The Local Area Distortion Factor (LADF): Resolving Property Area and Spatial Deviations from Geodetic Transformations in the Greek Cadastre

Abstract

The Hellenic Cadastre, which is expected to be fully operational by the end of 2025, represents a major modernization step in Greece’s technical and legal documentation of property rights as the successor to the country’s land registry system. It will also constitute a land administration system, since it will encompass not only property rights but also restrictions and regulations in the context of RRR. A significant technical but also legal challenge inherent to this system pertains to the resolution of deviations between surfaces calculated prior to 1990 based on older geodetic reference systems and recalculated today using the current Greek Geodetic Reference System, GGRS87. Deviations that arise from geodetic transformations between older and modern projected reference systems are compounded by limitations inherent in historical surveying techniques and in the geodetic infrastructure that was available at the time. To address this issue, we introduce the Local Area Distortion Factor (LADF), a novel metric factor designed to adjust and harmonize property areas across different geodetic systems. This real-world case study offers a practical illustration of the application of LADF, demonstrating its capacity to enhance the precision of cadastral records while preserving interpretability for both experts and non-experts. LADF can also be used to improve land adjustment processes during the implementation of urban plans, property valuation, taxation, and notary acts that are in different reference systems.

1. Introduction

The calculation of the area of a land parcel or a plot is a critical component in numerous technical and economic activities, mainly real estate exploitation, urban and spatial planning, and the overall development strategies at the local, regional, and state-wide levels. Apart from its purely mathematical nature, the determination of a property area is significantly important in legal systems worldwide, as it directly influences property determination, land valuation, and, consequently, the exercise of property rights, urban and spatial planning, and the overall development strategies.

Deviations in property area calculations are primarily rooted in technical challenges encountered within the disciplines of land surveying and geodesy. While similar patterns can be identified across these challenges, they are often deeply tied to specific national, technical, and legal contexts. Thus, scientific knowledge and best practice exchange are limited and hindered by a number of factors at a national level, such as the technical complexity of the issue, especially in the aspect of geodetic coordinate systems and the diversification of survey techniques over time, variations in property legislation and legislation on regulations and restrictions imposed on properties, and differences in the legal framework of a cadastral system, urban and spatial planning, and their relevant implementation.

The most prevalent factors contributing to deviations in the calculation of property areas are as follows:

• The misalignment between historical and modern geodetic coordinate systems, exacerbated by the degradation of older geodetic infrastructure.
• Distortions and wear observed in scanned historical survey/cadastral/urban plans, maps, or diagrams.
• Deviations between areas measured with modern techniques and current geodetic datums and the equivalent areas referred to in older titles as descriptive or qualitative entities that were not based on precise and analytical surveying and geodetic methods.
• Outdated cadastral information that does not conform to the current and updated technical standards of surveying, geodesy, and cadastral surveying.

It is, therefore, essential to develop innovative solutions, adapted to specific contexts, to enable the accurate and consistent calculation of a property area in a cadastral system in order to resolve spatial inconsistencies between cadastral records and various administrative acts or titles that are recorded in the land registry and are legally binding according to the Property Law but, at the same time, lack an accurate and firm spatial reference [1,2,3,4,5,6].

Several studies have modeled the error propagation resulting from boundary measurements using “traditional” and GNSS surveying techniques to calculate property areas [7,8,9]. Other researchers have advocated for a more robust integration of uncertainty metrics into property area estimation [10,11,12,13,14] or proposed new indices [15]. Research also focuses on the georeferencing of older cadastral maps to contemporary reference systems [16,17,18,19,20,21] that combine field measurements to recover lost geodetic control points to facilitate the localized transformations of historical maps. Finally, there are studies with a more specialized goal, such as estimating the true area of a property, taking into account projective distortions, map scale, terrain slope, and elevation [22], and investigating area estimation inaccuracies in real estate evaluations [23]. The main scope of current research is to bridge the gap between the legal determination of an area of a property and the calculated ones by past and current measurement methods and techniques and to integrate old cadastral maps or products into current cadastral systems, ensuring secure transactions.

In Turkey, the cadastral data are old, and various methods are being implemented according to the coordinate system used for the cadastral map production and its relevant parameters [24], while, in Serbia, the production of a single cadastral map and the integration of coordinate systems previously used pose great challenges and are costly, especially in terms of official cadastral boundary determination [25]. In both cases, the transformation processes are time-consuming and have to have on-site surveys and measurements that are costly, also taking into consideration the specific conditions and parameters of each previously used system. In Croatia, errors in cadastral boundaries are mainly due to maintenance processes, and the need for new on-field surveys is urgent, but a large-scale project of this kind is also time-consuming and costly [20]. In Italy, researchers propose local adjustments and georeference techniques by defining local datum parameters [26], while GNSS techniques are used in order to assess the accuracy of cadastral maps both at the 2D and 3D levels [27]. In Austria and Poland, the accuracy of cadastral maps in relation to the historic ones is based upon the available surveying and map-production methods, and, nowadays, accuracy improvement is based on GNSS technologies that always have limitations [28]. In France, efforts are guided toward the use of ground control points and locally adjusted geostatistical methods so as to transform historic maps to current reference systems [29]. In the Netherlands, there is an ongoing process of readjusting the cadastral maps in terms of geodetic aspects with the use of ground measurements [30].

Existing research is focused on solving the problem of the accuracy of cadastral maps and data, in general, of past periods at the state or region levels, with large-scale on-field surveying rounds and measurements usually using GNSS techniques. In the majority of the countries, the cadastral system functions alongside land registries, which facilitates the corrections of the cadastral map and the transformation processes. It is also obvious that every country addresses the issue of coordinate transformations by implementing localized methods adjusted to the parameters of the reference systems that were used in the past and those that are in use today in each country. Map reconstruction methods are also localized, as the local parameters define the transformation process.

