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Cross-dimensional adaptivity research on a 3D earth observation data cube model

  • Jinsongdi Yu EMAIL logo , Zhanying Cui , Peter Baumann , Ruiju Tong , Dandan Wei and Yuan Luo
Published/Copyright: April 7, 2025
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Open Geosciences
From the journal Open Geosciences Volume 17 Issue 1

Abstract

Earth observation (EO) data cubes have gained significance for their potential in providing comprehensive insights into dynamic earth phenomena. However, a significant challenge in their utilization is the interoperability among EO data cubes with varying dimensionalities. Existing efforts have primarily focused on enhancing analysis ready data cubes, yet cross-dimensional adaptivity remains relatively unexplored. This study proposes a novel approach to address this issue. The proposed method is based on a 3D adaptive data cube model constructed in a 3D adaptive space. The main objective is to achieve interoperability between EO data cubes of different dimensions while adhering to common geospatial standards. The core methodology involves cross-dimensional mapping, considering a 3D adaptive space containing spatial axes and adaptive axes. Importantly, the method applies to data cubes with the same coordinate reference system, resolution, and data type. To enable cross-dimensional mapping, a key requirement is the existence of a mapping function between the multidimensional space domain and the 3D adaptive space domain. When these conditions are met, data cubes with three or more dimensions can be interoperable. This becomes feasible by applying suitable serialization algorithms. This study demonstrates that data cubes can be successfully mapped into the proposed 3D adaptive data cube, achieving interoperability under specific conditions. This finding has significant implications in the field of EO data analysis, enabling seamless interaction between data cubes with different dimensions. The method not only facilitates cross-dimensional adaptability but also aligns with mainstream geospatial service standards. It is particularly suitable for multidimensional geospatial raster services based on the OGC WCS 2.0 standard. In conclusion, this study addresses a critical challenge in EO data analysis by proposing a 3D adaptive data cube model that promotes interoperability between data cubes of varying dimensions.

Keywords: imagery; EO data cube; interoperability; multidimensional space; 3D adaptive space

1 Introduction

Earth observation (EO) is essential for a wide range of applications, from environmental monitoring to urban planning and agriculture. However, the potential of EO data is often underutilized due to challenges in data processing and accessibility. The complexity arises from the diversity of data sources, formats, and resolutions, which contribute to the high cost and complexity of integrating these data into actionable insights. To overcome these obstacles, various approaches and technologies have been developed, including EO data cubes [1–3]. These cubes encapsulate vast and diverse EO datasets within a multi-dimensional framework, specifically designed to integrate, manage, and share massive and heterogeneous EO data. Examples of data cube implementations include EarthServer [4], the Open Data Cube initiative [5], the Google Earth Engine [6], the Euro Data Cube [7], the Swiss Data Cube [8], and the Brazil Data Cube [9], each aiming to enhance the understanding and utilization of EO data [1,10]. Other related platforms and services, while not implementing data cubes themselves, can also play a significant role in the broader ecosystem of EO data management and analysis. They provide the foundational data that can be organized and analyzed within data cube frameworks. For instance, the e-sensing platform [11] and the JRC Earth Observation Data and Processing Platform [12] offer valuable tools and services for processing and analyzing EO data, which can enhance the capabilities of data cube frameworks when integrated with them. Similarly, the Copernicus Data Space Ecosystem [13] provide vast amounts of satellite data, serving as a vital resource that can be ingested into data cube structures to facilitate advanced analytics and time-series analysis. This integration can be achieved through various tools, such as openEO [13], which offers access to satellite data and processing capabilities.

Despite the advancements in data cube implementations, a pivotal challenge persists: the absence of interoperability among these systems. Interoperability is tentatively defined as the ability of different data cube infrastructures to connect and communicate in a coordinated way, providing a rich experience to users [10]. The root of this issue does not lie solely in the lack of interoperability itself, but rather in the diverse and frequently incompatible approaches employed to structure and administer these data cubes. This incompatibility poses a barrier to seamlessly amalgamating data across various platforms, which is indispensable for conducting exhaustive analyses and informed decision-making. To address this challenge, there is a pressing need for the standardization of data cube structures and management methods, thereby fostering greater compatibility and enabling seamless data integration across disparate systems.

In this research, we introduce a solution to the prevailing interoperability challenge by presenting the 3D adaptive data cube model. The model incorporates a serialization function for the adaptive axis, which serves to model the intricate combination of axes embodying multiple variables. This strategic approach facilitates the integration of data originating from diverse dimensions into a cohesive and unified framework, thereby enhancing data interoperability and paving the way for more comprehensive and seamless data analysis. To clarify the problem and the solution, consider the scenario where a researcher seeks to analyze climate change impacts by integrating EO data on temperature, precipitation, and vegetation indices. Current data cube systems would require extensive preprocessing to align these variables, which are stored in different formats and resolutions. The proposed 3D Adaptive Data Cube model simplifies this process by providing a standardized method to serialize and integrate these variables into a single, coherent data structure.

This manuscript specifically explores data cube interoperability in terms of the exchange and utilization of information from different data services, with a focus on cross-dimensional adaptivity. The remainder of this work is organized as follows: Section 2 provides a detailed review of the related research and the current state-of-the-art. Section 3 introduces the 3D adaptive data cube model in depth. Section 4 demonstrates how our model can be adapted to achieve cross-dimensional interoperability. Section 5 presents a standard-based case study that exemplifies the practical application of our model. Finally, Section 6 concludes the findings and discusses the potential for future developments.

2 State-of-the-art

Normally, data cubes manage multidisciplinary imagery and gridded data in multidimensional arrays, ranging from 2D to nD, including complex structures like 3D x/y/t time series and 4 x/y/v/t EO data [14]. The primary challenge in this domain is developing a generic cube model that ensures cross-dimensional interoperability, allowing for the seamless integration of data across various dimensions and platforms.

