GIS ANALYSIS/ OPERATIONS

1. Interpolation based operations

Interpolation is the procedure of estimating the value of properties at unsampled points or areas

using a limited number of sampled observations.

Interpolation Techniques

Pointwise interpolation : Pointwise interpolation is used in case the sampled points are not

densely located with a limited influence or continuity in surrounding observations, for example

climate observations such as rainfall and temperature, or ground water level measurements at

wells.

1(a) Thiessen polygon: Thiessen polygons can be generated using distance operator which

creates the polygon boundaries as the intersections of radial expansions from the observation

points.

1(b) Weighted Average : A window of circular shape with the radius of dmax is drawn at a

point to be interpolated, so as to involve six to eight surrounding observed points.

1(c). INTERPOLATION by Inverse Distance Weighted (IDW)

1(d) Kriging

Similar to Inverse Distance Weighting (IDW), Kriging uses the minimum variance method to

calculate the weights rather than applying an arbitrary or less precise weighting scheme.

2. Interpolation by curve fitting: the principle of curve fitting respectively to interpolate the

value at an unsampled point using surrounding sampled points.

2.1 Exact interpolation: a fitted curve passes through all given points.

2. 1(a). Nearest neighbor: the same value as that of the observation is given within the

proximal distance

2. 1.(b) Linear interpolation: a piecewise linear function is applied between two

adjacent points.

2.2 Approximate interpolation :a fitted curve does not always pass through all given points

2.2(a) Moving Average: a window with a range of -d to +d is set to average the observation

within the region.

2.2 (b)Curve Fitting by Least Square Method: Least square method (sometimes called

regression model) is a statistical approach to estimate an expected value or function with the

highest probability from the observations with random errors. The highest probability is replaced

by minimizing the sum of square of residuals in the least square method.

3. Interpolation by surface fitting: the principle of surface fitting respectively to interpolate the

value at an unsampled point using surrounding sampled points.

3.1 Regular grid :

3.2 Random points: TIN ( Triangular Irregular Network)

DEM (Digital Elevationj Model) A DEM (digital elevation model) is digital representation of topographic surface with the

elevation or ground height above any geodetic datum. Followings are widely used DEM in GIS.

1.1 Density Analysis

Density analysis takes known quantities of some phenomenon and spreads them across the

landscape based on the quantity that is measured at each location and the spatial relationship of

the locations of the measured quantities.

Why map density?

Density surfaces show where point or line features are concentrated. For example, you might

have a point value for each town representing the total number of people in the town, but you

want to learn more about the spread of population over the region. Since all the people in each

town do not live at the population point, by calculating density, you can create a surface showing

the predicted distribution of the population throughout the landscape.

The following graphic gives an example of a density surface. When added together, the

population values of the cells equal the sum of the population of the original point layer.

Population density surface example

Applications of density analysis

The Density tool distributes a measured quantity of an input point layer throughout a landscape

to produce a continuous surface.

For an example application of density analysis, consider a retail store chain that has multiple

stores in a particular district. For each store, management has sales figures on customers.

Management assumes that customers patronize one store over another based on how far they

have to travel. In this example, it is natural to assume that any single customer will always

choose the closest store. The farther away from the closest store, the farther the customer will

need to travel to that store. But shoppers farther away may also shop at other stores. Management

wants to study the distribution of where the customers live. From the sales figures and the spatial

distribution of the stores, management wants to create a surface of customers by intelligently

spreading the customers out across the landscape.

To accomplish this task, the Density tool considers where each store is in relation to other stores,

the quantity of customers shopping at each store, and how many cells need to share a portion of

the measured quantity (the shoppers). The cells nearer the measured points, the stores, receive

higher proportions of the measured quantity than those farther away.

II. Understanding overlay analysis

Overlay analysis is the operation in which more than one layers in GIS environment are

collectively utilized with attribute information contained within the attribute tables. This may be

simple addition of the attributes to complex interactive tools as per requirement of the user.

Following are certain examples of the overlay tools which can be sued in different conditions to

interactively use the information in multilayer database.

Overlay analysis is a group of methodologies applied in optimal site selection or suitability

modeling. It is a technique for applying a common scale of values to diverse and dissimilar

inputs to create an integrated analysis.

