Advantages Easy to understand. Disadvantages. Systematic sampling pattern Easy Samples spaced uniformly at fixed X, Y intervals Parallel lines

Size: px
Start display at page:

Download "Advantages Easy to understand. Disadvantages. Systematic sampling pattern Easy Samples spaced uniformly at fixed X, Y intervals Parallel lines"

Transcription

1 INTERPOLATION Procedure to predict values of attributes at unsampled points Why? Can t measure all locations: Time Money Impossible (physical- legal) Changing cell size Missing/unsuitable data Past date (eg. temperature)

2 Systematic sampling pattern Easy Samples spaced uniformly at fixed X, Y intervals Parallel lines Advantages Easy to understand Disadvantages All receive same attention Difficult to stay on lines May be biases

3 Random Sampling Select point based on random number process Plot on map Visit sample Advantages Less biased (unlikely to match pattern in landscape) Disadvantages Does nothing to distribute samples in areas of high Difficult to explain, location of points may be a problem

4 Cluster Sampling Cluster centers are established (random or systematic) Samples arranged around each center Plot on map Visit sample (e.g. US Forest Service, Forest Inventory Analysis (FIA) Clusters located at random then systematic pattern of samples at that location) Advantages Reduced travel time

5 Adaptive sampling More sampling where there is more variability. Need prior knowledge of variability, e.g. two stage sampling Advantages More efficient, homogeneous areas have few samples, better representation of variable areas. Disadvantages Need prior information on variability through space

6 INTERPOLATION Many methods - All combine information about the sample coordinates with the magnitude of the measurement variable to estimate the variable of interest at the unmeasured location Methods differ in weighting and number of observations used Different methods produce different results No single method has been shown to be more accurate in every application Accuracy is judged by withheld sample points

7 INTERPOLATION Outputs typically: Raster surface Values are measured at a set of sample points Raster layer boundaries and cell dimensions established Interpolation method estimate the value for the center of each unmeasured grid cell Contour Lines Iterative process From the sample points estimate points of a value Connect these points to form a line Estimate the next value, creating another line with the restriction that lines of different values do not cross.

8

9

10 Example Base Elevation contours Sampled locations and values

11 INTERPOLATION 1 st Method - Thiessen Polygon Assigns interpolated value equal to the value found at the nearest sample location Conceptually simplest method Only one point used (nearest) Often called nearest sample or nearest neighbor

12 INTERPOLATION Thiessen Polygon Advantage: Ease of application Accuracy depends largely on sampling density Boundaries often odd shaped as transitions between polygons are often abrupt Continuous variables often not well represented

13 Thiessen Polygon Draw lines connecting the points to their nearest neighbors. Find the bisectors of each line. Connect the bisectors of the lines and assign the resulting polygon the value of the center point Source:

14 Thiessen Polygon Start: 1) 1. Draw lines connecting the points to their nearest neighbors Find the bisectors of each line. 4 2) 3) 3. Connect the bisectors of the lines and assign the resulting polygon the value of the center point

15

16

17

18

19

20

21 Sampled locations and values Thiessen polygons

22

23 INTERPOLATION Fixed-Radius Local Averaging More complex than nearest sample Cell values estimated based on the average of nearby samples Samples used depend on search radius (any sample found inside the circle is used in average, outside ignored) Specify output raster grid Fixed-radius circle is centered over a raster cell Circle radius typically equals several raster cell widths (causes neighboring cell values to be similar) Several sample points used Some circles many contain no points Search radius important; too large may smooth the data too much

24 INTERPOLATION Fixed-Radius Local Averaging

25 INTERPOLATION Fixed-Radius Local Averaging

26 INTERPOLATION Fixed-Radius Local Averaging

27 INTERPOLATION Inverse Distance Weighted (IDW) Estimates the values at unknown points using the distance and values to nearby know points (IDW reduces the contribution of a known point to the interpolated value) Weight of each sample point is an inverse proportion to the distance. The further away the point, the less the weight in helping define the unsampled location

28 INTERPOLATION Inverse Distance Weighted (IDW) Zi is value of known point Dij is distance to known point Zj is the unknown point n is a user selected exponent

29 INTERPOLATION Inverse Distance Weighted (IDW)

30 INTERPOLATION Inverse Distance Weighted (IDW) Factors affecting interpolated surface: Size of exponent, n affects the shape of the surface larger n means the closer points are more influential A larger number of sample points results in a smoother surface

31 INTERPOLATION Inverse Distance Weighted (IDW)

32 INTERPOLATION Inverse Distance Weighted (IDW)

33 INTERPOLATION Trend Surface Interpolation Fitting a statistical model, a trend surface, through the measured points. (typically polynomial) Where Z is the value at any point x Where a i s are coefficients estimated in a regression model

34 INTERPOLATION Trend Surface Interpolation

35 INTERPOLATION Splines Name derived from the drafting tool, a flexible ruler, that helps create smooth curves through several points Spline functions are use to interpolate along a smooth curve. Force a smooth line to pass through a desired set of points Constructed from a set of joined polynomial functions

36 INTERPOLATION : Splines

37 INTERPOLATION 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

38 Interpolation Kriging Method relies on spatial autocorrelation Higher autocorrelations, points near each other are alike.