A robust Data Cube model consistently maintains coherence across multiple axes, including spatial, temporal, and variable axes, which can exhibit significant variation in their attributes and resolutions. While harmonizing data cubes with matching axis extents is often feasible through interpolation, semantic gaps can emerge due to differences in desired levels of detail or when combining data from disparate sources. To address these, a 3D spatial-variable data cube has been proposed, enabling analysis across both spatial axes (latitude and longitude) and variable axes [15]. This model supports the arrangement of variables in sequence, with each coordinate on the variable axis represented by an integer referring to a variable description. However, existing models are yet to provide a comprehensive solution for adapting to data cubes of unlimited dimensions, which is essential for achieving globally adaptive interoperability.

A generic cube model is pivotal for advancing global data cube interoperability, which would significantly benefit from the widespread adoption of commonly available geospatial standards. To promote Analysis Ready Data Cube programs and ensure the seamless interoperability of imagery or gridded data services, several standard-based conformance testing approaches have been employed. These approaches validate whether a product or system complies with commonly available geospatial standards. One such approach is the OGC’s Test, Evaluation, and Measurement (TEAM) Engine [16], which executes an executable test suite to evaluate the implementation of imagery or gridded data services. It verifies that the services adhere to declared standards. Another notable tool is the INSPIRE Reference Validator [17], which assesses data, metadata, and web services against defined specifications or technical guidelines. These tests rely heavily on data cube standards, such as the ISO 19123-x series for fundamental models and OGC WCS 2.0 [18] for service interfaces. These standards facilitate standardized solutions up to n dimensions, encompassing the standardization of axes and multiple attributes, commonly referred to as bands or variables. Additionally, the Discrete global grid systems (DGGS) offer yet another novel framework for managing and analyzing geospatial data [19]. DGGS divides the earth into a multi-scale, hierarchical grid system, providing a unique approach to data integration that can potentially complement or integrate with existing data cube models. However, it has inherent limitations in terms of supporting an unlimited number of dimensions.

The interoperability of data cubes with different dimensionalities remains an open challenge. Current methods, such as domain variable identification [15] via a standardized resolver approach [20], support the modeling of multi-variable data cubes for multidisciplinary applications. However, these do not fully address the complexity of interoperation among variables with different dimensionalities. For instance, integrating a 3D x/y/t image time-series with 4D x/y/z/t ocean and climate dataset requires a sophisticated variable serialization function to stack variables on the same spatial surface effectively. The stacking results tend to be undecidable without a proper variable serialization function.

3 Methods

3.1 3D adaptive data cube model

3.1.1 Basic concepts

The 3D adaptive data cube model is a novel approach designed to address the challenges of interoperability and integration among multidimensional EO data. This section provides a detailed explanation of the model, including its key components, the adaptive nature of the model, and its practical application. The model is defined on basic concepts. Specifically, these include variable, dimension, axis, and data cube. Variables are the different measurable quantities or attributes that are recorded or observed in a dataset. In the context of our data cube, variables represent the different types of environmental data, such as temperature or salinity. Dimensions represent the different aspects or characteristics of a variable. Common dimensions in EO data include spatial dimensions (latitude and longitude), temporal dimensions (time), and thematic dimensions (different variables). In the context of data cubes, an axis represents a dimension along which data are organized. For instance, the x and y axes typically represent spatial dimensions, while additional axes can represent time or different variables. A data cube is a multi-dimensional array of data points that are defined by a set of axes. Each point in the cube represents a single data value at the intersection of the dimensions.

3.1.2 Adaptive axis

An adaptive axis is a conceptual framework used to organize variables within a data structure. In the context of this study, an adaptive axis is defined based on a variable axis [15], which sequentially arranges each variable while ensuring that each variable shares the same spatial coordinate reference system (CRS), resolution and data type [15]. A variable on an adaptive axis encompasses ordered dimensions such as depth, time, and/or other information. Formally, an adaptive axis can be specified as:

(1) A = 〈 v 1 , v 2 , … , v n 〉 , n ≥ 1 ,

where A is an adaptive axis, and each v i represents a variable that can be ordered depth, time, or other information.

For example, a 3D adaptive space is used to analyze deep ocean data, where the X and Y axes represent geographic locations on Earth, and the adaptive axis A represents different ocean variables such as salinity, chlorophyll a, dissolved oxygen, etc., where each frame is a variable v i ordered in the variance inflation factor (VIF) [14], Figure 1.

Figure 1 Schematic of 3D adaptive data cube.
Figure 1

Schematic of 3D adaptive data cube.

3.1.3 3D adaptive space

The 3D adaptive space in this study is constructed by integrating latitude and longitude spatial axes with an adaptive axis, creating a multi-dimensional space. This space is mathematically denoted as

(2) AS = X × Y × A ,

where x ∈ X , y ∈ Y , v ∈ A ; X and Y represent the spatial axes, each x coordinate on the X axis corresponds to a latitude, each y coordinate on the Y axis corresponds to a longitude, and each integer on the adaptive axis A refers to a specific variable. A point ( x , y , v ) represents a location in the 3D adaptive space.

3.1.4 3D adaptive data cube

A 3D adaptive data cube is a formal data structure defined as a function representing the 3D adaptive space domain

(3) f : AS → R ,

where AS represents the 3D adaptive space domain, consisting of bounded axes and containing a set of one or more cube cell primitives. R specifies the range of values that can be associated with data cube locations, and AS → R represents the phenomenon in this 3D adaptive space. In this study, each cell within an adaptive data cube maintains the same structural characteristics, allowing for consistent data analysis and manipulation.

3.2 Cross-dimensional adaptivity

3.2.1 Cross-dimensionality mapping

The cross-dimensionality investigated in this study is under the condition that data cubes share the same spatial domain. Consequently, only data cubes with a dimensionality equal or lager than 3 is considered as interoperation input. A 2D single-band spatial imagery or gridded data are treated as a special 3D spatial-variable data cube in this study, where the band is arranged as a coordinate on the variable axis.