Suitability models identify the best or most preferred locations for a specific phenomenon. Types

of problems addressed by suitability analysis include:

Where to site a new housing development

Which sites are better for deer habitat

Where economic growth is most likely to occur

Where the locations are that are most susceptible to mud slides

Overlay analysis often requires the analysis of many different factors. For instance, choosing the

site for a new housing development means assessing such things as land cost, proximity to

existing services, slope, and flood frequency. This information exists in different rasters with

different value scales: dollars, distances, degrees, and so on. You cannot add a raster of land cost

(dollars) to a raster of distance to utilities (meters) and obtain a meaningful result.

Additionally, the factors in your analysis may not be equally important. It may be that the cost of

land is more important in choosing a site than the distance to utility lines. How much more

important is for you to decide.

Even within a single raster, you must prioritize values. Some values in a particular raster may be

ideal for your purposes (for example, slopes of 0 to 5 degrees), while others may be good, others

bad, and still others unacceptable.

The following lists the general steps to perform overlay analysis:

1. Define the problem.

2. Break the problem into submodels.

3. Determine significant layers.

4. Reclassify or transform the data within a layer.

5. Weight the input layers.

6. Add or combine the layers.

7. Analyze.

Steps 1–3 are common steps for nearly all spatial problem solving and are particularly important

in overlay analysis.

1. Define the problem

Defining the problem is one of the most difficult aspects of the modeling process. The overall

objective must be identified. All aspects of the remaining steps of the overlay modeling process

must contribute to this overall objective.

The components relating to the objective must be defined. Some of the components may be

complimentary, and others competitive. However, a clear definition of each component and how

they interact must be established.

Not only is it important to identify what the problem is, a clear understanding needs to be

developed to define when the problem is solved, or when the phenomenon is satisfied. In the

problem definition, specific measures should be established to identify the success of the

outcome from the model.

For example, when identifying the best location for a ski resort, the overall goal may be to make

money. All factors that are identified in the model should help the ski area be profitable.

2. Break the problem into sub-models

Most overlay problems are complex, and it is recommended that you break them down into

submodels for clarity, to organize your thoughts, and to more effectively solve the overlay

problem.

For example, a suitability model for identifying the best location for a ski resort can be broken

into a series of submodels that all help the ski area be profitable. The first submodel can be a

terrain submodel identifying locations that have a wide variety of favorable terrain for skiers and

snowboarders.

3. Determine significant layers

The attributes or layers that affect each submodel need to be identified. Each factor captures and

describes a component of the phenomena the submodel is defining. Each factor contributes to the

goals of the submodel, and each submodel contributes to the overall goal of the overlay model.

All and only factors that contribute to defining the phenomenon should be included in the

overlay model.

For certain factors, the layers may need to be created. For example, it may be more desirable to

be closer to a major road. To identify the distance each cell is from a road, Euclidean Distance

may be run to create the distance raster.

Because of the potential different ranges of values and the different types of numbering systems

each input layer may have, before the multiple factors can be combined for analysis, each must

be reclassified or transformed to a common ratio scale.

Common scales can be predetermined, such as a 1 to 9 or a 1 to 10 scale, with the higher value

being more favorable, or the scale can be on a 0 to 1 scale, defining the possibility of belonging

to a specific set.

4. Weight

Certain factors may be more important to the overall goal than others. If this is the case, before

the factors are combined, the factors can be weighted based on their importance. For example, in

the building submodel for siting the ski resort, the slope criteria may be twice as important to the

cost of construction as the distance from a road. Therefore, before combining the two layers, the

slope criteria should be multiplied twice as much as distance to roads.

6. Add/Combine

In overlay analysis, it is desirable to establish the relationship of all the input factors together to

identify the desirable locations that meet the goals of the model. For example, the input layers,

once weighted appropriately, can be added together in an additive weighted overlay model. In

this combination approach, it is assumed that the more favorable the factors, the more desirable

the location will be. Thus, the higher the value on the resulting output raster, the more desirable

the location will be.

Other combining approaches can be applied. For example, in a fuzzy logic overlay analysis, the

combination approaches explore the possibility of membership of a location to multiple sets.

