geostatistics

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

Basic definitions

• Variance:

• Standard Deviation:

n

meani KKn

K1

21)var(

)var(2 K

)var(K

Basic definitions

• Number of pairs

Basic definitions

• Number of pairs:

2

)1(

nnnpairs

Basic definitions

• Lag (h)– Separation distance

(and possibly direction)

h

Basic definitions

• Variance:

• Variogram:

)(

1

2)()()(2

1 h

hxxh

hn

KKn

h n

meani KKn

K1

21)var(

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

Basic definitions

Kriging:

N

iiKwK1

x

N

iw1

1BLUE

Kriging Estimates

Where to get software:

http://www.ucc.ie/gnuplot/Release 4, gp400win32.zip

ftp://globec.whoi.edu/pub/software/kriging/easy_krig/V3.0.1/

http://sgems.sourceforge.net/doc/sgems_manual.pdf

http://sgems.sourceforge.net/

http://www.ucc.ie/gnuplot/





http://sgems.sourceforge.net/

http://www.gstat.org/

S-GeMS Object file formatww (49x30)3xypore1 1 121 1 141 1 161 1 181 1 1101 1 0121 1 0141 1 0161 1 0181 1 0201 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 IdentificationSites 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 PlaneNGS 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/ftDriscoll, F. G. 1986. Groundwater and Wells, Johnson Division, Minneapolis.

Specific Capacity Data

Specific CapacityVariance of data: 3,509,048 (gpm/ft)2

Slow initial growth in variance with lag => Gaussian variogram model

Range: 0.07 degrees

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

Gaussian Simulation/KrigingHistogram

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5 conditioning points

1 conditioning point

Simulation

5 conditioning points

1 conditioning point