In Greece, the cadastral system of the Hellenic Cadastre (HC) totally replaces the system of land registries, while in property transactions, e.g., property sales, detailed topographic diagrams, drafted by freelancer surveyors, must be appended to titles transcribed to cadastral offices. The current cadastral map of the operational Hellenic Cadastre uses the Greek Geodetic Reference System 1987 (GGRS87). On-field surveys and measurements present significant deviations from the current Hellenic Cadastre’s cadastral map. The deviations are due to the methodologies used to incorporation older cadastral maps, topographic diagrams, and other relevant products into the Hellenic Cadastre Spatial Database, during the Cadastral Survey stage for the creation of the Hellenic Cadastre. Those deviations often cause delays or even halt transactions on properties, as large-scale corrections of the cadastral map are needed, which are time- and money-consuming, and, in many cases, they have to go through the Cadastral Judge.

This paper introduces the Local Area Distortion Factor (LADF) as a solution to the longstanding challenges of the deviations in property area calculations between GGRS87 and older reference systems. The LADF introduces a robust and standardized adjustment mechanism that aligns old with contemporary geodetic datums, such as GGRS87, incorporating transformation parameters and distortion factors into a simple calculation.

The LADF derived from the 2D similarity transformation should be implemented carefully and only for limited areas. This fact is dictated by the significant inconsistencies of the older geodetic reference systems of Greece and the lack of a sufficient number of common benchmarks between the new and the old geodetic reference systems.

This approach not only eliminates deviations in the calculation of property areas between HC spatial records and older records but also facilitates the effective communication between stakeholders and experts, including urban planners, surveyors, notaries, lawyers, and citizens involved in real estate transactions and exploitation, as it is easily understood. Its use can facilitate and speed up Greece’s cadastral map corrections, as the complete replacement of land registries by the Hellenic Cadastre poses many restrictions to the cadastral map’s corrections due to the legal rules of the land registries that have to be followed.

2. Property Area Determination in Greece: A Brief Review

In Greece, the area of a property, land parcel, or plot has a substantial role in urban and regional planning and overall development [31]. Property and ownership rights must be proven by titles transcribed to land registries and, in many cases, are dated back to the establishment of the Greek state in 1830. It is essential for titles and deeds to be transcribed to land registries or recorded in the cadastral offices of the HC [2,31,32]. Additionally, the continuous expansion of Greece’s territory, from 1830 to 1947, and the various official land distributions and redistributions made by the state in order to avoid social unrest led to the production of still-valid cadastral mapping products that are referenced in older coordinate systems. Furthermore, the legislative provision of appending topographic diagrams to property transactions led to the production of topographic products of small accuracy, as they were not tied to firm technical specifications until 2011.

When the independence of Greece was finalized in 1830, the then Greek state, known as the Kingdom of Greece, had to deal with the determination of the public lands, inherited from the Ottoman Empire, on the one hand, and the private lands owned by Ottomans who wanted to sell them to leave the state or by Greek citizens, on the other hand. The area of a property was calculated in numbers of “cattle-pairs”, with one cattle-pair corresponding to the area that can be cultivated by a pair of cattle in one year, with a general spatial reference to local landmarks and place names for both public and private properties. This definition of a property area has led to long-lasting legal disputes between the state and private owners, up to nowadays.

In 1834, following the proclamation of Athens as the capital of Greece, replacing Nafplio (located in the northeast part of Peloponnese), there was an imperative need for urban regeneration and urban development. In order to formulate and implement urban development plans, mainly in Athens and Syros Island, within the existing urban and peri-urban landscape, experts in urban planning and surveying, initially from Bavaria and, subsequently, from Greece, were recruited. Legislation on the implementation of Athens’ urban plan, enacted by two royal decrees in 1836, foresaw the regularization and standardization of plots, private or public, so that the necessary land could be allocated to public roads, public spaces, and common spaces so as to make them functional. This marked the first official procedure for the regularization of landownership through the allocation of private to public land, named “boundary reform”, overseen by city-employed engineers. In 1852 and 1856, the construction of urban roads and urban infrastructure (pavements, sewage systems, etc.) was enacted by two laws on road construction and pavement construction, respectively, describing all of the legal and administrative processes, but not in a detailed spatial and geometric aspect, for parts of private land that need to be allocated for the creation of public and municipal roads and public spaces, in general, forming new property rights for public and private properties that are valid until nowadays.

The establishment of the Hellenic Military Geographical Service (GYS) in 1889, initially known as the “Geodetic Mission” under the responsibility of Austrian army officers, as the Hellenic Military Cartographic Service in 1895, and as HMGS in 1926, played a crucial role in establishing precision procedures in surveying, geodetic, and other associated works. Under the HMGS, the development of the official geodetic infrastructure of the country was implemented, while the Service had a key role in the optimization of the methods of measuring both public and private property. The optimization measurement methods were of great importance, especially for large private lands that gradually passed from Ottoman to Greek ownership from 1830 onward as Greece kept succeeding the Ottoman Empire.

In the late 1880s, the German Archaeological Institute in Attica initiated the creation of detailed maps, which were completed in 1903 under the supervision of the Bavarian army officer Johann August Kaupert. The maps were of high accuracy, with topographic, cartographic, and archaeological value, and also constituted the first systematic and accurate mapping of the urban, suburban, and peri-urban/rural environment of the Attica Prefecture. The Kaupert maps were produced using a geodetic network that was established by observations and measurements of spatial distances, direction angles, and astronomical azimuths of its geodetic control points, with the fundamental control point being located at the National Observatory of Athens, near the Acropolis Hill at Thissio, and the maps are still used by the state as proof of property rights, especially in suburban areas.

