18
SD Resource Inventory Notes BLM 18 February 1979 BLM LIBRARY 88049704 by MULTI-STAGE AND MULTI-PHASE SAMPLING J.D. Nichols 1/ Historically sampling and estimation procedures have been mis- named and misused. One of the most abused of these terms is multi-stage sampling. As a result of several studies multi- stage sampling has taken on the connotation of any sampling and estimation procedure that calls on multiple levels of data to provide information. Multi-stage sampling has a rather simple meaning. 2/ The multi- stage sampling frame, Figure 1, consists of a list of sample units (Primary Sample Units)which are made up of smaller units (Secondary Sample Units), which are in turn made up of smaller units (Third Stage Sample Units). The number of stages and the size and number of sample units at each stage is dependent on the objectives of the inventory and the characteristics of the population to be sampled. The size and number of units may vary at each stage. The method of selecting a PSU, SSU and TSU for measurement depends on the objectives of the inventory and population characteristics. They can include simple random, variable probability and stratified selection. The objective of multi-stage sampling is to provide a sample unit that can be cost efficiently measured and to cluster these samples in the higher level (larger) sample unit to reduce the travel cost between measurement units. The estimators for multi- stage sampling are well documented in several texts (see references) including Forest Mensuration , by B. Husch, C. Miller, and T. Beers. 1/ Owner, Resource Inventory Services, 650 Aram Ave, San Jose, Ca. 2/ Source: B. Husch, C. Miller, and T. Beers, Forest Mensuration , 2nd Edition, pages 219, 224, and 226. b l 8 ' 2 Published by. N534 USDI, Bureau of Land Management, D 340 1979 Denver Service Center, Denver Federal Center , Bldg. 50 C £ttf E* "•» Denver, Colorado, 80225 f*

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Page 1: Multistage Multi p 19 Nich

SD

Resource Inventory NotesBLM 18 February 1979

BLM LIBRARY

88049704by

MULTI-STAGE AND MULTI-PHASE SAMPLING

J.D. Nichols 1/

Historically sampling and estimation procedures have been mis-

named and misused. One of the most abused of these terms is

multi-stage sampling. As a result of several studies multi-

stage sampling has taken on the connotation of any sampling and

estimation procedure that calls on multiple levels of data to

provide information.

Multi-stage sampling has a rather simple meaning. 2/ The multi-

stage sampling frame, Figure 1, consists of a list of sample units

(Primary Sample Units)which are made up of smaller units

(Secondary Sample Units), which are in turn made up of smaller

units (Third Stage Sample Units). The number of stages and the

size and number of sample units at each stage is dependent on

the objectives of the inventory and the characteristics of the

population to be sampled. The size and number of units may

vary at each stage. The method of selecting a PSU, SSU and TSU

for measurement depends on the objectives of the inventory and

population characteristics. They can include simple random,

variable probability and stratified selection.

The objective of multi-stage sampling is to provide a sample unit

that can be cost efficiently measured and to cluster these

samples in the higher level (larger) sample unit to reduce the

travel cost between measurement units. The estimators for multi-

stage sampling are well documented in several texts (see

references) including Forest Mensuration , by B. Husch, C. Miller,

and T. Beers.

1/ Owner, Resource Inventory Services, 650 Aram Ave, San Jose, Ca.

2/ Source: B. Husch, C. Miller, and T. Beers, Forest Mensuration ,

2nd Edition, pages 219, 224, and 226.

b

l8 ' 2 Published by.

N534 USDI, Bureau of Land Management, D 340

1979 Denver Service Center, Denver Federal Center ,Bldg. 50

C£ttfE*"•» Denver, Colorado, 80225 f*

Page 2: Multistage Multi p 19 Nich

Primary Sample UnitPSU

SecondarySampleUnitSSU

Third Stage Sample UnitTSU

Figure 1: Hypothetical 3-stage multi-stage sample layout withequal size at each stage.

The optimization of a multi-stage design depends on the datacollection cost, travel cost, between unit variability, andprecision objectives. Given a two stage sampling frame thenumber of second stage samples is obtained from

-2-

£B

DfcN^O.1P

Page 3: Multistage Multi p 19 Nich

Jj >H-

n = optimum number of secondary units per primary unit.

