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Review

Development, Status and Future Perspectives of Croatian Gravimetric Reference System

by
Tedi Banković
* and
Marko Pavasović
Faculty of Geodesy, University of Zagreb, Fra Andrije Kačića Miošića 26, 10000 Zagreb, Croatia
*
Author to whom correspondence should be addressed.
Geomatics 2026, 6(3), 62; https://doi.org/10.3390/geomatics6030062
Submission received: 8 April 2026 / Revised: 23 May 2026 / Accepted: 2 June 2026 / Published: 3 June 2026
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Highlights

What are the main findings?
  • The Croatian Gravimetric Reference System 2003 (HGRS03) is based on the IGSN71 framework, which, although historically significant, no longer fully meets the requirements of modern geodetic and gravimetric applications.
  • The current gravimetric infrastructure in Croatia depends on outdated absolute gravity measurements, whose present validity is uncertain due to possible temporal gravity changes over the past three decades.
What are the implications of the main findings?
  • Re-observation of the Zero-Order Network and adjustment of the entire Basic Gravimetric Network are necessary to ensure reliability and compatibility with current geodetic standards.
  • Developing national absolute gravimetry capacity is essential for future integration into the International Terrestrial Gravity Reference System (ITGRS).

Abstract

Stable, homogeneous, and internationally comparable gravimetric reference systems are fundamental components of modern geodetic infrastructure, supporting height system realization, geoid modeling, geodynamics, and the integration of national gravity networks into global reference frames. This paper reviews the historical development of gravity reference systems, from early pendulum-based realizations to modern absolute gravimetry, with particular emphasis on their application in the Republic of Croatia. The evolution of international gravity datums is presented through the Vienna Gravity System, the Potsdam Gravity System, and the International Gravity Standardization Network 1971 (IGSN71), outlining their methodological foundations, accuracy levels, and limitations. The role of IGSN71 in harmonizing national gravity networks is discussed in the context of international cooperation. Within this framework, the development of gravimetric research in present-day Croatia is outlined, from surveys conducted during the Yugoslav period to the establishment of an independent national gravimetric datum. The realization of the Croatian gravimetric reference system through absolute gravity measurements between 1996 and 2000, the formation of the Zero-Order Gravimetric Network, and the establishment and densification of the First- and Second-Order Gravimetric Networks are described. The Croatian Gravimetric Reference System 2003 (HGRS03), based on IGSN71, is presented as the official national gravity reference. In addition to documenting its historical development, the paper provides a critical assessment of the current status of HGRS03, including limitations inherited from its historical reference framework, the absence of repeated absolute observations, and the uneven spatial distribution of Zero-Order stations. The paper also discusses future modernization perspectives, particularly in the context of advances in absolute gravimetry and the long-term maintenance of the Croatian gravimetric reference infrastructure.

1. Introduction

Systematic observation and monitoring of the Earth’s gravity field require stable, homogeneous, and internationally comparable gravimetric reference systems. These systems are a fundamental component of modern geodetic infrastructure, providing the basis for gravity-related geodetic and geophysical applications, including height system realization, geoid modeling, geodynamics, and integration of national gravity networks into global reference frames.
Historically, national gravimetric systems were primarily established through relative measurements and later linked to international reference systems [1,2,3]. Contemporary approaches increasingly rely on absolute gravity observations as the fundamental reference. A major milestone in the unification of gravity systems was the establishment of the International Gravity Standardization Network 1971 (IGSN71), which enabled the harmonization of national gravity systems and ensured their mutual consistency [4].
In the Republic of Croatia, the gravimetric reference system is officially defined by the Decision of the Government of the Republic of Croatia on the establishment of official geodetic datums and cartographic projections [5], which designates IGSN71 as the reference gravimetric system. The practical implementation of IGSN71 began between 1996 and 2000, when absolute gravity measurements were conducted at six locations across the Croatian territory within the IGSN71 framework [6].
Densification and spatial realization of the Croatian gravimetric reference system were completed in 2003 through relative gravity measurements at 36 points distributed across the national territory. Along with six absolute gravimetric points, these points form the Basic Gravimetric Network of the Republic of Croatia, which officially represents the Croatian Gravimetric Reference System 2003 (hrv. Hrvatski gravimetrijski referentni sustav 2003—HGRS03) [2,5]. Beyond serving as the national gravity reference, HGRS03 is also an important component of the Croatian vertical geodetic infrastructure, providing the terrestrial gravity basis for national geoid modeling and practical height system realization [7,8].
Given the significant technological advances in absolute gravimetry, the development of modern international gravity reference frameworks, and the long period without systematic re-observation of the Croatian gravimetric infrastructure, this paper presents a historical and technical review of the development of gravimetric reference systems in Croatia, from early international connections to the establishment of HGRS03. It also critically assesses current limitations and future modernization pathways in the context of contemporary international gravimetric reference concepts.

2. History of Gravimetric Reference Systems

The need for gravity reference systems arose from the growing importance of gravity measurements in geodesy over the past two centuries, driven by advances in physical geodesy, increasing demands for precise geodetic products, and technological progress [9]. Early 19th-century pendulum experiments to determine absolute gravity values were laborious and subject to significant uncertainties [10]. These experiments also demonstrated that relative gravity measurements are generally more accurate than absolute determinations, a trend that continued until the early 1990s [9].
This reliance on relative gravimetry highlighted the need for well-defined reference points with accurately known absolute gravity values, which serve as gravity origins for determining differences between stations [9]. To ensure consistency across regions and countries, such points had to be internationally recognized, leading to the concept of an international gravity datum for unified and accurate measurements [11]. With the rapid increase in observations, particularly during Helmert’s period, facilitated by van Sterneck’s relative pendulum apparatus in 1887, it became evident that measurements were tied to different absolute values, and lacked a common reference [12].
To address this, Helmert, after becoming Director of the International Association of Geodesy (IAG) Central Bureau in 1886, developed the classical approach of defining an absolute gravity standard at one or several carefully determined stations, to which all relative measurements of a global network would be referred to [13]. This method led to successive homogeneous gravity reference systems, laying the foundation for a worldwide gravity reference system with a unified datum and scale compatible with modern instrumentation [10,13]. Historically, three realizations of gravity reference systems can be distinguished: the Vienna Gravity System, the Potsdam Gravity System, and the IGSN71 [4].

