Determination of altitudes of the three main Ecuadorian summits through GNSS positioning

Mrí Josˊe Merizlde Mor , Cˊesr Alerto Leiv Gonzˊlez ,Dennys Alexnder Enríquez Hidlgo , Theofilos Toulkeridis ,c,*

a Universidad de Las Fuerzas Armadas ESPE, Sangolquí, Ecuador

b Instituto Geogrˊafico Militar IGM, Quito, Ecuador

c Universidad de Especialidades Turísticas UDET, Quito, Ecuador

Keywords:Altitude Volcanoes GNSS GPS leveling Geopotential

ABSTRACT Determining the altitude of mountains is one of the most fundamental challenges for humankind.Therefore, the main objective of the study is to determine the altitudes of the three main summits in Ecuador through GNSS positioning, referring to the official vertical datum of Ecuador and the geopotential surface(Wo).The three peaks are active volcanoes named Chimborazo,Cotopaxi and Cayambe,all of which are known to be over 5700 m above sea level. Positioning GNSS was performed on the summit of the volcanoes, and the GPS leveling method was applied on nearby plates.At these summits,the correction of the potential difference between the mean sea level and Wo was used. The altitudes referred to the mean sea level were compared with other registered heights, and the results are more accurate than previous geodetic missions.

1. Introduction

Determining the altitude of mountains and volcanoes has always been a challenge for humanity. In the 18th century, the determination of altitude with trigonometric methods was mainly used to study geotectonic movements[1,2].The official cartography of any country records the heights of the most essential elevations in geography. Since most measurements are not derived by direct methods, they are often not accurate data [3-5]. Geometric and trigonometric leveling methods were generally used to measure the altitude [6-8]. With the development of satellite positioning technology, it is possible to apply methodologies such as GPS leveling for measurements, which has been validated in many countries[9-11].In terms of height systems,the global trend is to unify them into a single geopotential surface (W) established by the International Association of Geodesy (IAG) [12,13].

The geography of Ecuador is very diverse,with altitudes ranging from mean sea level to 6000 m above sea level, which is why an authentic description of the territory is of general interest. The official cartography of Ecuador is one of the most used inputs in projects that require geographical information.The altitudes of the main volcanoes and mountains can be found in the topographic maps. Most of these data came from the results of expeditions conducted in the last century and were determined using barometric and triangulation methods. In this context, it can be concluded that there are no precise data on these altitudes.

Currently, the GNSS positioning methods provide facilities to obtain coordinates. Therefore, the update of the cartography and reliable data of the main geographical elements can be implemented. Additionally, the Vertical Basic Control Network (VBCN)was generated using geometric leveling techniques based on the vertical datum of Ecuador [14-16]. However, the current trend in the region is to establish a vertical reference system harmonized with the global Wdatum, which in turn is a physical surface[17-19].

Worldwide, many studies have focused on the precise determination of the altitude of the most iconic mountains. A series of measurements are recorded at Mount Everest,which compiles the measurement campaigns using GNSS equipment and traditional techniques such as leveling[20].In 2005,a new measurement was conducted to ensure the accuracy of the altitude of Mount Everest,and a laser ranging integrated with a GPS was used to establish three geodetic networks by trigonometric leveling. For Denali, the highest mountain in North America,experts from the United States Geological Survey (USGS) determined its altitude with GPS equipments in 2015.

In 2016,the“Third Geodesic Mission”was performed in Ecuador with the participation of the French Research Institute for Development(IRD),the Military Geographical Institute of Ecuador(IGM)and the National Polytechnic School (EPN) with the Geophysical Institute of Ecuador (IG). This mission aimed to measure the summit altitude of the Chimborazo volcano using GPS technology,with an altitude of 6263.47 m obtained by IGM and 6268 m by EPN-IG[21]. It should be noted that the height determined by the IGM used the EGM08 geoid model without reference to the official vertical datum of Ecuador[21].Additionally,to align with the global trend, the country should obtain approximations of physical heights referred to geopotential surface (W). Carriˊon (2017) et al.linked the VBCN of Ecuador to the International Height Reference System(IHRS)by calculating geopotential numbers with reference to the global vertical datum, resulting in the potential difference between the mean sea level concerning the tide gauge of the Libertad and Westablished by the IAG [22,23].

