 70 km to 90 km. The next layer is called the E layer and extends from approximately 90 km to 150 km. The upper layer is called F layer, which sometimes can be split into the F1 and F2 layer during the day and extends from approximately 150 km to 1000 km. The free electrons existing in the ionosphere can affect the propagation path of HF waves. Therefore, research about the ionosphere is significant for space weather and short-wave communication. The ground-based ionosonde, which has a long history, is a significant means for studying the ionosphere characteristics. Vertical incident ionograms are recorded by the ground-based ionosonde that vertically projects the radio wave to the ionosphere. Ionograms contain the characteristics of the ionosphere, and thus, scaling of ionograms is a significant task for studying ionospheric characteristics. Manual scaling of ionograms is a time-consuming and laborious process, which requires an experienced person and cannot meet the real-time performance of the ionosonde. Moreover, with manual scaling, it is hard to avoid human errors. For these reasons, it is necessary to develop an automatic scaling technique for deriving the ionospheric characteristics from ionograms. Although the automatic scaling technique is widely used in real-time ionosondes and scaling of historical ionograms, it is always a challenging task to achieve a good quality of the autoscaled data.
 Since the 1960s [Galkin, 1962], automatic scaling methods have been developed to automatically scale vertical incident ionograms. The most widely used system is the automatic real-time ionogram scaling with true-height (ARTIST) [Reinisch and Xueqin, 1983], which was developed by the University of Lowell that used a hyperbolic trace-fitting method to extract the ionospheric characteristics from the digisonde ionograms that provide O/X wave polarization tags. Recently, many studies [Galkin et al., 1996; Reinisch et al., 2005; Galkin and Reinisch, 2008] have focused on improving the performance of ARTIST. Fox and Blundell  developed a system to automatically scale ordinary-ray ionograms using mathematical extrapolations. Igi et al.  developed an automatic scaling algorithm using the parabolic and hyperbolic curve-fitting method. Tsai and Berkey  used fuzzy segmentation and connectedness techniques to develop an automatic scaling method. Scotto and Pezzopane  designed a program named Autoscala to interpret ionograms by using a template matching technique with a hyperbolic shape of the traces near the foF2 cusp. Zabotin et al.  developed a method to perform a three-dimensional electron density profile inversion for ionograms by using an iterative ray-tracing approach and the output of the autoscaling technique for Dynasonde [Wright and Pitteway, 1998]. A method was developed by Ding et al.  to automatically scale the parameters of the F2 layer by a template matching method based on a model of the F2 profile shape that uses empirical orthogonal functions (EOFs). Rice et al.  developed an approach named Expert System for Ionogram Reduction to automatically extract ionospheric characteristics by using a combination of physics-based modeling and knowledge-based pattern recognition techniques. Liu et al.  presented an automatic algorithm which combined with the fuzzy logic computation and constraint extrapolating. Chen et al.  developed a method that was mainly based on mathematical morphology, graph theory, and the echo characteristics of the ionosphere to scale F layer trace. The presented technique described in this paper is a template matching algorithm that obtains trace templates from a candidate pool of Ne profiles represented as quasi-parabolic segments (QPS), whose size is reduced by the EOF and image technique.
 The template matching approach to ionogram autoscaling, based on finding the best matching template from a pool of synthesized trace shapes, has been practiced since the early 1970s [Wright et al., 1972]. Wright et al.  developed the automatic processing technique using this template matching technique. The process described by Wright et al.  estimated the virtual heights coordinates at the specified optimum radio frequencies, and then selected the observations nearest the predicted coordinates from a subsequent digital ionogram. Barnes et al.  developed some estimation techniques to fit recorded ionograms, and the approach described by Barnes et al. selected ARTIST-3 values as the initial values. Pezzopane and Scotto  used simultaneous fit of O polarization and X polarization traces near critical frequency cusps using a template set of typical trace shapes. In addition, Scotto  developed a method to calculate the electron density profile by adapting the parameters of a model to match recorded ionograms. Ding et al.  used the match technique to automatically scale the parameters of the F2 layer based on empirical orthogonal functions of the ionospheric electron density profiles defined using the International Reference Ionosphere (IRI) profile shape formalism [Bilitza, 1990]. Vesnin et al.  introduced a technique of adding plasma irregularities to the initial Ne profile to better match ionograms showing signatures of traveling ionospheric disturbances.