At the same period, with the production of the Kaupert maps, the Technical Department of the Directorate of Public Lands, Ministry of Finance, was established. The creation of the department responded to the need to conserve, utilize, or distribute public property, particularly national lands. Staffed mainly by engineers specializing in topography, the department was responsible for surveying, documenting, and allocating national lands to beneficiaries, selected by the central administration, with legal and valid titles registered in the relevant land registry. In parallel, the department recorded the remaining public land.

In 1910, legislation was enacted regarding the creation of a “Cadastral Map” that would cover all of Greece’s territory at the time and would be undertaken by the Hellenic Military Geographical Service through the densification of its then triangular network. The 1910 legislation of cadastral maps was supplemented by legislation on “Cadastral Map for urban properties” in 1923, but the foreseen cadastral maps were conducted and finalized only for two urban areas, the Municipality of Kallithea and part of the Municipality of Paleo Falliro, located at the seaside front of the Athens Greater Area.

In 1917, when the Ministry of Agriculture, which until then had been part of the Ministry of Finance, was established, the Survey Agency of the Ministry of Agriculture, SAMA, was established. Initially, SAMA was part of the Technical Department of the Directorate of Public Lands of the Ministry of Finance, and, in 1930, it became part of the Directorate of Technical Works of the Ministry of Agriculture. SAMA was the responsible agency for the successful completion of large-scale distributions of urban and agricultural land to over 1,500,000 Greek refugees that fled to Greece after the Asia Minor Disaster in 1922 and of landless Greek citizens, especially in southern mainland Greece, mainly between 1920 and 1940. From 1950 onward, in addition to distributions, SAMA has been carrying out large-scale redistributions, which aim at the optimization of agricultural production.

The agency’s distribution and redistribution activities are characterized by their large-scale and comprehensive nature, involving detailed and accurate geodetic, topographic, and cadastral procedures, resulting in official topographic/cadastral maps. The establishment of official geodetic networks facilitated the conduct of the topographic/cadastral maps that were correlated to definitive governmental titles for each beneficiary, transcribed to the relevant land registry, recognized as official administrative documents of legal effect, and, in their entirety, valid up to today, regardless of their issuance date.

The 1922 refugees fled, which also led to the revision of the urban planning legislation. The necessity to reorganize the existing urban space and to provide new urban areas via urban plan expansion resulted in the enactment of the 1923 legislative decree on “urban plans”, which included specific procedures on plan production and implementation, including their spatial and geometrical aspects. Under the 1923 decree on “urban plans”, numerous powerful administrative acts were issued, legally binding at the spatial level, determining not only the geometrical characteristics of roads and relevant public and common spaces but also the area of private plots. These acts had to be applied in situ by private surveying engineers under the supervision of public authorities. This posed significant challenges, particularly in areas of high relief, where the calculation of geometric elements, especially the area of the property, proved to be a complex undertaking. The same prevailed in other official administrative acts, also legally binding on a spatial level, such as expropriations or the definition of the boundaries of seashore and beach borderlines, affecting the legal and spatial definition of both private and public properties, with these acts often not being referenced to the country’s official geodetic reference system.

By the early 1950s, more precise methods were introduced in both land surveying (e.g., classical tacheometry) and area calculations. Areas were calculated using the Gauss method, which relied explicitly on boundary coordinate geometry, or were measured with planimeters [33]. However, ground surveys were not referenced in the official state coordinate system. Thus, in many cases, the topographic diagrams appended to titles transcribed to land registries were missing spatial references.

The advances of computers and computer-aided design (CAD) programs in the early 1980s led to the predominance of digital area calculations based on vector-based geometries. This coincided with two major reforms in the Greek legal framework: the prerequisite of detailed topographic diagrams appended to titles related to transactions on properties transcribed to the relevant land registry, enacted in 1977, and the obligation of the administration at any level to ensure the integration of legally binding administrative acts to the country’s concurrent official geodetic reference system after 1975.

However, a considerable proportion of topographic diagrams appended to titles on property transactions transcribed to land registries have varying accuracies, as it was not obligatory to be integrated to the officially adopted in 1990 Greece’s Reference System, GGRS87; thus, they have limited metric and spatial quality. In 2011, when Law 4014 was enacted, it foresaw that any topographic diagram appended to titles, transcribed to land registries, or registered to cadastral offices was ought to be referenced to Greece’s official reference system, GGRS 1987. It was the first time that the Greek legislation foresaw the official use of the country’s reference system by freelancer surveyors and the private sector [1].

3. The Hellenic Cadastre

The Hellenic Cadastre (HC) is a parcel-based system for property registration and publicity, legally and officially adopted in 1995. In 1995, legislation on the transition from the land registry system to the HC operational system through the completion of the cadastral survey for its creation was launched. This transition is considered a huge reform in property spatial and descriptive documentation, in property law implementation, and in the overall land administration procedures in Greece, as the HC completely replaces the land registry system. In the cadastral survey stage for the creation of the HC, the Cadastre SA, a publicly owned company, was created in 1995 under Law 2308/1995, and in 1998, the company was also responsible for the operational HC. In 2013, Cadastre SA was renamed Hellenic Cadastre and Mapping SA (HCM SA), absorbing the Hellenic Cadastral and Mapping Organization, and in 2018, HCM SA was replaced by the Hellenic Cadastre as a legal entity of public law.

The HC is planned to be fully operational throughout the country by the end of 2025. The cadastral survey for the creation of the HC is still ongoing and will be completed within the operational HC, according to the latest legislation adopted in 2024 [1].