7. Analyze

The final step in the modeling process is for you to analyze the results. Do the potential ideal

locations sensibly meet the criteria? It may be beneficial not only to explore the best locations

identified by the model but to also investigate the second and third most favorable sites.

The identified locations should be visited. You need to validate what you think is there is

actually there. Things could have changed since the data for the model was created. For example,

views may be one of the input criteria to the model; the better the view, the more preferred the

location will be. From the input elevation data, the model identified the locations with the best

views; however, when one of the favorable sites is visited, it is discovered that a building has

been constructed in front of the location, obstructing the view.

Taking the input from all of the steps above, a location is selected.

As with all overlay analysis, in weighted overlay analysis, you must define the problem, break

the model into submodels, and identify the input layers.

Since the input criteria layers will be in different numbering systems with different ranges, to

combine them in a single analysis, each cell for each criterion must be reclassified into a

common preference scale such as 1 to 10, with 10 being the most favorable. An assigned

preference on the common scale implies the phenomenon's preference for the criterion. The

preference values are on a relative scale. That is, a preference of 10 is twice as preferred as a

preference of 5.

III. An overview of the Surface toolset

With the Surface tools, you can quantify and visualize a terrain landform.

Starting with a raster elevation surface as input, with these tools, you can gain information by

producing a new dataset that identifies a specific pattern within an original dataset. You can

derive patterns that were not readily apparent in the original surface, such as contours, angle of

slope, steepest downslope direction (Aspect), shaded relief (Hillshade), and Viewshed.

Each surface tool provides insight into a surface that can be used as an end in itself or as input

into additional analysis.

Tool Description

Aspect

Derives aspect from a raster surface. The aspect identifies the downslope

direction of the maximum rate of change in value from each cell to its neighbors.

Contour Creates a line feature class of contours (isolines) from a raster surface.

Contour List Creates a feature class of selected contour values from a raster surface.

Contour with

Barriers

Creates contours from a raster surface. The inclusion of barrier features will

allow one to independently generate contours on either side of a barrier.

Curvature Calculates the curvature of a raster surface, optionally including profile and plan

curvature.

Cut Fill

Calculates the volume change between two surfaces. This is typically used for

cut and fill operations.

Hillshade

Creates a shaded relief from a surface raster by considering the illumination

source angle and shadows.

Observer

Points

Identifies which observer points are visible from each raster surface location.

Slope

Identifies the slope (gradient, or rate of maximum change in z-value) from each

cell of a raster surface.

Viewshed Determines the raster surface locations visible to a set of observer features.

1. Cut and Fill

IV. Types of network analysis layers

Network Analyst allows you to solve common network problems, such as finding the best route

across a city, finding the closest emergency vehicle or facility, identifying a service area around a

location, servicing a set of orders with a fleet of vehicles, or choosing the best facilities to open

or close.

• Network: a set of interconnected line entities, whose attributes share some common

theme primarily related to flow

• Network in GIS: a topology-based line coverage

• Geometric Network in ArcGIS: a feature data set comprised of feature classes: edges and

junctions, and their connectivity defined by topology rules

Network Elements

• Links - “Conduits” for movement

• Intersections - Link joins

• Stops - Sources/sinks where resources can enter or exit the network

• Centers - node locations which may receive or provide

resources. Attributes for total amount of resource supplied to

or taken from a center, e.g., total water capacity for a reservoir

• Barriers - nodes which prevent flow through links, or links with infinite impedance

• Impedance - a resistance to flow through a link. Impedance may be directionally

dependent , Impedance is assumed to be uniform over the link.

Impedance = 5 min/mile

Impedance = 10 min/mile

Preparing a Network

Step 1: Prepare a network coverage,

Step 2: edit the coverage to represent network elements and update its topology

Step 3: attribute with link impedances

Step 4: generate attribute based on input attributes

Step 5: display results

Network Applications

1. Shortest / Critical Path Analysis

Paths, flow, tours

2. Allocation

Supply, impedance

3. Location-Allocation

supply and demand, objective function

Shortest Path Analysis

Finding the shortest or least-cost manner in which to visit a series of locations in a

network. The cost may be determined by distance or by travel-time or a

combination of factors calculated as a cost value.

Often the parameter that is minimized in path finding is travel time. This factors in

things like topography, traffic volume, average speed, stops etc.

