Contents 1 Introduction 1 1.1 Introduction to GIS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.2 Related work and contribution : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.3 Scope and Outline of Paper : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 Data Modeling Requirements 3 2.1 Data Input Unit : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2.2 Data Model : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Data Manipulation Capabilities : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.4 Result Presentation Facilities : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 3 The GISER Data Model 6 3.1 Data Input Unit : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 3.2 Data Model : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 3.3 Data Manipulation Capabilities : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 3.4 Result Presentation Facilities : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 4 Case Study 9 4.1 An Example GIS Application : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 4.2 The GISER Model of the application : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 5 Discussions 12 A Basic Concepts in Data Models 14 List of Figures 1 Road Map -LRB- Network -RRB- and Traffic Properties : : : : : : : : : : : : : : : : : : : : : : : 5 2 Enhanced Entity Relationship -LRB- EER -RRB- Model : : : : : : : : : : : : : : : : : : : : : : : 6 3 The GISER Model : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 4 ITS Data Flow : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 5 Model of Loop Detector Dataset : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 List of Tables 1 Summary of Requirements : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 Experiences with Data Models in Geographic Information Systems Shashi Shekhary Mark Coyle ? Brajesh Goyaly Duen-Ren Liu ? Shyamsundar Sarkarz y Department of Computer Science , University of Minnesota 4-192 EE/CS , 200 Union St. SE , Minneapolis , MN 55455 -LSB- shekharjbrajesh]@cs.umn.edu TEL : -LRB-612-RRB- 6248307 FAX : -LRB-612-RRB- 6250572 z Tata Research Development & Design Center 1 Mangaldas Road , Pune , India 411001 ? Oracle Corporation mcoyle@us.oracle.com ? Institute of Information Management National Chaio Tung University dliu@iim.nctu.edu.tw 1 Introduction 1.1 Introduction to GIS Geographic Information Systems -LRB- GISs -RRB- are used to collect , analyze , and present information describing the physical and logical properties of the geographic world . Taken in its broad sense , a GIS is any manual or computer-based set of procedures used to store and manipulate geographically referenced data . Geographically referenced data is the spatial data that pertain to a location on the earth 's surface . There are four major functional units in a typical GIS : Data Input Unit : Measurements in GISs are taken by sensors such as cameras and global positioning systems . A manual process is then used for inputting data which can not easily be processed automatically . The measurements are discretized , for example by imposing a regular , multi-dimensional discrete grid over the surface to be measured , allowing points of interest to lie only at the intersection of the grid lines . In addition to the error imposed by this discretization process , measurement errors also reduce the accuracy of attribute collection at a given 3-d coordinate . The measurements therefore need validation . Various integrity constraints including topological constraints also need to be checked . An example of a topological constraint is \ Minneapolis should be inside Minnesota '' . Data Model : A conceptual data model -LSB- 14 -RSB- is a type of data abstraction that hides the details of data-storage . It uses logical concepts which may be easier for most users to understand . It supports data input , manipulation and result presentation . Many GISs are organized as a collection of themes . Each theme represents the values of a unique attribute of the geographic space . A theme may independently partition , decompose , and fragment the continuous space for a particular value -LRB- or value range -RRB- of the attribute . The partitions and fragments of space within each theme are often stored within the database and can be treated as entities or objects . Data Manipulation Capabilities : Geographic data is queried and analyzed for various operations . Some of the queries on geographic data involve spatial searches and overlays -LSB- 18 -RSB- . Operations on primitive vector data-types include geometric operations -LRB- e.g. area or boundary , intersection -RRB- , topological operations -LRB- e.g. connectedness -RRB- and metric operations -LRB- e.g. distance -RRB- . For example , a GIS containing the Minneapolis road network may have to compute a path between two locations which does not pass via downtown 's congested streets -LSB- 17 -RSB- . Result Presentation Facilities : Unlike the typical text-based output supported by most databases , a GIS presents results visually -LRB- e.g. cartographically -RRB- in the form of maps . The visual representation of the output of spatial operations can include graphic images with vector data displayed over raster data ; the composition of several maps , each representing a single \ theme '' ; 3-D display ; animation ; and cartographic production . However , cartographic presentation sometimes highlights semantically interesting information at the expense of locational accuracy . This phenomenon is called map-generalization . 