 The proposed work uses the same principle as previous work [Wright et al., 1972; Barnes et al., 1998; Pezzopane and Scotto, 2007; Scotto, 2009; Ding et al., 2007; Vesnin et al., 2011], but it improves the performance in several aspects. The QPS model is used to simplify the trace synthesis task. The empirical orthogonal functions and the image processing technique are used to reduce the size of the candidate traces for a more accuracy initial parameters in the QPS model. The presented technique calculates the candidate traces with the parameters of the QPS model based on the IRI model and then uses the empirical orthogonal functions and the image processing technique to reduce the size of the candidate traces. Furthermore, it selects the initial candidate trace from the new smaller candidate traces based on fit quality. Finally, we adjust the initial candidate trace to obtain the best fit candidate trace by using the parameters of the QPS model.
 In the presented work, the results of the automatic scaling of ionograms are sorted into three categories. The first category is formed by all ionograms whose fit quality exceeds a threshold value Cth. The second category is the initial estimation when the fit quality does not exceed Cth. The worst result is the third category which represents no signal echo trace in the ionograms. In the following paragraphs, we first introduce the flow of the automatic scaling technique and then describe the technique in detail. Finally, this paper verifies the performance of the technique by comparing the results with those obtained using the manual method.
2 The Automatic Scaling Technique for F1 Critical Frequency and F2 Parameters
 Before automatic scaling of ionograms, the proposed technique needs to provide the sample parameters for establishing the initial parameters of the QPS model. First, the presented technique obtains the sample parameters from the IRI. However, because the size of the sample parameters from the IRI is large, it uses the EOF to reduce the data size so as to decrease the calculation time. Once the new sample parameters have been calculated by the EOF, the technique uses image processing methods to obtain critical frequency parameters of the F1 layer and the F2 layer, and then it defines the critical frequencies as initial frequencies. With the initial frequencies determined by image processing methods, the proposed technique can further reduce the size of the sample parameters by choosing the parameters near the critical frequencies. Finally, we determine the initial height parameters of the ionograms from the smallest sample parameters by using the projection of image processing technique and correlation. As a result, the initial values, including the frequencies and height parameters, are close to the best fit values. Furthermore, the best fit values of the parameters would be determined by fine-tuning the initial values. Figure 1 illustrates the flowchart of the automatic scaling technique that is described in this paper. In addition, once the sample parameters have been established by the IRI and EOF, this technique will no longer establish the sample parameters before it dynamically selects the smallest sample parameters from the sample parameters.
2.1 Quasi-Parabolic Segments Model
 In the present study, the technique uses the QPS model to calculate the electron density profile and synthesize the trace. Compared with other models [Reinisch and Xueqin, 1983; Titheridge, 1985, 1988; Zabotin et al., 2006; Scotto, 2009], the QPS model has a smaller number of parameters of the ionospheric model and facilitates the calculation of the synthesized trace.
 The quasi-parabolic (QP) model is an ionospheric theoretical model that can calculate the ionospheric electron density with determined parameters. The QP model is represented by the following formula [Croft and Hoogasian, 1969; Dyson and Bennett, 1988]:
where Ne is the electron density at a radial distance r from the Earth′s center, Nm is the max electron density at the layer, rb is the radial base height of the layer, rm is the radial height of Nm, and ym is the layer′s semilayer thickness.
 The ionosphere can be reconstructed by the QP models which describe the ionospheric layers and the QP segments which describe the junction of the layers. This model is named QPS, and it is represented by the following formulae [Croft and Hoogasian, 1969; Dyson and Bennett, 1988]:
where a = Nm, b = Nm(rb/ym).
where , ajFE = aE, rjFE = rE,
 Much work has been devoted to inversion of VI ionograms [Norman, 2003] and backscatter ionograms [Rao, 1974; Song et al., 2011] based on the QPS model. In this paper, the automatic scaling technique uses the QPS model to calculate the synthesized trace and correlates it with the recorded ionogram. In this work, we assume that both the effect of the magnetic field and the collision are neglected, and then the ordinary trace can be calculated by the formulae written as [Xiong et al., 1999]
where f is the working frequency, hb is the bottom of the ionosphere, hr is the height of the reflecting position, u′ is the group refraction index, and fp is the plasmas frequency.
 Because of the divergence of the group reflective index in the vicinity of the height of reflection, the synthesized trace calculated by formulae (7)–(8) is instable. The divergence phenomenon was addressed by both Titheridge [1985, 1988] and Scotto et al. . The presented work uses the method developed by Scotto et al. to avoid the divergence phenomenon.
 In the presented study, the parameters of the QPS model for the E layer are defined as
 The parameters of the QPS model for the F1 layer are defined as
 The parameters of the QPS model for the F2 layer are defined as
 In formulae (9)–(11), the subscript IRI indicates that the value is from the IRI model.
