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Comparison of observed ionospheric vertical TEC over the sea in Indian region with IRI-2016 model
Accepted Manuscript Comparison of observed ionospheric vertical TEC over the sea in Indian region with IRI-2016 model Rajat Acharya, Saibal Majumdar PII: DOI: Reference:
S0273-1177(18)30837-8 https://doi.org/10.1016/j.asr.2018.10.049 JASR 14004
To appear in:
Advances in Space Research
Received Date: Revised Date: Accepted Date:
18 April 2018 28 October 2018 31 October 2018
Please cite this article as: Acharya, R., Majumdar, S., Comparison of observed ionospheric vertical TEC over the sea in Indian region with IRI-2016 model, Advances in Space Research (2018), doi: https://doi.org/10.1016/j.asr. 2018.10.049
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Comparison of observed ionospheric vertical TEC over the sea in Indian region with IRI-2016 model Rajat Acharya1, Saibal Majumdar2 1 Space Applications Centre, ISRO, Ambawadi Vistaar, Ahmedabad 380058, Gujarat, INDIA 2 Indian Navy, Integrated HQ of Ministry of Defence (Navy), New Delhi 110011, INDIA Abstract: The vertical ionospheric TEC values obtained from GAGAN grid based ionospheric delay correction values over the sea in the Indian equatorial region have been compared with the corresponding values derived from the International Reference Ionosphere model, IRI-2016. The objective of this work is to study the deviation of the vertical TEC derived from the IRI model from ground truths over the sea for different conditions. This will serve the basic intention of assessing the candidature of the IRI model as an alternative ionospheric correction model in navigation receivers in terms of accuracy. We have chosen different solar activity periods, seasons, geomagnetic conditions, locations etc. for our comparison and analysis. The TEC values by the IRI-2016 were compared with the actual measured values for the given conditions and errors were obtained. The measured vertical TEC values at the ionospheric grid points were derived from the GAGAN broadcast ionospheric delay data and used as reference. The IRI model with standard internal functions was used in estimating the TEC at the same ionospheric grid points. The errors in the model derived values are statistically analysed. Broadly, the results show that, for the Indian sector over the sea, the IRI model performs better on quiet days in off equatorial regions, particularly in the northern region. The overall performance degrades for other conditions with the model generally underestimating the true TEC values and most severely in the equatorial region. The performance is worst in this region for the disturbed days of the equinoctial period. The comparison study is also done with the TEC data measured directly by dual frequency GPS receivers. The results were found to be in general agreement with those obtained by comparing the model with GAGAN broadcast data as reference. This study will be useful in considering the IRI-2016 model for real time estimates of TEC as an alternative to the current parametric model in a satellite navigation receiver in absence of other options.
1. Introduction: The ionosphere is the region extending from 50 km to more than 1000 km above the earth surface. It consists of free electrons in large numbers and affects the propagation of electromagnetic waves across it due to the induced variation in the effective refractive index. Out of the global distribution, the equatorial ionosphere, extending up to around 20° latitudes about the geomagnetic equator, constitute one of the most dynamic regions. This region exhibits ionospheric equatorial anomaly, in which large volume of plasma is transported from the geomagnetic equator to higher latitudes on both sides of it. This leads to large spatio-temporal variability in the ionospheric TEC. This also leads to the degradation in the performance of the empirical models in estimating TEC. The satellite based navigation system uses the time of propagation of the signals from the satellite to the receiver to measure of the range between them. In the process, it assumes a constant velocity 1
of the signal, equal to that in free space. However, when the signal passes through the ionosphere, it experiences an additional delay due to the difference in the refractive index of the ionosphere with the free space. This causes erroneous range measurements and lead to error in position estimates. Therefore, this ionospheric delay needs to be corrected. The delay is proportional to the total electron content (TEC) of the ionosphere along the signal path and hence the TEC estimation is necessary in such systems (Acharya, 2014). The dual frequency receivers estimate their own ionospheric delay using the delay dispersive relation in two different frequencies. However, for single frequency standalone receivers, this estimate is to be done using empirical models. But the accuracy of these empirical models is comparatively poor, particularly in the equatorial region due to the reasons discussed above. Even, in the very recent works, it has been reported that using the Klobuchar model, the residual vertical TEC errors can go beyond 30 TECU, particularly in the high solar activity periods (Li et al., 2017; Wang et al., 2016, Jongsintawee et al., 2016). It is important mentioning here that with the advent of highly capable processors, the state of the art navigation receivers can accommodate more processing loads for ionospheric estimations. So, for single frequency receivers, it can resort to a better estimation model than those currently used, for obtaining better accuracy, particularly in the equatorial region. The International Reference Ionosphere (IRI) is an empirical model developed jointly by the International Union of Radio Science (URSI) and Co-Operation in Space Research (COSPAR). It was basically a climatological model with its previous versions representing the monthly average behaviour of the ionosphere at a given place and time, for a given level of solar activity (Bilitza, 2001). Previous versions of IRI were found to provide good monthly predicted averages, but could not respond to the real, daily solar activity (Figurski and Wielgosz, 2002). So IRI model predictions were not useful in obtaining the ionospheric day to day behaviour. But IRI is a data-driven model which has been undergoing periodic updates in order to improve the model prediction. Now, many current applications require a description of the day-to-day and diurnal variations, satellite navigation being is one of them. In view of this fact, the IRI in its current and subsequent models are going to introduce the real time prediction capability (Bilitza et al, 2013). This will enable the model to predict the temporal variations in the electron densities and hence the instantaneous TEC which in turn may be used for correcting the range errors due to the ionosphere in the navigation receivers (Bilitza, 2015; Bilitza et al., 2017). Thus, IRI can become one of the potential candidates for using with the satellite navigation receivers. In the process of introducing improved capability of the IRI model in a navigation receiver, a study of the performance of the current model, in the context of generating the ionospheric corrections, is very useful. Therefore, in this work, we observe the deviations of the model predicted TEC values with respect to the true variations for individual days with different conditions. For the purpose we compare the model TEC outputs of IRI-2016, the current version of the IRI model (Bilitza et al., 2016), with the measured reference values obtained from the Indian SBAS system, named GPS Aided Geo Augmented Navigation (GAGAN). Comparison is done for two extreme geomagnetic conditions. At one end, we choose the quietest day of the month, for which the model is developed and expected to give best results. At the other end, we select the most disturbed day of the month, when we can expect the maximum deviations. Further, this is done for two different periods, viz. for high solar activity period and for low solar activity period. The data selected and the locations of comparison are described in details in Sec. 2. We have compared the results for these mentioned contrasting conditions for two main purposes, (i) to evaluate how the current version performs in 2
estimating TEC over the sea and (ii) to have a comprehensive understanding of the quantitative improvement needed in the model to make it useful for daily predictions for navigation receivers over the sea. Substantial amount of work has been done in validating the IRI model by observing the day to day deviations of the ionospheric parameters, particularly after the resolution of including real time estimation capability in the model (Bradley, 2004; Ezquer, 2004(a); Ezquer, 2004(b); Batista and Abdu, 2004; Miro Amarante, 2004). However, it is a fact that the model has been developed, modified and validated with a large amount of data from the global network of ionosonde and few incoherent scatter radar (Bilitza, 2006; Bilitza, 2015), which are primarily located on the land, in addition to the data from the top side sounders and sounder rocket measurements. On the contrary, our interest remains on the applications over the sea. Therefore, it calls for evaluating the performance of the current model for locations over the sea. For this reason, the present study examines the ionospheric estimation accuracy of IRI-2016, with the measurements done over the sea in the Indian Ocean region for different individual days with varied geomagnetic conditions.
