=Paper=
{{Paper
|id=None
|storemode=property
|title=MappingSets for Spatial Observation Data Warehouses
|pdfUrl=https://ceur-ws.org/Vol-1075/06.pdf
|volume=Vol-1075
|dblpUrl=https://dblp.org/rec/conf/immoa/ViqueiraMVT13
}}
==MappingSets for Spatial Observation Data Warehouses==
https://ceur-ws.org/Vol-1075/06.pdf
MappingSets for Spatial Observation Data Warehouses
José R.R. Viqueira Sebastián Villarroya
COGRADE - CITIUS COGRADE - CITIUS
Universidade de Santiago de Universidade de Santiago de
Compostela, Spain Compostela, Spain
jrr.viqueira@usc.es sebastian.villarroya@usc.es
David Martı́nez José A. Taboada
COGRADE - CITIUS COGRADE - CITIUS
Universidade de Santiago de Universidade de Santiago de
Compostela, Spain Compostela, Spain
david.martinez.casas joseangel.taboada@usc.es
@usc.es
ABSTRACT quency. The latter are started by some external event at
The amount of time evolving spatial data that is currently any moment in time.
being generated by automatic observation processes is huge. Observation data has an inherent temporal nature. Be-
In general, observation data consists of both heterogeneous sides, in many cases FOIs are also spatial. Therefore, sys-
spatio-temporal data and relevant observation metadata. tems devoted to observation data analysis should cope with
The former includes data of Spatial Entities (cities, roads, spatial and spatio-temporal data analysis. In particular,
vehicles, etc.) and data of temporal evolution of both prop- they should support relevant functionality for the manage-
erties of Spatial Entities (population of a city, position of ment of Spatial Entities and Spatial Coverages, and their
a vehicle, etc.) and properties of space (temperature, el- evolution with respect to time [9, 20, 6]. Spatial Entities are
evation, etc.). Real uniform integrated management of all entities of a given application domain that have geometric
these types of data is still not achieved by current models valued properties (rivers, municipalities, cities, etc.). Spatial
and systems. The present paper describes the design of a Coverages are sets of functions with a common spatial do-
data modeling and management framework for observation main that describe the continuous or discrete variation over
data warehouses. A hybrid logical-functional data model space of some specific phenomenon (temperature, humidity,
based on the concept of MappingSet and relevant language elevation above sea level, etc.).
enables the specification of spatio-temporal analytical pro- The amount of data that is currently being obtained from
cesses. The framework in currently being implemented. automatic observation processes is huge and the estimated
tendency is to have an exponential growth during the up-
coming years. The analysis of all these data to support
1. INTRODUCTION appropriate decision making is key challenge for future in-
According to [16], properties of entities (called Features formation systems. Many application domains exist that
of Interest - FOI) are either exact values assigned by some would benefit from innovative technologies in this area, in-
authority (names, prices, geometry of a municipality, etc.) cluding environmental observation and monitoring, natural
or estimated by some observation process (height, classifica- disaster management, e-health, etc.
tion, color, etc.). Observation processes may be classified in Based on the above, in the present paper a data modeling
various different ways [15]. Physical Processes produce their and management solution is proposed that enables spatio-
data in some spatial context. They are usually hardware temporal analysis in data warehouses of observation data. In
sensing devices that perform measurements either locally or particular, a proposed E-R extension enables the insertion
remotely. Besides, they may be installed in either static or of observation metadata in spatial models at a conceptual
mobile platforms. Non-Physical Processes are computations level. At a logical level, a new data model based on Map-
that may be defined in some mathematical way. Any pro- pingSets enables the integrated management of any kind of
cess may be either Time-triggered o Event-triggered. The spatial and temporal data. A MappingSet is a collection of
former perform their results at some predefined time fre- Mappings, in the functional programming sense, defined on
a common domain. Both Spatial Entities and Spatial Cov-
erages and both Time-triggered and Event-triggered obser-
vation data are modeled uniformly with MappingSets.
