Study of a coincident observation between the ROCSAT-1 density irregularity and Ascension Island scintillation

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1 RADIO SCIENCE, VOL. 47,, doi: /2011rs004908, 2012 Study of a coincident observation between the ROCSAT-1 density irregularity and Ascension Island scintillation Y. H. Liu, 1 C. K. Chao, 2 S.-Y. Su, 2,3 and C. H. Liu 1,4 Received 26 October 2011; revised 10 July 2012; accepted 16 July 2012; published 7 September [1] A coincident observation that occurred on 24 March 2000 between the irregularity structure measured by ROCSAT-1 and the scintillation experiment at the Ascension Island has been studied. The study of scintillation statistics is carried out first, and the results show that the Nakagami distribution can portray the normalized intensity of the L-band scintillation at various S4 values, up to S4 equal to 1.4. Moreover, the departure of frequency dependence on S4 predicted by the weak scintillation is noticed due to multiple forward scattering effects. The coincident feature between the characteristics of irregularity structure and the scintillation variation are then studied. The causal relationship between the fluctuation of ion density and the scintillation variation is obtained. A numerical simulation using the parabolic wave equation has been carried out with the ROCSAT-1 data in space to compare with the ground scintillation observation. The results show the reasonable scintillation level at the coincident time to indicate a direct relationship between the irregularity structure and the scintillation in both temporal and amplitudinal variations. Finally, some assumptions and limitations of the simulation model are discussed. Citation: Liu, Y. H., C. K. Chao, S.-Y. Su, and C. H. Liu (2012), Study of a coincident observation between the ROCSAT-1 density irregularity and Ascension Island scintillation, Radio Sci., 47,, doi: /2011rs Introduction [2] As the radio wave propagates through the ionospheric random media, the irregularities scatter the wave, the phase mixing occurs on the path to the receiver. Thus, scintillation phenomena, temporal phase and amplitude fluctuations in the received wave, are observed in the presence of relative motion of the irregularity and the receiver. It is known that the electron density fluctuation in the ionosphere is a direct quantity of concern in the scintillation phenomenon. [3] Since the study of ionospheric scintillation belongs to the problem dealing with the wave diffraction and propagation through a random media, the scintillation problem can be solved by finding the description that maps a point in the probability space of fluctuating media onto a point in the probability space of wavefield. Although the description in the analytical method is preferred, no such method is available at this moment. Therefore, by relaxing the requirements in the problem, a more modest answer can be achieved in the 1 Department of Electrical Engineering, National Central University, Chung-Li, Taiwan. 2 Institute of Space Science, National Central University, Chung-Li, Taiwan. 3 Center for Space and Remote Sensing Research, National Central University, Chung-Li, Taiwan. 4 Academia Sinica, Taipei, Taiwan. Corresponding author: Y. H. Liu, Department of Electrical Engineering, National Central University, Chung-Li, Taiwan. (yhliu168@gmail.com) American Geophysical Union. All Rights Reserved /12/2011RS mathematical manipulation with some approximations [Yeh and Liu, 1982]. Rino [1979, 2011] has derived a thin phase screen method for case of weak scintillation caused by the propagation of electromagnetic wave through a turbulent media with some approximations such as the forward propagation approximation, far field approximation and weakly inhomogeneous media. While, to describe the wave propagation through the ionospheric media, Yeh and Liu [1982] adopted a parabolic equation approach applicable for various levels of scintillation. [4] In the past, there are some scintillation studies using the in situ measurements to compare the electron density fluctuations in the ionosphere with the ground scintillation observation. In the study of Wernik and Liu [1974], the Rytov solution is carried out using the numerical computation of scintillation with the assumed irregularity spectra. Basu et al. [1976] used the OGO-6 ion density measurement and the power law phase screen model with some assumed geophysical parameters to derive the occurrence rate of VHF scintillation in winter. In the report of Wernik et al. [2007], a scintillation climatological model for the Northern Hemisphere high-latitude region was obtained using the density observations from DE2 satellite and a closed form expression of the phase screen theory of Rino [1979]. The methodology of Wernik et al. [2007] was modified by Liu et al. [2012] in the study of scintillation morphology in the lowlatitude region using the ROCSAT-1 data taken during the years of 2000 to In the modified method, Liu et al. [2012] was able to obtain additional parameter of the outer scale distribution for the irregularity structures. In Franke 1of12

