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<div class=3DSection1>

<h2 align=3Dcenter style=3D'text-align:center'><span style=3D'font-size:17.=
0pt;
mso-bidi-font-size:12.0pt;font-family:"Times New Roman","serif";font-style:
normal;mso-bidi-font-style:italic'>Geostatistical Analyst<o:p></o:p></span>=
</h2>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Prepared by=
 Parikshit
Ranade, Dr Ayse Irmak and David R. Maidment</p>

<h2><span style=3D'mso-bidi-font-size:12.0pt;font-family:"Times New Roman",=
"serif";
font-style:normal;mso-bidi-font-style:italic'>Spatial Interpolation Methods=
 <o:p></o:p></span></h2>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shapetype id=3D"_x0000_t75" coor=
dsize=3D"21600,21600"
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dth:297pt;
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</v:shape><![endif]--><![if !vml]><img width=3D396 height=3D316
src=3D"ExGeostat_files/image002.jpg" v:shapes=3D"_x0000_i1025"><![endif]></=
p>

<p class=3DMsoNormal>Figure 1<b style=3D'mso-bidi-font-weight:normal'> : </=
b>The
interpolated value at the unmeasured yellow point is a function of the
neighboring red points (From ArcGIS Help Menu).</p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'>A very basic problem in spatial analysis is interpolati=
ng a
spatially continuous variable from point samples. Many spatially explicit
hydrologic/watershed models require continuous surfaces of temperature. Thr=
ee
commonly used interpolation methods to model spatially distribution from po=
int
data are Inverse Distance Weighting (IDW), spline and ordinary kriging.</p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'>The IDW is simple and intuitive deterministic interpola=
tion
method based on principle that sample values closer to the prediction locat=
ion
have more influence on prediction value than sample values farther apart. U=
sing
higher power assigns more weight to closer points resulting in less smoother
surface. On the other hand, lower power assigns low weight to closer points
resulting in smoother surface. We optimized power parameter using ArcGIS. M=
ajor
disadvantage of IDW is &#8220;bull's eye&#8221; effect (higher values near
observed location) and edgy surface. Spline is deterministic interpolation
method which fits mathematical function through input data to create smooth
surface. Spline can generate sufficiently accurate surfaces from only a few
sampled points and they retain small features (<st1:City w:st=3D"on"><st1:p=
lace
 w:st=3D"on">Anderson</st1:place></st1:City>, 2008). Spline works best for =
gently
varying surfaces like temperature. In ArcGIS Spline is Radial Basis Functio=
n.</p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'>Unlike IDW and spline, kriging is method based on spati=
al
autocorrelation. It uses semivariogram. <a name=3D"Basics_of_Kriging"></a><=
/p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'><span style=3D'mso-bookmark:Basics_of_Kriging'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></span></p>

