
Research Article


Production of Optimized DEM Using IDW Interpolation Method (Case Study; Jam and Riz BasinAssaloyeh) 

K. Soleimani
and
S. Modallaldoust



ABSTRACT

In this research, preparing the optimized Digital Elevation Model (DEM)of Jam and Riz basin was studied by use of Inverse Distance Weighting (IDW) and utilization of GIS technique. Performing of IDW method depends on several factors including cell size, number of neighbor`s points, point searching radius and optimized power. On this basis, two Geostatistical methods were used for determination of points searching radius of standard ellipse and standard deviation ellipse. Considering the fixed cell size in network with value of 3 which represents weighting degree of points and with determining the rotation angle and measure of axis of standard deviation ellipse and calculation of optimized radius in standard ellipse by use of statistical method, then optimized power was automatically derived in ArcGIS 9.2 environment. In this method the number of neighbor`s points was selected with four repetition points of 3, 5, 7 and 15. However, 8 digital elevation models were gained after the mentioned processes. Finally, digital elevation models of 1 to 8 were compared with control points using compare means test in SPSS11.5 statistical software which shown the IDW3 with the best conditions recommended as the optimized model. Although the results are showing a similar forms but from them IDW3 model has the lowest mean standard error of 0.26842 which is used seven neighbor points.





INTRODUCTION
Topographic conditions of the watershed are one of the integrated physical
factors which can be seen in nature. In other word, every part of the land characterized
with an elevation which in most cases is more similar to the other points of
the catchments, however using some indicated points as ground control points
the other unknown point will identified. Estimation and assessment method of
continuous variable value in area where there is no any experimental model and
the ground control points are scattered, interpolation method can be used (Bob
and Booth, 2000). In fact, interpolation method indicates the continuous spatial
variations as identified surface. For the mentioned purpose IDW can be used
in interpolation method. In this way, the value of each variable will be calculated
base on neighbors mean in specific distance. So that, distance inverse is weighted
from unknown points. The distance of unknown point's decreases from control
points is related to their neighboring so the value weight of the nearest points
will increase and unknown points will be estimated by use of surrounding points
of a certain radius (Childs and Colin, 2004). When the power is zero, the distance's
role can be ignored and unknown points reached from the neighbor points mean.
While the power increases the distance affect would increase and closer distances
reached to the higher weight. Usually, in IDW model is recommended to use a
power higher than 1 (Meyers, 1994). The gained results layers of this method
depend on searching radius and number of neighbor points which including the
recent points. It can be decided to have an equal weight for the all directions
and specified circle or ellipse which included unknown points in their center,
if there is no any trend of direction for the remind data. The value of point
which placed in ellipse which is not clear so it can be calculate using the
existent points in ellipse. Then the space of every point will be measured.
Finally the distance inverse will be computed according to the unknown pint
so, the power obtains and its average will be considered for unknown points
(Tali, 2004). In fact the power degree is a weight which is given to the related
distances. Therefore, the point's distances increases from unknown point with
lower weight in assessment of these points (Johnston and Kevin, 2001). A DEM
is a numerical representation of topography, usually made up of equalsized
cells, each with a value of elevation. Its simple data structure and widespread
availability have made it a popular tool for land characterization. Because
topography is a key parameter controlling the function of natural ecosystems,
DEM_{s} are highly useful to deal with everincreasing environmental
issues. Since many GIS applications rely on DEM_{s}, their intrinsic
quality is critical, particularly for hydrologic modeling (Beven and Krikby,
1979; O’loughlin, 1986; Darboux et al., 2002) or soil distribution
analysis (Bloschl and Sivalapan, 1995; Chaplot et al., 2000; Mc Bratney
et al., 2003). The applications of DEM_{s }are very diverse,
ranging from basin characterization which requires the investigation of large
areas, to the evaluation of water pounding capacity at the clod level that requires
very accurate height estimates. The development of numerical representations
of landscapes over large area with a high resolution DEM is thus one of the
most important scientific challenges of environmental studies. Several factors
affect the quality of DEM_{S}. An initial source of errors can be attributed
to the data collection. The quality of the estimation of height for each data
points depends on the technology applied. Some of the methods available include
the ground based or airborne automatic laser scanner which is of a very high
resolution and suitable for relatively small areas (Darboux and Huang, 2003).