2 Figure 1. The coincidental measurements. (a) The irregularity measurement from ROCSAT-1 in the satellite time line. (b) The VHF scintillation measurement. (c) The VHF S4 value. (d) The L-band scintillation measurement. (e) The L-band S4 value. and Liu [1983], the multifrequency scintillations measured at the Ascension Island were used to derive the irregularity model from the numerical simulation under the assumption of weak scintillation. The scintillation spectrum derived from the two component model of the irregularities was shown to be consistent with the spectrum from the scintillation measurement. [5] Therefore, it is realized that ionospheric scintillation phenomena have been investigated using two approaches in the past. One approach depends on the measured ionospheric electron density distributions. Numerical computations of radio waves propagating through an ionosphere modeled by the measured electron density distributions are used to simulate the scintillation pattern observed on the ground. The second approach uses the scintillation signals recorded on the ground at different locations to derive the statistical properties of the ionospheric irregularities. It is quite obvious that better test of the ionospheric scintillation theory can be achieved if we have coincidental observations of electron density in the ionosphere and scintillation signals on the ground. [6] Through the efforts of many studies in the past, weak scintillation models, phase screen theory and the Rytov solution, have been verified. As the multiple forward scattering effect dominates the fluctuations of both phase and amplitude, the scintillation becomes strong and the weak scintillation model cannot be applied any longer [Yeh and Liu, 1982; Rino, 1992]. In this paper, we will study one such rare strong scintillation event with the coincident observation of the ionospheric irregularities to test the strong scintillation model. We will use the ionospheric irregularity density observed by ROCSAT-1 at 600-km altitude and the coincident scintillation observations recorded at the Ascension Island to study the characteristics of interaction between the radio waves and the density irregularities that produces the observed ground scintillation data. Moreover, the relationship of frequency dependence on S4, the normalized variance of the signal intensity, predicted by the weak scintillation theory will be studied in the scintillation measurement. The discussion of multiple scattering effects will be presented with the spectral and time series analyses of the ground measurements. Finally, we will use the parabolic equation method (PEM) to simulate the scintillation on the ground from the wave propagation through the observed irregularity structure in space. The result of the simulation study is then used to discuss the assumptions and limitations of the simulation model by comparing with the ground observation. 2. Observations [7] On 24 March 2000, the flight path of ROCSAT-1 orbiting at 600-km altitude entered the region above the Ascension Island (7 58 S, W, S dip latitude) near the southern peak of Appleton anomaly region and encountered the irregularities. At the same time, scintillations in the radio bacon experiments were recorded at 50 Hz sampling rate at the Ascension Island from two geostationary satellites, FLEETSAT (23 W) for the VHF (244 MHz) channel and MARISAT (15 W) for the L-Band (1.541 GHz) channel. The ROCSAT observation and the ground scintillation event indicate that a coincident observation between space and ground seems to take place. A coincident geometry is thus constructed with the magnetic field line geometry from the IGRF model and the flight path of ROCSAT for detailed study. Here we present the observations in space and on the ground during the coincident period in Figure 1 first. 2of12

3 Figure 2a. The 3-D geometry of the flight path of ROCSAT-1, the lines of sight between the satellites and ground receiver. The geomagnetic field lines that are cut by ROCSAT and the two beacon lines at 350 km altitude are shown by open circles. [8] Figure 1a, we show the ion density measurement sampled at 1024 Hz. The density irregularity structure is detected by ROCSAT-1 at 21:33:05 UT for 113 s. The irregularity structure can be approximately divided into three depletion regions from the results using a bubble detection algorithm [Su et al., 2006]. The duration of the first depletion region is from 21:33:05 to 21:33:30 UT, the second depletion region is from 21:33:45 to 21:34:35 UT, and from 21:34:40 to 21:35:03 UT is the third