The Dijkstra’s algorithm is used to solve a single-source shortest-path problem

At each step the algorithm chooses the shortest path from a list of candidate paths

and places the node of the shortest path in the solution list

Route

Network Analyst can find the best way to get from one location to another or to visit several

locations. The locations can be specified interactively by placing points on the screen, entering an

address, or using points in an existing feature class or feature layer. If you have more than two

stops to visit, the best route can be determined for the order of locations as specified by the

user. Alternatively, ArcGIS Network Analyst can determine the best sequence to visit the

locations.

What's the best route?

Whether finding a simple route between two locations or one that visits several locations, people

usually try to take the best route. But "best route" can mean different things in different

situations.

The best route can be the quickest, shortest, or most scenic route, depending on the impedance

chosen. If the impedance is time, then the best route is the quickest route. Hence, the best route

can be defined as the route that has the lowest impedance, where the impedance is chosen by

the user. Any valid network cost attribute can be used as the impedance when determining the

best route.

In the example below, the first case uses time as an impedance. The quickest path is shown in

blue and has a total length of 4.5 miles, which takes 8 minutes to traverse.

In the next case, distance is chosen as the impedance. Consequently, the length of the shortest

path is 4.4 miles, which takes 9 minutes to traverse.

Along with the best route, Network Analyst provides directions with turn-by-turn maps that can

be printed.

Closest facility

Finding the closest hospital to an accident, the closest police cars to a crime scene, and the

closest store to a customer's address are all examples of closest facility problems. When finding

closest facilities, you can specify how many to find and whether the direction of travel is toward

or away from them. Once you've found the closest facilities, you can display the best route to or

from them, return the travel cost for each route, and display directions to each facility.

Additionally, you can specify an impedance cutoff beyond which Network Analyst should not

search for a facility. For instance, you can set up a closest facility problem to search for hospitals

within 15 minutes' drive time of the site of an accident. Any hospitals that take longer than 15

minutes to reach will not be included in the results.

The hospitals are referred to as facilities, and the accident is referred to as an incident. Network

Analyst allows you to perform multiple closest facility analyses simultaneously. This means you

can have multiple incidents and find the closest facility or facilities to each incident.

Service areas

With Network Analyst, you can find service areas around any location on a network. A network

service area is a region that encompasses all accessible streets, that is, streets that lie within a

specified impedance. For instance, the 10-minute service area for a facility includes all the

streets that can be reached within 10 minutes from that facility.

What is accessibility?

Accessibility refers to how easy it is to go to a site. In ArcGIS Network Analyst, accessibility can

be measured in terms of travel time, distance, or any other impedance on the network.

Evaluating accessibility helps answer basic questions, such as, How many people live within a

10-minute drive from a movie theater? or How many customers live within a half-kilometer

walking distance from a convenience store? Examining accessibility can help you determine how

suitable a site is for a new business. It can also help you identify what is near an existing

business to help you make other marketing decisions.

Evaluating accessibility

One simple way to evaluate accessibility is by a buffer distance around a point. For example, find

out how many customers live within a 5-kilometer radius of a site using a simple circle. However,

considering people travel by road, this method won't reflect the actual accessibility to the site.

Service networks computed by ArcGIS Network Analyst can overcome this limitation by

identifying the accessible streets within five kilometers of a site via the road network. Once

created, you can use service networks to see what is alongside the accessible streets, for

example, find competing businesses within a 5-minute drive.

Multiple concentric service areas show how accessibility changes with an increase in impedance.

It can be used, for example, to show how many hospitals are within 5-, 10-, and 15-minute drive

times of schools.

V. Location-allocation

Location-allocation helps you choose which facilities from a set of facilities to operate based on

their potential interaction with demand points. It can help you answer questions like the

following:

Given a set of existing fire stations, which site for a new fire station would provide the

best response times for the community?

If a retail company has to downsize, which stores should it close to maintain the most

overall demand?

Where should a factory be built to minimize the distance to distribution centers?

In these examples, facilities would represent the fire stations, retail stores, and factories;

demand points would represent buildings, customers, and distribution centers.