The remainder of this paper is organized as follows. Sec-
tion 2 describes other pieces of work related to the pro-
posed solution. The MappingSet based spatio-temporal log-
ical model is described in Section 3. The conceptual level
E-R extension for observation data is described in Section
4, as it is also its translation to the MappingSet based logi-
cal model. Section 5 illustrates the spatio-temporal analysis
Proceedings IMMoA’13 601 http://www.dbis.rwth-aachen.de/IMMoA2013/
capabilities of the model for the definition of Non-Physical on those input streams. Continuous query languages [1, 11]
spatio-temporal analytical processes. Finally, Section 6 con- enable the definition of those continuous queries on both
cludes the paper and outlines lines of future work. data streams and recorded relations. Operations to create
relations from streams and streams from relations are at the
2. RELATED WORK core of those languages. A similar approach is followed by
some languages specifically designed to access sensor net-
The OGC defines an abstract specification of a data model
works [13, 7]. It is important to notice that spatial data,
for Observations and Measurements [16] in a Geographic
including spatial entities and spatial coverages and spatial
Information context. Various types of observations are sup-
analysis is not explicitly supported in these solutions.
ported, according to the data type of their values. Simple
observations include: i) measurements that combine a value
of a real type with a unit of measure, ii) categories whose 3. SPATIO-TEMPORAL MAPPINGSET
results are items of enumerated types, iii) counts of inte- BASED DATA MANAGEMENT
ger types, iv) truth observations of boolean type, v) time This section introduces the MappingSet based data model
observations and vi) geometric observations. Complex ob- that is the basis of the proposed framework. Temporal and
servations are record structures that combine various simple spatial data types are first defined. Based on them Mappings
observation types. Metadata of each observation is also rep- and MappingSets are next formalized. Data management
resented in the model. In particular, each observation refer- will be based on the intensional definition of MappingSets
ences its observation Process, the observed Property and its using both logical and functional paradigms.
related FOI, the time instant when the observation applies Conventional data types include Boolean, CString (vari-
to the FOI observed property (phenomenon time) and the able size character strings), Int16, Int32, Int64 (integers),
time instant when the Process obtained the result value (re- Float32, Float64 (reals with floating point representation).
sult time). Notice for example that if a sample of water is Fixed point parametric type Numeric(P,D) consists of real
obtained from a river and next analyzed in a laboratory two numbers with a maximum of P digits, D of them are in the
different observation time instants are involved. Optionally, fractional part. In order to define temporal and spatial data
other metadata, parameters, data quality information and types, 1D and 2D samplings are first formalized. Let R and
observation context may also be provided. I denote the set of real and integer numbers, respectively,
In [4] a conceptual model to represent observation data se- then 1D and 2D samplings are defined as follows.
mantics is defined. Annotating the conventional data mod-
els of available heterogeneous datasets with observation and Definition 1. A 1D-sampling S with resolution r ∈ R
measurement conceptual constructs enables their integra- and phase p ∈ R is defined as the infinite subset of R
tion at a semantic level. Integrated query of heterogeneous {x|x = i · r + p, ∀i ∈ I}
observation datasets becomes therefore possible after the an-
notation process. A similar approach is followed by the E-R Definition 2. Let vr1 , vr2 , vp1 and vp2 be four vectors
extension proposed in the present paper. in R2 defined by respective directions D1 , D2 , D1 , D2 ∈
Observation data has always a temporal nature. Besides, (−π, π] and respective magnitudes r1 , r2 , p1 and p2 . A 2D-
the spatial components of observation data and metadata is sampling S with directions D1 , D2 , resolutions r1 , r2 and
centric to many application domains, such as those related phases p1 ∈ [−r1 /2, r1 /2], p2 ∈ [−r2 /2, r2 /2] is defined as
to environmental observation and monitoring. Spatial and the infinite subset of R2
temporal extensions of conceptual and logical data models {(x, y) ∈ R2 |
have to be considered. Examples of spatio-temporal concep- x = (i1 r1 + p1 ) cos(D1 ) + (i2 r2 + p2 ) cos(D2 )∧
tual models are [18, 17]. Relational and object-relational y = (i1 r1 + p1 ) sin(D1 ) + (i2 r2 + p2 ) sin(D2 ),
spatio-temporal extensions are defined in the area of Spa- ∀i1 , i2 ∈ I}
tial Databases [9, 20] to support spatial entity management.