depletion region. It is noted that the time duration for traversing the three depletions is very short and the spatial extent of the depletions is about 860 km in space. [9] The scintillation data at the two frequency bands are presented in Figures 1b 1e. We notice that the two scintillation events in both frequency bands occurred, a long fluctuation event and a short one. In Figures 1b and 1c, the relative intensity of the scintillation and the S4 variation for the VHF signal are shown. The first VHF scintillation event starts around 21:24:01 UT then increases the scintillation level gradually and ends around 22:21:56. The period of the second event is from 22:39:41 to 22:56:01 UT. In both events, the S4 value indicates strong scintillation with saturation value around 1. In Figures 1d and 1e, we present the relative intensity of the scintillation and the S4 value for the L-band. The L-band scintillation begins around 21:33:21 UT with an amplitude fluctuation of 26 db and ends around 22:35:03. The second event starts at 22:45:51 UT and lasts for 10 min. In the L-band scintillation, the S4 value shows strong scintillation with variable values around and above 1. The L-band scintillation does not seem to suffer from saturation. [10] For different propagation paths, zenith angles and sensitivities to the irregularity structure of the two signals, there exists a time lag between the onsets of scintillation between the two bands. These time lines are also different from the observed time lines of the depletions in the ROCSAT-1 data. The maximum amplitude fluctuation of 30 db peak-to-peak is observed in the L-band and 21 db peak-to-peak is observed in the VHF band. In general, the VHF band should indicate a larger scintillation level than the L-band signal, but this is not observed here. The reason of observing a higher scintillation in the L-band will be discussed later in section 3.1. [11] A 3-D geometry of this coincident observation is presented in Figure 2a with the lines of sight from the two geosatellites to the ground receiver, the flight path of ROCSAT-1 and the geomagnetic field lines that pass through the depletion structure. In this figure, we identify the coincident times for the satellite measurement at 21:34:58 UT and the ground coincident times for the VHF and L-band channels at 21:28:18 UT and at 21:35:06 UT, respectively. The sequence of coincident observation is such that the black solid line represents the field line that contains the depletion structure which intersects the VHF signal observes a rapid rise of scintillation has not been traversed by ROCSAT yet. Then, ROCSAT passed the existing depletion structure on the geomagnetic line denoted by the black dashed line at a velocity of 7.6 km/s. As the depletion structure drifts eastward to the geomagnetic line (the green line) that intersects the line of sight of the L-band signal, the L-band scintillation begins. It should be noted that the time duration for ROCSAT to traverse the space structure is much shorter than the time periods of the ground scintillation observations as were seen in Figure 1. We have used the field lines of the IGRF model to identify the coincident points for the L-band and VHF channels. The longitudes of the magnetic field lines intersecting the lines of sight for the L-band and VHF channels at 350-km altitude are anchored 3of12

4 Figure 2b. The 2-D geometry of the flight path of ROCSAT-1, the lines of sight between the satellites and ground receiver. at W and W, respectively. The separation distance for the lines of sight of the VHF and L-band channels at the 350-km altitude is around 20 km. The 2-D geometry is also presented in Figure 2b for additional visualization of the coincident geometry. [12] The characteristic of density irregularity structure is studied next. The results of the characteristics of irregularity structure from the spectral index of density fluctuation (the slope in the power law spectrum), the outer scale (the largest scale in the power law spectrum) and DN (rms ion density fluctuation) are shown in Figure 3. These results are derived by performing the spectral analysis on an 8-s segment data of the density irregularity structure. In the figure, the detected irregularity structure is indicated by a circle, while the asterisk denotes the density variation that is not detected as a bubble. To obtain the parameters in Figure 3, the 8-s data is detrended first by a second-order parabolic equation to perform the spectral analysis. A least squares curve fitting in the Figure 3. (a d) The parameters, spectral index, outer scale and DN, describing the irregularity. The detected structure is signified as a circle and an asterisk denotes a structure not detected as a bubble. 4of12

