VERTICAL ACCURACY ASSESSMENT OF SRTM3 V2.1 AND ASTER GDEM V2 USING GPS CONTROL POINTS FOR SURVEYING & GEOINFORMATICS APPLICATIONS

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VERTICAL ACCURACY ASSESSMENT OF SRTM3 V2.1 AND ASTER GDEM V2 USING GPS CONTROL POINTS FOR

SURVEYING & GEOINFORMATICS APPLICATIONS - Case Study of Rivers State, Nigeria

By

Emmanuel M. Menegbo

A Thesis

Submitted in Fulfilment of the Requirements for the Degree Of

Master of Science in

Geographic Information Science and Systems (UNIGIS)

Department Of Geoinformatics - ZGIS University of Salzburg

Hellbrunnerstrasse 34, A-5020 Salzburg, Austria October, 2014.

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Science Pledge

The result presented in this thesis is based on my own research, except where otherwise acknowledged, and that this thesis in whole or in part has not been submitted for an award, including a higher degree, to any other university or institution.

Signed: Emmanuel M. Menegbo

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Abstract

This thesis investigates the vertical accuracy and relevance of two widely available digital elevation models (DEMs) in surveying and Geoinformatics using Global Positioning System (GPS) ground control points. The two DEMS assessed are the Advanced Spaceborne Thermal Emission and Reflectance Radiometer (ASTER), and the Shuttle Radar Topography Mission (SRTM3). These datasets are accessed using GPS ground control points in Rivers State, Nigeria.

If vertical error is normally distributed, the factor 1.9600 is applied to compute linear error at the 95% confidence level. Vertical accuracy at 95% confidence of the Root- Mean-Square Error (RMSE) is used as the standard measure of accuracy for Vertical Accuracy positioning. Their vertical accuracy with reference to differential GPS ground control points used in this study as true heights shows the RMSE for ASTER GDEM V2 and SRTM3 V2.1 is ± 8.861734m and ± 6.307187m, with vertical accuracy of ± 17.362089m and ± 12.362086m respectively. The SRTM3 and ASTER is suitable for topographic map with contour interval of 14m and 18m interval in the region Other includes geomorphologic activities, and estimating the terrain corrections in quasi-geoid modelling in Rivers State.

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Preface

This thesis Submitted in Fulfilment of the Requirements for the Master of Science in Geographic Information Science and Systems (UNIGIS) Degree. The thesis has been made solely by me; most of the text, however, is based on the research of others, and references to these sources.

The whole thesis is divided into five (5) chapters; the introduction, literature review, accuracy assessments of DEM, results & analysis, and summary, discussion & outlook.

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Acknowledgements

The author wishes to thank all people who have provided support and encouragement for this research and its outcomes. I would also like to thank Surveyor-General of Rivers State, Surveyor Gaius and Surv. Peter Ogolo for the GCP controls and administrative map of Rivers state used for this validation, without which this would not have been possible. To my late father my appreciation for your ideas and dream for my success. Finally I would like to thank the UNIGIS Team South Africa for their understanding at my difficult moment.

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Table of Contents

Science Pledge ... ii

Abstract ... iii

Preface ... iv

Acknowledgements ... v

List of Figures ... viii

List of Tables ... ix

List of abbreviations ... ix

CHAPTER 1: INTRODUCTION ... 1

1.1 Overview... 1

1.2 Problem Statement ... 2

1.3 Aim and Objectives ... 3

1.3.1 Aim ... 3

1.3.2 Objectives ... 3

CHAPTER 2: LITERATURE REVIEW ... 5

2.1 Background Terms and Information ... 5

2.1.1 Vertical Reference System ... 5

2.1.2 Ellipsoidal Heights ... 5

2.1.4 Normal Heights ... 6

2.1.5 Geoid – Earth Gravitational Model (EGM) ... 6

2.2 Description of ASTER GDEM and SRTM3 Digital Elevation ... 6

2.2.1 Description of ASTER GDEM ... 6

2.2.1 Accuracy Assessments study cases ... 8

2.2.2 Description of SRTM3 version 2 Digital Elevation ... 9

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CHAPTER 3: ACCURACY ASSESSMENTS OF ASTER GDEM V2 AND SRTM3 V2.1

... 13

3.1 Height Relationships ... 13

3.1.1 Ellipsoid ... 13

3.1.2 Geoid model and EGM96 ... 13

3.2 Methods for Comparing ASTER GDEM V2 and SRTM3 V2.1 Digital Elevation Models ... 14

3.2.1 Spatial Accuracy ... 14

3.2.1 Vertical Accuracy ... 15

3.3 Methods ... 15

3.3.1 Data Collection ... 16

3.3.2 Dem Mosaicking, Masking, and Extraction of DEM Based Heights... 17

3.3.3 Calculating Vertical Error of ASTER and SRTM DEMs... 17

3.4 Tools ... 19

3.4.1 R Software environment ... 19

3.4.1 Photomod Geographical calculator and ArcGIS ... 19

3.5 Study Area ... 20

CHAPTER 4: RESULTS AND ANALYSIS ... 22

4.1 Vertical Accuracy Assessments of Aster GDEM V2 and Srtm3 V2.1 ... 22

4.1.1 Test of significance between the two DEMs and GPS Height... 25

CHAPTER 5: SUMMARY, DISCUSSION AND OUTLOOK ... 28

5.1 Summary and Discussion ... 28

5.1.1 Outlook ... 29

BIBLIOGRAPHY ... 30

Appendix ... 33

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List of Figures

FIGURE 2:1 VERTICAL HEIGHT RELATIONSHIPS. ... 5 FIGURE 3:1 RELATIONSHIP BETWEEN ELLIPSOID, GEOID AND

ORTHOMETRIC HEIGHTS. ... 14 FIGURE 3.2: GIS METHODOLOGY OF THE SRTM3 AND ASTER GDEM

VALIDATION WITH GPS CONTROL POINTS. ... 16 FIGURE: 3.3 SHOWING THE STUDY AREA RIVERS STATE WITH GPS

CONTROLS ... 20 FIGURE 3.4 SHOWING GPS CONTROLS RVOSG – X1 ... 21 FIGURE 3.5 SHOWING DEM AND GPS CONTROLS. (SOURCE: OFFICE OF THE

SURVEYOR ... 21 FIGURE 4:1: SHOWING GOODNESS OF FIT WITH HISTOGRAPH. ... 25 FIGURE 4.2: SHOWING GOODNESS OF FIT WITH BOXPLOT. ... 25

