METHOD

A sample design for Landsat-based estimation of national trends in forest disturbance and regrowth

Presented by Kennedy at the Joint Workshop on NASA Biodiversity, Terrestrial Ecology, and Related Applied Science, Adelphi, MD, August 21-25, 2006.

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, NASA’s Goddard Space Flight Center, Greenbelt, MD 20771

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

DISCUSSION

INTRODUCTION

a) b)

c) d)

FINAL SAMPLE

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.

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 Service’s 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.

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.

GOALS

Western sampling fame Eastern sampling fame

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 >2% cumulative forest cover (n= 156 East, n= 122 West).

Example of TSAs for scenes in Maryland

FIA Forest type map with eastern and western frames delineated

4. For eastern and western frames separately, create 100,000 randomized ordered lists of TSAs (ROTLs).5. Define the potential sample for each ROTL as the first n*1.4 scenes, where n=11 East and n=9 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

1. Scene Dispersion.

Across scenes in the sample, calculate euclidean distance of each scene’s nearest neighbor and rank ascending among scenes. Score is the total of distances in bottom half of ranked distances.

2. Forest diversity

Divide forest area by type in the sample by forest area in the stratum and rank ascending among types. Score is the total of proportions in bottom half of ranked proportions.

3. Total forest area

Rank ascending forest area among scenes in sample. Score is the total of scenes in bottom half of ranked areas.

4. Focal scenes

Score is count of focal scenes (see below) included in sample.

Foc

al s

cene

s

6. 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.

7. 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.

8. 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.

9. Pick one ROTL from the final list for each sampling frame. The ordered list of scenes is the final sample.

10. 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.

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.

Final Sample

Probabilities of inclusion for use in estimation

West

37/34

35/34

34/37

37/32

47/28

36/37

41/32

43/33

41/29

35/32

45/29

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

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 scene’s 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.

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.

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.

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