The ionosondes used for this study are located in Kototabang, West Sumatra (0.20∘ S, 100.32∘ E), and Pontianak, West Kalimantan (0.02∘ S, 109.33∘ E). For the 26 December 2019 annular solar eclipse, the maximum solar obscuration at these two locations (cf. Fig. 1) ranges between 91 % and 94 %. From 1 d prior to the eclipse event until 1 d after the eclipse event, ionosondes at these two stations were set to record one ionogram every 5 min. On other days, ionograms were recorded once every 15 min.

At the Kototabang station, a frequency-modulated continuous-wave (FMCW) ionosonde owned by the Japanese National Institute of Information and Communications Technology (NICT) was in operation. Meanwhile, at the Pontianak station, a Canadian Advanced Digital Ionosonde (CADI) owned by the Indonesian National Institute of Aeronautics and Space (LAPAN) was in operation. Both ionosondes have been in continuous operation since 2004, and they were in the midst of some repair and maintenance work during the 26 December 2019 annular solar-eclipse event. As a result, the noise level in the recorded ionograms was high, which necessitated a manual scaling process for the ionogram data analysis and interpretation. Figure 2 shows sample ionograms that were recorded at these two stations during the solar-eclipse event.

Manual scaling of ionospheric parameters from the ionograms was performed based on standard procedures provided in the UAG-23A handbook (Piggott and Rawer, 1972). Essential ionospheric parameters that were derived through ionogram scaling include the critical frequency of the F1 layer (foF1), critical frequency of the F2 layer (foF2), and apparent parabolic-layer peak height (hpF2). The scaling process was performed for all ionograms recorded in December 2019.

Dual-frequency GNSS receiver data can be used to derive TEC along the line of sight. The theory and algorithm for calculating TEC from GNSS data are based on the refractive properties of the ionospheric layer as a function of the frequency of the GNSS signal. For a given frequency f, the time delay τ along the GPS signal path is inversely proportional to the GPS signal carrier frequency as τ=40.3TEC/(cf2), where c is the speed of light (Klobuchar, 1996). From the two frequencies f1 and f2, we have a differential time delay of Δτ=τ2-τ1, from which the TEC value can be obtained using the following equation: 1Δτ=40.3cTEC1f22-1f12. This equation can be rewritten in terms of slant TEC (STEC) and the pseudorange P as 2STECp=f12(P1-P2)-bs-Br40.3(1-γ2) or in terms of STEC and the carrier phase ϕ as 3STECϕ=f12(λ1ϕ1-λ2ϕ2)-(λ1N1-λ2N2)-bs-Br40.3(1-γ2), where bs is the satellite bias, Br is the receiver bias, and λ1,2=c/f1,2, γ=f1/f2, and N1,2 are integers. STEC measurements from pseudoranges produce TEC values with high noise levels, while those from carrier phases produce more precise TEC values, albeit with ambiguity. Mannucci et al. (1993) and Skone (1998) provided a way to combine the two measurements to produce a precise TEC without the ambiguity. It is also necessary to convert STEC to the equivalent vertical TEC (VTEC), which can be written as 4VTEC=M(θ)⋅STEC,with M(θ)=1-RERE+h2sin⁡2θ, where RE is the Earth's radius, h is the height of the ionospheric shell, and θ is the zenith angle.

We derived the regional TEC using GNSS observation data in receiver-independent-exchange (RINEX) format from the Indonesian Continuously Operating Reference Station (INACORS) network, which is maintained by the Indonesian Geospatial Information Agency (BIG). The observation data are catalogued at http://inacors.big.go.id/sbc/ (last access: 4 April 2023) by the BIG. In 2019, the INACORS network consisted of 207 receiver stations. In this study, we used data from 46 receiver stations that are distributed in Sumatra and Kalimantan (cf. Fig. 1). Geographic coordinates of the INACORS stations that we used in this study are provided in the Supplement. The number of GNSS receiver stations in Sumatra is greater than that in Kalimantan, since the INACORS network is used primarily for geodetic mapping and monitoring of the Eurasian tectonic plate.