The operational HC fulfills a dual role. Firstly, it entirely replaces the existing system of property registration and publicity, a person-based system of land registries (launched in 1856 but existing as public offices since the late 1830s), in which the spatial relation to the legal documentation of properties (plots or land parcels) is incomplete and vague [2]. Secondly, it will serve as the primary tool for the pursuit of the rational organization and sustainable development of Greece, as outlined in Law 2664/1998 on the operational HC. According to Law 2664/1998, the operational HC is responsible for maintaining legal and technical information with the objective of accurately determining the boundaries of any real property, mainly plots or land parcels, located within Greece’s territory. HC ensures the publicity of all titles and relevant data and information that registers and records, safeguarding public faith of any bona fide, physical, or legal person who relies on its records for transactions on properties.

Based on six essential principles—parcel-based organization, verification of title (and other necessary spatial data/information) legality, temporal priority of submissions, publicity of cadastral records, safeguarding public faith, and open and interoperable cadastre—the HC constitutes a powerful land management system for both Greece’s public administration and private sector. The principle of open and interoperable cadastre guarantees that the HC record rights, regulations, and restrictions (RRRs) on properties are attributes of modern and integrated cadastral systems.

The HC is organized into a spatial database, which is correlated to a descriptive database, forming the Hellenic Cadastre Database. As HC is a parcel-centered system, its spatial DB records property spatial and geometrical data, referenced in the current Greek Geodetic Reference System, the GGRS87, while the descriptive BD records all of the legal and relevant data of the property, e.g., owner or beneficiary data, title data, etc. Each property, plot, or land parcel receives a unique code, the Code Number of National Cadastre, KAEK in Greek, in both the spatial and descriptive DB.

All official administrative acts must be integrated into the HC in GGRC87, and the same stands for every property deriving from any legal document, e.g., titles transcribed to land registries. Initially, the cadastral survey phase for the creation of HC, and later the operational HC, revealed numerous and serious spatial and geometrical inconsistencies amongst the HC cadastral records, official administrative acts, and topographic diagrams appended to titles transcribed to land registries. As the integration to the HC of existing administrative acts or topographic diagrams appended to titles was based on empirical methods, in many cases, these inconsistencies can actually lead to the halt of transactions on properties or their exploitation.

The registration of any property and any property right in the HC, whether in the cadastral survey stage or the functional cadastre stage, depends, to an extremely important extent, on historical topographic materials that are the outcome of past and old topographic and geodetic techniques. Those techniques were used to generate official charts, maps, or diagrams that documented and were appended to official administrative acts, such as governmental land distribution/redistribution for refugees and indigenous landless farmers, especially in the first half of the 20th century; the adaptation and implementation of urban plans, expropriations, and the designation and protection of forest areas were also documented.

It is important to note that official administrative acts are legally binding processes, proving and securing property rights for both the state and natural/legal persons, and are applied on the ground with the use of analytical topographical methods. Furthermore, these acts remain legally and spatially valid, regardless of the year in which they were issued. Historical surveying techniques were also used for the production of topographic diagrams appended to titles or deeds drawn up by notaries and transcribed to the relevant land registry related to the sale of plots or land parcels, plots or land parcels subdivision/consolidation diagrams, or land readjustment plans, which also produce valid legal rights upon their transcription, regardless of their spatial integrity.

Compared to contemporary surveying and topographic products, the spatial or geometric quality and accuracy of the equivalent historical products is not optimal. Historic surveying techniques and technologies used for their production are directly linked to national geodetic infrastructures and reference systems of past eras. The majority of property ownership titles were issued prior to 1990, thus prior to the adoption and implementation of the current geodetic reference system, GGRS87. This resulted in the definition of the property area, as it appears on the ownership title, on older geodetic datums, or even on no datums at all, as, in many cases, topographic diagrams appended on ownership titles were not based on the official geodetic control points and official reference systems.

As a result, there are deviations between the area of a property, as defined by its legal documentation, e.g., official administrative acts, titles, or deeds transcribed in land registries and calculated on the accompanying survey diagram, map, or chart, and the corresponding area that is measured today using modern surveying technology and the updated reference systems of GGRS87.

In the case of official administrative acts, deviations in property area calculations that arose between the GGRS87 and older official reference systems, in many cases, render the acts invalid, either due to the non-integration of the act to the HC or, in the case that the act is integrated to the HC, due to official administrative bodies, such as urban or spatial planning authorities and bodies, rejecting the concurrent record provided by the HC.

4. Greek Geodetic Reference Systems and Property Area Calculation in Greece

It was not until 1990 that a new geodetic reference system, GGRS87, superseded the older GR-Datum system, which had previously been utilized for mapping and surveying in Greece [34]. GR-Datum comprises two distinct versions that can be regarded as two different and separate geodetic datums, realized in different periods.

(a) The Old Version of GR-Datum (OVGRD) was realized prior to 1940, utilizing the ellipsoid of Bessel 1841 and the azimuthal equidistant Hatt projection (e.g., [35]). The OVGRD aimed to fill the absence of a nationwide and official projected reference system, mainly addressing the pressing demand for housing and agricultural land distribution that arose from the population exchange between Greece and Turkey and the influx of refugees following the 1922 Minor Asia Disaster. Under the OVGRD, Greece’s territory was divided into 132 1:100,000 map sheets, projected using Hatt’s method. Each map sheet center constituted its own local datum, thereby ensuring simple calculations and manageable map distortions (approximately 5 cm at the map border edges).

(b) The New Version of the GR-Datum (NVGRD) was developed in the mid-1970s. New measurements of the existing geodetic control points were carried out, followed by the adjustment of the triangulation network. NVGRD also used the Bessel 1841 ellipsoid, and two projections were used as follows:

-

The Hatt projection, which covered the whole country and was used in official administrative acts, like expropriation or seashore boarder line determination.