5 Figure 4. The probability distribution of the normalized L-band intensity measurements at different scintillation levels. trust region method is then adopted to fit the spectrum to obtain the optimal solution for the spectral index of density fluctuation, the outer scale and DN, within the preset trust regions [Liu et al., 2012]. [13] We noted that the spectral indices are distributed between 1 and 4 as seen in Figure 3b. The mean value is 2.12 and the variance is In Figure 3c, over 75 percent of the outer scale is seen to be smaller than 25 km. In Figure 3d, we notice that DN has a lower value in the center part of the irregularity structure and becomes larger at the edge of the structure. In addition, DN in depletion 2 is higher than that in depletion 1 and 3. Later, we will show that such variation corresponds to the occurrence of scintillation observed on the ground. [14] It is known that the statistics of scintillation measurement can be fitted with the Nakagami distribution for the intensity of scintillation [Fremouw et al., 1980; Aarons, 1982; Yeh and Liu, 1982; Rino, 1992]. Aarons [1982] reported that the Nakagami distribution provides a reasonable approximation to the scintillation; but the Rayleigh probability density function (PDF) provides a better one in the case of strong scintillation (S4 > 0.9). On the other hand, Rino [1992] demonstrated that the Nakagami distribution presents a reasonable fit to the measured data up to S4 > 1. In Figure 4, we present the probability distributions of normalized intensities in the L-band scintillation at different S4 values. The normalized intensity, I/<I>, is obtained from the measurements shown in Figure 1d at certain S4 ranges. I is the scintillation intensity and <I> is the averaged value. There are about 3000 data points in each panel of Figure 4. From the figure, we notice that the Nakagami distribution can be used to characterize the statistics of normalized intensity in our case for different L-band scintillation level up to S 1.4. Although not shown here, the Rayleigh power density function does not indicate a reasonable fit to the intensity of the scintillation in our case when S4 is larger than 0.9. [15] In the Figure 5 (left), four spectra for the VHF and L-band scintillation with S4 > 0.8 at the same time interval are shown in the blue and red lines, respectively. In Figure 5 (right), the corresponding normalized correlation coefficients from the data in the same respective time intervals for both frequencies are presented by the same respective colors. The decorrelation time for both channels is set when 50 percent of the data are decorrelated. Each data point shift in the correlation study corresponds to 0.02 s. The spectra on the left are normalized to the Fresnel frequency which can be expressed by f m = u m /F, where u m is the drift velocity of the irregularity structure which is 160 m/s measured p ffiffiffiffiffiffiffi by ROCSAT. The Fresnel scale, F, is given by F ¼ 2lz, where l is the wavelength of the radio frequency; z is the slant range from the observing site to the bottom of the ionospheric irregularity layer. In the case of normal incidence, the bottom of the irregularity layer is set at 300-km in altitude. The Fresnel scale is about 1 km for a wave frequency of the VHF band and 400 m for the L-band. In the case of weak scintillation, the roll-off frequency in the spectrum is dominated by the Fresnel frequency. Also, we expect to have a lower Fresnel frequency as frequency decreases. However, we notice in the figure that the roll-off frequencies in the VHF spectra extend much further than those in the L-band spectra. The broadening of VHF spectrum leads to the shorter decorrelation interval in comparing with that for the L-band. For example, in the top two panels in Figure 5 (left), the broadening of VHF spectrum is 5of12

6 Figure 5. (left) The spectra of VHF (blue lines) and L-band (red lines) as a function of frequency normalized to Fresnel frequency. (right) The corresponding normalized correlation coefficients to the left spectra are presented. The green dotted line of 0.5 is used to calculate the decorrelation time. observed. The corresponding correlation coefficients for both channels in Figure 5 (right) show that the calculated decorrelation time for the VHF band is 0.06 s in comparison with 0.34 s for the L-band. In all four cases, the decorrelation time for the L-band is about 3 to 8 times longer than that of the VHF band. 3. Results and Discussion 3.1. The Comparison of the Coincident Observations [16] To study the causal relationship between the scintillation and the irregularity structure, we need to identify the portion of coincident observation from the Ascension Island and ROCSAT-1 in the same time scale. As the irregularity structure with different scale sizes is assumed to map along a magnetic flux tube, we can present the coincident geometry from the flight path of ROCSAT-1 and the lines of sight between