39 INTERPOLATION Kriging A statistical based estimator of spatial variables Components: Spatial trend Autocorrelation Random variation Creates a mathematical model which is used to estimate values across the surface

40 Kriging - Lag distance Z i is a variable at a sample point h i is the distance between sample points Every set of pairs Z i,z j defines a distance h ij, and is different by the amount Z i Z j. The distance h ij is the lag distance between point i and j. There is a subset of points in a sample set that are a given lag distance apart

41 Kriging - Lag distance

42 INTERPOLATION Kriging Semi-variance Where Z i is the measured variable at one point Z j is another at h distance away n is the number of pairs that are approximately h distance apart Semi-variance may be calculated for any h When nearby points are similar (Z i -Z j ) is small so the semivariance is small. High spatial autocorrelation means points near each other have similar Z values

43 INTERPOLATION Kriging When calculating the semi-variance of a particular h often a tolerance is used Plot the semi-variance of a range of lag distances This is a variogram

44 INTERPOLATION Kriging When calculating the semi-variance of a particular h often a tolerance is used Plot the semi-variance of a range of lag distances This is a variogram

45 Idealized Variogram

46 INTERPOLATION (cont.) Kriging A set of sample points are used to estimate the shape of the variogram Variogram model is made (A line is fit through the set of semi-variance points) The Variogram model is then used to interpolate the entire surface

47 Variogram

48

49 INTERPOLATION (cont.) Exact/Non Exact methods Exact predicted values equal observed Theissen IDW Spline Non Exact-predicted values might not equal observed Fixed-Radius Trend surface Kriging

50 Class Vote: Which method works best for this example? Systematic Random Original Surface: Cluster Adaptive

51 Class Vote: Which method works best for this example? Original Surface: Thiessen Polygons Fixed-radius Local Averaging IDW: squared, 12 nearest points Trend Surface Spline Kriging

52 Interpolation in ArcGIS: Spatial Analyst

53 Interpolation in ArcGIS: Geostatistical Analyst

54

55

56 Validation

57

58 Interpolation in ArcGIS: arcscripts.esri.com

59 What is the Core Area?

60 Core Area Identification Commonly used when we have observations on a set of objects, want to identify regions of high density Crime, wildlife, pollutant detection Derive regions (territories) or density fields (rasters) from set of sampling points.

61 Mean Circle

62 Concave Hull Convex Hull

63

64

65 Kernal Mapping

66 Smooth density function One centered on each observation point

67 Sum these density functions

68 Sum the total, for a smooth density curve (or surface)

69 How much area should each sample cover (called bandwidth)

70 Varying bandwidths a)medium b)low h c)high h d through f are 90% density regions

71 Time-Geographic Density Estimation (TDGE)

72

73

Geography 4203 / 5203. GIS Modeling. Class (Block) 9: Variogram & Kriging

Geography 4203 / 5203. GIS Modeling. Class (Block) 9: Variogram & Kriging Geography 4203 / 5203 GIS Modeling Class (Block) 9: Variogram & Kriging Some Updates Today class + one proposal presentation Feb 22 Proposal Presentations Feb 25 Readings discussion (Interpolation) Last

More information

EXPLORING SPATIAL PATTERNS IN YOUR DATA

EXPLORING SPATIAL PATTERNS IN YOUR DATA EXPLORING SPATIAL PATTERNS IN YOUR DATA OBJECTIVES Learn how to examine your data using the Geostatistical Analysis tools in ArcMap. Learn how to use descriptive statistics in ArcMap and Geoda to analyze

More information

Understanding Raster Data

Understanding Raster Data Introduction The following document is intended to provide a basic understanding of raster data. Raster data layers (commonly referred to as grids) are the essential data layers used in all tools developed

More information

Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary

Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary Shape, Space, and Measurement- Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two- and three-dimensional shapes by demonstrating an understanding of:

More information

Using Spatial Statistics In GIS

Using Spatial Statistics In GIS Using Spatial Statistics In GIS K. Krivoruchko a and C.A. Gotway b a Environmental Systems Research Institute, 380 New York Street, Redlands, CA 92373-8100, USA b Centers for Disease Control and Prevention;

