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INTRODUCTIONThe analysis and interpretation of spatial datasets
forms an important part of geostatistics andis, unfortunately,
highly human dependent(Genton and Furrer, 1998). For instance, it
is wellknown that different individuals will take differ-ent
approaches, yielding a large assortment of dis-tinct solutions. It
is often the case where judge-ment and experience play a key role
in selectingthe proper spatial interpolation technique for
each individual case (Englund, 1990). This is part-ly due to the
variety of available spatial interpola-tion methods, which range
from simple intuitivepredictions to more sophisticated and
complexprocedures (Cressie, 1991). Estimating both rain-fall at
ungaged locations and mean areal rainfallover an area (e.g. a
catchment) based on theresults of meteorological observations,
motivatedthe development of gridded estimates of precipi-tation to
provide inputs to spatially distributed
Global Nest: the Int. J. Vol 6, No 1, pp 1-20, 2004
Copyright 2004 GLOBAL NEST
Printed in Greece. All rights reserved
RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED
DSS
1 Department of Civil Engineering,
McMaster University,
1280 Main Street West,
Hamilton, Ontario, Canada, L8S 4L72 Laboratory of Water
Resources
Management & Coastal Engineering
Technical University of Crete
Polytechnioupolis, Chania,
73100, Crete, Greece
*to whom all correspondence should be addressed:
Tel:+(30) 2821037799
Fax: +(30) 2821037849
e-mail: [email protected]
ABSTRACTA GIS-based Decision Support System (DSS) was developed
to select the appropriate interpolationtechnique used in studying
rainfall spatial variability. The DSS used the ArcView GIS platform
byincorporating its spatial analysis capabilities, the programming
language "AVENUE", and simple sta-tistical methods. The system
consists of a series of modules and can be applied in spatial
studies ofother hydrological parameters. A test case from the
country of Switzerland is used to demonstrate theapplicability of
the system. This should aid in better input to hydrological
models.
KEYWORDS: ArcView GIS, AVENUE, Mean, Raingages, Spatial
Interpolation Techniques, StandardDeviation.
S. NAOUM1
I.K. TSANIS2, *
Received: 15/05/02Accepted: 17/12/02
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hydrologic and management models. Although there are numerous
articles have beenwritten that are concerned with spatial
interpola-tion, there is little or no agreement among theauthors on
the superiority of some techniquesover others. Additionally, the
increasing interestin Geographic Information Systems (GIS)
withtheir broad usage and popularity, made it crucialto simply
investigate the credibility and applica-bility of the different
ready-to-use spatial interpo-lation techniques that are embedded in
those sys-tems. Generated with that in mind, this work hasalso been
inspired by the Journal of GeographicInformation and Decision
Analysis initiative'sspecial edition on spatial interpolation
(SpatialInterpolation Comparison SIC97).
APPROACH AND PROCEDUREVariability is often a result of changes
in conditionsunder which observations are made, differences inthe
way people do the work, difference in processvariables, difference
in environmental factors, themeasurement system, or sampling.