the ground receiver and the two geosynchronous satellites in the same magnetic flux tubes as shown in Figure 2. After comparing the signature between the ion density variation and the scintillation, we conclude that the onset of the irregularity should be the time that initiates the scintillation. Thus, the coincident time on the ROCSAT observation is identified at 21:34:58 UT. Then, the coincident times on the ground are 21:28:18 UT for the VHF band and 21:35:06 UT for the L-band. [17] The ground scintillation sequence in time will indicate that the scintillation is caused by a space structure which is traversed by ROCSAT at a later time. As the density structure in space is observed by ROCSAT to drift eastward at 160 m/s, we need to invert the density structure (and time) to compare with the ground scintillation time. The section of density structure in the coincident observation can be converted to the time line in the scintillation observation by the following equation where ð t g ¼ t cg t s t cs Þ v sg ð1þ v dg t s the time tag on the satellite t cg the coincident time on the ground t cs the coincident time on the satellite v sg the satellite ground velocity v dg the irregularity drift velocity t g the time tag on the ground [18] The ground velocity of ROCSAT-1 is 7.6 km/s. From the ROCSAT-1 measurement, the eastward drift velocity of the irregularity used in equation (1) is taken as 160 m/s. t cs is 21:34:58 UT for both frequencies. tcg is equal 6of12

7 Figure 6. (top, middle, bottom) The time conversion between the duration of satellite measurement to the time line of scintillation of L-band. to 21:35:06 UT and 21:28:18 UT for the L-band and VHF links, respectively. Using equation (1), we convert the duration of irregularity observation to the ground observational times with reference to the derived ground and satellite coincident times for both channels. The results are shown in Figure 6. As seen in Figure 6 (top), the duration (around 150 s) of the irregularity observation in the satellite time line is converted to the ground observation time for about 2 h (Figure 6, middle). Thus we have the irregularities and the L-band scintillation measurements (shown in Figure 6 (bottom)) in the same time line, the L-band ground observation time, for the study. The L-band ground coincident time 21:35:06 UT is shown in Figures 6 (middle) and 6 (bottom) by the dotted line for reference. Similarly, the ROCSAT data is converted to the same time line to compare with the ground VHF scintillation. [19] The comparison for the characteristics of irregularity with the L-band scintillation for the coincident observation is presented in Figure 7a and for the VHF band, in Figure 7b. In both figures, the dotted line indicates the ground coincident time of each corresponding frequency band. In the report of Rino [1979], the scintillation is shown to be proportional to DN and inversely proportional to the radio wave frequency in a single scattering case of weak scintillation. The irregularity sizes smaller than the Fresnel scale are more effective in causing scintillation. In Figure 7a, we present the DN variation, the scintillation index and the power spectral density at the Fresnel scale for the L-band, and the same arrangement for the case of VHF band in Figure 7b. Each S4 value is derived from a 1-min segment of data. [20] From the first and third panels of both Figures 7a and 7b, we notice that depletion 2 and depletion 3 of the irregularity structure contribute mainly to the first scintillation event, and depletion 1 causes the second scintillation event at both frequencies. In addition, in the third panel of Figure 7a, the L-band scintillation is strong except during the periods from 21:40:00 to 21:45:00 UT and from 22:24:00 to 22:34:00 in event 1. During these two periods, S4 drops to smaller than 0.6 and DN is observed to decrease. In the other period in event 1, the scintillation is strong and there are more fluctuations in the power spectral density and DN. Although DN in depletion 2 is higher than that in depletion 3, S4 is high in both depletions. Furthermore, a relationship of S4 and DN in the L-band seems existed during the periods when S4 decreases below 1 from 21:40:00 to 21:45:00 UT and from 22:24:00 to 22:34:00 UT. For other periods, when S4 fluctuates around or above unity, the variation of DN does not seem to correlate with S4. This 7of12

