ENERO / JUNIO 2020 - VOLUMEN 30 (1)
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DOI 10.15517/RI.V30I1.35839
Ingeniería 30 (1): 75-94, enero-junio, 2020. ISSN: 2215-2652. San José, Costa Rica
Geoid Heights in Costa Rica,
Case of Study: Baseline Along the Central Pacic Zone
Alturas Geoidales en Costa Rica, caso de estudio:
Línea base a lo largo de la Zona Pacíco Central
Alonso Vega Fernández
Surveying Engineering School, University of Costa Rica, San José, Costa Rica
alonso.vega_f@ucr.ac.cr
Oscar H. Lücke Castro
Central American School of Geology, University of Costa Rica, San José, Costa Rica
oscar.luckecastro@ucr.ac.cr
Jaime Garbanzo León
Surveying Engineering School, University of Costa Rica, San José, Costa Rica
jaimegarbanzo@gmail.com
Recibido: 8 de enero 2019 Aceptado: 23 de setiembre 2019
_________________________________________________________
Abstract
A precise orthometric height (H) and orthometric height difference (ΔH) determination is required in
many elds like Construction, Geodesy and Geophysics. H is often obtained from an ellipsoidal height
(h) and geoid height (N) of a geopotential model (GM) because this computation does not have the spirit
leveling restrictions on long distances. However, the H accuracy depends on the GM local area adaptation,
and current global geopotential models (GGMs) have not been yet evaluated for Costa Rica. Therefore, this
paper aims to determine which GGM maintains a better t with a GPS/levelling baseline that contains the
gravity full spectrum. A 74 km baseline was measured using GPS, spirit leveling and gravity measurements
to validate the N computed from EGM2008, EIGEN-6C4, GECO, EGM96, GGM05C and GOCO05C. First,
an absolute N assessment was made, where geoid height from the GGMs (N
GGM
) were directly compared to
the geometric geoid heights (N
geo
) obtained from GPS and spirit levelling. A bias t (N
bias
) was computed
from this comparison to the GGMs with respect to the local vertical reference surface (W
0
). This N
bias
value
differs from model to model but the best t is given by GECO. By subtracting the N
bias
, a relative geoid height
(ΔN) assessment was designed to compare the differences between GGM relative geoid height (ΔN
GGM
)
and geometric relative geoid height (ΔN
geo
) on segments along the baseline. The ΔN comparison shows that
EGM2008, EIGEN-6C4 and GECO better represent the Costa Rican Central Pacic Coastal Zone and over
long distances, ΔH can be computed with a decimeter to centimeter precision.
Keywords:
Geodesy, Geoid, Geodetic Levelling, Ortometric Hight, Hight Systems.
VEGA, LÜCKE Y GARBANZO: Geoid Heights in Costa Rica, Case of Study...
76
Resumen
La determinación de alturas ortométricas (H) y diferencias de altura ortométrica (ΔH) precisas es requerida
en campos como construcción, geodesia y geofísica. La H puede obtenerse midiendo altura elipsoidal (h) y
calculando altura geoidal (N) de un modelo geoidal (GM), evitando limitaciones de la nivelación geodésica en
largas distancias. Sin embargo, la precisión de H dependerá de la adaptación del GM al sitio, y la adaptación
de los modelos de geopotencial globales (GGMs) actualmente se desconoce para Costa Rica. Por tanto, el
presente artículo busca determinar cuál GGM mantiene mayor congruencia con una línea base de GPS /
Nivelación que contenga el espectro de gravedad completo. Para esto, se midió una línea base de 74 km
utilizando GPS, nivelación geodésica y mediciones gravimétricas, para validar el N calculado con EGM2008,
EIGEN-6C4, GECO, EGM96, GGM05C y GOCO05C. Primero, se evaluó el valor absoluto de N, donde
N de los GGMs (N
GGM
) se comparó directamente con N geométrica (N
geo
) obtenida con GPS y nivelación
geodésica. Se obtuvo un sesgo (N
bias
) de los GGMs respecto de la supercie de referencia vertical local (W
0
).
Este valor diere de modelo a modelo, pero GECO se ajusta más a la zona. Al sustraer el Nbias, se aplicó una
evaluación de la altura geoidal relativa (ΔN
GGM
) respecto de la altura geoidal geométrica relativa (ΔN
geo
) en
segmentos a lo largo de la línea base. La comparación de ΔN mostró que EGM2008, EIGEN-6C4 y GECO
representan de mejor forma la zona costera del Pacíco Central de Costa Rica, y que en largas distancias es
posible obtener ΔH con precisiones decimétricas a centimétricas.
Palabras clave:
Geodesia, Geoide, Nivelación, Nivelación Geodésica, Altura Ortométrica, Sistemas de Altura.