-

The tri-zonal TM3 projection (Traverse Mercator projection), exclusively used in the most significant urban planning reform, initiated in 1983 under Law 1337/1983, for the expansion and modification of urban plans. It included a legally binding and complete cadastral survey that defined each owner’s land contribution for the creation of public and common spaces as a prerequisite for the implementation of the plan [36].

In 1986, the Hellenic Cadastral and Mapping Organization (HCMO) was established as a legal person under the public law under Law 1647/1986. HCMO was responsible for the creation and update of existing topographic diagrams and maps for the whole territory of Greece, large-scale photogrammetric campaigns for the production of high-quality aerial photos, and the creation and operation of the HC.

Under the HCMO, the current Greek (Hellenic) Geodetic Reference System of 1987, GGRS 1987, was launched in 1990 under the supervision of the NTUA professor George Veis [37]. GGRS87 is a projected reference system that uses the GRS80 ellipsoid and a conformal Transverse Mercator (TM87) projection [37,38], with a central meridian of 24 degrees. A scale factor of 0.9996 is applied at the central meridian in order to distribute map distortions more evenly in the Greek geographical space.

Consequently, a significant proportion of older surveying plans, cadastral maps, and urban plans refer to different versions of GR-Datum while using different projections as well. In parallel, the use of the Hatt projection with two datums has been identified as a significant source of confusion for both experts and non-experts alike, as older plans do not clarify which datum is used in conjunction with Hatt [39]. The utilization of multiple Hatt-projected local maps in the case of SAMA land distributions or redistributions is yet an additional technical, spatial, and geodetic challenge, as each map possesses its own distinct “mini-datum”; thus, multiple transformations between map sheets are required for their integration in GGRS87.

Although an officially recognized coordinate transformation procedure exists from NVGRD to GGRS87 and vice versa, no such procedure exists for the transformation between OVGRD and GGRS87 (or even between OVGRD and NVGRD). In many cases, surveyors (either of the public or private sector) use ad hoc empirical techniques of dubious spatial and geometrical quality.

The above issues, combined with more practical concerns, such as the loss and degradation of geodetic control points of older reference systems and the lack of quality control in the majority of old survey plans, diagrams, and maps, have a detrimental effect on property area calculations in Greece.

Therefore, concrete transformation procedures covering the full range of reference systems are required.

4.1. Transformation Procedures

(a) From NVGRD to GGRS87.

This is formally established through the utilization of second-degree polynomials, as demonstrated below [40]:

$$E_i^{GGRS1987}=A_0+A_1{x}_i^2+A_2{y}_i^2+A_3{x}_i{y}_i+A_4{x}_i+A_5{y}_i$$

(1a)

$$N_i^{GGRS1987}=B_0+B_1{x}_i^2+B_2{y}_i^2+B_3{x}_i{y}_i+B_4{x}_i+B_5{y}_i$$

(1b)

$E_i^{GGRS1987}$ is the easting coordinate in GGRS87; $N_i^{GGRS1987}$ is the northing in GGRS87; and $x_i,y_i$ $A_0, A_1, A_2, A_3,A_4, A_5, B_0, B_1, B_2, B_3, B_4, B_5$ are the Hatt coordinates with respect to NVGRD and the 12 polynomial coefficients. Hundreds of polynomial coefficient sets exist, one per 1:100,000 map sheet, also known as Hellenic Mapping and Cadastre Organization (HMCO) polynomials [40], as shown in Figure 1.

(b) From OVGDR to GGRS87.

Despite the prevalence of numerous official surveying plans, particularly in rural areas all over Greece, which refer to OVGDR, as shown in Figure 2, there is no formal method for OVGDR to GGRS87 transformations.

This deficit is a permanent challenge in the context of the cartographic and topographic practices of the Greek state, performed either in the public or private sector. Thus, professional surveying engineers and public agencies apply transformation techniques at shared points between the two geodetic datums. The most commonly used method is the 2D similarity transformation (e.g., [41]). It can also be adopted by policymakers in order to speed up corrections of the current cadastral map so as to facilitate property transactions in the operational HC prior to the overall revision of the HC cadastral map, as presented in Equation (2a,b).

$$E_i^{GGRS1987}=\mu \cos \theta x_i^{Hatt}+\mu \sin \theta y_i^{Hatt}+t_x$$

(2a)

$$N_i^{GGRS1987}=-\mu \sin \theta x_i^{Hatt}+\mu \cos \theta y_i^{Hatt}+t_y$$

(2b)

where $E_i^{GGRS1987}$ is the easting coordinate in GGRS87; $N_i^{GGRS1987}$ is the northing coordinate in GGRS87; $\mu$ is the scale factor; $\theta$ is the rotation; $x_i^{Hatt}$ is the projected x coordinate in the HATT projection (OVGDR); $y_i^{Hatt}$ is the projected y coordinate in the HATT projection (OVGDR); and $t_x$, $t_y$ are the shifts of the X and Y axes.

However, the transformation from OVGDR to GGRS87 can be a challenging task [42], as a significant proportion of the original geodetic control points of the OVGDR have either been destroyed or have experienced a decline in their integrity over time. In exceptional circumstances, the implementation of rubbersheeting with non-linear techniques (e.g., thin-plate spline) is undertaken subsequent to the determination of the coordinates of identified landmarks or geodetic control points on the map via field measurements.

4.2. Property Area Calculations in Greece: Two Empirical Approaches

The calculation of a property area can be performed in two distinct ways. It can be either determined through the measurement of the boundaries, as recorded in the field, or it can be estimated from existing cadastral maps using graphical [43] or analytical [44,45] methods. Still, the Gauss method remains the most prevalent polygon area calculation method [46], also referred to as the “shoelace” method, which is essentially a special case of a Green’s theorem. Inaccuracies in the estimation of boundary coordinates always lead to proportional inaccuracies in property area calculations.