2.1. Vienna Gravity System

The Vienna Gravity System, formally adopted by the IAG in 1900, was the first internationally recognized gravity reference system [13,14]. It was based on the absolute gravity value determined by Oppolzer at the Vienna Observatory in 1884 and connected approximately 1400 stations through relative pendulum observations [9,11,13,14]. The introduction of Sterneck’s pendulum significantly improved regional gravity surveying, including in the Austro-Hungarian Empire [10,12]. However, limitations in the absolute reference value caused systematic inconsistencies, which ultimately motivated the development of improved international gravity reference systems [14].

2.2. Potsdam Gravity System

Due to systematic inconsistencies identified in the Vienna Gravity System, the Potsdam Gravity System was adopted by the IAG in 1909 as a new international gravity reference system [4,10,11]. It was based on absolute gravity measurements performed at the Geodetic Institute in Potsdam, providing a single reference datum to which national and regional relative gravity networks were connected worldwide [13,14,15].
Over time, improved absolute gravity measurements revealed that the original Potsdam reference value contained a systematic bias, limiting its long-term suitability as a global standard [11,15,16,17,18]. Despite these limitations, the Potsdam system remained widely used throughout much of the 20th century and served as the reference framework for gravimetric work in the former Yugoslavia, including the territory of present-day Croatia [1,3,19]. These early networks formed the basis for subsequent gravimetric development in the region, although detailed historical data from this period are largely unavailable to Croatian institutions today [20].

2.3. IGSN71

IGSN71 was formally adopted at the XV General Assembly of the International Union of Geodesy and Geophysics (IUGG) in 1971, replacing the Potsdam Gravity System as the global gravimetric datum [4,14]. The transition involved a systematic correction of −14 mGal relative to the Potsdam datum [9]. Unlike the Potsdam system, which was based on a single absolute reference value, IGSN71 represented a major conceptual advancement by establishing a globally adjusted gravimetric reference framework based on a network of stations rather than a single datum point [21].
IGSN71 includes 1854 gravity stations worldwide, with its datum realized through eight absolute gravity stations and its scale established through a global adjustment of extensive relative gravity observations [4,14,21,22]. The principal gravimeter connections forming the international structure of the network are shown in Figure 1. According to Morelli et al. (1974) [21], the standard errors of gravity values within the network were generally better than ±0.1 mGal. Compared to previous systems, IGSN71 provided a significantly more consistent international gravity reference and became the basis for national and regional gravimetric networks worldwide [4,22]. However, Morelli et al. (1974) [21] also emphasized that the actual accuracy of gravity values was limited by the distribution and structure of observations, as well as imperfect knowledge of gravimeter performance, while formal adjustment errors reflected only the internal consistency of the network and could underestimate true errors if systematic effects were not fully accounted for. Since the practical reliability of IGSN71 values was therefore not spatially homogeneous, these limitations are particularly relevant for parts of Europe with historically less dense gravity observation coverage, including the region in which Croatia is located, and should also be considered when assessing the inherited accuracy characteristics of the Croatian national gravimetric reference system.
Beyond its structural and observational design, an important aspect of IGSN71 concerns the treatment of permanent tidal effects in gravity observations. With improvements in spring gravimeter accuracy during the mid-20th century, defining gravity values with respect to tidal conventions became increasingly important. According to Mäkinen and Ihde (2009) [23], gravity observations may be expressed in three different tidal systems: mean tide, tide-free (non-tidal), and zero tide.
Honkasalo (1964) [24] demonstrated that gravity values expressed in the tide-free system do not correspond to the time-averaged acceleration of free fall, since the permanent luni-solar gravitational influence is excluded. To address this, he introduced the Honkasalo correction, which transforms tide-free gravity values into mean-tide values. Because this correction was adopted in the realization of IGSN71, the system is formally referenced to the mean-tide convention [23].
However, this convention later raised theoretical concerns. Heikkinen (1979) [25] demonstrated that retaining the permanent direct gravitational contribution of the Sun and Moon in gravity anomalies introduces theoretical inconsistency in geoid determination, since Stokes’ integral assumes that anomalies originate solely from the Earth’s mass distribution [26]. Consequently, the International Association of Geodesy initially recommended in 1979 the complete removal of tidal effects from geodetic observations, effectively introducing the conventional tide-free system. This recommendation was revised in 1983, following the proposals of Groten (1980) [27] and Ekman (1981) [28], when the IAG adopted the zero-tide system for gravity field quantities, in which the direct permanent luni-solar contribution is removed while the Earth’s permanent deformation response is retained [23]. As a result, modern absolute gravity observations and national gravimetric reference systems are generally expressed in the zero-tide system, creating an important compatibility issue with the historical IGSN71 realization.
All European countries, including those bordering the Republic of Croatia, established their national and regional gravity networks within the framework of the IGSN71. Consequently, the gravity values at stations in neighboring countries, as well as at all points of the Croatian gravimetric network, are referred to the IGSN71 reference system, either directly through absolute gravity measurements or indirectly via connections to IGSN71 compatible networks [29,30,31,32,33,34,35,36]. The implementation of IGSN71 in individual countries was accomplished through a series of national and international absolute gravity campaigns conducted from the second half of the 20th century onward. These campaigns established fundamental reference stations and verified and maintained the long-term stability of existing gravity networks [10].
Within this common reference framework, the neighboring countries of the Republic of Croatia have established and maintained their gravity networks through national absolute gravity measurement campaigns conducted at different epochs. In Montenegro, Albania, and Kosovo, absolute gravity measurements were carried out in 2015 at eight stations, providing a modern realization of gravity values consistent with the IGSN71 [30]. In Serbia, absolute gravity observations were performed at three stations in 2007, forming the basis for the national gravity reference and its connection to surrounding networks [3]. Bosnia and Herzegovina conducted absolute gravity measurements at four stations in 2013 [37], while in North Macedonia, three absolute stations were measured in 2010, contributing to the stabilization and modernization of the national gravity framework [38]. In Slovenia, a remeasurement campaign was carried out in 2014 at six absolute gravity stations to ensure consistency with contemporary absolute gravimetry standards [39]. Hungary follows a systematic strategy of repeated absolute gravity measurements at its reference stations, typically at intervals of seven to ten years [40]. In addition, continuous absolute gravity observations were conducted from 2001 to 2010 using an absolute gravimeter, allowing for detailed analysis of temporal gravity variations and long-term trends [41]. In Italy, absolute gravity measurements are performed almost continuously as part of national and international monitoring programs, reflecting a long-standing commitment to high precision gravimetry and the maintenance of a robust and up-to-date gravity reference system [42,43,44].
In the Republic of Croatia, the national realization of the IGSN71 reference system was established through the UNIGRACE project (Unification of Gravity Systems in Central and Eastern Europe) during 1996–2000 [45]. In this project, six absolute gravity points were determined, providing the first independent definition of the national gravity datum and ensuring direct compatibility with IGSN71 [6,46]. To densify the network, a set of 36 First-Order Gravimetric points was established across the Croatian territory in 2003, complementing the Zero-Order Gravimetric Network [47]. The combination of the six absolute points and these 36 First-Order points, all referenced to the IGSN71 system, formed a total of 42 points, constituting the HGRS03 [5]. This system represents the official realization of the national gravity reference and serves as the foundation for all subsequent gravimetric measurements, geodetic applications, and integration into regional and international gravity networks. HGRS03 is connected to neighboring national gravimetric networks through the common IGSN71 reference framework and the regional harmonization efforts of the UNIGRACE project, enabling cross-border consistency of gravity data [48].