More information

Spatial Data Analysis

Spatial Data Analysis 14 Spatial Data Analysis OVERVIEW This chapter is the first in a set of three dealing with geographic analysis and modeling methods. The chapter begins with a review of the relevant terms, and an outlines

More information

Introduction to Modeling Spatial Processes Using Geostatistical Analyst

Introduction to Modeling Spatial Processes Using Geostatistical Analyst Introduction to Modeling Spatial Processes Using Geostatistical Analyst Konstantin Krivoruchko, Ph.D. Software Development Lead, Geostatistics kkrivoruchko@esri.com Geostatistics is a set of models and

More information

An Introduction to Point Pattern Analysis using CrimeStat

An Introduction to Point Pattern Analysis using CrimeStat Introduction An Introduction to Point Pattern Analysis using CrimeStat Luc Anselin Spatial Analysis Laboratory Department of Agricultural and Consumer Economics University of Illinois, Urbana-Champaign

More information

Geographically Weighted Regression

Geographically Weighted Regression Geographically Weighted Regression CSDE Statistics Workshop Christopher S. Fowler PhD. February 1 st 2011 Significant portions of this workshop were culled from presentations prepared by Fotheringham,

More information

Algebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard

Algebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express

More information

ANALYSIS 3 - RASTER What kinds of analysis can we do with GIS?

ANALYSIS 3 - RASTER What kinds of analysis can we do with GIS? ANALYSIS 3 - RASTER What kinds of analysis can we do with GIS? 1. Measurements 2. Layer statistics 3. Queries 4. Buffering (vector); Proximity (raster) 5. Filtering (raster) 6. Map overlay (layer on layer

More information

5.3.1 Arithmetic Average Method:

5.3.1 Arithmetic Average Method: Computation of Average Rainfall over a Basin: To compute the average rainfall over a catchment area or basin, rainfall is measured at a number of gauges by suitable type of measuring devices. A rough idea

More information

A Method Using ArcMap to Create a Hydrologically conditioned Digital Elevation Model

A Method Using ArcMap to Create a Hydrologically conditioned Digital Elevation Model A Method Using ArcMap to Create a Hydrologically conditioned Digital Elevation Model High resolution topography derived from LiDAR data is becoming more readily available. This new data source of topography

More information

NEW MEXICO Grade 6 MATHEMATICS STANDARDS

NEW MEXICO Grade 6 MATHEMATICS STANDARDS PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical

More information

ArcGIS Geostatistical Analyst: Statistical Tools for Data Exploration, Modeling, and Advanced Surface Generation

ArcGIS Geostatistical Analyst: Statistical Tools for Data Exploration, Modeling, and Advanced Surface Generation ArcGIS Geostatistical Analyst: Statistical Tools for Data Exploration, Modeling, and Advanced Surface Generation An ESRI White Paper August 2001 ESRI 380 New York St., Redlands, CA 92373-8100, USA TEL

More information

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 4: LINEAR MODELS FOR CLASSIFICATION Introduction In the previous chapter, we explored a class of regression models having particularly simple analytical

More information

Hydrogeological Data Visualization

Hydrogeological Data Visualization Conference of Junior Researchers in Civil Engineering 209 Hydrogeological Data Visualization Boglárka Sárközi BME Department of Photogrammetry and Geoinformatics, e-mail: sarkozi.boglarka@fmt.bme.hu Abstract

More information

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small

More information

Comparison of Programs for Fixed Kernel Home Range Analysis

Comparison of Programs for Fixed Kernel Home Range Analysis 1 of 7 5/13/2007 10:16 PM Comparison of Programs for Fixed Kernel Home Range Analysis By Brian R. Mitchell Adjunct Assistant Professor Rubenstein School of Environment and Natural Resources University

More information

Location matters. 3 techniques to incorporate geo-spatial effects in one's predictive model

Location matters. 3 techniques to incorporate geo-spatial effects in one's predictive model Location matters. 3 techniques to incorporate geo-spatial effects in one's predictive model Xavier Conort xavier.conort@gear-analytics.com Motivation Location matters! Observed value at one location is

More information

Remote Sensing, GPS and GIS Technique to Produce a Bathymetric Map

Remote Sensing, GPS and GIS Technique to Produce a Bathymetric Map Remote Sensing, GPS and GIS Technique to Produce a Bathymetric Map Mark Schnur EES 5053 Remote Sensing Fall 2007 University of Texas at San Antonio, Department of Earth and Environmental Science, San Antonio,

More information

Local classification and local likelihoods

Local classification and local likelihoods Local classification and local likelihoods November 18 k-nearest neighbors The idea of local regression can be extended to classification as well The simplest way of doing so is called nearest neighbor