The VBCN of Ecuador manages level heights,where the leveling networks are under adjustment. Assuming the effect of gravity as another measurement error,the heights we use officially are purely geometric quantities without the consideration of the gravity error.

Based on the aforementioned context, the study aims to determine the altitudes of the three main peaks of Ecuador(Chimborazo,Cotopaxi and Cayambe)using GNSS technology.These altitudes will be referred to mean sea level and approximated to W, which corresponds to the global vertical datum established by the IAG.

2. Fieldwork and methodology

The fieldwork mainly consisted of two aspects:the ascent to the three highest elevations and the corresponding GNSS positioning[24-27]. On the technical side, the locations of the volcanoes and leveling plates belonging to Ecuadorian VBCN were analyzed. To assume the expected error, it is necessary to determine in which zone of variation of geoidal undulation the points are located.Similarly, to estimate the optimal time for GPS tracking, the Continuous Monitoring Stations (CMSs) of the GNSS Network closest to these three elevations were located.

Fig.1 illustrates the locations of the Chimborazo, Cotopaxi and Cayambe volcanoes in the zones of variation of the geoidal undulation. The closest plates were determined, where CHASQUI B is 17 km from Cotopaxi,IV-L3-99A is 17 km from Cayambe and XI-L5-20 is 7 km from Chimborazo volcano. The corresponding information was from the Military Geographical Institute. For the Cotopaxi volcano, the closest leveling plate is along the Quito-Latacunga E35 highway, at the entrance to the Cotopaxi National Park in the north-south direction. In the Cayambe volcano, the leveling plate IV-L3-99A is located on the edge of the Yaznˊan Park of the Cayambe canton and the Quito-Cayambe E35 highway. The leveling plate closest to the Chimborazo volcano called XI-L5-20 is situated on the Riobamba-El Arenal highway,a few meters from the entrance to the Chimborazo Wildlife Production Reserve.

The expected error in applying the GPS leveling method is generated by several factors, including observation time,tropospheric delay, and obstructions [28,29]. To minimize errors and achieve the maximum possible precision,it is recommended to use the static differential positioning method with doublefrequency GNSS equipment, as well as the Hopfield and Neill tropospheric models based on the length of the baselines. According to the standards of the processing software,the coordinates of the summits are determined by segmentation to generate a short baseline toward the target point. Hopfield and Neill tropospheric models have shown good results in determining GNSS observations with short baselines, where the tropospheric delay is a distancedependent error [30]. Auh et al. assessed the effect of tropospheric delay on the altimetry at a high mountain in South Korea[31].They found that with the baseline of 19-65 km,the difference in ellipsoid height was 1.53 cm when the Neill tropospheric delay model was applied.The baselines from the peaks to GNSS stations are short,and the snow conditions vary seasonally in Ecuador.If the differences due to the use of tropospheric models are less than a centimeter, the superficial snow may change more than that.

The GPS leveling method has been validated for the Ecuadorian territory based on the geoidal undulation[32].The validation errors are given by location in the geoidal wave variation zone, and we calculate the distance from a point with known level height to the target point (Table 1).

The GNSS positioning was divided into two phases. The first is the positioning on summits and shelters of the volcanoes, and the second is the positioning on leveling plates. GNSS R4 dualfrequency antennas, tripods and tribraches were used in this work. For positioning the equipment on the summits, a metal extension was used for the tribrach, then the equipment could remain level all the time on the glacier surface. In addition, to ensure the high accuracy of the work,a GNSS device was placed on the volcano shelter as a base and remained constant throughout the ascent and return journey.

