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SPATIAL MODELING

SPATIAL MODELING. SUMBER: www.people.iup.edu/.../ Spatial %20 Analysis %20Techlectures%20fall06. p ...‎. Spatial Modeling. According to Chou (1997), a Spatial Model:

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SPATIAL MODELING

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  1. SPATIAL MODELING SUMBER: www.people.iup.edu/.../Spatial%20Analysis%20Techlectures%20fall06.p...‎

  2. Spatial Modeling • According to Chou (1997), a Spatial Model: • 1. Analyzes phenomena by identifying explanatory variables that are significant to the distribution of the phenomenon and providing information about the relative weight of each variable • 2. Is useful for predicting the probable impact of a potential change in “control” factors (independent variables)

  3. Spatial Modeling: Pemikiranttg Model Model dapatbersifat : • Descriptive atauPrescriptive • Deterministic atauStochastic • Static atau Dynamic • Deductive atau Inductive .

  4. Spatial Modeling Tipe-tipe Model Spatial: • Descriptive: characterization of the distribution of spatial phenomena • Explanatory: deal with the variables impacting the distribution of a phenomena • Predictive: once explanatory variables are identified, predictive models can be constructed • Normative: models that provide optimal solutions to problems with quantifiable objective functions and constraints

  5. Spatial Modeling • More specific types of spatial models: • Binary models (descriptive): use logical expressions to identify or select map features that do or do not meet certain criteria…How? • Index models (descriptive): use index values calculated for variables to produce a ranked spatial surface…How? • Weighted Linear Combination Model • Regression models (explanatory or predictive): a dependent variable is related or explained by independent variables in an equation…How? • Linear and logistic regression • Process (explanatory or predictive): integrate existing knowledge about environmental processes into a set of relationships and equations for quantifying those processes…How?

  6. Spatial Modeling • Steps in the Modeling Process • Define the goals of the model • Break down the model into elements • Implementation and calibration of the model • Model validation • Sometimes difficult or not feasible

  7. The Role of GIS in Spatial Modeling • How can GIS enable spatial modeling? • GIS is a tool that can integrate a myriad of data sources • GIS can incorporate raster and/or vector data into modeling schemes • Modeling may take place within a GIS, or require linking to other computer programs • Loose coupling • Tight coupling • Embedded System

  8. Spatial Modeling • Important Issues in Conducting Spatial Analysis: • Delineation of geographic units of analysis • How do you choose geographic units of analysis so that spatial analyses are valid? • Identification of structural and spatial factors that impact spatial analysis • Structural – impact site • Spatial – impact situation (absolute and relative location, neighborhood effects)

  9. Stormwater modeling project logic Based on TR-55 • First issued by the US SCS in 1975, today Natural Resource Conservation Service (NRCS) • Presents simplified procedures for addressing stormwater during initial overland flow (runoff, peak discharge, hydrographs, and storage volumes for detention ponds)

  10. Stormwater modeling project logic TR-55 • Stormwater runoff calculation • based on Runoff Curve Number (CN) method • CN - empirically derived number • Product of hydrologic soil group, cover type, treatment, hydrologic condition, and antecedent runoff condition • Also – Percent impervious surface

  11. Network Analysis • Network analysis: the spatial analysis of linear (line) features • Your text distinguishes between several different types of lines • Network analysis involves 2 types of problems: • analyzing structure (connectivity pattern) of networks • analyzing movement (flow) over the network system • Network analysis is often a major part of subfields that are related to transportation: transportation geography, transportation planning, civil engineering, etc.