The TEC values were calculated from the RINEX observation files using the Gopi data-analysis software (Rama Rao et al., 2006; Seemala and Valladares, 2011). Only signals from the GPS constellation were used in the TEC computation, and the elevation angle cutoff was set at 20∘. For the purpose of spatial mapping of TEC data in this study, we selected an altitude of 350 km for the ionospheric piercing points (IPPs). Figure 3a–c show sample snapshots of TEC observations obtained from basic processing of the data, illustrating the spatial coverage provided by these receiver stations. Observations at 05:30 UTC on 25, 26, and 27 December 2019 are shown in these snapshots, with the IPPs represented as open circles and the TEC values indicated using a color map. The solar-eclipse path on 26 December 2019 is shown as a dashed blue curve, and the instantaneous position of the lunar shadow at that time is indicated by a solid gray circle. A significant decrease in TEC values around the eclipse path on 26 December 2019 is quite visible on the data map. An animated version of Fig. 3a–c is also provided in the Supplement.

As part of the analysis, TEC data detrending was also performed. Two types of data detrending were performed, (1) to derive ΔTEC (general deviations from the normal condition) and (2) to derive TEC perturbation (TECP) (wavelike perturbations with much smaller amplitudes and finer structures). The derivation of ΔTEC was performed on TEC values that had been spatially mapped from individual IPPs onto fixed grid point(s). The baseline for detrending the TEC data into ΔTEC was based on the average diurnal TEC variation from calendar dates other than the solar-eclipse day. In contrast, the derivation of TECP was performed using TEC time series on the individual IPPs. The baseline for detrending the TEC data into TECP was obtained via a 30 min running average of the TEC time series being examined. After the TEC detrending process along the IPP trajectory was completed, the resulting TECP values were spatially mapped onto fixed grid points.

In addition, we also used the keogram technique to analyze detailed spatiotemporal variations of TEC, ΔTEC, and TECP data. A keogram was traditionally defined as a plot with latitude on the y-axis, time on the x-axis, and a color scale to represent the intensity of auroral emission (Eather et al., 1976). In the present paper, we use a broader definition of keograms: data plots with a geographic dimension (latitude or longitude) on one axis and time on the other axis, showing a certain physical quantity (e.g., TEC) with a color-scale representation. Keograms had been used widely in ionospheric data analysis. For example, Wang et al. (2020) used TEC keograms to analyze the dynamics of large-scale irregularities in the polar ionosphere. Coster et al. (2017) used a keogram of differential TEC to show the appearance of ionospheric disturbances during the 21 August 2017 solar eclipse over North America. In order to construct keogram plots of TEC, ΔTEC, and TECP data, we defined a few cross-sectional cut lines along and perpendicular to the eclipse trajectory. The TEC, ΔTEC, and TECP data are then spatially mapped/projected onto the defined cut lines, and the cut line-projected data at various epochs were stacked sequentially to form the keograms. Figure 3d shows an example keogram of TEC values at longitude 104∘ E on 25 December 2019.

We investigated changes in EUV radiation that illuminated various points in the Earth's upper atmosphere during the eclipse. For computational purposes, the solar EUV illumination was considered at 100 km altitude above the Earth's surface. EUV images of the Sun were obtained from the Atmospheric Imaging Assembly (AIA) instrument on board the Solar Dynamics Observatory (SDO) satellite to represent the solar EUV emissions from the corona. We used an AIA 193 Å image taken at 03:10:04 UTC on 26 December 2019 as the representative solar-disk image. Because there was no solar flare activity recorded during the eclipse, we assumed that there was no significant change on the Sun's surface, and therefore a single sample image was sufficient to represent the Sun at all times during the eclipse event. Although there was no solar flare at that time, there were two active regions (ARs) on the Sun with higher levels of emission: one in the southeast of the solar disk and the other in the northwest of the solar disk.

