GIS Final Exam Ms state

Local operation

Cell By Cell operations , a local operation computes each cell value in the output raster as a math function of input cell

Neighborhood Operations

It involves a focal cell and a set of its surrounding cells

Zonal operations

Working with two raster data layers.

-One layer defines the zones

-the other contains the values to be analyzed within those zones

Global Operation- Distance

Euclidean Distance and Cost Distance.

-Euclidian Distance tool measures Straight line Distance from each cell to the closest source.

Map algebra operations

-Local operations

-Neighborhood operation

-Zonal operation

-Global Operation

Two types of Terrain analysis

Raster based- DEM (Digital elevation Model)

Vector Based- TIN (Triangulated irregular network )

Errors in DEM -how are they classified

Global Error -Displacement of DEM can
be corrected by geometric transformation

Relative Error - errors are local - significant errors
relative to neighboring elevations
– Artificial peaks and sinks
– This can be corrected by Filling DEM data

Slope

Identifies the maximum rate of change in value fro each cell to its neighbors.

Output raster can be calculated as

Percent slope or degree of slope

Viewshed Analysis

refers to the portion of the land surface that is visible from one or more viewpoints

Basis of analysis in viewshed is

line of sight operation or sight line connects the point and the target

WaterShed

is an area of land that drains all the
streams and rainfall to a common outlet such as the
outflow of a reservoir, mouth of a bay, or any point
along a stream channel (USGS).
• A watershed is a hydrological unit that is often used
for the management and planning of natural
resources

Watershed Delineation

Process of using DEMs and raster data operations to Delineate watersheds and to derive topographic features such as stream networks

WaterShed delineation takes place at various scales

-for the entire stream system

-an individual tributary

-area based or point based

Most DEMs include local

Sinks or Depressions

Sinks are problematic bc

any water that flows into them cannot flow out. To ensure
proper drainage mapping, these depressions
can be filled using the Fill tool

• The number of sinks in each DEM is normally
higher for coarser resolution DEMs

• It is not uncommon to find 1% of the cells in a
30-meter-resolution DEM to be sinks

Flow Direction

this raster shows the direction water will flow out of a cell of a filled elevation raster

Water can flow only into

One Cell

GIS models assumes

No sinks

Calculation for flow direction of the center cell

maximum_drop = change_in_z-value /
distance * 100

Flow accumulation

-tabulates for each cell the number of cells that will flow to it

-It record the number of upstream cells contributing to drainage to each cell

Stream Links

Each section of the stream raster line is assigned a unique value
and is associated with flow direction

Strahler Method

It is the most common Stream ordering Method

Streve Method

All exterior Links are assigned an order of 1

Point based watershed

Task is to delineate watershed basin for a
point of interest – ex.
Dam
• These points of interest
are called pour points
or outlets
• The point should be on
the stream link

Descriptive Analysis what to describe

What is the “location” or “center” of the
data? (“measures of location”)
• How do the data vary? (“measures of
variability”)

Measures of location

Mean

Median

Mode

1st Law Of Geography/ Tobler’s Law

Everything is related to everything else, but near things are more related than distant things. - Waldo Tobler

Spatial patterns

Clustered

Dispersed

Random

Spatial AutoCorrelation

correlation of a variable with itself through space.
• Measures of spatial autocorrelation describe the
degree to which observations (values) at spatial
locations (whether they are points, areas, or raster
cells), are similar to each other. So we need two
things: observations and locations.

positive spatial autocorrelation

If nearby or neighboring areas are more alike, this is

Negative autocorrelation

Describes patterns in which neighboring areas are unlike

No spatial autocorrelation

Random Pattern exhibit

Measuring spatial autocorrelation

Morans I

Oldest indicators of spatial autocorrelation
(Moran, 1950)
• It is a Global indicator
• Compares the value of the variable at any one
location with the value at all other location

Moran’s I > 0

Indicates positive spatial autocorrelation (similar values
cluster together)

Moran’s I < 0

Indicates negative spatial autocorrelation (dissimilar
values cluster together)

Moran's I ≈ 0

Suggests a random spatial pattern with no significant
autocorrelation

P- value

indicates the statistical significance of the observed spatial
autocorrelation. It helps determine whether the spatial pattern is likely
due to chance or if it reflects a meaningful spatial structure.

p-value < 0.05

Typically indicates significant spatial autocorrelation
(either positive or negative) with a 95% confidence level, suggesting that
the observed spatial pattern is unlikely due to random chance.

High/Low Clustering :
G - Statistic

s also a Global statistic
• Defined: a spatial statistic that measures the clustering of
high and low values in a dataset

G-statistic computes Z score

+ Z values and significant p value = clustering of high values
• -Z values and significant p value = clustering of low values
• (Z score is basically a Std. Deviation)

Local Indicator of Spatial Association

LISA = a local statistic (local Moran’s I)

Computes a Z score and p values for every
point or polygon.
• A high I score indicates that the feature is
adjacent to features of similar values
• A high negative I score indicates that the
feature is adjacent to features of dissimilar
values.

Hotspot Analysis (Ord – Getis)

Local G statistic
• Computes a Z score for every feature
– A cluster of high positive z scores suggests the
presence of a cluster of high values or a ‘hotspot’
– A cluster of high negative z scores suggests the
presence of a cluster of low values or a ‘coolspot’

Moran’s I = measure of autocorrelation

Tells whether like values are close to each other
• Based on distance and the value

LISA = local measure of autocorrelation

For each point/polygon indicates whether the adjacent of nearest
feature is similar of dissimilar

G-statistic = global statistic

shows if there is significant clustering of like high values

Ord-Getis = hot spot analysis, local statistic

tells whether a particular high value is close to one another
• Or whether a low value is close to another low value (coolspot)

Statistical Surfaces

Terrain is one type of surface. Here input data are typically limited to a sample of point data

Spatial Interpolation

process of using points
with known values to estimate values at other
points
– Precipitation, Snow accumulation, ..