Ingeniería 30 (1): 75-94, enero-junio, 2020. ISSN: 2215-2652. San José, Costa Rica DOI 10.15517/RI.V30I1.35839
77
1. INTRODUCTION
A precise determination of an orthometric height (H) is required in many elds like Construc-
tion, Geodesy and Geophysics. Orthometric heights are often obtained using the GNSS positioning
technique and a geopotential model to replace conventional leveling techniques because there is no
restriction in distances, and spirit leveling can be time-consuming. For these reasons, the behavior
of these models, in terms of accuracy, is always a concern. Geopotential models (GMs) are used
to correct ellipsoidal heights (h) value, which allows to obtain an H because it can supply a geoid
height (N). This N value is a difference between h and H that occurs because of the heterogeneities
in distribution of Earth’s masses (Vaníček, Kingdon, & Santos, 2012).
There are many Global Geopotential Models (GGMs) such as the EGM2008, EIGEN-6C4,
GECO (Förste et al., 2014; Gilardoni, Reguzzoni, & Sampietro, 2016; Pavlis, Holmes, Kenyon,
& Factor, 2012), which provide high global accuracy. However, these accuracies are derived from
error estimates of the least squares adjustment results called “internal error” and the challenge lies
on the determination of the “external error” (Gruber, 2004). The external error determines how
similar is a GM to the real geoid. Thus, a GGM sometimes does not provide a good representation
for local areas, especially if the GGM does not have terrestrial or aerial gravity of the local area.
Consequently, there are adaptations of the models for local areas which provides a more precise
representation (Sánchez, 2003; Sobrino, Mourón, & Fernández, 2009). However, this situation is
not the case for some developing countries in Central America and among them Costa Rica.
Currently, there is no local GM adapted to Costa Rica, and the performance of GGMs has not
yet been evaluated in detail for the country. Köther et al. (2012) provide a regional evaluation of
EGM2008 in terms of gravity anomalies compared to surface gravity data. Moreover, there has
been also an attempt to measure the quality of the OSU-91A by comparing a N computed from
GPS measurements and known H Benchmarks (BMs) of the National Geographic Institute (Diaz,
1997). However, it was found that these N were not comparable, and a quality measure could not
be done. There were studies carried out on local geoid determination (Cordero, 2010; Moya &
Dörries, 2016) but the areas taken into account for these studies were less than 50 km
2
. Thus, the
t of different geoid models in most of the country remains unknown.
GNSS measurements and spirit leveling are frequently used for quality assessment by com-
puting a geometric N (N
geo
). This GNSS measurements are available with their respective (H) in
areas such as United States, Canada, Japan, Brazil and the European Countries. In addition, GGMs
accuracy determination studies are abundant.
For instance, Gruber (2009) tested EGM08, EGM96 and other GGMs in Canada, Japan, and
Europe; Szűcs (2012) compared GOCE and GRACE derived models to GNSS/H corrected with
EGM08 to match the spectral contents; Guimarães et al. (2012) assessed various models for the
State of Sao Pablo, Brazil. All these studies either tried to match the spectral contents or estimate
an omission error for each model.
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78
Regarding, Kotsakis and Katsambalos (2010), they used the full spectral contents of the GNSS/H
to evaluate EGM08, EGM96 and other EIGEN derived models and, they found a bias after a
least-squares determination. This bias was corrected to compare the different studied models.
Although to match the spectral contents of the model is a more rigorous approach, the full spectrum
of gravity effects is contained in measurements in practical applications. Thus, scientist, engineers,
geographers and other common GGM users could chose a determined GGM model knowing what
uncertainties are in their measurements.
Consequently, this paper aims to determine which geoid maintains a better t with a GPS/
leveling baseline that contains the full spectrum of gravity contents for engineers and researchers
having better criteria for choosing between GGMs for their application. Also, GPS/leveling baseline
was independently measured to avoid problems presented by other studies (Cordero, 2010; Diaz,
1997; Moya & Dörries, 2016), which relied on the erroneous local leveling network or studied a
small area to be compared to GGMs.
2. METHODS
2.1 Data collection
The required data for this evaluation is: latitude, longitude, ellipsoidal height, spirit leveling
and gravity measurements. These data are used as listed below.
1. GNSS latitude (φ) and longitude (λ) are used to obtain the geoid heights for each GGM
(N
GGM
).
2. Orthometric heights (H) are obtained from gravity measurements, spirit leveling, and a
known point referred to the mean see level.
3. A geometric N (N
geo
) can be computed from an ellipsoidal height (h) and a H.
These GNSS measurements were obtained on 6 BMs set along 74 km of the Central Pacic of
Costa Rica; two GNSS receivers (Dual-frequency Topcom GR-3) collected the data simultaneously
using the relative static method. This technique allows to have a correlation between the two recei-
vers to calculate relative position with the highest precision in data post-processing. Even, it is use
to determine geometric height difference referred to an ellipsoid (Instituto Geográco Agustín
Codazzi, 1997).