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List of Tables

TABLE 2.1 BASIC FEATURES OF DEMS ... 6 TABLE 2.2 ASTER GDEM CHARACTERTICS (CONUS, 2009). ... 8 TABLE 2.3 ASTER RESULTS FOR CONUS. (SOURCE: CONUS, 2009) ... 8 TABLE 2.4 ASTER RESULTS FOR ONDO STATE ( ODUTOLA, ET. AL, 2013) . .. 9 TABLE 2.5 CONTINENTAL RESULTS FOR SRTM3 (SOURCE: JPL, 2009) ... 11 TABLE 2.6: DEM RESULTS FOR AUSTRALIA. SOURCE: (HIRT ET AL. 2010) . 11 TABLE 4.1: SHOWS THE RMSE AND VERTICAL ACCURACY ANALYSIS ... 23 TABLE 4.2: STATISTICAL ANALYSIS FOR ASTER, GPS, AND SRTM3 ... 24 TABLE 4.3: CORRELATION COEFFICIENT RABLE ... 24

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List of abbreviations

American Society for Photogrammetry and Remote Sensing‟s (ASPRS) SRTM (Shuttle RADAR Topographic Mission)

ASTER GDEM (Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model)

Digital Elevation Model (DEM)

Geographic Information Systems (GIS) Global Navigation Satellite System (GNSS) Italian Space Agency (ASI)

German Aerospace Centre (DLR)

National Aeronautics and Space Administration (NASA) METI (the Ministry of Economy, Trade and Industry Global Positioning System (GPS)

Root Mean Square Deviation, RMSD Root-mean-square error (RMSE)

Aeronautical Information Services (AIS) - Aeronautical Information Management (AIM) Study Group (AIS-AIMSG).

Earth Gravitational Model (EGM) Mean Sea Level (MSL)

Earth Observing System (EOS) Near-infrared (VNIR)

World Geodetic System 1984 (WGS84) Conterminous United States (CONUS) United States Geological Survey (USGS)

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Chapter 1: Introduction CHAPTER 1: INTRODUCTION

1.1 Overview

A good knowledge of the earth topography helps in effective Planning of the land use, and is one of the essential information for the preparation of construction projects and territorial planning. The attainment of these elevations data can be acquired through on- site survey, with the use of topographical equipment, or in an indirect way using the data generated by sensors installed on orbital platforms.

Koch et al, 2000; Smith et al, 2003; Falorni et al., 2005 believed that after the availability of SRTM (Shuttle RADAR Topographic Mission), several studies have been carried out in different areas, for example, in surveying.

The needs for consistent height information; direct access to the Vertical Datum at any point via Geographic Information Systems (GIS) elevation data, Digital Elevation Model (DEM) from SRTM and ASTER GDEM (Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model) without heights transfer from existing benchmarks.

The ASTER GDEM is said to have three spectral bands in the visible and near infrared, with six bands in the shortwave infrared region and five spectral bands in the thermal area of the electromagnetic spectrum, and has 15, 30 and 90 meters spatial resolution, respectively (Yamaguchi et. al., 1998).

The space mission for the Shuttle Radar Topography Mission (SRTM) was released in 2000 in order to obtain information about the earth relief. Koch and Lohmann (2000) believed that the possible sources of error in SRTM data can be divided in the characterization of parameters for SAR data acquisition, processing, and the influences of vegetation.

Kervyn et al. (2006) states the various advantages and limitations of Aster and SRTM with respect to topographic mapping in a volcanic. Kervyn et al. (2006), further emphasis that SRTM and ASTER overall assessment of the accuracy requires more studies at local level involving control of ground truth and accuracy of test methods with higher precision and accuracy, as the GNSS system.

Stevens et al. (2004) results of validation concluded that there is better representation of the topography of active volcanoes with Aster data than with the SRTM data. GIS elevation data (DEM) from SRTM (Shuttle RADAR Topographic Mission) and ASTER

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Chapter 1: Introduction GDEM (Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model) have many application areas in Surveying and Geoinformatics, especially in area such as land cover mapping and demands high absolute vertical height accuracy standard.

The ASTER GDEM version 2 (GDEM2) and SRTM3 version 2 is a joined product of NASA and METI (the Ministry of Economy, Trade and Industry of Japan), the Italian Space Agency (ASI) and the German Aerospace Center (DLR). The horizontal datum is the World Geodetic System 1984 (WGS84), the vertical datum is by the Earth Gravitational Model geoid (EGM96 geoid). The Global Positioning Systems control points used in evaluation of ASTER GDEM and SRTM3 elevation data are Primary Control Points Referenced to the WGS84(horizontal datum) and GPS ellipsoidal height(vertical datum) from the office of the Surveyor General, Rivers State.

ASTER GDEM and SRTM3 are GIS dataset that present Surveyors and Engineers, and other professionals free open source dataset and to evaluate their accuracy and relevance to their area of applications. GIS database helps in the integration of different dataset sources/formats.

Two freely global elevation datasets vertical accuracy will be evaluated in this study.

Aster and Srtm3 will download and mosaicked and masked to study area using ArcGIS 10. VTBuilder 1.52 will convert DEM to grids to be read in R software. R software (maptools package) will be used for extraction of DEM based heights (EGM96).

Photomod geographical calculator converts DEM based heights (EGM96) to ellipsoidal heights. Microsoft excels computes the heights residuals, root-mean-squared error, and accuracy (95% confidence levels). R software was used for linear regression and hypotheses.

In this thesis, the vertical accuracy assessment of the interferometry terrain elevation data (DEM) from SRTM3 and ASTER GDEM will be determined using 71 GPS control points distributed all over the study area(Rivers State, Nigeria).

1.2 Problem Statement

In recent years the impact of climate change have leads to tidal rise (ocean), city flooding, and change in rainfall pattern. So, there is the need for increased vertical accuracy of various data sources for Surveying, Geoinformatics, and Engineering Applications.

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Chapter 1: Introduction Remote sensing data provides cost effective dataset and the freely global terrain elevation data (DEM) from SRTM3 and ASTER GDEM as one of the most complete high resolution digital topographic datasets of the world so far, there is the needs to evaluate their vertical accuracy and relevance.

So it will be a useful product for many applications of Surveying, & Geoinformatics, such as city planning, construction, and telecommunication etc.

1.3 Aim and Objectives 1.3.1 Aim

This thesis aim to investigate the vertical accuracy performance of ASTER GDEM version 2 (GDEM2) and SRTM3 version 2 in order to define the suitability and relevance for Surveying & Geoinformatics Applications in Rivers State, south-south of Nigeria using Global Positioning System (GPS) ground control points..

1.3.2 Objectives Objectives include;

a. Determinations of mean error, standard mean error, maximum and minimum error standard deviation and root-mean-square error (RMSE) of both DEMs.

b. A test of hypotheses (t-test statistic) at 5% significance level will be conducted between the two DEMs and GPS Height.

c. A further analysis to test the relationship of both DEM and the referenced GPS elevation will be carried out using linear regression.

