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pdfStatistical Methodology for the
NRI-CEAP Cropland Survey
J. Jeffery Goebel
Natural Resources Conservation Service
U.S. Department of Agriculture
Beltsville, MD
[draft – May 2009]
I. Introduction
The National Resources Inventory (NRI) is a longitudinal survey conducted by the USDA
Natural Resources Conservation Service (NRCS), in cooperation with the Iowa State University
Center for Survey Statistics and Methodology. The purpose of the NRI is to provide support for
agricultural and environmental policy development and program implementation. The NRI is a
panel survey of land use and associated natural resource attributes, conducted at 5-year intervals
from 1982 through 1997, and annually from 2000 through the present.
Scientists, economists, resource managers, and policy makers have found the NRI to be a source
of scientifically credible and nationally consistent data that help them formulate policy proposals
and analyze economic and environmental impacts. The NRI was developed in the 1970's by the
United States Department of Agriculture (USDA) as a tool to assess status, condition, and trend
of soil, water, and related resources on the Nation's non-Federal lands, as mandated by the Rural
Development Act of 1972 and the Soil and Water Resources Conservation Act of 1977 [see
Goebel (1998)]. The NRI survey system was built upon the survey system used for the
Conservation Needs Inventories of 1956 and 1967 [see Nusser and Goebel (1997)].
A variety of natural resource issues have been analyzed using the NRI. These issues include:
land use change with emphasis on loss of agricultural lands to urban development; conservation
provisions of the 1985 Farm Bill; trends in soil erosion; gains and losses of wetlands due to
agricultural activities; transport of agricultural chemicals into water supplies; the role of
agriculture in sequestering carbon.
USDA has made significant investments in developing a methodology that assesses the
environmental effects of various conservation practices and systems. This methodology utilizes
physical process models and the framework provided by USDA’s NRI survey program. The
models simulate resource condition changes that occur over time on a cropland field, taking into
account both natural factors and farm operator decisions. The methodology developed by USDA
has been used to: estimate environmental effects of existing conservation programs; assess
current conservation needs; analyze on-going Technical Assistance; and examine the effects of
alternate conservation systems and proposed conservation policies and programs. The NRI
provides basic inputs into the models and a scientifically-credible method for assimilating and
interpreting model results. [see Goebel and Kellogg (2002)]
Previous NRI modeling efforts used generalized information about farming practices that were
not specific to the soils and climate data associated with the specific sample sites [see Potter et al,
2006]. Modeling capabilities have been greatly enhanced for the NRI-CEAP Cropland
Assessment, to provide simulations that better reflect specific cropland field conditions and to
provide results for a broader suite of resource issues. These enhancements required that
additional data be collected for NRI sample sites and that the scope of existing process models be
broadened. These additional data were acquired through the “NRI-CEAP Cropland Survey”,
which was designed to obtain detailed data describing farming activities and conservation
practices for the field associated with selected NRI sample points. Trained enumerators working
for the National Agricultural Statistics Service conducted interviews with the individuals (farm
owner and/or operator) responsible for making management decisions for these fields.
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II. Overview of Survey Design
The objective of the NRI-CEAP Cropland Survey was to obtain additional site specific data
needed to utilize the field-level process model APEX to estimate field-level effects of
conservation practices. The process model was run for a sub-sample of NRI sample points;
inputs for a sample point included historical NRI site specific data, data obtained from the NRICEAP Cropland Survey for the agricultural field where the sample point is located, additional
information on conservation practices from Field Office records, soil properties and
characteristics associated with the particular soil at the sample point location, and climate data
associated with the sample point location. The input data associated with a particular point
describe a “representative field;” outputs from the process model runs include losses of materials
(such as sediment and chemicals) from this field and changes in condition (such as accumulation
of carbon). These outputs are used to estimate both on-site and off-site effects.
The APEX model outputs can be treated like other NRI variables; the site specific results for each
sample point can be aggregated or averaged for some meaningful portion of the landscape using
statistical weights. The statistical (survey) weight for an NRI sample point is the acreage value
assigned to that sampling unit based upon the sampling design and certain control figures
[derivation of weights for the NRI-CEAP Cropland Survey is discussed in Section VI, Estimation
Procedure]. The APEX model outputs also serve as inputs into hydrologic models that simulate
transport of water, sediment, and chemicals from the land into and through stream networks and
eventually into estuaries and oceans. The NRI-CEAP data and the models can then be used to
estimate changes in in-stream concentration of sediment and chemicals that result from changes
in land management.
The sampling strategy utilized for the NRI-CEAP Cropland Survey was to select a sub-sample of
NRI sampling units from the NRI Foundation Sample; in particular, a subset of sample points was
selected from those sampling units used for the 2002 and 2003 Annual NRI surveys. Sampling
strategies for the NRI Foundation Sample, Annual NRI surveys, and the NRI-CEAP survey are
discussed below. The NRI sampling structure provided a natural framework for the data
collection and modeling activities needed to support the CEAP national cropland assessment; it
also provided efficiency to the process because sample locations were already identified and
significant data already existed for these sites. The full collection of NRI sample sites provides a
statistically credible representation of the diversity of soils, climate, cropping systems, and
natural resource issues for the Nation’s agricultural lands. Data collection activities were spread
over a four-year period because of financial constraints and operational considerations. A
different set of sample points was selected for each year. The goal was to develop a data base
that supported statistical analysis of the benefits of conservation practices at the national and
regional levels.
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III. NRI Foundation Sample
The universe of interest for the National Resources Inventory (NRI) survey consists of all surface
area [land and water] of the U.S., including all 50 states, Puerto Rico, the U.S. Virgin Islands, and
certain Pacific Basin islands. The NRI Foundation Sample only covers the 48 contiguous states,
Hawaii, Puerto Rico, and the U.S. Virgin Islands; it does not cover Alaska and the various Pacific
Basin islands. The sample does cover all land ownerships categories including Federal, although
NRI data collection activities have historically concentrated on non-Federal lands. Federal land
area is covered by the NRI Foundation Sample for several reasons, including: ownership maps
and data bases have typically been out-of-date and incomplete; ownership patterns change over
time; and data collection activities have occasionally included all ownership categories.
The NRI Foundation Sample was selected on a county-by-county basis; units analogous to
counties were used where county designations do not exist. Each county sample was selected
using a stratified, two-stage, area sampling scheme; specific procedures and sampling rates varied
from county to county. The foundation sample is basically that which was used for the 1997
NRI. The sample was initially established for the 1982 NRI; modifications occurred for a number
of counties during the 1990’s [see Goebel and Baker (1987), and Nusser and Goebel (1997)]
Area Sampling
The NRI survey system uses pre-defined areas of land and specific point locations as sampling
units. Fixed geographical locations are used rather than features that can change due to the
effects of human activities and natural occurrences. Some agricultural surveys use farms, farm
enterprises, fields, tracts, farmers, and/or operators as sampling units. The boundaries or
definitions for those units are subject to change over time; this would not work for the NRI,
where the same sampling units are visited periodically.
