geostatistics revisited: patterns in the united states david r. maidment 6 november 2008
TRANSCRIPT
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Geostatistics Revisited:Patterns in the United States
David R. Maidment6 November 2008
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Election as Geostatistics:Location 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: 125,225,901Spread – Obama: 53% to McCain: 46%
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Election “Sample”(Stratified Random Sampling)
National Survey of 1,000 Likely Voters
Sample size: 1000Spread – 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 Fields:Probabilistic 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
Easting, X
Northing, Y
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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
Standard Normal Variate, z
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Normal Q-Q Plot
zx
Plotting posn = (i-0.5)/n, i=1 is lowest value and i= n is highest value
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Trend Analysis
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Semivariogram and Covariance
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Semivariogram
2,2
1ji
ji
zz
2,
9.118.32
1
ji
805.32
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 °CStandard Deviation = 2.07 °CStandard 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_id=10484
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National Water Use Estimation
i
ititititititititt TEMNINLSIRCMDMPSTW )( ,,,,,,,,
TW = total water usePS = public water supplyDM = domestic useCM = commercial useIR = irrigation useLS = livestock useIN = industrial useMN = mining useTE = thermoelectric use
All variables defined for state i in year t
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1
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
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
j
ititjjit XbaY ,,,, t
n
ktkt y
n
NY
1,
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0
20
40
60
80
100
120
140
160
1960 1965 1970 1975 1980 1985 1990 1995
YEAR
Irrigation and Livestock
Thermoelectric Power
Industrial and Commercial
Domestic and Public Use
Water Use in the United States, by CategoryW
AT
ER
US
E, I
N B
ILL
ION
GA
LL
ON
S P
ER
DA
Y
Trends in Water Use in the US
Solley et al., 1998
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Total Water Use
Nuclear power plant in Pope County
(1/12 of all water use in the State)
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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 pointsSurface water: 5,600 points
Data are reported to AWSCC in acre-ft per month or yearData are reported to USGS national summary in MGD
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Arkansas Aquifers
Edwards-Trinity
Mississippi Embayment
Mississippi River Valley Alluvium
Ozark Plateaus
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Withdrawals from the Mississippi Alluvium33,700 wells (86%) out of39,100 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 h2 = variance of
water use at a site in stratum h
L
hhh
L
h h
hT N
n
NV h
1
2
1
22
L2
22
12h=1
h=2
h=L
PWS
Domestic
Industrial
Irrigation
Comm.
L
hhh
hhh
N
Nnn
1
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Number of Samples RequiredArkansas, irrigation from groundwater
Desired standard error = 549,273 MGrequires 111 samples 2
22
NV
Nn
T
Random sampling:
Total use = 5,492,730 MG
% Standard Error
No. of Samples
10% 111
5% 445
1% 8600
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A Sampling Scheme(for 10% standard error in total water use)
Category Number Mean Use (MG)Coeff Var Samples Std Err (%)Irrigation 41,102 165 3.0 330 16Agriculture 1918 211 1.6 10 49Water Supply 1026 536 7.2 64 876Industrial 200 959 4.0 12 112Commercial 120 362 3.6 3 202Fossil-fuel Power 49 8520 3.9 26 52Minerals Extraction 33 975 5.6 3 310Nuclear Power 15 74,869 3.9 15 0Domestic 4 2.5 2.0 2 100Waste Treatment 4 98 1.2 2 58Hydropower 2 1,560,228 0.2 2 0Unknown 197 178 1.5 2 105All Categories 44,670 284 471 10
Power uses have complete inventory, others are randomly sampled
Nhnh
n =
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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