1.4 Thesis structure

The thesis is organized into five chapters as follows:

Chapter 1: Research outline, this chapter presents overview of the thesis. It describes the motivation, problem statement, aim & objectives, and thesis structure.

Chapter 2: Literature Review, It briefly describes background terms and information, Description of ASTER GDEM and SRTM3 Digital Elevation, review of local cases study, and Applications of Digital Elevation Models.

Chapter 3: this chapter describes the basic theoretical background, methods applied, tools used, and the study area.

Chapter 4: this chapter discusses the results obtained and statistics analysis.

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Chapter 1: Introduction Chapter 5: summary, discussion and outlook; this chapter provides the answer of the research questions in concluded form and highlights recommendations for further study.

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Chapter 2: Literature Review

CHAPTER 2: LITERATURE REVIEW 2.1 Background Terms and Information

2.1.1 Vertical Reference System

According to the Aeronautical Information Services (AIS) - Aeronautical Information Management (AIM) Study Group(AIS-AIMSG) ATTACHMENT A, ANNOTATED AIS-AIMSG/4-SN/14 ATTACHMENT; “A vertical (height) reference system can be defined by only two parameters: A point with a known elevation from which vertical differences are calculated, and the reference surface”. The vertical height relationships are shown in Figure 2.1 below.

Orthometric height (H) – Physical surface of the Earth

Geoid

H

Geoid Height

Ellipsoidal height(h) h N WGS 84 Ellipsoid

Figure 2:1 Vertical Height Relationships.

2.1.2 Ellipsoidal Heights

According to (AIS-AIMSG, 2014), the ellipsoid, which is used as part of the definition of a geodetic datum, is also used as a reference surface. “The Ellipsoidal Height (h) is the orthogonal distance between a point and the reference ellipsoid.

Therefore, it does not take into account the Earth‟s gravity field”.

2.1.3 Orthometric Heights

AIS-AIMSG, 2014, also define the “Orthometric Height as the distance (H) along a line of force from the geoid to a given point (P) on the physical surface of the earth (the line is perpendicular to the equipotential surfaces at different levels)”.

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2.1.4 Normal Heights

“The Normal Height (H) of a point is computed from its geopotential difference to that of sea level. It takes into account the normal gravity, computed along the plumb line of the point (height difference of a point to the quasi-geoid)” (AIS-AIMSG, 2014). Height difference between Normal Height and the Ellipsoidal Height is known as height-anomaly or quasi-geoid-height.

2.1.5 Geoid – Earth Gravitational Model (EGM)

Geoid is the equipotential surface of the earth‟s gravity field, as chosen at a particular level (approximately Mean Sea Level (MSL)) which is use as the reference surface for height measurements. The difference in height between the geoid and the geocentric WGS 84 ellipsoid is said to be between ± 100m (AIS-AIMSG, 2014). This difference in elevation is the geoid undulation (N).

2.2 Description of ASTER GDEM and SRTM3 Digital Elevation In Table 2.1; Basic features of

the two global digital elevation models ASTER GDEM2, and SRTM3 USGS v2.1 are shown.

ASTER GDEM2 SRTM3 USGS v2.1 Satellite Mission Terra Shuttle Radar Topography

Mission

Institutions METI, NASA NASA, USGS, JPL Instrument ASTER (optical) Space Shuttle Radar

C / X-band SAR Height Reference WGS84 / EGM96 WGS84 / EGM96 Coverage +83 N to -83 S latitude +60 N to -56 S latitude Resolution 30 m / 1 arc-second 90 m / 3 arc-seconds Elevation Accuracy < 17 m

(at 95 % confidence)

< 16 m

(at 90 % confidence) Download http://gdem.ersdac.

jspacesystems.or.jp/

http://dds.cr.usgs.gov/srtm/

version2_1/SRTM3

Table 2.1 Basic features of DEMs (Source: JPL, 2009).

2.2.1 Description of ASTER GDEM

The ASTER is an imaging instrument on board the Earth Observing System (EOS) Terra Satellite which is operated jointly by NASA and Japan‟s Ministry of International Trade and Industry (Jensen, 2000). According to the Jet Propulsion Laboratory, the sensor collects both emitted and optical reflected energy. Near- infrared stereo imagery is collected simultaneously at both nadir and off nadir angles

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with a long-track alignment. Stereo imagery is utilized to develop a DEM through stereocorrelation technologies (Hirano, et. al, 2003).

Hirano, et. al, 2003, states that ASTER imagery is also available with multiple resolutions, with the ½ arcsecond (15m) resolution which is good dataset for this study. Evans, et. al, 2008, reported vertical accuracy of ASTER DEMs in the range of

±7 meters to ±15 meters. Evans, et. al, 2008, also reported ASTER horizontal accuracy as cited to approximate ±20 meters. According to the Jet Propulsion Laboratory, ASTER Global Digital Elevation Model (GDEM), which was released to the public on June 2, 2009, offers the most extensive global DEM coverage available remote sensing data. ASTER GDEM data covers 99% of the Earth‟s surface. ASTER imagery is referenced horizontally to the World Geodetic System 1984 (WGS84) reference ellipsoid and vertically to the Earth Gravitational Model 1996 (EGM96) reference geoid (Hirano, et. al, 2003).

Jet Propulsion Laboratory further states that the ASTER instrument was built by METI and launched onboard NASA‟s Terra spacecraft in December 1999, and has an along-track stereoscopic capability using its near infrared spectral band and its nadir- viewing and backward-viewing telescopes to acquire stereo image data with a base- to-height ratio of 0.6. others properties includes one nadir-looking ASTER visible and near-infrared (VNIR) scene consists of 4,100 samples by 4,200 lines, corresponding to about 60 kilometers (km)-by-60 km ground area.

According to the ASTER GDEM Validation Team in his ASTER Global DEM Validation Summary Report, 2009, the methodology used to produce the ASTER GDEM involved automated processing of 1.5-million-scene ASTER archive, stereocorrelation used to produce 1,264,118 individual scene-based ASTER DEMs, cloud masking which remove cloudy pixels, while stacking all cloud-screened DEMs, removing residual bad values and outliers, the averaging selected data is use to create final pixel values, and finally the correcting residual anomalies and the data is then partitioning into 1°-by-1° tiles.