2. Data, Methodology and Analysis The IRI-2016 predictions of the vertical TEC are compared with the TEC data derived from the ionospheric delay correction values of GAGAN. GAGAN is the satellite based augmentation system in India providing the corrections to the users over the primary GPS system. GAGAN has been implemented by the Indian Space Research Organisation (ISRO) in collaboration with the Airport Authority of India (AAI) for providing precise positioning services for the civil aviation and other applications. The area of service of this system includes the Indian flight information region (FIR), within which GAGAN provides civil aeronautical navigation signal consistent with the standard and recommended practices (SARPs) of the International Civil Aviation Organization (ICAO). To provide this service, GAGAN has a network of 15 reference stations (INRES) equipped with dual frequency receivers with redundancy which are located at different airports across the service area in India. These stations, called the Indian Reference Stations (INRES), receive the GPS data in an uninterrupted manner. The measurements include the satellite ranges for each GPS satellite visible with corresponding elevation, azimuth and time stamps at every second. Measurements are recorded up to a lowest elevation of 15°. These receivers are placed at the locations, surveyed for multipath and noise and are installed on elevated platforms. These receivers are also equipped with choke rings to eliminate any multipath. Therefore, this elevation cut-off is sufficient to avoid any perturbation in the signal due to multipath, which in turn can influence ionospheric estimations. These measurements are send directly to both of the two Master Control Centres (INMCC) through the dedicated optical fibre data communication subsystem. At the INMCC, the correction and integrity parameters are derived and are uploaded to the SBAS satellite through the Indian Land Uplink Station (INLUS) for transmitting them to the users in correct format. The architecture of the GAGAN network including the numbers of INRES receivers used and their locations across India along with the INMCC and INLUS are shown in Fig. 1a. (Acharya et al., 2007, Ganeshan et al., 2016). One of the correction parameters provided by GAGAN is the ionospheric delay. The ionospheric delay corrections terms, which vary geographically, are provided as vertical delays in the L1 frequency (1575.42 MHz), at definite discrete grid points. These delays are the scaled versions of the 3
vertical TEC, where the scaling factor from vertical TEC to vertical delay in L1 is 40.3/(1575.42x10 6)2 ≈ 1/6. The grid points, called the Ionospheric Grid Points (IGP) are distributed over the earth at an interval of 5° x 5° along the latitude and longitude over most of the globe including the equatorial region (RTCA 1999, FAA 2001). Out of all defined IGPs, GAGAN provided the correction data for those grid points which are within its service area. The IGPs served by GAGAN extends from 55° E to 110° E in longitude and -05° N to 40° N in latitude (Ganeshan et al., 2016). These values are updated at an interval of less than 300 seconds as per the recommendations of the RTCA (RTCA 1999). For generation of these correction values, the slant TEC values are derived for each signal path for each constituent INRES receiver using the range measured in two different frequencies, the GPS L1 (1575.42 MHz) and L2 (1227.6 MHz) using the relation
(1a)
where, TEC are in electrons/m2, R1 and R2 are the two ranges in metres measured in two frequencies f1 and f2 respectively. Commonly, TEC is expressed in TEC units (TECU) where 1TECU = 1016 electrons/m2. The slant TEC values are converted to vertical TEC values. For this, the slant to vertical conversion factor ‘f’ is used, where ‘f’ is given by f=
(1b)
Here, Re is the mean radius of the earth, h is the effective ionospheric height, taken as 350 km and E is the elevation angle. These converted vertical TEC values are defined at the Ionospheric Pierce Points (IPP). For a definite signal, the IPP is the point where the signal intersects the effective ionospheric height. The location of the IPP can be obtained from the location of the receiver and from the elevation and azimuth angle and is given by Ψ
π
– E – asin { (
) cos E }
λ
asin ( sin λs cos Ψ + cos λs sin Ψ cos Z
ϕ = ϕs + sin Ψ sin Z cos λ
(1c)
where, λ is the IPP latitude and ϕ is the IPP longitude. Ψ is the angular distance, measured at the earth’s centre, between the receiver location and the IPP. λs and ϕs are the station latitude and longitude respectively while E and Z are the elevation and azimuth of the satellite at the receiver location, the signal of which is in consideration. The ionospheric correction data at the IGPs are derived by combining all the vertical ionospheric TEC values at their IPP derived from individual receivers in the network. Using these, the TEC values at the IGP are derived with the use of a model. The ionospheric model used to estimate the delay at the grid points from the IPP values is called the ISRO Grid Model – Multi Level Data Fusion (IGMMLDF). This model captures the ionospheric variability in TEC at two different shell heights and finally provides the delay value in L1 frequency at these IGPs (Ganeshan et al., 2016). During the process, all other errors are thoroughly removed, including receiver and satellite bias, tropospheric errors, satellite and receiver hardware differential delay, etc. Therefore, these data are the most 4
accurate and dependable data we have at hand to be used as reference and are better than any individual dual frequency estimate. TEC derived from the vertical delays transmitted by GAGAN are therefore used as reference ground truth for our comparison. The GAGAN data has the advantage that, it is always accompanied by a confidence parameter, called the Grid Ionospheric Vertical Error Index (GIVEI) parameter. These associated GIVE indices are simultaneously transmitted with the delay data. It is an integrity parameter and gives us the indication of whether or not the delay associated values are accurate enough for the application purpose. A definite GIVEI value indicates a range of 1σ value of probable error in the ionospheric delay correction provided or equivalently for the TEC at the IGPs. The values are over bound so that it remains valid even when the values are interpolated by the user. In our work, we have disregarded all the data which has GIVEI values more than 10. This means that the precision of the ionospheric TEC will always be better than around 6TECU. However, the occurrence of GIVEI values near this threshold number is very infrequent. Typically, the accuracy figure is much better than this and the ionospheric 1σ precision value remains around 2-3 TECU. While the IGP values from the SBAS system are already made free from any inter-frequency and other bias occurring during the measurements, GIVEI indicates the effect of the residual errors of measurement and the modelling errors of the delay at the IGP points. Hence, selection of data on the basis of GIVEI ensures that the necessary accuracy exists in the reference with which the model is to be compared. The IGP points under the GAGAN service area are pre-selected and comparisons are done only at these points. Out of about 90 numbers of grid points served by GAGAN, 40 are on the sea, which thus provides us with a considerable portion of the total data points for any instant. Figure 1b shows the IGP points served by the GAGAN system which are over the sea. The IGP points are marked as circles. For these IGP points, TEC values are obtained from the GAGAN data and are compared with the IRI derived vertical TEC values at the same point and time. Since our objective is to observe the performance of the current IRI version with respect to the different forcing factors, the data is selected judiciously, for the days with prominence of the important driving forces of the TEC, like the solar activity, seasons, geomagnetic disturbance etc. which may cause variations to deviate from the typical values. Data were selected for two different years, viz. 2012 which is a high solar activity year and for 2015, which was near the trough of the solar cycle 24 with less solar activity. Largely, to keep the data handling convenient and yet to derive meaningful inference, data with the seasonal variation were included from the two equinoctial months of March and September and from the summer solstice month of June and the winter solstice month of December. Now, for each of these different months, the two quietest and two most disturbed days were selected. On these days, the TEC values obtained from the GAGAN data at the selected grid points were compared with IRI-2016 and analysed for this study. The list of quiet and disturbed days was obtained from the website of Kyoto World Geodetic Centre. The days selected for this work are shown in Table-1. Their corresponding Kp indices, representing the geomagnetic activity over the total day are also given in the parenthesis. In addition to this, the IRI derived TEC values are also compared with the direct TEC measurements made by dual frequency GPS receivers installed at different locations across India. The measured slant TEC, derived from the differential ranges measured in two different frequencies using Eq. 1(a), 5
is first corrected for receiver and satellite inter-frequency biases. The receiver inter-frequency biases are pre-determined while those for the satellites are obtained from those derived at the GAGAN INMCC. Then, these slant TEC is converted to the vertical TEC values at their respective IPP points, using equations 1(b) and 1(c). Once, these vertical TEC values are obtained, the IRI 2016 model is then used to derive the VTEC values at these same IPP points at the same instants of time. Finally, these values are compared and the statistics of the estimation errors is obtained. The observational TEC values are compared with the IRI-2016 model where the model output is obtained from a software code. The Fortran code for the IRI- 2016 model was available from http://irimodel.org and was used for the purpose. Since, our interest is to use the model as an alternative to the existing models for satellite navigation receivers in real time, where there is no option to input any current geomagnetic or solar activity parameter, all the default IRI-CCIR options in the IRI-2016 model were used to obtain the final vertical TEC values. Most importantly, the NeQuick option is used for topside modelling as it was found to be performing very well by previous researchers (Grynyshyna et al., 2015) Besides other factors, the ionospheric characteristics are different for the equatorial and offequatorial regions, primarily due to the transport processes of the plasma prevailing in this region. Therefore, to distinctly observe the model performance in these regions, the total observations were spatially divided into three distinct spatial regions depending upon the geomagnetic locations of the grids, viz. southern region, the northern region and the equatorial region, and the IRI performance were analysed for each of them. The distinction of the available IGP points on the sea into these regions is described in Sec. 3.
3. Results and Discussions: The data derived from IRI model and data observed at GAGAN IGP points were compared and the errors were analysed. As mentioned in Sec. 2, data were considered and analysed for two different years, 2012 and 2015, the former being the year with high solar activity and the latter with low solar activity. March and September were taken as the equinoctial months while June is taken as the month for summer solstice and December as the one for winter solstice. Two most disturbed and two most quiet days of the above mentioned months were taken for comparison and analysis. Thus, a total of 32 days were considered for the whole comparison, as shown in Table-1. Data were compared at the predefined grid points which were on the sea. To distinctly observe the performance, the total numbers of grids under observations were spatially divided into three distinct regions depending upon the geomagnetic locations of the grids. These regions are viz. southern region for grids below geomagnetic 5° S, the northern region for grids above geomagnetic 5° N and the equatorial region, lying in between these two regions. As the IGP points are defined in geographic coordinates and the grids are 5° apart here, the grids lying on geographic 0° and below constitute the southern region, while the grids on 5° N and 10° N geographical latitudes constitute the equatorial region and those on 15° N geographical latitude and above constitute the Northern region, as per our categorization. In fig. 1b, where IGPs under consideration are marked as circles, those grid points on the equatorial region are demarcated with cross marks within the circles. Those 6
towards the north of this section constitute the IGPs of the northern region and those towards its south constitute the southern region defined for this work. Since the grid ionospheric vertical TEC values are updated within 300 seconds, about 288 values of TEC were obtained for comparison over a single day for each such grid point. These vertical TEC in TECU units, are compared with the IRI model values estimated at the same time and at the same locations. The difference of the measured values from the corresponding IRI estimates, i.e. TEC IRI – TECGAGAN, is referred to as the estimation error. The analysis of the errors in estimation is described in the following sub-sections.
