By analyzing the data of experimental DEM creation using three popular interpolation techniques inverse đistance weighted - IDW, spline, and kriging in four diíĩerent survey projects Tha
Trang 1VNU Joum al of Science, Earth Sciences 24 (2008) 176-183
Assessment o f the iníluence o f interpolation techniques
on the accuracy o f digital elevation model
Tran Quoc Binh'’*,Nguyen Thanh Thuy2
a> Colỉege o f Science, VNU (2> Institute o f Surveying and Mapping, MoNRE
Received 10 December 2008; received in revised form 26 December 2008
Abstract Digital Elevation Model (DEM) is an important component of GIS applicatíons in many socio-economic areas Especially, DEM has a very important role in monitoring and managing natural resources, preventing natural hazards, and supporting spatial decision making
Usually, DEM is built by interpolation from a limited set of sample points Thus, the accuracy
of the DEM is depended on the used interpolation method By analyzing the data of experimental DEM creation using three popular interpolation techniques (inverse đistance weighted - IDW, spline, and kriging) in four diíĩerent survey projects (Thai Nguyen, Go Cong Tay, Co Loa, and Duong Lam), the paper has made an assessment of iníluence of interpolation technique on the DEM accuracy Based on that, some recommendations on choosing interpolation technique has been made: for mountainous areas the spline regularized is the most suitable, for hilly and flat areas, the IDW or kriging ordinary with exponential model of variogram are recommended
Keywords: Digital elevation model (DEM); DEM accuracy; Interpolation technique.
1 Introduction
Digital elevation model (DEM) is an
important part o f the spatial data ừifrastnicture
(SDI) DEMs are widely used in natural
resource management, natural hazard
prevention, land-related decision making, etc
ưsually, the DEMs are produced by
interpolating the elevations o f a set o f sample
points for predicting the elevations at all
positions inside the DEM area [4]
Consequently, interpolation technique will
contribute to the error budget o f DEM
* Corresponding author Tel.: 84-4-38581420
E-inail: binh.geomatics@gmail.com
Several researches were conducted on the relation between DEM accuracy and interpolation technique Fencík and Vajsáblová [3] investigated the DEM accuracy o f Morda- Harmonia territory (Hungary) created by using kriging interpolation with various variogram models The author concluded that the linear model o f variogram is the most suitable for the study area
Research o f E1 Hassan [2] on the accuracy comparison o f some spline interpolation algorithms for the test areas in Caừo (Egypt) and Riyadh (Saudi Arabia) shown that the pseudo-quintic spline algorithm gives the best accuracy o f DEM
176
Trang 2T.Q Binh, N T T huy / V N U Ịoum al o f Science, Earth Sáences 24 (2008) Ì76-Ĩ83 177
Chaplot et al [1] used some interpolation
techniques (kriging, inverse distance weighted,
multiquadratic radial basis íunction, and spline)
for creating DEM in various regions o f Laos
and France The author.has concluded that for a
high density o f sample points, all o f the
interpolation techniques períòrm similarly; and
for a low density o f sample points, kriging and
inverse distance weighted interpolation
techniques are better than the others However,
the research carried out by Peralvo [8] ÚI the
two watersheds o f Eastem Andean Cordillera o f
Ecuador shows other results: the inverse
distance weighted interpolation produced the
most inaccurate DEM
Our review o f conducteđ researches shows
that they usually were carried out in small areas
(less than 100 ha) Due to the differences in
types o f topography, surveying methods, and
levels o f technology application in various
countries, the results o f these research
sometimes are contrary each to others
This research investigates the influence o f
interpolation techniques on the accuracy o f
DEM in the examples o f four projects in
Vietnam The projects ha ve various areas, and
are belonging to typical types o f topography o f
Vietnam The research is limited to two
surveying methods: digital photogrammetry, and
total station / GPS The LIDAR and contour
digitizing methods are out o f scope
2 R esearch m eth o d
2.1 The íested interpoỉation techniques
This research uses three popular
interpolation m ethods for experimental creation
o f DEMs: inverse distance weighted, spline,
and kriging
- The inverse distance weighted (IDW)
interpolation determines the elevation o f a
speciíĩc point using a linearly weighted
combination o f the elevations o f nearby located
sample (known) points [5] The weight W( of a
sample point i is a íunction o f inverse distance
as follows:
w,.=l/</,', (1)
where d is the distance from point o f interest
to the sample point i; and the power p
conừols the signiíĩcance o f sample points to the interpolated values, based on their distance to the output point The higher the power, the more emphasis can be put on the nearest points Thus, nearby data will have the most iníluence, and the surface will have more detail (less smooth)
- The spline iníerpolation estimates the
