spaal&analysis&and&modeling& (gist&4302/5302)&
TRANSCRIPT
Spa$al Analysis and Modeling (GIST 4302/5302)
Guofeng Cao Department of Geosciences
Texas Tech University
Representa$on of Spa$al Data
Representa$on of Spa$al Data Models
• Object-‐based model: treats the space as populated by discrete, iden$fiable en$$es each with a geospa$al reference – Buildings or roads fit into this view – GIS SoNwares: ArcGIS
• Field-‐based model: treats geographic informa$on as collec$ons of spa$al distribu$ons – Distribu$on may be formalized as a mathema$cal func$on from a spa$al
framework to an aRribute domain – PaRerns of topographic al$tudes, rainfall, and temperature fit neatly into
this view. – GIS SoNware: Grass
Field-‐based Approach
Spa$al fields • If the spa$al framework is a Euclidean plane and the aRribute domain is a subset of the set of real numbers; – The Euclidean plane plays the role of the horizontal xy-‐plane – The spa3al field values give the z-‐coordinates, or “heights” above
the plane
Imagine placing a square grid over a region and measuring aspects of the climate at each node of the grid. Different fields would then associate locations with values from each of the measured attribute domains.
Regional Climate Varia/ons
Proper$es of the aRribute domain • The aRribute domain may contain values which are
commonly classified into four levels of measurement – Nominal a7ribute: simple labels; qualita$ve; cannot be ordered; and arithme$c operators are not permissible
– Ordinal a7ribute: ordered labels; qualita$ve; and cannot be subjected to arithme$c operators, apart from ordering
– Interval a7ributes: quan$$es on a scale without any fixed point; can be compared for size, with the magnitude of the difference being meaningful; the ra$o of two interval aRributes values is not meaningful
– Ra3o a7ributes: quan$$es on a scale with respect to a fixed point; can support a wide range of arithme$cal opera$ons, including addi$on, subtrac$on, mul$plica$on, and division
Con$nuous and differen$able fields
• Con3nuous field: small changes in loca$on leads to small changes in the corresponding aRribute value
• Differen3able field: rate of change (slope) is defined everywhere
• Spa$al framework and aRribute domain must be con$nuous for both these types of fields
• Every differen$able field must also be con$nuous, but not every con$nuous field is differen$able
One dimensional examples • Fields may be ploRed as a graph of aRribute value against spa$al framework
Continuous and differentiable; the slope of the curve can be defined at every point
One dimensional examples The field is continuous (the graph is connected) but not
everywhere differentiable. There is an ambiguity in the slope, with two choices at the articulation point between the two
straight line segments.
Continuous and not differentiable; the slope of the curve cannot be defined at one or more points
One dimensional examples The graph is not connected and so the field in not continuous
and not differentiable.
Not continuous and not differentiable
Two dimensional examples
• The slope is dependent on the par$cular loca$on and on the bearing at that loca$on
Representa$ons of Spa$al Fields
• Points • Contours • Raster/La`ce • Triangula$on (Delaunay Trangula$on)
Example
• Contour lines and raster
Example
• Trangula$ons
Side Note: Delaunay Triangula$on and Voronoi Diagram
• Dual Graph
Opera$ons on fields
• A field opera$on takes as input one or more fields and returns a resultant field
• The system of possible opera$ons on fields in a field-‐based model is referred to as map algebra
• Three main classes of opera$ons – Local – Focal – Zonal
Neighborhood func$on • Given a spa$al framework F, a neighborhood func3on
n is a func$on that associates with each loca$on x a set of loca$ons that are “near” to x
Local opera$ons • Local opera3on: acts upon one or more spa$al fields to produce a new field
• The value of the new field at any loca$on is dependent on the values of the input field func$on at that loca$on ● is any binary opera$on
Local opera$ons • Typical opera$ons:
– Raster calculator
Focal opera$ons • Focal opera3on: the
aRribute value derived at a loca$on x may depend on the aRributes of the input spa$al field func$ons at x and the aRributes of these func$ons in the neighborhood n(x) of x
Focal opera$ons • Typical opera$ons:
– Slope – Aspect – Hill shade
• Focal sta$s$cs
Zonal opera$ons • Zonal opera3on: aggregates values of a field over a set of zones (arising in general from another field func$on) in the spa$al framework
• For each loca$on x: 11 Find the Zone Zi in which x is contained
22 Compute the values of the field func$on f applied to each point in Zi
3 Derive a single value ζ(x) of the new field from the values computed in step 2
Zonal opera$ons • Typical opera$ons:
– Zonal – Viewshed – Watershed
More on Watershed Analysis
The terrain flow informa$on model for deriving channels, watersheds, and flow related terrain
informa$on. Raw DEM Pit Removal (Filling)
Flow Field Channels, Watersheds, Flow Related Terrain Information
Watersheds are the most basic hydrologic landscape elements
