SPATIAL MODELING

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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)

Spatial Modeling: Pemikiran ttg Model

Model dapat bersifat :–Descriptive atau Prescriptive–Deterministic atau Stochastic–Static atau Dynamic–Deductive atau Inductive .

Spatial Modeling

Tipe-tipe Model Spatial:1. Descriptive: characterization of the distribution of

spatial phenomena2. Explanatory: deal with the variables impacting the

distribution of a phenomena3. Predictive: once explanatory variables are

identified, predictive models can be constructed 4. Normative: models that provide optimal solutions

to problems with quantifiable objective functions and constraints

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?

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

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

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)

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)

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

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.

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

Analisis Network

Kosenp-konsep:1. Network2. Line segment(s)/Links3. Nodes (and vertices)4. Impedance5. Topology 6. Dynamic Segmentation

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

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)

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?

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?

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.)

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).

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

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

Interpolasi Spatial

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Interpolasi Spatial

Ordinary Kriging Comparison

• 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

Universal Kriging Comparison

• 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

Persamaan Regresi

1. TWOYR = -3.538 + 0.06031 * AVGCURV + 0.03331 * PERCIMPV

2. TENYR = -4.156 + 0.07806 * AVGCURV + 0.04368 * PERCIMPV