<h1><span style=3D'mso-bookmark:Basics_of_Kriging'><span style=3D'font-size=
:14.0pt;
mso-bidi-font-size:12.0pt;font-family:"Times New Roman","serif"'>Basics of
Kriging </span></span><span style=3D'font-size:14.0pt;mso-bidi-font-size:12=
.0pt;
font-family:"Times New Roman","serif"'><o:p></o:p></span></h1>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Kriging was developed in the 1960s by the French
mathematician Georges Matheron.<span style=3D'mso-spacerun:yes'>&nbsp; </sp=
an>The
motivating application was to estimate gold deposited in a rock from a few
random core samples.<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>Kr=
iging
has since found its way into the earth sciences and other disciplines.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>It is an improvement over inverse =
distance
weighting because prediction estimates tend to be less bias and because
predictions are accompanied by prediction standard errors (quantification of
the uncertainty in the predicted value).<span style=3D'mso-spacerun:yes'>&n=
bsp;
</span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The basic tool of geostatistics and kriging is the
semivariogram.<span style=3D'mso-spacerun:yes'>&nbsp; </span>The semivariog=
ram
captures the spatial dependence between samples by plotting semivariance
against separation distance (semivariance will be explained in the next
paragraph).<span style=3D'mso-spacerun:yes'>&nbsp; </span>The premise of any
spatial interpolation is that close samples tend to be more similar than
distant samples (this is also called spatial autocorrelation).<span
style=3D'mso-spacerun:yes'>&nbsp; </span>This property of spatial data is
implicitly used in IDW.<span style=3D'mso-spacerun:yes'>&nbsp; </span>In kr=
iging,
one must model the spatial autocorrelation using a semivariogram instead of
assuming a direct, linear relationship with separation distance.<span
style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Semivariance equal one-half the squared difference bet=
ween
points separated by a distance d&plusmn;&#8710;d (assuming no direction
preference).<span style=3D'mso-spacerun:yes'>&nbsp; </span>As the distance
between samples increase, we expect the semivariance to also increase (agai=
n,
because near samples are more similar than distant samples).<span
style=3D'mso-spacerun:yes'>&nbsp; </span>This is true, however, only up to =
some
given separation distance.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Fo=
r this
distance and up, points are unrelated.<span style=3D'mso-spacerun:yes'>&nbs=
p;
</span>Stated another way, if 50m is this critical separation distance, two=
 points
separated by 50m are likely to be just as similar (or dependent on one anot=
her)
as samples separated by 100, 200, 300, or any distance greater than 50m.<sp=
an
style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Suppose we have the semivariogram shown in Figure 2.<s=
pan
style=3D'mso-spacerun:yes'>&nbsp; </span>What information does the plot
provide?<span style=3D'mso-spacerun:yes'>&nbsp; </span>Well, the semivarian=
ce
between samples separated by no distance is about 1.5E-4.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>This is called the nugget.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>What it says is that if you measur=
e the
variable at locations very, very close to one another, the values measured
might be quite different.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Why=
 would
this happen?<span style=3D'mso-spacerun:yes'>&nbsp; </span>Suppose you had =
a gold
nugget in the middle of an otherwise gold-free rock.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>If you sample just on the edge of =
the
nugget you get a high gold estimate.<span style=3D'mso-spacerun:yes'>&nbsp;
</span>If you sample just outside of the edge, you get no gold in your
estimate.<span style=3D'mso-spacerun:yes'>&nbsp; </span>The presence of a n=
ugget
in the semivariogram therefore tells you that, assuming no measurement erro=
r,
the variable is not spatially continuous.<span style=3D'mso-spacerun:yes'>&=
nbsp;
</span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The semivariogram also tells us that points separated =
by
60,000 m are likely to have the same average difference as points separated=
 by
100,000, 150,000, 200,000 m or any distance above 60,000m.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>60,000 m is the range of the
semivariogram and suggests the area of influence for any given point.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>An unmeasured location can be pred=
icted
based on its neighboring samples closer than 60,000m.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>A sample collected 61,000 m away f=
rom
the sample will likely have no influence on the actual value at the unmeasu=
red
location.<span style=3D'mso-spacerun:yes'>&nbsp; </span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>When you look at the model of a semivariogram, you'll =
notice
that at a certain distance, the model levels out. The distance where the mo=
del
first flattens out is known as the range Sample locations separated by
distances closer than the range are spatially autocorrelated, whereas locat=
ions
farther apart than the range are not. The value that the semivariogram model
attains at the range (the value on the y-axis) is called the sill. The part=
ial
sill is the sill minus the nugget</p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'><b style=3D'mso-bidi-font-weight:normal'><!--[if gte vm=
l 1]><v:shape
 id=3D"_x0000_i1026" type=3D"#_x0000_t75" style=3D'width:225pt;height:142.5=
pt'>
 <v:imagedata src=3D"ExGeostat_files/image003.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D300 height=3D190
src=3D"ExGeostat_files/image004.jpg" v:shapes=3D"_x0000_i1026"><![endif]><o=
:p></o:p></b></p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'>Figure 2 : The semivariogram is used to model the spati=
al
relationships between samples separated by some distance, d</p>

<p class=3DMsoNormal>For kriging estimation, the semivarogram model (the ye=
llow
line in figure 2) is used to obtain estimates for the weighting parameters =
of
Equation 1.<span style=3D'mso-spacerun:yes'>&nbsp; </span>This process is d=
one
automatically by the geostatistical analyst once the user is satisfied with=
 the
semivariogram.<span style=3D'mso-spacerun:yes'>&nbsp; </span>If you are
interested in the derivation of the weighting parameters (or any of the oth=
er
topics discussed here), <u>Applied Geostatistics</u> by Edward H. Isaaks an=
d R.
Mohan Srivastava is an excellent resource.<span style=3D'mso-spacerun:yes'>=
&nbsp;
</span>Or for the more mathematical folks, try <u>Statistics for Spatial Da=
ta</u>
by Noel A.C. Cressie.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'>Case study <o:p></o:p>=
</span></b></p>

<p class=3DMsoNormal>Now we know the basics of spatial interpolation. Lets =
use
our knowledge to estimate mean annual air temperature for each <st1:place
w:st=3D"on"><st1:PlaceType w:st=3D"on">county</st1:PlaceType> of <st1:Place=
Name
 w:st=3D"on">Nebraska</st1:PlaceName></st1:place>. </p>

<h2><span style=3D'mso-bidi-font-size:12.0pt;font-family:"Times New Roman",=
"serif";
font-style:normal;mso-bidi-font-style:italic'>Study Area<o:p></o:p></span><=
/h2>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1083" type=
=3D"#_x0000_t75"
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ht:226pt;
 z-index:251645952'>
 <v:imagedata src=3D"ExGeostat_files/image005.emz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><span style=3D'mso-ignore:vglayout'>

<table cellpadding=3D0 cellspacing=3D0 align=3Dleft>
 <tr>
  <td width=3D84 height=3D0></td>
 </tr>
 <tr>
  <td></td>
  <td><img width=3D480 height=3D301 src=3D"ExGeostat_files/image006.gif" v:=
shapes=3D"_x0000_s1083"></td>
 </tr>
</table>

</span><![endif]><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<br style=3D'mso-ignore:vglayout' clear=3DALL>