An element s of a 1D-sampling (2D-sampling) S is called a
Field [6] and array algebras [3] are behind spatial cover-
1D-sample (2D-sample). Integer i, i1 , i2 are called the sam-
age and array management systems [14, 5, 2]. Integrated
pling coordinates of s. s(i), s(i1 , i2 ) denote respectively the
management of spatial entities and coverages is also objec-
1D-sample and 2D-sample with sampling coordinates i and
tive of some approaches [19, 12], that incorporate different
(i1 , i2 ). Figure 1 illustrates the above definitions with a
structures for those data types. Integrated management of
geometrical representation.
entities and coverages in a uniform manner is achieved by
the MappingSet data model proposed in the present paper. Definition 3. TimeInstant(D) is defined as a finite sub-
Various different data management approaches are pos- set of elements s(i) of a 1D-sampling S with resolution 10−D
sible to deal with spatio-temporal observation data auto- and phase 0 such that
matically generated by sensing devices. If we consider the −263 < i < 263 + 1
data generated by each sensor as a virtual temporal rela- where each s(i) is interpreted as the time instant 1/1/1970+
tion, then the simplest approach is to consider Materialized s(i) seconds. Maximum allowed D is 6 (microsecond).
Views of such virtual relations. Automatic maintenance of
such views on the arrival of new data from sensors has to Definition 4. TimeInstantSample(D, R) is defined as
be solved by the system [8]. Automatically updating these a finite subset of elements s(i) of a 1D-sampling S with
views through Extraction Transformation and Load (ETL) resolution R · 10−D and phase (R · 10−D )/2 such that
processes on sensor data is the approach followed by the −263 < i < 263 + 1
present framework. where each s(i) is interpreted as the time interval [1/1/1970+
A more sophisticated solution is to consider sensor data s(i) seconds, 1/1/1970 + (s(i) + R · 10−D ) seconds). Again,
streams and to enable the continuous execution of queries maximum allowed D is 6 (microsecond).
Proceedings IMMoA’13 612 http://www.dbis.rwth-aachen.de/IMMoA2013/
p r • LineString(S): Vector polylines defined by sequences
s(-2) s(-1) s(0) s(1) s(2) of elements of S.
0
(a) 1D Sampling • Polygon(S): Vector polygons, possibly with holes, whose
borders are defined by sequences of elements of S.
y
• GeometryCollection(S): Heterogeneous collections
s(1,1) of Geometries.
s(0,1)
• MultiPoint(S): Homogeneous collection of elements
of S.
vr2
• MultiLineString(S): Homogeneous collection of ele-
vr 1 ments of LineString(S).
s(1,0)
s(0,0)
vp2 • MultiPolygon(S): Homogeneous collection of elements
vp1 of Polygon(S).
(0,0) x
Definition 8. If ADT1 , ADT2 , . . . ADTn are not necessar-
ily distinct data types, A1 , A2 , . . . , An are distinct names
and RDT is a data type, then:
(a) 2D Sampling
1. A Mapping with signature M () : RDT is defined as
a value of type RDT
Figure 1: Illustration of 1D and 2D samplings.
2. A Mapping with signature
M (A1 : ADT1 , A2 : ADT2 , . . . , An : ADTn ) : RDT
Definition 5. Date is defined as a shorthand of TimeIn- is defined as a partial function
stantSample(0, 86400). M : ADT1 × ADT2 × ADTn → RDT
Definition 6. Point2D(P,D) is defined as the finite sub- Operations are syntactic sugar for Mappings. Implicit
set of elements s(i1 , i2 ) of a 2D-sampling S with directions castings between compatible data types are applied during
D1 = 0 and D2 = π/2, resolutions R1 = R2 = 10−D and Mapping invocations, enabling transparent transformation
phases P h1 = P h2 = 0 such that between temporal and spatial elements of different resolu-
−10P < i1 , i2 < 10P tions by applying constant interpolation. Various primitive
mappings and operations are provided by the model. How-
Definition 7. Point2DSample(P,D,R) is defined as the
ever, formalizing a complete set of them is out of the scope
finite subset of elements s(i1 , i2 ) of a 2D-sampling S with im-
of the paper. Informal descriptions of required primitive
plementation dependent directions D1 and D2 , resolutions
mappings will be given throughout the paper.
r1 = r2 = K · R · 10−D and phases p1 = p2 = 0 such that
A MappingSet is nothing but a set of Mappings that share
1. −10P < i1 , i2 < 10P a common domain defined as a n-ary relation over data
¯ ¯ ¯ ¯ types. Formalism is given below.