The objective may be to minimize the overall distance between demand points and facilities,

maximize the number of demand points covered within a certain distance of facilities, maximize

an apportioned amount of demand that decays with increasing distance from a facility, or

maximize the amount of demand captured in an environment of friendly and competing facilities.

The map below shows the results of a location-allocation analysis meant to determine which fire

stations are redundant. The following information was provided to the solver: an array of fire

stations (facilities), street midpoints (demand points), and a maximum allowable response time.

The response time is the time it takes firefighters to reach a given location. The location-

allocation solver determined that the fire department can close several fire stations and still

maintain a three-minute response time.

VI. Buffer (Analysis)

One of the most basic questions asked of a GIS is "what's near what?" For example:

How close is this well to a landfill?

Do any roads pass within 1,000 meters of a stream?

What is the distance between two locations?

What is the nearest or farthest feature from something?

What is the distance between each feature in a layer and the features in another layer?

What is the shortest street network route from some location to another?

The Proximity toolset contains tools that are used to determine the proximity of features

within one or more feature classes or between two feature classes. These tools can identify

features that are closest to one another or calculate the distances between or around them.

This operation Creates buffer polygons around input features to a specified distance. An optional

dissolve can be performed to combine overlapping buffers.

BUFFER OPERATIONS

Tools Description

Buffer Creates buffer polygons around input features to a specified distance. An optional

dissolve can be performed to combine overlapping buffers.

Create

Thiessen

Creates Thiessen polygons from point input features.

Each Thiessen polygon contains only a single point input feature. Any location within

Polygons a Thiessen polygon is closer to its associated point than to any other point input

feature.

Multiple Ring

Buffer

Creates multiple buffers at specified distances around the input features. These

buffers can optionally be merged and dissolved using the buffer distance values to

create non-overlapping buffers.

Generate

Near Table

Determines the distances from each feature in the input features to one or more

nearby features in the near features, within the search radius. The results are

recorded in the output table.

Near Determines the distance from each feature in the input features to the nearest

feature in the near features, within the search radius.

Point Distance Determines the distances from input point features to all points in the near features

within a specified search radius.

Feature-based proximity tools

For feature data, the tools found in the Proximity toolset can be used to discover proximity

relationships. These tools output information with buffer features or tables. Buffers are usually

used to delineate protected zones around features or to show areas of influence. For example,

you might buffer a school by one mile and use the buffer to select all the students that live more

than one mile from the school to plan for their transportation to and from school. You could use

the multiring buffer tool to classify the areas around a feature into near, moderate distance, and

long distance classes for an analysis. Buffers are sometimes used to clip data to a given study

area or to exclude features within a critical distance of something from further consideration in

an analysis.

Buffer and Multiple Ring Buffer create area features at a specified distance (or several specified

distances) around the input features.

Below are examples of buffered lines and points:

Buffers can be used to select features in another feature class, or they can be combined with

other features using an overlay tool, to find parts of features that fall in the buffer areas. Below

is an example of buffered points overlaid with polygon features:

The Near tool calculates the distance from each point in one feature class to the nearest point or

line feature in another feature class. You might use Near to find the closest stream for a set of

wildlife observations or the closest bus stops to a set of tourist destinations. The Near tool will

also add the Feature Identifier and, optionally, coordinates of and the angle toward the nearest

feature.

Below is an example showing points near river features. The points are symbolized using

graduated colors based on distance to a river, and they're labeled with the distance.

Point Distance calculates the distance from each point in one feature class to all the points within

a given search radius in another feature class. This table can be used for statistical analyses, or

it can be joined to one of the feature classes to show the distance to points in the other feature

class.

You can use the Point Distance tool to look at proximity relationships between two sets of things.

For example, you might compare the distances between one set of points representing several

types of businesses (such as theaters, fast food restaurants, engineering firms, and hardware

stores) and another set of points representing the locations of community problems (litter,

broken windows, spray-paint graffiti), limiting the search to one mile to look for local

relationships. You could join the resulting table to the business and problem attribute tables and

calculate summary statistics for the distances between types of business and problems. You

might find a stronger correlation for some pairs than for others and use your results to target the

placement of public trash cans or police patrols.

You might also use Point Distance to find the distance and direction to all the water wells within a

given distance of a test well where you identified a contaminant.

