RESEARCH ARTICLE

CO-Kriging Approach for Cartosat-1 Height Productwith ICESat/GLAS Data for Digital ElevationSurface Generation

Anil Kumar & Parul Trivedi

Received: 10 March 2011 /Accepted: 15 June 2011 /Published online: 1 July 2011# Indian Society of Remote Sensing 2011

Abstract Nowadays, Geostatistics and its variousinterpolation techniques have become a major thresh-old area in the field of research in GIS. In this researchwork poorly sampled (less accurate height data relativeto ICESat/GLAS height data) Cartosat-1 height datahas been used with well sampled (more accurate heightdata relative to Cartosat-1 height data) ICESat/GLASLiDAR (Light Detection and Ranging) height pointdata using Cokriging Interpolation technique, to studythe effect of ICESat/GLAS on Cartosat-1 height data.Space borne LiDAR data has led researchers to exploreits utilities in many applications. Space borne LiDARdata can be acquired through space borne LiDARsensors also, like; GLAS (Geoscience Laser AltimeterSystem) system onboard ICESat (Ice, Cloud and landElevation Satellite) satellite. In this study, it has beentried to apply Cokriging interpolation on two differentsources of data sets, with a common variable (eleva-tion) to generate DES and assessment of this surfacehas been conducted by DGPS data. After optimizingCokriging parameters, results of digital elevationsurface (DES) generated using Cokriging showed thatRMSE has been second least than global polynomial incomparison to Kriging interpolation RMSE after beingevaluated by GPS values. So, global polynomial aswell as cokriging interpolation technique out performswhile comparing with kriging technique for DESgeneration.

Keywords ICESat/GLAS satellite data . Geostatisticalanalysis . DES . Cokriging

Introduction

The basic premise of Geostatistics is that observationscloser together are more similar on an average than thosefarther apart. Although geostatistics was developedindependently of GIS, it has become an integral part ofGIS (Barton et al. 1999). The geostatistical techniquesquantify the spatial autocorrelation among measuredpoints and account for the spatial configuration of thesample points around the prediction location (Goulardand Voltz 1992). It creates surfaces incorporating thestatistical properties of the measured data. Geostatisticaltechniques are also applied for generation of DigitalElevation Surface (DES) using height point data (Krige1994, 1999). One of the geostatistical procedures isCokriging, which allows one or more secondary orancillary variables to be included in the model andassuming that the primary and ancillary variables aremoderately correlated, the estimation accuracy of theprimary variable should increase. Cokriging requires amodel of spatial continuity (Myers 1982, 1983). Themost common models of spatial continuity are thevariogram or semivariogram which is used to model theaverage degree of similarity or dissimilarity as afunction of both distance and direction (Stein andCorsten 1991; Pelletier et al. 2004). In this study DESresult are obtained by using poorly sampled (relativelyless height accurate compared to ICESat/GLAS-LiDARdata) Cartosat-1 height data with well sampled (rela-

J Indian Soc Remote Sens (March 2012) 40(1):11–17DOI 10.1007/s12524-011-0144-9

A. Kumar (*) : P. TrivediIndian Institute of Remote Sensing,Dehradun, Indiae-mail: anil@iirs.gov.in

tively more height accurate compared to Cartosat-1data) ICESat/GLAS LiDAR data through cokriginginterpolation technique. This study has been conductedto analyze the interpolation technique for deriving DESfrom poorly sampled Cartosat-1 stereo data and wellsampled ICESat/GLAS data to find out level ofconfidence for Cokriging interpolation technique,whether it can generate better interpolated continuoussurface compared to kriging method and improve theheight accuracy of DES from Cartosat-1 points dataadded with ICESat/GLAS point set.

Study Area and Data Used

The study area, which is moderately hilly, lies in thenorth western part of Dehradun, Uttarakhand State,India, with boundary coordinates as 77°50′9.30″E–77°52′16.32″E and 30°23′23.15″N–30°25′35.00″N asshown in Fig. 1. The data used in this study was

Cartosat-1 height point data, which was derived fromCartosat-1 Stereo pairs. The Cartosat-1 stereo dataused was of 2nd October 2005. The ICESat heightpoint data set considered was acquired from February2003 to February 2008 and were of release 28, wasordered from the NSIDC (National Snow and IceData Center) site for this study. The Geoscience LaserAltimeter System (GLAS) instrument on the Ice,Cloud, and land Elevation Satellite (ICESat) providesglobal measurements of polar ice sheet elevation todiscern changes in ice volume (mass balance) overtime. Secondary objectives of GLAS are to measuresea ice roughness and thickness, cloud and atmo-spheric properties, land topography, vegetation cano-py heights, ocean surface topography, and surfacereflectivity. GLAS has a 1,064 nm laser channel forsurface altimetry and dense cloud heights, and a532 nm LIDAR channel for the vertical distribution ofclouds and aerosols. This covers seven data sets:

a) GLA01: Level-1A altimetry data include thetransmitted and received waveforms from theinstrument.