2

1st Law of Geography

Waldo Tobler Law: "Everything is related to
everything else, but near things are more related
than distant things.

Global Interpolation

Uses every known available value to estimate and unknown value to capture general trend

Local interpolation

uses a sample of known points to estimate an unknown value to estimate local or short range variation

Exact interpolation

predicts a value at the point location that is the same as its known value , the surface passes through the control point

Inexact interpolation

Predicts a value at the point location that differ from its known value

Deterministic Interpolation

Provides no assessment of errors with predicted values

stochastic method

offers assesment of prediction errors with estimated variances

Thiessen polygons method

It assumes that any point within a
polygon is closer to the polygon’s
known point than any other known
points
– Initially developed to estimate
the areal averages of
precipitation
– These are also called Voronoi
polygons

IDW

Inverse distance weighted interpolation

IDW

assumes that each measured point has a local influence that diminishes with distance.
• It gives greater weights to points closest to the prediction location, and the weights diminish as a function of distance, hence the name inverse distance weighted.

In IDW

all the estimated values are between Max and Min values of known points

Spline

an exact interpolation model

Spline details

spline bends a sheet of rubber that passes
through the input points while minimizing the
total curvature of the surface.
• This method is best for generating gently
varying surfaces such as elevation, water table
heights.

Regularized Type

creates a smooth, gradually
changing surface with values that may lie
outside the sample data range

Tension Type

controls the stiffness of the surface according to the character of the
modeled phenomenon. It creates a less smooth surface with values more closely constrained by the sample data range

Spline vs IDW

Unlike IDW, the predicted values from thin-
plate splines are not limited within the range
of min and max of known points
• Problem in Spline– It can create steep
gradients in data poor areas

Line Density

Calculates a magnitude per unit
area from polyline features that fall within a
radius around each cell

Point density

Calculates a magnitude per unit
area from point features that fall within a
neighborhood around each cell.

Two density estimation methods

Simple density estimation

Kernal Density Estimation

Simple density estimation

This tool calculates the density of point
features around each output raster cell.
• A neighborhood is defined around each raster
cell center, and the number of points that fall
within the neighborhood is totaled and
divided by the area of the neighborhood.

Point density

calculates a magnitude-per-unit area from point features
that fall within a neighborhood around each cell

Line density

Calculates a magnitude-per-unit area from polyline
features that fall within a radius around each cell.

Kernal density

Calculates a magnitude-per-unit area from point
or polyline features using a kernel function to fit a
smoothly tapered surface to each point or
polyline.

Kriging -interpolation

Kriging is a geostatistical method
• It includes autocorrelation—that is, the
statistical relationships among the measured
points.
• Kriging is most appropriate when you know
there is a spatially correlated distance or
directional bias in the data

Semi variance

s a measure of the degree of spatial
dependence between observations along a specific
support

Semivariogram:

plots the average
semi-variance against the average
distance

Nugget

s the initial semi-variance
when the autocorrelation typically is
highest

Sill

is the point where the
variogram levels off; background
noise; where there is little
autocorrelation

Range

he range is the lag distance at
which the sill is reached

Anisotropy

is the term describing the existence of directional differences
in spatial dependence

Stationary:

local variation doesn’t change in different areas of the
map

Ordinary Kriging

Assumes there is no
drift or trend
Focuses only spatially
correlated component
Uses the fitted semivariogram directly
for interpolation

Universal Kriging

Assumes – that there
is a drift/trend in addition to spatial correlation between sample points
Typically universal
kriging uses 1st order
or 2nd order polynomial

Trend tool

uses a global polynomial interpolation that fits
a smooth surface defined by a mathematical function (a
polynomial) to the input sample points

A flat plane

(no bend in the piece of paper) is a first-order
polynomial (linear). Allowing one bend is a second-order
polynomial (quadratic), two bends a third-order (cubic), and
so forth. A maximum of 12 bends (twelfth order) are allowed
with this tool.

Binary model –

uses logical expressions to select spatial
features from a composite raster or multiple rasters
– 1 (true) and 0 (false)

Index model

calculate index value for each unit area

Model builder

A Model builder is generally used for simple programming where
a series of simple operations (e.g. union, clip) are chained
together to perform complex operations.

Reasons for using Model Builder

Models provide visual representation of the data and
workflow
• -Models can be reused and shared, and are easy to modify if
necessary
• -Models are much more convenient than running many tools
individually
• Reasons for not using ModelBuilder:
• -Only simple loops and conditions in comparison to “real”
programming, such as Python, C++, JAVA

Pure network

if only its topology and connectivity are
considered

flow network

If a network is characterized by its topology and flow
characteristics it is referred to as

Direct path

If a network is characterized by its topology and flow
characteristics it is referred to as

Optimum routing

Helping a pizza deliveryman visit numerous
houses in the most time – efficient manner

Closest facility:

Finding the closest hospital to an automobile
accident

A link

refers to a road segment defined by two end points
• This is a basic geometric feature of a network
• Link impedance is the cost of traversing a link

How to measure link impedance

Simple method: – measure the distance
• Distance + speed limit is more realistic
– 5 miles street & 30 miles per hour speed limit
How to measure link impedance?

Junction

a street intersection

turn

transition from one streetsegment to another at a junction

Turn impedance

time taken to complete a turn
• Turn impedance is directional

Non-planar features –

overpass and a street
underneath are shown as
continuous lines without a
node at their intersection

Multimodal network datasets

A network dataset is capable of modeling a single mode of
transportation, like roads, or a multimodal network made up of
several transportation modes like roads, railroads, and
waterways.