We have implemented a computer model of a solar eclipse that can reproduce the obscuration of the Sun as viewed from any point on Earth. The EUV image of the Sun was placed at the center of the field of view of the simulation, and a model of the Moon was moved across the Sun based on the DE421 ephemeris data developed by the Jet Propulsion Laboratory, NASA. We used the Skyfield library in the Python programming language to develop the simulation and plotted the sequential motion of the artificial Moon with a 1 min time cadence to represent the eclipse. Changes in the EUV radiation received on Earth during the eclipse can be approximated as the change in total intensities of all pixels in the image, with some of the pixels blocked by the artificial Moon. This is based on an approach previously performed by Huba and Drob (2017).

Figure 4 illustrates this modeling of solar EUV illumination during the eclipse. Here we calculated the time evolution of solar illuminance and EUV 193 Å irradiance received at the lower ionosphere (at 100 km altitude) over a geographic site near the greatest eclipse point in Siak (1.01∘ N, 102.25∘ E), Indonesia. In order to enhance the eclipse effect on the solar EUV radiation received on Earth, we changed the contrast of the image. This was done to emphasize the presence of ARs on the Sun by darkening the low-intensity regions and intensifying the bright regions, such as the ARs. An emphasis on ARs is needed because ARs are small concentrated areas with high brightness, which would abruptly disappear as the solar obscuration gradually changes. By performing this procedure, variation in the solar EUV radiation (i.e., the EUV obscuration factor) during the eclipse can become more obvious, as shown by the purple line in the time series plot.

Further, at various epochs during the eclipse, we also computed the total solar EUV irradiance over a number of evenly spaced grid points within a rectangular region from latitude 12∘ S to 7∘ N and from longitude 90 to 150∘ E with 1∘ spatial resolution. At any given epoch, spatial nonuniformity of the solar EUV irradiance can then be quantified. We followed the approach by Huba and Drob (2017) and Mrak et al. (2018) to identify this nonuniformity by calculating the second spatial derivative (i.e., the Laplacian) of the distribution of solar EUV radiation received on Earth. This is a reasonable approach, as the Laplacian has been frequently used in image processing for edge detection (e.g., Wang, 2007). The Laplacian operator can be applied to enhance features in an image that has sharp discontinuity or rapid change in intensity (Gonzalez and Woods, 2018). The main advantage of the Laplacian operator is its low computational cost. In addition, the Laplacian operator is isotropic, which simplifies the interpretation of results. On the other hand, a Laplacian operator does not provide the edge direction, which is its disadvantage (Nixon and Aguado, 2002). Nevertheless, edge direction is not very important in our situation, and our analysis was not adversely impacted.

Results from ionosonde observations and manual scalings of the recorded ionograms are presented here in terms of foF2, foF1, and hpF2 variations. In order to provide additional contexts, the corresponding relations to NmF2, NmF1, and apparent vertical drift velocity are also presented.

Figure 5 shows the time series plots of foF2 over Kototabang and Pontianak on 26 December 2019. Based on the ionosonde observations, changes in foF2 as a response to the solar eclipse were generally found to exhibit two distinct phases: a reduction phase and a recovery phase.

Over Kototabang, a reduction in foF2 was seen starting at 04:35 UTC (11:35 LT) from an initial value of 6.70 MHz (NmF2≈5.54×105 elcm-3) to reach its minimum value of 5.50 MHz (NmF2≈3.73×105 elcm-3) at 05:45 UTC (12:45 LT). During the 70 min of this reduction phase, foF2 dropped by 1.20 MHz. This foF2 reduction is equivalent to a drop in NmF2 by 1.81×105 elcm-3, which gives us an average rate of ionospheric-density reduction of -43 elcm-3s-1. The recovery phase started at 05:45 UTC (12:45 LT) and ended at 08:45 UTC (15:45 LT) with an increase in foF2 by 1.60 MHz, from 5.50 to finally reach 7.10 MHz (NmF2≈6.22×105 elcm-3) over a 180 min duration. This is equivalent to a rise in NmF2 by 2.49×105 elcm-3 during the recovery phase, which gives us an average rate of ionospheric-density increase of +23 elcm-3s-1.