3.1 High Solar Activity Period
Selected days of 2012 were utilized to observe the performance of IRI model in predicting vertical TEC during the high solar activity periods. Two most quiet and the most disturbed days of the selected months were analysed, the results of which are described below. a. Quiet days
On the quiet days of the vernal equinoctial period, the North & South regions showed a very close proximity of the predictions by IRI model to the observed GAGAN data. However, for equatorial latitudes, the TEC estimates were under predicted by the IRI model as compared to the observed GAGAN data. In contrast, during the autumnal equinoctial time, the North and South regions have shown tendency of over predictions while the performance at the equatorial region was much better. Figure 2 (a and b) shows the temporal plots of the TEC for the three different regions and for two different equinoctial months. The temporal variations for different IGP points of a region are shown in continuum and thus appear in the same plot. Figure 2 (c and d) represents the error distributions for these periods with the three subplots representing different regions. The same constitution is maintained for all subsequent plots representing other seasons and conditions. Instances, when no measurements could be done have been disregarded. During both the summer and winter solstice, the North and South latitudes exhibited over prediction in TEC values by the model, just like the autumnal equinoctial period. Over prediction is comparatively more in the northern region and winter solstice as compared to the southern region and summer solstice. Further, the deviations are largest during midday. For the equatorial latitudes, the IRI model estimation was much closer to the observed GAGAN data. Minor over estimations during the noon and underestimations at night, particularly during the summer solstice while for winter, it was mostly overestimations. The corresponding plots are shown in fig. 3.
b. Disturbed days
As shown in fig. 4, for the disturbed days and during both the equinoctial period, the North and South Latitudes showed moderate under prediction of TEC when the IRI estimations were compared with the observed GAGAN data. At the same time, the model predictions at the equatorial latitudes
7
were highly under predicted. The under predictions were very conspicuous with differences going up to 40 TECU with respect to the GAGAN reference data. Similarly, during the solstice periods, for North latitudes, the predictions were close with minor over and under predictions. However, for the southern latitudes, it is mostly over predictions in summer and under predictions in winter. The equatorial region showed considerable under predictions in both the seasons extending the errors up to more than 20 TECU. This is evident from Fig. 5.
3.2 Low Solar Activity Period
For solar cycle 24, the peak was observed in 2012 and by 2015 the activity moved towards the trough. The days of 2015 were selected to observe the performance of IRI during the comparatively low solar activity periods. As done for 2012, for this low solar activity period of 2015, the quiet and disturbed days of the selected months were analysed, the results of which are described below.
a. Quiet days
For the equinoctial quiet days, the IRI model mostly under predicted the TEC in all regions when compared to the observed GAGAN data with comparatively fewer instances of over predictions. Over predictions are typically observed in the morning period while under predictions occurred mostly in post midmorning and in the afternoon. However, under prediction was more conspicuous in terms of numbers of occurrences and in extent as well, in the equatorial region. Over predictions are dominant in the southern region during the autumnal equinoctial period. The corresponding plots are shown in Fig. 6. Plots in fig. 7 indicate that the performance of the model during the solstice period. The summer solstice was mostly characterised by overestimations. For both North and South Latitudes, large overestimation was observed in the IRI model predictions. However, in the Equatorial Latitudes, the afternoon period showed very slight underestimation. During the winter, in both equatorial and southern regions, the model estimations were close to the observed data. The performance in the northern region is also better in winter than that in the summer.
b. Disturbed days
During the disturbed days, most conspicuous deviations are observed during the vernal equinox where the IRI model estimations were under predicting the TEC, particularly in the equatorial region and southern with a difference extending to more than 35 TECU as compared to the observed GAGAN data. Predictions in the Northern region are comparatively better. Estimates during the autumnal equinoctial period were comparatively better with northern and southern region showing moderate over predictions. The equatorial region showed much better accuracy with minor over predictions observed typically during the evening and night hours while under predictions are observed just before achieving the peak. The corresponding variations are shown in Fig. 8. 8
Mixed over and under estimation were observed in both the Southern and Northern regions in both the solstice periods with only southern region showing predominantly under predictions in winter. In the equatorial Latitudes, the IRI model estimations were still conspicuously under predicted during both the solstices, with deviations extending up to around 30 TECU. This is evident in Fig. 9.
3.3 Other Perspectives:
From the overall observations, the performance of the IRI model may be expressed in other perspectives. The relative variation of the IRI predictions showed a fixed spatial trend with the equatorial region always having relatively lower estimates with respect to the reference than the off equatorial region. That is, the equatorial region typically exhibited moderate to large under predictions, when the northern and southern region showed good accuracy or moderate under predictions respectively. Only when the northern and southern region showed a tendency of over estimations, the equatorial region showed better agreements. This is true for both quiet and disturbed days. Further, although the errors in both the northern and southern regions have mostly shown similar trends for the same conditions, this is not true for all cases. The seasonal variations in the performance show that for the equinoctial times, the model has more tendency of severe under predicted the TEC, particularly for disturbed periods, although, moderate under predictions were also observed for solstice periods and for quiet days. Expectedly, the performances of the model on quiet days are better than that disturbed days. Standard deviation of error during the higher solar activity year of 2012 is more than that in 2015. The results of comparison of the IRI estimates with measured TEC values at the standalone GPS receivers are given in table 2. This has been done for the year 2015, for the same quiet and disturbed days of the equinoctial and solstice months considered above. For equinoctial months, on quiet days, the IRI 2016 model has shown dominant under predictions. This is true for both vernal and autumnal equinoxes. For disturbed days, under predictions are conspicuous in vernal equinox while estimates in autumnal equinoctial period showing moderate over predictions. Standard deviations slightly increased in vernal equinoxes for both quiet and disturbed cases. For the solstice periods, the quiet days showed much closer estimates by IRI than the corresponding disturbed days. Winter solstice estimates on quiet days are marginally better than the summer values. For disturbed days, the estimations are grossly under predicting. The standard deviations are also larger than the quiet days, particularly during the summer solstice. These observations are in general agreement with those obtained by comparing the model values taking the GAGAN grid data as reference. The minor deviations may have occurred due to the residuals in the receiver bias corrections and due to the errors arising out of the slant to vertical conversions of the measured TEC data by the receivers. Finally, considering the fact that this work has been done for the purpose of using IRI 2016 model for the single frequency user to improve the positioning accuracy, we discuss the aspect of the effects of the TEC estimation inaccuracies on the estimation of receiver positions. The error in estimating TEC will lead to ranging errors in single frequency GNSS receivers. For a definite error of δTEC in TEC 9
estimation expressed in electrons/m2, the corresponding error in ranging will be dependent upon the signal frequency ‘f’ and is related as, δR
40 3 f2 x δTEC
(2)
where δR is the ranging error in metres and ‘f’ is the frequency of the signal in Hz. Now, there exist fixed relation between the ranging error (due to ionosphere or else) and positioning accuracy through the term, ‘Dilution of Precision’ (DOP), particularly the PDOP (Position Dilution of Precision). They are related as, σP
σR * PDOP
(3)
where σP is the standard deviation in the position estimates, σR is the standard deviation of the range errors (Acharya, 2014). The PDOP is dependent upon the satellite geometry at any instant. So, even for the same residual ionospheric error, it will be different for different user positions for different times and for different configuration of the space segment of the navigation systems. Therefore, relating any definite position accuracy of any receiver or any definite system with the corresponding ionospheric errors may turn deceptive. Typically, the PDOP for over Indian region for GPS typically remains around 2 but can go up to more than 3 at times. Accordingly, the 1σ accuracy in position due to the ionospheric error will typically go up 2 times the corresponding ranging errors due to error in TEC estimation and more than 3 times, in the worst cases.
Conclusion The vertical total electron content values obtained from the IRI-2016 predictions were compared with TEC values derived from the corresponding GAGAN vertical ionospheric delay correction values at the pre-defined ionospheric grid points over the sea. Standard IRI-2016 functions were used for the purpose with default model parameters without any input which are measured in-situ, regarding the prevailing solar or geomagnetic activity. This is done for particular days of different seasons and for two extreme geomagnetic conditions. Days were selected for the years 2012 and 2015, with high and low solar activities, respectively. The errors were studied for the mentioned conditions. From the major observations done from the results of this work, we conclude that, for the Indian sector over the sea, the IRI model, in its current form performs better on quiet days in off equatorial regions, particularly in the northern region. The overall performance degrades for other conditions. Under most of the other conditions, the model generally underestimated the true TEC values. Most severe errors have occurred in the equatorial region, where the performance observed is worst for the disturbed days of the equinoctial period. However, few cases of over estimations were observed, mostly in off-equatorial region on both quiet and disturbed days. No significant difference has been observed in performance between the periods of low and high solar activities. When compared with the TEC data obtained from direct measurement of the receivers, the model derived values were found to be in general agreement with those obtained by comparing the model values taking the GAGAN grid data as reference. Overall, it can be inferred that, the IRI model in its current form, even without any requirement of the coefficients to represent day to day variations, have performed satisfactorily on the sea, in terms 10
of predicting TEC with finite and bound errors. This has a special significance considering that for these locations the input that has gone in developing the model is sparse. It implies that it has the potential of performing even better when more input from measurements over the sea are assimilated in the process of improving the model.
