<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>B. De Meester, T. Seymoens, A. Dimou, R. Verborgh, Implementation-independent function
reuse, Future Generation Computer Systems</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.1109/ICSC</article-id>
      <title-group>
        <article-title>Querying OpenEO Datacubes through Virtual Knowledge Graphs</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Albulen Pano</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Free University of Bozen-Bolzano, Faculty of Engineering</institution>
          ,
          <addr-line>39100 Bolzano</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2016</year>
      </pub-date>
      <volume>110</volume>
      <issue>2020</issue>
      <fpage>176</fpage>
      <lpage>178</lpage>
      <abstract>
        <p>Earth Observation (EO) data are becoming a ubiquitous and readily exploitable source of data for decision making. The openEO platform is a renowned solution to query EO data using webAPIs. Running integrated queries encompassing both EO data and data from diverse domains is achieved using Knowledge Graphs (KGs). However, the volume of EO data makes its materialization in a knowledge graph impractical. In this contribution we look at the integration of data from openEO with other data sources using the Virtual Knowledge Graph paradigm, providing the advantages of KGs while avoiding the need of creating copies of the data. Our approach enables answering cross-domain user queries over openEO federated with data coming from other sources.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Virtual knowledge graph</kwd>
        <kwd>Earth observation</kwd>
        <kwd>Ontology-based data access</kwd>
        <kwd>Raster data</kwd>
        <kwd>openEO</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>perform cross-domain queries from EO data to other domains, and leverage the VKG approach to avoid
storing any EO data locally.</p>
      <p>The paper is organized as follows: Section 2 reviews related work, while Section 3 details the paradigm
and outlines preliminary implementation details in Ontop. Finally, Section 4 ofers concluding remarks
and discusses future research directions.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>
        Software solutions are available to query raster data, including, e.g., relational database extensions such
as PostGIS3 in PostgreSQL, or multi-language solutions such as RasterFrames4 (using Python, Scala, and
SQL). However, the challenge of analyzing EO data and specifically their raster representation using
knowledge graphs has not yet garnered consensus. The Spatial Data on the Web Working Group [
        <xref ref-type="bibr" rid="ref7 ref8">7, 8</xref>
        ]
recognizes the dificulty of representing all raster spatial data as linked data. Indeed, a spectrum of
linkiness is introduced whereby practitioners who wish to publish EO data do not have to either
(i) publish all EO data points as RDF triples, which would be resource constraining, or conversely
(ii) publish metadata on the data sources, which would be uninformative. We advocate for an approach
that balances these two extremes by leveraging the Ontology-Based Data Access (OBDA) paradigm to
construct VKGs. Through virtualization, raster data is published on-demand at query time, mitigating
the challenge of converting large volumes of RDF triples. Additionally, OBDA provides a high-level
conceptualization through an ontology, enabling greater abstraction beyond specific data points. This
facilitates the integration of EO data with diverse sources while enhancing explainability.
      </p>
      <p>
        Research has been conducted on extending the GeoSPARQL syntax for vector functions to raster data,
and respective prototype implementations have been built. GeoSPARQL+ [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ] implements via Apache
Jena an extension of GeoSPARQL that can handle raster operations and map individual observations
within geospatial rasters or coverages to IRIs. GeoLD [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ] provides its own syntax extensions and uses
a SPARQL optimization engine built over the Apache Jena ARQ engine and a Web Coverage Processing
Service (WCPS) node to delegate some of the computations to WCPS services using Petascope on the
Rasdaman5 array database. GeoLD outperforms GeoSPARQL+ in terms of query response time.
      </p>
      <p>
        Additional approaches [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] used to analyze EO using VKGs include using PL/pgSQL, the PostgreSQL
SQL Procedural Language, to first transform the data into a tabular format and then expose them as a
VKG. This approach involves an expensive computational step of calculating all needed measurements
for each raster grid cell, significantly increasing both the storage requirements and processing time.