8 Figure 7. (a) The L-band scintillation with the ion density measurements with the power density of Fresnel scale and DN. (b) The VHF scintillation with the ion density measurements with the power density of Fresnel scale and DN. The symbol of a circle denotes the detected structure and the asterisk denotes the structure not detected as a bubble. could be due to the fact that multiple scattering effect exists and causes S4 to fluctuate around unity. This will be further discussed in the following paragraph when the frequency dependence of S4 breaks down due to multiple scattering effect. On the other hand, in Figure 7b for the VHF scintillation, the S4 is strong regardless of the variation in DN. Scintillations are strong in both channels and saturation in the VHF band is noticed in the figure. [21] When scintillation increases, the effect of multiple scattering becomes important. The irregularities at the scale size much larger than the Fresnel scale begin to dominate the scintillation and contribute to the phase fluctuation causing focus and defocus on the signal [Yeh and Liu, 1982; Franke and Liu, 1983; Rino, 1992]. Since the autocorrelation and the power spectral analysis are the Fourier transform pairs, the short correlation time indicates the fact that 8of12

9 how a relationship between the ion density and the scintillation observation could have existed. Details of the PEM model have been described in Yeh and Liu [1982]. Here we briefly recapitulate the model in the following paragraphs. [23] The assumptions of the PEM model are (1) the temporal variations of the irregularities are much slower than the wave period and (2) the characteristic size of the irregularity is much greater than the wavelength. [24] The vector wave equation is then replaced by a scalar one which is given by r 2 E þ k 2 ½1 þ ɛ 1 ðþ ~r ŠE ¼ 0 ; 0 < z < L ; ð2þ Figure 8. The scenario of the PEM simulation for the wave propagation through the ionosphere [Yeh and Liu, 1982]. the frequency spectrum has been broadened. Therefore, the effect of multiple scattering in the scintillation spectrum will increase the roll-off frequency beyond the Fresnel frequency to indicate a broadening of the spectrum. In Basu et al. [1987], the strong scintillation measurements in the L-band and VHF signals have been observed, and the spectral analyses of the measurements have shown the strong scattering effect in both frequencies. With the effect of multiple scattering, saturation of S4 will not only occur but the frequency dependence on S4 will also deviate from the trend predicted by the weak scintillation. In Figure 5, we notice that the spectra of VHF signal are broadened and the roll-off frequency increases to a higher frequency. On the other hand, the roll-off frequency is close to the Fresnel frequency in the L-band spectrum. Moreover, the calculated VHF decorrelation time is smaller than that for the L-band. This implies that the VHF signal suffers more multiple scattering effects than the L-band does. Rino and Liu [1982] introduced a symbol S4 0, an extrapolation value of the scintillation index in the case of weak scattering, to be scaled with frequency as a universal parameter to test the agreement between the theory and experiment. From their result, the observed S4 increases with the increase of S4 0 when S4 0 is small. For a large S4 0 value, S4 will asymptotically approach to unity due to the effect of multiple scattering. From the variation of S4 in the current observation, we can reason that the L-band scintillation index seems to fall into the region of 1 < S4 0 < 2 and S4 exceeds unity. On the other hand, S4 of the VHF signal lies in the region of S4 saturation, 5 < S4 0 < 6. Thus, the departure of frequency dependence on S4 is observed between VHF and L-band in our case. We also notice that in the gap between depletion 2 and 3 in Figure 7, the density perturbation was not identified as bubble by the bubble detection algorithm [Su et al., 2006]. However, the S4 values are large at both channels. It could be due to a possible cause that the irregularity structure below or above the height of satellite might be different from what is observed at the ROCSAT altitude PEM Simulation of the Coincident Observations [22] To study more about the strong scintillation observed at the Ascension Island, we adopt the parabolic equation method (PEM) approach with the density measurement from ROCSAT to simulate the scintillation on the ground to see where k 2 = k 2 0 ɛ, k 0 is the wave number in the free space, ɛ is the background average dielectric permittivity and ɛ 1 ðþis ~r the fluctuating part characterizing the random variation caused by the irregularities. In the case of normal incidence, the electric field of the complex amplitude is E ¼ u ðþexp ~r ð jkzþ; ð3þ [25] Under the assumptions of Yeh and Liu [1982], (1) the Fresnel approximation in computing the phase of the scattered field is valid and (2) in forward scattering the wave is scattered mainly into a small angular cone centered around the direction of propagation. The wave equation of equation (2) can be simplified into a parabolic equation given by 2jk u z þr2? u ¼ k2 ɛ 1 ðþu ~r ; 0 < z < L ; ð4þ u x ¼ 0; at boundary ð5þ 2 h f p d N i f N0 ɛ 1 ðþ¼ r 2 ; ð6þ 1 fp = f where f is the operating frequency and f p is the