elevation o f a speciíic point using a mathematical íunction that minimizes the overall surface curvature, resulting in a smooth surface ứiat passes exactly through the input points [5] Conceptually, the sample points are extruded to the height o f their magnitude; spline bends a sheet o f rubber that passes through the input points while minimizing the total curvature o f the suríace It fits a mathematical íimction to a speciíied number o f nearest input points while passing through the sample points There are two spline methods: regularized and tension The regularized method creates a smooth, gradually changing surface with values that may lie outside the sample data range The tension method Controls the stiffhess o f the surface according to the character o f the modeled phenomenon It creates a less smooth surface with values more closely constrained by the sample data range The main parameters o f the spline interpolation are the number o f sampled points used for interpolation, and the weight For the regularized spline, the higher the weight, the smoother the output suríace For the tension spline, the higher the weight, the coarser the output suríace More detailed information about the spline interpolation can
be found in [6]
- The kriging interpoỉation assumes that the
distance or direction between sample points
Trang 3178 T.Q Binh, N.T Thuy / VN U Ịoum al of Science, Earth Sciences 24 (2008) 176-Ĩ83
reílects a spatial correlation that can be used to
explain the variation in the surface [5] Kriging
íĩts a mathematical íunction to a specified
number o f points, or all points within a
specified radius, to determine the output value
for each location It is a multistep process
including: exploratory statistical analysis o f the
data, variogram modeling, creating the surface
Kriging is most appropriate when there is a
spatially correlated distance or directional bias
in the data Kriging is similar to IDW in that it
weights the surrounding measured values to
derive a prediction for an unmeasured location
However, in kriging, the weights are based not
only on the distance between the measured
points and the prediction location but also on
the overall spatial arrangement o f the measured
points To use the spatial arrangement in the
weights, the spatial autocorrelation must be
quantiíĩed through empirical semivariograms
The semivariogram can have one o f the
following models: circular, spherical, exponential,
gaussian, and linear There are two kriging
methods: ordinary and universal The ordinary
kriging assumes that the constant mean is
unknovvn, while the universal kriging assumes
that there is an overriding trend in the data and
this ữend is modeled by a polynomial Detailed
iníbrmation about the kriging interpolation can
be found in [7]
Among the three tested interpolation
techniques, LDW is the fastest and kriging is the
slowest technique Spline gives the smoothest
DEM surface
2.2 The workfỉow
The assessment o f iníluence o f intetpolation
technique on the accuracy o f DEM is carried
out according to the workflow presented in Fig
1 The computation is done by using ArcGIS
software developed by ESRI [5]
The input data consists o f two point sets: the
set o f source (sample) points, and the set o f
control (check) points The conừol points are
evenly đistributed and accurately measured The
number o f control points is about 0.5-1.0% o f the number o f source points, but not less than 50 Both point sets are imported into a geodatabase as point feature classes having an
attribute fíeld Elevation The source point set is
then interpolated to create a raster DEM with a relatively high resolution The high resolution is defmed in order to eliminate the iníluence o f the output resolution on the accuracy o f DEM The three described above interpolation techniques are applied with varying parameters
Fig 1 The workflow for asscssing the iníluencĩ of interpolation technique on the accuracy of DEM by
using ArcGIS software
In the next step, the elevations of interpolated DEM are exừacted to the control
points by using the ArcGIS's tool Exiract
Values to Points Thus, the output poữits vvill
have two attributes: the original Elevation, and the extracted from DEM ínt_Elevation Tiese
attributes are compared each with other to
đerive the elevation diíĩerence A( for each pont i:
A, = Int _Elevation - Eỉevation (2)
Trang 4T.Q Binh, N.T Thuy / V N U Ịoum al o f Science, Earth Sãences 24 (2008) 176-183 179
The calculated differences are stored in a
newly created attribute íìeld Elev_Diff.
In the fínal step, the RMSE (root mean
square error) o f the interpolated DEM is
calculated by using the following formula:
where N ỉ s the num ber o f control points
For automated execution o f the workflow,
we have developed a model in the Model
Builder extension o f ArcGIS software For each
project, the user only has to change the
interpolation m ethod and deíine its parameters
in order to re-run the entire process The model
for IDW interpolation is presented in Fig 2
Fig 2 Automated workflow execution
by using ArcGIS’s Modẹl Buiỉder.