The observation time determined for GNSS positioning was based on the IGM recommended specifications through the relationship:observation time=30 min+(2 min×distance in km)[33].The distance from the CMS to the study area is shown in Fig.1.The observation time was determined for each elevation towards the closest monitoring station. In data processing, station data were used to determine the coordinates of the bases,calculating 102 min for Chimborazo,110 min for Cayambe,and 88 min for Chimborazo.As noted by the IGM,these would be the optimal observation times for a geodetic job. However, the base team in each shelter served more observation time than previously. Considering their distance from each shelter and the meteorological conditions, the observation time for the team at the summits was 1 h.In this context,two phases of the field work were realized from April to August 2019(Table 2).Fig.2 demonstrates how the positioning was performed on the summits.

The static method was used for the GNSS positioning of the base equipment. The antenna configuration for positioning has a recording interval of 1 s,a position dilution of precision(PDOP)of 6,and an elevation mask of 10.For GNSS positioning at the summits,the method used with the same configuration was fast static. Two TRIMBLE R4 double frequency GNSS antennas, a tripod, and tribraches were used for this phase. One team left the device at the fixed reference point as a base,and the second team placed it on the summits. The positioning specifications are listed in Table 2, and the corresponding satellites are GPS and GLONASS.

For Cotopaxi and Cayambe, the positioning on the leveling plates was completed on different days. While in Chimborazo, it was achieved on the same day as the summit positioning,since the leveling plate was quite close to the shelter of this volcano. In Cotopaxi, a simultaneous positioning was performed on the CHASQUI B leveling plate.Before that,the infrastructure was placed in this position for about an hour.For Cayambe,the positioning was performed only on the leveling plate due to the difficulty of accessing to the shelter.Therefore,this point was connected to two continuous monitoring stations for processing.

Fig.1. Chimborazo, Cotopaxi and Cayambe volcanoes on the geoidal undulation variation zones. The corresponding distances toward each CMS are also given.

Table 1 Expected errors when applying the GPS leveling method [32].

3. Results

The Trimble Business Center (TBC) version 3.9 software was used to process the data,and it was linked to two CMSs closer to the shelters by a differential static method (Fig. 3). The main configuration of the processing was an elevation mask of 10with GPS and GLONASS. The weekly solutions of the SIRGAS-CON network were used to obtain the coordinates related to the completion time of the fieldwork. The data used to process the bases are listed in Table 3,and the processing scheme of these points is illustrated in Fig.3a-c.The coordinates of Cotopaxi, Cayambe and Chimborazo are in the IGS14 reference frame (Table 4).

Once the data from the shelters had been processed, the coordinates shown in the previous tables were set as the base points and applied by the radial static method,which was processed in the Trimble Business software Center (TBC). The results of processing the baselines from the shelters to the summits are summarized in Table 4.

Finally, the positioning data on leveling plates were processed.For Cotopaxi and Chimborazo, the baselines were processed with the base points. And for Cayambe, they were processed with twoCMSs close to the plate since there was no simultaneous processing(Table 5).

Table 2 Positioning specifications of two phases.

Fig. 2. Positioning on the summit of the Chimborazo volcano.

Some input parameters are required for applying the GPS Leveling method, such as summits and leveling plates. The geoid undulation was obtained using an application developed by the US National Geospatial-Intelligence Agency (NGA), which is executed based on two files called Tide Free Spherical Harmonic Coefficients and Correction Model. The results are presented in Table 6.

For the calculation of the altitude determined with reference to the vertical datum of Ecuador,the data listed in Table 7 were used.

The leveled heights were determined by Eq. (1). Table 8 shows the leveled heights and approximate errors.

Fig. 3. Processing scheme of (a) Cotopaxi, (b) Cayambe and (c) Chimborazo volcanoes.

Table 3 Processing results of different shelters.

Table 4 Summit processing results.

Table 5 Leveling plate processing results.

Table 6 Geoid undulations of summits and leveling plates.