2.4. ITGRS—The Future

With the development of precise absolute gravimetry and the growing need to monitor and understand the Earth system, it has become clear that the IGSN71 no longer meets the requirements of modern geodetic and geophysical applications [49,50,51,52]. The accuracy of contemporary absolute gravimeters reaches a few µGal, while the IGSN71 does not provide a sufficient reference for the reliable detection and interpretation of temporal gravity variations [49,50,51,53,54].
In response to these limitations, the International Association of Geodesy (IAG) initiated the development of the International Terrestrial Gravity Reference System (ITGRS) and its realization, the International Terrestrial Gravity Reference Frame (ITGRF) [50,52]. The ITGRS will be defined by the instantaneous acceleration of free fall expressed in SI units and will include conventional corrections for time-independent components of gravity, such as the zero-tide system, the standard atmosphere, and polar motion corrections. The ITGRF is the practical realization of this system and should be established using observations from absolute gravimeters, intercomparisons of absolute gravimeters, and a set of conventional models applied to account for temporal gravity variations [52,55].
The implementation of the ITGRF requires a globally distributed set of reference stations to ensure long-term stability by combining continuous superconducting gravimeter measurements with periodic absolute gravimeter campaigns. A key prerequisite for this implementation is the development of national and regional gravity networks based on absolute gravity observations, which provide the necessary infrastructure for the realization and densification of the global gravity reference system [50,52,55].
With the support of national and international institutions and the systematic development of gravity networks based on absolute gravity measurements, the ITGRF is expected to evolve into a modern, globally homogeneous, and long-term stable gravity reference system. Such a system can replace IGSN71 and fulfill the requirements of future geodetic and scientific applications, particularly for high-precision geoid determination and regional gravity field studies [50,52,55].
Several countries have already begun implementing the ITGRS establishing and modernizing their national gravity systems based on absolute gravity observations [49,51,54,56,57]. A crucial component of these national initiatives is continuous participation in international and regional absolute gravimeter comparison campaigns. These comparisons enable the traceability of national gravity realizations to the emerging global reference frame and ensure consistency between different instruments [55,56]. Through this approach, national gravity systems contribute directly to the realization and densification of the ITGRF while ensuring the reliability and homogeneity of gravity data at national and regional levels.

3. Review of Previous Gravimetric Measurements in Croatia

3.1. Croatia as Part of Yugoslavia

The first significant fundamental gravimetric surveys in the territory of Yugoslavia, of which Croatia was a member from 1945 to 1991, were conducted between 1951 and 1953. Through these measurements, the fundamental network point in Zemun (Serbia) was connected to a reference point in Paris, thereby aligning the national network with the Potsdam Reference System [1,3]. Following this connection, the establishment of the Yugoslavian First-Order Gravimetric Network began in late 1952 and continued throughout 1953. Using relative gravimetric measurements, 15 first-order points were established with a connection to the fundamental point in Zemun, six of which were located within the territory of the present-day Republic of Croatia: Borovo, Dubrovnik, Pula, Sinj, Zadar, and Zagreb [58].
The First-Order Gravimetric Network was later complemented by the Second-Order Gravimetric Network, which was established in the territory of Croatia between 1958 and 1960 by the company Geofizika d.d. [58]. These measurements, together with those conducted in other Yugoslav states, served as the basis for the Basic Gravimetric Network, established between 1964 and 1967 by the Federal Geodetic Administration (Figure 2) [2].