Li the model in Fig 2, the tools (denoted by
rectangles) are used as follows:
-ID W : interpolate source points into raster
DEM (it can be substituted by spline or kriging
for o:her interpolation techniques)
-Extract Values to Points: extract interpolated
elevítions from the created DEM into the
control point feature class, and create a new feature class (Extracted Pts)
- Add Field: add the E lev_D iff íield to the
feature class Exữacted Pts
- Calculate Field: calculates the elevation difference A, by using Eq 2 and takes its square value
- Summary Statistics: calculates RMSE o f the interpolated DEM by using Eq 3
2.3 The study areas
This research is based on the survey data o f four topographic mapping projects: Thai Nguyen, Go Cong Tay, Co Loa, and Duong Lam The projects are located in areas belonging
to diíĩerent topography types Table 1 lists the short description o f these projects Since the Thai Nguyen prọịect is relatively large and covers three types o f topography, it was divided into three subprojects: Plain Thai Nguyen, Hilly Thai Nguyen, and Mountainous Thai Nguyen
3 R esults and discussion
The results o f testing the inAuence o f interpolation technique on the accuracy o f DEM
is presented in íigures 3+6 as combined graphs The horizontal axes represent interpolation techniques with varying parameters, and the vertical axes represent the root mean square errors (RMSE) o f DEMs in the unit o f meter Fig 3 uses the following notation:
- Plain, Hill, Mountain: the subprojects o f Thai Nguyen project that are located in plain, hilly and mountainous areas respectively
- s, c, E, G, L: spherical, cừcular, exponential, gaussian, and linear models o f experimental variogram for the ordinary kriging interpolation method
- LD, QD: linear with linear drift and linear with quadratic drift for the universal kriging interpolation method
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Table 1 Characteristics of the DEM prọịects
topography Survey method
Project's area Thai
Nguyen
South of Thai Nguyen Province
21°18'-ỉ-22o00’N,
105°26'-h106°25' E
Combined plain, hills, and
mountains
Digital photogrammetry by using aerial photos at 1:30,000 scalc Source point sampling interval ~25m
14,000 ha
Go Cong
Tay
South of Go Cong Tay Dist.,
Tien Giang Prov., Cuu Long
River Delta K n ý + l t m N ,
106°32,4-106°4ơ E
Plain Digital photogrammetry by
using aerial photos at 1:22,000 scale Source point sampling interval ^30m
1,295 ha
Co Loa South-East of Dong Anh Dist.,
H a n o i^ r O ó ^ r o ^ N ,
105°5r-rl05o53' E
Plain Digital photogrammetry by
using aerial photos at 1:7,000 scale Sourcc point sampling interval ~20m
245 ha
Duong Lam North-West of Son Tay Town,
Hanoi 21°08'-i-21o10, N,
105o27'-rl05o29' E
Midland, hills, mounds
Total station in combination with GPS Source point sampling interval 2-r30m
211 ha
RMSE (m )
7
6
6
4
3
2
T h a i N gu yen p ro ject
* ■ MAI ■
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ln w o * D M anc* w«tgr<t«d vory%xj p ơ « *f
p)
a i a»6 0 2 a.3 04 Spến* (to g iia rM d (w*n varyt^g
0 06 a i 0 16 a 2 0 5 04
Ỉ T tto n Cw*ti varytXỈ
c c 6
•Mg*»o OrdTiory ) 101^0 GO
'ÚTỶvmat