Acknowledgements:
The authors are grateful to the Centre for Space Science and Technology education – Asia Pacific for providing the opportunity of doing this work. We also convey our gratitude to the whole GAGAN and IRNSS team of Indian Space Research Organization for allowing us to use their data. Finally, we thank DD-SNAA, GD-NAG and Head-NAD for their kind co-operation during the execution of this work. The contribution of the World Data Centre for Geomagnetism, Kyoto is sincerely acknowledged with thanks.
References Acharya, R., 2014. Understanding Satellite Navigation, Ed. 1, Academic Press, Waltham, MA, USA Acharya, R., Nagori, N., Jain, N., Sunda, S., Regar, S., Sivaraman, M.R., Badyopadhyay, K., 2007. Ionospheric Studies for the Implementation of GAGAN. Indian Journal of Radio and Space Science, 36, October-2007, 394-404 Batista, I.S., Abdu, M.A., 2004. Ionospheric variability at Brazilian low and equatorial latitudes: comparison between observations and IRI model, Advances in Space Research, 34, 1894–1900 Bilitza, D., 2001. International Reference Ionosphere 2000. Radio Sci. 36 (2), 261–275 Bilitza, D., 2006. The International Reference Ionosphere – Climatological Standard for the Ionosphere. In Characterising the Ionosphere, Meeting Proceedings RTO-MP-IST- 56, Neuilly-surSeine, France: RTO. Paper 32, 32-1 – 32-12. http://www.rto.nato.int/abstracts.asp. Bilitza, D., 2015. Preface: IRI and GNSS, Advances in Space Research, 55(8), 1913 Bilitza, D., Altadill, D., Truhlik, V., Shubin, V., Galkin, I., Reinisch, B. and Huang, X., 2017. International Reference Ionosphere 2016: From ionospheric climate to real-time weather predictions, Space Weather, 15, 418–429, doi:10.1002/2016SW001593. Bilitza, D., Boding Rodriguez, L., Joseph E., 2013. Description of Day-to-Day Variability in IRI, Presentation at the EGU General Assembly 2013, April, 2013 in Vienna, Austria, EGU2013-12650 Bilitza, D., Watanabe, S., Truhlik, V., Altadill, D., 2016. RI-2016: Description and Introduction, Abstract submitted for 41st COSPAR Scientific Assembly, July 2016, Istanbul, Turkey. http://cospar2016.tubitak.gov.tr Bradley, P.A., Kouris, S.S., Stanislawska, I., Fotiadis, D.N., Juchnikowski, G., 2004. Day-to-day variability of the IRI electron density height profile, Advances in Space Research 34, 1869–1877 11
Ezquer, R.G., Brunini, C., Mosert, M., Meza, A., del V. Oviedo, R., Kiorcheff, E., Radicella, S.M., 2004a. GPS–VTEC measurements and IRI predictions in the South American sector, Advances in Space Research 34, 2035–2043 Ezquer, R.G., Mosert, R. Corbella, Erazu, M., Radicella, S.M., Cabrera, M., de la Zerda, L., 2004b. Dayto-day variability of ionospheric characteristics in the American sector, Advances in Space Research 34, 1887–1893 FAA, 2001. Specifications for the WAAS, DTFA01-96-C-00025 FAA-E-2892b, Federal Aviation Administration, Washington, DC, USA. Figurskil, M. and Wielgosz, P., 2002. Intercomparison of the TEC obtained from the IRI model to the one derived from GPS measurements, Advances in Space Research, 30(11), 2563-2568 Ganeshan, A.S., Satish, S.V., Kartick, A., Srinivasan, N., Ramesh, G., 2016. GAGAN - Redifining Navigation over the Indian Region, Inside GNSS, Jan-Feb 2016, 42-48 Grynyshyna Poliuga, O., Stanislawska, I., Pozoga, M., Tomosik., A., 2015. Comparison of TEC values from GNSS permanent station and IRI model. Advances in Space Research, 55(8), 1976-1980 Jongsintawee, S., Rungraengwajiake, S., Supnithi, P., Panachart, C., 2016. Comparison of GPS Positioning accuracy using Klobuchar model and IGS TEC model in Thailand, KMITL Science and Technology Journal, 16(1), 01-16 Li, J., Wan, Q., Ji, M., Zhang, J., Wan, X., Fan, J., 2017. Evaluation of the Klobuchar Model in Taiwan, Advances in Space Research, 60, 1210-1219 Miro Amarante, G., Cueto Santamarı, M., Mosert de Gonzalez, M., Radicella, S.M., Ezquer, R., 2004. Day-to-day changes in experimental electron density profiles and their implications to IRI model, Advances in Space Research, 34, 1878–1886 RTCA, 1999. Minimum Operational Performance Standards, DO 229B, Radio Technical Commission for Aeronautics, Washington, DC, USA Wang, N., Yuan, Y., Li, Z., Huo, X., 2016. Improvement of Klobuchar model for GNSS ionospheric delay corrections, Advances in Space Research, 57(7), 1555-1569
12
LIST OF FIGURES:
Fig.1: (a) Ground Segment of GAGAN (b) Ionospheric Grid Points on the sea served by GAGAN
Fig.2: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the equinoctial quietest days of (a) March 2012 and (b) September 2012. (c) and (d) are corresponding error distributions
Fig.3: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the quietest days of (a) summer solstice in June 2012 and (b) winter solstice in December 2012. (c) and (d) are corresponding error distributions
Fig.4: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the most disturbed equinoctial days of (a) March 2012 and (b) September 2012. (c) and (d) are corresponding error distributions
Fig.5: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the most disturbed days of (a) summer solstice in June 2012 and (b) winter solstice December 2012. (c) and (d) are corresponding error distributions
Fig.6: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the quietest equinoctial days of (a) March 2015 and (b) September 2015. (c) and (d) are corresponding error distributions
Fig.7: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the quietest days of (a) summer solstice in June 2015 and (b) winter solstice in December 2015. (c) and (d) are corresponding error distributions
Fig.8: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the most disturbed equinoctial days of (a) March 2015 and (b) September 2015. (c) and (d) are corresponding error distributions
Fig.9: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the most disturbed days of (a) summer solstice in June 2015 and (b) winter solstice in December 2015. (c) and (d) are corresponding error distributions
13
LIST OF TABLES: Table-1. Selected Days for analyses Table-2. Performance of IRI-2016 with respect to TEC measured by GAGAN station receivers
14
Figure_1a
Figure_1b
Figure_2a
Figure_2b
Figure_2c
Figure_2d
Figure_3a
Figure_3b
Figure_3c
Figure_3d
Figure_4a
Figure_4b
Figure_4c
Figure_4d
Figure_5a
Figure_5b
Figure_5c
Figure_5d
Figure_6a
Figure_6b
Figure_6c
Figure_6d
Figure_7a
Figure_7b
Figure_7c
Figure_7d
Figure_8a
Figure_8b
Figure_8c
Figure_8d
Figure_9a
Figure_9b
Figure_9c
Figure_9d
Table-1 Selected Days for analyses Years
Seasons Equinox
2012 Solstice
Equinox 2015 Solstice
Months March September June December
Quiet Days 26(7-), 29(6-) 23(0+), 28(0+) 15(3), 19(2) 06(1-), 08(1)
Disturbed days 09(44), 07(39+) 03(33-), 05(31+) 03(25), 17(37-) 15(18-), 17(19-)
March September June December
05(11-), 10(8) 27(6), 30(3-) 05(2), 20(1+) 03(7-), 04(8)
17(48), 09(43-), 23(42-), 20(45-),
15
18(39+) 11(39+) 22(35+) 21(31)
Table-2. Performance of IRI-2016 with respect to TEC measured by GPS receivers Quiet Region
Northern Equatorial Southern Northern Equatorial Southern Northern Equatorial Southern Northern Equatorial Southern
Month
Disturbed Mean Error Std. Dev (TECU) (TECU)
Mean Error (TECU)
Std. Dev (TECU)
Sep
-0.858 -3.050 -4.643
6.419 6.777 5.474
5.372 1.061 0.717
7.274 6.447 4.500
Mar
-9.623 -2.608 -9.189
8.278 10.398 7.275
-5.605 -0.651 -6.180
9.304 10.990 10.136
Dec
1.064 -1.915 -3.080
5.156 4.582 4.351
-7.678 -8.432 -13.676
6.976 6.075 5.969
Jun
3.3282 2.6068 3.3393
4.564 3.894 3.160
-8.361 -8.988 -6.872
10.911 10.612 9.216
16
S0273-1177(18)30837-8 https://doi.org/10.1016/j.asr.2018.10.049 JASR 14004
To appear in:
Advances in Space Research
Received Date: Revised Date: Accepted Date:
18 April 2018 28 October 2018 31 October 2018
Please cite this article as: Acharya, R., Majumdar, S., Comparison of observed ionospheric vertical TEC over the sea in Indian region with IRI-2016 model, Advances in Space Research (2018), doi: https://doi.org/10.1016/j.asr. 2018.10.049
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Comparison of observed ionospheric vertical TEC over the sea in Indian region with IRI-2016 model Rajat Acharya1, Saibal Majumdar2 1 Space Applications Centre, ISRO, Ambawadi Vistaar, Ahmedabad 380058, Gujarat, INDIA 2 Indian Navy, Integrated HQ of Ministry of Defence (Navy), New Delhi 110011, INDIA Abstract: The vertical ionospheric TEC values obtained from GAGAN grid based ionospheric delay correction values over the sea in the Indian equatorial region have been compared with the corresponding values derived from the International Reference Ionosphere model, IRI-2016. The objective of this work is to study the deviation of the vertical TEC derived from the IRI model from ground truths over the sea for different conditions. This will serve the basic intention of assessing the candidature of the IRI model as an alternative ionospheric correction model in navigation receivers in terms of accuracy. We have chosen different solar activity periods, seasons, geomagnetic conditions, locations etc. for our comparison and analysis. The TEC values by the IRI-2016 were compared with the actual measured values for the given conditions and errors were obtained. The measured vertical TEC values at the ionospheric grid points were derived from the GAGAN broadcast ionospheric delay data and used as reference. The IRI model with standard internal functions was used in estimating the TEC at the same ionospheric grid points. The errors in the model derived values are statistically analysed. Broadly, the results show that, for the Indian sector over the sea, the IRI model performs better on quiet days in off equatorial regions, particularly in the northern region. The overall performance degrades for other conditions with the model generally underestimating the true TEC values and most severely in the equatorial region. The performance is worst in this region for the disturbed days of the equinoctial period. The comparison study is also done with the TEC data measured directly by dual frequency GPS receivers. The results were found to be in general agreement with those obtained by comparing the model with GAGAN broadcast data as reference. This study will be useful in considering the IRI-2016 model for real time estimates of TEC as an alternative to the current parametric model in a satellite navigation receiver in absence of other options.