  12. Linear Regression Models: Logic and Assumptions • Assumptions (predicted vs. actual values): • Errors have the expected mean value of zero • Errors are independent of each other • Correlations among independent variables should not be high

  13. Analisis Network Kosenp-konsep: • Network • Line segment(s)/Links • Nodes (and vertices) • Impedance • Topology • Dynamic Segmentation

  14. Network Analysis: Network Structure • Evaluation of Network Structure: • Index: the ratio of the actual number of links to the maximum possible number of links 3(n-2) (n = # of nodes)…range between 0-1 • Index: the ratio of the actual number of circuits to the maximum number of circuits (c/(2n-5))…evaluation in terms of the number of ways to get from one node to another

  15. Network Analysis: Network Structure • Network Diameter: the maximum number of steps required to move from any node to any other node using shortest possible routes over as connected network • Network Connectivity: an evaluation of nodal connectivity over a network based on direct and indirect connections (expressed through the construction of matrices c1, c2, c3)

  16. Network Analysis: Network Structure • Network Accessibility: can be evaluated based on nodes or the entire network…the accessibility network is many times called the T matrix • T matrix is the sum of all connectivity matrices up to the level equal to the network diameter (i.e. c3 or c4) • Logically this makes sense if you are trying to evaluate total connectivity of a node or the entire network • How do we read the matrix?

  17. Network Analysis: Network Structure • Network Structure in a Valued Graph • The previously discussed measures of network structure are based on either counting links and/or nodes….what element are we missing with these? • Q. What is a valued graph? A. A matrix is constructed in which every link (line segment) in a network is coded with an impedance measure (such as what?) • An often-used type of valued graph is the minimal spanning tree…satisfies 3 criteria: • Can a GIS construct a minimal spanning tree?

  18. Network Analysis: Normative Models of Network Flow • Normative models are those that are designed to determine a best or optimal solution based on specific criteria • Simple Shortest Path Algorithm: • Involves finding the “path” or route with the minimum cumulative impedance between nodes on a network • Requires an impedance matrix (such as a valued graph) and a set of interative procedures: • GIS must know which nodes are connected to which…multi-step evaluation of connectivity and least cumulative impedance (distance, time, cost, etc.)

  19. Network Analysis: Normative Models of Network Flow • The Traveling Salesman Problem: • 2 “constraints” – 1) the salesman must stop at each location once 2) the salesman must return to the origin of travel (there can be variations) • The objective is to determine the path or route that the “salesman” can take to minimize the total impedance value of the trip • Often a heuristic method is used…beginning with an initial random tour, a series of locally optimal solutions is run by swapping stops that cause a reduction in cumulative impedance (an iterative procedure is also described in your book on pp. 236-244).

  20. Network Analysis: Normative Models of Network Flow • Various Types of Network Problems: • Shortest Path Analysis (Best Route) • Simple shortest path • Traveling Salesman • Closest Facility • Allocation (Define Service Area) • Location-Allocation: solves problems matching supply and demand by using sets of objectives and constraints • P-median, max covering, max equity

  21. Network Analysis: Normative Models of Network Flow • Dynamic Segmentation Data Model: The ability to derive the locations of events in relation to linear features dynamically…not reliant upon the existing topology of a network • Models linear features using routes and events… • Routes: represent dynamic linear features • Events: phenomena that occur at locations along line segments • Dynamic segmentation is used to operationalize network analysis in ArcInfo/ArcGIS

  22. Interpolasi Spatial

  23. Interpolasi Spatial

  24. Interpolasi Spatial

  25. With Anisotopy Mean= .01694 RMS = 2.862 Avg. Stan Error = 3.441 Mean Stan. = .004232 RMS Stan. = .8324 Without Anisotopy Mean= .0002331 RMS = 2.857 Avg. Stan Error = 3.424 Mean Stan. = .0006747 RMS Stan. = .8347 Ordinary Kriging Comparison

  26. With Anisotopy Mean= .04253 RMS = 2.595 Avg. Stan Error = 2.354 Mean Stan. = .01806 RMS Stan. = 1.102 Without Anisotopy Mean= .0001592 RMS = 3.054 Avg. Stan Error = .8181 Mean Stan. = .001031 RMS Stan. = 3.731 Universal Kriging Comparison

  27. PersamaanRegresi • TWOYR = -3.538 + 0.06031 * AVGCURV + 0.03331 * PERCIMPV • TENYR = -4.156 + 0.07806 * AVGCURV + 0.04368 * PERCIMPV

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