A data cube can be mapped to the proposed adaptive 3D data cube if there exists a mapping function between the corresponding multi-dimensional space domain and 3D adaptive space domain. The mapping process can be expressed as

(4) f : DS → AS ,

where DS = X × Y × D 1 × ⋯ × D n , d i ∈ D i , AS = X × Y × A , D i is a bounded time or other dimension axis and contains ordered coordinate values. In this case, each combination of ( d 1 , d 2 , ⋯ , d n ), consisting of nD cells be { ( index d 1 , ⋯ , index d n ) } , needs to be arranged in sequence on the axis of A , and there is at least one one-to-one mapping between D 1 × ⋯ × D n and A . A corresponding serialization algorithm is as below:

(5) index v = ( index d n − 1 ) × width d n − 1 × width d n − 2 × ⋯ × width d 1 + ⋯ + ( index d 2 − 1 ) × width d 1 + ⋯ + index d 1 ,

where index v is a serialized variable index on the adaptive axis, index d i is a cell index in the axis of dimension d i , width d i is the cell number in the axis of dimension d i . Hence, under the aforementioned conditions, a data cube can be mapped to an adaptive 3D data cube, resulting in a spatial-variable data cube, where A = 〈 v 1 , v 2 , ⋯ , v l 〉, 1 ≤ index v ≤ l , and l = width d 1 × width d 2 × ⋯ × width d n . However, serialization result can be different depending on the order of axes.

To illustrate the above serialization formula, a 5D data cube, with domain X × Y × D 1 × D 2 × D 3 , and with each index of d 1, d 2, and d 3 starting from the lower left corner, consisting of 3D cells { ( index d 1 , index d 2 , index d 3 ) } , is shown in Figure 2. Let red target cell (3, 1, 2) be n = 3, index d 1 = 3 , index d 2 = 1 , index d 3 = 2 , width d 1 = 4 , width d 2 = 3 , width d 3 = 4 , the serialized variable index on the adaptive axis can be derived as follows: index v = ( 2 − 1 ) × 3 × 4 + ( 1 − 1 ) × 4 + 3 = 15 . In this way, all cells can be arranged in sequence on the adaptive axis.

Figure 2 A case study of transformation from 5D data cube to 3D data cube.
Figure 2

A case study of transformation from 5D data cube to 3D data cube.

3.2.2 Cross-dimensionality combination

Two data cubes of dimensionality equal to or lager than 3 can be interoperated as long as they share the same spatial domain. The transformation allows for combining data cubes across dimensionalities.

Let

DS a = X × Y × D a 1 × ⋯ × D bm ,

DS b = X × Y × D b 1 × ⋯ × D b n .

Then,

f : DS a → AS a and f : DS b → AS b ,

where

AS a = X × Y × A a , A a = < v a 1 , v a 2 , ⋯ , v al > ,

AS b = X × Y × A b , A b = < v b 1 , v b 2 , ⋯ , v bl > ,

then

AS ab = AS a + AS b = X × Y × A a + X × Y × A b ,

AS ab = X × Y × 〈 v a 1 , v a 2 , ⋯ , v al 〉 + X × Y × 〈 v b 1 , v b 2 , ⋯ , v bl 〉 ,

AS ab = X × Y × 〈 v a 1 , v a 2 , ⋯ , v al , v b 1 , v b 2 , ⋯ , v bl 〉 .

In this way, more data cubes can be concatenated. The methodology transcends the limitations of static data cube manipulation by introducing a dynamic framework that enables cross-dimensional interoperability among data cubes of equal or greater than 3D, provided they share the same spatial domain. This framework is designed to be inherently flexible, allowing for the continuous integration of data cubes as they are generated or updated. The dynamic transformation process leverages advanced algorithms that properly align and serialize the variables within each data cube, regardless of their dimensionality.

3.2.3 Standard-based adaption

The transformation allows us to set up a 3D spatial-variable data cube, which permits arbitrary combinations of trim or slice operations on the data cube using standardized operations, e.g. the operations defined in OGC WCS 2.0 [18], as long as the constructed data cube follows the corresponding coverage standards [21]. Retrieval functions of 3D spatial-variable data cube based on OGC WCS 2.0 is provided in Table 1.

Table 1

Retrieval functions of 3D spatial-variable data cube based on OGC WCS 2.0

Operation Function Sample WCS 2.0 request
Trim Let, f trim be the trim function, c be the 3D spatial-variable data cube, lo i and hi i be the low and high boundary of the trimed axis i , which can be x, y and variable axis, then http://{service entry}?
&service=WCS
&version=2.0
&request=GetCoverage
f trim ( c , 〈 ( lo i : hi i ) , ⋯ , ( lo n : hi n ) 〉 ) = c [ a i ( lo i : hi i ) , ⋯ , a n ( lo n : hi n ) ] , lo i ≤ hi i , 1 ≤ i ≤ n ≤ 3 &coverageId=datacubeId
&subset=x(lo, hi)
&subset=y(lo, hi)
&subset=order(lo, hi)
Slice Let f slice be the slice function, c be the 3D spatial-variable data cube, s i be the slice position on the sliced axis i , which can be x, y and variable axis, then http://{service entry}?
&service=WCS
&version=2.0
&request=GetCoverage
f slice ( c , 〈 ( s i , ⋯ , s n 〉 ) = c [ a i ( s i ) , ⋯ , a n ( s n ) ] , 1 ≤ i ≤ n ≤ 3
&coverageId=datacubeId
&subset=x ( s 1 )
&subset=y ( s 2 )
&subset=order ( s 3 )

4 Case study

4.1 Scenario

Species distribution modeling predicts the potential distribution of species using environmental variables. It plays a crucial role in understanding the current potential distribution of species and predicting how it might change in response to different climate change scenarios in the future [22–24]. Species distribution modeling is frequently utilized in conservation planning, invasive species management, and identifying areas that are vital for preserving biodiversity, which is particularly important for marine species due to their remoteness [25,26]. The environmental datasets used in modeling frequently originate from diverse sources with varying dimension, such as SRTM 15+V2 (the gridded seabed bathymetry) and Bio-ORACLE V 2.1 (the environmental dataset of bottom layer and surface layer for benthic species distribution modeling). This study demonstrates how a 3D adaptive data cube can be used to organize and manage cross-dimensional cubes to support variable retrieval and online analytics for species distribution modeling, using modeling of benthic species cold-water coral Desmophyllum pertusum as a case study. To demonstrate the approach, this research employs three datasets of various dimensions, including relevant variables, such as depth, temperature, and water chemistry factors, sourced from published papers and public databases, detailed in Table 2.

