MONITORING LANDSCAPE LEVEL PROCESSES USING 
REMOTE SENSING OF LARGE PLOTS 
Raymond L. Czaplewski 
Mathematical Statistician 
USDA Forest Service Research 
Rocky Mountain Forest and Range 
Experiment Station 
240 W. Prospect Street 
Fort Collins, CO 80526 U.S.A. 
ABSTRACT 
Global and regional assessments require timely information on landscape level status (e.g., 
areal extent of different ecosystems) and processes (e.g., changes in land use and land cover). 
To measure and understand these processes at the regional level, and model their impacts, 
remote sensing is often necessary. However, processing massive volumes of remotely sensing 
data can be infeasible if high resolution data are required for very large regions. Remote 
sensing of sample plots, rather than a census of the entire area, can solve certain problems. 
Statistical aspects of remote sensing for large plots are described, concentrating on methods 
needed to produce sample estimates, combine time series of ancillary estimates from other 
sources, calibrate for misclassification bias, and combine remotely sensed data with model 
predictions. These methods might improve spatial and temporal accuracy, and test our 
understanding of processes that are captured in landscape level models. 
KEY WORDS: Kalman filter, composite estimator, classification error, calibration, landscape 
models, landscape models, spatial autocorrelation, spatial heterogeneity. 
1. INTRODUCTION 
A simple example is used in the following 
discussion, where status is defined as the 
proportion forested area, and ground-based field 
work is used to determine if a point is truly 
forested. This hypothetical example uses the 
sampling frame and certain design features 
proposed by the U.S. Environmental Protection 
Agency as part of its Environmental Monitoring 
and Assessment Program (EMAP). This is a 
cooperative program among several agencies of the 
United States Government, including the USDA 
Forest Service. The EMAP sampling frame is 
composed of a triangular grid. Each 640 km 2 
hexagon on this grid contains a 40 km 2 hexagon 
(i.e., a 1/16 sample by area) that is observed 
using Landsat data and high altitude aerial 
photography. However, the statistical models 
readily apply to sampling frames used in other 
programs, such as that proposed by the Food and 
Agricultural Organization of the United Nations 
for monitoring and assessment of the world’s 
tropical forests, or that proposed by Czaplewski 
et al. (1987) for updating forest inventory 
estimates made by the USDA Forest Service. 
Underlining statistical models for estimated 
status of the stratum and each sample unit are 
presented in Section 2. Section 3 gives a 
calibration model for measurement error that 
occurs when true status can not be perfectly 
classified with remotely sensing. Section 4 
presents an illustration of the statistical 
composite estimator, which combines estimates 
from different sources. In Section 5, the 
composite estimator is used to combine 
calibrated, remotely sensed estimates from many 
sample units into an estimate of stratum status. 
The Kalman filter, which is a more general 
composite estimator, is introduced in Section 6. 
In Section 7, the Kalman filter is used to update 
estimates of status for each sample unit, and 
combine them into an estimate of status for the 
stratum. Section 8 uses the Kalman filter to 
combine ancillary estimates for aggregations of 
sample units. The cycle of landscape monitoring 
and process modeling is discussed in Section 9. 
2. SAMPLE FRAME 
Consider a sampling frame composed of a grid of 
large sample units that are well suited for 
monitoring using remote sensing. The frame is 
confined to a contiguous, homogeneous geographic 
area, i.e., a stratum. Estimates for status of 
multiple strata could be summed for regional or 
global assessments if definitions for true status 
are shared among strata. 
2.1 Example sampling frame 
Assume a large, homogeneous, geographically 
contiguous stratum is comprised of a known number 
of cells (n), e.g., 640 km 2 hexagons. A stratum 
might be the coastal plain in the southeastern 
United States, which is 320,000 km 2 in size; the 
number of cells n would be (320,000/640)=500. 
Each 640 km 2 cell is sampled with a single 40 km 2 
sample unit, which is centered on the 640 km 2 
cell. Each 40 km 2 sample unit is treated as a 
permanent plot, and each is periodically observed 
over time using remote sensing. 
2.2 Statistical model for status 
The status of the stratum (e.g., proportion 
forest) is denoted as unknown nonrandom variable 
X. Since the stratum is assumed spatially 
homogeneous, status of each sample unit in the 
stratum is assumed equal to the stratum status X. 
Deviation of the observed status of sample unit i 
from the stratum status is the unknown random 
variable Wi . The statistical model for estimated 
status of sample unit i is 
Xi = X + K, for i = {1, 2, ... , n} (1) 
Xi is assumed an unbiased estimate of X, i.e., 
E[¥i] = 0. Variance of Wi, denoted var(ffi), is 
assumed heterogeneous among the n sample units in 
the stratum, i.e., var( Wi) does not necessarily 
equal the var( Wj ) for i not equal to j. 
Deviations among sample units are not assumed 
independent, i.e., Et&’i&'j] might be nonzero. No 
other distributional assumptions are made.