1.2 Related work and contribution The GIS data models can be categorized into field-based models and object-based models . Fieldbased models see the world as a continuous surface -LRB- layer -RRB- over which features vary -LRB- e.g. elevation -RRB- . Layer algebra -LSB- 6 -RSB- provides a field-based view . It defines a set of operations which can manipulate different layers to produce new layers . The object-based model treats the world as a surface littered with recognizable objects , which exist independent of their locations -LRB- e.g. cities , mountains , rivers -RRB- . GeO2 -LSB- 2 -RSB- , GraphDB -LSB- 11 -RSB- , GODOT -LSB- 9 -RSB- , Worboy -LSB- 22 -RSB- , OGIS -LSB- 7 -RSB- and GeoOOA -LSB- 13 -RSB- are some attempts to model GISs using the object-based approach . GeO2 provides a library of spatial types -LRB- e.g. point , line , chain -RRB- and operations on these types -LRB- e.g. intersect , overlap -RRB- . OGIS provides a set of geometric classes to facilitate data exchange across different GISs . It focuses on interoperability . GeoSAL , Worboy and GODOT propose extensive class hierarchies to model the geometry and topology of spatial objects . GraphDB supports the explicit modeling and querying of graphs . GeoOOA uses classical object-oriented analysis for geographical applications . It adds a geographic dimension to each object-modeling and spatial entity , and it supports a fixed set of geometric types and topological relationships . The GERM -LSB- 19 -RSB- model attempts to unify the two approaches and provides a set of concepts as an add-on to the ER model for modeling GISs . These models do not explicitly support the discretization process , which consists of interpolation to invert the discretization and processing of raw sensor data . This omission leads to several complexities in the existing models , including the dichotomy between field and object-based approaches . This paper proposes a new model called the GISER model -LRB- Geographic Information System Entity Relational Model -RRB- . This model explicitly represents the discretization aspects so as to unify the two approaches . GISER distinguishes two types of features . One has objects like rivers , mountains , etc. which are identified by names and which sometimes change their locations -LRB- e.g. rivers -RRB- . Others such as elevation , water-level , etc. are dependent on their locations in space and time and are usually identified by their locations . As an example , a mound 10 feet high may not have a name , whereas every mountain -LRB- elevation > 2000 feet -RRB- has a name . So it is natural to use the field view to model elevation , and to use the object view to model mountains . GISER extends the Enhanced Entity Relationship -LRB- EER -RRB- -LSB- 14 -RSB- model to include continuous fields . The continuous fields are associated with discretizations and interpolation models . GISER also uses procedure-valued attributes within the EER model . This is not a major departure , as most modern databases support procedure-valued fields , e.g. the interpolation model . GISER also attempts to support the whole GIS process : from the input of data measured and discretized to the display of this entity and all the data processing that must be performed . GISER has distinct identifiable components corresponding to each functional unit . 1.3 Scope and Outline of Paper The remainder of this paper focuses on the data-modeling aspects of a GIS . Section 2 presents various data-modeling requirements of a GIS . Section 3 defines and presents the GISER model . Section 4 presents modeling of the TMC application using the GISER Model . Section 5 concludes the paper with the implications of the GISER model for the implementation of GISs and future work . 2 Data Modeling Requirements In this section , various requirements of a GIS in relation to each of its functional units will be outlined in an informal manner . Readers are referred to -LSB- 16 -RSB- for a more formal discussion . Table 1 summarizes the modeling requirements on which this paper will focus . Functional Unit Data Modeling Requirement Examples / Issues Data Input Data Consistency and Quality Constraints , Interpretation Continuous Space Discretization , Interpolation models Data Modeling Geometry Points , curves , polygons etc Topology Networks , Partitions Data Manipulation Set Operations , Spatial Relationships , Topological , Direction , Metric Network Analysis Result Presentation Visual Representation Visualization constraints , Maps Table 1 : Summary of Requirements 2.1 Data Input Unit The key data-modeling issues for the data-input unit relate to data quality and to the discretization of continuous space . Data Consistency and Quality : The measurement and discretization process is prone to errors and inaccuracies . Raw geographic measurement data is often processed and interpreted . It is processed to filter noise or out-of-range data . Then it is interpreted to fit a domain prototype , and from that , outliers are removed . If such data is used in an analysis , the results of the analysis would need to be interpreted within the error tolerance of the data . Thus , accurate representation of data is critical for the proper use