More information

Intro to GIS Winter 2011. Data Visualization Part I

Intro to GIS Winter 2011. Data Visualization Part I Intro to GIS Winter 2011 Data Visualization Part I Cartographer Code of Ethics Always have a straightforward agenda and have a defining purpose or goal for each map Always strive to know your audience

More information

AP Physics 1 and 2 Lab Investigations

AP Physics 1 and 2 Lab Investigations AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks

More information

Measuring Line Edge Roughness: Fluctuations in Uncertainty

Measuring Line Edge Roughness: Fluctuations in Uncertainty Tutor6.doc: Version 5/6/08 T h e L i t h o g r a p h y E x p e r t (August 008) Measuring Line Edge Roughness: Fluctuations in Uncertainty Line edge roughness () is the deviation of a feature edge (as

More information

Chapter 6. The stacking ensemble approach

Chapter 6. The stacking ensemble approach 82 This chapter proposes the stacking ensemble approach for combining different data mining classifiers to get better performance. Other combination techniques like voting, bagging etc are also described

More information

University of Arkansas Libraries ArcGIS Desktop Tutorial. Section 2: Manipulating Display Parameters in ArcMap. Symbolizing Features and Rasters:

University of Arkansas Libraries ArcGIS Desktop Tutorial. Section 2: Manipulating Display Parameters in ArcMap. Symbolizing Features and Rasters: : Manipulating Display Parameters in ArcMap Symbolizing Features and Rasters: Data sets that are added to ArcMap a default symbology. The user can change the default symbology for their features (point,

More information

Data Mining Practical Machine Learning Tools and Techniques

Data Mining Practical Machine Learning Tools and Techniques Ensemble learning Data Mining Practical Machine Learning Tools and Techniques Slides for Chapter 8 of Data Mining by I. H. Witten, E. Frank and M. A. Hall Combining multiple models Bagging The basic idea

More information

Using kernel methods to visualise crime data

Using kernel methods to visualise crime data Submission for the 2013 IAOS Prize for Young Statisticians Using kernel methods to visualise crime data Dr. Kieran Martin and Dr. Martin Ralphs kieran.martin@ons.gov.uk martin.ralphs@ons.gov.uk Office

More information

MATHS LEVEL DESCRIPTORS

MATHS LEVEL DESCRIPTORS MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and

More information

Raster Operations. Local, Neighborhood, and Zonal Approaches. Rebecca McLain Geography 575 Fall 2009. Raster Operations Overview

Raster Operations. Local, Neighborhood, and Zonal Approaches. Rebecca McLain Geography 575 Fall 2009. Raster Operations Overview Raster Operations Local, Neighborhood, and Zonal Approaches Rebecca McLain Geography 575 Fall 2009 Raster Operations Overview Local: Operations performed on a cell by cell basis Neighborhood: Operations

More information

This is Geospatial Analysis II: Raster Data, chapter 8 from the book Geographic Information System Basics (index.html) (v. 1.0).

This is Geospatial Analysis II: Raster Data, chapter 8 from the book Geographic Information System Basics (index.html) (v. 1.0). This is Geospatial Analysis II: Raster Data, chapter 8 from the book Geographic Information System Basics (index.html) (v. 1.0). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/

More information

Big Ideas in Mathematics

Big Ideas in Mathematics Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards

More information

Objectives. Raster Data Discrete Classes. Spatial Information in Natural Resources FANR 3800. Review the raster data model

Objectives. Raster Data Discrete Classes. Spatial Information in Natural Resources FANR 3800. Review the raster data model Spatial Information in Natural Resources FANR 3800 Raster Analysis Objectives Review the raster data model Understand how raster analysis fundamentally differs from vector analysis Become familiar with

More information

Data Exploration Data Visualization

Data Exploration Data Visualization Data Exploration Data Visualization What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping to select

More information

Regression III: Advanced Methods

Regression III: Advanced Methods Lecture 16: Generalized Additive Models Regression III: Advanced Methods Bill Jacoby Michigan State University http://polisci.msu.edu/jacoby/icpsr/regress3 Goals of the Lecture Introduce Additive Models

More information

Representing Geography

Representing Geography 3 Representing Geography OVERVIEW This chapter introduces the concept of representation, or the construction of a digital model of some aspect of the Earth s surface. The geographic world is extremely

More information

Geostatistical Analyst Tutorial

Geostatistical Analyst Tutorial Copyright 1995-2012 Esri All rights reserved. Table of Contents Introduction to the ArcGIS Geostatistical Analyst Tutorial................... 0 Exercise 1: Creating a surface using default parameters...................