The eld survey was planned in order to measure a GNSS baseline during at least 1 hour of
continuous observation on two consecutive BMs. One of the receivers remains in observation
while the other receiver is transferred to the next BM to link the consecutive GNSS baselines. In all
cases, a 15º elevation cut-off angle, PDOP values of less than 7, and 15 seconds sampling rate were
used in data collection. The data post-processing took into account the IGS precise orbits (epoch:
2016.270) with respect to the WGS84 ellipsoid (National Imagery and Mapping Agency, 1997)
79
Moreover, several GGMs (see Table 1) were chosen based on the following selection criteria:
the popularity, the geoid model maximum degree (
max
), maximum spatial resolution (ψ
max
) and the
satellite missions used for its calculation. Most are recent GGMs that have been developed with
combined satellites missions, satellite altimetry data, and some GGMs have terrestrial gravity data.
The International Centre for Global Earth Models (ICGEM) provided these GGMs, which can be
downloaded from the online computation platform, where N is determined from the height anomaly
plus spherical shell approximation of the topography (Barthelmes, 2013). The calculation service
uses a web-interface (http://icgem.gfz-potsdam.de/) to calculate gravity eld functionals from the
spherical harmonic models on grids (for this study, grids are referring to WGS84, and unmodied
model tide system). In order to obtain a N for each GGM in the exact location a script was progra-
med to apply an Inverse Distance Weighted Interpolation (IDW) on the grid.
Table 1. GGMs used on N evaluation.
GGM
max
ψ
max
(km) Data Reference
EGM2008 2190 9.132 S (Grace), G, A (Pavlis et al., 2012)
EIGEN-6C4 2190 9.132 S (Goce, Grace, Lageos), G, A (Förste et al., 2014)
GECO 2190 9.132 S (Goce), EGM2008 (Gilardoni et al., 2016)
EGM96 360 55.556 S, G, A (Lemoine et al., 1998)
GGM05C 360 55.556 S (Grace, Goce), G, A (Ries et al., 2016)
GOCO05C 720 27.778 S, G, A
(Fecher, Pail, & Gruber,
2016)
S = Satellite Tracking Data, G = Terrestrial Gravity Data, A = Altimetry Data.
The EGM2008 is a high resolution GGM that has been well studied worldwide, showing good
results for many regions (Dawod, Mohamed, & Ismail, 2009; Gruber, 2009; Kotsakis & Katsam-
balos, 2010; Łyszkowicz, 2009). EIGEN-6C4 and GECO use the EGM2008 terrestrial gravimetric
data as calculation input thus there is a correlation between these GGMs.
Furthermore, both EIGEN-6C4 and GECO also include satellite data that was not available
for EGM2008, so the comparison of the N results with these GGM is necessary. The GECO geoid
model combines the GOCE satellite-only global model and EGM2008 to improve the model accu-
racy in the low to medium wavelengths in some areas (Gilardoni et al., 2016). EIGEN-6C4 uses
LAGEOS, GRACE and GOCE satellite data and incorporates an EGM2008 geoid height grid for
the continents (Förste et al., 2014).
VEGA, LÜCKE Y GARBANZO: Geoid Heights in Costa Rica, Case of Study...
80
In the case of the spirit leveling, it was carried out following the NOAA standards to match the
maximum precision (NOAA, 1981, 1995), except for the staff material because of resource limi-
tations. NOAA requires IDS (Invar Doubled Scale) but a bar-code metal staff was used. This staff
add some uncertainties associated with thermal expansion. Moreover, the automatic level used in
this study was a Leica Sprinter 250M. The accuracy of the instruments used in spirit leveling was
veried with ISO 17123-2:2001 test (International Organization for Standarization, 2001).
It was necessary to use gravity measurements in order to apply orthometric corrections to the
levelling height differences along the baseline. These corrections can be found in the work of Kao
and Ning (2008). The gravity survey was carried out with a relative Burris gravity meter (B-106).
The survey started on a known gravity value of a station at University of Costa Rica (UCR) to set
up a secondary gravity station near to the baseline middle, on the EST BM (see Figure 1). The gra-
vity values were translated to the other stations.
The initial and nal measurements of the gravity campaign were made on the gravity station
at UCR, and three others were performed on the secondary station (EST). Both procedures were
made to control the instrumental drift and the effects caused by atmospheric pressure changes
(Seigle, 1995).
Finally, observed gravity values were corrected to get the gravity value on the ground surface.
The corrections related with variation in latitude and elevation were applied on the eld. Other as
earth tides correction and instrument drift correction were applied after the measurement works.
For each BM, the N
geo
was calculated applying Equation 1 (Hofmann-Wellenhof & Moritz,
2006).
(1)
Figure 1. The BM distribution in the Central Pacic Coastal Zone. Coordinates are shown in WGS84.