0M 0 6 g ạ 191 0.3106 02070 0Ì912 0 2 fW 0 3<O6 0.6000 a60B6 ftậW 6 g ạ p g 069 0-6868 0.4144 (X4132 (L4Ì26 0.4121 0-4114 Q4>0> 0362 0363 OMO 0360 0 364 O M ? Q296 -n 06266 06018 0 6607 0 6486 0 6276 06142 06066 0ỏ047 a«M 7 0.61B6 0 l 6208 0423 0634 06137 06136 a6136 06136 05115 0 6136 0691 0491 0486 Oôốò Oởỡl 0 Ô&3 0536
• M a r t O ì 6 ii3 1 <9761 4.666 Í2 J M 4066 40677 4 1236 2 400 2 4141 241M 2-4213 2 42*2 24277 26360 2 5062 2 5366 2 637 2 U M 7 M ỗ* 6 M 2 6«08 6806 6 OM 6040 6623 2966
Fig 3 Results of testing DEM accuracy in the Thai Nguy en project
R M S E (m )
0.5
0.4
-0.3
Co Loa p ro ie ct
0 2
01
LD QO SpttTM R«ọuá«riz*d (vrith varylng Spto« T«n»ton (w *h va/ytng w *ígN ) Khgtng O rd ta ry Kriging
RMSC 0 345 0 359 0 3S3 0 343 0 1 3 4 0 328 0 323 0 431 0.439 0 442 0 444 0 446 0 447 0 375 0 375 0 375 0.375 0 374 0 374 0 304 0 364 0 361 0 3Ỗ4 0 384 0 378 0 3ÔC
1 1.5 2 J 4 s 0
lrtv«na O átan c* WMghl«d (wrth varytng
0 06 0.1 0.1S 0 2 0 3 0.4 0.06 0.1 0.15 0.2 0 3 0 4 s
Spto« T«n»ton <wtlh varytng w»ígM)
c E G L Krigmg Ordếrury
Fig 4 Results of tcstừìg DEM accuracy in the Co Loa project
Trang 6r.Q Binh, N.T T huy / V N U Ịoum aỉ o f Science, Earth Sciences 24 (2008) 176-183 181
R M IS E (m) G o C o n g T a y p r o j e c t
0
>0 -(U0ft
0.1« -*
O a OO
InvvrM Dtatance (wttn vorytig POww p ) Spln* R tợ iio rtM d 0 " * * vor/T Q we*Qhí) Spềr* Taraksn (wllh varylng w*tght)
K/tgíng Ordkiary
10 QD Unh/wrt
— RVASỈ 0.073 0.072 0-071 a.060 0.066 006« 0.066 0066 0.067 0.067 0.067 0 067 0.067 a066 0.066 0066 O.Cbố 0.06Ỏ 0066 0076 0.076 0.076 0.076 0076 0.078 0.070
Fig 5 Results of testing DEM accuracy in the Go Cong Tay prọịect
8M 5E (m ) D u õ n g Lam p r o J ê C t
4.0
v.w
1 1.5 2 3 4 5 6
Irvene Dto»arc» W e ^ t e d (wtth varylnQ p o w «
p )
0.06 01 0 16 a 2 0.3 0.4 Splne Q«guÉarto*d varyt-iQ w « 0 rtf)
0.06 ịa i 0.16 0 2 0.3 0.4 Spin* ĩ*n*íon M t t i vorytig w»íght)
s c E 6 l KrtQtnQ OrcUnaíY
ID OD KHgtno UnfwB*cí
— 3MSE 0 4 » 0 M J 0 3Ô7 0.3S6 0.360 0.366 0.371 3 347 3.66» 3 6*7 1789 3 «20 3.Ỗ20
„
1.143 1.093 1 067 1.061 I.02B 1010 0.279 0.278 0.276 0.378 0.284 0.346 0 346
Fig 6 Results of testing DEM accuracy in the Duong Lam prọịect
3.1 The Thai Nguy en prọịect
The results o f testing DEM accuracy in the
Thai Nguyen project is presented in Fig 3 For
this project, some remarks can be made as
follows:
- The error o f DEM in the mountainous
subproject is much higher than those in the
plain and hilly subprojects The reason is that
the elevation in mountainous areas strongly
varies, while the interpolation techniques can
account only for gradual changes over space
- Among the three tested interpolation
techniques, the spline One (regularized or
tension) produces a much lower level o f error in
the mountainous area
- In the plain and hilly areas, all three
interpolation techniques give roughly comparable
results The IDW is slightly better than others in
the plain area, while the kriging with exponential model o f semivariogram gives the smallest RMSE (0.485m) ừi the hilly area
- For the IDW interpolation, when the
power p increases, the error o f DEM decreases,
but only by a small amount Thus, for improving the computational speed, one can
choose a relatively small value o fp.