More information

INTRODUCTION TO GEOSTATISTICS And VARIOGRAM ANALYSIS

INTRODUCTION TO GEOSTATISTICS And VARIOGRAM ANALYSIS INTRODUCTION TO GEOSTATISTICS And VARIOGRAM ANALYSIS C&PE 940, 17 October 2005 Geoff Bohling Assistant Scientist Kansas Geological Survey geoff@kgs.ku.edu 864-2093 Overheads and other resources available

More information

Computer Graphics. Geometric Modeling. Page 1. Copyright Gotsman, Elber, Barequet, Karni, Sheffer Computer Science - Technion. An Example.

Computer Graphics. Geometric Modeling. Page 1. Copyright Gotsman, Elber, Barequet, Karni, Sheffer Computer Science - Technion. An Example. An Example 2 3 4 Outline Objective: Develop methods and algorithms to mathematically model shape of real world objects Categories: Wire-Frame Representation Object is represented as as a set of points

More information

Geostatistics Exploratory Analysis

Geostatistics Exploratory Analysis Instituto Superior de Estatística e Gestão de Informação Universidade Nova de Lisboa Master of Science in Geospatial Technologies Geostatistics Exploratory Analysis Carlos Alberto Felgueiras cfelgueiras@isegi.unl.pt

More information

GIS EXAM #2 QUERIES. Attribute queries only looks at the records in the attribute tables to some kind of

GIS EXAM #2 QUERIES. Attribute queries only looks at the records in the attribute tables to some kind of GIS EXAM #2 QUERIES - Queries extracts particular records from a table or feature class for use; - Queries are an essential aspect of GIS analysis, and allows us to interrogate a dataset and look for patterns;

More information

Charlesworth School Year Group Maths Targets

Charlesworth School Year Group Maths Targets Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve

More information

ArcGIS 9. Geostatistical Analyst

ArcGIS 9. Geostatistical Analyst ArcGIS 9 Using ArcGIS Geostatistical Analyst Copyright 2001, 2003 ESRI All Rights Reserved. Printed in the United States of America. The information contained in this document is the exclusive property

More information

Page 1 of 7 (document version 1)

Page 1 of 7 (document version 1) Lecture 2 - Data exploration This lecture will cover: Attribute queries Spatial queries Basic spatial analyses: Buffering Voronoi tessellation Cost paths / surfaces Viewsheds Hydrological modelling Autocorrelation

More information

Environmental Remote Sensing GEOG 2021

Environmental Remote Sensing GEOG 2021 Environmental Remote Sensing GEOG 2021 Lecture 4 Image classification 2 Purpose categorising data data abstraction / simplification data interpretation mapping for land cover mapping use land cover class

More information

Data Visualization Techniques and Practices Introduction to GIS Technology

Data Visualization Techniques and Practices Introduction to GIS Technology Data Visualization Techniques and Practices Introduction to GIS Technology Michael Greene Advanced Analytics & Modeling, Deloitte Consulting LLP March 16 th, 2010 Antitrust Notice The Casualty Actuarial

More information

Lesson 15 - Fill Cells Plugin

Lesson 15 - Fill Cells Plugin 15.1 Lesson 15 - Fill Cells Plugin This lesson presents the functionalities of the Fill Cells plugin. Fill Cells plugin allows the calculation of attribute values of tables associated with cell type layers.

More information

Why Count Birds? (cont.)

Why Count Birds? (cont.) AVIAN CENSUS TECHNIQUES: Why count birds? Descriptive Studies = asks what types of birds occur in a particular habitat? - Provides gross overview of bird occurrence and perhaps a crude estimate of abundance

More information

Descriptive Statistics and Measurement Scales

Descriptive Statistics and Measurement Scales Descriptive Statistics 1 Descriptive Statistics and Measurement Scales Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample

More information

Northumberland Knowledge

Northumberland Knowledge Northumberland Knowledge Know Guide How to Analyse Data - November 2012 - This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about

More information

EE4367 Telecom. Switching & Transmission. Prof. Murat Torlak

EE4367 Telecom. Switching & Transmission. Prof. Murat Torlak Path Loss Radio Wave Propagation The wireless radio channel puts fundamental limitations to the performance of wireless communications systems Radio channels are extremely random, and are not easily analyzed

More information

Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

More information

GEOENGINE MSc in Geomatics Engineering (Master Thesis) Anamelechi, Falasy Ebere

GEOENGINE MSc in Geomatics Engineering (Master Thesis) Anamelechi, Falasy Ebere Master s Thesis: ANAMELECHI, FALASY EBERE Analysis of a Raster DEM Creation for a Farm Management Information System based on GNSS and Total Station Coordinates Duration of the Thesis: 6 Months Completion

More information

Tennessee Mathematics Standards 2009-2010 Implementation. Grade Six Mathematics. Standard 1 Mathematical Processes