Stratification
Stratification serves to make sampling more efficient by subdividing the entire population of
interest (data universe) into non-overlapping portions (layers or strata) that are more
homogeneous than the population as a whole. The NRI design uses both geographical
stratification and stratification based upon specific resource conditions and general ownership
patterns.
The Public Land Survey System (PLSS) provides the basis for geographical stratification in
counties covered by this system, except for Arkansas and Louisiana. The PLSS subdivides
counties into townships and sections. Townships are nominally square areas of land that are six
miles on a side; a township is typically divided into 36 one-mile square areas of land called
“sections”. Sections are numbered from 1 to 36 in a serpentine manner, starting in the northeast
corner of the township. For sampling purposes, three strata of 12 sections each were formed
within each township; one stratum contained the top two rows of sections [sections 1 thru 12], a
second stratum contained sections 13 thru 24, and the third contained sections 25 thru 36. Each
of these geographical strata, therefore, was a two -mile by six -mile rectangular areas of land. A
number of townships and sections have dimensions that differ from the “standard” system, due to
operational difficulties encountered while conducting a land survey.
The PLSS does not cover the 13 northeastern states, Texas, Hawaii, parts of Ohio, and the
southeastern states of Georgia, South Carolina, North Carolina, Kentucky, and Tennessee. In
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these 6 southern states and the non-PLSS portions of Ohio, lines analogous to township lines and
section lines were superimposed on county highway maps, and geographical strata were
developed in the same manner as counties covered by the PLSS. For counties in the 13
northeastern states, a sampling system based upon latitude and longitude was developed; strata
are rectangular areas of land two minutes of latitude by four minutes of longitude.
Stratification based upon specific resource conditions occurred mostly in large counties located in
the Western portion of the U.S. Three or four types of strata were usually constructed, in addition
to the geographic stratification described above.
o First, many areas that were under irrigation (or potentially irrigated) were identified and
placed into specific strata, and then sampled in a manner analogous to that used in
irregularly shaped counties.
o The second type of strata typically included land that supported non-irrigated farming
operations.
o Additional resource-based strata were formed for areas that would not support farming
operations. Sometimes large tracts of Federal land were identified and placed into
specific strata.
Stratification was modified and sampling was augmented in about 200 counties between 1982
and 1997. Analysis of historical NRI data showed these modifications were needed to better
estimate conversion of prime farmland and other rural lands into urban lands. Most augmentation
occurred in exurbia areas outside of already established cities and suburban communities.
Selection of Segments
Each two-mile by six-mile stratum contains 12 sections. For most standard counties the sections
were subdivided into four half-mile square “quarter sections”, with nominal size 160 acres. This
meant there were 48 quarter sections within a standard stratum, and each quarter section was
considered a potential sample unit, or segment. Sampling rates differed from county to county,
and sometimes within county, depending upon factors such as county size, complexity of soils
and agricultural practices, and number of counties within the state; workload and budget issues
were balanced with statistical reliability. The most common sampling rates were one per stratum
(1 out of 48, or approximately 2%) and two per stratum (approximately 4%). Some strata had
lower sampling rates; for example, a one-half percent sampling rate was accomplished by
grouping four adjacent strata and randomly selecting one of the 192 quarter sections. For
portions of counties where some sections (and partial sections) did not fit within the regular twomile by six-mile strata, groups of 12 sections were formed and segments were randomly selected
in a manner similar to the procedure used for regular strata.
Many counties in Western states contained additional stratification and different sized segments.
Strata formed in irrigated areas often contained 40-acre segments because of the greater
heterogeneity in these areas. Strata formed in relatively homogeneous areas of range, forest, and
barren land often contained 640-acre segments, both for statistical reasons and because of the
difficulty in locating sample sites on the ground in areas where landmarks are limited.
For counties in the 13 Northeastern states, sampling units are 20 seconds of latitude by 30
seconds of longitude; because of the curvature of the earth, they range in size from 96 acres in
northern Maine to 113 acres in Virginia. Each stratum contains 48 segments, and selection
procedures were handled in a manner similar to that described for 2-mile by 6-mile strata.
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The Universal Transverse Mercator (UTM) grid system was used to define sampling units for
counties in Arkansas and parishes in Louisiana. For Arkansas, the sampling units were square
kilometers of land [approximately 247 acres]. Segments were numbered sequentially in a
geographic order starting in the northwest corner. The initial sample in 1982 was selected
systematically at a rate of 1 out of 10; less than a half of these sample segments [about 6,100] are
part of the NRI Foundation Sample. For Louisiana, the sampling units were half-kilometer
squares of land and the strata were 4-kilometer squares. Randomization with control was used to
select segments within strata.
Selection of Points within Selected Segments
Three specific sample point locations were selected within most selected segments. Fewer points
were originally selected for segments in Louisiana, Arkansas, and 40-acre segments within
portions of the Western U.S. The procedure used for a standard 160-acre segment is outlined
below; it is a restricted random procedure that assured the points were spread throughout the
sample segment.
o Step 1. The segment was conceptually sub-divided into 36 square blocks, each
approximately 440 feet on a side. These 36 blocks were assigned numbers from 1 to 12,
with each integer assigned to three blocks [see Figure 1]. As indicated by the double
lines in Figure 1, the segment could also be pictured as having three rows and three
columns of blocks; numbers were assigned to blocks so that each integer occurs only
once in each row and once in each column. In addition, no two blocks with the same
number are contiguous. These restrictions assured as wide a dispersal as possible within
the segment.
o Step 2. Sample point #1 was determined by selecting two random integers between 1 and
2,640. These numbers designated the point location in terms of feet north and east from
the southwestern corner of the segment.
o Step 3. Sample points #2 and #3 were located in the other two blocks having the same
number [from 1 through 12] as the block in which Point #1 fell; the designation of which
was Points #2 was made randomly. The relative location of Points #2 and #3 within
these blocks was the same as for Point #1.
The selection of two sample points within a standard 40-acre segment can be expressed as
follows:
o Step 1. Sample point #1 was determined by selecting two random integers between 1 and
1,320, say N1 and E1, where N1 designates feet north and E1 designates feet east of the
southwest corner of the segment.
o Step 2. The coordinates for point #2 were then:
N2 = mod1320 (N1 + 660), and
E2 = mod1320 (E1 + 660).
In 640-acre sample segments and in the 13 northeastern states, three sample points were selected
in a manner analogous to that used for standard 160-acre segments. In Arkansas and Louisiana,
initially only one point was randomly selected within each sample segment; this has been
modified so that those segments also contain three sample points.