1. Introduction: The ionosphere is the region extending from 50 km to more than 1000 km above the earth surface. It consists of free electrons in large numbers and affects the propagation of electromagnetic waves across it due to the induced variation in the effective refractive index. Out of the global distribution, the equatorial ionosphere, extending up to around 20° latitudes about the geomagnetic equator, constitute one of the most dynamic regions. This region exhibits ionospheric equatorial anomaly, in which large volume of plasma is transported from the geomagnetic equator to higher latitudes on both sides of it. This leads to large spatio-temporal variability in the ionospheric TEC. This also leads to the degradation in the performance of the empirical models in estimating TEC. The satellite based navigation system uses the time of propagation of the signals from the satellite to the receiver to measure of the range between them. In the process, it assumes a constant velocity 1
of the signal, equal to that in free space. However, when the signal passes through the ionosphere, it experiences an additional delay due to the difference in the refractive index of the ionosphere with the free space. This causes erroneous range measurements and lead to error in position estimates. Therefore, this ionospheric delay needs to be corrected. The delay is proportional to the total electron content (TEC) of the ionosphere along the signal path and hence the TEC estimation is necessary in such systems (Acharya, 2014). The dual frequency receivers estimate their own ionospheric delay using the delay dispersive relation in two different frequencies. However, for single frequency standalone receivers, this estimate is to be done using empirical models. But the accuracy of these empirical models is comparatively poor, particularly in the equatorial region due to the reasons discussed above. Even, in the very recent works, it has been reported that using the Klobuchar model, the residual vertical TEC errors can go beyond 30 TECU, particularly in the high solar activity periods (Li et al., 2017; Wang et al., 2016, Jongsintawee et al., 2016). It is important mentioning here that with the advent of highly capable processors, the state of the art navigation receivers can accommodate more processing loads for ionospheric estimations. So, for single frequency receivers, it can resort to a better estimation model than those currently used, for obtaining better accuracy, particularly in the equatorial region. The International Reference Ionosphere (IRI) is an empirical model developed jointly by the International Union of Radio Science (URSI) and Co-Operation in Space Research (COSPAR). It was basically a climatological model with its previous versions representing the monthly average behaviour of the ionosphere at a given place and time, for a given level of solar activity (Bilitza, 2001). Previous versions of IRI were found to provide good monthly predicted averages, but could not respond to the real, daily solar activity (Figurski and Wielgosz, 2002). So IRI model predictions were not useful in obtaining the ionospheric day to day behaviour. But IRI is a data-driven model which has been undergoing periodic updates in order to improve the model prediction. Now, many current applications require a description of the day-to-day and diurnal variations, satellite navigation being is one of them. In view of this fact, the IRI in its current and subsequent models are going to introduce the real time prediction capability (Bilitza et al, 2013). This will enable the model to predict the temporal variations in the electron densities and hence the instantaneous TEC which in turn may be used for correcting the range errors due to the ionosphere in the navigation receivers (Bilitza, 2015; Bilitza et al., 2017). Thus, IRI can become one of the potential candidates for using with the satellite navigation receivers. In the process of introducing improved capability of the IRI model in a navigation receiver, a study of the performance of the current model, in the context of generating the ionospheric corrections, is very useful. Therefore, in this work, we observe the deviations of the model predicted TEC values with respect to the true variations for individual days with different conditions. For the purpose we compare the model TEC outputs of IRI-2016, the current version of the IRI model (Bilitza et al., 2016), with the measured reference values obtained from the Indian SBAS system, named GPS Aided Geo Augmented Navigation (GAGAN). Comparison is done for two extreme geomagnetic conditions. At one end, we choose the quietest day of the month, for which the model is developed and expected to give best results. At the other end, we select the most disturbed day of the month, when we can expect the maximum deviations. Further, this is done for two different periods, viz. for high solar activity period and for low solar activity period. The data selected and the locations of comparison are described in details in Sec. 2. We have compared the results for these mentioned contrasting conditions for two main purposes, (i) to evaluate how the current version performs in 2
estimating TEC over the sea and (ii) to have a comprehensive understanding of the quantitative improvement needed in the model to make it useful for daily predictions for navigation receivers over the sea. Substantial amount of work has been done in validating the IRI model by observing the day to day deviations of the ionospheric parameters, particularly after the resolution of including real time estimation capability in the model (Bradley, 2004; Ezquer, 2004(a); Ezquer, 2004(b); Batista and Abdu, 2004; Miro Amarante, 2004). However, it is a fact that the model has been developed, modified and validated with a large amount of data from the global network of ionosonde and few incoherent scatter radar (Bilitza, 2006; Bilitza, 2015), which are primarily located on the land, in addition to the data from the top side sounders and sounder rocket measurements. On the contrary, our interest remains on the applications over the sea. Therefore, it calls for evaluating the performance of the current model for locations over the sea. For this reason, the present study examines the ionospheric estimation accuracy of IRI-2016, with the measurements done over the sea in the Indian Ocean region for different individual days with varied geomagnetic conditions.