2. K < max(¯cos( D2 −D2
1 ¯ ¯
) , sin( D2 −D
2
1 ¯
))
Definition 9. Let C1 , C2 , . . . , Cn be distinct names, ADT1 ,
TimeInstant and Point2D data types provide discrete rep-
ADT2 , . . ., ADTn be not necessarily distinct data types
resentations for both time and space, where the user has con-
and RDT1 , RDT2 , . . ., RDTm be not necessarily distinct
trol over the supported precision. Types TimeInstantSam-
data types. Let also D be a n-ary relation with scheme
ple and Point2DSample provide representations for temporal
D(C1 : ADT1 , C2 : ADT2 , . . ., Cn : ADTn ) defined as
and spatial samplings at user defined resolution. It is noticed
a finite subset of ADT1 × ADT2 × . . . × ADTn . Then
that each time instant is approximated by its closest lower
a MappingSet is defined in either of the three following
TimeInstantSample, whereas each 2D point is approximated
forms:
by its closest Point2DSample. It is out of the scope of this
paper to demonstrate that K factor above ensures that any 1. A 1-tuple M S = hDi.
2D point is approximated by a sample at a distance lower or
equal to R · 10−D . Type castings are available for the above 2. A m-tuple M S = hM1 , M2 , . . . , Mm i, where each Mi
data types. is a Mapping with signature Mi () : RDTi defined as a
If T is either a numeric or temporal type, then data type value of RDTi .
Interval(T) is a new data type whose values are closed in-
tervals over data type T. If t1 , t2 are two elements of data 3. A (m+1)-tuple M S = hD, M1 , M2 , . . . , Mm i, where
type T, then [t1 , t2 ] is used to denote the relevant closed each Mi is a Mapping with signature Mi (C1 : ADT1 , C2 :
interval. Similarly, if S is spatial data type then the follow- ADT2 , . . . , Cn : ADTn ) : RDTi defined as a partial
ing geometric data types are also supported, based on the function Mi : ADT1 × ADT2 × ADTn → RDTi .
standard specification given by [10].
The evolution with respect to time of spatial entities and
• Geometry(S): Abstract type. Represents any vector spatial coverages may be modeled with appropriate Map-
geometry or set of geometries defined with elements of pingSets that contain both Domain and Mappings. n-ary
S. relationships are also modeled with MappingSets, usually
Proceedings IMMoA’13 623 http://www.dbis.rwth-aachen.de/IMMoA2013/
without Mappings. MappingSets without Domain are also keyProperty property GeoProperty property1 property2
useful to record short collections of key-value pairs that are
C
common in the specification of configuration settings. SpatialEntity SpatialCoverage
The Domains and Mappings of a MappingSet may be de-
fined either extensionally or intensionally. If a extensional (a) Spatial Entities (b) Spatial Coverages
definition of the Domain is given, then both extensional EO TO
and intensional definitions of Mappings are allowed. On EO TO
Entity Entity relat. relat.
the other hand, an intensional definition of the Domain may
only be accompanied by intensional definitions of Mappings. (c) Observed Entities (d) Observed Relationships
Generally, an extensional definition is a sequence of all the
elements of Domain and Mappings in some specific order. component1 component2
simpleProperty TO
Both row-wise and column-wise orderings may be used. It
is even possible to combine row and column-wise orders for
simpleProperty EO multiValued TO
different components and Mappings. If the data type of complexProperty EO
a Domain component is of some integer or sampling data
(e) Observed Properties
type, then its extensional definition might be given in the
form of a collection of sequence definitions. In general, a
sequence definition has an start element, a size and a step.
For example, for an integer data type, a sequence start- Figure 2: E-R Diagram Notation for Spatial and
ing at 5, with size 4 and step 2 describes the following list Observation Data.
