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Evaluation of Projection Methods to Predict
Wetland Area Sizes 1
Gerardo H. Terrazas Gonzalez2
David C. Bowden 3
Kenneth Burnhamm 4
Abstract-This research concerns different methods to estimate
projections of wetland area sizes at selected times. These methods
address mainly two objectives. One objective is to estimate the total
of wetland area sizes at any given time. The other objective is to
estimate the amount of change among wetland types between a
beginning time, TB and an ending time T E , to obtain annual rates of
changes (trends). A method developed by W.E. Frayer in collaboration with D.C. Bowden USFWS to address these objectives has been
used by the USFWS. The method applies when the sampling units
have been measured in two times, T 1 and T 2 with T 1 < T 2' A change
matrix giving the amount of each wetland at time Tl that in each
wetland type at time T 2 for each sampling unit is computed.
Projections are based on an annual rate of change matrix at stratum
basis for a time Tl < T 2. This method will be identified as the FBSB
estimator.
Methods of evaluating the reliability ofFBSB estimator have not
been given previously. Variance estimators to evaluate the method
using the jackknife and the bootstrap techniques are provided.
Direct analytic techniques seem to be very complicated given the
complexity of the estimator.
Interest in having projections at an arbitrary time T led to a more
general description ofthe FBSB estimator t include projections for
a time T < T 1 and for T between T 1 and T 2' Variatio~s in the
measurements times Tl and T2 among sampling units within
stratum and other considerations like the complexity of the FBSB
estimator, motivated the use of simpler estimators.
The methods discussed can be classified in methods based on the
sum of estimated change matrices and methods based on a product
of normalized estimated change matrices. Besides, methods within
each class can be based whether the change matrices are on annual
basis or observed time period (T 1 - T 2) basis. The FBSB estimator is
a method that uses a sum of estimated matrices of changes and is
based on an annual basis matrix of change's. Two additional estimators are provided in this paper and then compared to the FBSB
method. The first is a modification of the FBSB estimator that uses
the average of the change matrices of the sampling units within
stratum using the ratio estimator to calculate the projections to a
desired time T (FB DB estimator). The second method uses a product
of normalized change matrices (transition matrices) based on the
observed period (T 1 - T 2); and then linear interpolation to estimate
the projections at a desired time T is applied (CNTM estimator).
Because the estimates for the totals were not statistically insignificant, the selected method was the CNTM estimator since it is the
simplest to apply.
Ipaper presented at the North American Science Symposium: Toward a
Unified Framework for Inventorying and Monitoring Forest Ecosystem
Resources, Guadalajara, Mexico, November 1-6,1998.
2Acciones y Valores de Mexico S.A. de C.V.
3Statistics Department, Colorado State University, Fort Collins, CO.
4Fish and Wildlife Department, Colorado State University, Fort Collins,
CO.
58
USDA Forest Service Proceedings RMRS-P-12. 1999