Meanwhile, over Pontianak, a reduction in foF2 started at 04:50 UTC (11:50 LT) from an initial value of 6.21 MHz (NmF2≈4.76×105 elcm-3) to reach its minimum value of 5.44 MHz (NmF2≈3.65×105 elcm-3) at 06:20 UTC (13:20 LT). During the 90 min of this reduction phase, foF2 dropped by 0.77 MHz. This foF2 reduction is equivalent to a drop in NmF2 by 1.11×105 elcm-3, which gives us an average rate of ionospheric-density reduction of -20.6 elcm-3s-1. The recovery phase occurred over a duration of 155 min, starting at 06:20 UTC (13:20 LT) until 08:55 UTC (15:55 LT), with an increase in foF2 by 1.23 MHz (from 5.44 to 6.67 MHz). This is equivalent to a rise in NmF2 by 1.84×105 elcm-3 during the recovery phase, which gives us an average rate of ionospheric-density recovery of +19.9 elcm-3s-1.

Observations over Kototabang and Pontianak indicate that there was some lag between the start of the eclipse and the initial decrease in foF2. Over Kototabang, there was a time lag of 77 min before foF2 started to decrease, while the corresponding time lag over Pontianak was around 65 min. Likewise, the recovery phase extended well beyond the end of the eclipse. The extra time between the end of the eclipse and the end of the recovery phase over Kototabang was 97 min, whereas that over Pontianak was 83 min.

With respect to the normal baseline (derived based on averaging and smoothing of ionosonde observations from other days in December 2019), the magnitude of foF2 reduction over Kototabang and Pontianak was quite similar. The reduction in foF2 over Kototabang with respect to the normal baseline was -1.62 MHz (a 24.0 % relative reduction); meanwhile, that over Pontianak was -1.90 MHz (a 27.5 % relative reduction).

Figure 6 shows the time series plots of foF1 over Kototabang and Pontianak on 26 December 2019. Similar to what we have observed for foF2, changes in the critical frequency of the ionospheric F1 layer as a response to the solar eclipse also exhibited two distinct phases: a reduction phase and a recovery phase.

Over Kototabang, reduction in foF1 started at 03:30 UTC (10:30 LT), which was 12 min after the start of the eclipse, with an initial foF1 of 4.13 MHz which corresponds to an NmF1 of 2.11×105 elcm-3. The minimum foF1 of 2.9 MHz (NmF1≈1.04×105 elcm-3) was reached at 05:20 UTC (12:20 LT), which was 9 min after the maximum eclipse. Afterwards, foF1 started its recovery phase to finally reach 4.73 MHz (NmF1≈2.76×105 elcm-3) at 06:25 UTC (13:25 LT), which was 43 min before the end of the eclipse.

The duration of the reduction phase was 110 min, in which foF1 dropped by 1.23 MHz (from 4.13 to 2.90 MHz). This foF1 reduction corresponds to a drop in ionospheric density by 1.07×105 elcm-3 (from 2.11×105 to 1.04×105 elcm-3). This gives an average rate of ionospheric-density reduction of -16 elcm-3s-1. With respect to the normal baseline value of 4.33 MHz, the minimum foF1 was 1.43 MHz lower (a 33 % relative reduction). The recovery phase occurred over a duration of 65 min, with an increase in foF1 by 1.83 MHz (ΔNmF1≈1.72×105 elcm-3), which gives us an average rate of ionospheric-density recovery of +44 elcm-3s-1.

Meanwhile, over Pontianak, observations indicate that foF1 started to decrease at 04:30 UTC (11:30 LT), which was 45 min after the start of the eclipse, with an initial foF1 of 4.89 MHz (NmF1≈2.97×105 elcm-3). The minimum foF1 of 3.34 MHz (NmF1≈1.38×105 elcm-3) was reached at 06:00 UTC (13:00 LT), which was 16 min after the maximum eclipse. Afterwards, foF1 started its recovery phase to finally reach 4.77 MHz (NmF1≈2.83×105 elcm-3) at 07:20 UTC (14:20 LT), which was 12 min before the end of the eclipse.