Table 2

Environmental variables used in the case study. Salinity, temperature, and current velocity of Bio-ORACLE v2.1 are variables of three time periods, including present, 2040–2050, and 2090–2100, under the Representative Concentration Pathway 4.5 (RCP4.5) scenario

Environment variables of bottom layer Dataset Resolution
SRTM 15+ v2 SRTM 15+ v2 [27] 15″ × 15″
Aragonite saturation states, calcite saturation states, chlorophyll a, dissolved oxygen, silicate, particulate organic carbon Davies & Guinotte (2011) [28] 30″ × 30″
Salinity, temperature, current velocity Bio-ORACLE v2.1 [29,30] 5′ × 5′

SRTM 15+ v2, Davies & Guinotte (2011) dataset, and Bio-ORACLE v2.1 dataset were used to construct a 2D space data cube, a 3D variable data cube, and a 4D space-variable-time data cube, respectively, with a resolution of 500 m, data type Float 32, and coordinate system EPSG 6933, using Geospatial Data Abstraction Library (GDAL) and netCDF Operator (NCO), as shown in Figure 3. Specifically, the 2D data cube represents a spatial data cube in (latitude, longitude) coordinates, the 3D data cube is a space-variable data cube in (X, Y, V) coordinates, and the 4D data cube is a space-variable-time data cube in (X, Y, V, time) coordinates. Within the context of Bio-ORACLE v2.1, the variables include salinity, temperature, and current velocity, each of which are associated with three different time periods: the present, 2040–2050, and 2090–2100, all under the RCP4.5 scenario. Then, these data cubes were transformed into the 3D adaptive data cube by employing the serialization algorithm and the tools GDAL and NCO, as depicted in Figure 4. Finally, the result is imported to Rasdaman, a OGC WCS 2.0 reference implementation, as a OGC Coverage Implementation Schema (CIS) as an online 3D variable cube [31].

Figure 3 (a–c) 2D–4D data cube sketches.
Figure 3

(a–c) 2D–4D data cube sketches.

Figure 4 Transformation of 2D–4D data cubes into 3D adaptive data cube.
Figure 4

Transformation of 2D–4D data cubes into 3D adaptive data cube.

4.2 Standard-based solution

The 3D adaptive data cube is implemented as a standardized coverage, leveraging mainstream geospatial information sharing and interoperability standards, concretely, ISO TC211 and OGC coverage related standards. The data cube structure is implemented based on ISO 19123-2:2018 [32], also known as OGC CIS 1.0, which is designed to provide a consistent structure for encoding and sharing geospatial data in various formats, including potential support for spatial and variable domains [14]. The corresponding metadata for the data cube is described in Numerical Thematic Data following ISO 19163-2:2020 [21], which is an implementation schema based on content models for imagery and gridded data [33]. These metadata are embedded in CIS using a modular approach [18], as illustrated in Figure 5, to construct a interoperable coverage. This coverage is then published through OGC WCS 2.0 to support standardized sharing applications, as demonstrated in Figure 6. OGC WCS 2.0 offers three key operations, specifically, GetCapabilities, DescribeCoverage, and GetCoverage, which return service description, coverage data description, and coverage itself, respectively. Furthermore, the integration of WCS-T [34], an extension of the OGC WCS 2.0 standard, into this experiment via Rasdaman, facilitates transactions on the data cube. This enables support for updates, insertions, and deletions of geospatial data, enhancing the flexibility and dynamicity of data management within the system. QGIS supports the OGC WCS 2.0 through its QgsWcsClient2 [35] plugin, which allows users to send WCS2.0 queries to OGC WCS 2.0 server, Rasdaman and loading the returned results in QGIS.

Figure 5 Interoperate ISO 19163-2:2020 metadata together with ISO 19123-2:2018 (taking numerical thematic data as an example).
Figure 5

Interoperate ISO 19163-2:2020 metadata together with ISO 19123-2:2018 (taking numerical thematic data as an example).

Figure 6 Request and response of the 3D adaptive data cube by OGC WCS 2.0.
Figure 6

Request and response of the 3D adaptive data cube by OGC WCS 2.0.

The implemented 3D adaptive data cube in OGC WCS 2.0 was tested using OGC Team Engine [16], and ISO 19163-2:2020 metadata validation in XML schema. In this way, the approach ensures that the 3D adaptive data cube can be shared and used by different software applications and systems that support the main stream geospatial standards.

4.3 Demonstration

Based on the 3D adaptive data cube constructed in this study, Rasdaman [36] is used to provide prototype service for the cube testing, supporting access, and retrieval of data along spatial and variable dimensions. For instance, the environmental variable calcite saturation states can be obtained by selecting the corresponding coordinates on the variable dimension using GetCoverage, returning the calcite saturation states grid data from the 3D adaptive data cube.

http://localhost:8080/rasdaman/ows?&SERVICE=WCS&VERSION=2.0.1&REQUEST=GetCoverage&COVERAGEID=AdaptiveDatacube&SUBSET=order(“21”)&FORMAT=image/tiff

In this way, 16 variables in present time in the 3D adaptive data cube, including SRTM 15+ v2, eleven variables from Davies & Guinotte (2011) dataset, and four variables from Bio-ORACLE v2.1 were retrieved through multiple GetCoverage operations, Figure 7. The images were retrieved by QGIS.

Figure 7 Retrieval of environmental variables from the constructed 3D adaptive data cube using GetCoverage operations of WCS 2.0.
Figure 7

Retrieval of environmental variables from the constructed 3D adaptive data cube using GetCoverage operations of WCS 2.0.

Correlation of the 16 variables were investigated using VIF. Eleven environmental variables with a VIF < 10 [37,38], including regional current velocity, vertical current velocity, aspect, bathymetric position index 9, slope, plane curvature, profile curvature, particulate organic carbon, salinity, chlorophyll a, and dissolved oxygen, were retrieved for further predictive modeling, Figure 8.

Figure 8 A case study – variables retrieved for the predictive modeling.
Figure 8

A case study – variables retrieved for the predictive modeling.