Table 2.2 ASTER GDEM Characteristics

Tile Size 3601 x 3601 (1°-by-1°)

Posting interval 1 arc-second

Geographic coordinates Geographic latitude and longitude

DEM output format format GeoTIFF, signed 16 bits, and 1m/DN Referenced to the WGS84/EGM96 geoid

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Special DN values -9999 for void pixels, and 0 for sea water body

Table 2.2 ASTER GDEM Charactertics (CONUS, 2009).

2.2.1 Accuracy Assessments study cases

ASTER GDEM Validation Team also in his ASTER Global DEM Validation Summary Report, 2009, reported that 934 ASTER GDEM tiles that comprise the conterminous United States (CONUS) were compared with more than 13,000 ground control points (GCPs).

Table 2.3 presents results where GDEM values were compared to GCPs at more than 13,000 benchmarks scattered across the CONUS. Results are shown both for the elevation of the pixel containing the benchmark nearest neighbor (NN) and for elevations calculated by interpolation (I) with surrounding pixels.

The 9.35 RMSE reported in Table 2.3 convert, to vertical errors of just over and just under the preproduction estimated ASTER GDEM vertical error of 20 m at 95%

confidence.

Table 2.3: Absolute-control-based ASTER GDEM vertical accuracy results for CONUS. All values are in meters.

(NN = nearest neighbor; I = interpolated)

Number of Benchmarks

Mean RMSE Average Mean

Average RMS GDEM minus Benchmark Elevations

(NN)

13,193 -3.71 9.33

GDEM minus Benchmark Elevations (I)

13,193 -3.69 9.37 -3.70 9.35

Table 2.3 ASTER results for CONUS. (Source: CONUS, 2009) 2.2.1.1 Case Study in Ondo State Nigeria

Another study area for DEM validation in ondo lies between Latitudes 40 15‟ E and 60 45‟ E and Longitudes 60 45‟ N and 80 30‟ N (Odutola, et. al, 2013). The study area is a state in the South-Western part of Nigeria, with a total area of: 14788.723 square kilometers which covers low-level, midlevel and high-altitude terrain with elevation ranging from 288m to 414m and 9m to 118m. A total number of 119 and 118 differential GPS points for the region, and were obtained from the Survey Depart- ment, Ministry of Lands, Housing and Environment, Akure, Ondo State, Nigeria(Odutola, et. al, 2013).

Odutola, et. al, 2013 reported results that shows absolute vertical accuracy of

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Table 2.4: ASTER vs GPS Statistical Analysis

Parameter ASTER Eleva-tion (m)

GPS Eleva-tion (m)

Δh (GPS- ASTER)(m)

ASTER Eleva-tion (m)

GPS Eleva-tion (m)

Δh (GPS- ASTER)(m)

Count 119 119 119 118 118 118

Maximum 407.5 407.5 35.26 82.2 117.25 42.09 Minimum 284.36 284.36 -22.15 28.26 9.27 -38.87

Mean 355.9 355.9 10.14 63.67 60.6 -3.07

S.E.M 1.93 1.93 1.1 1.12 1.86 1.19

Std Dev 19.18 19.18 8.71 12.21 20.24 12.94 RMSE

±12.72

RMSE

±13.25

Table 2.4 ASTER results for Ondo State ( Odutola, et. al, 2013) .

From the statistical analysis carried out by Odutola, et. al, 2013 , it was observed that in the mountainous region A, the Root Mean Squared Error (RMSE) was ASTER DEM; ±12.72, while in the less mountainous region B, it was ±13.25 for ASTER DEM. The results from both assessments revealed their level of suitability for geomatics application for the concerned region of the Study areas.

2.2.2 Description of SRTM3 version 2 Digital Elevation

According to the Jet Propulsion Laboratory (JPL, 2009), the Shuttle Radar Topography Mission (SRTM) obtained elevation data on a near-global scale to generate the most complete high-resolution digital topographic database of Earth.

SRTM consisted of a specially modified radar system that flew onboard the Space Shuttle Endeavour during an 11-day mission in February of 2000.

The SRTM DEM dataset was generated through the use of stereoscopy by measuring the amplitude of the return phase of InSAR microwave frequencies (Kervyn et al., 2006).

SRTM data is offered in 3 arcsecond resolution for all extents of global coverage and 1 arcsecond for the U.S. and U.S. Territories (Guth, 2006). SRTM vertical accuracy is reported at ≤7 meters (Slater, et. al, 2006). SRTM absolute height accuracies were calculated at 9 m in North America (Rodriguez et al., 2006). Horizontal accuracy for SRTM is reported at ±20 meters horizontal accuracy (Huggel, et al., 2008). SRTM coverage is available for 80% of the Earth‟s surface from 60˚N to 60˚S latitudes (Guth, 2006). SRTM DEM data is referenced horizontally to the WGS84 ellipsoid and vertically to the EGM96 geoid heights (Hoffman and Walter, 2006). JPL, 2009 reported that during the Shuttle Radar Topography Mission, a specially modified radar system flew onboard Space Shuttle Endeavour for 11 days in February of 2000.

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The radar system used gathered data that will result in an accurate and complete topographic map of Earth's surface (JPL, 2009).

The processed SRTM radar data was tailored to meet the needs of the military, civil, and scientific user communities. Other uses of this data according JPL, 2009 include improved water drainage modelling, more realistic flight simulators, navigation safety, better locations for cell phone towers, and even improved maps for backpackers.

The mission project like any other mission requires accurate knowledge of the shape and elevation of the land surface that can benefit different area of applications. Some examples are flood control, soil conservation, reforestation, volcano monitoring, earthquake research, and glacier movement monitoring (JPL, 2009). Radar interferometry uses two radar images are taken from slightly different locations. The difference between these images is used for the calculation of surface elevation. The two radar images is gotten from taken different locations and the SRTM hardware consisted of one radar antenna in the shuttle payload bay and a second radar antenna attached to the end of a mast that extended 60 meters (200 feet) from the shuttle(JPL, 2009). SRTM was launched into an orbital inclination of 57 degrees. At 57 degrees SRTM's radars cover most of Earth's land surface that lies between 60 degrees north and 56 degrees south latitude which is about 80 percent of Earth's land mass (JPL, 2009).

2.2.2.1 SRTM Validation

Rodriguez et al., 2005; 2006 states that SRTM data products were validated on continental scales through comparison with reserved ground control (i.e. control not used in the mosaicking bundle adjustments). He further describes the kinematic GPS data acquired by JPL and NGA specifically for SRTM validation as best quality control data for the study. He also states that long tracks of GPS estimates were acquired along roads on most major continents. The results shows that data were accurate to better than 1 m, and could characterize SRTM errors on spatial scales from hundreds of meters up to thousands of kilometers. With these data, it was possible to develop a spatial error spectrum, and a total absolute error estimate that have high confidence and are generally applicable away from the kinematic tracks themselves.

