Atmospheric Lidar Data Storage Model Based on Ontology

. Ontology is an effective method to solve the problem of heterogeneous data in lidar measurements. Due to complexity and diversity of data structure, traditional method of ontology storage cannot be directly applied to lidar data. In this work, we proposed a novel ontology storage model based on the object-oriented data model, in which the mapping mechanism was established from ontology of lidar data to the object-oriented data model. A new storage model of lidar data is then obtained by a combination of the characteristics of lidar data and the syntax of OWL DL. Compared to the traditional method of ontology storage, we believe that the new storage model can better serve the sharing of lidar data.


Introduction
Air pollutions, such as Acid rain, haze, and light chemical smoke, have become increasingly prominent in China, which has been considered as a serious threat to public health and environmental safety.In order to better understand the pollutions, many tools have been developed to monitor the environment.Lidar is an active instrument for vertical structure of atmospheric profiling with high accuracy and high spatial and temporal resolution.Recently, a number of regional atmospheric monitoring networks have been built based on lidar [1][2][3][4].Analysis of lidar data from every monitored site is the key to investigating the regional air quality and temporal and spatial distribution of pollutants and to forecasting the emergency incidents, such as dust storms, forest fires, and volcanic eruptions [5][6][7].
Lidar observations have been carried out by many independent institutes, which leads to inconsistence of standards in terms of the protocol of data acquisition and data storage.Current lidar data structures which vary degrees of heterogeneity in structure and semanteme are hard to be shared without uniform data standard.The existing differences include the meaning of various concepts and the units of collected information.With the abilities of expressing and reasoning in semantic, ontology which has been widely used in data sharing and integration can describe the inner relationships between various parameters' concepts or terms and reveal the hidden relationships by logical reasoning [8].The ontology storage model of lidar data could be the prerequisite for exploring its huge quantity [9].
At present, there are four storage methods for ontology [10]: memory-based, plain text, specific management tools [11], and database [12,13].Methods of memory-based, plain text, and specific management have limitations in efficiency, analysis management, universality, and extensibility.The database storage model can further divide into three methods: relational database method, Native XML method, and object-oriented database method [14].Among them, relational database method is the most popular and matured method in ontology storage.The limitation of this method is that database's pattern does not match ontology and has poor extensibility and semantic support.The Native XML method has better expansibility but lower efficiency.Objectoriented database method has higher semantic integrity and query efficiency but lacks the ability of storing the complex relationship between ontology's concepts [15].
The lidar data have complex structures [16,17] and mass storage [18] because the lidar data contained many atmospheric parameters with strong correlations.The abovementioned storage methods have not been applied successfully to atmospheric lidar data storage.Based on the study of the relationship between lidar data and ontology structure, 2 Scientific Programming we proposed and developed a mapping mechanism for lidar data ontology and object-oriented storage model.
In our previous work, the representation method and mapping mechanism of OODM of atmospheric lidar data were proposed and show that the OODM for lidar data is effective [19].In present work, the details of database state of lidar data's OODM, the mapping mechanism of lidar data ontology to OODM, the data storage mode, and structure based on the OODM and the detailed process of the experiment are given.

Related Technologies
Ontology consisting of three elements, individual (instance), class (concept), and attribute [20], is a description of the concepts and relationships.The concept is the main part of the ontology, and the instance is the embodiment of the concept.Both the concept and the instance are the entity elements of the ontology, while the attributes are the descriptive elements.
Object-oriented data model (OODM) composed of object, class, and inheritance concept has been widely used in data modeling due to its flexibility in expressing the objects.Class describes a set of common characteristics of objects, and it is considered as a collection of objects with the same characteristics, where each object has the same properties and operations.Class is also associated with each other by inheritance, overwrite, and relationship [21].
The structure of ontology is similar to object-oriented data model in many respects.Concepts and attributes of ontology can be described and expressed with the classes and its attributes.Instances can be saved as object.Axiom and function of ontology can be simulated by the methods of OODM.Object-oriented method considers everything as a set of various objects.The complex objects can be decomposed into a combination of simple objects.Similarly, any complex knowledge of the ontology can be decomposed into a combination of basic concepts.

