1. Spatio-Temporal Database Constraints for Spatial Dynamic Simulation Bianca Maria Pedrosa Luiz Camolesi Júnior Gilberto Câmara Marina Teresa Pires Vieira INPE UNIMEP

2. Outline Spatial dynamic systems TerraML computational environment Variability in simulation process A land-use change application

3. Spatial dynamic systems f ( I (t n ))... F F f ( I (t) )f ( I (t+2) )f ( I (t+1) ) Spatial dynamic systems simulates spatio-temporal processes in which the state of a location, on the Earth´s surface, changes over time, due to some physical phenomena.

4. t p - 20 t p - 10 tptp calibration t p + 10 Forecast Dynamic spatial models fonte: Almeida et al (2003)

5. Spacial dynamic system elements Transition Rules FuzzyL(Clue) Expander(Dinâmica) LocalMean (Riks) Models discrete hybrid continuous Dinâmica Riks Clue

6. Space representation Neighborhood modelo celular Spacial dynamic system elements uniform proprieties regular structure proximitry matrix non stationary

7. TerraML Cell-based modeling languageTerraLib Modeling Language Hybrid Automata Temporal database constraints control mode jump condition flow condition New

8. Constraints Transitions are processes representing evolution and therefore subject to constraints, which are preconditions to limit, avoid or force a change Variability is a feature to establish the possibility and the change limits of objects Variability is associated to object attributes or processes to model the structural, functional and behavioral characteristics of elements in real world

9. Variability in simulation process Invariant –Defined to attributes that cannot be changed –Are used to represent immutable or stable characteristics Variant –Defined to attributes whose alterations are highly provable –Support Evolution, involution or revolution of object or processes

10. Dimensioning the limits Moment –A time instant value Granularity –Precision domain of time instant (ISO 2000) Orientation –Reference system (Gregorian calendar) Direction –All orientation has a origin moment and everything happens after or before this moment (UTC) Application –The use of temporal representation, allowing the semantic recognition of the time datatype

11. Expressing Variability conditions M in I M before I M after I M before I time MI I M I M M I M I

12. TerraML Schema

15. A land use change applicattion

16. GLOBAL LOCAL Demand > 0 Potential >0 Global mode (for all cells) –Calculate/update the Demand in each time step –Calculate/update the Global Demand in each time step Local mode (for each cell) –Calculate the cell´s potencial for change –Select/alocate cells to change, based on demand

17. Local mode equations

18. TerraML script <database host="localhost" path="c:/tese_dados/" name="rondonia.mdb" user="" pass=" />

19. TerraML script <constraint <mode name=LOCAL

20. TerraML script

21. 19851988 19911994 Simulation result samples

22. Conclusion The constraints model proposed is based on semantic representation of variability to transitions in simulations. The model proposed support both variant and invariant conditions and seems to cover the most frequent situations in environment systems. Future efforts will focus on extending constraints to support the orientation and direction aspects of time representation