Transcript Geostatistics2

Geostatistics Revisited:
Patterns in the United States
David R. Maidment
6 November 2008
Election as Geostatistics:
Location matters!!
Statistical sampling of voters
Final Preelection Polls
Election on (11/4/08)
Election “Population”
Population size: 125,225,901
Spread – Obama: 53% to McCain: 46%
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%
Air Temperature: “Population”
Nebraska
Air Temperature “Sample”
(Mean annual values from Nebraska)
What are Statistics?
How do Geostatistics Differ from
Statistics?
Random Fields:
Probabilistic processes in space
Voters: A finite population
of spatially discrete objects
Air Temperature: An
infinite population which
forms a spatial continuum
Air Temperature on an X-Y plane
Northing, Y
Easting, X
Geostatistics: Orientation matters!
Temperature vs Northing, Y
Temperature versus Easting, X
14.00
14.00
12.00
12.00
10.00
10.00
8.00
8.00
6.00
6.00
4.00
4.00
2.00
2.00
0.00
0
200000
400000
600000
800000
1000000
0.00
4300000
4400000
4500000
4600000
4700000
4800000
4900000
Temperature and Elevation
Temperature vs Elevation
14.00
12.00
10.00
8.00
6.00
4.00
2.00
0.00
0
1000
2000
3000
4000
5000
6000
7000
Contrary trend to normal, where temperature decreases with elevation
Histogram of Air Temperature
Degrees Centigrade * 10-1
Normal Q-Q Plot
Standard Normal Variate, z
Normal Q-Q Plot
Plotting posn
= (i-0.5)/n,
i=1 is lowest
value and i= n
is highest value
x
z
Trend Analysis
Semivariogram and Covariance
Semivariogram

1
   zi  z j
2 i, j


2
1
2


3
.
8

11
.
9

2 i, j
  32.805
Dist = 4.75 x 105m
Detrending with an first order (linear)
surface
Trend removal
Semivariogram with no trend removal
Long memory data
Semivariogram with linear trend removal
Short memory data
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
Prediction and Standard Error Maps
Estimating Water Use in the United States
http://www.nap.edu/catalog.php?record_id=10484
National Water Use Estimation
TWt   ( PSt ,i  DM t ,i  CM t ,i  IRt ,i  LSt ,i  IN t ,i  MN t ,i  TEt ,i )
i
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
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
1
2
3
Water Use Estimation
• Direct Estimation:
sample n and
extrapolate to
population of size N
N
Yt 
n
n
y
k 1
k ,t
 t
• Indirect Estimation: use
regression or a water
use coefficient model to
get water use in each
state
Yt ,i  a   b j X j ,t ,i   t ,i
j
Trends in Water Use in the US
WATER USE, IN BILLION GALLONS PER DAY
Water Use in the United States, by Category
160
140
Irrigation and Livestock
Thermoelectric Power
120
100
80
60
Industrial and Commercial
40
20
Domestic and Public Use
0
1960
1965
1970
1975
1980
YEAR
1985
1990
1995
Solley et al., 1998
Total Water Use
Nuclear power plant
in Pope County
(1/12 of all water use
in the State)
Arkansas Site-Specific Water-Use Database
~50,000
points with
monthly water
withdrawal
estimates
Surface and Groundwater Points
Surface water: 5,600 points
Groundwater: 39,100 points
Data are reported to AWSCC in acre-ft per month or year
Data are reported to USGS national summary in MGD
Arkansas Aquifers
Ozark Plateaus
Edwards-Trinity
Mississippi River
Valley Alluvium
Mississippi
Embayment
Withdrawals from the Mississippi Alluvium
33,700 wells (86%) out of
39,100 total draw from the Mississippi
Alluvium
Stratified Random
Sampling
nh  n
N hs h
L
N s
h 1
• 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
L
N h2s 2h
h 1
nh
VT  
h=L
sL2
h
h
L
  N hs h2
h 1
Domestic
Comm.
Industrial
h=2
s22
Irrigation
h=1
s12
PWS
Number of Samples Required
Arkansas, irrigation from groundwater
Total use = 5,492,730 MG
% Standard
Error
No. of
Samples
10%
111
5%
445
1%
8600
Random sampling:
Desired standard error = 549,273 MG
requires 111 samples
N 2s 2
n
VT  Ns 2
A Sampling Scheme
(for 10% standard error in total water use)
Nh
Category
Irrigation
Agriculture
Water Supply
Industrial
Commercial
Fossil-fuel Power
Minerals Extraction
Nuclear Power
Domestic
Waste Treatment
Hydropower
Unknown
All Categories
nh
Number Mean Use (MG)
Coeff Var Samples Std Err (%)
41,102
165
3.0
330
16
1918
211
1.6
10
49
1026
536
7.2
64
876
200
959
4.0
12
112
120
362
3.6
3
202
49
8520
3.9
26
52
33
975
5.6
3
310
15
74,869
3.9
15
0
4
2.5
2.0
2
100
4
98
1.2
2
58
2 1,560,228
0.2
2
0
197
178
1.5
2
105
n = 471
44,670
284
10
Power uses have complete inventory, others are randomly sampled
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.)
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