2. Data, Methodology and Analysis The IRI-2016 predictions of the vertical TEC are compared with the TEC data derived from the ionospheric delay correction values of GAGAN. GAGAN is the satellite based augmentation system in India providing the corrections to the users over the primary GPS system. GAGAN has been implemented by the Indian Space Research Organisation (ISRO) in collaboration with the Airport Authority of India (AAI) for providing precise positioning services for the civil aviation and other applications. The area of service of this system includes the Indian flight information region (FIR), within which GAGAN provides civil aeronautical navigation signal consistent with the standard and recommended practices (SARPs) of the International Civil Aviation Organization (ICAO). To provide this service, GAGAN has a network of 15 reference stations (INRES) equipped with dual frequency receivers with redundancy which are located at different airports across the service area in India. These stations, called the Indian Reference Stations (INRES), receive the GPS data in an uninterrupted manner. The measurements include the satellite ranges for each GPS satellite visible with corresponding elevation, azimuth and time stamps at every second. Measurements are recorded up to a lowest elevation of 15°. These receivers are placed at the locations, surveyed for multipath and noise and are installed on elevated platforms. These receivers are also equipped with choke rings to eliminate any multipath. Therefore, this elevation cut-off is sufficient to avoid any perturbation in the signal due to multipath, which in turn can influence ionospheric estimations. These measurements are send directly to both of the two Master Control Centres (INMCC) through the dedicated optical fibre data communication subsystem. At the INMCC, the correction and integrity parameters are derived and are uploaded to the SBAS satellite through the Indian Land Uplink Station (INLUS) for transmitting them to the users in correct format. The architecture of the GAGAN network including the numbers of INRES receivers used and their locations across India along with the INMCC and INLUS are shown in Fig. 1a. (Acharya et al., 2007, Ganeshan et al., 2016). One of the correction parameters provided by GAGAN is the ionospheric delay. The ionospheric delay corrections terms, which vary geographically, are provided as vertical delays in the L1 frequency (1575.42 MHz), at definite discrete grid points. These delays are the scaled versions of the 3
vertical TEC, where the scaling factor from vertical TEC to vertical delay in L1 is 40.3/(1575.42x10 6)2 ≈ 1/6. The grid points, called the Ionospheric Grid Points (IGP) are distributed over the earth at an interval of 5° x 5° along the latitude and longitude over most of the globe including the equatorial region (RTCA 1999, FAA 2001). Out of all defined IGPs, GAGAN provided the correction data for those grid points which are within its service area. The IGPs served by GAGAN extends from 55° E to 110° E in longitude and -05° N to 40° N in latitude (Ganeshan et al., 2016). These values are updated at an interval of less than 300 seconds as per the recommendations of the RTCA (RTCA 1999). For generation of these correction values, the slant TEC values are derived for each signal path for each constituent INRES receiver using the range measured in two different frequencies, the GPS L1 (1575.42 MHz) and L2 (1227.6 MHz) using the relation
(1a)
where, TEC are in electrons/m2, R1 and R2 are the two ranges in metres measured in two frequencies f1 and f2 respectively. Commonly, TEC is expressed in TEC units (TECU) where 1TECU = 1016 electrons/m2. The slant TEC values are converted to vertical TEC values. For this, the slant to vertical conversion factor ‘f’ is used, where ‘f’ is given by f=
(1b)
Here, Re is the mean radius of the earth, h is the effective ionospheric height, taken as 350 km and E is the elevation angle. These converted vertical TEC values are defined at the Ionospheric Pierce Points (IPP). For a definite signal, the IPP is the point where the signal intersects the effective ionospheric height. The location of the IPP can be obtained from the location of the receiver and from the elevation and azimuth angle and is given by Ψ
π
– E – asin { (
) cos E }
λ
asin ( sin λs cos Ψ + cos λs sin Ψ cos Z
ϕ = ϕs + sin Ψ sin Z cos λ
(1c)
where, λ is the IPP latitude and ϕ is the IPP longitude. Ψ is the angular distance, measured at the earth’s centre, between the receiver location and the IPP. λs and ϕs are the station latitude and longitude respectively while E and Z are the elevation and azimuth of the satellite at the receiver location, the signal of which is in consideration. The ionospheric correction data at the IGPs are derived by combining all the vertical ionospheric TEC values at their IPP derived from individual receivers in the network. Using these, the TEC values at the IGP are derived with the use of a model. The ionospheric model used to estimate the delay at the grid points from the IPP values is called the ISRO Grid Model – Multi Level Data Fusion (IGMMLDF). This model captures the ionospheric variability in TEC at two different shell heights and finally provides the delay value in L1 frequency at these IGPs (Ganeshan et al., 2016). During the process, all other errors are thoroughly removed, including receiver and satellite bias, tropospheric errors, satellite and receiver hardware differential delay, etc. Therefore, these data are the most 4
accurate and dependable data we have at hand to be used as reference and are better than any individual dual frequency estimate. TEC derived from the vertical delays transmitted by GAGAN are therefore used as reference ground truth for our comparison. The GAGAN data has the advantage that, it is always accompanied by a confidence parameter, called the Grid Ionospheric Vertical Error Index (GIVEI) parameter. These associated GIVE indices are simultaneously transmitted with the delay data. It is an integrity parameter and gives us the indication of whether or not the delay associated values are accurate enough for the application purpose. A definite GIVEI value indicates a range of 1σ value of probable error in the ionospheric delay correction provided or equivalently for the TEC at the IGPs. The values are over bound so that it remains valid even when the values are interpolated by the user. In our work, we have disregarded all the data which has GIVEI values more than 10. This means that the precision of the ionospheric TEC will always be better than around 6TECU. However, the occurrence of GIVEI values near this threshold number is very infrequent. Typically, the accuracy figure is much better than this and the ionospheric 1σ precision value remains around 2-3 TECU. While the IGP values from the SBAS system are already made free from any inter-frequency and other bias occurring during the measurements, GIVEI indicates the effect of the residual errors of measurement and the modelling errors of the delay at the IGP points. Hence, selection of data on the basis of GIVEI ensures that the necessary accuracy exists in the reference with which the model is to be compared. The IGP points under the GAGAN service area are pre-selected and comparisons are done only at these points. Out of about 90 numbers of grid points served by GAGAN, 40 are on the sea, which thus provides us with a considerable portion of the total data points for any instant. Figure 1b shows the IGP points served by the GAGAN system which are over the sea. The IGP points are marked as circles. For these IGP points, TEC values are obtained from the GAGAN data and are compared with the IRI derived vertical TEC values at the same point and time. Since our objective is to observe the performance of the current IRI version with respect to the different forcing factors, the data is selected judiciously, for the days with prominence of the important driving forces of the TEC, like the solar activity, seasons, geomagnetic disturbance etc. which may cause variations to deviate from the typical values. Data were selected for two different years, viz. 2012 which is a high solar activity year and for 2015, which was near the trough of the solar cycle 24 with less solar activity. Largely, to keep the data handling convenient and yet to derive meaningful inference, data with the seasonal variation were included from the two equinoctial months of March and September and from the summer solstice month of June and the winter solstice month of December. Now, for each of these different months, the two quietest and two most disturbed days were selected. On these days, the TEC values obtained from the GAGAN data at the selected grid points were compared with IRI-2016 and analysed for this study. The list of quiet and disturbed days was obtained from the website of Kyoto World Geodetic Centre. The days selected for this work are shown in Table-1. Their corresponding Kp indices, representing the geomagnetic activity over the total day are also given in the parenthesis. In addition to this, the IRI derived TEC values are also compared with the direct TEC measurements made by dual frequency GPS receivers installed at different locations across India. The measured slant TEC, derived from the differential ranges measured in two different frequencies using Eq. 1(a), 5
is first corrected for receiver and satellite inter-frequency biases. The receiver inter-frequency biases are pre-determined while those for the satellites are obtained from those derived at the GAGAN INMCC. Then, these slant TEC is converted to the vertical TEC values at their respective IPP points, using equations 1(b) and 1(c). Once, these vertical TEC values are obtained, the IRI 2016 model is then used to derive the VTEC values at these same IPP points at the same instants of time. Finally, these values are compared and the statistics of the estimation errors is obtained. The observational TEC values are compared with the IRI-2016 model where the model output is obtained from a software code. The Fortran code for the IRI- 2016 model was available from http://irimodel.org and was used for the purpose. Since, our interest is to use the model as an alternative to the existing models for satellite navigation receivers in real time, where there is no option to input any current geomagnetic or solar activity parameter, all the default IRI-CCIR options in the IRI-2016 model were used to obtain the final vertical TEC values. Most importantly, the NeQuick option is used for topside modelling as it was found to be performing very well by previous researchers (Grynyshyna et al., 2015) Besides other factors, the ionospheric characteristics are different for the equatorial and offequatorial regions, primarily due to the transport processes of the plasma prevailing in this region. Therefore, to distinctly observe the model performance in these regions, the total observations were spatially divided into three distinct spatial regions depending upon the geomagnetic locations of the grids, viz. southern region, the northern region and the equatorial region, and the IRI performance were analysed for each of them. The distinction of the available IGP points on the sea into these regions is described in Sec. 3.
3. Results and Discussions: The data derived from IRI model and data observed at GAGAN IGP points were compared and the errors were analysed. As mentioned in Sec. 2, data were considered and analysed for two different years, 2012 and 2015, the former being the year with high solar activity and the latter with low solar activity. March and September were taken as the equinoctial months while June is taken as the month for summer solstice and December as the one for winter solstice. Two most disturbed and two most quiet days of the above mentioned months were taken for comparison and analysis. Thus, a total of 32 days were considered for the whole comparison, as shown in Table-1. Data were compared at the predefined grid points which were on the sea. To distinctly observe the performance, the total numbers of grids under observations were spatially divided into three distinct regions depending upon the geomagnetic locations of the grids. These regions are viz. southern region for grids below geomagnetic 5° S, the northern region for grids above geomagnetic 5° N and the equatorial region, lying in between these two regions. As the IGP points are defined in geographic coordinates and the grids are 5° apart here, the grids lying on geographic 0° and below constitute the southern region, while the grids on 5° N and 10° N geographical latitudes constitute the equatorial region and those on 15° N geographical latitude and above constitute the Northern region, as per our categorization. In fig. 1b, where IGPs under consideration are marked as circles, those grid points on the equatorial region are demarcated with cross marks within the circles. Those 6
towards the north of this section constitute the IGPs of the northern region and those towards its south constitute the southern region defined for this work. Since the grid ionospheric vertical TEC values are updated within 300 seconds, about 288 values of TEC were obtained for comparison over a single day for each such grid point. These vertical TEC in TECU units, are compared with the IRI model values estimated at the same time and at the same locations. The difference of the measured values from the corresponding IRI estimates, i.e. TEC IRI – TECGAGAN, is referred to as the estimation error. The analysis of the errors in estimation is described in the following sub-sections.