Table 2.3 summarizes the 90% errors estimated using the available ground truth as

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than 9 m, indicating that SRTM improved on its design goal of 16 m absolute by almost a factor of 2.

Table 2.5: show Summary of GPS GCP comparison with SRTM data. All quantities are in meters.

Continent Mean Standard Deviation 90% Absolute Error

Africa 1.3 3.8 6.0

Australia 1.8 3.5 6.0

Eurasia -0.7 3.7 6.6

North America 0.1 4.0 6.5

New Zealand 1.4 5.9 10.0

South America 1.7 4.1 7.5

Table 2.5 Continental results for SRTM3 (source: JPL, 2009) 2.2.2.2 Case Study of Australia

According to Hirt et al. 2010, many parts of Australia are rather flat with about 6% of the landmass exceeding elevations of 600 m with mountainous terrain over few areas of the continent, such as Australia‟s eastern highlands and the Great Dividing Range.

For these reasons a large part of the continent have little vegetation of about ~ 40%

which are beneficial for creating accurate topography models from space- or airborne sensors, as they favours a direct line-of-sight to bare ground. Three DEMs, were used in the Australia study case namely SRTM3 version 2.1 released by United States Geological Survey (USGS), and ASTER GDEM2 (version 2), are compared and evaluated against ground control points.

The data set used contains station heights from the Australian National Gravity Database and which provides a much larger set of ground truth points than previously work (Hirt et al. 2010).

Table 2.6; Statistical analyses result of the height differences to GCPs stations of ASTER GDEM2, and SRTM3 v2.1 for the two highest ANGD positioning confidence levels for different land cover groups (in metres); GCPs located in SRTM3 void cells are excluded from all statistics.

Number of Stations Min [m] Max[m] Mean [m] STD[m] RMS [m]

ASTER GDEM2 773330 -165.08 167.99 -3.23 8.64 9.22

SRTM USGS v2.1 772696 -553.11 639.16 3.02 5.52 6.29

Table 2.6: DEM results for Australia. Source: (Hirt et al. 2010)

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2.3 Applications of Digital Elevation Models

There are many application areas of which includes civil engineering and military planning tasks etc. DEM has been used in areas such as industry, medicine, architecture, mining, agriculture, mapping (Habib, 2005). Yılmaz et al., 2006 states many fields which include;

 Planning of transportation and optimization of transportation

 Planning of irrigation and drainage work

 Analyze of communication network

 Planning of dam area

 Planning of measurement network

 Land information system

 Navigation and direction

 City and region planning

 Disaster emergence planning

 Erosion control

 Evaluation of mining reserves

 Planning of use of weapon system

 Three-dimensional city modeling

According to (JPL, 2009), the processed SRTM radar data can be tailored to meet the needs of the military, civil, and scientific user communities. But other uses of this data include improved water drainage modeling, more realistic flight simulators, navigation safety, better locations for cell phone towers, and even improved maps for backpackers.

JPL, 2009 reported other areas of application to include flood control, soil conservation, reforestation, volcano monitoring, earthquake research, and glacier movement monitoring.

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Chapter 3: Accuracy assessments of Aster GDEM V2 And Srtm3 V2.1

CHAPTER 3: ACCURACY ASSESSMENTS OF ASTER GDEM V2 AND SRTM3 V2.1

3.1 Height Relationships

According to Dennis et. al,1996, the difference between GPS ellipsoid heights, h, and leveled orthometric heights, H, is called geoid height(EGM96), N, and the geoid height is the vertical distance from the ellipsoid to the geoid level surface. These heights obey a simple equation as stated Dennis et. al,1996;

h = H + N:………Equation (3.1) 3.1.1 Ellipsoid

As first approximation, the Earth is a rotating sphere. As a second approximation, it can be regarded as an equipotential ellipsoid of revolution.

Moritz, 1980 states that the theory of the equipotential ellipsoid was first given by P.

Pizzetti in 1894 and was further elaborated by C. Somigliana in 1929.

According to NOAA, Department of Defense (DoD) established the original WGS 84 reference frame in 1987 using Doppler observations from the Navy Navigation Satellite System (NNSS) or TRANSIT and named it as WGS 84(TRANSIT). NOAA further explained the latest realization of WGS 84, as adopted in 20 January 2002, was termed WGS 84 (G1150). It is generally assumed to be identical to ITRF 2000 (epoch 1997.0) at one centimeter level.

3.1.2 Geoid model and EGM96

Li et. al, 2001 define the geoid to be a surface of constant potential energy that coincides with mean sea level over the ocean. Li et. al, 2001 states that firstly, the mean sea level is not quite a surface of constant potential due to dynamic processes within the ocean. Second, the actual equipotential surface under continents is warped by the gravitational attraction of the overlying mass. They concluded that the main function of the geoid in geodesy is to serve as a reference surface for leveling and the elevation measured by leveling is relative to the geoid (Li et. al, 2001).

From Equation (3.1) connects h is the ellipsoid height relative to the ellipsoid,and N is the geoid undulation relative to the ellipsoid, while H isthe elevation relative to the geoid.

According to NASA EGM96 general description page; “EGM96 is a geopotential

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and order 360. It is a composite solution, consisting of: (1) a combination solution to degree and order 70; (2) a block diagonal solution from degree 71 to 359; and (3) the quadrature solution at degree 360”.

The Earth Gravitational Model 1996 (EGM96) is one of the global models which is the vertical datum of ASTER GDEM V2 AND SRTM3 V2.1

Earth surface

Ellipsoid P

h Q

N plumb line

Mean sea level PO Geoid

Ocean

h (Ellipsoidal height) = Distance along ellipsoid normal (Q to P) N (Geoid height) = Distance along ellipsoid normal (Q to Po) H (Orthometric height) = Distance along plumb line (Po to P)

Figure 3.1 Relationships between ellipsoid, geoid and orthometric heights.

3.2 Methods for Comparing ASTER GDEM V2 and SRTM3 V2.1 Digital Elevation Models

3.2.1 Spatial Accuracy

The Federal Geographic Data Committee (NSSDA) recommended root-mean-square error (RMSE) to estimate positional accuracy. “RMSE is the square root of the average of the set of squared differences between dataset coordinate values and coordinate values from an independent source of higher accuracy for identical points”

(NSSDA, 1998).

The Federal Geographic Data Committee (NSSDA) said that accuracy should be reported in ground distances at the 95% confidence level, and accuracy reported at the 95% confidence level means that 95% of the positions in the dataset will have an error with respect to true ground position that is equal to or smaller than the reported accuracy value. The reported accuracy value reflects all uncertainties, including those introduced by geodetic control coordinates, compilation, and final computation of ground coordinate values in the product (NSSDA, 1998).