Remarks
The stratification described above was mostly established for the 1956 Conservation Needs
Inventory (CNI), except for counties and parishes in Arkansas, Louisiana, and the 13
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Northeastern states. Where possible, subsets of segments established for the 1956 CNI were used
for the 1982 NRI; soils information had already been detailed for these segments, and this
provided a more efficient start-up. Stratification and segment selection for Arkansas, Louisiana,
and counties in the 13 northeastern states were new for the 1982 NRI. Development of strata and
selection of sample segments was done manually, by staff at the Statistical Unit, Iowa State
University; precise rules and random number tables were supplied.. The procedure for
computerized selection of sample points within sample segments was developed for the 1977 and
1982 NRI surveys; sample point coordinates were printed on self-adhesive labels that were
affixed to the data collection worksheets.
Figure 1. Sub‐Division of Segment
for Sample Point Selection
1
2
3
4
5
6
7
8
9
10
11
12
4
6
12
7
1
3
11
10
2
5
9
8
5
3
1
6
4
2
9
12
8
11
7
10
7
IV. Annual NRI Sample Design
Introduction
The National Resources Inventory (NRI) was conducted every five years during the period 1977
through 1997. During the second half of the 1990’s, NRCS worked with the Statistical Unit at
Iowa State University on development of a statistical design for transitioning to an annual survey
approach. Several types of factors needed consideration:
o
o
o
o
o
programmatic factors – budgets and staffing requirements needed to be constant from
year to year
statistical factors – reasonable statistical efficiency for estimators of short-term change,
long-term change, and condition/level for any given year
analysis capabilities – the new approach needed to continue support of development of a
data base that supports complex analysis
inter-agency cooperation – an annual survey approach makes it easier to work with other
Federal agencies on development of collaborative inventory approaches
adaptability to changing information needs.
The desire was to continue to use the NRI Foundation Sample sampling units but to use some
subset each year rather than to sample all units every five years. Four alternative longitudinal
designs were considered [see Figure 2]:
o
o
o
o
Independent Samples – the entire collection of sample units would be split into equal
non-overlapping groups (panels), and each year one of the panels would be sampled until
all panels were completed, at which time the first panel would be re-sampled – this is the
basic design used for the USFS Forest Inventory and Analysis (FIA) program, which
operates on a 5 – 10 year cycle depending upon the state; there could be variations, such
as sampling with replacement and having varying rates of re-sampling for certain
categories of sampling units
Pure Panel – each year’s sample would be the same as that used for the previous year,
which means 100% of the sample would be revisited every year – this was the basic NRI
design between 1982 and 1997, except the panel was observed every five years rather
than annually
Rotating Panel – the samples are split into groups (panels) of samples, and in any one
year two or three panels are being sampled, which means that a given panel is sampled
for two or three consecutive years and then “rotated” out of the sample and replaced by
the next panel – this design has been used by the National Agricultural Statistics Service
(NASS) for some agricultural surveys
Supplemented Panel – this is a type of split plot design where one specified (core) panel
is sampled each year and each year a rotating panel is also sampled
The supplemented panel design was selected for the Annual NRI survey system because it serves
as a compromise design. The Core Panel that is sampled every year provides an efficient method
for estimating net change over time; the Rotation or Supplemental Panel provides efficiency for
estimation of status at a given point in time. [see Fuller (1999) and McDonald (2003) for further
discussion]
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Figure 2: Longitudinal Survey Designs Considered for Annual NRI
1) Independent Samples
Observation Period (Time)
Group 1
2
3
4
5
6 .
1
X
2
X
3
X
4
X
5
X
6
X
2) Pure Panel
Group
1
Observation Period (Time)
1
2
3
4
5
6 .
X
X
X
X
X
X
3) Rotating Panel
Group
1
2
3
4
5
6
7
Observation Period (Time)
1
2
3
4
5
6 .
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
4) Supplemented Panel
Group
1
2
3
4
5
6
7
Observation Period (Time)
1
2
3
4
5
6 .
X
X
X
X
X
X
X
X
X
X
X
X
9
NRI Special Study data collected during 1995 – 1997 for 5,972 sample segments in 538 counties
were used to estimate correlations and measurement error variances, so that the four designs
could be compared [see Breidt and Fuller, 1999] Observations from 1982, 1987, and 1992 were
also available for these sample units.. A first-order autoregressive process was assumed. Yearto-year correlations were quite high, with the estimated Autoregressive Coefficient, ф, being
> 0.95 for all tested variables, and > 0.99 for many. Measurement error was significant for soil
erosion estimates, non-cultivated cropland, large water bodies, and small streams; the estimated
portion of variability due to measurement error, ν, is 23% for soil erosion and 13% for noncultivated cropland. Measurement error estimates were needed to study the make-up of the
autoregressive process because it has a large effect upon the estimated First-Order
Autocorrelation, ρ(1). This parameter is above 0.96 for items like forest land and area in roads
that change very little from year to year and are measured with very little measurement error; ρ(1)
was 0.74 for soil erosion estimates and 0.84 for non-cultivated cropland. Area in CRP was the
only estimate studied that did not show a good fit to the first-order autoregressive process; this is
understandable given the nature of that type of land.
The estimated parameters for the measurement error and the first-order autoregressive process
were used to study Ө, which is the portion of the sample to place in the pure panel (or Core
Panel). Recall that Ө = 1 provides the best efficiency for measuring change and Ө = 0 provides
the best estimates for a single point in time. Moving from using Ө = 1.0 to Ө = 0.5 showed that
estimates of change degraded slower than the gains made in estimating a period mean (i.e.,
status/condition at one point in time, or level). The conclusion of this analysis was that Ө = 0.5
was a good statistical compromise and also provided adaptability if there was a need to change
survey items [see Breidt and Fuller (1999)]. Several of the effects of implementing a
Supplemented Panel longitudinal survey design for the Annual NRI survey, using Ө = 0.5, are
shown in Tables 1 and 2.
The design that was implemented in 2000 for the Annual NRI survey process was a
Supplemented Rotation Panel design with Ө slightly greater than 0.6. This design was selected
because there is only a moderate loss of precision relative to other designs, and it provides
flexibility for status and gross change estimates. Several strategies have been implemented to
minimize loss relative to the 5-year cycle (full 300,000 segment panel) estimates, including:
selection of Core Panel and Rotation Panels using stratification and non-proportional allocation;
utilization of historical information from the full NRI Foundation Sample of 300,000 segments in
estimation process; and implementation of techniques such as constrained generalized least
squares.
Selection of Segments for Core Panel P00
The Core Panel P00 for the Annual NRI survey program was selected from the 300,000 segments
in the NRI Foundation Sample. Samples were selected on a state-by-state basis. The same basic
procedure was used for the contiguous 48 states, Hawaii, Puerto Rico, and the U.S. Virgin
Islands.
Segments were placed in categories based upon historical data available for all samples, and then
varying sampling rates were assigned to each category.