Then, we used the often used species distribution prediction method Random Forest (RF) of Biomod2 package, to construct the predictive model, as shown in Figure 9. NOAA (NOAA Deep Sea Coral Data Portal) [39], ICES (ICES Vulnerable Marine Ecosystems data portal) [40], and OBIS (Ocean Biogeographic Information System) [41] are all public datasets, from which we obtain geographic presence record data of cold-water corals. The same number of remaining records to the presence are randomly selected as background points. Then, the 11 retrieved target environmental variables, species presence, and background points were used to predict the potential distribution of scleractinian cold-water coral Desmophyllum pertusum in the Bay of Biscay. The statistical method area under the receiver operating characteristic curve (AUC) was calculated to evaluate the model performance, with a value range of [0, 1], and a larger value indicates a better prediction performance, Figure 10, the image is made using QGIS. The model evaluation showed that the model performed well with AUC 0.987.

Figure 9 A case study – cold-water coral distribution prediction using raster data from 3D adaptive data cube combined with coral occurrence records.
Figure 9

A case study – cold-water coral distribution prediction using raster data from 3D adaptive data cube combined with coral occurrence records.

Figure 10 Predicted habitat suitability for reef-forming scleractinian cold-water coral Desmophyllum pertusum in the Bay of Biscay.
Figure 10

Predicted habitat suitability for reef-forming scleractinian cold-water coral Desmophyllum pertusum in the Bay of Biscay.

5 Results

This research provides an elaborated account of the results obtained from the implementation and testing of the 3D adaptive data cube model. The primary objective of our study was to achieve interoperability among EO data cubes with varying dimensionalities, adhering to common geospatial standards. Our approach involves the use of a 3D adaptive data cube model that facilitates cross-dimensional mapping and integration of data from different sources and formats.

To demonstrate the practical application of our model, we conducted a case study focusing on species distribution prediction, specifically the cold-water coral Desmophyllum pertusum. This case study allowed us to test the model's ability to integrate and analyze data from various dimensions, including spatial, variable, and temporal axes.

5.1 Data integration and serialization

This research successfully integrated data from three different datasets, each with varying dimensions, into our 3D adaptive data cube. The datasets included:

  • SRTM 15+ v2: A 2D spatial dataset providing seabed bathymetry information.

  • Davies & Guinotte (2011): A 3D dataset offering variables such as aragonite saturation states, calcite saturation states, and chlorophyll a.

  • Bio-ORACLE v2.1: A 4D dataset with variables like salinity, temperature, and current velocity for different time periods.

Using our serialization algorithm, these datasets were transformed into a unified 3D adaptive data cube, enabling seamless data retrieval and analysis across different dimensions.

5.2 Cross-dimensional interoperability

The results confirmed that our model can achieve cross-dimensional interoperability among EO data cubes, provided they share the same spatial CRS, resolution, and data type. This finding is crucial as it demonstrates the potential for integrating diverse EO data sources into a single, coherent framework.

5.3 Standard-based implementation

The proposed 3D adaptive data cube was implemented as a standardized coverage, leveraging ISO 19123-2:2018, also known as OGC CIS 1.0. This ensures compatibility with mainstream geospatial information sharing and interoperability standards. The metadata for the data cube was described using ISO 19163-2:2020, embedded within CIS, to construct an interoperable coverage. This demonstration relies on Rasdaman to demonstrate the cross-dimensional interoperability. The interoperability achieved is based on relevant OGC and ISO TC211 standards, which can be implemented by systems that successfully complete the corresponding standard-based conformance testing [16].

5.4 Case study outcomes

The case study on cold-water coral distribution prediction yielded promising results. By integrating environmental variables from our 3D adaptive data cube with species presence records, this research was able to predict the potential distribution of Desmophyllum pertusum in the Bay of Biscay. The model’s performance was evaluated using the AUC, with a value of 0.987, indicating excellent predictive accuracy.

5.5 Finding validation

To further validate our findings, this research conducted a statistical analysis of the variables used in the case study. The VIF was used to assess the multicollinearity among the variables. Variables with a VIF less than 10 were selected for the predictive model, ensuring that the model’s predictions were not overly influenced by any single variable.

6 Discussion and conclusion

This research introduced a 3D adaptive data cube model designed to enhance the interoperability of EO data cubes with varying dimensionalities. The model was developed with the aim of aligning with mainstream geospatial standards, thereby facilitating seamless data interaction and analysis across different platforms.

The primary contribution of this research is the development and validation of a 3D adaptive data cube model that enables cross-dimensional interoperability among EO data cubes. First, the model successfully integrates data from diverse sources into a unified framework, allowing for comprehensive data analysis and retrieval across different dimensions. Second, the variable serialization method proposed in this study effectively orders and manages variables across data cubes, ensuring data alignment and consistency. Third, the case study on species distribution prediction demonstrated the practical applicability of our model in environmental data analysis, contributing to a high predictive accuracy for the potential distribution of the cold-water coral Desmophyllum pertusum. Fourth, the model aligns with geospatial standards such as ISO 19123-2:2018, also known as OGC CIS 1.0, ensuring compatibility with mainstream geospatial information sharing and interoperability standards.

While the proposed methodology for achieving cross-dimensional interoperability among EO data cubes is generalizable and can be applied to various scenarios where data integration across different dimensions is required, the development and implementation of our 3D adaptive data cube model may also be influenced by several factors, including data quality, data sharing policies, technological advancements, and computational resources. Furthermore, this study focuses on EO data and the static nature of the case study data, with untested scalability for various fields, including environmental monitoring, urban planning, and agriculture.

Despite demonstrating the potential of the 3D adaptive data cube model, there are several areas that warrant further investigation, such as expanding data sources, real-time data processing, scalability and performance assessment, and the incorporation of advanced analytics.

In conclusion, this study presents a significant step forward in addressing the interoperability challenge among multidimensional EO data cubes. The 3D adaptive data cube model, with its adherence to geospatial standards and dynamic framework, offers a robust solution for integrating and analyzing complex EO data. We envision that this research will inspire further developments in data cube modeling and contribute to the broader field of geospatial data analysis and applications.

Acknowledgement

This work is supported by the National Key R&D Program of China (No. 2019YFE0127100) and National Natural Science Foundation of China (No. 42006140).