< 5, 7, 9, 11 >. For a TimeInstantSample data types, a se-
quence starting at “2013 − 05 − 0215 : 00 : 45.06”, with by the system including both statistical and rank functions.
size 2 and step 30.42 describes the following sequence of MappingSet domains may also be intensionally defined.
type TimeInstant(2, 3042) ¡“2013 − 05 − 0215 : 00 : 20.22”,
“2013 − 05 − 0215 : 00 : 50.64”¿. 1 . For Point2DSample data
types, starting element is fo type Point2D and step has to
Intensional Domain. Let e be a functional expression that
yields a value s of either Interval(T) or Geometry(S) data
be given by two pairs (direction, resolution).
type, whose base type T, S is either some integer type or
Spatio-temporal analysis is enabled through the inten-
some sample type. Then, SAMPLING(e) yields all the el-
sional definition of Mappings and MappingSets. Mappings
ements of type T or S contained in s. Based on this, the
may be intensionally defined with functional, conditional
domain D of a MappingSet M may be defined by an expres-
and aggregate expressions.
sion of the form
{(e1 , e2 , . . . , en )|P }
Functional expression. A Mapping M with signature M(D): where P is a domain relational calculus predicate and each ei
DT may be defined by a expression of the form is either a functional expression or an expression of the form
M(D) := e SAM P LIN G(e), where e is also a functional expression.
where e is a functional expression of data type DT that may Expressions e and ei may include variable names bounded
include variables referencing components of D, mappings, to MappingSet domain components in P. Given that nested
operations, constants and castings. structures are not allowed in the model, if an expression
SAM P LIN G(e) is used then the result relation has to be
Conditional Expression. A Mapping M with signature unnested.
M(D): DT may be defined by a expression of the form
M(D) := CASE b1 THEN e1
CASE b2 THEN e2
4. MODELING OBSERVATION DATA WARE-
... HOUSES
CASE bn THEN en The data model described in this section captures observa-
[OTHERWISE en+1 ] tion data semantics and integrates them with spatial entities
where each bi is a functional expression that yields a value and coverages. An E-R extension is proposed in Subsection
of Boolean type and each ei is a functional expression that 4.1 to model observation metadata. The translation of such
yields a value of type DT. The semantics are the obvious a conceptual model to the MappingSet based logical model
ones. is explained in Subsection 4.2.
Aggregate Expression. A Mapping M with signature M(D): 4.1 Conceptual Data Model
DT may be defined by a expression of the form Contrary to conventional metadata that is recorded at the
M(D):= agge level of entity and property types, some observation meta-
OVER {P} data has to be recorded at the level of entity and property
where P is a domain relational calculus predicate and agge instances, i.e., combined with the data itself. This is the
is an functional expression where variables bounded to Map- case for example of observation time instants and observa-
pingSet domains in P must be used as arguments of aggre- tion processes.
gate functions. Various aggregate functions are provided An extension of the E-R model is next proposed to incor-
porate spatial and observation data semantics in conceptual
1
Notice that the start instant of the sequence is automati- models. Spatial Entity types are represented in diagrams
cally adapted to match the underlying time representation as conventional entities (see Figure 2(a)). Spatial Coverage
for type TimeInstant(2, 3042) Types are represented as entities tagged with the symbol
Proceedings IMMoA’13 634 http://www.dbis.rwth-aachen.de/IMMoA2013/
load
cond temp depth ProcessType ObsProperty
EO
EO
catches
ctd EO
EO
Process
vesId
name
comfort stock TO quota ObsFOI NonObsFOI
(0..*) (0..*) loc TO
(0..*)
Species (0..*) capacity Vessel difTem EO
(0..*) (0..*)
speId comfGeo TO power FOI MappingSet
EO
(0..*) enters
C TO
(0..*) stock TO
SST ICES Effort
quota
(1..*)
temp DomComponent Mapping
zoneId geo
Figure 4: E-R Diagram of the Frameworks Catalog.