C]_ = cost of establishing a primary unit.

C2

= cost of establishing and measuring a secondary unit.

Sw ^ = estimate of variance within the groups of secondarysample units.

S B" = estimate of the variance between the means of the

secondary sampling units within the primaries.

Given a fixed budget, the number of primaries is

,tf-£

5V-

C 2-

m=C 1+nC 2

The points to be made are: Dthe optimization is dependent on costand variance and 2) the procedure does not use multiple levels of data,

The sampling scheme that is most often confused and confoundedwith multi-stage sampling is multi-phase sampling (double samplingfor two phases). Multi-phase sampling in general consists ofselecting a large first phase sample of an auxiliary variable (x^)which will provide a precise estimate of the primary variable (y^)

.

A subset of the first phase units are then selected and accuratemeasurements of the primary variable (yj_) are taken. In operationalforest inventories this has included basal area (xj ) as an auxiliaryestimator of timber volume (yO and aerial photo estimates of timbervolume (Xj) as an auxiliary variable for ground measured timbervolume (yi) . In range sampling a common practice is to make anocular (professional) estimate of the weight of available forage(xj_) as an auxiliary variable for clipped, oven dry weight of theforage (yj_) on sample plots.

The procedure assumes that the observation of the Xj_s are paired(Figure 2) with the yj_s, that there is a strong relationship betweenthe Xj_ and the yi, that the relationship can be estimated and thatthe x^_ measurement is much less expensive to collect and process persample than the y^ measurement.

The procedure to estimate the relationship between the y and x cantake one of several forms. The form depends on the functionalrelationship between the x and y observation and the form ofdistribution of errors in estimating the y from x. An introductionto these principles and their associated estimators is containedin Elementary Statistical Methods For Foresters, AgricultureHandbook #317 (literature cited).

-3-

;;%^'"%

Page 4: Multistage Multi p 19 Nich

Photo estimate of timbervolume of a tree

Ground estimate oftimber volume of atree

Figure 2; Multi-Phase Sampling

If conditions are such that a simple linear relationship existsbetween x and y, the ratio (A) of the number of primary observations(n) to auxiliary observation (m) is estimated by the following. 3/

a = am

1- Pxy2 C^p 2 rxy z ^2

xy = correlation between x and y.

C]_ = cost of obtaining and processing an observation of anauxiliary variable.

C2 = cost of obtaining and processing on observation of theprimary variable.

3/ L.C. Wensel, Wildland Resource Sampling (Draft), University ofCalifornia, Berkeley, pages 4-75 to 4-79.

-4-

Page 5: Multistage Multi p 19 Nich

The total cost (C) of the collecting and processing of the inventorydata is

C = C1m+C

2n.

Therefore for a fixed budget

CmC1+C2X ; n = mX

The points to be made here are: l)the allocation of effort in multi-phase sampling is a function of relative cost of the primary andauxiliary variable and 2 ) the strength of the relationship betweenthe x and y observations (correlation for simple linear relation-ships). This is different than the multi-stage sampling procedurewhich depended on cost and variance rather than cost and correlation.

The above discussion of sample size has been restricted to fixedbudget sample allocation. For procedures to optimize a givenprecision level, the reference by L.C. Wensel provides a goodintroductory discussion.

The two simple cases just describes are easily named. When multipledata levels and information extraction methods are used the samplingand estimation procedures become complex and the naming of theprocedure becomes difficult. The sampling systems are combinationsof multi-stage and multi-phase with multiple stratifications.Care must be taken to optimize the system and adequately describethe resultant sampling procedure, including the estimators of thecharacteristics of interest and the confidence bound for theseestimates.

Literature Cited

B. Husch, C.I. Miller, and T. Beers; Forest Mensuration; 2ndEdition; The Ronald Press Company.

Freese, F.; Elementary Statistical Methods For Foresters;Agriculture Handbook #317; U.S. Department of Agriculture,Forest Service; Jan. 1967.