The foF1 reduction phase over Pontianak took place over a 90 min duration, in which foF1 dropped by 1.55 MHz (from 4.89 to 3.34 MHz). This foF1 reduction corresponds to a drop in NmF1 by 1.59×105 elcm-3 (from 2.97×105 to 1.38×105 elcm-3). This gives an average rate of ionospheric-density reduction of -29 elcm-3s-1. With respect to the normal baseline value of 4.58 MHz, the minimum foF1 was 1.24 MHz lower (a 27 % relative reduction). The recovery phase occurred over a duration of 80 min, with an increase in foF1 by 1.43 MHz (from 3.34 to 4.47 MHz). This rise in foF1 corresponds to an increase in NmF1 by 1.43×105 elcm-3 (from 1.38×105 to 2.83×105 elcm-3). This gives us an average rate of ionospheric-density recovery of +30 elcm-3s-1.

Figure 7 shows the time series plots of hpF2 measurements at Kototabang and Pontianak on 26 December 2019. Based on these observations, changes in hpF2 as a response to the solar eclipse can be categorized into three phases: a descending phase, a rising phase, and a recovery phase.

The ionospheric response over Kototabang in terms of hpF2 is shown in Fig. 7a. During the first phase that started at 03:20 UTC (10:20 LT), which was 12 min after the start of the eclipse, hpF2 descended from an initial altitude of 516 km. The descent occurred for a 95 min duration until 04:55 UTC (11:55 LT), when hpF2 reached an altitude of 466 km. With hpF2 descending by 50 km, the average rate of descent during this first phase was approximately -32 kmh-1 or -8.8 ms-1. At 05:30 UTC (12:30 LT), hpF2 started to rise from an altitude of 486 km to reach 682 km at 06:40 UTC (13:40 LT). With hpF2 rising by 196 km during this second phase, the average rate of ascent was 168 kmh-1 or 47 ms-1. The recovery phase subsequently occurred over a 20 min duration, ending at 07:00 UTC (14:00 LT), when hpF2 returned to the baseline level.

The ionospheric response over Pontianak in terms of hpF2 is shown in Fig. 7b. The first phase started at 03:55 UTC (10:55 LT), which was 10 min after the start of the eclipse, with an initial hpF2 of 616 km. This phase occurred over a 120 min duration until 05:55 UTC (12:55 LT), when hpF2 reached an altitude of 480 km. In other words, hpF2 descended by 136 km, which means that the average rate of descent was -68 kmh-1 or -19 ms-1. The second phase occurred for a 100 min duration, starting from 05:55 UTC (12:55 LT) until 07:35 UTC (14:35 LT), during which hpF2 rose from 480 to 747 km. With hpF2 rising by 267 km, the average rate of ascent was 160 kmh-1 or 44 ms-1. The recovery phase subsequently occurred over a 15 min duration, ending at 07:40 UTC (14:40 LT), when hpF2 returned to the baseline level.

Figure 8 shows a map depicting the location of four discrete checkpoints where we examined the TEC time series data. These checkpoints are code-named KTB (co-located with the Kototabang station), GEC (point of greatest eclipse), GDU (point of the longest annularity duration), and PTK (co-located with the Pontianak station). By examining the TEC time series at these four fixed checkpoints, we remove some of the ambiguity that may arise from the movement of the IPPs. The TEC values from individual IPPs are spatially interpolated onto the checkpoints using a form of the inverse-distance-weighting (IDW) interpolation technique (Pradipta et al., 2014). The westernmost and easternmost checkpoints (KTB and PTK) were chosen since there are ionosondes at these locations. The other checkpoints (GEC and GDU) were chosen because of the special conditions of the solar-eclipse parameters there. At each checkpoint, time series of absolute TEC and ΔTEC were examined. The ΔTEC values were obtained by subtracting a smooth baseline from the absolute TEC values, which would reveal net changes in TEC relative to normal conditions. The baseline TEC was determined by averaging the TEC values on 25 and 27 December 2019, which are the days prior to and after the solar eclipse. We also determined the upper and lower bounds for the baseline TEC based on the standard deviation of the International Reference Ionosphere (IRI) model output for 18–25 December 2019.