Tennessee Mathematics Standards 2009-2010 Implementation. Grade Six Mathematics. Standard 1 Mathematical Processes Tennessee Mathematics Standards 2009-2010 Implementation Grade Six Mathematics Standard 1 Mathematical Processes GLE 0606.1.1 Use mathematical language, symbols, and definitions while developing mathematical

More information

We can display an object on a monitor screen in three different computer-model forms: Wireframe model Surface Model Solid model

We can display an object on a monitor screen in three different computer-model forms: Wireframe model Surface Model Solid model CHAPTER 4 CURVES 4.1 Introduction In order to understand the significance of curves, we should look into the types of model representations that are used in geometric modeling. Curves play a very significant

More information

Seminar. Path planning using Voronoi diagrams and B-Splines. Stefano Martina stefano.martina@stud.unifi.it

Seminar. Path planning using Voronoi diagrams and B-Splines. Stefano Martina stefano.martina@stud.unifi.it Seminar Path planning using Voronoi diagrams and B-Splines Stefano Martina stefano.martina@stud.unifi.it 23 may 2016 This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International

More information

Assessment of Groundwater Vulnerability to Landfill Leachate Induced Arsenic Contamination in Maine, US - Intro GIS Term Project Final Report

Assessment of Groundwater Vulnerability to Landfill Leachate Induced Arsenic Contamination in Maine, US - Intro GIS Term Project Final Report Assessment of Groundwater Vulnerability to Landfill Leachate Induced Arsenic Contamination in Maine, US - Intro GIS Term Project Final Report Introduction Li Wang Dept. of Civil & Environmental Engineering

More information

In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.

In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target

More information

Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering

Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques

More information

EXPERIMENTAL ERROR AND DATA ANALYSIS

EXPERIMENTAL ERROR AND DATA ANALYSIS EXPERIMENTAL ERROR AND DATA ANALYSIS 1. INTRODUCTION: Laboratory experiments involve taking measurements of physical quantities. No measurement of any physical quantity is ever perfectly accurate, except

More information

NCTM Curriculum Focal Points for Grade 5. Everyday Mathematics, Grade 5

NCTM Curriculum Focal Points for Grade 5. Everyday Mathematics, Grade 5 NCTM Curriculum Focal Points and, Grade 5 NCTM Curriculum Focal Points for Grade 5 Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers Students

More information

An Interactive Tool for Residual Diagnostics for Fitting Spatial Dependencies (with Implementation in R)

An Interactive Tool for Residual Diagnostics for Fitting Spatial Dependencies (with Implementation in R) DSC 2003 Working Papers (Draft Versions) http://www.ci.tuwien.ac.at/conferences/dsc-2003/ An Interactive Tool for Residual Diagnostics for Fitting Spatial Dependencies (with Implementation in R) Ernst

More information

First published in 2013 by the University of Utah in association with the Utah State Office of Education.

First published in 2013 by the University of Utah in association with the Utah State Office of Education. First published in 201 by the University of Utah in association with the Utah State Office of Education. Copyright 201, Utah State Office of Education. Some rights reserved. This work is published under

More information

Introduction to time series analysis

Introduction to time series analysis Introduction to time series analysis Margherita Gerolimetto November 3, 2010 1 What is a time series? A time series is a collection of observations ordered following a parameter that for us is time. Examples

More information

Create a folder on your network drive called DEM. This is where data for the first part of this lesson will be stored.

Create a folder on your network drive called DEM. This is where data for the first part of this lesson will be stored. In this lesson you will create a Digital Elevation Model (DEM). A DEM is a gridded array of elevations. In its raw form it is an ASCII, or text, file. First, you will interpolate elevations on a topographic

More information

3D Drawing. Single Point Perspective with Diminishing Spaces

3D Drawing. Single Point Perspective with Diminishing Spaces 3D Drawing Single Point Perspective with Diminishing Spaces The following document helps describe the basic process for generating a 3D representation of a simple 2D plan. For this exercise we will be

More information

Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds

Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative

More information

GRADES 7, 8, AND 9 BIG IDEAS

GRADES 7, 8, AND 9 BIG IDEAS Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for

More information

Multi-scale upscaling approaches of soil properties from soil monitoring data

Multi-scale upscaling approaches of soil properties from soil monitoring data local scale landscape scale forest stand/ site level (management unit) Multi-scale upscaling approaches of soil properties from soil monitoring data sampling plot level Motivation: The Need for Regionalization

More information

In comparison, much less modeling has been done in Homeowners

In comparison, much less modeling has been done in Homeowners Predictive Modeling for Homeowners David Cummings VP & Chief Actuary ISO Innovative Analytics 1 Opportunities in Predictive Modeling Lessons from Personal Auto Major innovations in historically static