Lidar Data Ontology
The definitions of the lidar data's ontology and the objectoriented model are given as follows.
Definition 1.A lidar data ontology O consists of five elements {, , , , }, where  is a set of lidar data's concepts;  is a set of relationships;  is a collection of attribute sets for each concept and relationship;  is a set of lidar data's instances and  is a set of axioms [22].
Each concept   , where   ∈ , represents a set of the same kind of objects and can be described by the same set of attributes, denoted by   (  ).Each relationship   (  ,   ), then   ∈ , represents a binary association between concepts   and   , and the instances of such a relationship are pairs of (  ,   ).The attributes of   are denoted by   (  ).Each axiom in  is either a constraint on the attribute values of concept and relationship or a constraint on the relationships between concepts objects.Each constraint can be expressed as a prolog (rule).Definition 2. An object-oriented data model (OODM) of lidar data is a finite set of class declarations.Each class describes a series of atmospheric parameter objects with common attributes and methods.The OODM is a tuple  = {, , }, where Cs is a finite set of classes; As is a finite set of attributes; Ds is a finite set of class declarations.Ds contains exactly one declaration.The definition of declaration is defined as follows: where  denotes a type expression which was built based on the following syntax: The part of is-a is optional, which represents class inheritance, for example, specified inclusion within the sets of instances of the involved classes, while the part of type-is which can be used to assign objects of the instances of  by the type expression T restricts the structures of the classes., . . .,  represents summary between an abstract class and a series of object classes.Definition 3. The database instance  is a database state of lidar data's OODM.The instance  is defined by the notions of object identifier and value.Given finite atomic domains Given an infinite set ID, set  of value, and each A database instance  is constituted by   ,   ,   , where   is a finite set of object identifiers,   is a mapping assigned to each class in   to a subset of   , denoted by  ∈ ,    () ⊆   , and   is a mapping assigned a value in  to each object in   , denoted by   ∈ ,    (  ) ⊆ .

The Mapping Mechanism of Lidar Data Ontology to OODM
As the definitions given in Section 3, ontology is constituted of structure and instance, while an object-oriented database is constituted of OODM and database instance.They share some commons in structure; for example, both of them express the concepts of the real world based on class concepts and relationships; both of them have also class and the correspondence properties.
The metamodel elements of ontology can be transformed into the metamodel elements of the OODM in structural and instance.In order to fully support the object-oriented features, ontology concepts of lidar data have to be abstracted to core class, and ontology relationships would be abstracted to relationship class.The core class stores simple and fixed concepts with few correlation attributes.The relationship class stores relationships between different concepts and the relationship attributes of ontology [23].
Let  = {, , }, which is the corresponding OODM of lidar data's ontology   , and  is the mapping rule of structure transformation; thus  = () = {, , }.The mapping rules are described as follows: We supposed that the instance of the ontology   and the data instance of the corresponding OODM are derived as follows: The mapping algorithm from the lidar data ontology to the OODM is given by OWL DL syntax in Tables 1 and 2.

The Storage Mode Based on the OODM
Currently, the object-oriented database management system has implemented most of the features of the OODM; however, it lacks the mathematical theory and is relatively inefficient compared to the relational database system with a rigorous mathematical foundation, which was based on the relational algebra theory and set theory [24].
Figures 3, 4, and 5 show that the XML costs the longest query time compared to the other two storage models.Figure 6 shows that increase in the number of instances results in a bigger size of data file and leads to a longer query time, which can be related to the speed of parsing the file and the read-write speed of the disk.Frequent reading and writing files will definitely cost much more time.In addition, the XML method must load the files into the memory for every operation, and thus a large amount of memory usage  causes an inefficiency operation.In query method type  and ontology with size 1 × 10 4 and 2 × 10 4 , the data records are more than one million, which will exceed the total usable memory size of the testing machine after 49 s and 91 s, respectively.It reveals that, with the increase of atmospheric lidar data instances of ontology, XML storage model will consume much more time and memory compared to the other methods.Obviously, the OODM and RMDB storage methods are superior to the Native XML method in query time and data file size.Figures 3, 4, and 5 also show that the consuming time of the RMDB method is greater than that of the OODM in all three types of queries.The RMDB method is associated with the data in the form of the tables which joined with each other in the querying process.The OODM  method can easily obtain the object data due to its simplified data table.