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3.2.1 Vertical Accuracy Let:

RMSE_Z= sqrt

[(

^Zdata I - Z_{check I}

)

^2/n

]

---(3.2) where,

z data i = the vertical coordinate of the i th check point in the dataset.

z check i = the vertical coordinate of the i th check point in the independent source of higher accuracy

n = the number of points being checked i is an integer from 1 to n

According to (NSSDA, 1998), it is assumed that systematic errors have been eliminated as best as possible and if vertical error is normally distributed, the factor 1.9600 is applied to compute linear error at the 95% confidence level cited in Greenwalt and Schultz, 1968. Therefore, vertical accuracy, Accuracy z, reported according to the NSSDA shall be computed by the following formula:

Accuracyz = 1.9600 *RMSEz. - ---(3.3)

In Geodesy, vertical accuracy is computed by vertical Root-Mean-Squared Error (RMSE) (also called the root mean square deviation, RMSD as use in social sciences).

The American Society for Photogrammetry and Remote Sensing‟s (ASPRS) Specifications and Standards Committee, cited in Greenwalt and Schultz (1962) and Greenwalt and Schultz (1968) established RMSE as the pivotal map accuracy parameter. The RMSE measures the difference between the values of the DEM elevations and the values of referenced GPS elevations. These individual point differences are also called residuals as used in this study, and the RMSE serves to aggregate them into a single measure of predictive power.

3.3 Methods

The diagram below shows the approach for estimation of the vertical accuracy of the DEMs data using GPS control measurements is summarized as shown in figure 3.2.

Firstly, the two DEM in this study was mosaicked and masked to study area shape files (administrative map of Rivers State) using ArcGIS 10. VTBuilder 1.52 was used to converts DEM to grids to be read in R software enviroment. R software package maptools was used for extraction of DEM based heights in EGM96. Then Photomod geographical calculator was used to converts DEM based heights in EGM96 to ellipsoidal heights. Lastly, Microsoft excels sheet was used for computation of the

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heights residuals, root-mean-squared error, and accuracy (95% confidence levels). R software was used for linear regression and hypotheses.

3.3.1 Data Collection

The ASTER GDEM version 2 (GDEM2) and SRTM3 version 2 was downloaded from http://gdem.ersdac.jspacesystems.or.jp/, and http://dds.cr.usgs.gov/srtm/

Version2_1/SRTM3 respectively.

Figure 3.2 GIS methodology of the SRTM3 and ASTER GDEM validation with GPS Control Points.

The horizontal datum is the World Geodetic System 1984 (WGS84), the vertical datum is the Earth Gravitational Model geoid (EGM96 geoid). The Global Positioning Systems(GPS) control points used are Primary Control Points Referenced to the WGS84(horizontal datum) and GPS ellipsoidal height(vertical datum) from the office of the Surveyor General, Rivers State.

CONVERSION OF EGM 96 TO ELLIPSOIDAL HEIGTHS EXTRACTION OF DEM BASED HEIGHTS(EGM 96)

DEM MOSAICKING AND MASKING

ASTER GDEM AND SRTM3 DEM

KNOWN (TRUE ) HEIGHTS Ellipsoidal Heights GPS CONTROL POINTS;

Longitude, Latitude and Ellipsoidal Heights

STATISTICAL ANALYSIS FOR DEMS VALIDATION

RESIDUALS:

Heights Difference

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3.3.2 Dem Mosaicking, Masking, and Extraction of DEM Based Heights The ASTER GDEM version 2 (GDEM2) and SRTM3 version 2 were independently mosaicked, and Rivers state administrative shapefile was overlaid on the mosaic DEM, followed by a masking operation which was carried out to extract the areas of the DEM that falls within the boundary of Rivers State. All these were done using ArcGIS 10, mosaicking (ArcToolbox < management tool < Raster < mosaic to new raster). And for masked Dem (ArcToolbox < Spatial Analyst < extraction <extract by mask).

The ASTER GDEM version 2 (GDEM2) and SRTM3 version 2 file format of .tiff and .hgt respectively, was conversion to AsciiGrids file format(.asc) using VTbuilder version 1.52.

Extraction of Dem based heights (EGM 96) was carried out using maptools package (note maptools depends on other packages) in R software. R code;

Library (maptools)

DEM dataset filename<-readAsciiGrid (dataset path) GPS points filename<-readShapePoints (dataset path) Overlay (DEM dataset filename, GPS point‟s filename)

Conversion of EGM 96 to Ellipsoidal heights was carried out using the Photomod Geographical calculator.

3.3.3 Calculating Vertical Error of ASTER and SRTM DEMs

With the DEM based heights extracted in the preceding process, both control and test DEMs were converted to the same GPS ellipsoidal height (vertical datum) WGS84 datum. RMSE was then calculated for each of the ASTER, and SRTM elevation test raster through comparing the differences in heights to the respective GPS control points interpolated DEM by overlaying the raster. RMSE for DEM accuracy is defined by Equation (3.2) which can be deduced as:

RMSE=√ ∑ (errors)²

Number of GCPS ………equation (3.4) Where, GCPS= Ground control points.

Microsoft excel spreadsheet tool was used to determine the height differences between the test DEMs Ellipsoidal Heights and the GPS Ellipsoidal Heights, the RMSE was computed manually using the R software. From equation (3.3), the

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Screenshot 1: showing height extraction from DEMs using R Software.

Screenshot 2: showing conversion of DEMs to grids using VTBuilder 1.52

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Screenshot 3: showing conversion of DEMs Heights to ellipsoidal heights.

3.4 Tools

3.4.1 R Software environment

„R like S is a language and environment for statistical computing and graphics and mapping. R is free and open source software under the terms of the GNU General Public License and is also used for GIS mapping and analysis. R was designed around computer language, and it a uses to additional functionality by defining new functions and packages. For computationally-intensive tasks, C, C++ and Fortran code can be linked and called at run time. Advanced users can write C code to manipulate R objects directly. R can be extended using packages.

According to CRAN, Maptools package used in this thesis is a function of the Geospatial Data Abstraction Library to read and write GIS data with options to handling Coordinate Referent System (CRS).

3.4.1 Photomod Geographical calculator and ArcGIS

According to (Racurs, 2008), PHOTOMOD GeoCalculator user manual page 3, the program is intended for recalculating of ground control point‟s coordinates from one coordinate system into another. When you have no ground control point coordinates, you may need to recalculate height system to obtain correct results. PHOTOMOD GeoCalculator includes parameters of predefined geoid for such recalculation – EGM-

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ArcGIS is GIS software enables mapping, data analysis, data management and manipulation, data storage, and advanced predictive modeling.