Since the VBCN of Ecuador assumes that the mean sea level coincides with a point on the geoid (i.e., the vertical datum), we assume that H≅H.

The errors are approximated to those detailed in Table 1 [32].Carriˊon (2017) et al. linked the Ecuadorian vertical datum to the IHRS, determined an offset to compensate for the difference between the reference mean sea level geopotential (W) and the global vertical datum (W) [34]. Eq. (2) shows the relationship for the approximation.

The results show that the offset between the two geopotential surfaces is 2.8014 m/s, dividing this value by the gravity of the Earth's surface(9.7809 m/s)to convert to 0.2864 m.Furthermore,to calculate the heights referred to the geopotential W, the offset value in metric units is added to the leveled heights.

According to the official cartography of Ecuador,the altitudes of the Chimborazo, Cotopaxi and Cayambe volcanoes are 6310 m,5897 m, and 5790 m, respectively. As previously reviewed, these altitudes were adopted from scientific expeditions in the last century. Table 9 compares the altitudes obtained in this study and those recorded in the topographic map.

Table 7 Data used for the calculation of leveled heights.

Table 8 Level heights of summits obtained by GPS leveling.

Table 9 Comparison of the determined altitudes and those published in the official cartography.

The results indicate that the most significant difference is the altitude of the Chimborazo volcano. The cartography of Ecuador adopted the data determined by Reiss and Stübel using “trigonometric methods” in 1871 [35]. However, no further details of determining this altitude are described in this document, and the measurement error cannot be verified. The Chimborazo volcano altitude obtained in this study is close to those determined by other expeditions,which will be discussed later.The differences obtained from the Cotopaxi and Cayambe volcanoes are about 5 m, which may be related to the precision of the equipment and the method used at the time.

To figure out how far the summits of the Chimborazo,Cotopaxi and Cayambe volcanoes are from the center of the Earth, the Euclidean distance formula (Eq. (3)) is used to determine the distance(D)based on the Cartesian coordinates(X,Y,Z).The results are presented in Table 10.

4. Discussion

The error of the data processing results is less than 15 cm,which is relatively small for the altitude. As mentioned before, the magnitude of the error depends on the geoid undulation variation zone and the distance to the leveling plates.The geoidal undulation variation zone where the three volcanoes are located corresponds to zone 1, which is considered low variation [32].

In the case of the Cotopaxi and Cayambe volcanoes,the distance of the leveling plate used in our work is 17 km,which is greater than the specified distance of 14.6 km, it can be deduced that the error would be more than 15 cm. For the Chimborazo volcano, the error obtained by this method is about 5 cm. These errors are close to those in the aforementioned study [32]. However, it would be feasible to better define the expected errors when applying the GPS leveling method in the country.Due to the meteorological conditions of the volcanoes (snowfall or winds), there could be an increase ordecrease in the snow level on the summits.Therefore,errors at the centimeter level are discarded. Regarding the errors obtained in similar studies, these are mainly attributed to the surface layer of snow, which does not allow the height of the glacier surface to be accurately determined [20]. In addition, errors of each method are attributed, such as the case of the determination of Mount Aconcagua's summit altitude, which generated information not taken into account by EGM08[36].The errors obtained in this work are related to the method and the terrain conditions on the summits, which were not affected by the correction of tropospheric delay[31].Due to the lack of technological equipment, it is not possible to determine the permanent glacial layer as similar works[20,37].

Table 10 Distances from summits to the center of the Earth.

The altitudes obtained from the three volcanoes are approximations of the geopotential surface W, due to the added offset to compensate for the difference between the reference mean sea level geopotential(W)and the global vertical datum(W)[38].However,this approach could be more rigorous if the height is orthogonal using gravity measurements.It should be noted that this is an approximation since inconsistencies were detected in some leveling lines[38].

Satellite positioning techniques have been used to determine the altitude of many iconic mountains around the world, as GNSS positioning devices are not limited to ground conditions like traditional leveling. At Latin America, the mountains measured using this technique are Huascarˊan (Peru),Aconcagua(Argentina),Ojos del Salado(Chile-Argentina),and Pico Bolívar(Venezuela).In the rest of the world, there are mainly Mount Everest (Nepal--China), Kilimanjaro (Tanzania-Kenya), Mont Blanc (France-Italy),and Denali (United States)[39-46].

However, the most relevant work was measuring the altitude of Mount Everest in 2005, which was realized by the Chinese government after several geodesic campaigns. The measurement was conducted with two techniques: GPS and classical leveling (trigonometric leveling and laser ranging).In addition,a penetration radar was integrated to measure the thickness of the ice and snow layer at the summit.The data from the summit and the points at base camps were linked to the country's GPS monitoring networks. They collected gravity data on the surrounding terrain to gain a better understanding of the local gravity field and the geoid on the summit of Mount Everest. The GPS device at the summit had optimal data reception, and the results had better precision than previous campaigns.At the summit, they collected data for 39 min and obtained heights above the snow with an accuracy of 0.180 m[20].

From the 18th century to the present, many scientific expeditions have used trigonometric methods to determine the heights of the three major peaks of Ecuador,and the results show differences of several meters. Table 11 shows a summary of these data.

The work realized by the Third French Geodetic Mission in 2016 determined two altitudes: one is 6263.47 m by the IGM using the EGM08 model, and the other is 6268 m by the EPN-IG. Since only one team was positioned at the top of the volcano and the processing methodology was different. It should be noted that the conditions of the volcano were also different when there were glacial blocks on the summit of the Chimborazo volcano.

During thismission,it was also determined that Chimborazo isthe farthest point from the center of the Earth,exceeding Mount Everest's distance by approximately two kilometers.The IGM also determined an ellipsoidal height of 6292.876 m and an orthometric height of 6270.703 m [21]. The difference between the altitude of the Chimborazo volcano determined in this study(6267.25 m)and the altitude determined by the IGM(6263.47 m)is 3.78 m,which may be mainly due to the use of the EGM08 model[51].For the altitude determined by the EPN-IG and IRD(6268 m),the difference is a few centimeters.

Table 12 lists the altitudes of the main highest mountains in the equatorial region, the distances from the Earth's center, and theirdifferences from the Chimborazo volcano.The information is from the official websites of each country. Most of the highest active volcanoes measured from the center of the Earth are in Ecuador.On the other hand,Peru is the territory with the highest elevations due to its extensive mountain systems that are part of the Andes.Although Ecuador is a relatively small country, its altitude is characteristic.

Table 11 Comparison of altitudes determined by different scientific expeditions [21,35,47-50] and Mission 2019 (this study).

Table 12 Main elevations furthest from the center of the Earth and their differences from the Chimborazo volcano(V: volcano; M: mountain).

5. Conclusions

For elevation measurements,the application of the GPS leveling method is effective and takes less time in terms of data acquisition.However, when applying this methodology, existing restrictions such as the distance to a leveling plate must be considered to determine the expected error. The errors do not significantly interfere with the height data,since the peaks are always exposed to snowfall or melting,resulting in the rise or fall on the surface.

With the approximation of the heights to W,the elevation data referred to the global vertical datum is obtained,which is the same as that established by the IAG. The current trend is to establish a single vertical reference system, so all the works in adapting the system of each country to the global one must be taken into account. The three highest volcanic peaks of Ecuador are accurately determined in this study, belonging to the eight farthest heights from the center of the Earth.

The author's contributions

M.J.M.M. and C.A.L.G designed the research; M.J.M.M., D.A.E.H.and C.A.L.G performed the research and analyzed the data of the study; M.J.M.M. and T.T. wrote the paper.

Con

fl

icts of interest

The authors declare that there is no conflicts of interest.

Acknowledgments

We would like to thank the reviewers for their constructive critiques,which we have clarified a number of points in this revised manuscript. Colleagues whose previous work contributed indirectly to this paper are appreciated.