<p class=3DMsoNormal>Figure 3 : Location of major river basins in <st1:place
w:st=3D"on"><st1:State w:st=3D"on">Nebraska</st1:State></st1:place>. </p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'><st1:State w:st=3D"on">Nebraska</st1:State> covers a to=
tal of
124496 square kilometers area, making it the 16th largest of the 50 states =
in <st1:country-region
w:st=3D"on"><st1:place w:st=3D"on">United States of America</st1:place></st=
1:country-region>.
It is the mid-western state between longitude coordinates 95&deg;25'W and
104&deg;W (~690km) and latitude coordinates 40&deg;N and 43&deg;N (~340 km).
The geographic center of the state is located in <st1:place w:st=3D"on"><st=
1:PlaceName
 w:st=3D"on">Custer</st1:PlaceName> <st1:PlaceType w:st=3D"on">County</st1:=
PlaceType></st1:place>
with a longitude: 99&deg; 51.7'W; and latitude of 41&deg; 31.5'N (Figure 1).
The sate comprises of UTM zones 13, 14 and 15. The highest point is Panorama
Point, at 1653 meters above sea level and the lowest point is 256 meters ab=
ove
sea level at the Missouri River in southeastern <st1:place w:st=3D"on"><st1=
:PlaceName
 w:st=3D"on">Richardson</st1:PlaceName> <st1:PlaceType w:st=3D"on">County</=
st1:PlaceType></st1:place>.
The Mean Elevation of the state is 792 meters above sea level. The major ba=
sins
in the state are <st1:State w:st=3D"on">Missouri</st1:State>, Niobrara, Pla=
tte,
and <st1:place w:st=3D"on">Republican River</st1:place>. State has 93 count=
ies. In
this case we have used 215 NWS weather stations in and around <st1:State w:=
st=3D"on"><st1:place
 w:st=3D"on">Nebraska</st1:place></st1:State> to model spatial variation of=
 mean
annual temperature.</p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'>Data Download<o:p></o:=
p></span></b></p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'mso-spacerun:yes'>&nbsp;</span></b>Download the <a
href=3D"http://www.ce.utexas.edu/prof/maidment/giswr2008/geostat/Nebraska.z=
ip">http://www.ce.utexas.edu/prof/maidment/giswr2008/geostat/Nebraska.zip</=
a>
folder on your computer. You will see the following subfolders in the folde=
r.</p>

<ol start=3D1 type=3D1>
 <li class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-a=
lt:auto;
     text-align:justify;mso-list:l1 level1 lfo1;tab-stops:list .5in'>Tmean
     &#8211; This is a shpefile of National Weather service and co-operative
     observer networks weather stations (NWS). The attributes of the file a=
re
     mean monthly and mean annual air temperature for each station.</li>
 <li class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-a=
lt:auto;
     text-align:justify;mso-list:l1 level1 lfo1;tab-stops:list .5in'>NE_Bou=
ndary
     &#8211; This is shapefile for <st1:State w:st=3D"on"><st1:place w:st=
=3D"on">Nebraska</st1:place></st1:State>
     border.</li>
 <li class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-a=
lt:auto;
     text-align:justify;mso-list:l1 level1 lfo1;tab-stops:list .5in'>NE_Cou=
nty
     &#8211; This is a shpefile of all the counties in <st1:State w:st=3D"o=
n"><st1:place
      w:st=3D"on">Nebraska</st1:place></st1:State>. </li>
 <li class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-a=
lt:auto;
     text-align:justify;mso-list:l1 level1 lfo1;tab-stops:list .5in'>NE_Cit=
ies
     &#8211; This is shapefile of all the cities in <st1:State w:st=3D"on">=
<st1:place
      w:st=3D"on">Nebraska</st1:place></st1:State>.</li>
</ol>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'>Getting Started <o:p><=
/o:p></span></b></p>

<p class=3DMsoNormal>In this exercise we need to use spatial analyst and
geospatial analyst toolbar. We need to enable this extension in the first
place. Open <b style=3D'mso-bidi-font-weight:normal'>Tools</b> <b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-family:Wingdings;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man";
mso-char-type:symbol;mso-symbol-font-family:Wingdings'><span style=3D'mso-c=
har-type:
symbol;mso-symbol-font-family:Wingdings'>&agrave;</span></span> Extension.<=
o:p></o:p></b></p>

<p class=3DMsoNormal>Check the <b style=3D'mso-bidi-font-weight:normal'>&#8=
216;Spatial
analyst&#8217;</b> <b style=3D'mso-bidi-font-weight:normal'>and &#8216;Geos=
patial
analyst&#8217;</b> box. Now we can use all the functions in both toolbars.<=
/p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'><!--[if mso & !supportInlineShapes & supportFields]><b
style=3D'mso-bidi-font-weight:normal'><span style=3D'mso-element:field-begi=
n;
mso-field-lock:yes'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>SHAPE<span
style=3D'mso-spacerun:yes'>&nbsp; </span>\* MERGEFORMAT <span style=3D'mso-=
element:
field-separator'></span></b><![endif]--><b style=3D'mso-bidi-font-weight:no=
rmal'><!--[if gte vml 1]><v:group
 id=3D"_x0000_s1092" editas=3D"canvas" style=3D'width:378.5pt;height:315.05=
pt;
 mso-position-horizontal-relative:char;mso-position-vertical-relative:line'
 coordorigin=3D"2527,12360" coordsize=3D"6308,5399">
 <o:lock v:ext=3D"edit" aspectratio=3D"t"/>
 <v:shape id=3D"_x0000_s1091" type=3D"#_x0000_t75" style=3D'position:absolu=
te;left:2527;
  top:12360;width:6308;height:5399' o:preferrelative=3D"f">
  <v:fill o:detectmouseclick=3D"t"/>
  <v:path o:extrusionok=3D"t" o:connecttype=3D"none"/>
  <o:lock v:ext=3D"edit" text=3D"t"/>
 </v:shape><v:shape id=3D"_x0000_s1089" type=3D"#_x0000_t75" style=3D'posit=
ion:absolute;
  left:2527;top:12373;width:1677;height:3840'>
  <v:imagedata src=3D"ExGeostat_files/image007.png" o:title=3D""/>
 </v:shape><v:shape id=3D"_x0000_s1090" type=3D"#_x0000_t75" style=3D'posit=
ion:absolute;
  left:4709;top:12360;width:4126;height:5399'>
  <v:imagedata src=3D"ExGeostat_files/image008.png" o:title=3D""/>
 </v:shape><w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:group><![endif]--><![if !vml]><img width=3D505 height=3D420
src=3D"ExGeostat_files/image009.gif" v:shapes=3D"_x0000_s1092 _x0000_s1091 =
_x0000_s1089 _x0000_s1090"><![endif]></b><!--[if mso & !supportInlineShapes=
 & supportFields]><b
style=3D'mso-bidi-font-weight:normal'><v:shape id=3D"_x0000_i1027" type=3D"=
#_x0000_t75"
 style=3D'width:378.5pt;height:315.05pt'>
 <v:imagedata croptop=3D"-65520f" cropbottom=3D"65520f"/>
</v:shape><span style=3D'mso-element:field-end'></span></b><![endif]--><b
style=3D'mso-bidi-font-weight:normal'><o:p></o:p></b></p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'>Add <b style=3D'mso-bidi-font-weight:normal'>State</b>
shapefile from <b style=3D'mso-bidi-font-weight:normal'>NE_Boundary</b> fol=
der to
your computer. Add the <b style=3D'mso-bidi-font-weight:normal'>Tmean</b> f=
ile to
your map. Add <st1:place w:st=3D"on"><st1:PlaceType w:st=3D"on"><b
  style=3D'mso-bidi-font-weight:normal'>County</b></st1:PlaceType> <st1:Pla=
ceName
 w:st=3D"on">shapefile</st1:PlaceName></st1:place>. Following view will app=
ear on
your screen. </p>

<p class=3DMsoNormal style=3D'mso-margin-top-alt:auto;mso-margin-bottom-alt=
:auto;
text-align:justify'><!--[if gte vml 1]><v:shape id=3D"_x0000_i1028" type=3D=
"#_x0000_t75"
 style=3D'width:396pt;height:221.25pt'>
 <v:imagedata src=3D"ExGeostat_files/image010.png" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img border=3D0 width=3D528 height=3D295
src=3D"ExGeostat_files/image011.jpg" v:shapes=3D"_x0000_i1028"><![endif]></=
p>

<h4><a name=3D"Exploratory_Spatial_Data_Analysis">Exploratory Spatial Data
Analysis</a></h4>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Exploratory Spatial Data Analysis (ESDA) is a process =
of
understanding the properties of a spatial dataset in order to best model th=
e data
using geostatistics.<span style=3D'mso-spacerun:yes'>&nbsp; </span>The word
&#8220;Explore&#8221; should tell you that ESDA is more of an adventure tha=
n a
strict &#8211; you must follow the path at all times &#8211; procedure.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>In this exercise we show how the
Geostatistical Analyst tools can be used to understand the population
distribution of the attribute of interest and how to understand the large-s=
cale
patterns in the dataset through 3D visualization.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>This is not a comprehensive list o=
f ESDA
procedures, but a good start.<span style=3D'mso-spacerun:yes'>&nbsp;
</span>Through this process, keep in mind that the better one understands t=
he
spatial characteristics of the data, the better kriging model one can build=
 to
interpolate the data, and, consequently, the better estimates one will prod=
uce.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt'>Histogram<o:p></o:p></span></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt'><o:p>&nbsp;</o:p></span></b></p>

<p class=3DMsoNormal>Open <b style=3D'mso-bidi-font-weight:normal'>Geospati=
al</b> <b
style=3D'mso-bidi-font-weight:normal'>analyst </b><b style=3D'mso-bidi-font=
-weight:
normal'><span style=3D'font-family:Wingdings;mso-ascii-font-family:"Times N=
ew Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span>
Explore Data </b><b style=3D'mso-bidi-font-weight:normal'><span style=3D'fo=
nt-family:
Wingdings;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti=
mes New Roman";
mso-char-type:symbol;mso-symbol-font-family:Wingdings'><span style=3D'mso-c=
har-type:
symbol;mso-symbol-font-family:Wingdings'>&agrave;</span></span></b> <b
style=3D'mso-bidi-font-weight:normal'>Histogram. </b></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1098" type=
=3D"#_x0000_t75"
 style=3D'width:261pt;height:129.9pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image012.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D348 height=3D173
src=3D"ExGeostat_files/image013.jpg" v:shapes=3D"_x0000_s1098"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Select the 10 bars and check the statistics option to =
view
th stastsitcs of mean annual air temperature. Keep the <b style=3D'mso-bidi=
-font-weight:
normal'>transformation</b> as <b style=3D'mso-bidi-font-weight:normal'>None=
</b>.
Select <b style=3D'mso-bidi-font-weight:normal'>layer</b> as <b style=3D'ms=
o-bidi-font-weight:
normal'>Tmean</b> and <b style=3D'mso-bidi-font-weight:normal'>Attribute</b=
> as <b
style=3D'mso-bidi-font-weight:normal'>ANNUAL</b>. Similar window will appea=
r on
screen.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1099" type=
=3D"#_x0000_t75"
 style=3D'width:396pt;height:215.9pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image014.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D528 height=3D288
src=3D"ExGeostat_files/image015.jpg" v:shapes=3D"_x0000_s1099"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>We will now analyze the histogram for mean annual air
temperature of <st1:State w:st=3D"on"><st1:place w:st=3D"on">Nebraska</st1:=
place></st1:State>.
Upper right corner shows the statistics of the statistics of mean annual air
temperature. Histogram shows that our data is not perfectly normally distri=
buted,
but it is fairly normally distributed. One of the crosscheck of normal
distribution of data is that mean should be closer to the median. In our ca=
se
mean is 6.9<sup>o</sup>C and median is 6.6<sup>o</sup>C. We can consider our
data as normally distributed. User can transform the data into <b
style=3D'mso-bidi-font-weight:normal'>log</b> or <b style=3D'mso-bidi-font-=
weight:
normal'>box-cox</b> distribution if it is not normally distributed. <span
style=3D'mso-spacerun:yes'>&nbsp;</span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'>QQ (Quantile-Quantile)=
 plot<o:p></o:p></span></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal>Another way to understand the data&#8217;s distributio=
n is
by using the Normal QQ Plot tool.<span style=3D'mso-spacerun:yes'>&nbsp;
</span>In a QQ (Quantile-Quantile) plot we test whether data are normally
distributed by plotting it against a dataset with a known normal
distribution.<span style=3D'mso-spacerun:yes'>&nbsp; </span>If the plot is =
linear
along the line Y=3DX, then the data follow a normal distribution.</p>

<p class=3DMsoNormal>Open <b style=3D'mso-bidi-font-weight:normal'>Geospati=
al</b> <b
style=3D'mso-bidi-font-weight:normal'>analyst </b><b style=3D'mso-bidi-font=
-weight:
normal'><span style=3D'font-family:Wingdings;mso-ascii-font-family:"Times N=
ew Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span>
Explore data </b><b style=3D'mso-bidi-font-weight:normal'><span style=3D'fo=
nt-family:
Wingdings;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti=
mes New Roman";
mso-char-type:symbol;mso-symbol-font-family:Wingdings'><span style=3D'mso-c=
har-type:
symbol;mso-symbol-font-family:Wingdings'>&agrave;</span></span></b> <st1:pl=
ace
w:st=3D"on"><b style=3D'mso-bidi-font-weight:normal'>Normal</b></st1:place>=
<b
style=3D'mso-bidi-font-weight:normal'> QQ plot.</b></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1100" type=
=3D"#_x0000_t75"
 style=3D'width:295.5pt;height:148.5pt;mso-position-horizontal-relative:cha=
r;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image016.gif" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D394 height=3D198
src=3D"ExGeostat_files/image016.gif" v:shapes=3D"_x0000_s1100"><![endif]></=
p>

<p class=3DMsoNormal>The QQ plot shows the linear relationship between log(=
Tmean)
and the standard normal distribution. Data is not exactly linear on lower e=
nd.
But we can say that Tmean is normally distributed. </p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1101" type=
=3D"#_x0000_t75"
 style=3D'width:450.65pt;height:245.55pt;mso-position-horizontal-relative:c=
har;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image017.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D601 height=3D327
src=3D"ExGeostat_files/image018.jpg" v:shapes=3D"_x0000_s1101"><![endif]></=
p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'>Trend analysis<o:p></o=
:p></span></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'><o:p>&nbsp;</o:p></spa=
n></b></p>

<p class=3DMsoNormal>The trend analysis tool provides a 3D plot of the samp=
les
and a regression on the attribute in the XZ and YZ planes.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>The purpose of the tool is to visu=
alize
the data and to observe any large-scale trends that the modeler might want =
to
remove prior to estimation.<span style=3D'mso-spacerun:yes'>&nbsp; </span>I=
t is
best to keep the kriging model as simple as possible and to only remove a t=
rend
if it significantly improves prediction errors.</p>

<p class=3DMsoNormal>Open <b style=3D'mso-bidi-font-weight:normal'>Geospati=
al</b> <b
style=3D'mso-bidi-font-weight:normal'>analyst </b><b style=3D'mso-bidi-font=
-weight:
normal'><span style=3D'font-family:Wingdings;mso-ascii-font-family:"Times N=
ew Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span>
Explore data </b><b style=3D'mso-bidi-font-weight:normal'><span style=3D'fo=
nt-family:
Wingdings;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti=
mes New Roman";
mso-char-type:symbol;mso-symbol-font-family:Wingdings'><span style=3D'mso-c=
har-type:
symbol;mso-symbol-font-family:Wingdings'>&agrave;</span></span>Trend analys=
is.</b></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1104" type=
=3D"#_x0000_t75"
 style=3D'width:295.5pt;height:148.5pt;mso-position-horizontal-relative:cha=
r;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image016.gif" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D394 height=3D198
src=3D"ExGeostat_files/image016.gif" v:shapes=3D"_x0000_s1104"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Screen will look similar to figure We can choose the
different graph options and rotate the location to see the trend in the dat=
a. </p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1103" type=
=3D"#_x0000_t75"
 style=3D'width:432.65pt;height:269pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image019.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D577 height=3D359
src=3D"ExGeostat_files/image020.jpg" v:shapes=3D"_x0000_s1103"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The trend analysis tool provides a 3D plot of the samp=
les
and a regression on the attribute in the XZ and YZ planes.<span
style=3D'mso-spacerun:yes'>&nbsp; </span>The purpose of the tool is to visu=
alize
the data and to observe any large-scale trends that the modeler might want =
to
remove prior to estimation.<span style=3D'mso-spacerun:yes'>&nbsp; </span>I=
t is
best to keep the kriging model as simple as possible and to only remove a t=
rend
if it significantly improves prediction errors.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'>Perform Kriging
interpolation</span><o:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal>Open <b style=3D'mso-bidi-font-weight:normal'>Geospati=
al</b> <b
style=3D'mso-bidi-font-weight:normal'>analyst </b><b style=3D'mso-bidi-font=
-weight:
normal'><span style=3D'font-family:Wingdings;mso-ascii-font-family:"Times N=
ew Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span>
Geospatial Wizard<o:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><!--[if gte v=
ml 1]><v:shape
 id=3D"_x0000_s1105" type=3D"#_x0000_t75" style=3D'width:136.5pt;height:78.=
75pt;
 mso-position-horizontal-relative:char;mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image021.gif" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D182 height=3D105
src=3D"ExGeostat_files/image021.gif" v:shapes=3D"_x0000_s1105"><![endif]><o=
:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal>Select the <b style=3D'mso-bidi-font-weight:normal'>Kr=
iging</b>
as <b style=3D'mso-bidi-font-weight:normal'>method</b> and <b style=3D'mso-=
bidi-font-weight:
normal'>Tmean</b> as <b style=3D'mso-bidi-font-weight:normal'>input</b> <b
style=3D'mso-bidi-font-weight:normal'>data</b>. Select <b style=3D'mso-bidi=
-font-weight:
normal'>attribute</b> as <b style=3D'mso-bidi-font-weight:normal'>ANNUAL. <=
o:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><!--[if gte v=
ml 1]><v:shape
 id=3D"_x0000_s1106" type=3D"#_x0000_t75" style=3D'width:423pt;height:320.8=
5pt;
 mso-position-horizontal-relative:char;mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image022.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D564 height=3D428
src=3D"ExGeostat_files/image023.jpg" v:shapes=3D"_x0000_s1106"><![endif]><o=
:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal>User can assign the <b style=3D'mso-bidi-font-weight:n=
ormal'>no
data value</b> as zero or any other desired value. Default no data value is
-9999.0. </p>

<p class=3DMsoNormal>Click <b style=3D'mso-bidi-font-weight:normal'>Next</b=
> to
proceed.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1107" type=
=3D"#_x0000_t75"
 style=3D'width:324pt;height:246.25pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image024.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D432 height=3D328
src=3D"ExGeostat_files/image025.jpg" v:shapes=3D"_x0000_s1107"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<h4><span style=3D'font-size:12.0pt'>We will choose th most widely used </s=
pan><span
style=3D'font-size:12.0pt;font-weight:normal;mso-bidi-font-weight:bold'>ord=
inary
kriging </span><span style=3D'font-size:12.0pt'>method and </span><span
style=3D'font-size:12.0pt;font-weight:normal;mso-bidi-font-weight:bold'>pre=
diction
map. As discussed in</span><span style=3D'font-size:12.0pt'> exploratory sp=
atial
data analysis </span><span style=3D'font-size:12.0pt;font-weight:normal;
mso-bidi-font-weight:bold'>we will keep </span><span style=3D'font-size:12.=
0pt'>transformation</span><span
style=3D'font-size:12.0pt;font-weight:normal;mso-bidi-font-weight:bold'> an=
d </span><span
style=3D'font-size:12.0pt'>order of trend removal</span><span style=3D'font=
-size:
12.0pt;font-weight:normal;mso-bidi-font-weight:bold'> as </span><span
style=3D'font-size:12.0pt'>none.<o:p></o:p></span></h4>

<p class=3DMsoNormal>Click <b style=3D'mso-bidi-font-weight:normal'>Next</b=
> to
proceed.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1108" type=
=3D"#_x0000_t75"
 style=3D'width:396pt;height:301.2pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image026.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D528 height=3D402
src=3D"ExGeostat_files/image027.jpg" v:shapes=3D"_x0000_s1108"><![endif]></=
p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal>We will choose widely used <b style=3D'mso-bidi-font-w=
eight:
normal'>spherical </b>semivariogram model. Other commonly used models are
exponential and Gaussian. Lag size and number of lags are the important
parameters to be selected. These two parameters are used to group the numbe=
r of
pairs of data. For our analysis we will use the default values. For given l=
ag
size and number of lags, ArcGIS automatically calculates the nugget, range =
and
sill. Check the <b style=3D'mso-bidi-font-weight:normal'>anisotropy</b> opt=
ion.
Anisotropy represents the trend in the data in particular direction. We can=
 see
that blue value have high covariance and they are oriented in one direction.
Semivariogram for particular direction can be investigated using <b
style=3D'mso-bidi-font-weight:normal'>show search direction</b> tool. </p>

<p class=3DMsoNormal>Click <b style=3D'mso-bidi-font-weight:normal'>Next</b=
> to
proceed.</p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1109" type=
=3D"#_x0000_t75"
 style=3D'width:369pt;height:280.75pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image028.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D492 height=3D374
src=3D"ExGeostat_files/image029.jpg" v:shapes=3D"_x0000_s1109"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Change <b style=3D'mso-bidi-font-weight:normal'>Neighb=
ours to include
</b>to <b style=3D'mso-bidi-font-weight:normal'>12</b> and include at least=
 <b
style=3D'mso-bidi-font-weight:normal'>10</b> stations. Since we have the to=
tal <b
style=3D'mso-bidi-font-weight:normal'>215</b> weather stations, 12 and mini=
mum 10
weather stations is an appropriate number for interpolation. Click on the f=
irst
circle for <b style=3D'mso-bidi-font-weight:normal'>sector type</b>. </p>

<p class=3DMsoNormal>Click <b style=3D'mso-bidi-font-weight:normal'>Next</b=
> to
proceed.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1110" type=
=3D"#_x0000_t75"
 style=3D'width:378pt;height:287.5pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image030.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D504 height=3D383
src=3D"ExGeostat_files/image031.jpg" v:shapes=3D"_x0000_s1110"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>This is the error statistics for the interpolation. Th=
is is
based on one-leave-out cross validation method. We can save the cross
validation table to perform further statistical analysis. </p>

<p class=3DMsoNormal>Click <b style=3D'mso-bidi-font-weight:normal'>Finish.=
</b></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1111" type=
=3D"#_x0000_t75"
 style=3D'width:208pt;height:252pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image032.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D277 height=3D336
src=3D"ExGeostat_files/image033.jpg" v:shapes=3D"_x0000_s1111"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>This is the summary of interpolation parameters chosen.
Click <b style=3D'mso-bidi-font-weight:normal'>Ok.<o:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal>Now you will see the following map of mean annual air
temperature. </p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1112" type=
=3D"#_x0000_t75"
 style=3D'width:378pt;height:302.4pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line' fillcolor=3D"#bbe0e3">
 <v:imagedata src=3D"ExGeostat_files/image034.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D504 height=3D403
src=3D"ExGeostat_files/image035.jpg" v:shapes=3D"_x0000_s1112"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>We will save this as a <b style=3D'mso-bidi-font-weigh=
t:normal'>raster</b>
dataset. <b style=3D'mso-bidi-font-weight:normal'>Right click</b> on the <b
style=3D'mso-bidi-font-weight:normal'>Ordinary Kriging</b> layer. Select <b
style=3D'mso-bidi-font-weight:normal'>Data </b><b style=3D'mso-bidi-font-we=
ight:
normal'><span style=3D'font-family:Wingdings;mso-ascii-font-family:"Times N=
ew Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span>
Export to raster.</b> </p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1114" type=
=3D"#_x0000_t75"
 style=3D'width:3in;height:145.65pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image036.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D288 height=3D194
src=3D"ExGeostat_files/image037.jpg" v:shapes=3D"_x0000_s1114"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Select output raster as folder and file name as <b
style=3D'mso-bidi-font-weight:normal'>Tmean_Clipped</b></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1115" type=
=3D"#_x0000_t75"
 style=3D'width:225pt;height:145.9pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image038.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D300 height=3D195
src=3D"ExGeostat_files/image039.jpg" v:shapes=3D"_x0000_s1115"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1116" type=
=3D"#_x0000_t75"
 style=3D'width:198pt;height:67.15pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image040.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D264 height=3D90
src=3D"ExGeostat_files/image041.jpg" v:shapes=3D"_x0000_s1116"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Add this layer to the map.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'>Raster extraction<o:p>=
</o:p></span></b></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>We will clip this map to the <st1:State w:st=3D"on"><s=
t1:place
 w:st=3D"on">Nebraska</st1:place></st1:State> border. Open <b style=3D'mso-=
bidi-font-weight:
normal'>ArcToolBox </b><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-family:Wingdings;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span>
Spatial analyst tools </b><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-family:Wingdings;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span></b>
<b style=3D'mso-bidi-font-weight:normal'>Extraction </b><b style=3D'mso-bid=
i-font-weight:
normal'><span style=3D'font-family:Wingdings;mso-ascii-font-family:"Times N=
ew Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span>
Extract by mask. <o:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1113" type=
=3D"#_x0000_t75"
 style=3D'width:132pt;height:315pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image042.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D176 height=3D420
src=3D"ExGeostat_files/image043.jpg" v:shapes=3D"_x0000_s1113"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Select input raster as <b style=3D'mso-bidi-font-weigh=
t:normal'>Tmean_Clipped</b>
raster or feature mask data as <b style=3D'mso-bidi-font-weight:normal'>Sta=
te. </b>Save
it on the desired output location with the name <b style=3D'mso-bidi-font-w=
eight:
normal'>NE_Tmean.</b></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1117" type=
=3D"#_x0000_t75"
 style=3D'width:378pt;height:252.45pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image044.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D504 height=3D337
src=3D"ExGeostat_files/image045.jpg" v:shapes=3D"_x0000_s1117"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Add this clipped layer to the map. </p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'>Zonal Statistics<o:p><=
/o:p></span></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal>We will compute zonal statistics to know the average r=
ainfall
for each county. </p>

<p class=3DMsoNormal>Select <b style=3D'mso-bidi-font-weight:normal'>spatial
analyst </b><b style=3D'mso-bidi-font-weight:normal'><span style=3D'font-fa=
mily:
Wingdings;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti=
mes New Roman";
mso-char-type:symbol;mso-symbol-font-family:Wingdings'><span style=3D'mso-c=
har-type:
symbol;mso-symbol-font-family:Wingdings'>&agrave;</span></span> Zonal
statistics<o:p></o:p></b></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1118" type=
=3D"#_x0000_t75"
 style=3D'width:2in;height:229.5pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image046.gif" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D192 height=3D306
src=3D"ExGeostat_files/image046.gif" v:shapes=3D"_x0000_s1118"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Select <b style=3D'mso-bidi-font-weight:normal'>zone d=
ataset</b>
as <b style=3D'mso-bidi-font-weight:normal'>County_07. </b>Select <b
style=3D'mso-bidi-font-weight:normal'>Zone file</b> das <b style=3D'mso-bid=
i-font-weight:
normal'>CTYNAME_LO </b>and <b style=3D'mso-bidi-font-weight:normal'>value r=
aster </b>as
<b style=3D'mso-bidi-font-weight:normal'>NE_Tmean. </b>Ignore NoData in
calculations and select <b style=3D'mso-bidi-font-weight:normal'>chart stat=
istics</b>
as <b style=3D'mso-bidi-font-weight:normal'>Mean</b>. Select the output tab=
le in
desired folder. </p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1119" type=
=3D"#_x0000_t75"
 style=3D'width:3in;height:188.3pt;mso-position-horizontal-relative:char;
 mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image047.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D288 height=3D251
src=3D"ExGeostat_files/image048.jpg" v:shapes=3D"_x0000_s1119"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Following chart should appear on the screen.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><span style=3D'mso-spacerun:yes'>&nbsp;</span><!--[if =
gte vml 1]><v:shape
 id=3D"_x0000_s1120" type=3D"#_x0000_t75" style=3D'width:434.15pt;height:25=
7.2pt;
 mso-position-horizontal-relative:char;mso-position-vertical-relative:line'>
 <v:imagedata src=3D"ExGeostat_files/image049.png" o:title=3D""/>
 <w:wrap type=3D"none"/>
 <w:anchorlock/>
</v:shape><![endif]--><![if !vml]><img width=3D579 height=3D343
src=3D"ExGeostat_files/image050.jpg" v:shapes=3D"_x0000_s1120"><![endif]></=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>This shows the mean annual temperature for each county=
. </p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt;mso-bidi-font-size:12.0pt'>Summary of items to be
turned in<o:p></o:p></span></b></p>

<h4 style=3D'margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo2;
tab-stops:list .5in'><![if !supportLists]><span style=3D'font-size:12.0pt;
mso-bidi-font-size:14.0pt;font-weight:normal;mso-bidi-font-weight:bold'><sp=
an
style=3D'mso-list:Ignore'>1.<span style=3D'font:7.0pt "Times New Roman"'>&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span style=3D'font-size:12.0pt;mso-bidi-fon=
t-size:
14.0pt;font-weight:normal;mso-bidi-font-weight:bold'>Explore the histogram =
and
QQ plot for the month of July and January. Summarize your observations. Show
the graphs and histograms for both months. <o:p></o:p></span></h4>

<ol style=3D'margin-top:0in' start=3D2 type=3D1>
 <li class=3DMsoNormal style=3D'mso-list:l0 level1 lfo2;tab-stops:list .5in=
'>Find
     the Root Mean Square Error of the interpolation for the mean annual
     temperature with following parameters. </li>
</ol>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

</div>

</body>

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