Statistical tech-niques are used to describe and understand
vari-ability. To provide a basis of comparison betweenthe different
techniques/models in this work, sim-ple statistical methods are
adopted. Since themethod is data-driven and fully automated, it
doesnot require preprocessing. This could be of value inan
emergency situation where rapid, yet justifiable,results are
required. At first, the concept of anobjective function has to be
established. This isnormally followed by defining the constrained
opti-mization of that function. The process initiates byrandomly
eliminating some of the available gages.The different interpolation
techniques are thenapplied to estimate the "unobserved/missing"
val-ues on the basis of the "observed/remaining" ones.The purpose
of the random selection of gages,which in this case takes the form
of twenty tries, isintended to overcome the problem of outliers,
ifthey exist. Experience shows that measured datacontains between
10 to 15 per cent of outlying val-ues due to gross errors,
measurement mistakes,and faulty recording. Identifying and
rejecting, orremoving, outliers is highly opinion dependent andis
not normally recommended since they, beingextremes, represent
critical cases or worst case sce-narios. The errors/residuals at
theunobserved/ungaged locations are then calculatedas the
difference between observed and estimated
values and categorized as positive and negativeresiduals. If the
absolute value of the sum of thepositive residuals is greater than
the absolute valueof the sum of the negative residuals, it implies
thatthe observed values are greater than estimatedones. The model
is then said to be underestimating.If the absolute value of the sum
of the positiveresiduals is less than the absolute value of the
sumof the negative residuals, it implies that the esti-mated values
are greater than observed ones. Themodel is then said to be
overestimating. At the sec-ond phase, three values are calculated
for eachtechnique. The errors at the ungaged (unobserved)locations
are grouped in one column as absolutevalues, where the mean and the
standard deviationare calculated as follows:
(1)
(2)
where: : the mean of absolute residuals, xobs: theobserved value
of rainfall, xest: the estimated valueof rainfall, n: the number of
observed/estimatedvalue (sample size), S: the standard deviation,
and
: the absolute value of the individual residual.Generally, for a
model to be considered satisfac-tory, the mean ( : MeanAbsErr) and
standarddeviation (S: StDevAbsErr) of the absolute valuesof
residuals are expected to be as low as possibleamong the other
techniques. From the rain sur-face (grid), which is generated using
the observedvalues, the average value is calculated as the sumof
the rain values at each grid cell divided by thetotal number of
cells in the grid. This representsthe mean areal precipitation
(MeanEst). Theaverage of the observed values at all
locations(observed and unobserved) is then calculated(MeanObs). A
good model should generate avalue (MeanEst) that matches (or be as
close aspossible to) the (MeanObs) and the differencebetween these
two values is minimal. The differ-ence is then calculated (Diff).
The main criterionfor judging the best model for each run is based
onthe minimum value obtained by averaging (Avg)the values (Diff,
MeanAbsErr, StDevAbsErr),
2 NAOUM and TSANIS
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assuming equal weights for all. The twelve tech-niques are
ranked accordingly from best(MinAvg) to the worst (MaxAvg) in
addition tomany other statistics in a report format.
SPATIAL INTERPOLATION METHODS IN A GISThe following is a
description of the interpolationtechniques available in ArcView GIS
3.2.
Spline (Regularized & Tension):Spline interpolation consists
of the approximationof a function by means of series of
polynomialsover adjacent intervals with continuous derivativesat
the end-point of the intervals. Smoothing splineinterpolation
enables to control the variance ofthe residuals over the data set.
The solution is esti-mated by an iterative process. It is also
referred toas the basic minimum curvature technique or thinplate
interpolation as it possesses two main fea-tures: (a) the surface
must pass exactly through thedata points, and (b) the surface must
have mini-mum curvature. The reader is referred to Franke(1982) and
Mitas and Mitasova (1988) for furtherreading about the
technique.
Inverse Distance Weighting (IDW)Inverse Distance Weighting (IDW)
is an interpo-lation technique in which interpolated estimatesare
made based on values at nearby locationsweighted only by distance
from the interpolationlocation. IDW does not make assumptions
aboutspatial relationships except the basic assumptionthat nearby
points ought to be more closely relat-ed than distant points to the
value at the interpo-late location. This technique determines cell
val-ues using a linearly weighted combination of a setof sample
points. The weight is a function ofinverse distance. IDW allows the
user to controlthe significance of known points upon the
inter-polated values, based upon their distance fromthe output
point. The reader is referred to Tung(1983) and Watson and Philip
(1985) for furtherreading about the technique.
KrigingKriging provides a means of interpolating valuesfor
points not physically sampled using knowledgeabout the underlying
spatial relationships in a dataset to do so. Variograms provide
this knowledge.Kriging is based on regionalized variable
theorywhich provides an optimal interpolation estimate
for a given coordinate location, as well as a vari-ance estimate
for the interpolation value. Itinvolves an interactive
investigation of the spatialbehavior of the phenomenon before
generating theoutput surface. It is based on the regionalized
vari-able theory, which assumes that the spatial varia-tion in the
phenomenon is statistically homoge-neous throughout the surface;
that is, the same pat-tern of variation can be observed at all
locations onthe surface. This hypothesis of spatial homogeneityis
fundamental to the regionalized variable theory.Data sets known to
have spikes or abrupt changesare not appropriate for the Kriging
technique. Insome cases, the data can be pre-stratified intoregions
of uniform surface behavior for separateanalysis. The reader is
referred to Burrough(1986); Heine (1986); McBratney and
Webster(1986); Oliver (1990); Press (1988); and Royle et al.(1981)
for further reading about the technique.
Trend SurfaceThe linear trend surface interpolator creates
afloating-point grid. It uses a polynomial regres-sion to fit a
least-squares surface to the inputpoints. It allows the user to
control the order ofthe polynomial used to fit the surface.
Trendinterpolation is easy to understand by consideringa
first-order polynomial. A first-order linear trendsurface
interpolation simply performs a least-squares fit of a plane to the
set of input points.Trend surface interpolation creates smooth
sur-faces. The surface generated will seldom passthrough the
original data points since it performsa best fit for the entire
surface. When an orderhigher than 1 is used, the interpolator may
gener-ate a grid whose minimum and maximum mightexceed the minimum
and maximum of the inputpoints. The most common order of
polynomials is1 through 3. The reader is referred to Chidley
andKeys (1970); Shaw and Lynn (1972); Lee et al.(1974); and
Kruizinga and Yperlaan (1978) forfurther reading about the
technique.
Theissen PolygonsAnother choice given in the software for
codingbased on the value of a chosen attribute of theseed feature.
This is appropriate if we wish todefine the "region of influence"
of a point or line.The region of influence is based on
"nearestneighbours" to the point or line. The region ofinfluence
for a series of points is represented by a
3RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED
DSS
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set of polygons encoded with the nominal valuefor each point.
These polygons are referred to asThiessen Polygons or collectively
as a proximalmap. Theissen (1911) came up with the first tech-nique
to estimate areal average precipitation.Theissen polygons are
probably the most com-mon approach for modeling the spatial
distribu-tion of rainfall. The approach is based on definingthe
area closer to a gage then any alternate gageand the assumption
that the best estimate of rain-fall on that area is represented by
the point mea-surement at the gage. Because the basis of themodel
is geometry and gage location, implemen-tation of Theissen polygons
in a GIS environmentis not difficult. However, one impact of the
use ofTheissen polygons is the development of discon-tinuous
surfaces defining the rainfall depth overthe area under study. This
effect arises at theboundaries of the polygons where a
discretechange in rainfall depth occurs (Ball and Luk,1998). The
reader is referred to Whitemore et al.(1961); Rainbird (1967);
Hutchinson (1969);Diskin (1969); and Diskin (1970) for further
read-ing about the technique.
As a result, and to summarize, the twelve spatialinterpolation
techniques employed in this studyare listed in Figure 1.
TEST CASEThe module is applied to a group of raingages
inSwitzerland to illustrate its applicability.Switzerland lies at
the heart of Western Europeand covers an area of 41,284 km2. A
DigitalElevation Model and some interpolated rain sur-faces
(interpolated from observed values usingdifferent techniques) are
shown in Figure 1. Thedata set being used is related to the period
ofChernobyl Nuclear Power Plant accident (April,26th 1986) (Dubois,
1998). During the days fol-lowing the accident, a radioactive
plume, led bythe action of atmospheric flow, was crossing
manyEuropean countries. Radioactive deposition onthe ground was
mainly a function of the rainfall.The primary set of data includes
467 daily rainfallrecords made in Switzerland on May 8th 1986.The
collection of the data was carried out by theAir Pollution Group at
Imperial College inLondon under financial support of JRC-Ispra.
4 NAOUM and TSANIS
Figure 1. Digital Elevation Model and Interpolated Rain Surfaces
in Switzerland
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The location of the data points was also provided.Both Digital
Elevation Model (DEM), with a res-olution of around 1 km * 1 km,
and the countryborder, used to define the area under study,
wereprovided as secondary information. The rainfallmeasurements
were in the form of text files, theDEM in the form of a normal
ASCII ARC/INFOformat, and country borders were available as
anAutoCad Interchange Drawing file.
STRUCTURE AND DESCRIPTION OF THE PROJECT A Geographic
Information System can be morepowerful when some added features,
representedin this case by statistical methods, are combinedwith
its many capabilities, as described above,resulting in the
generation of a good decision sup-port system. This GIS module, as
shown in Figure2, was developed in the ArcView GIS environ-ment
using AVENUE (the ArcView program-ming language). The programming
languageAVENUE provides a well-defined mechanism forallowing
user-written routines to be called fromwithin the normal user
interface of the GIS pack-
age. In addition, this language also provides amenu-driven
graphic interface, which makes itpossible to guide a user with
prompts and expla-nations throughout the application. The
DialogDesigner and Spatial Analyst extensions areloaded to the
ArcView project.The project is composed of AVENUE scripts,dynamic
link libraries (dlls), and designed dialogs.The scripts were mainly
created by the authors. Insome cases, however, they were modified
versionsof scripts that existed in the ArcView on-line help.As the
name implies, the "makedir.dll" and"deldir.dll" dynamic link
libraries were built tocreate and delete directories without the
use ofbatch files. A dialog, created for the convenienceof the
user, included all spatial interpolation tech-niques available in
ArcView but not available inthe normal interface of the program.
The devel-oped module allows for one-/multi-process inter-polation.
The main module uses four main piecesof information to perform its
task and generatethe new network: the location of gages,
rainfalldata, region boundary, and a Digital ElevationModel and it
consists of five sub-modules:
5RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED
DSS
Figure 2. The Main Module of the Interpolation Engine
Project
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Module 1: ReadMeThis module documents the project by
informingthe user of the different parts of the main moduleusing
many graphic illustrations. It can be viewedas either a Word
Perfect Document (help.wpd) oran HTML (help.htm). The advantage of
theHTML is that it provides links to all AVENUEscripts and examples
of output tables and text files.
Module 2: Data PreparationThis is a five-step module that
prepares the pro-ject for modules to follow. The data
inputrequirements for this module include informationon the
boundary of the region, the DigitalElevation Model, and the data
and location ofraingages.
DXF to Shapefile ConverterIn many cases, data is provided as
AutoCad draw-ing files (for example: dxf files) which must thenbe
converted to ArcView Shapefiles.
Polyline to Polygon ConverterAfter converting the AutoCad
drawing file to anArcView shapefile, the user should convert
theresultant "polyline" shapefile into a "polygon"shapefile, which
will be used in a later step.
Import Grid from ASCII Format A grid, DEM in many cases, will be
saved in theASCII ARC/INFO format. In this case, it has to
beimported into an ArcView grid format.
Grid ClippingAn area has to be extracted (clipped) from
theoriginal imported grid from the previous step inorder to
calculate mean areal rainfall or meanelevation over a specific
region. The clipping process (as shown in Figure 3) isaccomplished
by using the "polygon" shapefilegenerated in step 2 and the
imported grid fromstep 3.
6 NAOUM and TSANIS
Figure 3. Clipped DEM Using the Menu Item "Grid Clipping"
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Generate Shapefile from a Database FileA database file that
contains information aboutlocation of raingages and amounts of
rainfall canbe converted to a "point" shapefile and added tothe
project. It should be noted that this module was
createdspecifically for the purpose of this study. If allinput
requirements are satisfied and the data is inthe proper format,
there is no need to go throughthe five steps.
Module 3: InterpolatorsThis is a key four-step module that is
responsiblefor executing many tasks as shown in Figure 4,where a
number of gages are selected randomlyand a rain surface (grid) is
generated. The remain-ing number of gages (the unselected ones) is
thenprojected on the generated grid, and estimated val-ues for
rainfall at those locations are then extract-ed. A comparison
between the observed and esti-mated precipitation values is held
and the residu-
7RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED
DSS
Figure 4. Module 3 (Interpolators)
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als/errors are calculated. The results of the com-parison are
summarized in a text file and a data-base file from which
illustrative charts can be gen-erated if desired. The last item of
the module gen-erates Theissen polygons for the selected gages.
Random SelectionIn this step, the user is prompted to enter
therequired number of gages that should be random-ly selected. The
result is two shapefiles. One rep-resents the selected gages and
the other repre-sents the unselected ones.
Spatial Interpolation (ONE)The user is presented with the
interpolation dia-log (Figure 5) described earlier so that they
mayselect the type of interpolation technique theywill be using to
generate the rain surface from theselected gages (as shown in
Figure 6).
StatisticsThis task is executed on the shapefile of the
uns-elected gages. There is some interaction between
the user and the program. The user is promptedby some messages
and a text file and a databasefile are then generated, as shown in
Figure 7, inthe working directory.
Theissen PolygonsThis task is executed on the shapefile of
theselected gages. The mean areal rainfall will be cal-culated and
presented to the user.
Module 4: Spatial Interpolation (MANY)This module is an extended
(advanced) version ofmodule (3), where the user interference is
mini-mized. It simply generates grids using all the spa-tial
interpolation techniques available (includingTheissen polygons) by
using the shapefile of theselected gages. Twelve grids are then
generatedusing the interpolation techniques and the esti-mated
values are compared to the observed val-ues of the unselected
gages. The result is a textfile and twelve database tables. Each
table repre-sents the results of each interpolation techniquein the
same sequence as in the text file. At the end
8 NAOUM and TSANIS
Figure 5. The Developed Interpolation Dialog as Part of Module
(3)
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of the text file, the different interpolation tech-niques are
ranked from the best to the worstaccording to their
performance.
Module 5: Automated Interpolation OperationsThis module is an
advanced version of module (4)with the least interference from the
user. Threeinputs are required from the user at the start ofthe
operation: the number of iterations, the cellsize, and the number
of gages to be randomlyselected, and the files DEM, Rain.shp,
andCountry.shp as shown in Figure 8. The mainscript, when executed,
opens new views that areequal to the number of iterations specified
by theuser. It also generates new working directories foreach one
of the views inside the main workingdirectory "C:\Inter", sets the
properties of theviews (map units and distance units), sets
theanalysis properties (extent, cell size, and mask),and copies the
necessary themes (Rain.shp,Country.shp, and DEM) from the main view
tothe other views. The main script, then, triggersanother script
which, in turn, opens each of the
views and performs the random selection of thegages according to
the number that was initiallyspecified by the user. A third script
is run fromwithin the second, which is responsible for open-ing
each of the previously generated views andperforming the spatial
interpolation task usingthe different methods and generate the text
file,as shown in Figure 9, and the 12 database files.All output
files are located in the respective work-ing directory of each
view, each of which is namedafter the view (i.e. all work done in
view1 is storedin the sub-directory "C:\Inter\View1"). In
manycases, the user will choose to terminate the run.For example,
if the technique is not suitable for acertain data set or the user
would like to run thesame case with different cell size, the run
may beterminated. The user will then choose to resumeexecution
without generating new views or newshapefiles. At this point, the
menu item"Continue Operations ..." may be used to workwith the
existing files. This menu item is attachedto the script
"Inter_Continue" which will run thescript "Inter_Continue1" or it
will run the script
9RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED
DSS
Figure 6. Module 3 - Menu Item: Spatial Interpolation [ONE]
(Output)
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"Inter_DifferentCellSize" if the user would like torun the
"Automated Operations" using differentcell size on multiple views
that had been previ-ously generated.
Project AccessoriesThe project is equipped with more scripts
that areautomatically executed upon opening and closingthe project.
They perform additional functionswhich are intended to facilitate
the project/userinteraction and results presentation.
EXECUTIONSpeculating that the cell size and the number
ofavailable gages may influence the ranking of theinterpolation
techniques, a total of 12 runs were
performed. The first 4 runs were done using only40% of the
available gages (187 out of 467 gages)as observed records with a
cell size of 500m,1000m, 5000m, and 10000m. The second set of 4runs
used 60% of the available gages (280 out of467 gages) as observed
records with a cell size of500m, 1000m, 5000m, and 10000m. The
third andfinal set of 4 runs used 80% of the available gages(374
out of 467 gages) as observed records with acell size of 500m,
1000m, 5000m, and 10000m.Each of the 12 techniques was then
evaluatedbased on the average value of the 20 tries withineach of
the 12 runs. The evaluation was done ona scale of "0" to "10" with
"10" being a perfect tech-nique which means the smallest average
value forthe 20 (Avg) values; while a "0" is the worst tech-
10 NAOUM and TSANIS
Figure 7a. Module 3 - Menu Item: Statistics (Output)
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nique which means the largest average value forthe 20 (Avg)
values.
RESULTSRelying on the multiple random selection ofgages to
eliminate the effect of any errors or out-liers, no statistical
data preparation or prelimi-nary analysis was done. Descriptive
statistics wereemployed to provide inferences for the
differentmodels. The module output takes various forms: 1. Visual
Grids (Surfaces): as shown in Figure
10, where the user can see the distribution ofselected (solid
dots) and unselected gages (x-marked locations). In addition to
this, the dif-ferent techniques can be visually compared toeach
other.
2. Text Files (Report Format): as shown inFigures 7 and 9, the
user is able to obtain per-manent records of the various runs for
com-parison purposes with helpful statistics listedfor each
technique. In addition, the techniquesare listed in performance
sequence.
3. Database Files: as shown in Figure 7, databasefiles are
permanently stored and from whichplots can be generated (as shown
in Figure 11).This confirms the results previously obtainedin the
text (report) format in Figure 9.
Generally, the results are shown in Figure 12,where the
horizontal axis represents the interpo-lation techniques in the
same order as in Figure 1and the vertical axis represents the
0-to-10 scale.
11RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED
DSS
Figure 7b. Module 3 - Menu Item: Statistics (Output)
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12 NAOUM and TSANIS
Figure 8. Module 5 - Automated Interpolation Operations
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13RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED
DSS
Figure 9. Module 5 - Automated Interpolation Operations (Output:
Interp1.txt)
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The following can be concluded:a. the Spline_Regularized and the
2nd Order
Polynomial techniques showed poor perfor-mance in almost all
cases.
b. Theissen Polygons and Kriging (Linear;Gaussian; Circular;
Universal_2) techniquesfluctuated from one case to the other.
c. the Spline_Tension, IDW, and Kriging(Spherical; Exponential;
Universal_1) tech-niques were able to provide reliable
estimates.The Kriging_Exponential and Kriging_Universal_1 models
are recommended.
Results show that changing the cell size of theinterpolated grid
did not significantly affect theclassification/rank of the
interpolation techniqueswhen using small number of gages (187
gages), asshown in Figure 13a, except for the Theissen poly-gons
method which dropped on the scale signifi-cantly when a cell size
of 10000m was used.However, by increasing the number of gages,
thecell size started to show a more noticeable influ-ence as some
techniques show higher perfor-mance while the others show lower
performance.
It should be noted that the 2nd order polynomial(technique 11)
did not respond to any changesthroughout the analysis. It was
always ranked 12.Figure 13b shows that changing the number ofgages
used in the interpolation when using a cellsize of 10000m did not
have any effect on the per-formance of the different techniques. It
is clearthat increasing the number of gages available
forinterpolation enhanced the performance of thetechniques except
for three techniques: Spline_Regularized, Spline_Tension, and
TheissenPolygons. Because Spline tries to fit a smooth sur-face
that passes through the points, increasing thenumber of gages does
not help the techniqueespecially if there is abrupt changes in
rainrecords, resulting in erratic estimated values. ForTheissen
polygons, as the number of gagesincreases, the size of the polygons
decreases andtheir count increases resulting in erratic estimat-ed
rain values.
DISCUSSIONThis network is a relatively dense network with
adensity of one gage/88.4 km2 and it records daily
14 NAOUM and TSANIS
Figure 10. A Visual Comparison between Four Interpolation
Techniques
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15RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED
DSS
Figure 11. Residual Plots as well as Observed vs Estimated
Rainfall Values for Four Interpolation Techniques
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precipitation. Due to the high variability normallyassociated
with daily precipitation records and thehigh density of the
network, it is likely that tech-niques such as Trend and
Spline_Regularizedwould not provide nice estimates. Trend
surfacesare always smooth surfaces which do not normallypass
through the original data points but performsa best fit for the
entire surface. In other words itprovides an approximate direction
of the intensityof rain rather than an accurate description of
thespatial variability of rain. On the other hand, sur-faces
generated using Spline_ Regularized try topass through the points
which, in this case, is notsuitable because of the rapid changes in
gradi-ent/slope in the vicinity of the data points.However,
Spline_Tension is a more relaxed ver-sion of Spline which could fit
a less smooth curves.Kriging is generally a good interpolator.
TheOrdinary Kriging is represented in this case by theSpherical,
Circular, Exponential, Gaussian, and
Linear methods. With these options, Kriging usesthe mathematical
function specified by themethod to fit a line or curve to the
semi-variancedate in the semi-variogram. These five models
areprovided to ensure that the necessary conditionsof the variogram
model are satisfied. TheExponential and Spherical methods seem to
bet-ter fit the spatial variation of this data set. TheUniversal
Kriging, represented by the Universal1and Universal2 methods,
assumes that the spatialvariation across the surface has a
structural com-ponent (drift). Drift is a systematic change in
thecell values at a particular scale. This scale is relat-ed to the
radius of the search area. The goal is tochange the search radius
to find the scale at whichthe drift can be detected and the
variance is low-est. Universal1 uses a first order polynomial
toapproximate the drift and Universal2 uses a sec-ond order. The
first derivative (Universal1) wasappropriate for this specific
application.
16 NAOUM and TSANIS
Figure 12. Performance of All Interpolation Techniques.
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17RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED
DSS
Figure 13a.The Effect of Changing the Cell Size on the
Performance of the Interpolation Techniques.
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18 NAOUM and TSANIS
Figure 13b.The Effect of Changing the Number of Gages Used for
Interpolation on the Performance
of the Interpolation Techniques
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Theissen polygons and IDW techniques areknown to provide good
results when used for rel-atively dense networks as in this case.
However,increasing the number of gages can be problemat-ic for the
Theissen polygons technique.It should be noted that repeated runs
for differentdata sets is required to verify the results
obtained.For example, wet, moderate, and dry conditions;hourly,
daily, monthly, and yearly data; short andlong term average;
...etc. The one available dataset used as a test case in this study
does not pro-vide enough evidence that certain techniques arebetter
than others.
CONCLUSIONNo interpolation technique, no matter
howsophisticated, can accurately predict rainfallamounts at ungaged
locations and, subsequently,estimate mean areal rainfall. This work
establish-es an approach by using GIS and historical datato locate
the best technique. It should be notedthat the selection of a given
method to be used in
cases of emergency should be based on compar-isons dealing with
more than one data set.Rainfall data from different days, months,
oryears are likely to behave differently under vari-ous
meteorological conditions. Performances ofa method applied to a
partial data set are likelyto be different from performances of the
samemethod with a larger data set. By taking a sampleof the data
set, the problem scale is changed, andthe boundary between large
and small scale vari-ation is modified. For that reason, data sets
withdifferent sizes are recommended. Finally, it ishighly advisable
for any country or region toobtain data from the closest parts of
neighboringcountries or at least to have as many data as pos-sible
from locations within the country/region.Based on the one data set
available for this study,it was clear that the Kriging_Exponential
andKriging_Universal_1 models showed consistentperformance and
provided reliable estimatesregardless of the number of gages or the
cell sizeused in the interpolation.
19RANKING SPATIAL INTERPOLATION TECHNIQUES USING A GIS-BASED
DSS
REFERENCESBall J.E. and Luk K.C. (1998), Modeling Spatial
Variability of Rainfall Over A Catchment, Journal of Hydrologic
Engineering, 3, 122-130.
Burrough P.A. (1986), Principles of Geographic Information
Systems for Land Assessment, Oxford University
Press, New York.
Chidley T.R.E. and Keys, K.M. (1970), A Rapid Method of
Computing Areal Rainfall, Journal of Hydrology, 12,
15-24.
Cressie N. (1991), Statistics for Spatial Data, New York,
Wiley.
Diskin M.H. (1969), Thiessen Coefficients by Monte Carlo
Procedures, Journal of Hydrology, 8, 323-335.
Diskin M.H. (1970), On the Computer Evaluation of Thiessen
Weights, Journal of Hydrology, 11, 69-78.
Dubois G. (1998), Spatial Interpolation Comparison 97: Forward
and Introduction, Journal of Geographic
Information and Decision Analysis, 2, 1-10.
Englund E. J. (1990), A Variance of Geostatisticiansm, Journal
of Mathematical Geology, 22, 417-455.
Franke R. (1982), Smooth Interpolation of Scattered Data by
Local Thin Plate Splines, Journal of Computation
and Mathematics with Applications, 8, 273-281.
Genton M.G. and Furrer R. (1998), Analysis of Rainfall Data by
Simple Good Sense: Is Spatial Statistics Worth
The Trouble?, Journal of Geographic Information and Decision
Analysis, 2, 11-17.
Heine G.W.(1986), A Controlled Study of Some Two-Dimensional
Interpolation Method, COGS Computer
Contributions, 3, 60-67.
Hutchinson P. (1969), Estimation of Rainfall in Sparsely Gaged
Areas, International Association of Hydrologic
Sciences Bulletin, 14, 101-120.
Kruizinga S. and Yperlaan G. J. (1978), Spatial Interpolation of
Daily Total of Rainfall, Journal of Hydrology, 36,
65-73.
Lee P.S., Lynn P.S. and Shaw E.M. (1974), Comparison of
Multiquadratic Surfaces for the Estimation of Areal
Rainfall, International Association of Scientific Hydrology
Bulletin, 19, 303-317.
McBratney A.B. and Webster R. (1986), Choosing Functions For
Semi-Variograms of Soil Properties and Fitting
Them to Sampling Estimates, Journal of Soil Science, 37,
617-639.
Mitas L. and Mitasova H. (1988), General Variational Approach to
the Interpolation Problem, Journal of
Computation and Mathematics with Applications, 16, 983-992.
1naoum.qxd 7/7/2004 12:58 Page 19
-
20 NAOUM and TSANIS
Oliver M.A. (1990), Kriging: A Method of Interpolation for
Geographical Information Systems, International
Journal of Geographic Information Systems, 4, 313-332.
Press W.H. (1988). Numerical Recipes in C, The Art of Scientific
Computing, New York, Cambridge University
Press.
Rainbird A.F. (1967), Methods of Estimating Areal Average
Precipitation, Reports on WMO/IHD Projects,
Report No. 3, pp. 45.
Royle A.G., Clausen F.L. and Frederiksen P. (1981), Practical
Universal Kriging and Automatic Contouring,
Geoprocessing, 1, 377-394.
Shaw E.M. and Lynn P.O. (1972), Areal Rainfall Evaluation Using
Two Surface Fitting Techniques, International
Association of Scientific Hydrology Bulletin, 17, 419-433.
Thiessen A.H. (1911), Precipitation for Large Areas, Monthly
Weather Review, 39, 1082-1084.
Tung Y.K. (1983), Point Rainfall Estimation for a Mountainous
Region, Journal of Hydraulic Engineering, 109,
1386-1393.
Watson D.F. and Philip G.M. (1985), A Refinement of Inverse
Distance Weighted Interpolation, Geo-Processing,
2, 315-327.
Whitemore J. S., Van Efden F. J. and Harvey K. J. (1961),
Assessment of Average Annual Rainfall Over Large
Catchments, In: Inter-African Conference on Hydrology, C.C.T.A.
Publication No. 66, 100-107.
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