Conventional topographic surveys with a laser theodolite use at the meso scale
and with a centimetric accuracy and use of existing contour maps, stereoscopic
airphotos or high resolution satellite imagery for the characterization of
large areas (Toutin and Cheng, 2002; Poon et al., 2005). The use of DEM_{S}
generated from low density altitude data points may result in over estimations
of secondary topographic attributes such as the upslope contributing areas (Quinn
et al., 1991; Zhang and Montgomery, 1994; Brasington and Richards, 1998)
and under estimation of slope gradient (Chaplot et al., 2000; Thompson
et al., 2001; Toutin, 2002). Other sources of errors include the spatial
structure of altitude and the interpolation technique for DEM generation (Wood
and Fisher, 1993; Wilson and Gallant, 2000). The topographic modeler must be
particularly careful when selecting the techniques for interpolation between
the initial sampling data points of altitude, as this could have a great effect
on the quality of DEM_{S}. Many interpolation techniques exist. The
question of which is the most appropriate in different contexts is the central
question and has stimulated several comparative studies of interpolation accuracy
(Weber and Englund, 1992, 1994; Carrara et al., 1997; Robeson, 1997).
The existing literature, however, tends to be equivocal as to which interpolation
techniques is the most accurate. Some studies (Creutin and Obled, 1982; Laslett
and Mc Brantney, 1990; Laslett, 1994; Burrough and Mc Donnell, 1998; Zimmerman
et al., 1999; Wilson and Gallant, 2000) indicate that among the many
existing interpolation techniques, geostatistical ones better than the others.
In particular, Zimmerman et al. (1999) showed that Kriging yielded better
estimations of altitude than IDW did, irrespective of the land form type and
sampling pattern. This result is probably due to the ability of Kriging to take
into account the spatial structure of data. However, in other studies (Weber
and Englund, 1992; Gallichand and Marcotte, 1993; Brus et al., 1996;
Declercq, 1996; Aguilar et al., 2005), neighborhood approaches such as
IDW or radial basis functions were an accurate as Kriging or even better. Keranchenko
and Bullock (1999) have compared IDW, ordinary Kriging and log normal ordinary
Kriging for the soil properties (phosphorous (p) and potassium (k) of 30 experimental
fields. They have found that if the underlying data set is log normally distributed
and contains less than 200 points, log normal ordinary Kriging generally outperforms
both ordinary Kriging and IDW; otherwise ordinary Kriging is more successful.
Chaplot et al. (2006) in their study accuracy of interpolation techniques
for the derivation of digital elevation models in relation to landform types
and data density concluded that under conditions of high C.V, strong spatial
structure and strong anisotropy, IDW performs slightly better than the other
method. Robinson and Metternich (2006) in their study testing the performance
of spatial interpolation techniques for mapping soil properties have used IDW
method and concluded that IDW is able to interpolate subsoil PH with a sensible
accuracy. Ruhaak (2006) has developed a program which easily interpolates the
type of 3D scattered data and produces satisfied results. For the interpolation
algorithm has used a modified version of IDW. In this research, preparing the
optimized digital elevation model of Jam and Riz basin was studied by use of
Inverse Distance Weighting and utilization of GIS technique. With identified
cell size of pixels in network with 3 m and determining the rotation angle and
measure of axis of standard deviation ellipse, optimized radius was calculated
in standard ellipse by use of statistical method. Then optimized power was automatically
derived in ArcGIS 9.2 environment. In this method the number of neighbor's points
was selected with four repetition points of 3, 5, 7 and 15. However 8 digital
elevation models were gained after the mentioned processes. Finally, digital
elevation models of 1 to 8 were compared with control points using compare means
test in SPSS11.5 software which shown the IDW3 whit the best conditions recommended
as the optimized model.
