Geostatistics Revisited: Patterns in the United States

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Geostatistics RevisitedPatterns in the United
States

• David R. Maidment
• 6 November 2008

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Election as GeostatisticsLocation matters!!
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Statistical sampling of voters
Final Preelection Polls
Election on (11/4/08)
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Election Population
Population size 125,225,901 Spread Obama 53
to McCain 46
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Election Sample(Stratified Random Sampling)
National Survey of 1,000 Likely Voters
Sample size 1000 Spread Obama 52 to McCain
46 Sample Population 1000 120 million or
0.00083
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Air Temperature Population
Nebraska
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Air Temperature Sample(Mean annual values from
Nebraska)
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What are Statistics?
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How do Geostatistics Differ from Statistics?
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Random FieldsProbabilistic processes in space
Voters A finite population of spatially
discrete objects
Air Temperature An infinite population which
forms a spatial continuum
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Air Temperature on an X-Y plane
Northing, Y
Easting, X
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Geostatistics Orientation matters!
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Temperature and Elevation
Contrary trend to normal, where temperature
decreases with elevation
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Histogram of Air Temperature
Degrees Centigrade 10-1
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Normal Q-Q Plot
Degrees Centigrade 10-1
Standard Normal Variate, z
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Normal Q-Q Plot
Plotting posn (i-0.5)/n, i1 is lowest value
and i n is highest value
x
z
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Trend Analysis
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Semivariogram and Covariance
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Semivariogram
Dist 4.75 x 105m
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Detrending with an first order (linear) surface
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Trend removal
Semivariogram with no trend removal
Semivariogram with linear trend removal
Long memory data
Short memory data
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Mean, Standard Deviation and Standard Error of
Estimate
Air Temperature data in Nebraska (215
sites) Mean 6.96 C Standard Deviation 2.07
C Standard Error of Mean 0.47 C
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Prediction and Standard Error Maps
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Estimating Water Use in the United States
http//www.nap.edu/catalog.php?record_id10484
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National Water Use Estimation
All variables defined for state i in year t
TW total water use PS public water supply DM
domestic use CM commercial use IR
irrigation use LS livestock use IN industrial
use MN mining use TE thermoelectric use
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State Water Use Databases - Survey undertaken
with the assistance of USGS water use specialists

• Category 1 (10 states)
• Arkansas, Delaware, Hawaii, Indiana, Kansas,
  Louisiana, Massachusetts, New Jersey, New
  Hampshire, Vermont
• Category 2 (12 states)
• Alabama, Illinois, Maryland, Minnesota,
  Mississippi, New Mexico, North Dakota, Ohio,
  Oklahoma, Oregon, Utah, Virginia
• Category 3 (28 states PR)
• Alaska, Arizona, California, Colorado,
  Connecticut, Florida, Georgia, Idaho, Iowa,
  Kentucky, Maine, Michigan, Missouri, Montana,
  Nebraska, Nevada, New York, North Carolina,
  Pennsylvania, Puerto Rico, Rhode Island, South
  Carolina, South Dakota, Tennessee, Texas,
  Washington, West Virginia, Wisconsin, Wyoming

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Category
2
3
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Water Use Estimation

• Direct Estimation sample n and extrapolate to
  population of size N

• Indirect Estimation use regression or a water
  use coefficient model to get water use in each
  state

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Trends in Water Use in the US
Solley et al., 1998
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Total Water Use
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Arkansas Site-Specific Water-Use Database
50,000 points with monthly water withdrawal
estimates
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Surface and Groundwater Points
Groundwater 39,100 points
Surface water 5,600 points
Data are reported to AWSCC in acre-ft per month
or year Data are reported to USGS national
summary in MGD
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Arkansas Aquifers
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Withdrawals from the Mississippi Alluvium
33,700 wells (86) out of 39,100 total draw from
the Mississippi Alluvium
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Stratified Random Sampling

• VT variance of total water use
• Nh total number of sites in stratum h,
• nh sampled sites in stratum h,
• n total number of samples
• and sh2 variance of water use at a site in
  stratum h

sL2
hL
Domestic
Comm.
Industrial
s22
h2
Irrigation
s12
PWS
h1
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Number of Samples RequiredArkansas, irrigation
from groundwater
Total use 5,492,730 MG
Desired standard error 549,273 MG requires 111
samples
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A Sampling Scheme(for 10 standard error in
total water use)
nh
Nh
n
Power uses have complete inventory, others are
randomly sampled
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Summary of Recommendations

• Elevate the NWUIP to a water-use science program,
  emphasizing statistical estimation of water use
  and the determinants and impacts of water use.
• Systematically compare water-use estimation
  methods to identify the techniques best suited to
  the requirements and limitations of the NWUIP.
  Determine the standard error for every water-use
  estimate.
• (Move from an inventory model to a statistical
  model to produce national estimates.)

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Summary of Recommendations

• Systematically integrate datasets, including
  those maintained by other federal and state
  agencies, into datasets already maintained by the
  NWUIP.
• Focus on the scientific integration of water use,
  water flow, and water quality to expand knowledge
  and generate policy-relevant information about
  human impacts on both water and ecological
  resources
• Seek support from Congress for dedicated funding
  of a national component water-use science program
  to supplement the existing funding in the Coop
  Program

This is now funded and is called the Water for
America program