 Figure 2 is a typical synthesized trace and the electron density profile with the QPS parameters of the ionospheric layers, where foE is the critical frequency of the E layer, ymE is the semilayer thickness of the E layer, rmE is the peak height of foE from the Earth′s center, foF1 is the critical frequency of the F1 layer, ymF1 is the semilayer thickness of the F1 layer, rmF1 is the peak height of foF1 from the Earth′s center, foF1 is the critical frequency of the F2 layer, ymF2 is the semilayer thickness of the F2 layer, is the peak height of foF2 from the Earth′s center, and Ro is the radius of the Earth.
2.2 Empirical Orthogonal Functions
 In this study, the presented technique uses EOF to build an empirical model of the parameters of the QPS model to reduce the matching time. The EOF is an empirical model for extracting the characteristics of the history data, and it was first introduced by Lorenz who applied it for researching the weather in the early 1950s [Huang, 2004]. This method was firstly introduced into ionospheric research by Dvinskikh and Naidenova [Dvinskikh, 1988; Dvinskikh and Naidennova, 1991]. Recently, the EOF has been widely used to research ionospheric characteristics [Wang et al., 2004; Mao et al., 2005; Ding et al., 2007; Shi et al., 2010].
 The sample parameters of the QPS model are obtained from the IRI and represented by formulae (9)–(11), and the corresponding time varies from 1993 to 2003. Furthermore, the sample parameters can be represented by a one-dimensional random variable that is written using the following formula:
where t is the time variable and it varies from 1993 to 2003 with a 1 h step.
 To reduce the matching time, this work establishes a new data set Z(t), which can indicate the characteristics of ionospheric variation but smaller than the sample parameters from the IRI. By carrying out an analysis of the characteristics of the X(t) based on the EOF [Huang., 2004; Wang et al., 2004; Ding et al., 2007], the presented technique can obtain the linear expression of the ionospheric parameters, which is represented by formula (13).
where Z(t) is the smaller new data set, is the average of the X(t), N is the number of quantities of X(t), ai(t) is the ith-order time index of orthogonal function, and Ei is the ith-order orthogonal function.
 Previous work [Ding et al., 2007] suggested that the first four orders can indicate the variation of the ionospheric parameters. By adjusting the first four orders time index of orthogonal function, we can obtain the new data set Z(t) of the sample parameters.
2.3 Establishing the Initial Values of F2 Parameters and foF1
2.3.1 Initial Value of the F1 Critical Frequency
 This section introduces how to determine the initial value for the F1 critical frequency of ordinary waves. The typical F1 trace is regular, and there is a peak value on the left of the F layer trace. This work establishes the initial value of F1 critical frequency by calculating the slopes of the line between the signal points and the reference position. Figure 3 illustrates the flowchart of establishing the initial value of the F1 critical frequency, where N is the amount of signal points at the left of the maximum slope value, and Nth is the threshold value of N for estimating the F1 critical frequency.
 A recorded ionogram can be represented by a two-dimensional amplitude matrix and is represented by W(M,N), whose numbers are given by the following formulae:
where fw max, fw min, and Δf are the maximum frequency of the processing matrix, the minimum frequency of the processing matrix, and the resolution of the frequency, respectively; , , and Δh′ are the maximum virtual height of the processing matrix, the minimum virtual height of the processing matrix, and the resolution of the virtual height, respectively.
 In this study, the minimum frequency of the processing matrix fw min is defined as the starting frequency of the sounding system, and the maximum frequency of the processing matrix fw max is defined as the stopping frequency of the system. The virtual height range of the processing matrix is dynamic with the seasonal and diurnal changes. The minimum value varies from 200 km to 250 km, and the maximum value varies from 300 km to 600 km. In order to remove the interference of the trace of the E layer and the trace of the F1 layer extraordinary ray, the proposed technique selects the signal points of the maximum virtual height at the working frequency in the processing matrix. Furthermore, the algorithm calculates the slopes between the signal points and the reference point which is defined as the left-bottom point of the processing matrix. The slope is represented by the following formula:
where K is the slope, m0 = 1, n0 = 1, fw is the working frequency, is the maximum virtual height of the signal points at the working frequency fw, the signal point is (m,n), and the reference point is (m0,n0).
 Figure 4 illustrates the ionogram with the F1 layer trace and the characteristics of its slopes, where foF1 is scaled as 4.9 MHz. Figure 5 illustrates the ionogram without the F1 layer trace and the characteristics of its slopes. The results reveal that if the amount of signal points exceeds the threshold value Nth, the F1 critical frequency is at the position of the maximum slope, or the method considers the F1 layer not present.