Fig. 1 Study area: ICESat ground tracks displayed in the studyarea (yellow dots are footprint of ICESat/GLAS-LiDAR data)

Pointno

Latitude Longitude Height ICESat/GLASSheight (m)

ICESat/GLASS heightdifference (m)

1 77°50′42.36744″ 30°23′48.81819″ 493.4484 m 494.7730 −1.32462 77°51′11.37477″ 30°23′52.01163″ 507.8744 m 509.2990 −1.42463 77°51′32.03173″ 30°23′53.67582″ 522.6875 m 520.3230 2.3645

4 77°51′44.23666″ 30°23′46.61847″ 524.4993 m 525.9470 −1.4477

Table 1 Test data fromground based GPS pointobservation

Table 2 Accuracy of GCP’s acquired from geodetic singlefrequency GPS in relative mode

GCP no. PDOP Position quality (M) Height quality (M)

1 2.46 0.009 0.017

2 2.06 0.020 0.040

3 1.44 0.007 0.010

4 1.84 0.015 0.024

5 1.72 0.007 0.012

6 1.94 0.008 0.010

7 1.97 0.008 0.018

8 2.11 0.031 0.052

9 1.84 0.005 0.010

10 2.47 0.008 0.014

11 2.02 0.014 0.018

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b) GLA05: Level-1B waveform parameterizationdata include output parameters from the wave-form characterization procedure and other param-eters required to calculate surface slope and reliefcharacteristics.

c) GLA06: Level-1B elevation data include surfaceelevation, surface roughness assuming no slope,surface slope assuming no roughness, and geodeticand atmospheric corrections for range measure-ments. Both Level-1B products are geolocated tothe center of the laser footprint.

d) GLA12–GLA15: GLA06 is used in conjunctionwith GLA05 to create the Level-2 altimetryproducts. Level-2 altimetry data provide surfaceelevations for ice sheets (GLA12), sea ice(GLA13), land (GLA14), and oceans (GLA15).Data also include the laser footprint geo-locationand reflectance, as well as geodetic instrument andatmospheric corrections for range measurements.

GLA06 Global Elevation Data Product andGLA14 global land surface altimeter data product

ICESat/GLAS Data

GLAS Point maps

Point map Extraction

GLAS Point map and Cartosat - 1 Points

Experiment (2 variables)

Cokriging

Digital Elevation Surface

Point map sets:

2 variables: GLAS Point map and Cartosat - 1 Point map

Cartosat-1 Points

DGPS PointsAccuracy

Assessment

Fig. 2 Methodologyadopted

J Indian Soc Remote Sens (March 2012) 40(1):11–17 13

was used for ground point height information fromICESat/GLAS-LiDAR data.

Methodology

Initially height point information from ICESat/GLASdata and Cartosat-1 stereo data sets were generated.At preprocessing stage all data sets were brought tosame reference frame. Out of 15 products of ICESatdata, GLA06 and GLA14 were used in this study.These were transformed from TOPEX/Poseidon toWGS84 Ellipsoid/Datum using a transformationroutine written in JAVA, as well as height point datafrom Cartosat-1 stereo data set was also transformedinto WGS84 reference frame. Rational functioncoefficients along with Ground Control Points(GCP’s) were used for stereo model generation to

extract height point information from Cartosat-1stereo data set. The orthoimage from Cartosat-1 stereowas also generated to depict ICESat/GLAS data whileoverlaying on it, to be used during ground truthingwith the help of geodetic single frequency globalpositioning system in differential mode.

The GPS data was collected to be used as GCP’sfor generation of a stereo model from Cartosat-1stereo data sets as well as evaluating the DESgenerated using ICESat/GLAS data as well asCartosat-1 stereo data sets in this research work. Ithas been tried to observe the GPS data in DGPS modewith phase measurement techniques to have accuracyof GPS data within 1 cm to 30 cm±2 ppm. TheAccuracy of GCP’s acquired from Geodetic SingleFrequency GPS in Relative mode is shown in Table 2.While generating the stereo model, seven groundpoints were used as GCP’s and other four knownpoints on the ground were used as check point. Theobservation time for rover was kept 1 h each andobservation time for base was 72 h. Tables 1 and 2shows the list of GPS points used for evaluation ofDES generated from ICESat/GLAS data as well asCartosat-1 stereo data sets.

Fig. 5 Semivariogram model for covariable

Table 3 Cokriging parameters

Semivariogrammodel

Nugget Sill Range

Predictand (cartosat-1) Wave Model 50 8500 3000

Covariable (LiDAR) Wave Model 10 7500 3000

Crossvariogram Wave Model 0 3700 2000Fig. 4 Semivariogram model for predictand

Fig. 3 Crossvariogram model of predictand and covariable

14 J Indian Soc Remote Sens (March 2012) 40(1):11–17

After preprocessing data, 3 data sets weregenerated: Cartosat-1 height data, ICESat/GLASheight data, and GPS points that have been trans-formed into WGS84 reference frame. In this

research, Cokriging method was applied on ICE-Sat/GLAS point map and Cartosat-1 points. Meth-odology adopted in this research work has beenshown in Fig. 2.