MATERIALS AND METHODS Jam and Riz basin is located in 25 km toward North Kangan and Jam town and 220 km from Southern part of Boushehr Port. The geographical location of the study area is indicated 51°, 48’, 3.17″E. to 52°, 25’, 14″E and 27°, 44’, 28″N to 28°, 14’, 55″N (Fig. 1). Jam and Riz basin is surrounded with Zard Kouh range in north and Sarkhan Mountain in north easternen, Haft Chah, Takhteh Siah and Charm Ayne in south eastern, Kachhar in south and Sarcheshme in southern west. The only surface streams of Jam and Hramiaki flow in this area which is by end of spring after conjunction together are formed the main stream of Baghan and finally as the main branch joined to the Mond river. The area of the basin was estimated as 90919.2 ha using Arc GIS 9.2 software. The highest point of the study area shows 1414 m and its lowest point is 57.764 m from the sea level (Modallaldoust, 2007). Several materials have used for generating digital elevation models using IDW interpolation method as follow:
Topographic maps at 1:250000 scale of 1999 from the Iranian Geographical Organization.
For the IDW model to producing the elevation points on the maps at 1:25000 scale
of 2001 from the National Cartographic Centre of Iran have used. These documents
have processed as follow.
First of all they have scanned as topographic maps and then geo referenced
in Erdas Imagin 9.1 environment. The border of basin which was already limited
on the mentioned maps traced in ArcView3.2a environment and then border vector
layer was prepared. In next stage between 15156 elevations points of the base
map 10637 points were selected to consider the basin border in the form of digital
which was occurred during the process. These points were gained from ground
control using Global Positioning System (GPS) during 2003 to 2004 period in
the study area. These numbers of elevation points were selected to cover out
of the study area. The reason is related to the accurate results from the used
model of DEM. Table 1 shows some of the statistics characteristics
of these points.
In this method, 2 factors such as neighbor points and point searching radius assumed as model variables. Weight standard distance which is searching radius of standard ellipse (Fig. 2), calculated by the following relations of Eq. 1 and 2 (Ebdon, 1998).
Table 1: 
Descriptive statistics of the elevation points in Jam and
Riz basin 

 Fig. 1: 
Geographical location of Jam and Riz basin in Iran 
 Fig. 2: 
Standard ellipse and standard deviation ellipse for elevation
point group 
Where:
xmc and ymc 
= 
Represent coordinates of average center 
yi and xi 
= 
Coordinates of I points 
fi 
= 
Abundance of point I and n is the number of points 
During the past three decades, models that solve the catchment and/or solute transport equations in conjunction with an optimization technique have been increasingly used as watershed management tools (Rizzo and Dougherty, 1996; Minsker and Shoemaker, 1998; Zheng and Wang, 2002; Mayer et al., 2001). Simulationoptimization models have been developed for a variety of applications. Standard ellipse is an appropriate way to show the spatial protection of points group (Greene, 1991) but in geographic view the points group may have directional deviation. This problem is very important specially in preparing the numerical models by use of elevation points. In fact, elevation points in different directions to each other can represent several geomorphologic features of special area. The standard deviation ellipse is identified as follows: • 
Coordinates of average center (xmc, ymc) were calculated on
map which is starting points for transmission them. For every points of
pi in distribution, coordinates transmission was done as follows: 
After transmission, all points were concentrated on average center. • 
Rotation angle was calculated using Wong relation (Wong, 2000): 
• 
Deviation in length of X and Y axes have derived according
to the relations of Eq. 5 and 6 (Levine et al.,
1995). 
According to the mentioned methods, the model was tested with 4 categories of 3, 5, 7 and 15 dotted of neighbors points in two radius domains of standard searching circle and standard deviation ellipse. Therefore 8 digital elevation models were extracted then 10637 points equal to 10637 land dots evidence were driven for each model. Finally, the extracted points from each model using SPSS11.5 and by use of means difference test were compared with the land evidence point. RESULTS AND DISCUSSION
The described expansion of elevation points set based procedure by two hypothesized
of spatial dispersion and point's directional deviation was investigated using
standard and standard deviation ellipses. The extracted results of this study
are presented in Table 2. With an assessment of the necessary
factors such as cell size in network (value 3), number of neighbor points (3,
5, 7, 15), standard radius (for standard ellipse) and ellipse rotation angle
(in standard deviation ellipse), the optimized power was calculated for each
one of 8 digital models. This value is shown in (Table 3).