More information

3D Analysis and Surface Modeling

3D Analysis and Surface Modeling 3D Analysis and Surface Modeling Dr. Fang Qiu Surface Analysis and 3D Visualization Surface Model Data Set Grid vs. TIN 2D vs. 3D shape Creating Surface Model Creating TIN Creating 3D features Surface

More information

Content Sheet 7-1: Overview of Quality Control for Quantitative Tests

Content Sheet 7-1: Overview of Quality Control for Quantitative Tests Content Sheet 7-1: Overview of Quality Control for Quantitative Tests Role in quality management system Quality Control (QC) is a component of process control, and is a major element of the quality management

More information

Introduction to nonparametric regression: Least squares vs. Nearest neighbors

Introduction to nonparametric regression: Least squares vs. Nearest neighbors Introduction to nonparametric regression: Least squares vs. Nearest neighbors Patrick Breheny October 30 Patrick Breheny STA 621: Nonparametric Statistics 1/16 Introduction For the remainder of the course,

More information

Map Patterns and Finding the Strike and Dip from a Mapped Outcrop of a Planar Surface

Map Patterns and Finding the Strike and Dip from a Mapped Outcrop of a Planar Surface Map Patterns and Finding the Strike and Dip from a Mapped Outcrop of a Planar Surface Topographic maps represent the complex curves of earth s surface with contour lines that represent the intersection

More information

3. Interpolation. Closing the Gaps of Discretization... Beyond Polynomials

3. Interpolation. Closing the Gaps of Discretization... Beyond Polynomials 3. Interpolation Closing the Gaps of Discretization... Beyond Polynomials Closing the Gaps of Discretization... Beyond Polynomials, December 19, 2012 1 3.3. Polynomial Splines Idea of Polynomial Splines

More information

Annealing Techniques for Data Integration

Annealing Techniques for Data Integration Reservoir Modeling with GSLIB Annealing Techniques for Data Integration Discuss the Problem of Permeability Prediction Present Annealing Cosimulation More Details on Simulated Annealing Examples SASIM

More information

3D Drawing. Single Point Perspective with Diminishing Spaces

3D Drawing. Single Point Perspective with Diminishing Spaces 3D Drawing Single Point Perspective with Diminishing Spaces The following document helps describe the basic process for generating a 3D representation of a simple 2D plan. For this exercise we will be

More information

(Refer Slide Time: 1:42)

(Refer Slide Time: 1:42) Introduction to Computer Graphics Dr. Prem Kalra Department of Computer Science and Engineering Indian Institute of Technology, Delhi Lecture - 10 Curves So today we are going to have a new topic. So far

More information

AMARILLO BY MORNING: DATA VISUALIZATION IN GEOSTATISTICS

AMARILLO BY MORNING: DATA VISUALIZATION IN GEOSTATISTICS AMARILLO BY MORNING: DATA VISUALIZATION IN GEOSTATISTICS William V. Harper 1 and Isobel Clark 2 1 Otterbein College, United States of America 2 Alloa Business Centre, United Kingdom wharper@otterbein.edu

More information

What is GIS? Geographic Information Systems. Introduction to ArcGIS. GIS Maps Contain Layers. What Can You Do With GIS? Layers Can Contain Features

What is GIS? Geographic Information Systems. Introduction to ArcGIS. GIS Maps Contain Layers. What Can You Do With GIS? Layers Can Contain Features What is GIS? Geographic Information Systems Introduction to ArcGIS A database system in which the organizing principle is explicitly SPATIAL For CPSC 178 Visualization: Data, Pixels, and Ideas. What Can

More information

Data Mining: Exploring Data. Lecture Notes for Chapter 3. Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler

Data Mining: Exploring Data. Lecture Notes for Chapter 3. Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler Data Mining: Exploring Data Lecture Notes for Chapter 3 Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler Topics Exploratory Data Analysis Summary Statistics Visualization What is data exploration?

More information

How To Use Statgraphics Centurion Xvii (Version 17) On A Computer Or A Computer (For Free)

How To Use Statgraphics Centurion Xvii (Version 17) On A Computer Or A Computer (For Free) Statgraphics Centurion XVII (currently in beta test) is a major upgrade to Statpoint's flagship data analysis and visualization product. It contains 32 new statistical procedures and significant upgrades

More information

Introduction to the Monte Carlo method

Introduction to the Monte Carlo method Some history Simple applications Radiation transport modelling Flux and Dose calculations Variance reduction Easy Monte Carlo Pioneers of the Monte Carlo Simulation Method: Stanisław Ulam (1909 1984) Stanislaw