3.2. Zero-Order Gravity Network

After the breakup of Yugoslavia, the Republic of Croatia no longer had access to data from the Yugoslavian Basic Gravimetric Network, creating the need to establish a new national gravimetric reference system. The first step toward this goal was taken in 1996 within the framework of the international UNIGRACE project. During this project, four absolute gravimetric points (cro. apsolutna gravimetrijska točka—AGT) were initially established: two in Zagreb (Maksimir—AGT02 and Puntijarka—AGT03) and one each in Pula (AGT04) and Makarska (AGT05). The absolute measurements were carried out by the University of Zagreb—Faculty of Geodesy and the German Federal Agency for Cartography and Geodesy (former IfAG, todays BKG), with funding from the State Geodetic Administration of the Republic of Croatia. In the second phase of the project, two additional points were established (Osijek—AGT01 and Dubrovnik—AGT06), bringing the total to six absolute gravimetric points, which together constitute the Zero-Order Gravimetric Network of the Republic of Croatia and simultaneously define the Croatian gravimetric datum (Figure 3) [6,59].
Bašić et al. [58] proposed establishing an additional absolute gravimetric point near the Plitvice Lakes to reduce the large distances between the existing points in Zagreb, Pula, and Makarska. The expansion was proposed again in 2014 [59], but with significant modifications. The proposal noted that the Zagreb—Maksimir and Makarska points no longer met the criteria for absolute gravimetric points: the Maksimir point due to temperature instability in the room with a movable roof, and the Makarska point due to physical destruction. It was also emphasized that the Pula point is in a private building, which poses a risk of destruction due to potential renovations. The establishment of five new points was proposed (Čakovec, Gospić, Rovinj, Split, and Zabok), which would bring the total number of points in the Zero-Order Gravimetric Network to eight. However, this expansion was never implemented.

3.3. First-Order Gravity Network

In accordance with the Regulation on the Procedure for Performing Basic Geodetic Works [60], the Zero-Order Gravimetric Network needed to be densified by establishing the First-Order Gravimetric Network. Therefore, as part of the project Basic Gravimetric Network of the Republic of Croatia [2,36,61,62,63], relative gravimetric measurements were carried out between June 12 and August 13 using two Scintrex CG-3M gravimeters and one Scintrex CG-5M AUTOGRAV. Based on these measurements, the First-Order Gravimetric Network of the Republic of Croatia was established with an initial 36 gravimetric points (cro. gravimetrijska točka—GT). Markovinović (2009) [47] provided the gravity values for these 36 points, with tidal corrections determined using the ETERNA software [64], which considers the development of partial tidal components based on long-period observations. In Bašić et al. (2004) [62], the Longman model [65] was used to calculate the corrections, relying on a mathematical model based on known astronomical ephemerides of celestial bodies rather than actual observations.
Considering the requirement of the Regulation on the Procedure for Performing Basic Geodetic Works [60] that the accuracy of gravity in the Basic Gravimetric Network must be better than 0.05 mGal, and the fact that the average standard deviations reported in Bašić et al. (2004) [62] and Markovinović (2009) [47] were approximately 0.005 mGal, it can be concluded that both calculations achieved a very high level of accuracy.
During the 2003 survey of the First-Order Gravimetric Network, it was found that the absolute gravimetric point in Makarska had been destroyed, so measurements were conducted at an eccentric point in the Malakološki Museum (AGT05E) in Makarska [2,36,66].
As part of the Basic Gravimetric Network of the Republic of Croatia project, a horizontal calibration base for relative gravimeter calibration was established, consisting of nine points, with the absolute point AGT03 as the starting point and the eccentric of the absolute gravimetric point AGT05 as the endpoint [67,68]. Within the horizontal calibration base, a provisional vertical calibration base was defined using points AGT02 and AGT03 [68], which have a significant height difference, making these two points suitable for a vertical calibration base (Figure 4).
Because establishing absolute gravimetric points is a very expensive process, microgravimetric networks were established in 2003 [69]. Each microgravimetric network consists of eccentrics established near the absolute points. Three eccentrics were set up for each absolute point, except for two nearby points in Zagreb, for which a total of three eccentrics were stabilized for both points. The eccentrics were located at distances ranging from 500 m to 5 km. In November 2005 and April 2006, relative gravimetric and leveling measurements were carried out at the previously established microgravimetric networks (four networks with a total of 12 points). Due to the destruction of the absolute gravimetric point in Makarska (AGT05), measurements on its established eccentrics were not carried out [61].
The First-Order Gravimetric Network of 2003 covered only the mainland territory of the Republic of Croatia, while the islands were not included. Therefore, between 2007 and 2009, the network was expanded to the larger islands in three phases. In the first phase, in 2007, the network was extended to the islands of the northern Adriatic with the establishment of nine new points [70]. In 2008, the network was further extended to the northern Adriatic islands with five additional points [71], and in 2009, nine new points were established, extending the network to the southern Adriatic islands [72]. This expansion brought the First-Order Gravimetric Network of the Republic of Croatia to a total of 59 points (Figure 4).
Each phase was adjusted separately using different tide correction models. For the extension of the network to the Croatian islands, tidal corrections were based on the Longman model, while Markovinović (2009) [47] used the ETERNA software package. The adjustments related to the extension of the First-Order Gravimetric Network to the Croatian islands were documented in technical reports; however, the corresponding adjusted gravity values were not formally published. A unified adjustment of the complete First-Order Gravimetric Network was performed for the first time in Repanić (2017) [66], where tidal corrections were consistently modeled using the ETERNA software package and adjusted gravity values were provided for all 59 points of the First-Order Gravimetric Network.
To provide a quantitative assessment of the impact of the unified adjustment, gravity values published by Markovinović (2009) [47] and Repanić (2017) [66] were compared for the 36 First-Order gravimetric points common to both solutions. Since tidal corrections in both studies were computed using the ETERNA software package, the comparison is not affected by differences in tidal correction modeling and therefore primarily reflects the effect of the unified adjustment of the complete network. Summary statistics of the observed gravity differences are presented in Table 1.
The comparison shows that the observed differences are generally small, with an average of 0.027 mGal and a median of 0.021 mGal, indicating overall good consistency between the two solutions. The maximum difference of 0.116 mGal was observed at point GT127, followed by point GT131. Both stations are at high elevations and correspond to the lowest gravity values among the analyzed First-Order gravimetric points. Repanić (2017) [66] also reported the largest standard deviations at these locations, indicating that gravity value determination at these stations may involve greater uncertainty compared to the rest of the network.
It should be noted that the observed differences cannot be attributed exclusively to the unified adjustment, as other methodological differences in data processing, correction computation, or adjustment strategy may have existed but cannot be fully reconstructed from the available documentation.