Wensel, L.C; Wildland Resource Sampling (Draft); Universityof California, Berkeley; 1977.

Page 6: Multistage Multi p 19 Nich

PreliminaryP inon-JuniperVolume Tables

by

J. David Estola-

ABSTRACT : This article contains pinon-juniper cubic-volume equationsand tables (English and metric units) for northern New Mexico andsouth central Colorado.

Introduction

The Bureau of Land Management conducted extensive forest inventories intheir Albuquerque and Socorro, New Mexico and Canon City, ColoradoDistricts in 1974. The inventories included the pinon-juniper foresttype.

A total of 392 pinon pine trees (Pinus edulis Englm.) and 206 combinedRocky Mountain juniper trees (Juniperus Scopulorum Sorg.) and Utah junipertrees (J. osteosperma (Torr.) Little) were randomly selected and measuredin the course of the inventory.

Pinon and juniper trees are found in a myriad of sizes and shapes varyingfrom well formed single-stemmed trees to bushy multi-stemmed trees.

This extreme variation makes the task of developing accurate volume tablesdifficult.

The strategy used to build these cubic-volume equations and tables con-sisted of exploiting the following relationships:

1. diameter squared times height to predicted volume2. crown diameter to volume variation within a diameter-height class3. logarithmic volume equations and the least squares regression method

to construct volume tables.

Field Measurement

A wide variety of site and tree attributes were collected in the extensiveinventory.

—' Forester, Bureau of Land Management, Denver Service Center (D-340)

,

Denver Federal Center, Building 50, Denver, Colorado 80225

-6-

Page 7: Multistage Multi p 19 Nich

The following measurements were recorded and used to analyze certain treeattributes and cubic-volume relationships:

1. diameter stump height (outside bark at a one foot stump)-

2. average crown diameter3. total height Co)

4. tree segment— diameter large end, diameter small end and length.

1/ A tree forking at or below one-foot was considered two or more trees;a tree forking above one-foot was considered one tree.

2l A tree segment is defined as a piece of wood and bark at least 2 feet

long and 2 inches in diameter outside bark. Length measurements wererounded to the nearest whole foot and diameters were rounded to thenearest whole inch. A segment could not have a crook or fork that off-

set more than 1/2 of the average diameter of the segment. Segmentationdata was used to compute the cubic-volume of each sample tree.

Data Computation

Smalian's formula was used to compute the cubic-foot or cubic-metre volumeof each segment.

Smalian formula:

2

where:

V = cubic feet or metres volumeB and b = cross sectional areas of lower and upper bases, respectively,

in square feet or metresL = length in feet or metres

The total cubic volume of each sample tree is equal to the sum of its seg-

ments.

The logarithmic volume equation used to predict cubic-volume is

log 10V=b 1log

10(dsh2xh)+b 2

log 10Cr+log 10 C

where:

V = cubic foot or metre volume

bi & b2 = regression coefficientsdsh = diameter stump height

h = total heightCr = crown diameter

-7-

Page 8: Multistage Multi p 19 Nich

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Page 10: Multistage Multi p 19 Nich

log 10 C=base 10 log of volume intercept value,

(bj, b 2 and log 1Q C are obtained by regular least squares methods)

Results

Figures 1 through 4 are the resulting cubic-volume tables. Cubic-volumeequations and r values are located below each table. Cubic-volume includewood and bark. Wood and bark in the stump and limbs less than 2 inches is

excluded. (Refer to pages 7$ and 7b for Figures 1 through 4)

.

Conclusions

Due to the extreme variation in pinon and juniper, a volume table based on

three variables may not accurately state the volume of individual trees.

The Forest Service Intermountain Experiment Station at Ogden, Utah willsoon publish gross cubic-volume tables for pinon-juniper in northernNew Mexico. The Intermountain Station used a more complex regressionanalysis technique to screen many variables, combinations of variables andtransformation of variables from a large number of samples to develop the

tables. The tables will provide flexibility for estimating gross cubicvolumes to varying top diameters (1 inch through 7 inches) for single andmulti-stemmed trees.