Figure 3: E-R Diagram of a Running Application
Example.
using the quota and the vessels GPS information. The Fish-
ing Capacity gives the kilograms of each species that the ves-
C
(see Figure 2(b)). Entity Types, either spatial or not, sel may get from each zone. Again both quota is recorded
and Coverages whose whole data is obtained through an ob- and stock is computed by a Non-Physical Process.
servation Process are tagged with either symbol TO
if it is The translation of the above model to the MappingSet
EO
logical model of the framework is explained in the following
a Time-triggered Process or symbol if it is an Event- subsection.
triggered Process (see Figure 2(c)). Relationships resulting
from observation processes are tagged in the same way (see 4.2 MappingSet Based Logical Model
Figure 2(d)). Finally, properties of either Entity or Cover- To support the implementation of the conceptual model of
age types that are obtained through observation processes the previous section, observation metadata has to be added
are also tagged with the same TO and EO symbols, as it is to the frameworks catalog. Thus, the catalog contains meta-
shown in Figure 2(e) for simple, complex and multivalued data of the defined Mappings and MappingSets and meta-
properties. data related to the various observation processes, including
To illustrate the use of the above notation the E-R dia- observation properties and features of interest. The E-R
gram of a reduced running application example is given in diagram of such catalog structures is given in Figure 4.
Figure 3. Spatial Entity Type ICES records fishing zones de- Entity types MappingSet, DomComponent and Mapping
fined by the International Council for the Exploration of the record general metadata of the MappingSets. Entity type
Sea (ICES). Spatial Coverage SST records Sea Surface Tem- FOI records metadata of Features of Interest, and it refer-
perature at each location of the sea, daily produced by the ences the MappingSet that records its data. FOIs that are
Moderate Resolution Imaging Spectroradiometer (MODIS) fully generated by observation processes are registered in
sensor installed in the Terra and Aqua NASA satellites. En- ObsFOI. The remainder FOIs, i.e., those that combine ob-
tity type Vessel records data of fishing vessels, including an served with non observed properties are represented by en-
identifier (vesId ) and its engine power. Vessels incorporate tity type NonObsFOI. Each observed property of such a FOI
CTD sensors that enable obtaining triples of water conduc- is represented by a weak entity of type ObsProperty, which
tivity, water temperature and depth. Every time a ctd ob- references the MappingSet that records its data. Finally,
servation is performed a Non-Physical Process is executed ProcessType records metadata of the various types of ob-
that computes the difference with the value given by MODIS servation processes registered in the framework. Metadata
and provides it as a derived property difTemp. Vessels also of each specific instance of each process type is recorded in
incorporate GPS sensors from which locations are obtained weak entity type Process. Notice the difference between the
every 30 seconds. Entity type Species records data of fish- process type “Vessel Bascule” that obtains values of load
ing species, including an identifier specId, species name and property of relationships catches and the specific bascule
an interval of temperature values where the fish feels com- installed in each vessel that must be referenced from each
fortable (property comfort). The derived property comfGeo observation.
records the geometry of the area of the sea where comfort- The rules that enable the transformation of the concep-
able temperatures for the fish are located. This property tual model of the previous section to MappingSets are now
is obtained by a Non-Physical Process from the SST data. given next. Each Entity Type, either Spatial or not, gener-
Property load of relationship catches records the values mea- ates a relevant MappingSet, whose domain is defined by key
sured by the vessel bascule for each species. The autho- properties and whose Mappings are defined by the remain-
rized fishing capacity of a vessel is given by two parameters. der properties. See for example Entity Types Vessel, Species
The Fishing Effort gives a measure of the number of days and ICES in Figure 3 and relevant MappingSets in Figure 5.