- For the spline interpolation, the tension method has some advantages over the regularized one in the plain and hilly areas Conversely, the regularized method is better in the mountainous area
- For the kriging interpolation, the ordinary method using exponential model and the universal method using linear model with quadratic drift (QD) gives slightly smaller RMSEs than other methods
Trang 7182 T.Q Binh, N.T Thuy / V N U Ịoum al o f Science, Earth Sciences 24 (2008) 176-183
3.2 The Co Loa prọịect
The results o f testing DEM accuracy in the
Co Loa project are presented in Fig 4 It can be
readily seen that the graph for Co Loa is very
similar to the one for the plain area o f Thai
Nguyen project The EDW with a high value of
power p produces the best results, while the
spline regularized produces the worst
However, due to the relatively ílat characters of
topography in Co Loa, the interpolation
techniques do not have a strong effect on the
accuracy o f DEM: the eưors are within the
range írom 0.32m to 0.38m except for the cases
o f using the spline regularized method
3.3 The Go Cong Tay project
Fig 5 shows the DEM accuracy obtained in
the Go Cong Tay project Since the project area
is very flat with elevation varied only from 0 to
4 m, the interpolation does not have much
iníluence, and the accuracy o f DEM is very
high All three interpolation techniques give
almost the same results, only the kriging One
shows a slightly higher level o f error Thus, for
a very flat area like the Go Cong Tay project,
the DEM accuracy isn't the main criterion for
choosing interpolation technique The criterion
can be the computational speed (choosing IDW)
or the smoothness o f the DEM (choosing spline)
3.4 The Duong Lam prọịect
The results o f testing DEM accuracy in the
Duong Lam project are shown in Fig 6 Since
the survey method used in this project (total
station and GPS) differs from the one used in
other prọịects (digital photogrammetry), the
graph in Fig 6 has a shape that is dissimilar to
those in íĩgures 3-Ỉ-5 The spline regularized
interpolation gives an extreme (abnormal)
RMSE of DEM, reaching 3.8 m, what is 13.7
times more than the error given by kriging
ordinary interpolation (0.278 m) The spline
tension interpolation is much better than the
spline regularized one, but still has an error
significantly large than other techniques The phenomenon can be explained as follows:
- In total station / GPS surveying, the num ber o f surveyed (sampled) points is very limited Hovvever, these points are very well đistributed, usually along breaklines vvhere the terrain suríace sharply changes The location o f each surveyed point is chosen manually by the surveyors based on their interpretation of topography and with some statistical meaning Meanwhile, the spline interpolation assumes that the suríace is smoothly passed through sampled points, and thus it is not suitable for
the cases when most of these sample points are
allocated along breaklines
- The abnormal eư or given by spline regularized method is due to the fact that the elevation peaks in the Duong Lam project were already surveyed in the íĩeld by placing sample points on them The spline regularized tends to interpolate the elevation beyond the surveyed range, i.e might give a elevation far higher ứian the surveyed peaks that leads to the abnormal error
- Since the distribution o f sample points in total station (or GPS) surveying has some statistical meaning, kriging interpolation - the most statistically rigid interpolation technique - may have some advantages over others
A s it shows in Fig 6, among the three tested interpolation techniques, the kriging ordinary with circular or exponential model has the best accuracy (RMSE o f 0.278 m) The IDW interpolation is a bit less accurate with RMSE of 0.356 m However, the DDW is much faster than the kriging, and thus the choice o f optimal interpolation technique for the projects similar
to Duong Lam is not obvious, especially if they cover a large area
3.5 Recommendations on choosing interpolation technique
From the above discussions, we have made some recommendations on choosing appropriate interpolation techniques based on the type o f topography and surveying method (Table 2)
Trang 8T.Q Binh, N T T huy / V N U Ịoum al o f Science, Earth Sâences 24 (2008) 176-183
T able 2 Recom m endations on choosing interpolation technique
183
Type of Survey method Interpolation technique
Mountainous
Hilly
Plaừi (Flat)
Hilly or flat
Digital photogrammetry Digital photogrammetry Digital photogrammetry Total station / GPS
Spline regularized with any weight
IDW with power p > 3
IDW with power /7=3+5 Kriging ordinary with exponential model for small areas, EDW with p=2-r3 for large areas
Spline tension Spline tension spline or kriging
Kriging
Spline, especially spline regularized
If there are several topography types
available in the project area then the project can
be divided into subprojects with relatively
homogeneous type o f topography This can be
done automatically by analyzing the variation
o f elevation by using statistical indicators, such
as variance or Standard deviation
4 Conclusions
Interpolation technique plays an important
role in achieving a high accuracy o f DEM The
iníluence o f interpolation technique on the
DEM accuracy depends ồn the type o f
topography, and the distribution o f sample
points, what is directly related to the surveying
method This research has examined three
interpolation techniques (EDW, spline, and
kriging) in four diíTerent survey prọịects Based
on the analysis o f obtained results, some
recommendations on choosing the optimal
interpolation technique has been made: for
mountainous areas, the spline regularized is the
most suitable; and for hilly and flat areas, the
IDW or kriging ordinary with exponential
model o f variogram are recommended
A cknowledgem ents
This paper was completed within the
framework o f Fundamental Research Prọịect
702406 funded by Vietnãm Ministry o f Science
and Technology
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