10
Table 1: Projected Increase in Width of Confidence Intervals
[for Annual NRI Sample Design, Compared with Previous 5‐Year Cycle]
Type of Estimator
Estimator
Cultivated
Cropland
Developed
Land
Single year
+ 17 %
+ 18 %
Average of 3 years
+ 8 %
+ 7 %
Single year
+ 61 %
+ 61 %
Average of 3 years
+ 27 %
Status [for 2002]
Change [1997 – 2002]
+ 27 %
Table 2: Projected Size of 95 % Confidence Intervals, in Millions of Acres
Area of Cultivated Cropland
5‐year cycle
Annual – GLS
Annual – Mod
5‐Year Change in Cultivated Cropland
5‐year cycle
Annual – GLS
Annual – Mod
National
Missouri
Washington
325.4
10.72
5.60
( ± 1.7 )
( ± 2.0 )
( ± 1.8 )
( ± 0.25 )
( ± 0.29)
( ± 0.27 )
( ± 0.32 )
( ± 0.37)
( ± 0.34 )
‐ 25.4
‐ 1.61
‐ 0.64
( ± 1.02)
( ± 1.64 )
( ± 1.30)
( ± 0.15 )
( ± 0.24)
( ± 0.19 )
( ± 0.16 )
( ± 0.26)
( ± 0.20 )
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Classification of Segments:
1. Wetland: If the segment contained at least one point with a Cowardin wetland
classification for 1992 and/or 1997;
2. CRP: If the segment was not in Category 1, and at least one of the points in the segment
had a land cover/use of “land in CRP” for 1987 and/or 1992 and/or 1997.
3. Urban Change: If the segment is not in Category 1 or 2, and less than 90% of the
segment is classified as “Urban and Built-up” land, and either “Urban and Built-up” land
within the segment changed from 1987 to 1997 or acres of roads with the segment
changed by more than four acres.
4. Urban: If the segment is not in Category 1, 2, or 3, and the segment contains some land
classified as “Urban and Built-up” but less than 90% of the segment is classified as
“Urban and Built-up” land.
5. High Erosion: If the segment is not in Category 1, 2, 3, or 4, and at least one point within
the segment had a land cover/use of “cropland” for 1997
with (usle + weq) > 2T for 1997 [where ‘usle’ represents the estimated sheet and rill
erosion rate, ‘weq’ is the estimated wind erosion rate, and ‘T’ is the T-factor]
6. Cropland: If the segment is not in Category 1, 2, 3, 4, or 5, and at least one of the points
had a land cover/use of either “cultivated cropland” or “non-cultivated cropland” for
1982 and/or 1987 and/or 1992 and/or 1997.
7. Pastureland: If the segment is not in Category 1, 2, 3, 4, 5, or 6, and at least one of the
points had a land cover/use of “pastureland” for 1992 and/or 1997.
8. Rangeland: If the segment is not in Category 1, 2, 3, 4, 5, 6, or 7, and at least one of the
points had a land cover/use of “rangeland” for 1997.
9. Forest Land: If the segment is not in Category 1, 2, 3, 4, 5, 6, 7, or 8, and at least one of
the points had a land cover/use of “forest land” for 1997.
10. One Hundred Percent Urban or Water: If the segment is not in Category 1, 2, 3, 4, 5, 6,
7, 8, or 9, and 100% of the area of the segment is classified as “Urban and Built-up” plus
“Water”.
11. One Hundred Percent Federal or Water: If the segment is not in Category 1, 2, 3, 4, 5, 6,
7, 8, 9, or 10, and 100% of the area of the segment is classified as “Federal Land” plus
“Water”.
12. Remainder: All remaining segments
The conditional probabilities of selection were proportional to the “Weights” given in Table 3.
The state sample sizes were based upon a variety of factors, including the importance of certain
segment types for specified estimates, regional and state-level considerations, and budgets and
workforce availability. Small states were generally sampled at higher rates than large states.
There were two major complicating factors in selection of sampling units for the Core
Panel:
1. the 5,972 Special Study sample segments were specified as part of the Core Panel
2. the Core Panel was to include at least one sample segment in each HUCCO that
contained any 1997 NRI sampling units, where a HUCCO is a geographical unit
defined as the intersection of county and four-digit hydrologic units.
12
Table 3. Segment Weights for Annual NRI Sampling Strategy
Segment Category
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Weight
Wetland
CRP
Urban Change
Urban
High Erosion
Cropland
Pastureland
Rangeland
Forest Land
100% Urban or Water
100% Federal or Water
Remainder
3.4
3.2
3.2
2.0
2.0
1.5
1.0
1.0
1.0
0.7
0.6
1.0
The first step was to select sample segments for “small HUCCOs”. For HUCCOs containing
only one 1997 NRI segment, that single sample segment was included in the Core Panel with
certainty. For HUCCOs containing two 1997 NRI segments, both segments were included in the
Core Panel with certainty if at least one of the segments was a Special Study segment or was in
Segment Categories 1 – 5; otherwise, one segment was selected with each being given an equal
chance of selection. For HUCCOs with three to nine 1997 NRI sample segments, selection rules
were based upon the number of segments that fell within each of three groups – the first and
second groups were comprised of Segment Categories 1 – 3 and 4 – 6 respectively, and the
remainder were placed into the third group. Selection within each group for a small HUCCO was
with equal probability, except for Special Study sample segments being included with certainty.
In general, about one-half of the segments in the first group were selected for the Core Panel, a
third for the second group, and a fourth for the third group.
For “large HUCCOs” with more than nine 1997 NRI sample segments, the selection procedure
took into account the specified state sample size for the Core Panel, the number of 1997 NRI
sample segments in each Segment Category, the weights in Table 1 for each Segment Category,
the Special Study segments automatically placed into the state’s Core Panel, and the sample
segments selected for small HUCCOs. The process can be thought of as a systematic sampling
procedure with the following characteristics:
o
o
o
ordering or arrangement of eligible segments – the segments were ordered by Segment
Category within HUCCO within county, with the Segment Category order reversed for
adjacent HUCCOs
the eligible segments were those that were not part of the Special Study sample and were
within HUCCOs that contained at least ten 1997 NRI sample segments
(n - na - nb) segments were selected, where n = total Core Panel sample size specified for
the state, na = number of Special Study sample segments in the state, and nb = number of
sample segments in the state already selected for the Core Panel in small HUCCOs
13
o
an unequal sampling interval was used that took into account the Segment Category
weights and the distribution of na and nb by Segment Category.
Selection of Segments for Supplemental Panel P01
The Supplemental Panel for 2001, called P01, only contained sample segments in large HUCCOs.