weighted by the vessel engine power that the vessel may Each Spatial Coverage generates a MappingSet, whose do-
stay in each zone. Relationship Effort records both the ini- main has just one component of some Point2DSample type
tial quota and the available one (property stock ). Available and whose Mappings are generated from coverage proper-
Fishing Effort stock is obtained by a Non-Physical Procress ties. Each Relationship Type with cardinalities various to
Proceedings IMMoA’13 645 http://www.dbis.rwth-aachen.de/IMMoA2013/
MAPPINGSET Vessel MAPPINGSET Capacity
DOMAIN DOMAIN
vesId: CString vessel: CString
MAPPINGS ices: CString
power(vesId:CString):Numeric(6,2) species: CString
MAPPINGS
MAPPINGSET Vessel_loc quota(vessel:CString, ices:CString
DOMAIN species:CString):Numeric(7,3)
obsTime: TimeIntantSample(0, 30), quotaUOM(vessel:CString, ices:CString
vesId: CString species:CString):CString
MAPPINGS
loc(phenTime: TimeIntantSample(0, 30),
vesId:CString):Point2D MAPPINGSET Effort
process(obsTime: TimeIntantSample(0, 30), DOMAIN
vesId:CString):CString vessel: CString
ices: CString
MAPPINGSET Vessel_ctd MAPPINGS
DOMAIN quota(vessel:CString,
obsTime: TimeIntant(0), ices:CString):Numeric(7,3)
vesId: CString quotaUOM(vessel:CString,
MAPPINGS ices:CString):CString
cond(obsTime: TimeIntantSample(0, 30),
vesId:CString):Numeric(4,1) MAPPINGSET Catches
condUOM(obsTime: TimeIntantSample(0, 30), DOMAIN
vesId:CString):CString species: CString
temp(obsTime: TimeIntantSample(0, 30), vessel: CString
vesId:CString):Numeric(5,2) obsTime: TimeInstant(0)
tempUOM(obsTime: TimeIntantSample(0, 30), MAPPINGS
vesId:CString):CString load(species:CString, vessel:CString,
depth(obsTime: TimeIntantSample(0, 30), obsTime:TimeInstant(0)): Numeric(7,3)
vesId:CString):Numeric(5,2) loadUOM(species:CString, vessel:CString,
depthUOM(obsTime: TimeIntantSample(0, 30), obsTime:TimeInstant(0)): CString
vesId:CString):CString process(species:CString, vessel:CString,
process(obsTime: TimeIntantSample(0, 30), obsTime:TimeInstant(0)): CString
vesId:CString):CString
MAPPINGSET Species MAPPINGSET SST
DOMAIN DOMAIN
speId: CString loc:Point2DSample(9,2,100000)
MAPPINGS obsTime:Date
name(speId:CString):CString MAPPINGS
comfort(speId:CString):Interval(Numeric(5,2)) temp(loc:Point2DSample(9,2,100000),
obsTime:Date):Numeric(5,2)
MAPPINGSET ICES tempUOM(loc:Point2DSample(9,2,100000),
DOMAIN obsTime:Date):CString
zoneId: CString process(loc:Point2DSample(9,2,100000),
MAPPINGS obsTime:Date):CString
geo(zoneId:CString):Polygon(Point2D(9,2))
Figure 5: MappingSets for a Running Application Example.
Proceedings IMMoA’13 656 http://www.dbis.rwth-aachen.de/IMMoA2013/
various generates a MappingSet whose domain is defined MODIS (see difTemp derived property of Vessel in Figure
from the key properties of the participating Entity Types. 3).
Properties of those Relationship Types generate Mappings
MAPPINGSET Vessel difTem
in such a MappingSet. See for an example Relationship DOMAIN
Types capacity and effort in Figure 3 and MappingSets Ca- {(obsTime, vesId) | Vessel ctd(obsTime, vesId)}
pacity and Effort in Figure 5. If an Entity, Coverage or Re- MAPPINGS
difTem(obsTime, vesId):=
lationship Type is tagged with the symbol TO , then a com-
SST.temp(Vessel loc.loc(obsTime, vesId), obsTime) −
ponent named obsTime of some TimeInstantSample(D,R) Vessel ctd.temp(obsTime, vesId)
data type is added to the MappingSet Domain to enable the difTemUOM(obsTime, vesID):=
recording of observation time.2 Besides, a Mapping named Vessel ctd.tempUOM(obsTime, vesId)
process is also added to obtain the id of the process used process(obsTime, vesID):= “difTemProcess”
to produce the observation. See for example Spatial Cover- In the expression above it is noticed that automatic castings of
age Type SST in Figure 3 and relevant MappingSet SST in spatial and temporal types are performed during the evaluations
Figure 5. If symbol EO is used instead, then the data type of Mappings Vessel loc.loc and SST.temp.
of component obsTime is some TimeInstant(D). See for ex- Example 2. Define a Non-Physical Process that detects when
ample Relationship Type catches in Figure 3 and relevant a vessel leaves an ICES zone to enter a new one (see enters derived
Catches MappingSet in Figure 5. In any of the above cases, relationship in Figure 3).