More information

Florida Department of Education/Office of Assessment January 2012. Grade 6 FCAT 2.0 Mathematics Achievement Level Descriptions

Florida Department of Education/Office of Assessment January 2012. Grade 6 FCAT 2.0 Mathematics Achievement Level Descriptions Florida Department of Education/Office of Assessment January 2012 Grade 6 FCAT 2.0 Mathematics Achievement Level Descriptions Grade 6 FCAT 2.0 Mathematics Reporting Category Fractions, Ratios, Proportional

More information

Lecture 9: Geometric map transformations. Cartographic Transformations

Lecture 9: Geometric map transformations. Cartographic Transformations Cartographic Transformations Analytical and Computer Cartography Lecture 9: Geometric Map Transformations Attribute Data (e.g. classification) Locational properties (e.g. projection) Graphics (e.g. symbolization)

More information

SPATIAL DATA ANALYSIS

SPATIAL DATA ANALYSIS SPATIAL DATA ANALYSIS P.L.N. Raju Geoinformatics Division Indian Institute of Remote Sensing, Dehra Dun Abstract : Spatial analysis is the vital part of GIS. Spatial analysis in GIS involves three types

More information

Introduction to spatial data analysis

Introduction to spatial data analysis Introduction to spatial data analysis 3 Scuola di Dottorato in Economia, La Sapienza, 2015/2016 Instructors: Filippo Celata, Federico Martellozzo and Luca Salvati http://www.memotef.uniroma1.it/node/6524

More information

Data Mining: Exploring Data. Lecture Notes for Chapter 3. Introduction to Data Mining

Data Mining: Exploring Data. Lecture Notes for Chapter 3. Introduction to Data Mining Data Mining: Exploring Data Lecture Notes for Chapter 3 Introduction to Data Mining by Tan, Steinbach, Kumar What is data exploration? A preliminary exploration of the data to better understand its characteristics.

More information

Classification and probabilistic description of a sand site based on CPTU

Classification and probabilistic description of a sand site based on CPTU Classification and probabilistic description of a sand site based on CPTU K. Lauridsen, S. Andersen, L. Ibsen, B. Nielsen 1 Agenda Objective of the project The test site Probabilistic interpretation of

More information

Imputing Values to Missing Data

Imputing Values to Missing Data Imputing Values to Missing Data In federated data, between 30%-70% of the data points will have at least one missing attribute - data wastage if we ignore all records with a missing value Remaining data

More information

OUTLIER ANALYSIS. Data Mining 1

OUTLIER ANALYSIS. Data Mining 1 OUTLIER ANALYSIS Data Mining 1 What Are Outliers? Outlier: A data object that deviates significantly from the normal objects as if it were generated by a different mechanism Ex.: Unusual credit card purchase,

More information

Simple Regression Theory II 2010 Samuel L. Baker

Simple Regression Theory II 2010 Samuel L. Baker SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the

More information

Integrating WAsP and GIS Tools for Establishing Best Positions for Wind Turbines in South Iraq

Integrating WAsP and GIS Tools for Establishing Best Positions for Wind Turbines in South Iraq Integrating WAsP and GIS Tools for Establishing Best Positions for Wind Turbines in South Iraq S.M. Ali Remote Sensing Research Unit, College of Science, Univ. of Baghdad, Baghdad, Iraq deanoffice {at}

More information

The primary goal of this thesis was to understand how the spatial dependence of

The primary goal of this thesis was to understand how the spatial dependence of 5 General discussion 5.1 Introduction The primary goal of this thesis was to understand how the spatial dependence of consumer attitudes can be modeled, what additional benefits the recovering of spatial

More information

A HYBRID APPROACH FOR AUTOMATED AREA AGGREGATION

A HYBRID APPROACH FOR AUTOMATED AREA AGGREGATION A HYBRID APPROACH FOR AUTOMATED AREA AGGREGATION Zeshen Wang ESRI 380 NewYork Street Redlands CA 92373 Zwang@esri.com ABSTRACT Automated area aggregation, which is widely needed for mapping both natural

More information

Algebra 1 Course Information

Algebra 1 Course Information Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through

More information

CHAPTER 1 Splines and B-splines an Introduction

CHAPTER 1 Splines and B-splines an Introduction CHAPTER 1 Splines and B-splines an Introduction In this first chapter, we consider the following fundamental problem: Given a set of points in the plane, determine a smooth curve that approximates the

More information

Working with the Raster Calculator

Working with the Raster Calculator Working with the Raster Calculator The Raster Calculator provides you a powerful tool for performing multiple tasks. You can perform mathematical calculations using operators and functions, set up selection

More information

CALCULATIONS & STATISTICS

CALCULATIONS & STATISTICS CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents

More information