of geographic data in decision making -LSB- 3 -RSB- . Discretizing Continuous Space : Geographic phenomena occupy continuous space . However , computers and digital databases can only store and manipulate their discrete approximations . The process of discretization raises the issue of interpolation , which estimates the values at various points to generate a cartographic presentation . Triangulation-based discretization allows simple interpolation . Discretization could either be uniform , i.e. independent of the spatial entity that it is modeling -LRB- e.g. laying a rectangular grid over a continuous 2-dimensional domain -RRB- , or it could be dependent on it -LRB- e.g. a thematic layer -LSB- 19 -RSB- -RRB- . A layer is a mapping from a domain of non-overlapping geometric regions to a domain of attribute values . In a simple case , a thematic layer consists of a set of polygons , with each polygon being an area of constant value for an attribute . Thematic polygons are weak entities . These entities do not exist , except to determine the values of an attribute . 2.2 Data Model Geographic entities have geometric and topological aspects . Geometry : Geographical entities have geometric properties which can be modeled by the measurements , properties and relationships of points , lines , angles , surfaces , etc. . In GIS research and practice , two types of geometric data-types are prevalent : Vector data and Raster data . Vector entities include points , lines , and polygons , all of which are representations of the space occupied by real-world entities . Raster data is characterized as an array of points , where each point represents the value of an attribute for a real-world area . Baumann -LSB- 1 -RSB- gives a more thorough description of various raster image types . Topology : Some geographic entities have topological properties which are unaltered by elastic deformations . Examples include the connectedness of a region and the connectivity between road intersections via road segments . Primitives are required for representing networks , graphs and partitions as high-level entities -LSB- 11 -RSB- . Partitions are related to networks in that they associate regions with other regions by relationships such as next , adjacent , etc. . Networks and partitions can be decomposed into points , lines and regions for modeling ; however , that complicates behavioral modeling -LRB- e.g. an operation such as the shortest-path computation -RRB- and manipulation . It is more natural to use a direct construct for networks , partitions , etc. . Additional discussion of topology in GISs can be found in the Worboy model -LSB- 21 , 20 -RSB- . 2.3 Data Manipulation Capabilities Queries in GISs often involve set operations on the geometric and topological properties of spatial entities . These set operations could be classified into the following groups : ffl Spatial Selection : A subset from an entity set that fulfills a spatial predicate . Some examples are : Find all cities in Minnesota , Find all cities no more than 500 miles from Minneapolis . ffl Spatial Join : A spatial join produces a set of pairs of spatial objects from two layers/entities that satisfies a spatial predicate . For example : For each river , find all cities within 50 miles . ffl Transformation : A Transformation synthesizes a set of layers -LRB- a set of spatial objects -RRB- into a new layer using spatial predicates . Some examples are : Map generalization , transformation of vector layer to raster representation . ffl Network Analysis : A network Analysis represents a set of queries on spatial networks , such as route evaluation , network overlay and path optimization . A route evaluation is concerned with aggregating attribute data over route-units . A route-unit represents a collection of arcs with common characteristics -LRB- e.g. name -RRB- . A network overlay enables the integration of disparate network-attribute databases , which join two or more sets of attributes . Path Optimization models several problems , including shortest path analysis , optimum tour routing , etc. . Queries in GISs use spatial relationships within the query predicates . Spatial relationships can be distinguished into 3 categories -LSB- 10 -RSB- : ffl Topological relationships : These include connected , adjacent , inside , and disjoint . These are invariable under topological transformations like translation , scaling , and rotation . ffl Direction relationships : These include above , below , or north of , southwest of . ffl Metric relationships : These include relationships such as the distance between two entities . 