3.1 High Solar Activity Period
Selected days of 2012 were utilized to observe the performance of IRI model in predicting vertical TEC during the high solar activity periods. Two most quiet and the most disturbed days of the selected months were analysed, the results of which are described below. a. Quiet days
On the quiet days of the vernal equinoctial period, the North & South regions showed a very close proximity of the predictions by IRI model to the observed GAGAN data. However, for equatorial latitudes, the TEC estimates were under predicted by the IRI model as compared to the observed GAGAN data. In contrast, during the autumnal equinoctial time, the North and South regions have shown tendency of over predictions while the performance at the equatorial region was much better. Figure 2 (a and b) shows the temporal plots of the TEC for the three different regions and for two different equinoctial months. The temporal variations for different IGP points of a region are shown in continuum and thus appear in the same plot. Figure 2 (c and d) represents the error distributions for these periods with the three subplots representing different regions. The same constitution is maintained for all subsequent plots representing other seasons and conditions. Instances, when no measurements could be done have been disregarded. During both the summer and winter solstice, the North and South latitudes exhibited over prediction in TEC values by the model, just like the autumnal equinoctial period. Over prediction is comparatively more in the northern region and winter solstice as compared to the southern region and summer solstice. Further, the deviations are largest during midday. For the equatorial latitudes, the IRI model estimation was much closer to the observed GAGAN data. Minor over estimations during the noon and underestimations at night, particularly during the summer solstice while for winter, it was mostly overestimations. The corresponding plots are shown in fig. 3.
b. Disturbed days
As shown in fig. 4, for the disturbed days and during both the equinoctial period, the North and South Latitudes showed moderate under prediction of TEC when the IRI estimations were compared with the observed GAGAN data. At the same time, the model predictions at the equatorial latitudes
7
were highly under predicted. The under predictions were very conspicuous with differences going up to 40 TECU with respect to the GAGAN reference data. Similarly, during the solstice periods, for North latitudes, the predictions were close with minor over and under predictions. However, for the southern latitudes, it is mostly over predictions in summer and under predictions in winter. The equatorial region showed considerable under predictions in both the seasons extending the errors up to more than 20 TECU. This is evident from Fig. 5.
3.2 Low Solar Activity Period
For solar cycle 24, the peak was observed in 2012 and by 2015 the activity moved towards the trough. The days of 2015 were selected to observe the performance of IRI during the comparatively low solar activity periods. As done for 2012, for this low solar activity period of 2015, the quiet and disturbed days of the selected months were analysed, the results of which are described below.
a. Quiet days
For the equinoctial quiet days, the IRI model mostly under predicted the TEC in all regions when compared to the observed GAGAN data with comparatively fewer instances of over predictions. Over predictions are typically observed in the morning period while under predictions occurred mostly in post midmorning and in the afternoon. However, under prediction was more conspicuous in terms of numbers of occurrences and in extent as well, in the equatorial region. Over predictions are dominant in the southern region during the autumnal equinoctial period. The corresponding plots are shown in Fig. 6. Plots in fig. 7 indicate that the performance of the model during the solstice period. The summer solstice was mostly characterised by overestimations. For both North and South Latitudes, large overestimation was observed in the IRI model predictions. However, in the Equatorial Latitudes, the afternoon period showed very slight underestimation. During the winter, in both equatorial and southern regions, the model estimations were close to the observed data. The performance in the northern region is also better in winter than that in the summer.
b. Disturbed days
During the disturbed days, most conspicuous deviations are observed during the vernal equinox where the IRI model estimations were under predicting the TEC, particularly in the equatorial region and southern with a difference extending to more than 35 TECU as compared to the observed GAGAN data. Predictions in the Northern region are comparatively better. Estimates during the autumnal equinoctial period were comparatively better with northern and southern region showing moderate over predictions. The equatorial region showed much better accuracy with minor over predictions observed typically during the evening and night hours while under predictions are observed just before achieving the peak. The corresponding variations are shown in Fig. 8. 8
Mixed over and under estimation were observed in both the Southern and Northern regions in both the solstice periods with only southern region showing predominantly under predictions in winter. In the equatorial Latitudes, the IRI model estimations were still conspicuously under predicted during both the solstices, with deviations extending up to around 30 TECU. This is evident in Fig. 9.
3.3 Other Perspectives:
From the overall observations, the performance of the IRI model may be expressed in other perspectives. The relative variation of the IRI predictions showed a fixed spatial trend with the equatorial region always having relatively lower estimates with respect to the reference than the off equatorial region. That is, the equatorial region typically exhibited moderate to large under predictions, when the northern and southern region showed good accuracy or moderate under predictions respectively. Only when the northern and southern region showed a tendency of over estimations, the equatorial region showed better agreements. This is true for both quiet and disturbed days. Further, although the errors in both the northern and southern regions have mostly shown similar trends for the same conditions, this is not true for all cases. The seasonal variations in the performance show that for the equinoctial times, the model has more tendency of severe under predicted the TEC, particularly for disturbed periods, although, moderate under predictions were also observed for solstice periods and for quiet days. Expectedly, the performances of the model on quiet days are better than that disturbed days. Standard deviation of error during the higher solar activity year of 2012 is more than that in 2015. The results of comparison of the IRI estimates with measured TEC values at the standalone GPS receivers are given in table 2. This has been done for the year 2015, for the same quiet and disturbed days of the equinoctial and solstice months considered above. For equinoctial months, on quiet days, the IRI 2016 model has shown dominant under predictions. This is true for both vernal and autumnal equinoxes. For disturbed days, under predictions are conspicuous in vernal equinox while estimates in autumnal equinoctial period showing moderate over predictions. Standard deviations slightly increased in vernal equinoxes for both quiet and disturbed cases. For the solstice periods, the quiet days showed much closer estimates by IRI than the corresponding disturbed days. Winter solstice estimates on quiet days are marginally better than the summer values. For disturbed days, the estimations are grossly under predicting. The standard deviations are also larger than the quiet days, particularly during the summer solstice. These observations are in general agreement with those obtained by comparing the model values taking the GAGAN grid data as reference. The minor deviations may have occurred due to the residuals in the receiver bias corrections and due to the errors arising out of the slant to vertical conversions of the measured TEC data by the receivers. Finally, considering the fact that this work has been done for the purpose of using IRI 2016 model for the single frequency user to improve the positioning accuracy, we discuss the aspect of the effects of the TEC estimation inaccuracies on the estimation of receiver positions. The error in estimating TEC will lead to ranging errors in single frequency GNSS receivers. For a definite error of δTEC in TEC 9
estimation expressed in electrons/m2, the corresponding error in ranging will be dependent upon the signal frequency ‘f’ and is related as, δR
40 3 f2 x δTEC
(2)
where δR is the ranging error in metres and ‘f’ is the frequency of the signal in Hz. Now, there exist fixed relation between the ranging error (due to ionosphere or else) and positioning accuracy through the term, ‘Dilution of Precision’ (DOP), particularly the PDOP (Position Dilution of Precision). They are related as, σP
σR * PDOP
(3)
where σP is the standard deviation in the position estimates, σR is the standard deviation of the range errors (Acharya, 2014). The PDOP is dependent upon the satellite geometry at any instant. So, even for the same residual ionospheric error, it will be different for different user positions for different times and for different configuration of the space segment of the navigation systems. Therefore, relating any definite position accuracy of any receiver or any definite system with the corresponding ionospheric errors may turn deceptive. Typically, the PDOP for over Indian region for GPS typically remains around 2 but can go up to more than 3 at times. Accordingly, the 1σ accuracy in position due to the ionospheric error will typically go up 2 times the corresponding ranging errors due to error in TEC estimation and more than 3 times, in the worst cases.
Conclusion The vertical total electron content values obtained from the IRI-2016 predictions were compared with TEC values derived from the corresponding GAGAN vertical ionospheric delay correction values at the pre-defined ionospheric grid points over the sea. Standard IRI-2016 functions were used for the purpose with default model parameters without any input which are measured in-situ, regarding the prevailing solar or geomagnetic activity. This is done for particular days of different seasons and for two extreme geomagnetic conditions. Days were selected for the years 2012 and 2015, with high and low solar activities, respectively. The errors were studied for the mentioned conditions. From the major observations done from the results of this work, we conclude that, for the Indian sector over the sea, the IRI model, in its current form performs better on quiet days in off equatorial regions, particularly in the northern region. The overall performance degrades for other conditions. Under most of the other conditions, the model generally underestimated the true TEC values. Most severe errors have occurred in the equatorial region, where the performance observed is worst for the disturbed days of the equinoctial period. However, few cases of over estimations were observed, mostly in off-equatorial region on both quiet and disturbed days. No significant difference has been observed in performance between the periods of low and high solar activities. When compared with the TEC data obtained from direct measurement of the receivers, the model derived values were found to be in general agreement with those obtained by comparing the model values taking the GAGAN grid data as reference. Overall, it can be inferred that, the IRI model in its current form, even without any requirement of the coefficients to represent day to day variations, have performed satisfactorily on the sea, in terms 10
of predicting TEC with finite and bound errors. This has a special significance considering that for these locations the input that has gone in developing the model is sparse. It implies that it has the potential of performing even better when more input from measurements over the sea are assimilated in the process of improving the model.