Below is an example of point distance analysis. Each point in one feature class is given the ID,

distance, and direction to the nearest point in another feature class.

Below is the Point Distance table, joined to one set of points and used to select the points

that are closest to point 55.

Both Near and Point Distance return the distance information as numeric attributes in the input

point feature attribute table for Near and in a stand-alone table that contains the Feature IDs of

the Input and Near features for Point Distance.

Create Thiessen Polygons creates polygon features that divide the available space and allocate it

to the nearest point feature. The result is similar to the Euclidean Allocation tool for rasters.

Thiessen polygons are sometimes used instead of interpolation to generalize a set of sample

measurements to the areas closest to them. Thiessen polygons are sometimes also known as

Proximal polygons. They can be thought of as modeling the catchment area for the points, as the

area inside any given polygon is closer to that polygon's point than any other.

Below is an example of Thiessen polygons for a set of points.

You might use Thiessen polygons to generalize measurements from a set of climate instruments

to the areas around them or to quickly model the service areas for a set of stores.

Layer and Table View tools

Select Layer By Location allows you to change the set of selected features in ArcMap by finding

features in one layer that are within a given distance of (or share one of several other spatial

relationships with) features in another feature class or layer. Unlike the other vector tools, Select

By Location does not create new features or attributes. The Select Layer By Location tool is in

the Layers and Table Views toolset, or you can Select By Location from the ArcMap Selection

menu.

Below is an example where points within a given distance of other points are selected—the

buffers are shown only to illustrate the distance.

Network distance tools

Some distance analyses require that the measurements be constrained to a road, stream, or

other linear network. Network Analyst lets you find the shortest route to a location along a

network of transportation routes, find the closest point to a given point, or build service areas

(areas that are equally distant from a point along all available paths) in a transportation network.

Below is an example of a Route solution for three points along a road network. The Closest

Facility solution will find locations on the network that are closest (in terms of route distance) to

an origin.

Cost distance

In contrast with the Euclidean distance tools, cost distance tools take into account that distance

can also be measured in cost (for example, energy expenditure, difficulty, or hazard) and that

travel cost can vary with terrain, ground cover, or other factors.

Given a set of points, you could divide the area between them with the Euclidean allocation tools

so that each zone of the output would contain all the areas closest to a given point. However, if

the cost to travel between the points varied according to some characteristic of the area between

them, then a given location might be closer, in terms of travel cost, to a different point.

Below is an example of using the Cost Allocation tool, where travel cost increases with land-

cover type. The dark areas could represent difficult-to-traverse swamps, and the light areas

could represent more easily traversed grassland.

This is in some respects a more complicated way of dealing with distance than using straight

lines, but it is very useful for modeling movement across a surface that is not uniform.

Below is an example that contrasts the surface length of a line feature in rough terrain with its

planimetric length.

Proximity tools

Vector distance tools

Tool Location What it does

Buffer Proximity toolset Creates new feature data with feature boundaries at a

specified distance from input features

Near Proximity toolset Adds attribute fields to a point feature class containing

distance, feature identifier, angle, and coordinates of the

nearest point or line feature

Point

Distance

Proximity toolset Creates a new table with distance and feature identifier

attributes showing the distance from each point in the input

feature class to all points in the Near feature class, within a

given search radius

Select By

Location

Layers and Table

Views toolset

Selects features from a target feature class within a given

distance of (or using other spatial relationships) the input

features

Create

Thiessen

Polygons

Proximity toolset Creates polygons of the areas closest to each feature for a

set of input features

Make

Closest

Facility

Layer

Network

Analyst/Analysis

toolset

Sets analysis parameters to find the closest location or set

of locations on a network to another location or set of

locations

Make

Service Area

Layer

Network

Analyst/Analysis

toolset

Sets analysis parameters to find polygons that define the

area within a given distance along a network in all

directions from one or more locations

Make Route

Layer

Network

Analyst/Analysis

toolset

Sets analysis parameters to find the shortest path among a

set of points

Make OD

Cost Matrix

Layer

Network

Analyst/Analysis

toolset

Sets analysis parameters to create a matrix of network

distances among two sets of points

Table of vector distance tools with location and description

Raster To TIN (3D Analyst)

Summary

Converts a raster to a triangulated irregular network (TIN) dataset.