2.4 Result Presentation Facilities Results in GISs are visually represented in the form of maps , tables , plots , etc. . Visual representation should be able to present all the required information and should not present any information which is not intended . Geographic data is most often displayed on a map . But information on a map is sometimes distorted to show some useful feature . For example , the road map in Figure 1 shows each road-segment as a straight line . In light of such distortions , maps should be used with caution . Different traffic features related to the road-map are shown using other types of visual representation including a plot , a bar-chart , a scatter-plot , and a scatter-glyph-plot . A B C D E F G Volume of Traffic Time of the day on 4/1/96 number of traffic congestions month of year 1996 ramp meter interval in seconds hour of day on 4/1/96 accident severity low med high ct jan feb mar ct pc t t Truck : t Person : p Car : c month of year 1996 Scatter Glyph Plot Scatter Plot Plot Bar-chart Figure 1 : Road Map -LRB- Network -RRB- and Traffic Properties 3 The GISER Data Model d u o Attribute Entity Relationship Weak Entity Multivalued Attribute disjoint union overlappingIdentifying relationshipdirection inheritance sub-entitiessub-entities Figure 2 : Enhanced Entity Relationship -LRB- EER -RRB- Model The Geographical Information System Entity Relationship -LRB- GISER -RRB- model is shown in Figure 3 . It uses the Enhanced Entity Relationship -LSB- 14 -RSB- 1 diagram notation described in figure 2 , along with dashed lines for continuous fields and relationships . The GISER model is based on 4 major concepts : Space/Time , Features , Coverages and Spatial Objects . Space and time represent boundless multidimensional extents in which geographic phenomena and events can occur and have relative position and direction . GISER is a continuous field and may possibly be discretized into realms and calendars if needed . Examples include of realms the surface of the earth and its subsets of interest . Features represent geographic phenomena such as rivers , vegetation , cities , etc. . GISER models features as continuous fields varying over space and time , but features as such can not be stored in a GIS . These must go through the process of discretization in order to compute coverages which are then stored in a GIS . A feature may have multiple coverages based on multiple discretization with varying resolution , accuracy , and sources . A coverage consists of a set of spatial objects . A spatial object occupies a subset of space and time . It has geometric and/or topological properties . A geographic object -LRB- e.g. the Mississippi river -RRB- consists of a spatial object and a non-spatial object . The spatial object represents the location and spatial extent of the river at some point in time . The non-spatial object represents other attributes such as its name . 3.1 Data Input Unit The GISER model specifies the following characteristics for a data input unit of a GIS : Data Consistency and Quality : GISER provides the relationship refined by to support the data collection process as well as multiple levels of refinements . GISER states that raw data is refined into processed data , which is refined into interpreted data . Ancillary descriptive data , 1See Appendix A for an introduction to EER model . d d O Surface Curve Point consists of Visualization Constraints has metric topological direction rel . with Feature ProperCommon Feature Representation Visual by discretized Interpolation Model varies over located at topology of determines Topology Partitions Networks determines shape of Geometry Complex Primitive Volume d 1 n 11 1 n 1 1 n 1 n 1 n meta-data n refined by 1 n Feature Space , Time Coverage Spatial Object source/sencor displays join selection transform n/w analysis Figure 3 : The GISER Model often called meta-data , is provided to facilitate the interpretation and use of the processed data . Meta-data on each coverage would document the refinement procedure and the source . Continuous Space Modeling : GISER includes continuous fields named features and space/time as well as the relationship discretized by to support continuous space . Features represent the spacevarying characteristics of a GIS entity . Each feature represents a mapping from space to a domain of values . Examples of features include elevation , soil-type , and water-level . Some features are Proper Features , which represent a collection of uniquely named geographic places such as rivers , cities and countries . Each instance of these entities has a unique name , and the entity 's geographic location can sometimes change . For example , rivers like the Mississippi flood and change their courses over time . Features which are not proper features are Common Features . A common feature is identified by its location in space and time and does not have an identification of its own . These entities can be regarded as weak entities which are dependent on and identified by their spatial locations . Examples of common features are land parcels and political boundaries . In order to accurately model these entities , GISER makes explicit the fact that continuous entities are discretized for representation in the database system . Features are discretized to give coverages . There could be multiple coverages for the same feature depending on the source/sensor . Different interpolation models need to be used for different coverages to retrieve a feature . Specifically , GISER includes the relationship discretized by with the attributes interpolation model and source/sensor to model this . A coverage has multiple spatial objects , and is modeled with the rela - tionship consists of . A spatial object occupies a subset of space and time , and is modeled using the relationship located at . Features occupies a subset of space and time and its attribute takes values defined for a subset of space and time . This is modeled using the relationship varies over . 3.2 Data Model GISER provides the following concepts to meet the data modeling requirements of a GIS : Geometry : In the GISER model , Geometry is an entity which is related to a spatial object by the relationship determines shape of . Additional entities represent the primitives such as points , lines , polygons , etc. as proposed in related models -LSB- 7 , 20 -RSB- . Topology : Topology is a property belonging to a spatial object and that property remains unaltered even when the object deforms . An example is a road network . The two nodes in the network thus remain connected even if the path between the nodes is changed by road construction . In order to represent the topology , the basic primitives such as networks -LRB- i.e. graphs -RRB- and partitions are provided . Additional primitives can be added on lines of the Worboy model -LSB- 21 , 20 -RSB- . 3.3 Data Manipulation Capabilities Spatial relationships are added in the model to accommodate spatial operations in GIS . These relationships include topological relationships , direction relationships and metric relationships , as described in section 2.3 . These relationships serve as spatial predicates for queries in GIS . Directional relationships involve the location of the objects . Examples are north of , south of , northeast of , etc. . Topological relationships involve the regions occupied by the objects . Examples are adjacent to , inside , etc. . Metric relationships could involve the geometry and location of the objects . Examples include the distance between two objects , or the area occupied by an object . To simplify the figure , only the relationships involving Spatial Object are kept . A query in GIS is a set operation on one or more coverages to give another coverage . This set operation could be join , select , transform or analyze network . 3.4 Result Presentation Facilities GISER proposes that visual representation be specified in the database . It envisions this new database functionality as having the ability to communicate the essential properties of the display that the user requests , directly to the user interface . GISER adds the entity Visual Representation for this purpose . Visual representation consists of primitives such as text , icons , graphs and geometries like points , lines , polygons , etc. . These primitives are associated with their location and orientation inside a visual representation . In addition , certain visual constraints are associated with the relationship display . These constraints ensure that the visual representation does not convey any information which is not present in the geographic data , and that the visual representation should convey all the information requested by the user . Visualization constraints on a road map include maintaining : connectivity , i.e. that road segments which are connected should remain connected in the visual representation ; direction i.e. that the direction of various objects on the map should not change ; and location , i.e. that the distortion of the location of various objects should be maintained within acceptable ranges . Figure 1 shows a few examples of the visual representation of a road map and of the traffic properties associated with the road map . The representation plot assumes both of the keys to be continuous and ordered -LRB- e.g. time of the day , volume of traffic at the road segment -RRB- . The bar chart assumes that one attribute is discrete and that the other is continuous -LRB- e.g. month of the year , amount of traffic congestion at the intersection -RRB- . The scatter plot is a visual representation of a discrete feature and an ordered discrete feature -LRB- e.g. ramp meter interval , hour of the day -RRB- . The scatter-glyph plot is a visual representation of two discrete features -LRB- e.g. accident severity , month of the year -RRB- . 4 Case Study 4.1 An Example GIS Application Intelligent Transportation Systems -LRB- ITS -RRB- are being developed to improve the safety and efficiency of highway travel -LSB- 5 -RSB- . Major data sources and users in ITS are shown in Figure 4 . Three sources of Database Road Maps Researchers City Maps Construction Schedule Business Directory Traffic Controllers Drivers Based Highway Traffic Report 15 16 Sensors and Cameras Aerial Photographs ITS Figure 4 : ITS Data Flow data are pictured . First , sensors on the highways produce measurements of traffic flow at regular intervals . The road and highway maps represent a second source of data . The traffic reports represent a third source of information to an ITS . Data sent to drivers represents one type of result presentation in an ITS . Vehicles contain graphic display devices that display road maps and current congestions . Traffic controllers at a Traffic Management Center -LRB- TMC -RRB- may use the data . Also , researchers will often use the data from an ITS for driving simulation to study traffic management and human safety issues -LSB- 12 -RSB- . 