3.4. Second-Order Gravity Network

In accordance with the Regulation on the Procedure for Performing Basic Geodetic Works [60], the First-Order Gravimetric Network needed to be supplemented by the Second-Order Gravimetric Network to achieve sufficient point density and thus fully establish the Basic Gravimetric Network of the Republic of Croatia. The establishment of the Second-Order Gravimetric Network began in 2008 with the first phase in the Istria region [73] and was completed in 2015 with the tenth phase, which extended the gravimetric points to the larger islands. The work on establishing the Second-Order Network was carried out by the former Croatian Geodetic Institute (CGI) and the Croatian State Geodetic Administration (CSGA). During the network implementation, 15 points were established in the first phase in Istria; the second and third phases, covering eastern Croatia, added 36 points; the fourth phase in northern Croatia added 25 points; the fifth phase in central Croatia added 24 points; the sixth phase in Gorski Kotar added 13 points; the seventh phase in Lika added 21 points; the eighth phase in northern Dalmatia added 23 points; the ninth phase in southern Dalmatia added 23 points; and the tenth and final phase added 14 points on the larger islands, bringing the total to 194 points of the Second-Order Gravimetric Network of the Republic of Croatia (Figure 5).
Although Repanić (2017) [66] stated that the adjustment of the Second-Order Gravimetric Network of the Republic of Croatia was ongoing, the gravity values for these points were never officially adopted by CSGA.
To provide a clearer comparison of the current status, characteristics, and practical relevance of the Croatian gravimetric reference infrastructure, Table 2 presents a consolidated overview of the Zero-, First-, and Second-order Gravimetric Networks of the Republic of Croatia. It includes their observation periods, measurement methodologies, instrumentation, estimated uncertainties, inclusion in HGRS03, and the identified need for future reobservation.

3.5. Official Geoid Model of the Republic of Croatia (HRG2009)

The Croatian gravimetric reference system (HGRS03) also plays an essential role in national geoid determination and height system realization. The official Croatian gravimetric geoid model, HRG2009, was developed using a modern regional gravimetric geoid methodology based on the remove–restore approach [7,74,75]. Long-wavelength gravity field components were represented by the Earth Gravitational Model 2008 (EGM2008) [7,74,75], which marked a significant improvement over earlier global geopotential models, benefiting in part from advances in satellite gravity observations, particularly during the Gravity Recovery and Climate Experiment (GRACE) mission era [75,76,77]. These advances demonstrate the importance of satellite gravity information for contemporary regional gravity field modeling. Since the Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission was launched only in 2009, its gravity field products were not yet available when EGM2008 and HRG2009 were developed and therefore could not contribute to either model [78,79]. The medium-wavelength component originates from terrestrial point gravity field observations, and short-wavelength topographic effects were removed using a high-resolution digital terrain model, while the residual regional gravity signal was modeled by least-squares collocation [7,74,75].
The accuracy of HRG2009 was evaluated through internal and external validation by comparing geoid undulations derived from the model with undulation values obtained from GNSS/leveling observations. The internal accuracy assessment used 495 GNSS/levelling absolute orientation points, while the external validation relied on an independent set of 59 control points. Accuracy indicators for both internal and external control are provided in Table 3 [7,74,75].
These statistical indicators clearly confirm the substantial improvement of HRG2009 compared to the previous Croatian geoid model (HRG2000), whose performance indicators are presented in Table 4 [7,74,75].
In addition to its role in establishing the national gravimetric reference system, HRG2009 is essential for the practical implementation of the Croatian Height Reference System 1971 (HVRS71) [80,81]. Because the position of the geoid relative to the reference ellipsoid is defined by the geoid model, HRG2009, aligned with the HVRS71 height datum, provides the transformation surface needed to convert GNSS-derived ellipsoidal heights into Croatian normal-orthometric heights [7,8,75]. Since determining the geoid model depends directly on the availability of accurate and homogeneous terrestrial gravity data, the Croatian gravimetric reference system HGRS03 is a fundamental component of the national vertical geodetic infrastructure.

4. Discussion

Synthesizing the historical and technical review presented in this paper, the following discussion offers a structured assessment of the current status of the Croatian gravimetric reference system. It emphasizes evaluating the adequacy of the existing infrastructure, identifying its main limitations, and outlining future actions necessary for modernization and gradual integration into contemporary international gravity reference frameworks.