The state selection process was a systematic sampling procedure that was quite similar to that
used for the Core Panel. The conditional probability that a particular segment was selected for
panel P01, given that the segment was not part of the Core Panel, was the same as for any other
segment that was in the given Segment Category and was not in the Core Panel; the relative rates
are the same as the Table 1 values used for selection of the Core Panel. This procedure caused
selection probabilities to become slightly more equal. The probability that segment k in county q
was in the 2001 Annual NRI sample was:
p1qik = p0qik + (1 – p0qik) T-1 Si n2001 ,
= p0qik ,
if segment is in a large HUCCO
if segment is in a small HUCCO
where: p0qik = probability that the segment was selected for the Core Panel
Si = the Segment Category weight given in Table 1 for category i
T = ∑ i Ti
Ti = Si * Ži
Ži = number of segments in category i in the state that are in large HUCCOs
and not selected as part of P00
n2001 = number of segments specified for P01 for the state
The selection probabilities depend upon the county q because the Core Panel probabilities differ
depending upon whether the county was included in the Special Study sample. The closed form
for p0qik is not provided here. Table 4 provides panel sample sizes for the 48 states by Segment
Category, and Table 5 provides panel sample sizes by state. Panel P02 was selected using the
procedure used for P01; the selection procedure for subsequent panels has taken into account
numbers of samples already selected and remaining by Segment Category within state. Note that
the sample for Louisiana was modified following the 2001 Annual NRI survey; two additional
sample points were selected for each sample segment and sample sizes were reduced in order to
gain efficiency. This modification to the Louisiana sampling strategy is the reason that Table 4
does not contain segment counts for P01.
14
Table 4: Annual NRI Sample Design – Panel Sizes
for 48 Contiguous States, by Segment Category
NRI Foundation Sample
Segment
Category
1
2
3
4
5
6
7
8
9
10
11
12
Total
Large
HUCCO’s
Small
HUCCO’s
42,162
9,836
22,705
17,050
15,747
60,777
15,401
30,511
34,739
16,957
22,813
2,046
429
144
165
139
183
803
204
431
501
167
370
22
290,744
3,558
P02
9,810
2,960
5,202
2,614
2,603
7,427
1,198
2,901
2,558
923
1,300
148
P00
7,416
1,604
4,010
2,100
2,003
5,753
1,038
2,313
2,253
805
1,101
150
39,644
7,477
1,653
4,184
2,069
1,995
5,909
1,028
2,312
2,234
810
1,119
139
30,546
15
P03
30,929
Table 2: Annual NRI Sample Design – Panel Sizes for 48 Contiguous States, by State
State
Alabama
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana (#)
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
TOTAL
Available(*)
P00
P01
P02
P03
P04
P05
6,033
2,879
6,134
8,658
7,453
1,213
493
6,991
7,928
6,970
8,387
5,827
7,060
9,174
6,590
14,435
2,661
3,166
1,900
7,897
8,161
6,713
8,706
6,348
7,382
3,952
1,686
2,038
5,166
6,933
6,264
7,362
6,874
7,414
5,905
7,243
614
4,642
7,070
7,017
21,912
3,667
2,023
7,748
5,298
3,942
6,587
3,788
778
338
799
1,127
959
261
190
1,102
836
909
1,264
828
996
1,142
798
1,117
377
571
368
1,172
1,377
971
1,214
823
972
393
261
322
782
964
884
1,150
952
881
674
1,035
180
729
1,017
870
2,820
435
294
949
724
448
1,067
524
622
242
601
898
691
199
100
848
764
691
936
672
750
833
652
2,458
323
458
257
903
973
729
911
652
728
307
239
278
593
736
689
850
723
669
601
765
110
521
808
680
1,980
362
256
801
651
378
783
401
622
242
601
898
691
199
100
848
764
691
936
672
750
833
652
932
323
458
257
903
973
729
911
652
728
307
239
278
593
736
689
850
723
669
601
765
110
521
808
680
1,980
362
256
801
651
378
783
401
600
242
606
912
718
194
113
910
751
723
995
692
741
819
679
835
312
466
310
989
1,049
674
963
662
756
296
260
242
560
675
680
882
683
671
670
752
108
520
787
646
2,025
389
274
859
631
390
814
404
608
236
612
891
704
202
101
906
743
689
988
690
736
813
683
834
317
435
259
984
1,045
678
966
650
763
300
246
248
594
680
683
877
689
677
604
749
106
514
789
642
2,028
367
245
860
649
384
808
413
608
324
606
998
721
201
109
876
808
690
955
675
738
815
646
837
332
455
259
889
998
701
924
674
744
347
243
284
635
680
691
872
678
653
609
756
114
515
837
641
1,971
367
258
799
651
391
777
402
294,304
39,644
32,072
30,546
30,929
30,685
* Indicates number of segments in NRI Foundation Sample
# Design for Louisiana modified in 2002; only 7,800 segments now available for selection
16
30,754
V. Sub-Sampling Procedure for NRI-CEAP
The target population for the NRI-CEAP Cropland Survey was all land in the 48 contiguous
states that is classified by NRI as having a land cover/use of “cultivated cropland” or “land in
CRP.” Cultivated cropland is defined by NRI as “land in row or close-grown crops, including
hayland and pastureland in rotation with row or close-grown crops;” land in CRP is “land that
was under a Conservation Reserve Program (CRP) contract.”
The sampling approach utilized for the NRI-CEAP Cropland Survey was to select a sub-sample
of Annual NRI sample points. In particular, the sample comes from sampling units selected
initially for the 2002 and 2003 Annual NRI surveys. The sampling strategy developed for the
farmer surveys included:
o Collect data for 20,000 sample sites over a four year period, in order to obtain a full
representation of the diversity of cropping systems, resource concerns, farming activities,
conservation practices, soils, climate, and other natural resource conditions on cultivated
cropland; and to obtain insight into implementation of conservation systems associated
with the 2002 Farm Bill. [sample sites are cropland fields associated with NRI sample
points; the Foundation NRI sample contains about 200,000 cropland points].
o Sampling and data collection for 2003 and 2004 were to focus on developing a good
base-line for the most predominant cropping and conservation systems, to make sure that
credible statistical analyses could be made on a national basis for all U. S. cultivated
cropland.
o Sampling and data collection for 2005 and 2006 were to have a complementary focus:
(a) to obtain data for areas and systems that are less extensive but usually more
environmentally sensitive (vulnerable); and (b) to obtain data on actual changes in
conservation systems and practices that occurred due to implementation of 2002 Farm
Bill provisions – data collection in 2005 and 2006 provided a fuller and broader
perspective, since some practices were not installed until after 2003.
An NRI sample point is used to identify a field in order to determine land cover/use and
management systems; similar protocols are used to determine the natural or inherent features,
such as soil type or erosion equation factors. The NRI utilizes points as the sampling units rather
than farms or fields; land use and land unit boundaries change frequently in some parts of the
country, and factors such as soil type do not follow human-induced boundaries such as land unit
boundaries. Sample point coordinates are known based upon Digital Ortho-Photo Quadrangle
(DOQ) base maps and standards. The temporal nature of desired results was handled in several
ways: (i) the NRI-CEAP farmer survey collected site specific data for several years, and
historical NRI data are available for each sample point; (ii) conservation practices, other
agricultural management systems, and acts of nature have long-term effects upon the environment
– the process models used to quantify effects produce results by year and season; (iii) the Annual
NRI utilizes a supplemented panel survey design, wherein each year’s sample includes a Core
Panel (sampling units observed each year) and a Supplemental (or rotating) Panel – this provides
the flexibility to revisit sample units over the course of time.