4.2 The GISER Model of the application Detectors determines shape of Traffic Interpolation Model discretized by consists of located at route reference latitude longitude Time U clocked at Lane Segment Polygon Zone topology of Ramps Interchange Administration determines Connected Graph speed volume incident Visual representation e.g. congestion map measurement displays 1 n 11 1 n 1 n 1 meta-data refined by n visual constraints Traffic Feature Transportation Network Space Loop Detector Dataset Spatial Object Space varies over Figure 5 : Model of Loop Detector Dataset Figure 5 shows a fragment of the GISER data model for a traffic measurement data-set . It includes continuous fields -LRB- e.g. Traffic , Visual representation -RRB- , entities -LRB- e.g. loop detector dataset -RRB- and relationships -LRB- e.g. discretized by , displays -RRB- . It is based on four major concepts : transportation network space , traffic , loop-detector dataset and spatial objects . Transportation network space is a subset of geographic space consisting of freeways , highways and roads . It is a continuous space at the detailed level . It is often modeled as a collection of road interchanges and the road-segments connecting them . Traffic is the phenomenon of interest in an ITS application . It represents the movements of vehicles and pedestrians over the transportation network space . It is characterized by attributes such as speed and volume . Speed measures the average distance traveled by vehicles/pedestrians in time unit over a point or segment of transportation-network space . The volume of traffic on a road-segment refers to the number of vehicles moving across a cross-section . The loop detector dataset is a set of measurements of the traffic phenomena . The loop detector is a magnetic sensor embedded in the road pavement . It can measure the volume of traffic , i.e. the number of vehicles moving over the pavement per unit of time . Loop detectors are placed at location of interest on the transportation network . The detectors are linked to the central TMC to collect the traffic measurements over the entire network . The loop detector dataset consists of the traffic measurements and the detector locations . Detector locations are classified into area-types such as ramps , interchanges and lane segments . Several sensor groupings are of interest , including stations and administration zones . Stations group the detectors on different lanes of a road-segment at a mile-post . Administrative zones group detectors belonging to common administrative units such as cities , counties , etc. . Data Input Unit : Loop detectors provide continuous analog measurements . A local analogto-digital converter discretizes the analog readings and accumulates them for a specified time period -LRB- e.g. 30 seconds -RRB- . Errors can occur due to bad sensors , out-of-calibration sensors , communication hazards , etc. . This erroneous data needs to be filtered out at multiple levels . At one level , erroneous data may be filtered using range checks , parity checks , etc. . At another level , it may be removed by using traffic flow models and statistical methods . Traffic feature has attributes like speed , volume and occupancy . It could either be modeled as a proper feature or as a common feature . One instance of a proper feature is aggregate traffic on freeway 35W . One instance of a common feature is aggregate traffic on 35W at mile 5 . Measurements from magnetic loop detectors and cameras represent different coverages . Even the transportation network space is discretized by lanes across its width and by road segments across its length . Traffic measurements at adjacent detectors can also be interpolated over space and time using the traffic flow theory -LSB- 8 -RSB- . Data Model : The highways are often represented in more than one format , since different users of the data have different requirements . One class of users requires that the lane segments , interchanges , and ramps be represented as polygons . These users include construction engineers and researchers using driving simulators . Other users work with the topological relationships of the highway network to perform network computations . The Advanced Traveler Information Systems -LRB- ATIS -RRB- , for example , will compute routes under dynamically changing traffic conditions . Data Manipulation Capabilities : These are the useful aggregate queries for the TMC application . The metric , directional and topological relationships allow queries such as the following . ffl Spatial Selection : Show all the incidents on freeways within 5 miles north of downtown Minneapolis . ffl Spatial Join : Show the intersections of railway lines and roads in Minneapolis . ffl Spatial Transformation : Show traffic speeds on all freeway segments . Relative to speed-limit , transform 80 % ? 100 % to green , 60 % ? 80 % to yellow , blocked to red , and the rest to orange . ffl Spatial Closure : Find the shortest path between two places . Find the shortest path that covers all the road-segment to plan snow cleaning of all streets . Result Presentation Facilities : The primary visual representation for this application is a road map . A road map can visually show different road-types , i.e. one-way , two-way , or major roads , by using a different color for each road-type . A chosen path can be given a different color from other roads . Multiple attributes of the road -LRB- e.g. speed , volume -RRB- can be shown using different visual attributes of the lines -LRB- e.g. color , thickness , shape -RRB- . As an example , on the freeway map , show road segment as green if traffic is moving at 80 % ? 100 % of posted speed , as yellow if at 60 % ? 