According to this value and the represented factors, digital elevation models
was prepared for the study area. With comparing the 10637 extracted points of
8 digital elevation models by SPSS11.5 which due to geographic coordinates is
equal to 10637 land evidence points and using of means differences test, the
best digital elevation model was obtained. The related results to this analysis
are shown in Table 4. In fact, from the gained digital models
the accurate one is a model which it’s resulted elevation points has the
lowest difference with land elevation points. However it is logical that the
data which do not have main differences to land observation in significant 5%
is with most accurate. According to the Table 4, four elementary
digital models, from IDW1 to IDW4, can not show the main differences with the
land observations. To identifying that between 4 digital models which one is
with high accuracy, it can be determined with the average of fault value in
Table 4. It seems that this data are extremely similar but
between them the IDW3 digital elevation model has the lowest mean standard error
of 0.26842. Statistical investigation from Table 2 shows individual
characteristics of IDW3 which is used seven neighbor points. On the other hand
these conclusions show that digital earth data with standard ellipse had sensible
response rather than standard deviation ellipse (Fig. 3).
The described data have spatial dispersion and the points contain lower directional
deviation. However, it can concluded that, IDW3 digital elevation model with
optimized power of 3.299 using IDW interpolation is the best digital elevation
model for the study area of Jam and Riz basin in Iran which is recommended to
used for the same catchments.
Despite of the landscape morphology and land surface of the study area there
was a few differences existed between 8 digital elevations models due to the
high density sampling which was covered the whole study area. This could have
been predictable since increasing the sampling area which is lead to reduce
the impact of the interpolation method. The results of this research can be
confirmed the similar works of Borgan and Vizzaccara (1997) and Lazzaro and
Montefusco (2002). For lower values of sampling density the accuracy of height
estimation is related to the choice of neighbor points numbers (Keranchenko,
2003). IDW method is calculating only some adjacent data points and thus performs
well specially for the complex topography when data density increased to a high
level (Fisher et al., 1987). The results may help GIS users to select
the best alternative for the generation of DEM_{S}. The mentioned technique
is recommended not only for its performance on a specific land form type and
data density, but also for its capability to a wide range of spatial scales
which is applied in this research using two different scales of 1:25000 and
1:250000.
Table 2: 
Characteristics of the test samples in IDW model 

Table 3: 
The value of optimized power in digital elevation models 

Table 4: 
Test of compare means (paired t test) for observation elevation
value and elevation values of IDW model 

 Fig. 3: 
Optimized digital elevation model 
In particular field, DEM quality should be examined through the assessment
of primary and secondary DEM derivatives such as slope angle, slope curvature,
drainage network and the catchments boundaries as requirement of natural resources
to use this technique. These attributes would be more sensitive to the selection
of the interpolation technique than the altitude itself. Finally, it can be
concluded that the interpolation technique and sampling model of altitude data
on the accuracy of watershed management such as hydrologic, soil, land morph
modeling needs to be evaluated.
ACKNOWLEDGMENT The authors would like to thanks the University of Mazandaran Iran for valuable supports.

REFERENCES 
1: Aguilar, F.J., F. Aguera, M.A. Aguilar and F. Carvajal, 2005. Effects of terrain morphology, sampling density and interpolation methods on grid DEM accuracy. Photogrametric Eng. Remote Sens., 71: 805816. Direct Link 
2: Beven, K.J. and M.J. Kirkby, 1979. A physically based, variable contributing area model of basin hydrology. Hydrol. Sci. Bull., 24: 4369. CrossRef  Direct Link 
3: Bloschl, G. and M. Sivapalan, 1995. Scale issues in hydrological modelling: A review. Hydrol. Process., 9: 251290. CrossRef  Direct Link 
4: Bob and Booth, 2000. Using Arc GIS 3D analyst GIS by ESRI. Copy Right Environmental Systems Research Institute.