While physical data files can be hidden behind the openEO Web API, downloading EO data locally into,
e.g., a netCDF or GeoTIFF file in order to then store them in a relational database, completely foregoes
the storage advantage of querying data via openEO remotely.
      </p>
      <p>
        The Plato data cube semantic [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ] demonstrates an alternative use of Ontop over raster data by
leveraging the Python xArray package to virtually retrieve data from raster files in the NetCDF format.
The solution involves a caching mechanism over spatial indexes to improve query performance over
vector and raster data. A custom Raptor Join [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ], which eficiently filters raster data that overlap with
vector data, is also demonstrated avoiding any conversion costs between the data. While the solution
mentions Web APIs, it was not mentioned to have been tested over OpenEO. The approach provides
an original solution to joining vector-raster data, implementing it in the context of VKGs. However,
designing a new prototype solution for geospatial joins is unlikely to be as eficient as mature geospatial
solutions, such as the raster extension in PostGIS or Rasdaman, and Plato has not been benchmarked
with traditional geospatial systems.
      </p>
      <p>
        OntoRaster [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ] extends the GeoSPARQL syntax over VKGs to leverage the functionalities provided
by the array database Rasdaman. The approach involves the use of PL/Python6 queries over PostgreSQL
3https://postgis.net/docs/RT_reference.html
4https://rasterframes.io/
5http://www.rasdaman.org/
6https://www.postgresql.org/docs/current/plpython.html
acting as a data federator over Rasdaman. Rasdaman is a mature raster database which provides
performance benefits when performing raster filtering based on vector data, however its query language,
rasql, has limited features which pose limits to the OntoRaster solution. Furthermore, all raster files
such as NetCDF or GeoTIFF need to be first ingested into Rasdaman before being queried by a VKG,
which doubles storage requirements and introduces an additional data transformation step to the VKG
construction pipeline.
      </p>
      <p>Most of the research detailed earlier focuses on modelling EO classes and properties, as well as
functions that extend the oficial GeoSPARQL standard, instead of considering comprehensive EO
raster functions. Function calls that can execute raster or EO functions over remote endpoints have
been discussed and implemented for Apache Jena and Virtuoso [15, 16], even including the definition
of LDScript [17], a Linked Data script language on top of the SPARQL filter expression language.
Descriptions of custom EO-related SPARQL functions, have been developed so that their signatures and
expected output are independent of the development context, to facilitate interoperability [18].</p>
      <p>A further contribution in this direction is the development of a module within the RDF Mapping
Language (RML) called RML-FNML [19]. Rather than integrating a fixed set of functions, RML-FNML
enhances RML with declarative function descriptions using the Function Ontology (FnO)7, providing a
more flexible and extensible approach. Practitioners are realizing that built-in functions in RML systems
are insuficient to handle the heterogeneity in input data and to address data processing tasks where
more flexibility is needed [20]. User-defined functions can be therefore introduced and prototypes for
RML with custom functions have been demonstrated.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Implementation</title>
      <p>
        We extend here the OntoRaster framework [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ] to the openEO Web API. The architecture of the solution
remains similar and is presented in Figure 1, with the diference that it uses openEO as backend, instead
of Rasdaman. The following discussion of the implementation focuses on the challenges and additional
features introduced by the support of a Web API such as openEO.
      </p>
      <sec id="sec-3-1">
        <title>3.1. openEO Data</title>
        <p>Several openEO cloud-based infrastructure providers exist which provide computing resources, storage
capacity and the networking capabilities required to handle large scale data processing requirements.
Two such platforms are Copernicus8, hosted by Copernicus Data and Information Access Services
(DIAS), and the one hosted at the Institute for Earth Observation at EURAC Research9. Platforms such
as the one managed by EURAC provide, in addition to Sentinel satellite data10, a better integration with
regional datasets.</p>
        <p>EO data is typically represented as raster data, structured as an n-dimensional data cube that
encapsulates all collected dimensions. The data is retrieved primarily from satellites, e.g., Sentinel constellation.