3.5 Study Area

The Nigeria national bureau of statistics in its state information describes Rivers State as one of the 36 states of Nigeria with capital in Port Harcourt. It is bounded on the South by the Atlantic Ocean, to the North by Imo, Abia and Anambra States, to the East by Akwa Ibom State and to the West by Bayelsa and Delta states. Rivers state is home to a variety of ethnic groups, including Abua, Andoni, Ekpeye, Engenni, Etche, lbani, lkwerre, Kalabari, Ogba/Egbema/Ndoni, Okrika and Ogoni.

The inland part of Rivers state consists of tropical rainforest; towards the coast the typical Niger Delta environment features many mangrove swamps.

Rivers State lies at latitude 4°45‟ north and longitude 6°50‟ east and covers an area of 10,432.3 square kilometres. It has a population of 5,198,716 (census 2006) – 3.7%

of Nigeria‟s total – and a population density of 468 people per square kilometre.

Figure 3.3 showing the study area Rivers State with GPS Controls

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Figure 3.4 Showing GPS Controls RVOSG – X1

Figure 3.5 showing DEM and GPS controls. (Source: Office of the Surveyor-

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Chapter 4: Results and Analysis

CHAPTER 4: RESULTS AND ANALYSIS 4.1 Vertical Accuracy Assessments of Aster GDEM V2 and Srtm3 V2.1

Vertical accuracy of the Aster GDEM V2 and SRTM3 V2.1 was computed and the error Statistics of the control points was generated using Microsoft excel in tabular form as shown table 4.1. The summary statistics shows minimum error for Aster GDEM V2 and Srtm3 V2.1 are -24.682m and -16.29m while the maximum errors are 16.786m and - 0.466m with mean errors are -2.180254m and 5.8281549m. The RMSE error is ± 8.861734m for Aster GDEM V2 and ± 6.307187m for SRTM3 V2.1, with vertical accuracy of ± 17.362089m and ± 12.362086m respectively.

Table 4.1 shows the RMSE and vertical accuracy computation.

GPS Height ( m )

ASTER EGM96(Geoid Height) ( m)

ASTER HEIGHT Ellipsoidal

SRTM_EGM96 (Geoid Height) ( m )

SRTM3 HEIGHT Ellipsoidal

ERROR ASTER

ERROR SRTM3

SQUARED ERROR ASTER

SQUARED ERROR SRTM

28.453 16 34.919 10 28.919 -6.466 -0.466 41.809156 0.217156 19.368 7 25.929 7 25.929 -6.561 -6.561 43.046721 43.046721 24.733 13 31.884 11 29.884 -7.151 -5.151 51.136801 26.532801 19.934 5 23.872 2 20.872 -3.938 -0.938 15.507844 0.879844 27.603 12 30.841 14 32.841 -3.238 -5.238 10.484644 27.436644 30.005 20 38.676 20 38.676 -8.671 -8.671 75.186241 75.186241 40.696 24 42.974 25 43.974 -2.278 -3.278 5.189284 10.745284

20.965 11 29.73 8 26.73 -8.765 -5.765 76.825225 33.235225

29.046 6 24.553 13 31.553 4.493 -2.507 20.187049 6.285049 27.644 13 31.746 13 31.746 -4.102 -4.102 16.826404 16.826404

18.556 9 27.88 4 22.88 -9.324 -4.324 86.936976 18.696976

20.708 7 25.828 7 25.828 -5.12 -5.12 26.2144 26.2144

19.965 14 32.889 6 24.889 -

12.924

-4.924 167.029776 24.245776

19.936 13 31.858 7 25.858 -

11.922

-5.922 142.134084 35.070084

24.864 4 22.371 12 30.371 2.493 -5.507 6.215049 30.327049

24.524 6 24.42 10 28.42 0.104 -3.896 0.010816 15.178816

21.894 12 30.583 10 28.583 -8.689 -6.689 75.498721 44.742721

22.361 5 23.443 9 27.443 -1.082 -5.082 1.170724 25.826724

27.953 4 22.3 15 33.3 5.653 -5.347 31.956409 28.590409

54.69 33 51.663 46 64.663 3.027 -9.973 9.162729 99.460729

44.357 9 27.571 33 51.571 16.786 -7.214 281.769796 52.041796 29.398 -2 16.315 19 37.315 13.083 -7.917 171.164889 62.678889 28.228 0 18.337 17 35.337 9.891 -7.109 97.831881 50.537881 31.49 -3 15.485 19 37.485 16.005 -5.995 256.160025 35.940025 51.313 21 39.786 41 59.786 11.527 -8.473 132.871729 71.791729 32.762 4 22.696 21 39.696 10.066 -6.934 101.324356 48.080356

30.243 2 20.25 17 35.25 9.993 -5.007 99.860049 25.070049

61.7 41 60.04 49 68.04 1.66 -6.34 2.7556 40.1956

67.83 57 76.166 55 74.166 -8.336 -6.336 69.488896 40.144896

73.093 64 83.257 62 81.257 -

10.164

-8.164 103.306896 66.650896 39.271 19 38.079 26 45.079 1.192 -5.808 1.420864 33.732864 24.274 6 25.037 13 32.037 -0.763 -7.763 0.582169 60.264169

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29.055 11 29.961 12 30.961 -0.906 -1.906 0.820836 3.632836 36.069 13 32.084 23 42.084 3.985 -6.015 15.880225 36.180225

33.449 11 30.099 21 40.099 3.35 -6.65 11.2225 44.2225

36.335 17 36.267 24 43.267 0.068 -6.932 0.004624 48.052624 36.572 12 31.359 23 42.359 5.213 -5.787 27.175369 33.489369 32.763 4 23.187 22 41.187 9.576 -8.424 91.699776 70.963776 44.003 8 27.369 31 50.369 16.634 -6.366 276.689956 40.525956

18.61 24 43.292 5 24.292 -

24.682

-5.682 609.201124 32.285124

19.924 11 30.181 6 25.181 -

10.257

-5.257 105.206049 27.636049 18.217 8 27.008 9 28.008 -8.791 -9.791 77.281681 95.863681 19.944 8 27.053 4 23.053 -7.109 -3.109 50.537881 9.665881