plasma frequency of the ionosphere which is proportional to the square root of ion density. [26] When we analyze the wave propagation in the ionosphere with the existence of irregularity structure as shown in Figure 8, the wave propagates in the downward z direction and irregularity structure extends in the x and z axes. In our simulation, the thickness L of the irregularity structure is assumed to be 300 km within which the variation of irregularity along the propagation axis follows the background density of IRI-2007 model, with the maximum value at the height of 350 km. The wave is assumed normally incident on the slab at z = 0, propagates through the irregularity structure down to z = 300 km, then through the unperturbed background ionosphere of IRI-2007 model to reach the receiver at the ground station (x = r, z = 600 km). For the 2-D simulation, we let r? = 2 / 2 x and assume the density variation in the horizontal direction, x. In the simulation, we take the spatial resolution of the ROCSAT-1 data as Dx = 7.4 m. Equation (5) defines the boundary condition for the problem. In equation (6), ɛ 1 is a function of dn and the frequency of 9of12

10 Figure 9. (a) The irregularity and the amplitude simulation. (b) The S4 value of VHF simulation. incident wave. Following the work of Wernik et al. [2007], we assume that the relative RMS density fluctuation, DN/N 0, is height independent. Thus, the RMS density fluctuation at different altitudes can be derived from the background density ratio and the density fluctuation detected by ROCSAT-1, and DN h2 = DN h1 N h2 /N h1 where DN h and N h are the density perturbation and the mean ion density at different altitude. The values of N h1 and N h2 are obtained by scaling the ROCSAT-1 mean background density to the value obtained in the IRI-2007 model. By the numerical method of Crank- Nicolson scheme, we solve the parabolic equation. For accuracy consideration, Dz is constrained by the Courant condition which is given by [Potter, 1973; Wilkins, 1999] Dz < 2kDx 2 ; where k =2p/l is the wave number. Outside the layer, the amplitude satisfies 2jk u z þr2? u ¼ 0; [27] In Figure 9a, the upper plot shows the ion density measurement and the lower one is the normalized VHF amplitude fluctuation obtained from the PEM simulation. Figure 9b illustrates the S4 values calculated from the amplitude fluctuation. Both figures are shown in the time line of ROCSAT density structure. We notice that the variation of wave amplitude in the simulation result follows the trend of fluctuation in ion density very well in event 1 and 2. However, in the period from 21:35:10 UT to 21:36:00 UT, the variation of DN is zero but the simulation result indicates that S4 level is high. The cause for such high scintillation is still under investigation. Because the effect of multiple scattering has been included in the simulation, the S4 shows strong scintillation most of the time. The arrow at 21:34:58 UT indicates the VHF coincident time on the satellite. [28] For comparison with the ground scintillation, we convert the PEM simulation results to those in the ground ð7þ ð8þ time line and show the results in Figure 10. Figure 10 shows the VHF scintillation measurement (Figure 10a) and the L-band scintillation (Figure 10b). Figures 10c and 10d are the simulation results of the two respective channels in the same arrangement. At the first glance, we notice that the PEM simulation has reproduced a gross feature of scintillation variation similar to the observed one in both channels. This implies that we do have a coincident observation made by ROCSAT in space and scintillation on the ground. [29] In the first scintillation event, the PEM simulation of VHF scintillation almost reproduces the identical feature on the ground observation. However, the simulation results show a higher scintillation level than the measurement at the times of 22:18:00 UT and 22:30:00 UT. Furthermore, the simulation of L-band scintillation can also reproduce the scintillation measurement except for the period between depletion 2 and 3. However, in the second event of scintillation, the PEM simulation produces a lower scintillation level than the in situ measurement. This could be caused by the fact that other irregularities below or above the ROCSAT orbit could have existed to cause strong scintillation. Furthermore, the ion density fluctuation at the height of peak density could also be larger than the assumed extrapolation value in the simulation. In addition, because the coincident observation studied here does not have the same UT time of the density measurement with the VHF and L-band scintillation observations, the evolution of irregularity structure between the times of coincident observation could also cause some discrepancy between the PEM simulation results and ground scintillation measurements. [30] Finally, the PEM simulation suffers some limitations in the assumptions we have adopted. First, due to the assumption of normal incidence, it may underestimate the scintillation for a shorter propagation path within the irregularity layer when the signal with a larger zenith angle passes. However, this assumption should cause less bias in our case with the relatively small zenith angle noticed in Figure 2. Second, the assumption of similar density fluctuation at different altitudes in each simulated irregularity layer 10 of 12