2.3.2 Initial Values of the F2 Critical Frequency
 In order to determine the initial value of the F2 critical frequency, a searching window S(M,N) is defined to search the signal points for the F2 layer and is represented by the following formulae:
where ΔfS is the horizontal size of the searching window, Δf is the resolution of the frequency, is the minimum virtual height of the searching window, is the maximum virtual height of the searching window, and Δh′ is the resolution of the virtual height.
 In this work, we define the horizontal size of the searching window ΔfS as 0.5 MHz. The minimum virtual height varies from 250 km to 300 km, and the maximum virtual height varies from 300 km to 600 km in this paper. The vertical size of the searching window is dynamic with the seasonal and diurnal changes.
 The searching window starts from the maximum working frequency to the minimum working frequency. In order to remove noise interferences, the proposed technique determines the initial values of the F2 critical frequency only when more than half of signal points are in the searching window. Furthermore, it defines the middle value of the searching window as fxF2 and fxF2 −0.6 MHz as foF2, because we consider that the difference is 0.6 MHz between the initial ordinary and extraordinary ray critical frequency over Wuhan. The proposed technique further adjusts the initial values to obtain the best fit values in the following paragraph. Figure 6 illustrates the flowchart for establishing the initial value of the F2 critical frequency, where N is the number of signal points be in the searching window, and Nth is the threshold value of N to estimate the F2 critical frequency.
2.3.3 Initial Values of the Peak Height and Semilayer Thickness
 In this section, the presented technique calculates the fit quality between the recorded ionograms and the synthesized traces using the image projection [Sun et al., 2000] and correlation.
 Once the initial parameters of critical frequencies have been determined in the previous sections, it further obtains the smallest sample parameters Zmin(t) from the sample parameters Z(t) by choosing the sample parameters near the initial critical frequencies. Finally, the technique determines the initial parameters of the peak height and semilayer thickness from the smallest sample parameters Zmin(t) using image projection and correlation.
 A recorded ionogram can be defined as a two-dimensional matrix A(M,N), whose numbers are written as
where fmin is the minimum working frequency, fmax is the maximum working frequency and Δf is the resolution of the frequency, is the base virtual height of the E layer, is the maximum virtual height of the F2 layer which varies with the seasonal and diurnal changes, and Δh′ is the resolution of the virtual height.
 The projection of the ionogram matrix A(M,N) at the virtual height is given by the following formula:
where F is the projection of A(M,N), f, h′, fxF2, and δf are the working frequency, the virtual height corresponding to f, F2 layer extraordinary critical frequency determined by section 2, and the error estimation of fxF2, respectively.
 This work calculates the projection F of the recorded ionograms and the projections F′ of the synthesized traces using formula (21). Then the proposed technique calculates the correlation values between F and F′ using formula (22).
 Thus, it selects the corresponding height parameters of the max correlation values as the initial parameters of the peak height and semilayer thickness from the candidate synthesized traces.
 Figure 7 illustrates the matched projections of the recorded and synthesized traces and the corresponding matched ionograms. The result reveals that the algorithm performed well to obtain the matched initial parameters of the height. Furthermore, the next step is to fine-tune all of the initial parameters to obtain the best fit parameters. Figure 8 illustrates the best fit synthesized trace, which corresponds to Figure 7, using the proposed technique.
2.4 Confirming the Final Values of the F2 Parameters and foF1
 Once the initial parameters of the ionosphere have been determined, the discussed method will calculate the synthesized traces to match the recorded ionogram based on the QPS model and formulae (7)–(8). The primary task of this part of the method is to fine-tune the initial parameters of the best fit parameters with fit quality.
 The initial values of the ionospheric layers are determined by the proposed technique and are foF1 _ init, rmF1 _ init, foF2 _ init, fxF2 _ init, rmF2 _ init, and ymF2 _ init. In order to obtain the best fit values, foF1 varies from foF1 _ init − 0.2 to foF1 _ init + 0.2; rmF1 varies from rmF1 _ init − 50 to rmF1 _ init + 50; foF2 varies from foF2 _ init − 0.3 to foF2 _ init + 0.1; rmF2 varies from rmF2 _ init − 50 to rmF2 _ init + 50; ymF2 varies from ymF2 _ init − 50 to ymF2 _ init + 50. Lastly, fxF2 varies from foF2 + 0.5 to foF2 + 1. Once the parameters for the ordinary ray trace have been determined, it further obtains the extraordinary ray′s critical frequency. The varying step of the frequency is 0.1 MHz, and the varying step of the height is 20 km. After we obtain the best fit parameters, the present technique can obtain the virtual height h′F2 of the F2 layer from the trace synthesized by the QPS model.