5: Borgan, M. and A. Vizzaccara, 1997. On the interpolation of hydrologic variables: Formal equivalence of multi quadratic surface fitting and kriging. J. Hydrol., 195: 160171. Direct Link 
6: Brasington, J. and K. Richards, 1998. Interactions between model predictions, parameters and DTM scales for topmodel. Comput. Geosci., 24: 299314. CrossRef  Direct Link 
7: Brus, D.J., J.J. Gruijter, B.A. Marsman, R. Visschers, A.K. Bregt and A. Breeuwsma, 1996. The performance of spatial interpolation methods and choropleth maps to estimate properties at points: A soil survey case study. Environmetrics, 7: 116. CrossRef 
8: Burrough, P.A. and R.A. McDonnell, 1998. Principles of Geographical Information Systems. Oxford University Press, New York, Pages: 333.
9: Carrara, A., G. Bitelli and R. Carla, 1997. Comparison of techniques for generating digital terrain models from contour lines. Int. J. Geogr. Inform. Sci., 11: 451473. CrossRef 
10: Chaplot, V., C. Walter and P. Curmi, 2000. Improving soil hydromorphy prediction according to DEM resolution and available pedological data. Geoderma, 97: 405422. CrossRef  Direct Link 
11: Chaplot, V., F. Darboux, H. Bourennana, S. Leguedois, N. Silvera and K. Phachomphon, 2006. Accuracy of interpolation techniques for the derivation of digital elevation models in relation to landform types and data density. J. Geomorphol., 77: 126141. Direct Link 
12: Childs and Colin, 2004. Interpolating Surfaces in Arc GIS Spatial Analyst. Arc User ESRI, Redlands, CA.
13: Creutin, J.D. and C. Obled, 1982. Objective analyses and mapping techniques for rainfall fields: An objective comparison. Water Resour. Res., 18: 413431. CrossRef 
14: Darboux, F., C. GascvelOdoux and P. Davy, 2002. Effects of surface water storage by soil roughness on overlandflow generation. Earth Surface Processes Land Forms, 27: 223233. Direct Link 
15: Darboux, F. and C. Huang, 2003. An instantaneousprofile laser scanner to measure soil surface micro topography. Soil Sci. Am. J., 67: 9299. Direct Link 
16: Declercq, F.A.N., 1996. Interpolation methods for scattered sample data: Accuracy, spatial patterns, processing time. Cartogr. Geogr. Inform. Syst., 23: 128144. CrossRef  Direct Link 
17: Ebdon, D., 1998. Statistics in Geography. Basil Blackwell, New York.
18: Fisher, N.I., T. Lewis and B.J.J. Embleton, 1987. Statistical Analysis is of Spherical Data. Cambridge University Press, Cambridge, pp: 329.
19: Gallichand, J. and D. Marcotte, 1993. Mapping clay content for subsurface drainage in the Nile Delta. Geoderma, 58: 165179. CrossRef  Direct Link 
20: Greene, R., 1991. Poverty concentration measures and the urban underclass. Econ. Geogr., 67: 240252. Direct Link 
21: Johnston and Kevin, 2001. Using Arc GIS. Geostatistical Analyst ESRI.
22: Keravchenko, A.N., 2003. Influence of spatial structure on accuracy of interpolation models. Soil Sci. Soc. Am. J., 67: 15641571. Direct Link 
23: Keranchenko, A.N. and D.G. Bullock, 1999. A comparative study of interpolation methods for mapping soil properties. Agron. J., 91: 393400. Direct Link 
24: Laslett, G.M. and A.B. McBratney, 1990. Further comparison of spatial methods for predicting soil pH. Soil Sci. Soc. Am. J., 54: 15531558. CrossRef 
25: Laslett, G.M., 1994. Kriging and splines: An empirical comparison of their predictive performance in some application. J. Am. Stat. Assoc., 89: 391400. CrossRef  Direct Link 
26: Lazzaro, D. and L.B. Montefusco, 2002. Radial basis functions for the multivariate interpolation of large scattered data sets. J. Comput. Applied Math., 140: 521536. Direct Link 
27: Levine, N., K.E. Kim and L.H. Nitz, 1995. Spatial analysis of Honolulu motor vehicle crashes: I. Spatial patterns. Accident Anal. Prev., 27: 663674. CrossRef  Direct Link 
28: Mayer, A.S., C.T. Kelley and C.T. Miller, 2002. Optimal design for problems involving flow and transport phenomena in saturated subsurface systems. Adv. Water Resour., 25: 12331256. Direct Link 
29: McBratney, A.B., M.L.M. Santos and B. Minasny, 2003. On digital soil mapping. Geoderma, 117: 352. CrossRef  Direct Link 
30: Meyers, D.E., 1994. Spatial interpolation: An overview. Geoderma, 62: 1728. CrossRef 
31: Minsker, B.S. and C.A. Shoemaker, 1998. Dynamic optimal control of in situ bioremediation of ground water. J. Water Resour. Plant Manage., 124: 149161. CrossRef 
32: Modallaldoust, S., 2007. Estimation of sediment and erosion with use of MPSIAC and EPM models in GIS environment. M.Sc. Thesis. University of Mazandaran, Iran.