Figure 9 shows the TEC time series plots for 25–27 December 2019 at each of the four designated checkpoints. In these time series plots, the observed TEC values (red curves) are compared to the normal baseline (cyan curves) that represent the diurnal TEC variation in the absence of a solar eclipse. Over all of these four checkpoints, the TEC responded to the solar eclipse in a relatively similar fashion, with a significant reduction during the eclipse. This TEC reduction was subsequently followed by a recovery that went past the end of the eclipse. In general, the rate of TEC reduction was different for different checkpoints. More notably, although the TEC reduction at all of these four checkpoints happened monotonically, the TEC recovery process was not as monotonic. At certain checkpoints (KTB and GDU), the TEC recovery was quite uneven and occurred in graduated steps. Further, the minimum TEC at each checkpoint was reached with a different time delay relative to the moment of maximum eclipse. The details of these features can be seen more clearly in the ΔTEC time series.

Figure 10 shows the ΔTEC time series plots for 25–27 December 2019 at each of the four designated checkpoints. In comparison to the TEC variation on non-eclipse days, the reduction in TEC during the solar eclipse at these four locations was quite large. The depth of the TEC reduction valley was generally different for each checkpoint. Over checkpoint KTB, the depth of the TEC reduction valley was -4.2 TECU. Over checkpoint GEC, the depth of the TEC reduction valley was -4.5 TECU. Meanwhile, the depth of the TEC reduction valley over checkpoints GDU and PTK was -5.0 and -5.5 TECU, respectively. Among the four designated checkpoints, the smallest reduction was found over KTB. In general, the TEC reduction valley appears to be deeper for checkpoints located further east. In addition, we can also discern the non-monotonicity of the TEC recovery process over these four designated checkpoints, which was exhibited with varying degrees.

A full summary of the observed reduction in TEC over the four designated checkpoints as a response to the eclipse, with some comparison to the corresponding reduction in foF2 (for the KTB and PTK checkpoints), is presented in Table 1. The tabulated information includes the amount of reduction, the time delay between the maximum eclipse and the lowest point in the reduction valley, and the average reduction and recovery rates.

In order to gain a better understanding of the ionospheric response to the solar eclipse beyond the examination of TEC and ΔTEC time series over fixed checkpoints, we also conducted a more elaborate analysis using a set of cross-sectional cut lines. The TEC, ΔTEC, and TECP data along these cross-sectional cut lines are assembled into keograms, which enable us to reveal a greater complexity in the pattern of the ionospheric response to the solar eclipse. The results from this analysis are presented below.

Figure 11 shows a geographical map depicting a set of cross-sectional cut lines that were used for the analysis. One is oriented along the eclipse trajectory, which we refer to as the parallel evaluation arc. Meanwhile, the other four are oriented perpendicularly to the eclipse trajectory, which we refer to as x-cut line nos. 1–4. These cross-sectional cut lines were chosen according to their proximity to the eclipse trajectory and the availability of GNSS receiver stations. Further, x-cut lines nos. 2 and 4 were chosen to include the coordinates of the Kototabang and Pontianak ionosondes.