11 Figure 10. (a d) The comparison of the simulation result and the scintillation measurement. implies a high irregularity correlation in altitude. This could likely cause an overestimation of scintillation. However, the final simulation results seen in Figure 10 indicate that the PEM still can yield a good result for studying the strong scintillation event. 4. Conclusion [31] The 24 March 2000 coincidental measurements of the ROCSAT density data and the Ascension Island scintillation experiment present an opportunity to study the causal relationship between the density structure in space and the ground scintillation observation. The spectral analysis of the ground scintillation shows that the broadening of VHF spectrum is more obvious than that of L-band spectrum under the condition of strong scintillation. This indicates that S4 saturation in the VHF band is due to the effect of multiple scattering. Deviation of the frequency dependence of S4 predicted by weak-scintillation theory is noticed in the measurements. Moreover, the probability distribution of the variation of L-band normalized scintillation intensity fits the Nakagami distribution up to S4 1.4 in the current event. [32] The fluctuations in the density depletion structure indicate similar variations in the gross feature with the ground scintillation observations. However, the critical value of the density fluctuation to cause the strong scintillation on the ground cannot be identified in this single coincident observation. It is also noticed that some strong scintillation occurs at the place where the density depletion is not detected in a gap between the irregularity structures. This could be due to possible cause of the irregularity structures existed at altitudes below or above the ROCSAT orbit. The temporal evolution of the observed irregularity structure could also cause the scintillation in the gap. [33] A parabolic equation method (PEM) is adopted to simulate the scintillation with the observed and extrapolated ion density structure in the space. The level of reality for the assumed structure should be judged by the outcome of simulation results. In our simulation, the scintillation level can be reproduced reasonably well with the irregularity measurements at the coincident time. It also shows similar gross feature between the coincident depletion structure and the scintillation observation. Therefore, the extrapolated density structure used in the PEM simulation may not be far from reality. However, we recognize that the PEM model still suffers some limitations and causes biases in predicting the scintillation level. [34] As we test the relationship between the density structure and scintillation measurement in the case of a strong scintillation observation, we notice that the PEM simulation may not be able to reveal every detail in the observation. It does show a pretty good temporal variation in comparison with the ground observation in both frequency channels. It is hoped that there will be more cases to study the relationship between density fluctuations and scintillation variations. Further improvement of the simulation could also be useful to provide information for designing communication systems with the propagation channel through the ionosphere under the strong scintillation environment. [35] Acknowledgments. The work is supported in part by AFRL- AOARD research grants AOARD and and in part by the National Science Council of the Republic of China research grant NSC M The Ascension Island scintillation data was kindly provided by Santimay Basu at Boston College, Chestnut Hill, Massachusetts, USA. References Aarons, J. (1982), Global morphology of ionospheric scintillations, Proc. IEEE, 70(4), , doi: /proc Basu, S., S. Basu, and B. K. Khan (1976), Model of equatorial scintillation from in situ measurements, Radio Sci., 11(10), , doi: / RS011i010p Basu, S., E. M. Mackenzie, S. Basu, E. Costa, P. F. Fougere, H. C. Carlson, and H. E. Whitney (1987), 250 MHz/GHz scintillation parameters in the equatorial, polar, and auroral environments, IEEE J. Sel. Areas Comm., 5(2), Franke, S. J., and C. H. Liu (1983), Observations and modeling of multi-frequency VHF and GHz scintillations in the equatorial region, J. Geophys. Res., 88(A9), , doi: /ja088ia09p of 12

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