1. METHODS FOR ASSIGNING TREE GROWTH TO CLASSIFICATION VARIABLES James A. Westfall U.S. Forest Service Forest Inventory and Analysis

2. INTRODUCTION  FIA collects or creates numerous classification variables to assist in creating many tables of possible interest to users.  There are cases where the value of the classification variable is different at the initial measurement (T1) and the subsequent measurement (T2). Tree diameter class is one of the most common class changes over time, but others also occur, e.g., growing stock, forest type, stand size, ownership.  When these classification shifts occur, one must determine which class the change over the interval is assigned to. In the most common case, which diameter class should changes in tree volume be assigned to?

3. INTRODUCTION  Change estimation = GRM = Growth, Removals, Mortality  Net Growth = Gross growth – Mortality  Key sustainability metrics often compare Removals and Net Growth  Net Growth/Removals  Net Growth – Removals  Ray Sheffield noted at the 2010 FIA Symposium that estimates of inventory change derived by subtracting removals from growth do not closely match how inventories have actually changed by diameter class.

4. TRADITIONAL METHOD  Traditional FIA methods do not account for volume shifts across classified attributes that can change value between time 1 and time 2. They summarize the difference in volume on individual trees between time 1 and time 2 and assign this difference to either the previous or current classification.  Generally, the change value was assigned to the T1 classification, e.g., the diameter class the tree belonged to at time T1. Thus, growth tends to be ‘overestimated’ for the smaller diameter classes and ‘underestimated’ for larger diameter classes.

5. ISSUE Annual softwood inventory change using Net Growth minus Removals method and actual inventory change * from Ray Sheffield

6. SOLUTION  New Net Growth Accounting system accounts for movement out of and into classes that change between inventories.  Implemented by using a new table TREE_GRM_ESTN that contains multiple records per tree.  There is one record for the all live estimation type on forestland  Additional record if tree qualifies as growing-stock  Additional record if tree qualifies as a sawlog tree  Above records also exist for timberland where applicable  Possible total of six volume records per remeasurement tree in FIADB * from Jeff Turner

7. SOLUTION  Recall FIA midpoint methodology for GRM  Change is assumed to occur at the midpoint of measurement interval  Not applicable to survivor trees  For mortality, removals, diversions growth is from Time 1 to midpoint  For reversions, growth is from midpoint to Time 2  For Ingrowth, size threshold often used instead of midpoint  These concepts are incorporated into the Net Growth Accounting method.

8. SOLUTION  Survivor Trees  ANN_NET_GROWTH = (EST_END – EST_BEGIN)/ REMPER  (EST_END / REMPER) assigned to end class  – (EST_BEGIN / REMPER) assigned to begin class  Ingrowth Trees  ANN_NET_GROWTH = (EST_THRESHOLD + EST_END – EST_THRESHOLD) / REMPER  EST_END / REMPER assigned to end class  Reversion1 Trees (larger than threshold at interval midpoint)  ANN_NET_GROWTH = (EST_MIDPT + EST_END – EST_MIDPT) / REMPER  EST_END / REMPER assigned to end class * from Jeff Turner

9. SOLUTION  Reversion2 Trees (smaller than threshold at interval midpoint)  ANN_NET_GROWTH = (EST_THRESHOLD +EST_END – EST_THRESHOLD) / REMPER  EST_END / REMPER assigned to end class  Cut1/Diversion1 Trees (Removals)  ANN_NET_GROWTH = (EST_MIDPT - EST_BEGIN) / REMPER  (EST_MIDPT / REMPER) assigned to mid-point class  – (EST_BEGIN / REMPER) assigned to begin class  Cut2/Diversion2 Trees (crossed threshold before midpoint)  ANN_NET_GROWTH = EST_MIDPT / REMPER  EST_MIDPT / REMPER assigned to mid-point class * from Jeff Turner

10. SOLUTION  Mortality1 Trees  ANN_NET_GROWTH = (EST_MIDPT - EST_BEGIN - EST_MIDPT) / REMPER  – EST_BEGIN / REMPER assigned to begin class  Mortality2 Trees (crossed threshold before midpoint)  ANN_NET_GROWTH = (EST_THRESHOLD + EST_MIDPT - EST_THRESHOLD – EST_MIDPT)/REMPER  (EST_MIDPT – EST_MIDPT) / REMPER = 0  Why? Net growth = growth – mortality; so midpoint volume is subtracted out for mortality trees, but not for cut/diversions.  Much more detailed explanations in Jeff Turner’s 2012 FIA Symposium presentation – available upon request. * from Jeff Turner/Scott Pugh

11. SOLUTION Annual softwood inventory change using Net Growth minus Removals method and actual inventory change * from Ray Sheffield

12. CONCLUSION  The traditional FIA methods and net growth accounting methods are just 2 possible ways to handle change over time.  FIA EVALIDator tool now has up to 5 options to choose from – the most appropriate option depends on the question you are asking.  Accounting  Current  Previous  Previous if available else current  Current if available else previous

13. QUESTIONS ?? Balsam Fir - 1950 Red maple - 1937