an entity of type ObsFOI has to be added to the catalog with
relevant relationships to its process type and MappingSet. ICESFromLoc(loc):=
If a simple or complex property is tagged with symbol TO singleton(zone)
then such property is not added as a Mapping to the relevant OVER {ICES(zone) ∧ within(loc, ICES.geo(zone))}
MappingSet. Instead, a separate MappingSet is created for MAPPINGSET enters
the property whose domain has components to reference the DOMAIN
key of its Entity Type (FOI of the relevant observation) and {(vesId, ICESFromLoc(Vessel loc.loc(obsTime, vesId)),
has a component named obsTime of some TimeInstantSam- obsTime) |
Vessel loc(obsTime, vesId) ∧
ple(D,R) type to record observation time. The property ICESFromLoc(Vessel loc.loc(obsTime, vesId)) <>
itself is added as a Mapping to the MappingSet and an ad- ICESFromLoc(Vessel loc.loc(predecessor(obsTime), vesId))}
ditional Mapping named process is added to record the id of MAPPINGS
the process that generates the observation. An example is process(vesId, zoneId, obsTime):= “entersProcess”
loc property of Entity Type Vessel in Figure 3 and relevant In the above expression, Mapping within(g1 , g2 ) yields true if
Vessel loc MappingSet in Figure 5. If symbol EO is used geometry g1 is within geometry g2 . Aggregate function single-
instead then the transformation is exactly the same except ton(S) yields the element contained in the unitary set S. Finally,
for the fact that Domain component obsTime is of some Mapping predecessor (ts) yields the time sample that precedes
time sample ts in its data type.
TimeInstant(D) type. For an example see ctd property of
Vessel Entity Type in Figure 3 and relevant Vessel ctd Map- Example 3. Define a Non-Physical Process that produces a
pingSet in Figure 5. In any of the above cases an entity of measure of the remaining fishing effort for each vessel and ICES
type ObsProperty is added to the catalog, with appropriate zone for each of the preceding 60 days. Consumed fishing effort is
obtained from the temporal evolution of vessel location data and
references to its MappingSet, ProcessType and NonObsFOI.
ICES zone geometries (see derived property stock of relationship
Once the MappingSets are created and the required meta- type Effort in Figure 3).
data are added to the catalog, the insertion of observation
data may be started. ETL tasks are continuously executed ICESFromLoc(loc):=
to maintain the data warehouse updated with latest obser- singleton(zone)
OVER {ICES(zone) ∧ within(loc, ICES.geo(zone))}
vation data, using extensional MappingSet definitions. Each
observation is appended to the appropriate MappingSet with consumed effort(vesId, zoneId, obsTime) :=
its observation time and reference to its process and FOI. ((count(obsTime2)*30)/86400)*Vessel.power(vesId)
OVER {Vessel loc(obsTime2, vesId2) ∧
obsTime2 < obsTime ∧ vesId2 = vesId ∧
5. DEFINITION OF SPATIO-TEMPORAL AN- ICESFromLoc(Vessel loc.loc(obsTime2, vesId2)) = zoneId
}
ALYTICAL PROCESSES MAPPINGSET Effort stock
The capabilities provided by the framework for the inten- DOMAIN
sional definition of MappingSets enable the specification of {(vesId, zoneId,
spatio-temporal analytical processes. These capabilities are SAMPLING([cast(difTime(now(), 60 Days) AS Date),
now illustrated with some examples. cast(now() AS Date)])) | Effort(vesId, zoneId)}
MAPPINGS
stock(vesId, zoneId, obsTime):=
Example 1. Define a Non-Physical Process that obtains Effort.quota(vesId, zoneId) −
a derived observed property that computes the difference consumed effort(vesId, zoneId, obsTime)
between the temperature measured by the CTD and the stockUOM (vesId, zoneId, obsTime):=
sea surface temperature produced for the same location by Effort.quotaUOM(vesId, zoneId)
process(vesId, zoneId, obsTime):= “EffortStockProcess”
2
Currently we restrict to phenomenon time semantics, how- In the above expression, Mapping now () yields the current sys-
ever, it can be extended with result time and other required tem time instant. Mapping difTime(t, i) subtracts time interval
metadata. i from time instant t.
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