Geostatistics
Hydrogeologist III / Salary Range: $48,980 - $72,632 per year (DOQ).
First Published 02/03/04
Broward County Department of Planning and Environmental Protection Water Resources Division.
Position requires hydrologic modeling of surface water and groundwater flows in Broward County,
Florida in support of natural resource protection and restoration, and urban water resource planning.
Work requires the use of experienced judgment and advanced modeling and theoretical skills.
Candidates should have knowledge of reference sources, current trends, and recent research in
hydrogeologic modeling and water resource management; the ability to apply scientific and technical
knowledge with accuracy and sound judgment; and the ability to communicate effectively both orally
and in writing. Please see full position announcement for qualification requirements and how to apply
at http://205.166.161.20/hrcurrjobs/XML/1638.htm
Goals
Basic definitions
• Variance:
n
1
2
var( K )   Ki  K mean 
n 1
  var( K )
2
• Standard Deviation:
  var( K )
Basic definitions
• Number of pairs
Basic definitions
• Number of pairs:
n ( n  1)
n pairs 
2
Basic definitions
• Lag (h)
– Separation distance
(and possibly
direction)
h
Basic definitions
• Variance:
n
1
2
var( K )   Ki  K mean 
n 1
h
• Variogram:
n(h)
1
2
K (x)  K (x  h)
 h  

2n ( h ) 1
The variogram
• Captures the intuitive notion that samples
taken close together are more likely to be
similar than samples taken far apart
Common Variogram Models
Common Variogram Models
Basic definitions
Kriging:
N
K x    wi Ki
1
N
w
i
1
1
BLUE
Kriging Estimates
Where to get
software:
http://sgems.sourceforge.net/
http://sgems.sourceforge.net/doc/
sgems_manual.pdf
ftp://globec.whoi.edu/pub/software/
kriging/easy_krig/V3.0.1/
http://www.ucc.ie/gnuplot/
Release 4, gp400win32.zip
S-GeMS Object file format
ww (49x30)
3
x
y
pore
111
21 1 1
41 1 1
61 1 1
81 1 1
101 1 0
121 1 0
141 1 0
161 1 0
181 1 0
201 1 0
…
Load object
Import as point set
Random Numbers; Pure Nugget
Unconditioned Simulation
• Specify mean and neighborhood
• Specify variogram
• Simulation should honor variogram
Unconditional Simulation
Simulated Field/Known Variogram
USGS Sections
http://sofia.usgs.gov/publications/wri/90-4108/wri904108plates.pdf
http://sofia.usgs.gov/publications/wri/90-4108/wri904108plates.pdf
USGS Aquifer Tests
USGS Site Identification
Sites are identified by the standard U.S. Geological Survey (USGS)
identification number, which is based on an initial determination of latitude
and longitude of the site. The site identification serves as a unique
identification number in files and databases of the USGS and indicates the
approximate geographic location of each site. The identification consists of
15 digits: the first 6 digits denote the degrees, minutes, and seconds of
latitude; the next 7 digits denote degrees, minutes, and seconds of
longitude; and the last 2 digits (assigned sequentially) identify the site within
a 1-second grid. For example, site 363530116021401 is at approximately
36°35'30" latitude and 116°02'14" longitude, and it is the first site recorded in
that 1-second grid. Even if a more precise latitude and longitude are
subsequently determined, the site identification number remains unchanged.
Latitude and longitude shown for a site, therefore, are the most accurate
locators.
Coordinate Extraction
Lat/Lon State Plane
NGS Horizontal Blue Book format - *80* (Control Point) Record. Only the *80* records in a Blue Book file are used by
NADCON, the other records are passed through without change to the output. On the *80* records, only the latitude
and longitude are modified - the rest of the record is unchanged. Thus, this format can be used with either 'old' Blue Book
files or 'new' Blue Book files. On the *80* records, the direction of the latitude must be north positive ('N')
and the direction of the longitude must be west positive ('W'). The precision of the output will be the same as the precision of
the input latitude.
For more information on this format, please refer to:
'Input Formats and Specifications of the National Geodetic Survey Data Base' 'Volume 1. Horizontal Control Data'.
Published by the Federal Geodetic Control Committee in January, 1989 and available from: the National Geodetic Survey,
NOAA, Rockville, MD 20852.
The following input example is a *80* record from a Blue Book file with NAD 27 coordinates:
004560*80*096 KNOXVILLE CT HSE
411906578 N0930548534 W 277
The following example is of the output *80* record with the transformed NAD 83 latitude and longitude.
004560*80*096 KNOXVILLE CT HSE
411906566 N0930549268 W 277
http://www.ngs.noaa.gov/cgi-bin/nadcon.prl?explain=Y&input_format=3
http://www.ngs.noaa.gov/
Biscayne Aquifer K
Specific Capacity
•
•
•
•
•
•
•
Flow per Drawdown, Q/s (gpm/ft)
T (gpd/ft) ~ 2000 Q/s (gpm/ft)
T = 2 x 106 gpd/ft (extreme!)
Q/s = T/2000 = 103 gpm/ft
Q = 100 gpm =>
s = 1/10 ft (~3 cm)
Data: Q/s = 7000 gpm/ft
Driscoll, F. G. 1986. Groundwater and Wells, Johnson Division, Minneapolis.
Specific Capacity Data
Specific Capacity
Variance of data: 3,509,048 (gpm/ft)2
Range: 0.07 degrees
Slow initial growth in variance with lag =>
Gaussian variogram model
Specific Capacity
Variance of data: 3,509,048 (gpm/ft)2
Range: 0.07 degrees
Slow initial growth in variance with lag =>
Gaussian variogram model
Conditional Gaussian Simulation
• Specify data
• Fit and specify variogram
• Simulation should honor variogram and be
responsive to values at ‘conditioning’
points
Kriging
• Specify data
• Fit and specify variogram
• Simulation should honor variogram and
return exact values at sampling points
• Optimal estimate too far from sample data
is mean
Gaussian Simulation/Kriging
Kriging
500
400
300
200
100
0
Bin
5000
6000
7000
8000
9000
10000
More
6000
7000
8000
9000
10000
More
Histogram
5000
Bin
4000
3000
2000
1000
0
-1000
-2000
-3000
-4000
-5000
0
4000
3000
2000
1000
0
-1000
-2000
-3000
-4000
-5000
Frequency
Gaussian
Frequency
Gaussian Simulation/Kriging
Histogram
150
100
50
Kriging
1
conditioning
point
5
conditioning
points
Simulation
1
conditioning
point
5
conditioning
points