18.259 11 30.044 5 24.044 -

11.785

-5.785 138.886225 33.466225

16.896 14 33.223 9 28.223 -

16.327 - 11.327

266.570929 128.300929

17.66 19 37.95 15 33.95 -20.29 -16.29 411.6841 265.3641

21.211 13 31.856 3 21.856 -

10.645

-0.645 113.316025 0.416025

17.82 6 25.366 6 25.366 -7.546 -7.546 56.942116 56.942116

20.027 17 36.232 8 27.232 -

16.205

-7.205 262.602025 51.912025

19.69 13 31.817 8 26.817 -

12.127

-7.127 147.064129 50.794129

21.654 17 35.871 9 27.871 -

14.217

-6.217 202.123089 38.651089 32.308 10 28.897 19 37.897 3.411 -5.589 11.634921 31.236921 33.2518 13 31.957 17 35.957 1.295 -2.705 1.67650704 7.31810704 36.952 23 41.857 25 43.857 -4.905 -6.905 24.059025 47.679025 36.3064 16 34.768 24 42.768 1.538 -6.462 2.36667456 41.75227456 35.8246 11 29.769 24 42.769 6.056 -6.944 36.67029136 48.22469136 35.3949 6 24.771 25 43.771 10.624 -8.376 112.8672512 70.15905121 31.8876 18 36.831 19 37.831 -4.943 -5.943 24.43720356 35.32400356 31.9495 13 31.833 18 36.833 0.117 -4.884 0.01357225 23.84857225 31.9494 15 33.834 19 37.834 -1.885 -5.885 3.55171716 34.62851716

19.133 11 29.951 6 24.951 -

10.818

-5.818 117.029124 33.849124 19.6962 6 24.952 3 21.952 -5.256 -2.256 27.62343364 5.08863364 19.0288 9 27.95 2 20.95 -8.921 -1.921 79.58780944 3.69100944 34.0984 18 37.013 20 39.013 -2.915 -4.915 8.49489316 24.15329316 30.9613 9 28.012 16 35.012 2.949 -4.051 8.69837049 16.40817049 30.0939 13 32.012 16 35.012 -1.918 -4.918 3.67910761 24.18770761 40.9543 24 42.96 27 45.96 -2.006 -5.006 4.02283249 25.05703249 40.9279 19 37.958 27 45.958 2.97 -5.03 8.82030601 25.30190601 40.4192 21 39.956 27 45.956 0.463 -5.537 0.21455424 30.65615424 29.5344 14 32.898 15 33.898 -3.364 -4.364 11.31380496 19.04100496 41.1062 24 42.814 28 46.814 -1.708 -5.708 2.91658084 32.5789808 RMSEz ± 8.861734 ± 6.307187 Vertical Accuracy, Accuracyz = 1.9600 *RMSEz ± 17.368999 ± 12.362086

Table 4.1 shows the RMSE and vertical accuracy analysis

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Table 4.2: Statistical Analysis FOR ASTER, GPS, and SRTM3.

Statistical Analysis

Error parameters

GPS Ellipsoidal Height (m)

ASTER GDEM Ellipsoidal Height (m)

SRTM3 DEM Ellipsoidal Height (m)

ERROR = GPS - ASTER

ERROR=

GPS – SRTM3

Count 71 71 71 71 71

Min 16.896 15.485 20.872 -24.682 -16.29

Max 73.093 83.257 81.257 16.786 -0.466

Range 56.197 67.772 60.385 41.468 15.824

Sum 2167.7928 2322.59 2581.59 -154.798 -413.799

Mean 30.532293 32.7125352 36.3604225 -2.180254 -5.8281549

SE.Mean 1.383612 1.3149911 1.450575 1.026624 0.2881829

Std.Dev 11.658522 11.0803121 12.2227622 8.650484 2.4282726 RMSE ± 8.861734 ± 6.307187 Accuracyz =

1.9600

*RMSEz ± 17.368999 ± 12.362086

Table 4.2: Statistical Analysis for ASTER, GPS, and SRTM3.

Linear regression was carried out using with the free statistical software „R‟. R² and correlation coefficient (r) values were computed using statistical software „R‟.

For R²; summary(lm(HEIGHTS3.csv$SRTM3_HEIGHT~HEIGHTS3.csv$

GPS_Height))$r.squared [1] 0.9612379

>summary(lm(HEIGHTS3.csv$ASTER_HEIGHT~HEIGHTS3.csv$

GPS_Height))$r.squared [1] 0.5064542}

For r, as shown Table 4.3 below: correlation coefficient r Table 4.1 shows the RMSE and vertical accuracy, Table 4.2: Statistical Analysis for ASTER, GPS, and SRTM3, Table 4.3: Correlation coefficient r

GPS_Height ASTER_HEIGHT SRTM3_HEIGHT GPS_Height 1.0000000 0.7116559 0.9804274

ASTER_HEIGHT 0.7116559 1.0000000 0.7127271 SRTM3_HEIGHT 0.9804274 0.7127271 1.0000000

Table 4.3: Correlation coefficient r

Figure 4.1 & 4.2 below show the measure of association through their goodness of fit.

Scatter Plot depicting DEM elevation as a function of GPS elevation for the study area with histograph and boxplot.

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Figure 4:1 Showing goodness of fit with histograph.

Figure 4.2 Showing goodness of fit with boxplot.

4.1.1 Test of significance between the two DEMs and GPS Height

P-value is a statistical analysis tools in hypothesis testing. Null-hypothesis test of significance will help to do this. The free statistical software „R‟ was used to further

ASTER_HEIGHT

20 30 40 50 60 70 80

20406080

20304050607080

SRTM3_HEIGHT

20 40 60 80 20 30 40 50 60 70

203040506070

GPS_Height Scatterplot between DEMs and GPS elevation

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confirm hypothesis testing with p-values between the two DEMs and GPS elevation for the study area, a test of hypotheses (t-test statistic) at 5% significance level was carried out using a simple t-test of the difference in means between two DEMs and GPS Height.

Testing of Hypothesis: No correlation between Aster & SRTM, GPS elevation,

Null Hypothesis: H0: ρ = 0

Alternative Hypothesis: H₁: ρ≠0 Significance Level: 5%

Test Statistic: ρ = Pr (Dataset|H0) Where;

ρ = ρ - value

Pr = probability of sampling the dataset H₀= the null hypothesis given that is true.

For ASTER AND GPS HEIGHT (note = with equal variance) Two Sample t-tests

Data: HEIGHTS3.csv$ASTER_HEIGHT and HEIGHTS3.csv$GPS_Height t = 1.1422, df = 140, p-value = 0.2553

Alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval:

-1.593580 5.954087 Sample estimates:

mean of x mean of y 32.71254 30.53228

For SRTM3 AND GPS HEIGHT (note = with equal variance) Two Sample t-tests

Data: HEIGHTS3.csv$SRTM3_HEIGHT and HEIGHTS3.csv$GPS_Height t = 2.9073, df = 140, p-value = 0.00424

Alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval:

1.864877 9.791405 sample estimates:

mean of x mean of y 36.36042 30.53228