4.1. Expansion of the Croatian Zero-, First- and Second-Order Gravimetric Network

The Republic of Croatia currently has a point density of approximately one station per 10,000 km2 in the Zero-Order network, one station per 1000 km2 in the First-Order network, and one station per 290 km2 in the Second-Order network. The recommended densities are one station per 1000 km2 for the First-Order network and one station per 100 km2 for the Second-Order network [82], so Croatia maintains a satisfactory point density in its Basic Gravimetric Network.
Although the Croatian Zero-Order Gravimetric Network formally meets the recommended point density for the national territory, its principal limitation is the spatial distribution of stations rather than their total number. The current configuration includes stations in the eastern, western, and southern parts of the country, two stations in Zagreb, and the eccentric point in Makarska, which replaced the original destroyed absolute gravimetric station. This configuration leaves a substantial central portion of Croatian territory, particularly the regions of Lika, Gorski Kotar, and northern Dalmatia, without direct Zero-Order gravimetric coverage.
To establish a more homogeneous and geographically balanced national gravimetric reference framework, expansion of the Zero-Order network should be considered. Establishing at least one, and preferably two, additional Zero-Order stations in central Croatia and northern Dalmatia would significantly improve the network geometry and reduce the existing spatial gap. Since the two Zagreb stations form the northernmost part of the present network, establishing an additional station further north would also contribute to a more balanced territorial distribution.
An additional consideration concerns the current Makarska station, which serves as an eccentric replacement for the original absolute gravimetric point, with gravity values transferred through relative gravimetric observations rather than determined directly by absolute measurements. From the perspective of long-term modernization, its role within the Zero-Order network may require reassessment. In this context, the proposal by Repanić et al. (2014) [59] to establish new Zero-Order stations in locations such as Čakovec, Gospić, and Split represents a technically justified approach to improving the spatial distribution of the Croatian absolute gravimetric infrastructure. Although the final selection of locations would depend on technical, logistical and institutional factors, a more homogeneous configuration of Zero-Order stations appears necessary for the future modernization of the Croatian gravimetric reference system.
Following its extension to the Croatian islands, the First-Order Gravimetric Network achieved appropriate station density and sufficiently homogeneous spatial distribution across the entire territory of the Republic of Croatia. From this perspective, further expansion of the First-Order network is currently not considered necessary.
The Croatian Second-Order Gravimetric Network is also uniformly distributed across the national territory. However, based on the recommended station density for second-order gravimetric networks, further densification would be desirable to achieve full compliance with the prescribed spatial coverage criteria. Nevertheless, considering the substantial fieldwork and resources required for such an expansion, as well as the existence of more urgent modernization priorities within the Croatian gravimetric infrastructure, densification of the Second-Order network cannot currently be regarded as a priority. However, this issue remains a relevant consideration for the longer-term development of the national gravimetric reference system.

4.2. Re-Observation of the Croatian Zero-, First-, and Second-Order Gravimetric Network

The most recent absolute gravity observations at the Croatian Zero-Order stations were conducted nearly thirty years ago, far exceeding both current expectations for maintaining national gravity reference infrastructure and the ten-year reobservation interval prescribed by the Regulation on the Procedure for Performing Basic Geodetic Works [60].
During this period, absolute gravimetry has seen substantial technological advancement, and many European countries have already conducted repeated absolute gravity campaigns to maintain their national gravimetric reference systems. In contrast, Croatia has not yet undertaken a comparable reobservation campaign.
From a scientific perspective, repeated observations are equally justified because temporal gravity changes cannot be excluded. Mass redistribution, hydrological effects, local geological processes, crustal deformation and recent significant seismic events affecting Croatian territory may all have contributed to measurable gravity variations at individual stations. Consequently, the assumption that the original absolute gravity values still adequately represent the present-day national gravity datum should not remain unverified.
This concern is supported by studies from neighboring and regional European countries, where repeated absolute gravity observations over extended periods revealed measurable temporal gravity variations. In Slovenia, absolute gravity values at Zero-order stations established during the UNIGRACE project (1996–2000), as in Croatia, were reobserved in 2014, revealing differences of up to approximately 30 μGal [83]. Repeated absolute gravity observations in Hungary, Slovakia, and the Czech Republic between 1992 and 2010 identified gravity changes exceeding 20 μGal [41]. In Italy, repeated absolute gravity observations conducted between 2018 and 2023 at four stations revealed differences of up to 37 μGal at one location, while the remaining stations showed variations in the range of 15–20 μGal, primarily attributed to subsurface mass redistribution processes [84].
Although direct comparison with Croatia must be made cautiously due to differing geological, tectonic, and hydrological conditions, these studies clearly demonstrate that temporal gravity changes on the order of tens of μGal are entirely realistic over decadal timescales. Given Croatia’s geodynamically active setting, systematic reobservation of the Zero-Order Gravimetric Network should therefore be regarded not only as a regulatory obligation but also as a scientifically justified requirement for maintaining a reliable national gravimetric reference system.
The Croatian First-Order Gravimetric Network was established in two temporally separate phases. The initial mainland network was observed in 2003, while the extension to the Croatian islands was carried out through campaigns in 2007, 2008, and 2009. As a result, the present First-Order network does not represent a single temporally homogeneous realization. A future re-observation of the entire First-Order network within a single coordinated campaign would therefore be desirable to establish a temporally consistent realization of the network. However, since the most urgent modernization priority remains the Zero-Order network, reobservation of the First-Order network should be considered a medium- to long-term objective rather than an immediate priority.
The Croatian Second-Order Gravimetric Network, completed in 2015, represents the most recent component of the national gravimetric infrastructure. Consequently, its re-observation is not currently necessary. A more appropriate long-term strategy would be to reconsider reobservation in the context of future expansion or broader modernization of the Croatian gravimetric reference framework, where a coordinated reobservation of the complete network would ensure temporal consistency and overall homogeneity.