80 % , as red if blocked and all others as orange . Other ancillary visual representations like plots , bar-charts , etc. . can also be used , as shown in Figure 1 . The plot for the time of the day and the traffic volume is used for identifying rush hours . The bar chart for the amount of traffic congestion and month of the year is used to analyze seasonal variation . The scatter plot for the ramp-meter interval and the hour of the day can be used to correlate ramp-meter rates with traffic volumes for validation of ramp meter rates . The scatter-glyph plot for accident severity and month of the year can be used to analyze seasonal variation in type and frequency of accidents so as to improve safety . 5 Discussions The GISER data model integrates the field-based and object-based models of geographic data by using the discretizes relationship between feature fields and coverage entity . This leads to a simple data model for geographic data like the loop-detector dataset in transportation , which is based on the concepts of space/time , features , coverages and spatial objects . Several data management aspects of data input , modeling , query and result presentation can be supported by the simple integrated model . GISER implementation using current relational and object databases raises the issues of implementation of continuous fields -LRB- i.e. features -RRB- . A possible approach is to consider continuous fields to be derived data , which is not physically stored in the database . A procedure to derive continuous fields from various discretizations is assumed . In the context of GIS , each coverage has an interpolation model for the discretized feature . Given perfect interpolation models , each coverage will lead to the identical continuous field feature . However , given approximate interpolation models , each coverage would yield different estimates of the feature , and these estimates will differ from each other within an estimated range . The meta-data associated with coverage will allow the interpolation of estimated feature values in the context of the approximation errors . Future work includes the evaluation of the GISER model in different GIS application domains . We would also like to expand the data model to improve the modeling of dynamic and temporal features such as a water-front . A particular manifestation of the dynamic nature of geographic data occurs in modeling the boundaries of lakes , oceans and other natural phenomena . The geometric extent of oceans is dynamic , differing a great deal between low-tide and high-tide . Some work to model temporal structures in the context of object databases is in -LSB- 15 -RSB- . Acknowledgments This work was supported by the Federal Highway Authority -LRB- FHWA -RRB- , the Intelligent Transportation Institute -LRB- University of Minnesota -RRB- , Computing Devices International -LRB- Minneapolis -RRB- , and the Minnesota Department of Transportation . Portions of this work was done when S. Sarkar was at the Unisys RDBMS group in Roseville , Minnesota . The comments from A. Elhaddi -LRB- National Weather Service -RRB- , Christiane Mccarthy , Siva Ravada and Andrew Fetterer have greatly improved the readability and technical accuracy . References -LSB- 1 -RSB- Peter Baumann . \ Management of Multidimensional Discrete Data '' . Very Large Databases Journal , 3 -LRB- 4 -RRB- :401 -LCB- 444 , October 1994 . -LSB- 2 -RSB- D. Benoit , R. Laurent , and S. Guylaine . \ GeO2 : Why Objects in a Geographical DBMS ? '' . In D. Abel and B. C. Ooi -LRB- Eds . -RRB- , Advances in Spatial Databases 3rd Symposium , SSD ' 93 , Berlin , 1993 . Springer-Verlag . -LSB- 3 -RSB- C. R. Elshchlager and M. F. Goodchild . Dealing with Uncertainty in Categorical Coverage Maps . In Proceedings of the International Conference on ACM Geographical Information System Workshop , 1994 . -LSB- 4 -RSB- P. Chen . \ The Entity Relationship Model -LCB- Toward a Unified View of Data '' . ACM Transaction on Database System , 1 -LRB- 1 -RRB- , March 1976 . -LSB- 5 -RSB- W.C. Collier and R.J. Weiland . \ Smart Cars , Smart Highways '' . IEEE Spectrum , April 1994 . -LSB- 6 -RSB- V. Delis , Th . Hadzilacos , and N. Tryfona . \ An Introduction To Layer Algebra '' . Technical Report CTI-94 .01.2 , Computer Technology Institute , University of Patras , Greece , 1994 . -LSB- 7 -RSB- Draft Base Document-OGIS Project Document 94-025R1 . The Open Geodata Interoperability Specification , October 1994 . -LSB- 8 -RSB- Daniel L. Gerlough and Matthew J. Huber . \ Traffic Flow Theory : A Monograph '' . Special Report 165 , Transportation Research Board National Research Council , Washington DC , 1974 . -LSB- 9 -RSB- O. Gunther and W.F. Riekert . \ The Design of GODOT : An Object-Oriented Geographical Information System '' . IEEE Data Engineering Bulletin , 16 -LRB- 3 -RRB- , 1993 . -LSB- 10 -RSB- R. Guting . \ An Introduction to Spatial Database Systems '' . Very Large Databases Journal , 3 -LRB- 4 -RRB- , 1994 . -LSB- 11 -RSB- R. H. Guting . \ GraphDB : Modeling and Querying Graphs in Databases '' . In Proc . of Intl Conference on Very Large Data Bases , 1994 . -LSB- 12 -RSB- P.A. Hancock , S. Shekhar , J.K. Caird , and M. Coyle . \ Human Factors Safety Issues in IVHS '' . Human Factors Journal , 1991 . -LSB- 13 -RSB- Georg Kosters , Bernd-Uwe Pagel , and Hans-Werner Six . \ Object-Oriented Requirements Engineering for GIS - Applications '' . In Proceedings of the Internatinal Conference on ACM Geographical Information System , 1995 . -LSB- 14 -RSB- Shamkant B. Navathe . \ Evolution of Data Modeling for Databases '' . Communications of the ACM , 35 -LRB- 9 -RRB- , September 1992 . -LSB- 15 -RSB- N. Pissinou , K. Maki , and Y. Yesha . \ On temporal modeling in the context of object Databases '' . 