METHOD

1
A sample design for Landsat-based estimation of
national trends in forest disturbance and
regrowth
R. E. Kennedy 1, Cohen, W.B.1, Moisen, G.G.2,
Goward, S.N.3, Wulder, M.4, Powell, S.L1, Masek,
J.G.5, Huang, C.3, Healey, S.P.2
1 U.S.D.A. Forest Service, Pacific Northwest
Research Station, Corvallis, OR 97331 2 U.S.D.A.
Forest Service, Rocky Mountain Research Station,
Ogden, UT 84401 3 Department of Geography,
University of Maryland, College Park, MD 20742
4Canadian Forest Service, Pacific Forstry
Centre, Victoria, BC, Canada V8Z 1M5 5
Biospheric Sciences Branch, NASAs Goddard Space
Flight Center, Greenbelt, MD 20771
INTRODUCTION
FINAL SAMPLE
METHOD
Forest disturbance and recovery processes have
important impacts on carbon dynamics, but are
known to vary spatially by forest type and forest
ownership, as well as temporally by economic and
climatic condition. At a national scale, Landsat
data are ideal for capture of these spatial and
temporal variations because of their small grain
size, their spectral properties, and their
consistency over more than three decades.
Path/row
Path/row

1. Tessellate WRS-2 Landsat scene to Thiessen Scene
   Areas (TSAs). See Gallego, F. J. 2005. Stratified
   sampling of satellite images with a systematic
   grid of points. ISPRS Journal of Photogrammetry
   Remote Sensing 59 369-376.
2. Extract proportions of forest type from new FIA
   map.
3. Develop eastern and western sample frames using
   only scenes gt2 cumulative forest cover (n 156
   East, n 122 West).

East
21/37
27/38
22/28
18/35
25/29
17/31
19/39
16/36
26/36
12/31
21/39
12/27
West
37/34
35/34
34/37
37/32
47/28
36/37
41/32
43/33
41/29
35/32
45/29
Final Sample
Landsat data therefore constitute the core of the
NASA funded project North American Forest
Disturbance and Regrowth since 1972 Empirical
Assessment with Field Measurements and Satellite
Remotely Sensed Observations. Biennial stacks
of Landsat images are being linked with field
measurements from the USDA Forest Services
Forest Inventory and Analysis (FIA) program to
develop dense temporal estimates of forest
dynamics for the past three decades in the 48
contiguous states. The challenges in processing
and analyzing imagery and FIA data in each scene
are considerable, however, making wall-to-wall
coverage impractical. Therefore, a sampling
approach is needed to for national-level
estimates of forest dynamics, with each Landsat
scene a single sample unit. This poster describes
our sampling approach.
Probabilities of inclusion for use in estimation
Example of TSAs for scenes in Maryland
FIA Forest type map with eastern and western
frames delineated

1. For eastern and western frames separately, create
   100,000 randomized ordered lists of TSAs (ROTLs).
2. Define the potential sample for each ROTL as the
   first n1.4 scenes, where n11 East and n9 West.
   This allows for future expansion. Calculate the
   following four criteria scores for each potential
   sample.

Criteria scores for potential sample scenes in
each ROTL
GOALS
The sampling approach must fulfill several
competing goals

• Capture a diversity of forest types An ideal
  sample would capture the economic and ecological
  variation among forest types that leads to
  variation in disturbance and regrowth dynamics.
• Minimize inclusion of scenes with little or no
  forest cover Each scene chosen for the sample
  will incur significant cost. Therefore, scenes
  with little or no forest cover are undesirable.
• Disperse scenes spatially --Forest disturbance
  and regrowth patterns are likely to be spatially
  autocorrelated at a regional scale, arguing
  against adjacent sample scenes.
• Encourage inclusion of several focal scenes
  Significant processing has already occurred on
  several image stacks in prior projects and in the
  startup phase of this project. Inclusion of these
  scenes would increase sample size at marginally
  increased cost.
• Allow design-based estimation -- Design-based
  sampling allows estimation of national totals and
  errors from the samples alone, and is well
  understood as an unbiased approach for
  estimation.
• Facilitate robust regression-based estimation
  --The rich temporal dynamics inferred from the
  biennial Landsat stacks complement wall-to-wall
  decadal estimates of disturbance from the LEDAPS
  project, but require that the sample scenes
  capture the full suite of disturbance regimes
  across the country.
• Allow for future expansion of the sample
  Characterizing historical forest dynamics is of
  interest to other groups, and flexibility in
  sample design would allow collaboration on new
  sample scenes in the future.

DISCUSSION
Focal scenes
Two additional issues deserve discussion. When
MSS scenes are considered in image stacks,
look-up tables linking each WRS-2 scene to its
WRS-1 counterpart will be built, and
probabilities of inclusion mapped directly from
the existing probability of inclusion map. If a
given scene cannot be used, either for issues of
cloudiness or for lack of FIA data, then a
lookup-list will be constructed to locate the
scene closest in score to the missing scene.

1. For each frame, rank 100,000 ROTLs for each
   criteria score, and filter out any ROTLs below
   rank cutoffs of 0.90, 0.60, 0.70, and 0.70 for
   the four critera listed above, respectively. This
   results in filtered set sizes of 542 for the east
   and 392 for the west.
2. Re-rank sets according to forest diversity and
   forest area scores, add the two ranks, and
   re-sort ROTLs in order of descending total score.
   
3. Identify smallest set of ranked ROTLs where each
   scene is included at least once. All scenes have
   non-zero probability, but less desirable scenes
   occur less frequently in final filtered set. For
   the east, this final set had 253 ROTLs. For the
   west, this set had 196 ROTLs.

Estimates of forest area disturbed and regrowing
will be calculated for each year for each scene
in the sample, and yearly estimates of national
disturbance and regrowth-rates estimated using
Horvitz-Thompson estimators. Separately, decadal
estimates of disturbance and regrowth will be
modeled as functions of yearly rates and other
geospatial data.

• Pick one ROTL from the final list for each
  sampling frame. The ordered list of scenes is the
  final sample.
• Calculate probabilities of inclusion for each
  scene as the proportion of ROTLs in the final set
  in which that scene occurs. These probabilities
  allow for unequal-probability, design-based
  estimation.

The sampling design balances several competing
goals. Design-based estimation is possible
because the final sample is drawn at random from
a set in which each scenes probability of
inclusion can be calculated. By confining this
set to ordered lists of scenes that disperse
scenes and capture forest diversity, we diminish
the potential effects of spatial autocorrelation
and increase the range of conditions sampled,
both of which improve the likelihood of robust
model-based estimation. Scoring for focal scene
inclusion and for high-forest-area scenes
improves cost-efficiency. The use of ordered
lists of scenes (ROTLs) allows for easy expansion
of the sample the next scene in the ordered list
is chosen, and the probabilities of inclusion
re-calculated for the larger sample size.
a)
b)
EXAMPLE Probabilities of inclusion when each of
the four criteria scores is considered
separately. Higher probability of inclusion is
shown in warm colors. a). Scene dispersion forces
scenes to edges of forested area. b). Forest
diversity scoring captures scenes with many
forest types. c). Forest area scoring captures
with high total forest cover. d). Focal scene
scoring preferentially includes scenes whose
additional cost of analysis and processing is
much less than new scenes.
c)
d)
Presented by Kennedy at the Joint Workshop on
NASA Biodiversity, Terrestrial Ecology, and
Related Applied Science, Adelphi, MD, August
21-25, 2006.