Figure 12 shows the keograms for TEC, ΔTEC, and TECP as a function of UTC and longitude along the parallel evaluation arc. The TEC, ΔTEC, and TECP values are indicated using color maps. Figure 12a depicts 2 d (2×24 h) worth of data on 25 and 26 December 2019, whereas Fig. 12b shows a magnification around the period of the solar eclipse. In Fig. 12a.i, the normal diurnal pattern of TEC variation at various longitudes in the absence of a solar eclipse can be recognized from the first half of the data (covering 25 December 2019). During the solar eclipse (the period marked by the dashed/dotted lines on 26 December 2019), the pattern of TEC reduction was highly visible since, at this time of the day, TEC would normally have neared its daily maximum level. Figure 12b.i offers a greater visual detail. The pattern of eclipse-related TEC reduction along the parallel evaluation arc was generally found to be uneven. In the longitude span from 90 to 102∘ E during the eclipse, TEC was considerably lower than that at other longitudes. This uneven pattern in TEC reduction is likely due to the difference in solar local time at various points along the parallel evaluation arc when the solar eclipse happened.

In Fig. 12a.ii, we show the ΔTEC as a function of UTC and longitude along the parallel evaluation arc. Similar to the case of the four fixed checkpoints, the ΔTEC values were obtained by subtracting a smooth baseline from the absolute TEC values. However, in this case the smooth baseline for each individual longitude was determined by taking the average of the corresponding TEC data from the entire month (excluding 18–20 and 26 December 2019 due to geomagnetic activity and the solar eclipse). During the initial phase of the eclipse, the decrease in ΔTEC did not immediately take place. The drop in ΔTEC below zero only started when the time was approaching the maximum eclipse. At its lowest, ΔTEC reached approximately -6 TECU. The negative ΔTEC remained until the end of the eclipse. Figure 12b.ii offers a greater visual detail. We also recognized that the pattern of reduction in ΔTEC was highly uneven. The duration of the ΔTEC reduction valley varied slightly across different longitudes. However, more notably, over the longitude span from 96 to 107∘ E, the ΔTEC reduction valley was visibly not as deep as in other locations. This “shallow ΔTEC valley” occurred over Sumatra, which is a major land mass traversed by the solar eclipse. The precise cause of this shallow valley is uncertain at this point.

In Fig. 12a.iii, we show the TECP as a function of UTC and longitude along the parallel evaluation arc. The TECP was derived through a detrending process. However, unlike ΔTEC previously, here the TEC data detrending was performed on the IPPs before we spatially interpolated the detrended values onto the cross-sectional cut lines. The TECP values on individual IPPs were obtained by subtracting the 30 min running average. After detrending, the TECP values were spatially interpolated onto the parallel evaluation arc using the IDW technique. Generally speaking, there are wavelike fluctuations in the TECP data at nearly all times of the day. However, there were recognizable changes in the TECP pattern that matched the period of the solar eclipse. These distinct wavelike fluctuation patterns persisted until the end of the eclipse. The characteristics of the wavelike fluctuation patterns varied during different phases of the solar eclipse. From the start of the eclipse until the maximum eclipse, there was a wavelike fluctuation pattern where the average TECP was biased toward positive polarity. At the maximum eclipse, the TECP values dipped sharply to become negative. Finally, from the maximum eclipse until the end of the eclipse, there was another wavelike fluctuation pattern, but this time with the average TECP slightly biased toward negative polarity.

Figure 13 shows keograms of TEC values as a function of UTC and latitude along the four x-cut lines, covering the time interval 01:00–09:00 UTC on 25–27 December 2019 in different rows. A reduction in the TEC values can be seen along each of the four x-cut lines during the solar eclipse. At each x-cut line, however, there was a different time delay from the start of the eclipse (C1) until a significant decrease in TEC started to happen. This time delay ranged between 1 and 2 h. The TEC reduction occurred predominantly to the north of the greatest eclipse point for each x-cut line.

Figure 14 shows keograms of ΔTEC values as a function of UTC and latitude along the four x-cut lines, covering the time interval 01:00–09:00 UTC on 25–27 December 2019 in different rows. The patterns of TEC reduction along each of the four x-cut lines during the eclipse are more clearly visible in this case. These keograms confirm that the TEC reduction occurred more predominantly to the north of the greatest eclipse point for each x-cut line. This is signified by the ΔTEC in the northern part of the x-cut lines being more negative than that in the southern part.