The tables in this article were compared with an advance copy of theForest Service tables for single-stemmed trees to a 2 inch top. Becausethe tables are constructed differently, a direct comparison was not possibleGenerally, the tables compared favorably.

Though these tables may not provide accurate estimates of individual treevolumes, acceptable estimates can be achieved in northern New Mexico andsouth central Colorado for aggregations of trees.

Current Literature

Please order directly from addresses given.

General

"A Basic Inventory That Works" by Wendt in Rangeman's Journal 5(5) :164-166»

(Oct. '78) at your local conservation library.

Ecological Land Classification Series No. 5, "Land/Water Classification"from Canada Committee on Ecological (Bio-Physical) Land Classification,Lands Directorate, Environment Canada, Ottawa K1A 0H3.

"Focus on Renewable Natural Resources" Vol. 4(1)> from Forest, Wildlife &

Range Exp. Sta. , College of Forestry, Wildlife & Range Sciences, Moscow,ID 83843.

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FORESTRY

"Untersuchungen liber die Bestandes-Massenermittlung durch dieDeckpunkthohensumme" by Prof. Masami Kitamura, Dept . of Forestry, Univ.of Yamagata, 1-23 Wakabamachi, 997 Tsuruoka, Japan.

Forestry program for Oregon supplements No. 1 "Non-industrial PrivateForest Management: An Action Recommendation" and No. 2 "UnderproductiveForest Lands in the Oregon Coast Range" are available from State of

Oregon, Dept. of Forestry, 2600 State Street, Salem, OR 97310.

Tech. Note 323 "An Economic Analysis Series for Screening Proposed TimberManagement Projects - Report No. 2 - Precommercial Thinning Only -

Lodgepole Pine - Site Index 60" by Francis Horak. Drop us a linefor a copy.

Res. Paper PNW-235 "A Technique for Predicting Logging Residue Volumes in

the Douglas-Fir Region"

Reprint "New Tools Allow Examination of Skyline Alternatives Speedily"by Burke.

Both from: Pacific Northwest Forest & Range Exp. Sta. , P.O. Box 3141,Portland, OR 97208.

Drop us a line for Tech. Note 319 "Intensive Forest Inventory - A SelectedBibliography" by Costello and Pettijohn. Also ask for "Allowable Cuts,Forest Regulation, Economics - A Bibliography" by H. Gyde Lund.

Gen. Tech. Report PSW-24 "Tree Failures and Accidents in Recreation Areas:

A Guide to Data Management for Hazard Control" from Pacific SouthwestForest and Range Experiment Station, P.O. Box 245, 1960 Addison Street,Berkeley, CA 94701.

Reprint - "Advances in Information Systems and Services in the ForestryCommunity" by Dwinell.

Resource Bull. SE-43 "Coastal Virginia's Timber Resource - Trends, PresentConditions, and Opportunities for Improvement".

Resource Bull. SE-45 "Forestry Statistics for the Piedmont of South Carolina 1

Res. Note SE-263 "Predicting Logging Residues for the Southeast".

Res. Paper SE-174 "Predicting Fire Behavior in Palmetto - Gallberry FuelComplexes".

All from The Southeastern Forest Exp. Sta., P.O. Box 2570, Asheville, NC

28802.

9-

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Booklet - "How To Examine Branches For Spruce Budworm Egg Masses" fromCooperative Forestry Research Unit, School of Forest Resources,Room 227, Nutting Hall, University of Maine, Orono, ME 04473.

Bull. 664T "Preliminary Weight Yield Tables For Even-aged Upland OakForests", from Division of Forestry, West Virginia University,Morgantown, WV 26506.

Bull. 16 "Full Forest Utilization - A Bibliography" from Forest, Wildlifeand Range Exp. Sta. , University of Idaho, Moscow, ID 83843.

"Disc-Hammer Starter For Increment Borer" by Liu and Tang in Journal of

Forestry, November '78, p. 732-733 at your local conservationlibrary.

Gen. Tech. Report RM-58 "Computing Average Skidding Distance For LoggingAreas With Irregular Boundaries and Variable Log Densities" fromRocky Mt. Forest & Range Exp. Sta., 240 West Prospect Street,Ft. Collins, CO 80526.