Fig. 6 DES using Cokriging interpolation

GPSpoints

GPS–cartosat-1(m)

GPS–ICESat(m)

GPS–globalpolynomial (m)

GPS–Kriging(m)

GPS–Cokriging(m)

1 −0.452 −1.325 −2.347 −3.345 −1.0072 −11.876 −1.423 −1.274 −3.639 −1.9523 4.138 2.365 1.475 −2.458 3.409

4 0.119 −1.448 −0.620 −2.462 −0.752RMSE(±) 6.29 1.69 1.55 3.02 2.07

Table 4 DES height fromdifferent data/interpolationtechniques relative to GPSdata

The range height differencesof Cokriging digital eleva-tion surface are between−0.752 m and 3.409 m

J Indian Soc Remote Sens (March 2012) 40(1):11–17 15

Cokriging interpolation technique is applied usingparameters like semivariogram models, limiting dis-tance, etc. Different types of semivariogram modelswere analysed to obtain the best fit or goodnessmodel. Further, various combinations of limitingdistance and maximum and minimum number ofpoints were used so as to obtain best DES output.Figure 3 shows crossvariogram model of predictedand covariable, while Figs. 4 and 5 here demonstratesthe semivariogram model for predicted (Cartosat-1point data) and covariable (ICESat/GLAS data)respectively. Cokriging parameters that were used toobtained these best fit variogram models have seenshown in Table 3.

Result and Discussion

Digital elevation surface model generated with Cok-riging interpolation techniques using Cartosat-1 andICESat/GLAS can be seen in Fig. 6 wherein limitingdistance was 1,500 and minimum and maximumnumbers of points used were 1 and 30 respectively.

While digital elevation surface model generatedwith Cokriging interpolation technique using ICESat/GLAS height data with Cartosat-1 Point Map wascompared with sample ground coordinates fromDGPS data along with results of Global Polynomialand Kriging (Kumar and Vyas 2009) and differencesare shown in Table 4.

The GPS point data used here to evaluate relativeheight differences between the Global Polynomialinterpolation, Kriging interpolation and Cokriginginterpolation techniques output and GPS data. Heightof check point 1 and 4 observed by GPS were lying infallow agriculture fields, check point 3 was lying inarea and check point 2 was raod crossing surroundedby tall sal tree forest. As the check point 2 wassurrounded by tall sal tree forest that is why whilecomparing its height with GPS was found largedeviation. While evaluating height data generatedfrom Cartosat-1 stereo data, the height variation hasbeen observed from 2 to 12 m while comparing itwith GPS height data (Kumar 2006). This variation inheight has been found due to variation in contract inground features as well geometrical variation due to+26° tilt in fore scene. Geometrical variation due to+26° tilt in fore scene, comparion to aft scene hasbeen found more critical while observing the cartosat-

1 data sets of Badrinath rigion, where height variationare of the range of 500–800 m within very small span.From Figs. 7 and 8 it can be seen while applyingCokriging with detail parameter inputs, the RMSEobtained was 2.07 m in comparison to Kriginginterpolation RMSE height difference which has beenfound to be 3.02 m. Also Cokriging interpolatedheights of DES were close to interpolation techniqueslike; Global Polynomial applied on point height datagenerated from Cartosat-1 data.

Conclusion

Based on the analysis about the elevation differenceresult of interpolation type, the range of heightdifference of Cokriging DES is between −0.752 m and3.409 m. In line with this result, Cokriging interpolationmethod that gives the least height differences of −0.75mcompared with GPS that uses the data of Cartosat-1point map and ICESat/GLAS point map for Cokriginginterpolation, the highest elevation difference comesfrom Kriging method that uses only Cartosat-1 pointmap. The average height difference DES generatedusing ICESat/GLAS added with Cartosat-1 data withdifferent kriging interpolation techniques were between

DES Height of Cokriging Interpolation Technique Relative to GPS Data

-3

-2

-1

0

1

2

3

4

1 2 3 4

GPS Points

Hei

gh

t V

aria

tio

ns

(M)

Fig. 7 DES height of Cokriging interpolation techniquerelative to GPS data

Fig. 8 DES height from different interpolation techniquesrelative to GPS data

16 J Indian Soc Remote Sens (March 2012) 40(1):11–17

1.57 m and −4.88 m (Kumar and Vyas 2009). From thiswork it can be concluded that Cokriging interpolationmethod outperform, kriging method. This work con-cludes that ICESat/GLAS space based data, freelyavailable, which is also more accurate than height datagenerated from Cartosat-1 stereo data, if fused withheight data generated from Cartosat-1 stereo data, canproduce more accurate DES. There is also need forunderstanding each aspect and concept of all theparameters that are used for any interpolation tech-nique, as there might occur error which further can leadto improper conclusion.

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