Datacubes are routinely filtered by domain experts based on spatial extent, temporal extent, and the
light band of interest. In a datacube with dimensions , , , where  is the longitude (east-west), 
the latitude (north-south) and  the time, each spatio-temporal coordinate is associated with one or
more values corresponding to the spectral bands dimension. For example, the satellite Sentinel-2 has 13
individual bands (including, e.g., B02, which captures visible blue light, useful for water body analysis
and atmospheric studies).</p>
        <p>We will conduct our analysis and demonstration using openEO data accessed through the Copernicus
Data Space Ecosystem. Our study focuses specifically on cities within South Tyrol, utilizing municipal
boundary shapefiles obtained from the regional geocatalogue 11 as our vector data.</p>
        <sec id="sec-3-1-1">
          <title>7https://fno.io/rml/</title>
          <p>8https://dataspace.copernicus.eu/analyse/openeo
9https://www.eurac.edu/en/institutes-centers/institute-for-earth-observation/projects/openeo
10https://sentinels.copernicus.eu/
11https://geonetwork1.civis.bz.it/geonetwork/geonetwork/ita/catalog.search#/home</p>
        </sec>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. openEO queries</title>
        <p>Queries over the openEO Web API are expressed as a JSON process graph12, a directed acyclic graph
where nodes represent individual processes, and edges define the flow of data between them, and with
exactly one sink node (returning the final result). A process in openEO is an operation that performs a
specific task on a set of parameters and returns a result [ 21]. Processes are applied sequentially in the
process graph, e.g., a first process can load a collection of data and a second process can take the result
as input to filter that data. Individual processes can also be applied as subprocesses, e.g., statistical
functions such as mean, maximum, or minimum applied over the temporal dimension.
3.3. Ontop
As OBDA system, we use Ontop v5.2.0, providing query answering capabilities over VKGs. Ontop
supports the RDF data model, the SPARQL13 query language, the OWL 2 QL14 profile of the OWL
ontology language, and the R2RML15 mapping language. We have extended Ontop by implementing a
set of SPARQL functions mapped to corresponding openEO functions. In our setting, a SPARQL query
is able to emulate, through composition of SPARQL functions, a process graph which a user would
specify either in the openEO python package or via web interfaces. Our implementation takes the
SPARQL input and reformulates it into a corresponding process graph in JSON, which is then sent to
the openEO endpoint for execution.</p>
        <p>We illustrate our implementation with a query that uses the band S8 (thermal infrared) to
approximate temperature (ignoring atmospheric efects). For this query, we defined the SPARQL function
openeo:load_collection inside Ontop, and mapped it to the load_collection function of the
openEO API. The function accepts the satellite name, start time, end time, spatial extent, and bands as
arguments. These are then passed to a predefined PL/Python function, which in turn receives the
process name (e.g., load_collection) along with the arguments.</p>
        <p>PREFIX r d f s : &lt; h t t p : / / www. w3 . org / 2 0 0 0 / 0 1 / r d f −schema #&gt;
PREFIX geo : &lt; h t t p : / / www. o p e n g i s . n e t / ont / g e o s p a r q l #&gt;
PREFIX openeo : &lt; h t t p : / / www. openeo − ontop . org #&gt;
SELECT ? a v g _ t e m p _ k e l v i n {
? g geo : asWKT ?geomWKT .
? g r d f s : l a b e l ?name .</p>
        <p>FILTER (LANG( ? name ) = " i t " &amp;&amp; ( STR ( ? name ) = " Bolzano " ) ) .</p>
        <p>BIND ( "2 023 − 09 −0 1 T00 : 0 0 : 0 0 Z"^^ xsd : dateTime AS ? s t a r t _ t i m e ) .</p>
        <p>BIND ( "2 023 − 09 −0 7 T00 : 0 0 : 0 0 Z"^^ xsd : dateTime AS ? end_time ) .</p>
        <p>BIND ( " SENTINEL3_SLSTR " AS ? s a t e l l i t e ) .</p>
        <p>BIND ( " S8 " AS ? band ) .</p>
        <p>BIND ( openeo : l o a d _ c o l l e c t i o n ( ? s a t e l l i t e , ?geomWKT , ? s t a r t _ t i m e , ? end_time , ? band )</p>
        <p>AS ? c o l l 1 ) .