4.3. Current Limitations of the HGRS03

Despite remaining the official gravimetric reference framework of the Republic of Croatia, HGRS03 has several important technical and institutional limitations that reduce its compatibility with contemporary gravimetric standards and constrain its long-term sustainability.
One of the most significant limitations is the absence of a national absolute gravimeter. Without domestic absolute gravimetric instrumentation, Croatia relies on external institutions for absolute gravity observations, which limits the practical feasibility of regular reobservation campaigns and systematic temporal monitoring.
Another important limitation concerns the treatment of Earth tide corrections in Croatian gravimetric practice. Contemporary gravimetric standards recommend that Earth tide corrections should be based on locally determined tidal parameters derived from long-period gravimetric observations and harmonic analysis. However, such observations have never been conducted in Croatia, and no locally optimized tidal model currently exists for the Croatian gravimetric reference framework.
As a result, Earth tide corrections in previous Croatian gravimetric adjustments were computed using interpolated tidal parameters, based on the methodology implemented in the ETERNA software package developed by Timmen and Wenzel (1995) [85]. Although this approach is operationally acceptable, its long-term suitability for the realization of a modern national gravimetric reference system has not been comprehensively validated. Future modernization of HGRS03 should therefore include long-period gravimetric observations at one of the Zero-Order stations to determine locally representative tidal parameters.
Another limitation concerns the incomplete realization of the Croatian gravimetric reference infrastructure. Although the Second-Order Gravimetric Network has been physically established, its observations have never been officially adjusted, and no formal gravity values have been adopted. Consequently, in accordance with the Regulation on the Procedure of Performing Basic Geodetic Works [60], the Basic Gravimetric Network of the Republic of Croatia cannot be considered fully completed. This limits the availability of a homogeneous and officially validated densified terrestrial gravity dataset to support future geoid refinement, maintenance of the national vertical reference infrastructure, modernization of GNSS-based height determination and validation of regional gravimetric observations. Therefore, the official adjustment and formal adoption of the Second-Order Gravimetric Network should be considered a necessary step toward completing the Croatian national gravimetric reference framework.

4.4. Need for a New Croatian Geoid Model

HRG2009 represented a significant improvement over the earlier Croatian geoid model HRG2000, incorporating denser terrestrial gravity data and the then state-of-the-art global geopotential model EGM2008. However, substantial advances in gravity field modeling have occurred since its development. At the global level, the GOCE mission significantly improved the determination of the static gravity field, providing gravity field products that were unavailable during the development of EGM2008 and therefore could not contribute to HRG2009. At the regional level, these advances are reflected in the development of the European gravimetric (quasi)geoid model EGG2015 [86].
At the same time, the terrestrial gravimetric infrastructure underlying Croatian geoid modeling remains affected by several limitations, including the incomplete realization of the Second-Order Gravimetric Network, the lack of systematic long-term maintenance of the national gravimetric infrastructure and continued reliance on a historical gravity system that no longer satisfies the requirements of modern geodetic and geophysical applications. Since HRG2009 also plays a fundamental role in the practical realization and long-term maintenance of the Croatian height reference system HVRS71, as well as in GNSS-based transformation from ellipsoidal to normal-orthometric heights, modernization of the Croatian geoid model using updated gravity datasets, modern reference conventions, and new terrestrial observations appears scientifically justified and operationally necessary.

4.5. Integration into ITGRS

From the perspective of future integration into the International Terrestrial Gravity Reference Frame (ITGRF), Croatia holds an important initial advantage due to its Zero-Order Gravimetric Network, whose originally reported standard deviations ranged from 1.0 to 3.7 µGal. However, these values reflect only the internal precision of the original observations, not their current suitability as a modern international gravity reference realization. Since the absolute observations defining the Croatian Zero-Order network were conducted nearly 30 years ago, their long-term suitability must be critically reassessed in light of temporal gravity variations, station stability, and significant technological advances in absolute gravimetry. This is especially important given the increasing accuracy requirements of contemporary gravimetric applications, particularly high-precision geoid modeling and vertical reference system maintenance.
Additional limitations stem from the historical reference framework itself. As discussed earlier, HGRS03 remains tied to the IGSN71 system, whose inherited limitations include heterogeneous accuracy, dependence on the distribution of historical observations, and likely reduced robustness in regions with sparse original coverage, such as southeastern Europe. Transitioning to the ITGRF would therefore represent not just a formal reference system replacement, but a substantial modernization of the Croatian gravimetric reference framework, with expected benefits for national gravity field consistency, future geoid refinement, and GNSS-based height applications.
A significant practical limitation is that Croatia currently does not have a national absolute gravimeter, making systematic repeated absolute observations and continuous monitoring of temporal gravity changes unlikely in the near future. Nevertheless, repeating absolute observations at the existing Zero-Order stations after nearly three decades would already be a major step toward modernization. Encouragingly, the electronic procurement plan of the State Geodetic Administration for 2026 includes a project for re-observation of the Croatian Zero-Order Gravimetric Network [87]. If implemented, this would be a major advancement for the Croatian gravimetric reference system and could provide an important first step toward future integration into the ITGRF.

5. Conclusions

The gravimetric networks of zero, first, and second order in the Republic of Croatia were established and measured within the IGSN71, which remains the official gravimetric reference system for Croatia and most countries worldwide. The most recent absolute gravity measurements at the Zero-Order stations were conducted nearly thirty years ago, so their reobservation should be considered the highest modernization priority. This need has also been recognized by the Croatian State Geodetic Administration (CSGA), which included the re-observation of the Zero-Order Gravimetric Network in its 2026 procurement plan. Subsequent steps should include a new adjustment of the national gravimetric network, as well as the first official adjustment and adoption of the Second-Order Gravimetric Network. In the longer term, long-period gravimetric observations should be carried out to determine locally representative Earth tide parameters for the territory of the Republic of Croatia. Collectively, these measures would provide the necessary foundation for developing a new Croatian geoid model based on contemporary gravimetric standards, which would further contribute to the long-term maintenance and practical realization of the Croatian height reference system (HVRS71), particularly through improved determination of normal-orthometric heights.
Regarding the integration of the Republic of Croatia into the ITGRS, current possibilities are primarily limited by the lack of a national absolute gravimeter. As a result, continuous or frequent repeated absolute gravity measurements, which are essential for the long-term stability and reliability of reference stations within the ITGRF, cannot be performed. Although absolute gravity observations can be conducted through periodic campaigns involving foreign institutions and equipment, this approach does not allow for systematic monitoring of temporal gravity variations and is financially demanding for long-term implementation. Therefore, the Republic of Croatia is currently unable to contribute directly to the establishment and realization of the ITGRS. Nevertheless, developing national capacities in absolute gravimetry should be considered a long-term objective to enable gradual integration into international gravity reference systems in the future.