The area, in general, is calculated as follows for cadastral applications (e.g., [47]) and is presented in Equation (3a,b):

$$2A={\displaystyle \sum _{i=1}^n{x}_i}\left(y_{i-1}-y_{i+1}\right)$$

(3a)

or equivalently as follows:

$$2A={\displaystyle \sum _{i=1}^n{y}_i}\left(x_{i-1}-x_{i+1}\right)$$

(3b)

where A is the area of a region, and x and y are the projection coordinates.

The most commonly used empirical approaches for the transformation of a property area from the old GR-Datum to GGRS87 are as follows: approximation formula and ad hoc handling.

(a)

Approximation formula

A common approach is to use the distortion factor associated with the Transverse Mercator (TM) projection, which accounts for the conversion of distances from the ellipsoid (geodesic lines) to the TM projection. In Figure 3, the distortion factor of GGRS87, k, is depicted. For the TM projection in the GGRS87 system, the distortion factor is only applicable to areas not larger than 5 × 5 km and can be calculated as described by Veis [37], as shown in Equation (4).

$$k=0.012311(\overline{\mathrm{E}}-0{.5)}^2+0.9996$$

(4)

where $\overline{\mathrm{E}}$ is the mean easting coordinate of the area (expressed in 10⁶ m).

The calculation of the transformed area from OVGRD or NGVDR to GGRS87 is based on the assumption that the application of the squared distortion factor will enable a direct estimation of the area, as shown in Equation (5).

$$A^{GGRS1987}\approx A^{GRD}{k}^2$$

(5)

where $A^{GRD}$ is the area with respect to the GR-Datum (either the old or new versions); $A^{GGRS1987}$ is the area as measured in GGRS87; and k is the distortion factor of GGRS87.

While this approach is convenient for relevant small parcels, significant challenges have to be met for the rigorous calculations of bigger parcels.

• Systematic Effects between Datums: Severe systematic deviations, particularly between the OVGDR and GGRS87, are observed. Furthermore, inconsistencies in scale factors frequently arise, affecting and complicating the process of accurate transformations.
• Assumption of Rectangular Parcels is a key element of the method, yet it is well-documented that such parcels are seldom encountered in practice. Even in the absence of scale inconsistencies, this assumption imposes limitations on the approach’s accuracy and applicability, as Equation (5) is only valid for rectangular geometries.
• Distortion in Larger Areas: In the case of larger areas, such as city blocks or entire villages, distortions can amount to tens of square meters or even more. This renders the approach unsuitable for applications in large areas that require high precision and accuracy.
• Communication Challenges: The method has to be analytically explained to non-expert stakeholders, such as notaries and citizens, in a manner that is comprehensible to them. This is a significant barrier to its effective implementation.

(b)

Ad hoc handling

A prevalent method used to align the current cadastral framework with old survey plans, diagrams, and maps is the implementation of ad hoc techniques [49]. In this approach, the field-measured boundary geometries referenced in GGRS87 are inversely georeferenced to match the boundaries as they appear in the survey diagram or map attached to the ownership title, which could be an administrative act reference to old reference systems.

This adjustment is typically achieved by manipulating the GGRS87 geometry through rubbersheeting, i.e., moving, rotating, scaling, and shearing topographic or cadastral plans, diagrams, or maps without the use of field-measured control points. While this method offers a potential workaround, it presents significant limitations.

• Lack of Parameter Estimation: Ad hoc techniques are lacking a robust scientific foundation, as they do not involve parameter estimation. Consequently, they provide no indication of accuracy or reliability.
• Implicit Assumption of Perfect Accuracy in Old Layouts: the ad hoc approach presupposes that the older cadastral or topographical layouts are error-free, an assumption that is seldom valid.
• Inconsistencies in Application: the ad hoc approach has the potential to engender significant inconsistencies, which vary not only between different blocks but, in some cases, even among individual parcels.
• Stuck in the past: the ad hoc approach encourages the transformation of new geospatial data to older reference systems, an action that is outdated when considering the necessity to modernize cadastral records.

5. Local Area Distortion Factor

Herein, we propose a novel metric approach for the integration of old cadastral or topographical plans, diagrams, and maps, without reference or referenced in previous reference systems, based on previous Greece’s datums to the HC spatial database referenced in GGRS87: the Local Area Distortion Factor (LADF). The LADF is developed with the scope to address the deviation in property area calculations from the old to the current reference system by providing a systematic transformation approach.

The LADF method is practically the area equivalent of implementing a 2D similarity transformation. The most important factor for the LADF is the estimated scale factor (the axis rotation and shift play no role). The use of the distortion factor of the TM has been shown to lead to severe inconsistencies and is not justified from a purely geodetic or cartographic point of view. As described above, the geodetic networks associated with the OVDGR are reliable only in a limited area, e.g., not exceeding 10 × 10 km. Therefore, LADF is valid in relatively small areas, e.g., a single village or a suburb of a city. If one tries to implement a 2D similarity transformation for larger areas, the accuracy will deteriorate significantly (e.g., [49]). The LADF implementation is for small areas so as to address everyday survey activities performed either by freelancer surveyors or by public servants in respect to official HC cadastral records that have large-scale deviations compared to on-site measurements.

The transformation of each parcel’s boundary coordinates from the OVDGR or NVGDR to the GGRS87 system is a prerequisite for the process. For NVGDR, an officially accepted transformation procedure exists, while for OVDGR, georeferencing must be implemented by identifying common points on the map and in the field and measuring in situ their coordinates in GGRS87. Due to its ability to preserve the geometric shape of the parcels, a similarity transformation is recommended, although affine and second-order polynomial transformations may offer a superior fit at the expense of linearity. By the transformed boundary coordinates, the property area is calculated in GGRS87, and it is linked to the ownership title, while map distortions and systematic errors are absorbed.

