Estimating Forest Conversion Rates

1. Estimating Forest Conversion Rates Frank Roesch USDA Forest Service Southern Research Station Asheville, NC FRoesch@fs.fed.us (828)257-4871

2. FIA’s annual inventory Can Answer Not Only“What is There?”but also“How is it Changing?” Van Deusen, P.C. and F.A. Roesch. 2009. Estimating forest conversion rates with annual forest inventory data. Canadian Journal of Forest Research 39: 1993–1996. F. A. Roesch and P.C. Van Deusen . In review. Monitoring Forest/Non-Forest Land Use Conversion Rates with Annual Inventory Data.

3. Today – Some points to consider if you want to use FIADB for calculating conversion rates • The (not exactly) intuitively obvious question of how to define a conversion rate. • One Interesting Aspect of FIADB and its documentation that might lead the unwary into a world of unintended results. • Although FIA has always reported on change in some fashion, the calculation of conversion rates has not historically been a goal of FIA. However, every day, FIA data becomes better suited to the task.

4. Some foundation --Suppose There exists a “Universe” U of all Land And U can be completely and uniquely partitioned into identifiable categories: (Reserve category F for Forest) For each non-forest category there exists a probability function for a 1 step ahead transition to forest. Assume that future social and economic forces can be represented by a function which serves to act upon and change f. Ultimately of interest is an estimator of each f and a model g for each possible future scenario.

5. Forest at Time t U U-F F

6. Change in Forest from Times t to t+1 Forest to Non-Forest Non- Forest to Forest

7. Forest at Time t+1 If the Box should be the basis, should the box be defined as “all land” or as “all land that could be forest” ? If the latter, then FIA data could be treated as a “contaminated sample”. Box – (or U) as a basis for conversion rate? or Forest at Time t as a basis for the conversion rate?

8. FIA samples “All-Land”

9. South Carolina

14. A temporally-indifferent ratio estimator that you might think of as a “standard” FIA approach

15. Temporal Indifference vs. Stationarity • In a stationary process, a rate is constant, i.e. p%/yr. • Temporal indifference, as used by FIA, implies the observation interval is irrelevant. This is interpreted as meaning a change variable measured over n.r years can be divided by n.r to obtain an annual estimate. • Obviously a rate process cannot be both stationary and temporally indifferent.

16. The rate observed over Ti years on an FIA plot has this relationship to the annual rate: Note that we assume r is a stationary process – not temporally indifferent

17. A Better (Unbiased) Estimator that does not assume Temporal Indifference but does assume a stationary process is a weighted maximum likelihood estimatordescribed in:Van Deusen, P.C. and F.A. Roesch. 2009. Estimating forest conversion rates with annual forest inventory data. Canadian Journal of Forest Research 39: 1993–1996.

18. Overall conversion rate estimates from the most recent 5 panels (if available) of data for each of the 12 states in the study. The rates are based on the assumption that 20% of the observed non-forest to non-forest land could be forest. The forest to non-forest, non-forest to forest, and net loss conversion rates appear in the top, center, and bottom graphs, respectively.

19. Forest Conversion Trend Estimates. Forest to non-forest (top row), non-forest to forest (center row), and net forest loss (bottom row) conversion rates estimated from each the most recent 5 panels of data for Alabama (left side) and Virginia (right side). The rates are given based on the assumption that 20% of the observed non-forest to non-forest land could be forest. Confidence intervals of (+/-) 2(s.e.) are shown for the WML estimates.