 On the basis of the fit quality between the recorded and synthesized trace, the results of the automatic scaling technique will be sorted in three categories. This study sets a fit quality threshold value Cth. If the fit quality exceeds the Cth, the proposed technique will output the best fit values of ionospheric parameters; if the fit quality does not exceed the Cth and the foF2 _ init presents, then the initial values of the parameters will be given as output; if the foF2 _ init does not present, the output will be NA (Not Applicable). Figures 9 and 10 illustrate the automatic scaling results of the ionograms with the best fit values. Figure 9 corresponds to the VI ionogram with the F1 layer trace, and Figure 10 corresponds to the VI ionogram without the F1 layer trace. Figure 11 illustrates the initial values, of which the fit quality value does not exceed the threshold value Cth. In Figure 12, the technique cannot obtain the values and it displays NA values.
3 The Performance of the Automatic Scaling Technique
 To test the performance of the automatic scaling technique, the presented work compares the automatic scaling results with the manual scaling results. The test divides the recorded ionograms into two categories: a low level of radio noise and a high level of radio noise. To allow for a possible seasonal and diurnal variation in the performance of the automatic scaling technique, the test uses the ionograms recorded in May 2012, July 2012, August 2012, September 2012, and December 2012 at Wuhan. In this paper, a value is considered an accurate value if it is within ± 0.05 MHz of the manual value for the frequency and ± 5 km of the manual value for the height. An acceptable value is within ± 0.5 MHz of the manual value for the frequency and ± 25 km of the manual value for the height, which is in line with the Union Radio Scientifique Internationale limits of ± 5Δ (Δ is the reading accuracy).
 The results are verified by error calculations of the parameters which are represented by the following formula:
where the subscript auto indicates the automatic scaling value and the subscript manual indicates the manual value.
 To verify the performance of the technique described in this paper, a test was performed using 750 ionograms recorded in May 2012, July 2012, August 2012, September 2012, and December 2012 at Wuhan. These ionograms were selected from all recorded ionograms with a low level of radio noise, and these ionograms were scaled manually by the same person and scaled automatically using the proposed technique. Figure 13 reports the differences between the automatic scaling values of the technique described here and the standard manual values. Table 1 illustrates the percentages of error statistical distributions of parameters for the differences. Based on the comparison of Wuhan results, the technique is performed well, especially for the F2 layer parameters.
Table 1. The Percentages of Error Statistical Distributions of Parameters With a Low Level of Radio Noise
Total numbers of ionograms
 In order to study the robustness of the method described here, another test was performed using 1164 ionograms with a high level of radio noise. These ionograms were recorded in May 2012, July 2012, August 2012, September 2012, and December 2012 at Wuhan. Figure 14 reports the differences between the automatic scaling values of the technique described here and the standard manual values. Table 2 illustrates the percentages of error statistical distributions of parameters for these differences. When the technique is applied to the ionograms with a high level of radio noise, as Table 2 shows, the acceptable values are above 80% for the F2 layer parameters. The results demonstrate sufficient robustness for the proposed technique.
Table 2. The Percentages of Error Statistical Distributions of Parameters With a High Level of Radio Noise
Total numbers of ionograms
 This paper presents an automatic scaling method that is a template matching algorithm that obtains trace templates from a candidate pool of Ne profiles represented as QPS, whose size is reduced by the EOF and image technique. The method introduces how to determine the initial parameters and then fine-tunes the initial parameters to fit the recorded ionograms. Furthermore, to verify the performance of the technique, the presented work compares the automatic scaling results with the manual results. Our results reveal that it works sufficiently well in practical utility at Wuhan. However, the technique described in this paper is not in a final form, and it still requires some adjustments to improve the performance of the proposed technique. In particular, the performance of the automatic scaling of foF1 is still insufficient. Some future research activities include the following: the application of the proposed technique to the ionograms recorded at different locations and during spread F conditions, improving the performance of scaling of foF1 in combination with a model of the F1 layer, and removing the interference of the multiple reflection echoes.
 This work was supported by National Natural Science Foundation of China (NSFC grant NO.41304127 and NSFC NO.41204111). The authors are grateful to Carlo Scotto and two anonymous reviewers for their assistance in evaluating this paper. We thank editors for the useful comments and suggestions. We acknowledge Chen Zhou for his useful comments on this manuscript.