  1. Funding information: This work is supported by the National Key R&D Program of China (No. 2019YFE0127100) and National Natural Science Foundation of China (No. 42006140).

  2. Author contributions: Conception and design: J.Y. and P.B.; analysis and interpretation of the data: Z.C., D.W., R.T., and Y.L.; drafting of the article, revising it critically for intellectual content: J.Y. and Z.C.; and the final approval of the version to be published: J.Y. and P.B. All authors agreed to be accountable for all aspects of the work.

  3. Conflict of interest: The authors have no conflicts of or competing interests to declare that are relevant to the content of this article.

  4. Data availability statement: The data associated with this study are listed in Table 2, which come from existing publication. The data will be provided on request.

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Received: 2023-10-17
Revised: 2025-01-22
Accepted: 2025-02-21
Published Online: 2025-04-07

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/geo-2025-0783
Keywords for this article
imagery; EO data cube; interoperability; multidimensional space; 3D adaptive space
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Seismic response and damage model analysis of rocky slopes with weak interlayers
  3. Multi-scenario simulation and eco-environmental effect analysis of “Production–Living–Ecological space” based on PLUS model: A case study of Anyang City
  4. Remote sensing estimation of chlorophyll content in rape leaves in Weibei dryland region of China
  5. GIS-based frequency ratio and Shannon entropy modeling for landslide susceptibility mapping: A case study in Kundah Taluk, Nilgiris District, India
  6. Natural gas origin and accumulation of the Changxing–Feixianguan Formation in the Puguang area, China
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  10. The use of radar-optical remote sensing data and geographic information system–analytical hierarchy process–multicriteria decision analysis techniques for revealing groundwater recharge prospective zones in arid-semi arid lands
  11. Effect of pore throats on the reservoir quality of tight sandstone: A case study of the Yanchang Formation in the Zhidan area, Ordos Basin
  12. Hydroelectric simulation of the phreatic water response of mining cracked soil based on microbial solidification
  13. Spatial-temporal evolution of habitat quality in tropical monsoon climate region based on “pattern–process–quality” – a case study of Cambodia
  14. Early Permian to Middle Triassic Formation petroleum potentials of Sydney Basin, Australia: A geochemical analysis
  15. Micro-mechanism analysis of Zhongchuan loess liquefaction disaster induced by Jishishan M6.2 earthquake in 2023
  16. Prediction method of S-wave velocities in tight sandstone reservoirs – a case study of CO2 geological storage area in Ordos Basin
  17. Ecological restoration in valley area of semiarid region damaged by shallow buried coal seam mining
  18. Hydrocarbon-generating characteristics of Xujiahe coal-bearing source rocks in the continuous sedimentary environment of the Southwest Sichuan
  19. Hazard analysis of future surface displacements on active faults based on the recurrence interval of strong earthquakes
  20. Structural characterization of the Zalm district, West Saudi Arabia, using aeromagnetic data: An approach for gold mineral exploration
  21. Research on the variation in the Shields curve of silt initiation
  22. Reuse of agricultural drainage water and wastewater for crop irrigation in southeastern Algeria
  23. Assessing the effectiveness of utilizing low-cost inertial measurement unit sensors for producing as-built plans
  24. Analysis of the formation process of a natural fertilizer in the loess area
  25. Machine learning methods for landslide mapping studies: A comparative study of SVM and RF algorithms in the Oued Aoulai watershed (Morocco)
  26. Chemical dissolution and the source of salt efflorescence in weathering of sandstone cultural relics
  27. Molecular simulation of methane adsorption capacity in transitional shale – a case study of Longtan Formation shale in Southern Sichuan Basin, SW China
  28. Evolution characteristics of extreme maximum temperature events in Central China and adaptation strategies under different future warming scenarios
  29. Estimating Bowen ratio in local environment based on satellite imagery
  30. 3D fusion modeling of multi-scale geological structures based on subdivision-NURBS surfaces and stratigraphic sequence formalization
  31. Comparative analysis of machine learning algorithms in Google Earth Engine for urban land use dynamics in rapidly urbanizing South Asian cities
  32. Study on the mechanism of plant root influence on soil properties in expansive soil areas
  33. Simulation of seismic hazard parameters and earthquakes source mechanisms along the Red Sea rift, western Saudi Arabia
  34. Tectonics vs sedimentation in foredeep basins: A tale from the Oligo-Miocene Monte Falterona Formation (Northern Apennines, Italy)
  35. Investigation of landslide areas in Tokat-Almus road between Bakımlı-Almus by the PS-InSAR method (Türkiye)
  36. Predicting coastal variations in non-storm conditions with machine learning
  37. Cross-dimensional adaptivity research on a 3D earth observation data cube model
  38. Geochronology and geochemistry of late Paleozoic volcanic rocks in eastern Inner Mongolia and their geological significance
  39. Spatial and temporal evolution of land use and habitat quality in arid regions – a case of Northwest China
  40. Ground-penetrating radar imaging of subsurface karst features controlling water leakage across Wadi Namar dam, south Riyadh, Saudi Arabia
  41. Rayleigh wave dispersion inversion via modified sine cosine algorithm: Application to Hangzhou, China passive surface wave data
  42. Fractal insights into permeability control by pore structure in tight sandstone reservoirs, Heshui area, Ordos Basin
  43. Debris flow hazard characteristic and mitigation in Yusitong Gully, Hengduan Mountainous Region
  44. Research on community characteristics of vegetation restoration in hilly power engineering based on multi temporal remote sensing technology
  45. Identification of radial drainage networks based on topographic and geometric features
  46. Trace elements and melt inclusion in zircon within the Qunji porphyry Cu deposit: Application to the metallogenic potential of the reduced magma-hydrothermal system
  47. Pore, fracture characteristics and diagenetic evolution of medium-maturity marine shales from the Silurian Longmaxi Formation, NE Sichuan Basin, China
  48. Study of the earthquakes source parameters, site response, and path attenuation using P and S-waves spectral inversion, Aswan region, south Egypt
  49. Source of contamination and assessment of potential health risks of potentially toxic metal(loid)s in agricultural soil from Al Lith, Saudi Arabia