12https://api.openeo.org/v/0.3.0/processgraphs/
13https://www.w3.org/TR/sparql11-query/
14https://www.w3.org/TR/owl2-profiles/#OWL_2_QL
15https://www.w3.org/TR/r2rml/</p>
        <p>BIND ( openeo : r e d u c e _ d i m e n s i o n ( ? c o l l 1 , " t " , " mean " ) AS ? c o l l 2 ) .</p>
        <p>BIND ( openeo : a g g r e g a t e _ s p a t i a l ( ? c o l l 2 , ?geomWkt , " mean " ) AS ? a v g _ t e m p _ k e l v i n ) . }</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.4. PostGIS</title>
        <p>The vector data from the shapefiles is loaded directly into a geometry table in PostgreSQL 17 and
its geometry extension PostGIS 3.5.0. Ontop already supports queries over relational databases with
geospatial support such as PostGIS, but is limited to the Well-Known Text (WKT) RDF geometry
serialization for GeoSPARQL functions.</p>
        <p>PL/Python is a procedural language that exploits functions written in Python to return PostgreSQL
query results with PostgreSQL datatypes. There is a well-maintained openEO Python client16 that can
accept openEO process graphs as input. We use Python 3.11 with openEO 0.33.0 to connect to openEO
cloud backends of choice, and shapely 2.0.2 to convert geometries expressed as WKT into a format that
is compliant with openEO process graphs.</p>
        <p>As part of the Python implementation, we create several templates for openEO processes, which
can be completed with arguments coming from the SPARQL functions described above. The input
retrieved from Ontop will replace each of the arguments named argi (see, e.g., the example below for
load_collection).
u n i q u e _ n o d e _ i d : {
" p r o c e s s _ i d " : l o a d _ c o l l e c t i o n ,
" arguments " : {
" i d " : arg1 ,
" s p a t i a l _ e x t e n t " : { a r g 2 } ,
" t e m p o r a l _ e x t e n t " : [ arg3 , a r g 4 ] ,
" bands " : [ a r g 5 ]
}</p>
        <p>}</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Conclusions and Perspectives</title>
      <p>We have shown how to query openEO Web API via SPARQL, using the Ontop VKG system and
PostgreSQL as a federator with its PL/Python functions.</p>
      <p>An area that we plan to further explore are User Defined Processes inside openEO, which would
allow us to avoid the nesting of SPARQL functions and to use instead single functions calls over custom
process graphs. We are currently working on a new mapping language in Ontop to further improve the
mapping of geospatial concepts, rather than relying on SPARQL functions, as in our current proposal.
E.g., incorporating notions from RML-FNML will allow the modelling of concepts at a higher level of
abstraction, e.g., heatwaves and wildfires, again avoiding to use nesting of SPARQL function calls. This
would also improve interoperability with other ontologies. A further question that arises is how to
handle the important aspect of privacy in such a distributed, heterogeneous setting, which natural leads
to the presence of data with diferent degrees of confidentiality. To address this, we are considering
to incorporate into the new mapping language the facet of privacy-preservation, contingent upon the
identity of the user running a query.</p>
    </sec>
    <sec id="sec-5">
      <title>Declaration on Generative AI</title>
      <sec id="sec-5-1">
        <title>The author(s) have not employed any Generative AI tools.</title>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>This work has been carried out while Albulen Pano was enrolled in the Italian National Doctorate
on Artificial Intelligence run by Sapienza University of Rome in collaboration with Free University
of Bozen-Bolzano. This work was supported by Agenzia per la cybersicurezza nazionale under the
programme for promotion of XL cycle PhD research in cybersecurity – B83C24005640005. The views
expressed are those of the authors and do not represent the funding institution.</p>
    </sec>
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