Sample for 2003 Survey
The sample for the 2003 NRI-CEAP Farmer Survey was selected from the 2002 Annual
NRI sample points classified as having a land cover/use of either cultivated cropland or
land in CRP for the 2002 growing season. In particular, the samples were selected from
the supplemental panel P02, as follows:
17
(a) Any sample point in P02 classified as “land in CRP” for 2002 was included.
(b) Sample points classified as “cultivated cropland” were selected as follows:
o it was determined which segments in P02 contained at least one point
classified as “cultivated cropland” for 2002
o within each of those segments, one point classified as “cultivated
cropland” in 2002 was selected randomly.
(c) For South Dakota and North Dakota, one-half of these points were not sampled;
systematic sampling was used to select half of the points. The sampling rate was
reduced due to lack of available interviewers within these two states.
(d) An additional 333 points were removed from the sample because they represented
farm operators that had also been selected for the ARMS-II survey. These
samples were removed from the survey so that respondent burden for ARMS-II
would not be affected. An initial examination of these overlap samples indicated
that no bias should be expected; the samples were distributed across the country
in proportion to cropland occurrence. This will be verified as part of a postsurvey statistical evaluation of non-response, which will utilize historical NRI
information and operator information collected from NRCS field offices.
Sample sizes by state are presented in Table 6. The sample included 2,236 CRP sample
points and 9,580 cultivated cropland points.
Sample for 2004 Survey
The sample for the 2004 NRI-CEAP Cropland Survey was selected from the 2003 Annual NRI
sample points classified as having a land cover/use of either cultivated cropland or land in CRP
for the 2003 growing season. In particular, the samples were selected from the supplemental
panel P03, as follows:
(a) Any sample point in P03 classified as “land in CRP” for 2003 was included.
(b) Sample points classified as “cultivated cropland” were selected as follows:
o it was determined which segments in P03 contained at least one point classified
as “cultivated cropland” for 2003
o within each of those segments, one point classified as “cultivated cropland” in
2003 was selected randomly.
Sample sizes by state are presented in Table 6. The sample included 2,268 CRP sample points
and 10,148 cultivated cropland points.
Sample for 2005 Survey
The sample for the 2005 NRI-CEAP Cropland Survey was selected from the 2003 Annual NRI
sample points classified as having a land cover/use of either cultivated cropland or land in CRP
for the 2003 growing season. In particular, the samples were selected from the Core Panel P00,
as follows:
(a) Any sample point in P00 classified as “land in CRP” for 2003 was included.
(b) Sample points classified as “cultivated cropland” were selected as follows:
18
it was determined which segments in P00 contained at least one point classified
as “cultivated cropland” for 2003
o within each of those segments, one point classified as “cultivated cropland” in
2003 was selected randomly.
(c) The following randomization process was used to eliminate all cropland sample points in
10 states:
o Minnesota and Wisconsin were paired [placed in Stratum A]; each was given an
equal chance of selection. Minnesota was kept in the sample and Wisconsin was
selected for elimination.
o North Dakota and South Dakota were paired [placed in Stratum B]; each was
given an equal chance of selection. South Dakota was kept in the sample and
North Dakota was selected for elimination.
o The states of Maine, New Hampshire, Vermont, Massachusetts, Rhode Island,
and Connecticut were combined into a New England Grouping. New York and
the New England Grouping were paired [placed in Stratum C]; each was given
equal chance of selection. New York was kept in the sample and the New
England Grouping was selected for elimination.
o The states of Montana, Colorado, Wyoming, Utah, and New Mexico were
grouped [placed in Stratum D]; each was given an equal chance of selection.
Colorado, Montana, and Utah were kept in the sample; Wyoming and New
Mexico were selected for elimination.
(d) Sample sizes for cultivated cropland were reduced in 11 states, as follows:
o randomization techniques were utilized that reduced the sample by one-third in
four states: Kansas; Minnesota; North Carolina; Ohio
o randomization techniques were utilized that reduced the sample by one-half in
two states: South Dakota; Texas
o randomization techniques were utilized that reduced the sample by two-thirds in
five states: Illinois; Indiana; Iowa; Missouri; Nebraska
(e) No cropland points in Florida, Nevada, and West Virginia were included for the 2005
survey; problems had been encountered in the 2003 and 2004 surveys. These three states
were included for the 2006 survey.
o
Sample sizes by state are presented in Table 6. The sample included 3,893 CRP sample points
and 7,489 cultivated cropland points. The sample size for cultivated cropland was about 25% less
than for each of the earlier years; less funding was available for conducting farmer interviews.
Sample for 2006 Survey
The primary objective for sampling in 2006 was to provide a greater ability to make regionallevel assessments (rather than just national), particularly by Major River Basin. Stratified
sampling techniques were used to concentrate on fields in the most environmentally sensitive (or
vulnerable) areas in order to provide more precise estimates of the effects of conservation in areas
where the impacts of conservation are the greatest; sampling in 2003, 2004, and 2005 provided
appropriate representation for predominant situations that covered 90% of the cropland base.
Funding existed to conduct approximately 6,000 farmer interviews for cultivated cropland fields;
no additional tracts of CRP land were selected.
Each county was ranked relative to its potential for soil and nutrient loss from cropland, by using
the National Nutrient Loss and Soil Carbon (NNLSC) database which contains estimates based
19
upon EPIC model runs for 1997 NRI cropland sample points [see Potter et al (2006)]. The
NNLSC database used general information on farming practices that was imputed onto the NRI
cropland sample points. County level estimates were derived for: wind erosion, waterborne
sediment, nitrogen loss in sediment, phosphorus loss dissolved in runoff, nitrogen loss dissolved
in runoff, and nitrogen loss dissolved in leachate. County vulnerability rankings were derived
using these seven factors as follows:
o
o
o
o
A county was classified with vulnerability rank 1 if it had an estimated value for at least
one factor in the top 10%; for wind erosion, the factor needed to be in the top 3% of all
counties because 85% of all counties do not have significant cropland wind erosion. This
category contained 658 counties.
A county was classified with vulnerability rank 2 if it was not classified as vulnerability
rank 1 but had an estimated value for at least one factor in the top 20% [top 5% for wind
erosion]. This category contained 385 counties.
A county was given a vulnerability rank 3 if its vulnerability could not be estimated from
the NNLSC database and it contained at least 20,000 acres of cultivated cropland. This
category included 70 counties.
Counties with low and very low vulnerability according to these seven factors were given
vulnerability ranks 4 and 5 respectively. There were 736 counties with rank 4 and 1,255
counties with rank 5.
The sample for the 2006 NRI-CEAP Farmer Survey came from 2003 Annual NRI sample points
that had not been selected for previous farmer surveys. Each state and county had a different
assortment of available cultivated cropland sample points relative to the county vulnerability
rankings described above. The 2006 sample is not a stand-alone sample as are the samples for the
three previous years. Some areas had no probability of selection for the 2006 survey; the 2006
results can only be used in conjunction with data collected for previous survey years.