Figure 15 shows keograms of TECP values as a function of UTC and latitude along the four x-cut lines, covering the time interval 03:00–08:00 UTC on 25–27 December 2019 in different rows. At the time of maximum eclipse, the TECP values in the keogram formed a prominent trough that is oriented parallel to the maximum eclipse line. Meanwhile, along x-cut no. 3, a convex bulge with a positive TECP polarity was seen between latitudes -5 and 0∘ just after the C1 phase. The convex bulge lasted for approximately 30 min. The tip of this bulge started at latitude -2∘, and the rest of this bulge then widened north to south, resembling a left-facing wavefront. Between C1 and C4, there were a number of striped patterns that indicate oscillations in the TECP data. The contours of these striped patterns were oriented roughly parallel to the contours of the C1 and C4 epoch lines. These wavelike fluctuations might be caused either by intrinsic nonuniformity (wrinkles) embedded in the solar EUV irradiance patterns or by traveling ionospheric disturbances (TIDs) generated during the eclipse. The closer the alignment of the stripe patterns to the C1/max/C4 epoch lines, the more likely they are to be associated with the EUV modulation mechanism. The further away the striped patterns were from the alignment with the C1/max/C4 epoch lines, the more likely they are to be associated with a TID.

During the 26 December 2019 annular solar eclipse over the Indonesian sector, the Moon's umbra moved from west to east with a ground speed of approximately 1.1 kms-1 (Espenak, NASA GSFC, 2019). Despite this high speed, temporal and spatial variation in the solar EUV irradiance over eclipse-affected areas still happened gradually in stages. With a finite width of the eclipse central path (i.e., the umbra) of approximately 117–120 km, partial and annular eclipse also occurred consecutively along the eclipse central path in a gradual manner. Using the Laplacian as the main metric, we are able to capture the inhomogeneity in the solar EUV irradiance. This characterization was performed by computing the Laplacian of the solar EUV irradiance at various point locations at each epoch, which enabled us to map its full spatiotemporal evolution.

Figure 16 shows the pattern of the Laplacian of solar EUV irradiance calculated over a region that spans from longitude 70 to 150∘ E and from latitude 30∘ S to 30∘ N, evaluated at different times during the passage of the solar eclipse. From these snapshots, we can see the spatial variation of solar EUV irradiance that was present during the eclipse, which generally resembles the outline of the lunar shadow as it traversed across the region. Moreover, there were also signatures of ARs on the Sun's surface in the spatial inhomogeneity of solar EUV irradiance received on Earth. They appear as smaller ring patterns within the greater outline of the lunar shadow in the EUV Laplacian map. All of these patterns moved across the region, with velocity matching that of the lunar shadow.

Figure 17 shows the calculated spatiotemporal pattern of the EUV Laplacian along the parallel evaluation arc. From this contour/color-map plot, we can see how the solar EUV irradiance variation was spatiotemporally consistent with the timing of various eclipse phases. Outside of the eclipse period, there was no fluctuation in the Laplacian because all the ARs would have been fully visible from every point on Earth that was facing the Sun.

Figure 18 shows contour/color-map plots of the Laplacian of the solar EUV irradiance variation along x-cut line nos. 1 to 4 as a function of time and latitude, which exhibit some of the same basic patterns. As in the case of the parallel evaluation arc, there was no fluctuation in the Laplacian outside of the eclipse period. One major difference here is that there was a set of distinct features around the greatest eclipse point for each x-cut line, which appear as pairs of pod-shaped blobs that sandwiched the annularity region. In Fig. 18c and d, they resembled a macaron around the annularity region.

Although the basic outlines of the Laplacian of solar EUV irradiance found in Figs. 17 and 18 are generally consistent with the TECP profiles shown in Figs. 12 and 15, there are some important differences in the details of the patterns. We found that some of the large structures observed in the TECP profile were not part of the EUV Laplacian profile. Furthermore, several fine structures that appeared in the EUV Laplacian profile did not actually materialize in the TECP profile. More detailed discussion regarding the relations between the TECP and EUV Laplacian profiles is presented in Sect. 4.