In order to establish a connection between technical and legal practices, LADF is calculated based on Equation (6) as follows:

$$LAD{F}_i={\displaystyle \frac{A_i^{legal}}{A_i^{cadastral}}}$$

(6)

where $A_i^{legal}$ is the legal property area, and $A_i^{cadastral}$ is the cadastral property area derived from the cadastral survey calculated at GGRS87.

• The specific steps that have to be followed to apply LADF are as follows:

i.

Identify common stations (e.g., benchmarks, polygonometric points, etc.,) between OVDGR and GGRS1987. This is the most cumbersome part of the LADF procedure, since many of the benchmarks are either destroyed or severely damaged.

ii.

Apply the 2D similarity transformation using at least four common stations. Apply statistical tests (three-sigma criterion) to remove possible blunders.

iii.

Use the estimated scale factor (μ) for the calculation of LADF, as shown in Equation (7).

$$LAD{F}_i=1/{\mu }^2$$

(7)

where μ² is the scale factor of the similarity transformation, according to Equation (2a,b).

iv.

Consequently, the calculation of the property in GGRS87 derives by multiplying the measured area by a constant factor, as shown in Equation (8):

$$LAD{F}_i\times A_i^{cadastral}=A_i^{legal},$$

(8)

where $A_i^{legal}$ is the legal property area, and $A_i^{cadastral}$ is the cadastral property area derived from the cadastral survey calculated at GGRS87.

Similarly, LADF allows the land surveyor to easily quantify the deviations between the “title” area of the property and the area calculated from new field measurements. Figure 4 provides an overview of the LADF estimation process.

Regarding the limitation of the LADF estimation, we may underline that LADF should be realized for small areas, e.g., not exceeding 10 × 10 km. This is dictated due to the fact that the OVDGR is mainly realized by calculations (e.g., triangulations, intersections, traverses) valid only for surveying purposes not larger than the aforementioned area (10 × 10 km). We should also address that the OVDGR coordinates’ accuracy is in general at the level of a few dm [39], and it is also possible to deal with lower accuracies, e.g., 50 cm [42].

By this means, LADF is suitable for the majority of the Greek villages and small towns. It is uncommon for Greek villages and small towns to exceed the area of 100 km². Hence, the LADF, despite its obvious limitations, fits optimally to the needs of the Greek rural regions.

6. Case Study

The LADF was tested in Choristi village, located in the Eastern Macedonia–Thrace Region, Drama Prefecture, in Northern Greece.

SAMA had proceeded and completed official land distributions of urban plots for housing and land parcels for cultivation and agricultural exploitation to Greek refugees from Asia Minor. In 1933, the Choristi land distribution, consisting of detailed cadastral diagrams and tables, granted titles to beneficiaries based on the diagrams transcribed to the relevant land registry.

Unfortunately, the triangulation records are lost; benchmarks GYS_CHORISTH and DOXA_TEPE_II (shown in Figure 5) were confirmed as benchmarks used in the SAMA’s Choristi land distribution. A total of four common geodetic control points were identified in the vicinity of Choristi village, with coordinates recorded in both the OVGDR and GGRS87 systems, as shown in Figure 5.

The initial implementation of the 2D similarity transformation was undertaken in accordance with the procedure outlined above, and the results are shown in

Table 1. Results of the similarity transformation (Equation (2), ibid) from OVGDR to GGRS87.

μ	θ (deg)	tx (m)	ty (m)
0.9992294	−0.1082833	516,298.295	4,552,656.187

.

It is obvious that there is a deviation between the scale factor of the transformation, μ, and the distance distortion factor of the TM, and it is equivalent to 37.4 cm per km, which renders the deviation non-negligible. As a result, there are systematic inconsistencies between the two datums (OVGDR and GGRS87), which are revealed by the similarity transformation. According to Equation (7), the LADF for this particular region is as follows: $LAD{F}_i=1/{\left(0.9992294\right)}^2=1.00154298331$. Thus, the area in GGRS87 can be calculated by multiplying the original parcel area, as is recorded in the 1933 Choristi Land distribution, by the area’s LADF, which should be the area recorded in current HC cadastral records.

For the implementation of LADF, a specific area in SAMA’s 1933 Choristi village land distribution was selected, as shown in Figure 6.

Each distributed land parcel has its unique property number and its unique area recorded in SAMA’s distribution cadastral records and its unique area recorded in the title granted to the beneficiary and transcribed to the relevant land registry. For the present study plots, 1874, 1875, 1876, 1877, and 1878 were selected. In 2016, the cadastral survey for the creation of the cadastre in Choristi started and was completed in November 2024, and the operational HC began its function. Thus, the HC cadastral records are the official documentation for each property, as shown in Figure 7.

Table 2. SAMA’s 1933 Choristi village distribution selected land parcels and their cadastral record.

Parcel Number	KAEK	Ownership Title Area SAMA Distribution (m2)	Cadastral Area HC Records (m2)	Deviation (m2)	Deviation (m2)
1874	050661006011	8760	8990.62	230.62	2.41%
1875	050661006010	8760	8736.62	−23.38	−0.42%
1876	050661006014	8760	8624.50	−135.50	−1.73%
1877	050661006013	5720	5586.28	−133.72	−2.55%
1878	050661006009	6200	5998.04	−201.96	−3.53%

shows SAMA’s 1933 Choristi village land distribution data, number and area, the HC cadastral records, KAEK and area as recorded, and their deviations in square meters and percentage for the selected land parcels.

As SAMA’s 1933 Choristi village land distribution is an official administrative act, the recorded deviation between the distribution’s cadastral records and the HC cadastral records cannot be justified either on a technical or a legal level.