22 -LRB- 3 -RRB- , 1993 . -LSB- 16 -RSB- G.C. Roman . \ Formal Specification of Geographic Data Processing Requirements '' . IEEE Trans . on Knowledge and Data Engineering , 2 -LRB- 4 -RRB- , December 1990 . -LSB- 17 -RSB- S. Shekhar and D. R. Liu . \ CCAM : A Connectivity-Clustered Access Method for Aggregate Queries on Transportation Networks '' . In Proc . of the Eleventh Intl. . Conf . on Data Eng . -LRB- An extended version to appear in IEEE Transaction on Knowledge and Data Eng . -RRB- . IEEE , March 1995 . -LSB- 18 -RSB- S. Shekhar , S. Ravada , V. Kumar , D. Chubb , and G. Turner . \ Load-Balancing in High Performance GIS : Decluste polygonal Maps '' . In Proceedings of the 4th International Symposium on Large Spatial Databases . -LRB- An extended version to appear in IEEE Transaction on Knowledge and Data Eng . -RRB- , August 1995 . -LSB- 19 -RSB- Nectaria Tryfona and Thanasis Hadzilacos . \ Geographic Applications Development : Models and Tools for the Conceptual Level '' . In Proceedings of the International Conference on ACM Geographical Information System , 1995 . -LSB- 20 -RSB- M. F. Worboy . \ Object-oriented Approaches to Geo-referenced Information '' . Intl Journal of Geographical Information Systems , Taylor & Francis , 8 -LRB- 4 -RRB- , 1994 . -LSB- 21 -RSB- M. F. Worboy , H. M. Hearnshaw , and D. J. Maguire . `` Object-oriented Data Modeling for Spatial Databases '' . Intl Journal of Geographical Information Systems , Taylor & Francis , 4 -LRB- 4 -RRB- , 1990 . -LSB- 22 -RSB- M.F. Worboy , K.T. Mason , and B.R.P Dawson . The Object-Based Paradigm for a Geographic Database System : Modeling , Design , and Implementation Issues , chapter 10 , pages 91 -LCB- 102 . John Wiley & Sons , 1993 . A Basic Concepts in Data Models A GIS provides data abstraction by hiding details of data storage many database users do not need . A data model is the main tool for providing this abstraction . A data model is a set of concepts that can be used to describe the semantics of a GIS dataset . By the semantics of a GIS dataset we mean the data types , relationships , and constraints that should hold for the data . Data models can be categorized by the types of concepts they provide to structure data . High-level or conceptual data models provide concepts that are close to the way many users perceive data , whereas low-level or physical data models describe the details of how data should be stored . A popular conceptual data model , namely the entity relationship -LRB- ER -RRB- model , uses concepts such as entities , attributes and relationships -LSB- 4 -RSB- . An entity represents a concept or a real-world object , such as a city that is stored in the database . An attribute represents some property of interest that further describes an entity for example city 's name . A relationship among two or more entities represents an interaction among the entities . An entity type usually has an attribute whose values are distinct for each instance . Such an attribute is called a key attribute . Some entity types may not have any key attributes of their own ; they are called weak entity types . A weak entity is identified by its relation to a specific identity type called an identifying owner , and by some of their shared attribute values . The relationship of a weak entity to its identifying owner is the identifying relationship . ER diagrams are used to graphically represent instances of ER models . A representative symbols for ER diagrams is shown in figure 2 . The Enhanced-ER -LRB- EER -RRB- model enhances an ER model to include the concepts of subclass and superclass and the related concepts of specialization and generalization . In many cases , an entity type has numerous additional subgroupings of its entities that are meaningful and need to be represented explicitly because of their significance to the database application . For example , the entities that are members of the ROAD entity type may be further grouped into FREEWAY , HIGHWAY , and so on . The entity-type ROAD is the superclass for the subclasses FREEWAY , etc. . Also a subclass could be viewed as the specialization of the superclass or a superclass could be viewed as the generalization of the subclasses . A subclass inherits all the attributes of a superclass . This characteristic is called class inheritance . The notation d is used to specify that the subclasses of a specialization must be disjoint . If the subclasses are not disjoint , their sets of entities may overlap , and then the notation o is used . If a subclass is the union of multiple superclasses , the notation u is used . In an Object-Oriented -LRB- OO -RRB- data model each instance of an entity is modeled as an object which includes a behavior description . It provides object encapsulation . Objects are comprised of both methods and data operations . Methods could also be viewed as procedure-valued attributes . This model also provides the notion of class and inheritance .

O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B O B O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O B O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

data modeling
discretization
gis
interpolation

giser enhanced entity-relationship modeling