  50. Regional spatiotemporal evolution and influencing factors of rural construction areas in the Nanxi River Basin via GIS
  51. An efficient network for object detection in scale-imbalanced remote sensing images
  52. Effect of microscopic pore–throat structure heterogeneity on waterflooding seepage characteristics of tight sandstone reservoirs
  53. Environmental health risk assessment of Zn, Cd, Pb, Fe, and Co in coastal sediments of the southeastern Gulf of Aqaba
  54. A modified Hoek–Brown model considering softening effects and its applications
  55. Evaluation of engineering properties of soil for sustainable urban development
  56. The spatio-temporal characteristics and influencing factors of sustainable development in China’s provincial areas
  57. Application of a mixed additive and multiplicative random error model to generate DTM products from LiDAR data
  58. Gold vein mineralogy and oxygen isotopes of Wadi Abu Khusheiba, Jordan
  59. Prediction of surface deformation time series in closed mines based on LSTM and optimization algorithms
  60. 2D–3D Geological features collaborative identification of surrounding rock structural planes in hydraulic adit based on OC-AINet
  61. Spatiotemporal patterns and drivers of Chl-a in Chinese lakes between 1986 and 2023
  62. Land use classification through fusion of remote sensing images and multi-source data
  63. Nexus between renewable energy, technological innovation, and carbon dioxide emissions in Saudi Arabia
  64. Analysis of the spillover effects of green organic transformation on sustainable development in ethnic regions’ agriculture and animal husbandry
  65. Factors impacting spatial distribution of black and odorous water bodies in Hebei
  66. Large-scale shaking table tests on the liquefaction and deformation responses of an ultra-deep overburden
  67. Impacts of climate change and sea-level rise on the coastal geological environment of Quang Nam province, Vietnam
  68. Reservoir characterization and exploration potential of shale reservoir near denudation area: A case study of Ordovician–Silurian marine shale, China
  69. Seismic prediction of Permian volcanic rock reservoirs in Southwest Sichuan Basin
  70. Application of CBERS-04 IRS data to land surface temperature inversion: A case study based on Minqin arid area
  71. Geological characteristics and prospecting direction of Sanjiaoding gold mine in Saishiteng area
  72. Research on the deformation prediction model of surrounding rock based on SSA-VMD-GRU
  73. Geochronology, geochemical characteristics, and tectonic significance of the granites, Menghewula, Southern Great Xing’an range
  74. Hazard classification of active faults in Yunnan base on probabilistic seismic hazard assessment
  75. Characteristics analysis of hydrate reservoirs with different geological structures developed by vertical well depressurization
  76. Estimating the travel distance of channelized rock avalanches using genetic programming method
  77. Landscape preferences of hikers in Three Parallel Rivers Region and its adjacent regions by content analysis of user-generated photography
  78. New age constraints of the LGM onset in the Bohemian Forest – Central Europe
  79. Characteristics of geological evolution based on the multifractal singularity theory: A case study of Heyu granite and Mesozoic tectonics
  80. Soil water content and longitudinal microbiota distribution in disturbed areas of tower foundations of power transmission and transformation projects
  81. Oil accumulation process of the Kongdian reservoir in the deep subsag zone of the Cangdong Sag, Bohai Bay Basin, China
  82. Investigation of velocity profile in rock–ice avalanche by particle image velocimetry measurement
  83. Optimizing 3D seismic survey geometries using ray tracing and illumination modeling: A case study from Penobscot field
  84. Sedimentology of the Phra That and Pha Daeng Formations: A preliminary evaluation of geological CO2 storage potential in the Lampang Basin, Thailand
  85. Improved classification algorithm for hyperspectral remote sensing images based on the hybrid spectral network model
  86. Map analysis of soil erodibility rates and gully erosion sites in Anambra State, South Eastern Nigeria
  87. Identification and driving mechanism of land use conflict in China’s South-North transition zone: A case study of Huaihe River Basin
  88. Evaluation of the impact of land-use change on earthquake risk distribution in different periods: An empirical analysis from Sichuan Province
  89. A test site case study on the long-term behavior of geotextile tubes
  90. An experimental investigation into carbon dioxide flooding and rock dissolution in low-permeability reservoirs of the South China Sea
  91. Detection and semi-quantitative analysis of naphthenic acids in coal and gangue from mining areas in China
  92. Comparative effects of olivine and sand on KOH-treated clayey soil
  93. YOLO-MC: An algorithm for early forest fire recognition based on drone image
  94. Earthquake building damage classification based on full suite of Sentinel-1 features
  95. Potential landslide detection and influencing factors analysis in the upper Yellow River based on SBAS-InSAR technology
  96. Assessing green area changes in Najran City, Saudi Arabia (2013–2022) using hybrid deep learning techniques
  97. An advanced approach integrating methods to estimate hydraulic conductivity of different soil types supported by a machine learning model
  98. Hybrid methods for land use and land cover classification using remote sensing and combined spectral feature extraction: A case study of Najran City, KSA
  99. Streamlining digital elevation model construction from historical aerial photographs: The impact of reference elevation data on spatial accuracy
  100. Analysis of urban expansion patterns in the Yangtze River Delta based on the fusion impervious surfaces dataset
  101. A metaverse-based visual analysis approach for 3D reservoir models
  102. Late Quaternary record of 100 ka depositional cycles on the Larache shelf (NW Morocco)
  103. Integrated well-seismic analysis of sedimentary facies distribution: A case study from the Mesoproterozoic, Ordos Basin, China
  104. Study on the spatial equilibrium of cultural and tourism resources in Macao, China
  105. Urban road surface condition detecting and integrating based on the mobile sensing framework with multi-modal sensors
  106. Application of improved sine cosine algorithm with chaotic mapping and novel updating methods for joint inversion of resistivity and surface wave data
  107. The synergistic use of AHP and GIS to assess factors driving forest fire potential in a peat swamp forest in Thailand
  108. Dynamic response analysis and comprehensive evaluation of cement-improved aeolian sand roadbed
  109. Rock control on evolution of Khorat Cuesta, Khorat UNESCO Geopark, Northeastern Thailand