RANGE & WILDLIFE

"Comments on Browse Inventories in Louisiana" by Pearson & Sternitzke.Journal of Wildlife Management 42 (1) : 169-171 at your local conservationlibrary.

Contribution No. 165 "Evaluation of Streamside Bufferstrips For ProtectingAquatic Organisms" from Water Resources Center, University of California,Davis, CA 95616.

Division Report //9 "Live Trapping and Handling Coyotes For Research" from

Colorado Division of Wildlife, 6060 Broadway, Denver, CO 80216 - price$1.00.

Misc. Paper #12 "Topography, Climate and Soil Types As Indicators of

Fremont Regional Variation" from Museum of Natural History, IdahoState University, Pocatello, ID 83209 - price $1.00.

Fritzner, R.E. , L.E. Rogers and D.W. Uresk. 1977. "Techniques Useful For

Determining Raptor Prey-Species Abundance". Raptor Res. 11(3): 67-71 at

your conservation library.

Wildlife Digest No. 11 "Using Chest Circumference to Determine Bear Weight"from Arizona Game & Fish Dept., 222 W. Greenway Rd., P.O. Box 9099,Phoenix, AZ 85068.

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Gen. Tech. Rept. RM-57 "Manual of Saltbushes (Atriplex spp.) inNew Mexico"

Res. Paper RM-202 "Arizona Chaparral: Plant Associations and Ecology"from Rocky Mt. Forest & Range Exp., Sta., 240 W. Prospect St.,Fort Collins, CO 80526.

Ag. Handbook 511 "Cavity-Nesting Birds of North American" - for saleby Superintendent of Documents, U.S. Government Printing Office,Washington, D.C. 20402. Price unknown.

REMOTE SENSING

IAFHE RSL Res. Report 78-3 "Remote Sensing Analysis of the Vegetation of

the Mississippi River Headwaters - Leech Lake, Minnesota"

IAFHE RSL Res. Report 78-4 "Remote Sensing Applications to HabitatAnalysis of the Bering River - Controller Bay Trumpeter SwanManagement Area and Martin River Valley, Alaska".

IAFHE RSL Res. Report 78-5 "Water /Vegetation Conditions on the Lower St.

Croix River and on Mississippi River Pools 1-4 in 1939".

All from IAFHE Remote Sensing Lab. , University Minnesota, College of

Forestry, 1530 North Cleveland Ave., St. Paul, MN 55108.

Reprint "Inventory of Land Use and Land Cover of the Puget Sound RegionUsing LANDSAT Digital Data" by Gaydos & Newland.

Reprint "Low-cost Computer Classification of Land Cover in the PortlandArea, Oregon, by Signature Extension Techniques" by Gaydos.

Contact Land Information and Analysis Office, USGS National Center,Mail Stop 710, 12201 Sunrise Valley Drive, Reston, VA 22092.

SOILS & WATERSHED

Reprint "A Two-Element Ceramic Sensor for Matrix Potential and SalinityMeasurements" by Scholl.

Reprint "Some Measurement of Settlement in a Rocky Mountains Snow Cover"

by Bergen.

Both From Rocky Mt. Forest & Range Exp., Sta., 240 W. Prospect Street,Ft. Collins, CO 80526.

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"Northwater" A Newsletter dealing with notes on Water Resources Researchin Alaska is available free of charge from Northwater Editor, Instituteof Water Resources, University of Alaska, Fairbanks, AK 99701.

Meetings

Workshop on Remote Sensing Field Research - June 25-26 at Purdue University,scene characterization, spectral data acquisition and calibration, dataanalysis and instrumentation systems will be covered.

Machine Processing of Remotely Sensed Data - A symposium, June 27-29, 1979at Purdue University. Emphasis will be on Research Results in:

1. Digital representation and understanding of remotely sensed scenes.2. Utilization of digitally processed earth resource data.3. Extraction of information primarily from digital remotely sensed earth

resource data.