33: O'Lloughlin, E.M., 1986. Prediction of surface saturation zones in natural catchments by topographic analysis. Water Resour. Res., 22: 794804. CrossRef 
34: Poon, J., C.S. Fraser, C.S. Zhang, Z. Li and A. Gruen, 2005. Quality assessment of digital surface models generated from IKONOS imagery. Photogrametric Rec., 20: 162171. Direct Link 
35: Quinn, P., K. Beven, P. Chevallier and O. Planchon, 1991. The prediction of hillslope flow paths for distributed hydrological modelling using digital terrain models. Hydrol. Proc., 5: 5979. CrossRef 
36: Rizzo, D.M. and D.E. Dougherty, 1996. Design optimization for multiple management period groundwater remediation. Water Resourc. Res., 32: 25492561. CrossRef 
37: Robeson, S.M., 1997. Spherical methods for spatial interpolation: Review and evaluation. Cartogr. Geogr. Inform. Syst., 24: 320. CrossRef  Direct Link 
38: Robinson, T.P. and G. Mettemicht, 2006. Testing the performance of spatial interpolation techniques for mapping soil properties. J. Comput. Electron. Agric., 50: 97108. Direct Link 
39: Ruhaak, W., 2006. A java application for quality weighted 3D interpolation. J. Comput. Geosci., 32: 4351. Direct Link 
40: Tali, M.G., 2004. Applied of Arcview in Geomorphology. Jahad Daneshgahi, Tehran Iran, pp: 140.
41: Thompson, J.A., J.C. Bell and C.A. Bulter, 2001. Digital elevation model resolution: Effects on terrain attribute calculation and quantitative soil landscape modeling. Geoderma, 100: 6789. Direct Link 
42: Toutin, T., 2002. Impact of terrain slope and aspect on radar grammetric DEM accuracy. ISPRS J. Photogrametry Remote Sens., 57: 228249. CrossRef 
43: Toutin, T. and T. Cheng, 2002. Comparison of automated digital elevation model extraction results using along track ASTER and across track SPOT stereo images. Optical Eng., 41: 21022106. Direct Link 
44: Weber, D. and E. Englund, 1992. Evaluation and comparison of spatial interpolation. Math. Geol., 24: 381391. CrossRef 
45: Weber, D.D. and E.J. Englund, 1994. Evaluation and comparison of spatial interpolation II. Math. Geol., 26: 589603. CrossRef 
46: Wilson, J.P. and J.C. Gallant, 2000. Terrain Analysis Principles and Applications. Wiley, New York, pp: 479.
47: Wong, D.W.S., 2000. Ethnic integration and spatial segregation of the Chinese population. Asian Ethnicity, 1: 5372. Direct Link 
48: Wood, J.D. and P.F. Fisher, 1993. Assessing interpolation accuracy in elevation models. IEEE Comput. Graphics Appl., 13: 4856. CrossRef 
49: Zhang, W. and D.R. Montgomery, 1994. Digital elevation model grid size, landscape representation and hydrologic simulate. Water Resour. Res., 30: 10191028. CrossRef 
50: Zheng, C. and P.P. Wang, 2002. A field demonstration of the simulationoptimization approach for remediation system design. Ground Water, 40: 258265. Direct Link 
51: Zimmerman, D., C. Pavlik, A. Ruggles and M. Armstrong, 1999. An experimental comparison of ordinary and universal kriging and inverse distance weighting. Math. Geol., 31: 375390. CrossRef 