Author Contributions

Conceptualization, M.P. and T.B.; methodology, M.P. and T.B.; validation, M.P.; formal analysis, T.B.; investigation, T.B.; resources, M.P.; data curation, T.B.; writing—original draft preparation, T.B.; writing—review and editing, M.P.; visualization, T.B.; supervision, M.P. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

No new datasets were generated or analyzed in this study. The data discussed in this review are derived from previously published studies and official documents, all of which are cited in the reference list. In accordance with the Regulation on the Confidentiality of Defense Data of the Republic of Croatia, gravimetric data must not be disclosed without authorization; therefore, gravity values cannot be provided.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
AGTApsolutna gravimetrijska točka
BKGBundesamt für Kartographie und Geodäsie
CGICroatian Geodetic Institute
CSGACroatian State Geodetic Administration
EGM2008Earth Gravitational Model 2008
EGG2015European Gravimetric (quasi) Geoid 2015
GOCEGravity field and steady-state Ocean Circulation Explorer
GRACEGravity Recovery and Climate Experiment
GTGravimetrijska točka
HGRS03Hrvatski gravimetrijski referentni sustav 2003
HRG2000Hrvatski geoid 2000
HRG2009Hrvatski geoid 2009
IAGInternational Association of Geodesy
IfAGInstitut für Angewandte Geodäsie
ITGRFInternational Terrestrial Gravimetric Reference Frame
ITGRSInternational Terrestrial Gravimetric Reference System
IGSN71International Gravity Standardization Network 1971
IUGGInternational Union of Geodesy and Geophysics
UNIGRACEUNIfication of GRAvity systems in Central and Eastern Europe

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Figure 1. Eight absolute gravity stations and the main gravimeter connections in IGSN71 (according to Morelli (1999) [10] and Torge (1989) [4]).
Figure 1. Eight absolute gravity stations and the main gravimeter connections in IGSN71 (according to Morelli (1999) [10] and Torge (1989) [4]).
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Figure 2. Basic Gravimetric Network of Yugoslavia (according to Bašić i dr. (2006) [2] i Odalović i dr. (2012) [3]),the gray shaded area represents the territory of present-day Croatia.
Figure 2. Basic Gravimetric Network of Yugoslavia (according to Bašić i dr. (2006) [2] i Odalović i dr. (2012) [3]),the gray shaded area represents the territory of present-day Croatia.
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Figure 3. Zero-Order Gravimetric Network of the Republic of Croatia.
Figure 3. Zero-Order Gravimetric Network of the Republic of Croatia.
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Figure 4. First-Order Gravimetric Network of the Republic of Croatia after expansion (the inherited points from Yugoslavia are shown in blue, newly established points are shown in orange, while the points added during the expansion to the islands are shown in black) with horizontal and vertical calibration bases for relative gravimeter calibration.
Figure 4. First-Order Gravimetric Network of the Republic of Croatia after expansion (the inherited points from Yugoslavia are shown in blue, newly established points are shown in orange, while the points added during the expansion to the islands are shown in black) with horizontal and vertical calibration bases for relative gravimeter calibration.
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Figure 5. Basic gravimetric network of the Republic of Croatia.
Figure 5. Basic gravimetric network of the Republic of Croatia.
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Table 1. Summary statistics of gravity value differences between Markovinović (2009) [47] and Repanić (2017) [66] for 36 common First-Order gravimetric points.
Table 1. Summary statistics of gravity value differences between Markovinović (2009) [47] and Repanić (2017) [66] for 36 common First-Order gravimetric points.
Statistics/Gravity DifferenceMinMaxAverageMedian
Δg (mGal)0.0000.1160.0270.021
Table 2. Overview of the Zero-, First- and Second-order Gravimetric Networks of the Republic of Croatia [20,47,59,66,73].
Table 2. Overview of the Zero-, First- and Second-order Gravimetric Networks of the Republic of Croatia [20,47,59,66,73].
Network/
Metadata		Zero-OrderFirst-OrderSecond-Order
Land PartIslands
Observation year1996, 1999, 200020032007–20092008–2015
Measurement typeabsoluterelativerelativerelative
InstrumentFG5#101, FG5#206CG-3, CG-5CG-3, CG-5CG-3, CG-5
Number of points63623194
Estimated uncertainty ( 10 − 8 ms−2)1.0–3.7~5.0~10.0Not available
Official gravity values✓✓✓-
Included in HGRS03✓✓--
Table 3. Accuracy indicators for HRG2009 in meters [7,74,75].
Table 3. Accuracy indicators for HRG2009 in meters [7,74,75].
Accuracy TypeMinMaxAverageSt. Dev.
Internal
(495 points)		−0.0710.059−0.0040.027
External
(59 points)		−0.0780.058−0.0120.035
Table 4. Accuracy indicators for HRG2000 in meters [7,74,75].
Table 4. Accuracy indicators for HRG2000 in meters [7,74,75].
Accuracy TypeMinMaxAverageSt. Dev.
Internal
(495 points)		−0.4370.298−0.0120.093
External
(59 points)		−0.2750.242−0.0240.114
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Banković, T.; Pavasović, M. Development, Status and Future Perspectives of Croatian Gravimetric Reference System. Geomatics 2026, 6, 62. https://doi.org/10.3390/geomatics6030062

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Banković T, Pavasović M. Development, Status and Future Perspectives of Croatian Gravimetric Reference System. Geomatics. 2026; 6(3):62. https://doi.org/10.3390/geomatics6030062

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Banković, T., & Pavasović, M. (2026). Development, Status and Future Perspectives of Croatian Gravimetric Reference System. Geomatics, 6(3), 62. https://doi.org/10.3390/geomatics6030062

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