Conclusions
In this paper, a new ontology storage model is developed for lidar data based on object-oriented model to maximize the query efficiency and minimize the data storage file size by the representation method and mapping mechanism.The model is very useful for lidar data as (1) the lidar data ontology structure can be easily transformed into the OODM structure; (2) the relationship of lidar data ontology can be clearly expressed and stored; and (3) the OODM of lidar data have high expansibility and query efficiency.Some (a) Each individual object identifier and class identifier in   can be mapped to the object and class's instance of the OODM.(b) Each individual data type identifier and object type identifier in   can be mapped to the data type attribute and object type attribute.(c) The individual axiom V( ()) of   can be mapped to the class declaration of the OODM's instance.(d) The individual axiom of   : Individual(value( 1 ,  1 ), . . ., value(  ,   ), value( 1 , V 1 ), . . ., value(  , V  )) can be mapped to the class declaration of the OODM's instance  : [ 1 :  1 , . . .,   :   ].

Figure 5 :
Figure 5: Comparison of type 's query times.

Figure 6 :
Figure 6: Comparison of data file sizes.
can be mapped to the class   of the OODM,   ∈ , (  ) ∈ .(b) For each   ∈  in   , it can be mapped to the class   of the OODM,   ∈ , (  ) ∈ .(c) For each attribute set   (  ) of   in   ,   ∈ , it can be mapped to the attribute   of class  in the OODM, (  (  )) =   ∈ .
(d) For each attribute set   (  ) of   in   ,   ∈ , it can be mapped to the attribute   of class  in the OODM, (  (  )) =   ∈ .(e) For each expression axiom of   in   ,   ∈ , it can be mapped to the class 's declaration of the OODM: Class C is-a  1 , . . .,   or Class C type-is Union  1 , . . .,   End.(f) For each data type definition of   in   ,   ∈ , it can be mapped to the class 's declaration of the OODM: Class C type-is T End.(g) For each data attribute axiom of   in   ,   ∈ , it can be mapped to the class 's declaration of the OODM: Class C type-is Record  1 :  1 , . . .,   :   End.(h) For each data attribute axiom of   in   ,   ∈ , it can be mapped to the class C's declaration of the OODM: Class C is-a  1 , . . .,   type-is Record A: Set of T End.
1 Create  : () (,   ) :   or (, V  ) :   ,   ,   ∈ ,   ∈ To further improve query efficiency of lidar data ontology, we proposed a storage model based on the relational database.The data table is built based on the vocabulary of the OWL and Definition 3 given in Section 3. The table Class contains the information of ontology about the OODM, including types, class names, and class identifiers.The table Property contains the properties of class or of relationship class in ontology, including the identifiers, types, and characteristics; the table PropertyOf describes the affiliation between the property and the class; the table SubSupClass stores the structure information between two classes; the table InstanceValue describes the property values of the instance in the form of a triple; the table InstanceOf describes the affiliations of the class and the instance; the table Restriction describes the constraints of the properties.The mapping rule from the OODM to a relational database is defined as follows: for the class of the OODM, the class identifier, name, and type are created and stored in table Class; the variables of class are stored in the table Property, and property identifiers are then created.The properties and characters of the variables in class correspond to the Type and Character in Table Property.The table PropertyOf stores the identifiers of classes and of properties.The table SubSupClass stores the identifiers of the parent and child classes expressed the inheritance relationship of the two classes.The table InstanceValue stores the properties and the values of an object of the OODM.The identifier of Property corresponds to the identifier of the table InstanceValue and the property values are stored in the table Value.The table InstanceOf stores the identifiers of classes and of objects.The property values and the special constraints are stored in the table Restriction and correlated with each other in the identifiers of classes and of objects, as shown in Figure 1.
atmospheric lidar data ontology storage model was examined using the experimental data collected in Laser Radar Center of Remote Sensing of Atmosphere of Xi'an University of Technology.According to Definition 1, we can get a lidar data ontology   = {  ,   ,   ,   }, where   =    ∪    .The parts of   are defined as follows: Box 1: Definition of   's OODM.