Remote Sensing Short Course - ongoing throughout the year at Purdue. Thecourse is intended for individuals involved with the extraction of usableinformation from raw remote sensing data. The fee is $565.

For information on any of these meetings contact Purdue University,Laboratory for Applications of Remote Sensing, West Lafayette, IN 47907.

Sampling on Successive Occasions - A workshop sponsored by Department of

Forest and Wood Sciences, Colorado State University, S.A.F. InventoryWorking Group and IUFRO S4. 02-03 will be held July 17-20, 1979. Theworkshop is designed for resource managers and researchers engaged insampling projects such as national and state timber surveys, multi-resourceinventories, timber inventories on industry-owned lands, etc. A knowledgeof basic sampling technique is assumed. The course will be limited to 40people and will cover expected values, probability sampling, best linearunbiased estimates, independent estimates, remeasurement , sampling withpartial replacement, optimum sample sizes and sampling on more than twooccasions. The fee is $250. Contact Office of Conferences and Institutes,Residential Conference Center, Colorado State University, Fort Collins,Colorado 80523.

Dynamic Similarities of Oceans and Atmospheres - is the theme of theCanadian Meteorological and Oceanographic Society XIII Congress. This willbe held at the University of Victoria, Victoria, B.C., May 30-June 1. Fordetails contact Dr. Richard Bennett, Resource Analysis Branch, Ministry of

the Environment, Parliament Bldgs, Victoria, B.C., Canada V8V 1X4.

V an* 250*7

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Page 16: Multistage Multi p 19 Nich

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1979 Forest Inventory Workshop . Don't let the name fool you. Thisworkshop is designed to appeal to land managers, inventory specialists,practitioners, data analysts and biometricians. This national meeting is

sponsored by the SAF Inventory and Biometrics Working Groups, IUFROSubject Groups S4.02 and S6.02 and by Colorado State University. Over 84papers will deal with such subjects as Multi-Resource Inventories,Biometrics, Inventory Projection and Growth, Inventories on SuccessiveOccasions, Sampling Techniques, Sampling Aspects of Aerial Photography,Computer Uses in Resource Inventories, Tropical Inventories, BiomassMeasurement, Biomass Inventory, Metric Conversion Strategies, ProductEstimation and a series of contributed papers. Registration fee will beabout $75. The dates are July 23-26, 1979, at Colorado State University.For details contact Office of Conference and Institutes, ResidentialConference Center, Colorado State University, Fort Collins, Colorado 80523.

Remote Sensing for Natural Resources - An international view of problems,promises and accomplishments sponsored by the University of Idaho, IUFROand SAF. Dates are September 10-14, 1979.

Coming in 1980. Arid Land Resource Inventory - workshop sponsored by theMexican Forest Service and the Society of American Forester's InventoryWorking Group. Dates are November 30-December 6, 1980 and the placeLa Paz, Mexico. Watch the Notes for further details and plan to attend.

**********Miscellaneous

SAF Inventory Working Group elects new officers for 1979 & 1980.

Dave Bower of Weyerhaeuser is the incoming chairman, Skip House of

Great Northern Paper Company is chairman-elect and Dr. Harry Wiant of

West Virginia University is the new secretary for the 1100 member WorkingGroup.

Society for Range Management (SRM) forms Range Inventory StandardizationCommittee. The purpose is to promote uniform methodology and terminologyfor rangeland inventories and assessments. J. Kemmedson (Univ. of Ariz.)is the chairman. Other members include John Artz (Univ. of Nev.),Robert Barnes (SEA (ARS)), Richard Driscoll (USFS) Richard Eckert(SEA (ARS)), Floyd Kinsinger (BLM) , George Knoll (BIA) , Phil Ogden(Univ. of Ariz.), Don Pendleton (SCS) , C.B. Rumburg (SCS) and Lamar Smith(Univ. of Ariz. )

.

Wanted! Lead articles, current literature and meeting announcements for

publishing in the "Notes". If announcing a meeting, please allow at least

a four month lag time.

Change of Address ? Be sure to send us your old label. If you want to geton or off our mailing list, drop us a line.

**********

GPO 848 - 992

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BLM LIBRARY

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