For the 2003, 2004, and 2005 NRI-CEAP Farmer Surveys, sample points were spread out across
states and counties as much as possible given the nature of the 2002 and 2003 Annual NRI
samples. For example, only one cultivated cropland point per sample segment was selected for
the farmer surveys; this spread out the sample and also greatly reduced the chance that the same
farmer or operator was included in the sample more than one time in a given year. This was a
restriction put in place following discussions with USDA-NASS and the Office of Management
and Budget (OMB) in an effort to reduce respondent burden. For the 2006 sample, it was
necessary to select some sample points in sample segments that had been used for the 2004 or
2005 sample.
One of the basic methods of sample selection for 2006 was as follows:
o determine which segments in P00 and P03 had at least two points classified as cultivated
cropland in 2003
o if the segment had two points classified as cultivated cropland in 2003 and the county had
vulnerability rank less than 4, select the sample point not used for either the 2004 or 2005
survey
o if the segment had three points classified as cultivated cropland in 2003 and the county
had vulnerability rank less than 4, randomly select one of the two sample points not used
for either the 2004 or 2005 survey
o no sample points were selected in counties with vulnerability rank 4 or 5.
This procedure was used for Alabama, Arizona, California, Colorado, Kentucky, Michigan,
Mississippi, New Jersey, North Carolina, Oklahoma, Oregon, Tennessee, Utah, Virginia, and
20
Washington. The modified procedure used for Arkansas, Georgia, Idaho, Louisiana, Maryland,
Pennsylvania, and South Carolina was that only sample points from P03 were used.
Florida, Maine, Massachusetts, Nevada, New Mexico, Vermont, and West Virginia used sample
points in all P00 segments not used for the 2005 survey. For Indiana, Iowa, and Nebraska,
sample points were selected from all P00 segments not used for 2005 for counties with rank 1,
and half in counties with rank 2; for Delaware, Missouri, North Dakota, Wisconsin, and
Wyoming, all eligible P00 points were selected except only half in counties with rank >3. For
Kansas and Texas, sample points were selected from all P00 segments not used for 2005 for
counties with rank < 4; and sample points were selected from all eligible P03 segments in
counties with rank 1, and half were selected for counties with rank 2 or 3. For Minnesota and
South Dakota, all eligible sample points in counties with rank 1 or 2 were selected, and half of the
P00 rank 4 or 5 sample points. For Connecticut, half of the P00 points were selected. For
Illinois, sample points in P00 segments not used for 2005 were used in counties with rank 1;
sample points were selected for half of the segments in counties with rank > 1. For Montana, all
eligible sample points in counties with rank 3 were selected; sample points were selected from
segments in half of the eligible P03 counties with rank 4 or 5. For Ohio, all eligible points in
segments in counties with rank 1 and 2 were selected, except for half of the P03 segments with
rank 2. For New York, all eligible points in segments in counties with rank 1 and 2 were
selected, except for P00 segments with rank 2. No sample points were selected in New
Hampshire and Rhode Island.
21
Table 6. Number of Sample Points Selected for NRI‐CEAP Surveys, 2003 – 2006
Cultivated Cropland
2003
Alabama
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
All States
2004
2005
2006
Total
108
41
264
149
215
0
110
0
141
275
327
198
259
442
188
193
0
172
0
371
527
191
243
215
211
0
0
46
0
143
156
0
325
249
108
244
0
142
289
187
398
39
0
166
157
0
0
0
65
43
150
181
189
10
60
65
39
143
434
201
264
164
138
130
14
46
12
60
172
210
218
83
249
6
0
7
100
46
189
371
167
102
124
59
0
35
185
164
474
23
29
79
167
13
301
51
378
149
792
662
736
27
285
165
449
898
2,282
1,367
1,752
1,633
683
693
22
520
28
1,048
1,861
734
1,249
655
1,420
21
11
133
265
425
730
1,206
1,237
757
490
717
3
421
1,186
669
1,957
176
78
489
628
27
982
153
7,489
6,032
22
33,249
2003
90
30
194
166
167
9
61
45
130
245
785
484
609
500
194
184
4
148
11
308
594
157
400
197
497
7
5
38
85
116
183
551
370
188
140
184
1
126
470
153
541
59
30
119
155
9
355
54
Land in CRP
115
35
184
166
165
8
54
55
139
235
736
484
620
527
163
186
4
154
5
309
568
176
388
160
463
8
6
42
80
120
202
284
375
218
118
230
2
118
242
165
544
55
19
125
149
5
326
48
9,580 10,148
2004
21
0
17
10
68
0
1
4
14
90
79
25
146
196
33
26
1
3
0
29
95
87
159
101
99
0
0
0
79
2
4
255
31
27
34
2
0
22
92
23
184
18
0
2
79
0
49
29
2,236
2005 Totals
13
0
6
3
75
0
0
5
13
109
89
38
132
195
19
5
0
1
0
21
121
80
235
95
121
0
0
0
50
1
4
253
18
51
36
2
0
9
100
28
166
26
0
0
84
0
40
24
2,268
34
0
13
6
218
0
1
0
14
182
129
49
236
322
60
16
0
7
0
34
192
97
293
221
166
0
0
0
106
12
11
410
29
76
47
7
0
33
146
32
392
17
0
3
130
0
105
47
3,893
68
0
36
19
361
0
2
9
41
381
297
112
514
713
112
47
1
11
0
84
408
264
687
417
386
0
0
0
235
15
19
918
78
154
117
11
0
64
338
83
742
61
0
5
293
0
194
100
8,397
Figure 3. Density of Sample Points Selected for NRI‐CEAP Surveys
[includes Cultivated Cropland and Land in CRP]
23
VI. Estimation Procedure
Introduction
The Annual NRI estimation procedure combines information from several sources to produce a
final data set composed of records containing information for the years 1982, 1987, 1992, 1997,
2000, and annually thereafter. Each record represents data elements for a sample point; an
estimation weight is attached to each record. For each NRI survey year, data are collected at both
the segment level and at the point level. The areas measured for small water features, roads and
railroads, and urban and built-up lands are converted to point data during the estimation process.
Each of these created points is given an initial weight based on the area in the segment and the
probability that the segment is included in the sample; imputation is used for unobserved data
elements in order to complete the data record for these created points. Initial weights for created
points and for observed points are adjusted during the estimation process using ratio adjustments
and small area estimation. Control totals for surface area, federal land, and large water areas,
derived from GIS databases, are maintained throughout the process. Finally, the weights are
adjusted using iterative proportional scaling (raking) so that the new data base produces acreage
estimates for broad cover/use categories for historical years that closely match previously
published estimates [see Fuller (1999)].