Acknowledgements:
The authors are grateful to the Centre for Space Science and Technology education – Asia Pacific for providing the opportunity of doing this work. We also convey our gratitude to the whole GAGAN and IRNSS team of Indian Space Research Organization for allowing us to use their data. Finally, we thank DD-SNAA, GD-NAG and Head-NAD for their kind co-operation during the execution of this work. The contribution of the World Data Centre for Geomagnetism, Kyoto is sincerely acknowledged with thanks.
References Acharya, R., 2014. Understanding Satellite Navigation, Ed. 1, Academic Press, Waltham, MA, USA Acharya, R., Nagori, N., Jain, N., Sunda, S., Regar, S., Sivaraman, M.R., Badyopadhyay, K., 2007. Ionospheric Studies for the Implementation of GAGAN. Indian Journal of Radio and Space Science, 36, October-2007, 394-404 Batista, I.S., Abdu, M.A., 2004. Ionospheric variability at Brazilian low and equatorial latitudes: comparison between observations and IRI model, Advances in Space Research, 34, 1894–1900 Bilitza, D., 2001. International Reference Ionosphere 2000. Radio Sci. 36 (2), 261–275 Bilitza, D., 2006. The International Reference Ionosphere – Climatological Standard for the Ionosphere. In Characterising the Ionosphere, Meeting Proceedings RTO-MP-IST- 56, Neuilly-surSeine, France: RTO. Paper 32, 32-1 – 32-12. http://www.rto.nato.int/abstracts.asp. Bilitza, D., 2015. Preface: IRI and GNSS, Advances in Space Research, 55(8), 1913 Bilitza, D., Altadill, D., Truhlik, V., Shubin, V., Galkin, I., Reinisch, B. and Huang, X., 2017. International Reference Ionosphere 2016: From ionospheric climate to real-time weather predictions, Space Weather, 15, 418–429, doi:10.1002/2016SW001593. Bilitza, D., Boding Rodriguez, L., Joseph E., 2013. Description of Day-to-Day Variability in IRI, Presentation at the EGU General Assembly 2013, April, 2013 in Vienna, Austria, EGU2013-12650 Bilitza, D., Watanabe, S., Truhlik, V., Altadill, D., 2016. RI-2016: Description and Introduction, Abstract submitted for 41st COSPAR Scientific Assembly, July 2016, Istanbul, Turkey. http://cospar2016.tubitak.gov.tr Bradley, P.A., Kouris, S.S., Stanislawska, I., Fotiadis, D.N., Juchnikowski, G., 2004. Day-to-day variability of the IRI electron density height profile, Advances in Space Research 34, 1869–1877 11
Ezquer, R.G., Brunini, C., Mosert, M., Meza, A., del V. Oviedo, R., Kiorcheff, E., Radicella, S.M., 2004a. GPS–VTEC measurements and IRI predictions in the South American sector, Advances in Space Research 34, 2035–2043 Ezquer, R.G., Mosert, R. Corbella, Erazu, M., Radicella, S.M., Cabrera, M., de la Zerda, L., 2004b. Dayto-day variability of ionospheric characteristics in the American sector, Advances in Space Research 34, 1887–1893 FAA, 2001. Specifications for the WAAS, DTFA01-96-C-00025 FAA-E-2892b, Federal Aviation Administration, Washington, DC, USA. Figurskil, M. and Wielgosz, P., 2002. Intercomparison of the TEC obtained from the IRI model to the one derived from GPS measurements, Advances in Space Research, 30(11), 2563-2568 Ganeshan, A.S., Satish, S.V., Kartick, A., Srinivasan, N., Ramesh, G., 2016. GAGAN - Redifining Navigation over the Indian Region, Inside GNSS, Jan-Feb 2016, 42-48 Grynyshyna Poliuga, O., Stanislawska, I., Pozoga, M., Tomosik., A., 2015. Comparison of TEC values from GNSS permanent station and IRI model. Advances in Space Research, 55(8), 1976-1980 Jongsintawee, S., Rungraengwajiake, S., Supnithi, P., Panachart, C., 2016. Comparison of GPS Positioning accuracy using Klobuchar model and IGS TEC model in Thailand, KMITL Science and Technology Journal, 16(1), 01-16 Li, J., Wan, Q., Ji, M., Zhang, J., Wan, X., Fan, J., 2017. Evaluation of the Klobuchar Model in Taiwan, Advances in Space Research, 60, 1210-1219 Miro Amarante, G., Cueto Santamarı, M., Mosert de Gonzalez, M., Radicella, S.M., Ezquer, R., 2004. Day-to-day changes in experimental electron density profiles and their implications to IRI model, Advances in Space Research, 34, 1878–1886 RTCA, 1999. Minimum Operational Performance Standards, DO 229B, Radio Technical Commission for Aeronautics, Washington, DC, USA Wang, N., Yuan, Y., Li, Z., Huo, X., 2016. Improvement of Klobuchar model for GNSS ionospheric delay corrections, Advances in Space Research, 57(7), 1555-1569
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LIST OF FIGURES:
Fig.1: (a) Ground Segment of GAGAN (b) Ionospheric Grid Points on the sea served by GAGAN
Fig.2: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the equinoctial quietest days of (a) March 2012 and (b) September 2012. (c) and (d) are corresponding error distributions
Fig.3: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the quietest days of (a) summer solstice in June 2012 and (b) winter solstice in December 2012. (c) and (d) are corresponding error distributions
Fig.4: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the most disturbed equinoctial days of (a) March 2012 and (b) September 2012. (c) and (d) are corresponding error distributions
Fig.5: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the most disturbed days of (a) summer solstice in June 2012 and (b) winter solstice December 2012. (c) and (d) are corresponding error distributions
Fig.6: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the quietest equinoctial days of (a) March 2015 and (b) September 2015. (c) and (d) are corresponding error distributions
Fig.7: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the quietest days of (a) summer solstice in June 2015 and (b) winter solstice in December 2015. (c) and (d) are corresponding error distributions
Fig.8: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the most disturbed equinoctial days of (a) March 2015 and (b) September 2015. (c) and (d) are corresponding error distributions
Fig.9: Temporal variation of the measured VTEC from GAGAN at different IPP points and corresponding IRI predictions on the most disturbed days of (a) summer solstice in June 2015 and (b) winter solstice in December 2015. (c) and (d) are corresponding error distributions
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LIST OF TABLES: Table-1. Selected Days for analyses Table-2. Performance of IRI-2016 with respect to TEC measured by GAGAN station receivers
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Figure_1a
Figure_1b
Figure_2a
Figure_2b
Figure_2c
Figure_2d
Figure_3a
Figure_3b
Figure_3c
Figure_3d
Figure_4a
Figure_4b
Figure_4c
Figure_4d
Figure_5a
Figure_5b
Figure_5c
Figure_5d
Figure_6a
Figure_6b
Figure_6c
Figure_6d
Figure_7a
Figure_7b
Figure_7c
Figure_7d
Figure_8a
Figure_8b
Figure_8c
Figure_8d
Figure_9a
Figure_9b
Figure_9c
Figure_9d
Table-1 Selected Days for analyses Years
Seasons Equinox
2012 Solstice
Equinox 2015 Solstice
Months March September June December
Quiet Days 26(7-), 29(6-) 23(0+), 28(0+) 15(3), 19(2) 06(1-), 08(1)
Disturbed days 09(44), 07(39+) 03(33-), 05(31+) 03(25), 17(37-) 15(18-), 17(19-)
March September June December
05(11-), 10(8) 27(6), 30(3-) 05(2), 20(1+) 03(7-), 04(8)
17(48), 09(43-), 23(42-), 20(45-),
15
18(39+) 11(39+) 22(35+) 21(31)
Table-2. Performance of IRI-2016 with respect to TEC measured by GPS receivers Quiet Region
Northern Equatorial Southern Northern Equatorial Southern Northern Equatorial Southern Northern Equatorial Southern
Month
Disturbed Mean Error Std. Dev (TECU) (TECU)
Mean Error (TECU)
Std. Dev (TECU)
Sep
-0.858 -3.050 -4.643
6.419 6.777 5.474
5.372 1.061 0.717
7.274 6.447 4.500
Mar
-9.623 -2.608 -9.189
8.278 10.398 7.275
-5.605 -0.651 -6.180
9.304 10.990 10.136
Dec
1.064 -1.915 -3.080
5.156 4.582 4.351
-7.678 -8.432 -13.676
6.976 6.075 5.969
Jun
3.3282 2.6068 3.3393
4.564 3.894 3.160
-8.361 -8.988 -6.872
10.911 10.612 9.216
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