  110. Gradient response mechanism of carbon storage: Spatiotemporal analysis of economic-ecological dimensions based on hybrid machine learning
  111. Comparison of several seismic active earth pressure calculation methods for retaining structures
  112. Mantle dynamics and petrogenesis of Gomer basalts in the Northwestern Ethiopia: A geochemical perspective
  113. Study on ground deformation monitoring in Xiong’an New Area from 2021 to 2023 based on DS-InSAR
  114. Paleoenvironmental characteristics of continental shale and its significance to organic matter enrichment: Taking the fifth member of Xujiahe Formation in Tianfu area of Sichuan Basin as an example
  115. Equipping the integral approach with generalized least squares to reconstruct relict channel profile and its usage in the Shanxi Rift, northern China
  116. InSAR-driven landslide hazard assessment along highways in hilly regions: A case-based validation approach
  117. Attribution analysis of multi-temporal scale surface streamflow changes in the Ganjiang River based on a multi-temporal Budyko framework
  118. Maps analysis of Najran City, Saudi Arabia to enhance agricultural development using hybrid system of ANN and multi-CNN models
  119. Hybrid deep learning with a random forest system for sustainable agricultural land cover classification using DEM in Najran, Saudi Arabia
  120. Long-term evolution patterns of groundwater depth and lagged response to precipitation in a complex aquifer system: Insights from Huaibei Region, China
  121. Remote sensing and machine learning for lithology and mineral detection in NW, Pakistan
  122. Spatial–temporal variations of NO2 pollution in Shandong Province based on Sentinel-5P satellite data and influencing factors
  123. Numerical modeling of geothermal energy piles with sensitivity and parameter variation analysis of a case study
  124. Stability analysis of valley-type upstream tailings dams using a 3D model
  125. Variation characteristics and attribution analysis of actual evaporation at monthly time scale from 1982 to 2019 in Jialing River Basin, China
  126. Investigating machine learning and statistical approaches for landslide susceptibility mapping in Minfeng County, Xinjiang
  127. Investigating spatiotemporal patterns for comprehensive accessibility of service facilities by location-based service data in Nanjing (2016–2022)
  128. A pre-treatment method for particle size analysis of fine-grained sedimentary rocks, Bohai Bay Basin, China
  129. Study on the formation mechanism of the hard-shell layer of liquefied silty soil
  130. Comprehensive analysis of agricultural CEE: Efficiency assessment, mechanism identification, and policy response – A case study of Anhui Province
  131. Simulation study on the damage and failure mechanism of the surrounding rock in sanded dolomite tunnels
  132. Towards carbon neutrality: Spatiotemporal evolution and key influences on agricultural ecological efficiency in Northwest China
  133. High-frequency cycles drive the cyclical enrichment of oil in porous carbonate reservoirs: A case study of the Khasib Formation in E Oilfield, Mesopotamian Basin, Iraq
  134. Reconstruction of digital core models of granular rocks using mathematical morphology
  135. Spatial–temporal differentiation law of habitat quality and its driving mechanism in the typical plateau areas of the Loess Plateau in the recent 30 years
  136. Review Articles
  137. Humic substances influence on the distribution of dissolved iron in seawater: A review of electrochemical methods and other techniques
  138. Applications of physics-informed neural networks in geosciences: From basic seismology to comprehensive environmental studies
  139. Ore-controlling structures of granite-related uranium deposits in South China: A review
  140. Shallow geological structure features in Balikpapan Bay East Kalimantan Province – Indonesia
  141. A review on the tectonic affinity of microcontinents and evolution of the Proto-Tethys Ocean in Northeastern Tibet
  142. Advancements in machine learning applications for mineral prospecting and geophysical inversion: A review
  143. Special Issue: Natural Resources and Environmental Risks: Towards a Sustainable Future - Part II
  144. Depopulation in the Visok micro-region: Toward demographic and economic revitalization
  145. Special Issue: Geospatial and Environmental Dynamics - Part II
  146. Advancing urban sustainability: Applying GIS technologies to assess SDG indicators – a case study of Podgorica (Montenegro)
  147. Spatiotemporal and trend analysis of common cancers in men in Central Serbia (1999–2021)
  148. Minerals for the green agenda, implications, stalemates, and alternatives
  149. Spatiotemporal water quality analysis of Vrana Lake, Croatia
  150. Functional transformation of settlements in coal exploitation zones: A case study of the municipality of Stanari in Republic of Srpska (Bosnia and Herzegovina)
  151. Hypertension in AP Vojvodina (Northern Serbia): A spatio-temporal analysis of patients at the Institute for Cardiovascular Diseases of Vojvodina
  152. Regional patterns in cause-specific mortality in Montenegro, 1991–2019
  153. Spatio-temporal analysis of flood events using GIS and remote sensing-based approach in the Ukrina River Basin, Bosnia and Herzegovina
  154. Flash flood susceptibility mapping using LiDAR-Derived DEM and machine learning algorithms: Ljuboviđa case study, Serbia
  155. Geocultural heritage as a basis for geotourism development: Banjska Monastery, Zvečan (Serbia)
  156. Assessment of groundwater potential zones using GIS and AHP techniques – A case study of the zone of influence of Kolubara Mining Basin
  157. Impact of the agri-geographical transformation of rural settlements on the geospatial dynamics of soil erosion intensity in municipalities of Central Serbia
  158. Where faith meets geomorphology: The cultural and religious significance of geodiversity explored through geospatial technologies
  159. Applications of local climate zone classification in European cities: A review of in situ and mobile monitoring methods in urban climate studies
  160. Complex multivariate water quality impact assessment on Krivaja River
  161. Ionization hotspots near waterfalls in Eastern Serbia’s Stara Planina Mountain
  162. Shift in landscape use strategies during the transition from the Bronze age to Iron age in Northwest Serbia
  163. Assessing the geotourism potential of glacial lakes in Plav, Montenegro: A multi-criteria assessment by using the M-GAM model
  164. Flash flood potential index at national scale: Susceptibility assessment within catchments
  165. SWAT modelling and MCDM for spatial valuation in small hydropower planning
  166. Disaster risk perception and local resilience near the “Duboko” landfill: Challenges of governance, management, trust, and environmental communication in Serbia
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