Development of Estimation Weights for NRI-CEAP
Estimation weights for the NRI-CEAP cultivated cropland sample points in the Upper Mississippi
River Basin (UMRB) were developed in a manner consistent with development of weights for the
Annual NRI. Weights for other river basins will be developed in a similar fashion although some
additional ratio adjustment procedures may be utilized, for example, for irrigated conditions.
Estimation weights for points identified as “land in CRP” were basically those derived for the
Annual NRI data base.
The procedure for points identified as cultivated cropland follows:
o
Calculate initial weights, where WInit,q,k,j is the initial weight for point j, where point j
falls within 6-digit hydrologic unit q and has cropping system k
WInit,q,k,j = Aq,k,,j / (p q,k,j * mq,k,j ) , where:
A q,k,j = size of segment (q,k,j) in acres,
p q,k,j = probability that segment (q,k,j) is in the sample,
m q,k,j = number of sample points in segment (q,k,j)
o
Make the first adjustment to the initial weights
WAdj1, q,k,j = (WInit, q,k,j ) * (Yk / Xk ), where:
Yk = estimated acres of cultivated cropland in cropping system k
for the UMRB area, based upon 2003 Annual NRI
Xk = ∑ q,j WInit, q,k,j
o
Make the second adjustment to the initial weights
24
WAdj2, q,k,j = (WAdj1, q,k,j ) * ( Tq / Z1,q ), where:
Tq = estimated acres of cultivated cropland in 6-digit
hydrologic unit q, based upon 2003 Annual NRI
Z1,q = ∑ k,j WAdj1, q,k,j
o
Make the third adjustment to the initial weights
WAdj3, q,k,j = (WAdj2, q,k,j ) * ( Yk / X2,k ), where:
X2,k = ∑ q,j WAdj2, q,k,j
o
Make the fourth adjustment to the initial weights
WAdj4, q,k,j = (WAdj3, q,k,j ) * ( Tq / Z3,q ), where:
Z3,q = ∑ k,j WAdj3, q,k,j
o
Make further iterations to force the adjusted weights to sum closer to the controls – for
the UMRB, there were four additional adjustments using {Yk } and { Tq }
o
Designate the final adjusted weight for point (q,k,j) to be the estimation weight, W0, q,k,j
Development of Replicate Weights for Estimating Variances
A form of jackknife variance estimation is utilized for the Annual NRI because of the rather
complex nature of the estimation procedure. The Annual NRI survey process is a type of two
phase sampling, since the samples represent a subsample of segments selected from the 1997 NRI
sample. The replication method used for the NRI is a form of the “delete-a-group jackknife” [see
Kott (2001)]. The goal of the variance estimation procedure for an Annual NRI data set is to
construct a set of H modified weights for each observation, which allows computation of H
replicate estimates for a variable y. A variance estimate can then be calculated for an NRI
estimate, say Ŷ, as follows:
var( Ŷ ) = ∑ h c h * (Ŷh - Ÿ ) 2, where
c h is a constant determined by the replication procedure
Ŷh is the hth replicate estimate for Y, and
Ÿ = H-1 ∑ h Ŷh
For the 2003 Annual NRI and the NRI-CEAP cropland survey, H = 29 is used. To define the
replicates, a form of systematic sampling was used with the 1997 NRI sample units to create 29
groups of samples of approximately equal size. The same set of replicates is used for both the
2003 Annual NRI and the NRI-CEAP cropland database. This means that an estimation process
can be established so that variance estimates based upon the larger sample can be retained within
the smaller data base, if certain regression and/or ratio techniques are utilized.
25
The first set of replicate weights for the NRI-CEAP data set is derived as follows:
o
Calculate initial weights for the point (q,k,j) by modifying the estimation weight, W0, q,k,j ,
as follows:
WInit,1,q,k,j
o
= 0,
= (29/28) * W0, q,k,j ,
if point (q,k,j) is in replicate #1
otherwise
Make the first Adjustment to the Initial Weights
WAdj1,1,q,k,j
= (WInit, 1,q,k,j ) * (Yk / X1,k ), where:
Yk = estimated acres of cultivated cropland in cropping system k
for the UMRB area, based upon 2003 Annual NRI
X1,,k = ∑ q,j WInit, 1,q,k,j
o
Make the second adjustment to the initial weights
WAdj2, 1,q,k,j = (WAdj1,1, q,k,j ) * ( Tq / Z1,q ), where:
Tq = estimated acres of cultivated cropland in 6-digit
hydrologic unit q, based upon 2003 Annual NRI
Z1,q = ∑ k,j WAdj1, 1,q,k,j
o
Make the third adjustment to the initial weights
WAdj3,1, q,k,j = (WAdj2,1, q,k,j ) * ( Yk / X1,2,k ), where:
X1,2,k = ∑ q,j WAdj2,1, q,k,j
o
Make the fourth adjustment to the initial weights
WAdj4, 1,q,k,j = (WAdj3, 1,q,k,j ) * ( Tq / Z1,3,,q ), where:
Z1,3,q = ∑ k,j WAdj1,1, q,k,j
o
Make further iterations to force the adjusted weights to sum closer to the controls – for
the UMRB, there were four additional adjustments using {Yk } and { Tq }
o
Designate the final adjusted value for point (q,k,j) to be the first replicate weight, W1, q,k,j
A similar process is used for each of the remaining 28 replicates. Each point (q,k,j) then has an
estimation weight, W0, q,k,j , and a set of 29 replicate weights, { Wh, q,k,j, : h=1,2, …, 29 }, that are
used for variance estimation.
26
VII. Other Considerations
Preliminary results for the NRI-CEAP National Cropland Assessment are based upon data from
less than 60 percent of the sample sites originally selected for the NRI-CEAP Cropland Survey.
NASS enumerators were unable to complete questionnaires for about 25 % of the sample sites;
data from additional sample sites contained inconsistencies that could not be resolved for
inclusion in the preliminary results. A series of statistical analyses will be performed to test the
effects of these missing observations and to determine if a modified weighting process should be
employed. Other tests will be developed to analyze the effects of small sample sizes for
relatively small but influential and/or sensitive areas. Additional work is also needed to develop
methods for quantifying uncertainty due to the modeling employed for this project.
The expectation is that follow-up farmer surveys will be conducted starting in the year 2011, in
order to account for ongoing changes in cropping and conservation systems. In preparation for
this new series of surveys, several aspects of the 2003 – 2006 survey operations will be examined.
This includes development of an automated survey instrument as part of the quality assurance
process, utilization of improved sample location materials, and examination of response burden
including finding methods to shorten the length of each farmer interview.
27
References
Breidt, F.J. & W.A. Fuller (1999) Design of supplemented panel surveys with application to
the National Resources Inventory, Journal of Agricultural, Biological, and Environmental
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Goebel, J. J. (1998) The National Resources Inventory and its role in U.S. agriculture,
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| File Type | application/pdf |
| File Title | Statistical Methodology for the |
| Author | JJG |
| File Modified | 2009-05-27 |
| File Created | 2009-05-27 |