Geostatistics Revisited:Patterns in the United States

David R. Maidment6 November 2008

Election as Geostatistics:Location matters!!

Statistical sampling of votersFinal Preelection Polls Election on (11/4/08)

Election “Population”

Population size: 125,225,901Spread – Obama: 53% to McCain: 46%

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%

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

Easting, X

Northing, Y

Geostatistics: Orientation matters!

Temperature and Elevation

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

zx

Plotting posn = (i-0.5)/n, i=1 is lowest value and i= n is highest value

Trend Analysis

Semivariogram and Covariance

Semivariogram

2,2

1ji

ji

zz

2,

9.118.321

ji

805.32

Dist = 4.75 x 105m

Detrending with an first order (linear) surface

Trend removal

Semivariogram with no trend removal Semivariogram with linear trend removal

Long memory data Short memory data

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

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

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

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

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

nNY

1,

0

20

40

60

80

100

120

140

160

1960 1965 1970 1975 1980 1985 1990 1995

YEAR

Irrigation and LivestockThermoelectric Power

Industrial and Commercial

Domestic and Public Use

Water Use in the United States, by CategoryW

ATE

R U

SE, I

N B

ILLI

ON

GA

LLO

NS

PER

DA

Y

Trends in Water Use in the US

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

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

Arkansas Aquifers

Edwards-Trinity

Mississippi Embayment

Mississippi River Valley Alluvium

Ozark Plateaus

Withdrawals from the Mississippi Alluvium33,700 wells (86%) out of39,100 total draw from the Mississippi Alluvium

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

nN

V h

1

2

1

22

L2

22

12h=1

h=2

h=L

PWS

Domestic

Industrial

Irrigation

Comm.

L

hhh

hhh

N

Nnn

1

Number of Samples RequiredArkansas, irrigation from groundwater

Desired standard error = 549,273 MGrequires 111 samples 2

22

NV

NnT

Random sampling:

Total use = 5,492,730 MG

% Standard Error

No. of Samples

10% 111

5% 445

1% 8600

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 =

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