For the selected study area, its LADF was implemented to calculate the LADF area for each land parcel, as well as the boundary transformed coordinates in GGRS87.

Table 3. SAMA’s 1933 Choristi village distribution selected land parcel cadastral record and LADF transformed calculated area.

Parcel Number	KAEK	Cadastral Area HC Records (m2)	LADF Transformed and Calculated (m2)	Deviation (m2)	Deviation (m2)
1874	050661006011	8990.62	8773.52	217.10	2.41%
1875	050661006010	8736.62	8773.52	−36.90	−0.42%
1876	050661006014	8624.50	8773.52	−149.02	−1.73%
1877	050661006013	5586.28	5728.83	−142.55	−2.55%
1878	050661006009	5998.04	6209.57	−211.53	−3.53%

shows the deviations between the LADF transformed and calculated area and the HC recorded area.

Based upon the LADF boundary transformation, Figure 8 depicts the current HC spatial DB records for the study area and the respective spatial data of the selected land parcels after the implementation of the LADFs in their original spatial data (of SAMA’s 1933 Choristi village distribution). It is obvious that there are significant diversifications between the HC and LADF spatial depictions for the selected land parcels, even though both the HC and LADF borders and parcels are referenced in GGRS87. Those diversifications can cause problems for any future transaction or for the issuance of a building permit. As the LADF records are based on analytical mathematical calculations, the LADF depiction could be used for the improvement of the HC records in order to avoid any future problems and obstacles in the exploitation of the property and in any transactions concerning the property.

7. Discussion

The transformation of property areas between different geodetic datums in Greece is of critical importance, especially as the Hellenic Cadastre (HC) approaches the stage of full operational status throughout the country. A primary challenge is to reconcile deviations between legally documented areas as they appear in ownership titles and their relevant spatial data and calculated areas as surveyed under HC standards with the use of the current reference system, GGRS87. The challenge is further compounded by the coexistence of legacy geodetic systems, such as OVGDR and NVGRD, with the contemporary GGRS87, emphasizing the need for accurate solutions that align historical and contemporary geodetic data for property documentation.

Rigorous coordinate transformations, such as similarity or affine transformations, could be used to achieve this alignment but are time-consuming; thus, they disproportionately increase the cost of ordinary surveying work. On the other hand, empirical methods often lack the necessary accuracy for high-value land, a deficiency that is particularly evident in densely populated areas and recreational areas. Additionally, as the cadastral survey for the creation of HC is mainly based on empirical methods, the operational cadastre is constantly dealing with continuous corrections, especially of the spatial base, which is time-consuming and costly.

To address this, we introduce the Local Area Distortion Factor, LADF, a standardized ratio of the cadastral area of a property, as surveyed with contemporary equipment and matched with its previous spatial records or its title area. The LADF provides a scientifically grounded method for area reconciliation, as demonstrated in the Choristi village case study, delivering more accurate results than empirical techniques often used by land surveying practitioners.

LADF’s utility can be extended beyond property accuracy and into urban planning applications, especially in the case of old urban plans and their implementation acts. In early-planning phases, accurate cadastral data support the reliable assessments of public land and infrastructure needs. In land readjustment, where properties are adjusted to new layouts, LADF helps ensure fair and precise area reallocations, reducing the risk of errors that can disproportionately affect stakeholders. LADF’s adaptability facilitates improved communication among surveyors, planners, notaries, and property owners, promoting consistency and reducing potential disputes.

Regarding the limitations of the LADF implementation in terms of quality and distribution of common points, this is a matter of great concern. It is not uncommon that professional surveyor engineers cannot find old benchmarks, or he/she finds damaged or severely inclined ones. For these cases, a common practice is to establish common points of some old but still in-use infrastructure, such as property fences, rural roads, crop boundaries, and, of course, buildings. This last ad hoc remedy can adequately address the lack of official benchmarks.

The adoption of LADF could significantly enhance Greece’s cadastral practices. Recognizing LADF as a legal standard for area documentation can support greater transparency and trust in cadastral data and strengthen the foundation for urban development. Implementing LADF on a national scale can harmonize legacy and modern land record systems, advancing Greece’s progress toward a unified, reliable cadastre, essential for sustainable land management and urban planning.

8. Conclusions

This alignment between previous GR datums and reference systems to the current GGRS87 does not only facilitate the maintenance of the HC spatial cadastral records but also facilitates urban and spatial planning, the planning and implementing of major projects, everyday transactions on properties, and overall property exploitations.

As the HC spatial DB creation was based on empirical methods, numerous discrepancies arose, creating enormous difficulties in the operational phase of the HC. To overcome this, we propose the Local Area Distortion Factor, or LADF.

This new area transformation factor introduces a robust factor that is mathematically and technically consistent with defining the area at the projected plane and is easy to implement and use. The LADF is applicable to small-scale areas, maximum at the level of a village. The LADF can be adopted officially by the operational HC, can facilitate survey projects for both the public and private sectors, and can facilitate surveying engineers in their everyday survey work when it comes to property transactions that ought to be registered in the operational HC. It can also be adopted by notaries during the drifting of titles on property transactions. It can also be adopted by policymakers in order to speed up corrections of the current cadastral map to facilitate property transactions in the operational Hellenic Cadastre prior to the overall revision of the Hellenic Cadastre cadastral map.

The area limitation should be carefully examined, as it can potentially lead to erroneous calculations, and, therefore, it is strongly recommended to the responsible agencies and professionals to publicly release the LADF for each particular village.

LADF can also be applied to other cadastral systems in order to facilitate and speed up correction processes, prior to large-scale revisions of their official cadastral maps, in small-scale areas, maximum at the level of a village, by implementing their coordinate systems’ relevant parameters and factors.