Courtesy of Dr. David G. Tarboton
The Pit Removal Problem
• DEM crea$on results in ar$ficial pits in the landscape
• A pit is a set of one or more cells which has no downstream cells around it
• Unless these pits are removed they become sinks and isolate por$ons of the watershed
• Pit removal is first thing done with a DEM
Increase eleva$on to the pour point eleva$on un$l the pit drains to a neighbor
Pit Filling
7 7 6 7 7 7 7 5 7 79 9 8 9 9 9 9 7 9 911 11 10 11 11 11 11 9 11 1112 12 10 12 12 12 12 10 12 1213 12 10 12 13 13 13 11 13 1314 10 10 11 14 14 14 12 14 1415 10 10 10 10 15 15 13 15 1515 10 10 10 10 16 16 14 16 1615 11 11 11 11 17 17 14 17 1715 15 15 15 15 18 18 15 18 18
Pit Filling
7 7 6 7 7 7 7 5 7 79 9 8 9 9 9 9 7 9 911 11 10 11 11 11 11 9 11 1112 12 8 12 12 12 12 10 12 1213 12 7 12 13 13 13 11 13 1314 7 6 11 14 14 14 12 14 1415 7 7 8 9 15 15 13 15 1515 8 8 8 7 16 16 14 16 1615 11 11 11 11 17 17 6 17 1715 15 15 15 15 18 18 15 18 18
Pits Pour Points
Original DEM Pits Filled
Grid cells or zones completely surrounded by higher terrain
The lowest grid cell adjacent to a pit
80 74 63
69 67 56
60 52 48
80 74 63
69 67 56
60 52 48
30
45.02304867
=−
50.0305267
=−Slope:
Hydrologic Slope - Direction of Steepest Descent
30
2 2 4 4 8
1 4 16
1 2 4 8 4
4 1 2 4 8
2 4 4 4 4
2 1
Eight Direction (D8) Flow Model
32
16
8
64
4
128
1
2
Grid Network
0 0 0 0 0
0
0
1
0
0
0
0
0
0 2 2 2
10 1
0 14 4 1
19 1
0 0 0 0 0
0
0
1
0
0
0
0
0
0
2 2 2
10 1
0
1 4
14
19 1
Flow Accumulation Grid. Area draining in to a grid cell
0 0 0 0 0
0
0
1
0
0
0
0
0
0
2 2 2
10 1
0
1 4
14
19 1
Flow Accumulation > 10 Cell Threshold
0 0 0 0 0
0
0
1
0
0
0
0
0
0 2 2 2
1
0
4 1 1
10
14
19
Stream Network for 10 cell Threshold Drainage Area
1 1 1 1 1
1
1
2
1
1
1
1
1
1
3 3 3
11 2
1
2 5
15
20 2
The area draining each grid cell includes the grid cell itself.
1 1 1 1 1
1
1
2
1
1
1
1
1
1 3 3 3
11 2
1
5 2 2 25
15
Contribu$ng area conven$on
Watershed Draining to Outlet
Summary of Key Processing Steps
• [DEM Recondi$oning] • Pit Removal (Fill Sinks) • Flow Direc$on • Flow Accumula$on • Stream Defini$on • Stream Segmenta$on • Catchment Grid Delinea$on • Raster to Vector Conversion (Catchment Polygon, Drainage Line, Catchment Outlet Points)
Summary Concepts • The eight direc$on pour point model approximates the surface flow using eight discrete grid direc$ons
• The eleva$on surface represented by a grid digital eleva$on model is used to derive surfaces represen$ng other hydrologic variables of interest such as – Slope – Flow direc$on – Drainage area – Catchments, watersheds and channel networks
Summary: Object-‐based vs Field-‐based models
From: hRp://resources.arcgis.com/en/help/main/10.2/index.html#/How_features_are_represented_in_a_raster/009t00000006000000/
Summary: Object-‐based vs Field-‐based models
• Object-‐based models: – Greater precision – Less redundant informa$on (smaller storage footprints)
– Complex data structures • Field-‐based models:
– Simpler data structures – More redundant informa$on (larger storage footprints)
– Less precision • Raster is faster, but vector is corrector
Raster <-‐> Vector
• Vector-‐> Raster – Interpola$on
• Inverse distance weighted, Kriging, Spline – Density surface
• Kernel density – Rasteriza$on
• Raster-‐>Vector – Watershed – Vectoriza$on (raster to polygon) – …
Model Builder
Model Builder • Model Builder is a drag-‐and-‐drop interface to ArcToolbox called ModelBuilder allowing you to develop a flow chart of your GIS workflow
• This flowchart is then run step by step to perform your analysis
• ArcGIS allows for custom scrip$ng that can be added to ArcToolbox, introducing greater func$onality
• Custom export scripts, specialized versions of exis$ng tools, develop tools not available in ArcToolbox
Why Model Builder? • Developing a model for a GIS analysis allows for repeat tes$ng of a hypothesis using different data.
• The model can be coded into a GIS applica$on, so that the steps are performed automa$cally.
• Easier reproduc$on of results. • Simplifica$on of workflow. • Informs the computer how to conduct a series of steps that would be imprac$cal for you to do manually.
Reproducibility
• In performing an analysis, you must have your workflow clearly defined.
• This ensures that you are performing the steps in the correct order using the appropriate tools.
• Missteps are easy, especially when there can be hours of computer processing between steps.
• The GIS model can be exported as a graphic flowchart or a modeling data structure.
Workflow Efficiency
• There are many repe$$ve steps you will take in your daily workflow.
• Streamlining the process saves you $me. • If you always start working in a File Geodatabase with specific resolu$on and projec$on informa$on, a model for genera$ng your specialized GDB can be created.
Human Inefficiency
• You physically cannot perform the steps as fast as GIS can produce the results.
• Certain steps, such as itera$on through a feature set would be prohibi$vely $me consuming.
• Minimize the amount of $me spent “babysi`ng” GIS to perform complex analyses.
Inside ArcToolbox
Demo • Demo • Lab: Buffalo commons using Model Builder: