United States 

Department of 

Agriculture 

Forest Service 

Southern Forest 

Experiment Station 

New Orieans, 

Louisiana 

Resource Bulletin 

SO-1 34 

Forest Growth of Mississippi's 

North Unit-A Case Study 

of the Southern Forest Survey's 

Growth Estimation Procedures 

Dennis M. May 
SUMMARY 

This report presents the pro~edures by which the Southern Forest Inventory 

and Analysis unit estimates forest growth from permanent horizontal point 

samples. Inventory data from the 19'77-87 survey of Mississippi's north unit 

were used to demonstrate how trees on horizontal point samples are classified 

into one of eight components of growth (survivor growth, ingrowth, mortality 

growth, cut growth, cull increment, mortality, cut, or landclearing) and, in turn, 

how these components are combined to derive estimates of forest growth (gross 

growth, net growth, and net change). Results indicate that the current growth 

estimation procedures provide reasonable and unbiased estimates of growth, 

removals, and mortality while providing statistically additive estimates of net 

change. 

May 1988 
Forest Growth of Mississippi's North Unit-A Case Study of the 

Southern Forest Survey's Growth Estimation Procedures 

Dennis M. May 

INTRODUCTION 

One objective of the Southern Forest Inventory and 

Analysis (FIA) unit is to periodically assess forest 

growth (gross growth, net growth, and net change) for 

each state in the hfidsouth region. Before the 1980 

survey of Tennessee, growth estimates were calculated 

for the calendar year prior to the year of the inventory, 

with the inventory being dated on the January 1 closest 

to the midpoint of the field work in a state. Thesegrowth 

estimates were composed of six main components: 

survivor growth, ingrowth, growth on ingrowth, growth 

on cut, mortality, and cut. Periodic annual estimates of 

the first five were derived from permanent horizontal 

point samples (HPS). The last component (cut) was 

derived mainly from canvasses of forest industry timber 

consumption. Estimates of other removals (trees that 

were killed for stand improvement, killed by logging, or 

removed in landclearings) derived from permanent HPS 

were also included in the cut component. As a result, the 

growth estimates were a mixture of sample estimates 

and deterministic measures. During the 1980 survey of 

Tennessee, the transition to calculating all growth 

components from permanent HPS was made. By the 

1982 survey of Alabama, the Beers and Miller (1964) 

approach to estimating growth and growth components 

from permanent HPS was incorporated into the Southern FIA data reduction procedures. 

Alabama's growth estimates using the Beers and 

Miller approach were criticized because the old~nventory 

plus the net change did not sum to the new inventory. 

Under this approach to forest growth estimation, unbiased estimates of forest growth can be obtained. 

Additivity, however, is not assured because of 1) intersurvey population differences caused by additions to or 

deletions from the forest land base due to reversions or 

landclearings and 2) differences in successive HPS 

caused by trees growing onto the points over the survey 

period. The trees that grow onto the HPS can be divided 

into two types: those that were of merchantable size at 

the first survey (nongrowth) and those that were not 

(ongrowth) (Martin 1982). Under the Beers and Miller 

continue to provide unbiased estimates of growth, as 

well as enhance additivity, the Southern FIA adopted the 

growth estimation procedures proposed by Van Deusen, 

Dell, and Thomas (1986). Their approach employs a new 

est imator of survivor growth for remeasured HPS that 

adjusts for the nongrowth trees excluded by the Beers 

and Miller approach, thus alleviating one of the reasons 

for nonadditivity. This "additive" approach has been in 

place in the Southern FIA data reduction procedures 

since the 1984 survey of Louisiana. To date, it has been 

used in Texas, Oklahoma, and Mississippi. 

CURRENT GROWTH 

ESTIMATION PROCEDURES 

Although minor refinements have been made to accommodate state-to-state changes in field techniques, the 

growth estimation procedures have remained essentially 

the same for all states subsequent to Louisiana 1984. 

Currently, separate estimates of growth are calculated 

for the growing-stock and sawtimber portions of the 

inventory. With the useof attributefilters(appendices 1, 

2 and 3) trees on Southern FIA plots (permanent HPS) are 

processed into one of the following growth components 

or subcomponents thereof: 

Survivor Growth 

Survivors. -Trees that survived from the first survey 

to the second survey and were of merchantable size and 

growing-stock quality in both surveys. Estimates of 

survivor growth for these trees are based on the difference between the volume and number of trees in the 

second survey and the volume and number of trees in the 

first survey-the change in volume to basal area ratio. 

itrungrowth. -Tree that grew onto the plot over the 

survey period and fell outside the plot defined by the 

limiting distance of the minimum size merchantable tree 

and were of merchantable size (based on predicted past 

diameter) and growing-stock quality in both surveys. 

Their estimates of survivor growth are based on the 

volume and number of trees in the second survey. 

approach, only ongrowth trees are accounted for in the I~~~~~~~ 

growth estimation procedures, hence the problem of 

additivity due to the exclusion of nongrowt h trees. To Ingrowth.-Trees that were tallied and of submer1)ennis M. May is a forester with the Southern Forest E:xperrment Station, lJSDA Forest Service, Starkville, MS. 
chantable size in the first survey but were of mechantable size and growing-stock quality in the second survey. 

Ongrowth. -Trees that grew onto the plot over the 

survey period and fell within the plot defined by the 

limiting distance of the minimum size merchantable tree 

or were of submerchantable size in the first survey 

(based on predicted past diameter), but were of merchantable size and growing-stock quality in the second 

survey. The estimates of ingrowth for both subcomponent~ are based on the volumes and numbers of trees 

in the second survey. 

Mortality Growth 

i'lfortality. -Trees of merchantable size and growingstock quality in the first survey that died before the 

second survey. Estimates of mortality growth for them 

are based on the volume change between the first survey 

and the time of death and the past number of trees. 

Mortality Ingrowth.-Trees that were tallied and of 

submerchantable size and growing-stock quality in the 

first survey that grew to merchantable size and died 

before the second survey. Estimates of mortality growth 

for these trees are based on the volume at the time of 

death and the past number of trees. 

Cut Growth 

This component accounts for the growth of trees that 

were cut (trees removed for timber products, killed 

during logging, or killed for stand improvements) during 

the intersurvey period. The cut growth component 

handles cut trees in the same manner that the mortality 

growth component handles dead trees. 

Cull Increment 

These are trees that changed tree classes between 

surveys (from growing-stock quality to cull or vice 

versaj, resulting in an imbalance in thegrowth estimates 

due to trees being included in one survey but not the 

other. These trees fall into one of the two following 

su komponen t s: 

Sound lo Cull. -Trees of merchantable size that were 

of growing-stock quality in the first survey but cull in 

the second survey. Balance is attained by subtracting a 

volume estimate based on the volume and number of 

trees in the first survey from the growth estimates. 

Cull to Sound. -Trees of merchantable size that were 

cull in the first survey but of pouring-stock quality in 

the second survey. Balance is attained by adding a 

volume estimate based on the volume and number of 

trees in the second survey to the growth estimates. 

Mortality 

This component is composed of the same two subcomponents that make up the mortality growth component. The estimates of mortality volume for both 

subcomponents are based on the volume at the time of 

death and the number of trees at the first survey. 

Cut 

This component is handled in the same manner as the 

mortality component, except for the use of cut trees in 

place of mortality trees. 

Landclearing 

This component includes trees on forested plots that 

were of merchantable size and growing-stock quality in 

the first survey that, because of a land-use change, are 

classified as being on nonforest plots in the second 

survey. The estimates of the volumes landcleared are 

based on the volume and number of trees at the first 

survey. 

The component volumes for each tree are expanded to 

the county level using the remeasured expansion factor. 

The remeasured expansion factor is the current number 

of forested acres represented by each remeasured plot in 

a county. Plots that have reverted to forest and those 

that have been cleared are not considered to be remeasured plots. As a result, reversions receive the average 

growth of remeasured plots in a county, and landclearing 

volume estimates are expanded to the county level by the 

expected expansion factor for a Southern FIA plot, 5,760 

acres. Because reverted and cleared plots occur infrequently in most counties and the true number of acres 

they represent cannot be ascertained under the current 

sampling scheme, this method of handling reversion 

growth and landclearing removals is acceptable. From 

this point, the county level component volumes for each 

tree are either summed to yield periodic component 

estimates or divided by the intersurvey period for each 

plot and then summed to yield average annual component estimates. The algorithms used to process sample 

tree component volumes are shown in appendices 2 and 

3. From the component estimates, county, unit, or state 

level estimates of forest growth (gross growth, net 

growth, and net change) can be derived. 

GROWTH ESTIMATES AND COMPONENTS 

FOR MISSISSIPPI'S NORTH UNIT 

The recently completed 1977-87 inventory of the north 

unit of Mississippi provides an example of how forest 

growth estimates are derived from growth compnen t 

estimates (table 1. j. The growt h components are logically 

organized into two categories-t hose that add to the 

initial inventory and those that subtract from it. The 

four components that increment the initial inventory are 

survivor growth, ingrowth, mortality growth, and cut 

growth. The sum of these four growth components is an 

estimate of gross growth. 
Table 1.-Periodicgrouith contponents and atimates ofgross growth, net growth, and ilzventoq change for 

hi'ississifillli's north unit, 1977-87i 

Growth estimate-rowth commnent Subcommnent Softwood Hardwd Total 

Survivor grow h 

( f! 

Ingrowth 

i+i 

Mortality growth 

i+) 

Cut growth 

+i 

Total Gross growth 

Cull increment 

(+/-I 

Total Adjusted gross growth 

Mortality 

!-i 

Total Net growth 

Cut 

(-) 

(-1 Landclearing 

(-1 Total removal 

Total Net change 

Survivors 

Nongrowth 

Total 

Ingrowth 

Ongrow th 

Total 

Mortality 

Mortality ingrowth 

Total 

Cut 

Cut ingrowth 

Total 

Sound to cull 

Cull to sound 

Total 

Mortality 

Mortality ingrowt h 

Total 

Cut 

Cut ingrowth 

Total 

Landclearing 

lColumns may not add due to rounding. 

'if) or (-i indicate whether the subcomponent increments or decrements the initial inventory. 

Gross Growth of gross growth, mortality growth and cut growth, are 

In the north unit, gross growth, the measure of the 

initial inventory's gross increase over the survey period, 

averaged 6.8 percent per year, for a total increase of 66.5 

percent for the period. The survivor growth component 

constitutes 170 percent of thegrossgrowth estimate. The 

nongrowth subcomponent, in turn, accounts for 70 

percent of the survivor growth component. Because of 

the magnitude of the nongrowth subcomponent, which 

individually accounts for half of the gross growth 

estimate, the inclusion of nongrou~th trees in the survivor growth component would seemingly overestimate 

growth. However, this is not the case. Under the current 

growth estimation procedures, nongrow t h serves to 

offset the effect of survivor trees growing larger over the 

intersurvey period and having a corresponding smaller 

expansion to the acre (Van Deusen and others 1986, 

Martin 1982). 

Ingrowth, the next component that serves to increment the initial inventory, contributes 10 percent of the 

gross growth estimate for the north unit. The ongrowth 

subcomponent accounts for three-quarters of this 

component's contribution to gross growth. 

The contributions of the two remaining components 

dependent upon three factors: 1) the amount of mortality 

or cut during the intersurvey period, 2) the growth rate 

of the trees before death or removal, and 3) the elapsed 

time between the initial survey and the time of death or 

removal. The com bined effect of these three factors is the 

reason for cut growth's 15 percent contribution to the 

gross growth of the north unit being three times that of 

mortality growth. 

Adjusted Gross Growth 

Because the Southern FIA only estimates growth for 

the growing-stock portion of the inventory, the gross 

growth estimates must be adjusted to account for 

changes in tree class over the period, i.e., trees that 

changed from growing-stock to cull or vice versa because 

of tree deterioration, growth, or cruiser judgement. The 

changes in tree class cause imbalances in the growth 

estimates due to growing-stock trees being included in 

one survey but not the other. The adjustment is handled 

through the cull increment component, which can either 

increment or decrement the gross growth estimate, 

dependingon the net result of summing the sound-to-cull 
and cull-to-sound subcomponents. The sound-to-cull 

sukomponent accounts for trees that changed from 

growing stock to cu tl over the period and decreases the 

gross growth estimate. The cull- to-sound subcomponent 

accounts for trees that changed from cull to growing 

stock and increases the gross growth estimate. 

In the north unit, cull increment has a positive net 

effect (more volume went from cull-to-sound than soundto cull), increasing the gross growth estimate by half of 1 

percent. The sound-to-cull subcomponent is comprised 

of smaller trees than the cull-to-sound subcomponent, 

This indicates a tendency for cruisers to give smaller 

trees the benefit of the doubt when initially assigning a 

tree class, with the reclassification to cull occurring in 

subsequent surveys when the impacts of normal development and disturbances can be better assessed. In 

contrast, the cull-to-sound reclassification occurs more 

frequently in larger hardwood trees. This is primarily 

the result of cruiser subjectivity due to the higher 

incidence of decay and deformity within larger 

hardwoods. 

Net Growth 

Net growth is a measure of the increment of the initial 

inventory subsequent to the impacts of natural tree 

mortality. The mortality component accounts for the 

drain on the initial inventory caused by natural tree 

mortality. In the north unit, the vast majority, 86 

percent, of the mortality component estimate is due to 

the death of larger trees accounted for in the mortality 

subcomponent. However, the mortality ingrowth subcomponent is also responsible for a sizeable proportion as 

a result of high Ievels of mortality in the smaller size 

classes due to tree competition as part of normal stand 

development. As might be expected then, this subcomponent's volume was concent rated in the general1 y 

more intolerant softwoods. The same estimate of 

mortality ingrowth is used in both the mortality growth 

and mortality components. As a result, mortality ingrowth has no net effect upon the net growth or net 

change estimates. But, because it does provide a better 

estimate of the mortality occurring over the period, it is 

included and will impact the gross growth estimate. 

Decrementing the adjusted gross growth estimate for 

the impact of natural mortality results in a measure of 

the initial inventory's net growth. In the north unit, the 

initial inventory experienced an average mortality rate 

of 1.0 percent per year, resulting in an average net 

growth of 3.9 percent per year for the period. In total, the 

initial inventory increased by 37.2 percent over the 

period. 

Net Change 

Net change is a measure of the difference between the 

initial and final inventories. It is estimated by reducing 

the net growth to account for the impacts of man-caused 

removals over the period. The man-caused removals are 

accounted for in the cut and landclearing components. 

Over the period, the north unit experienced an average 

removals rate of 4.5 percent per year, resulting in an 

average net change of 1.4 percent per year. On the whole, 

the initial inventory increased by 13.3 percent over the 

period. The cut component is responsible for 90 percent 

of the removals in the unit. Because of the preference for 

cutting trees in the larger diameter classes, the cut 

sukomponent accounts for almost all of the cut estimate. This subcomponent is mainly composed of larger 

trees that were cut and utilized, while the cut ingrowth 

subcomponent is composed of smaller trees that were 

mainly killed during loggmg. Although contributing a 

small proportion of the total cut estimate, the cut 

ingrowth subcomponent does provide a better estimate 

of the cut volume over the period. And like mortality 

ingrowth, equal estimates of cut ingrowth are included 

in the cut growth and cut components so that cut 

ingrowth has no net effect upon the net change 

estimate. It does, however, impact the gross and net 

growth estimates. Overall, cutting reduced the initial 

inventory of the north unit by an average of 4.1 percent 

per year over the period. 

The landclearing component is responsible for the 

remainder of the total removals estimate. In contrast to 

the cut component, which is often composed predominantly of soft woods, the landclearing component is 

generally dominated by hardwoods because of the preference for bottomlands in agricultural conversions. 

Such was the case in the north unit, where hardwoods 

comprised over 60 percent of the landclearing component 

and the softwoods comprised over 60 percent of the cut 

component. 

The ratio of growth to removals for the unit is 1.3, 

which bodes well for the inventory as a whole. When 

broken down by species group, the ratios are 1.1 for 

softwoods and 1.6 for hardwoods. These follow a southwide trend of high utilization of the soft wood resource 

and underutilization of the hardwood resource. 

ADDITIVITY 

A check for additivity requires consideration of sampling errors. The Southern FIA sampling scheme was 

designed to provide st ate-level estimates of forest area 

and volume with acceptable sampling errors. Sampling 

error is a function of the inherent variability of the 

population being sampled and the number of samples 

taken. In most cases, the larger the sample, the lower the 

sampling error. Therefore, forest resource statistics for 

sub-state areas and for finer breakdowns of volume (i.e., 

gro~s-th component volumes) will involve fewer samples 

and larger sampiing errors. The additivity check for the 

north unit is shown in table 2. The predicted inventory 

volume (initial inventory plus net change) comes within 
2 percent of the actual current inventory. Although not 

perfectly additive, the predicted inventory is well within 

the 3.1-percent sampling error of the 1987 inventory. A 

95-percent confidence interval about the current inventory spans the range of 4,390.7 to 4,958.7 million 

cubic feet. This easily encompasses the predicted 

inventorq' volume. 

Another way of testing the estimate of net change is to 

compare it with the inventory change (volume #2- 

volume #I). These two estimates of the intersurvey 

change (537.8 and 632.8 million cubic feet, respectively) 

differ by 95.0 million cubic feet. Given the sampling 

errors for each of these change estimates, (25.6 percent 

for the net change estimate and 20.7 percent for the 

inventory change estimate), they are not statistically 

different (appendix 4). Although mathematical additivity 

has not been achieved, statistical additivity has. 

As expected, the additive approach yielded net change 

estimates that were almost identical to the inventory 

change estimates for remeasured plots (appendix 5). The 

cause of the variability in the net change estimate can 

best be described as the difference between the reconciled initial inventory, used to calculate net change, and 

the actual initial inventory, used to calculate inventory 

change. The difference is usually due to differences in 

volume estimation techniques or in field procedures. 

The first of these differences (volume estimation techniques) is ameliorated by matching trees in the initial 

inventory with trees in the current inventory. This 

ensures that the initial volume and the reconciled initial 

volume are the same for each remeasured tree. Since the 

initial and current volumes are calculated by using the 

same deterministic volume equation, any growth componen t changes are truly representative of biological 

change for each tree. 

The second of these differences (field procedures) is an 

inherent part of the survey and will always be present. 

These field differences include trees missed in either 

survey, substituted plots or points because the original 

could not be found, substituted points because of 

proximity to nonforest conditions, inaccessible plots 

(which receive the average plot volume for the county), 

and forked trees that (because of growth) are now 

considered to have only one stem. The differences 

resulting from these add to the variability of the growth 

estimates, but fortunately they occur infrequently. They 

are also responsible for the minor difference between the 

plot volume totals for the actual initial inventory (661,000 

Table 2.-Additivity check for illississi~pi's mrth unit, 1977-87 

Additivity Softwood Hardwood Total 

--.. lfi/jio12 czrbicfeef ---...-....- 

Initial inventory, 19177 1.791.4 2,250.5 4,041.9 

Net change +124.0 +413.23 +%537.8 

Predicted current inventorq, 1987 1,915.3 2,663.3 4,579.7 

Actual current inventory, 1987 1,9,55.7 2,718.9 3,674.7 

Difference -40.3 -54.6 -95.0 

cubic feet) and reconciled initial inventory (660,500 cubic 

feet). 

Therefore, forest population differences due to additions to or deletions from the forest land base as a result 

of reversions or landclearings are responsible for most of 

the nonadditivity o~curring in the north unit. As previously stated, the true number of reverted acres is 

unknown under the current sampling scheme. Thus, 

reverted plots receive the ak3erage growt h for remeasured 

plots. Over a large enough sample (state-level), this 

met hod of allocating growth to reverted acres should 

work reasonably well because some rekrersions have 

inventory volumes and some do not. This approach, 

however, can cause additivity problems if there are not 

enough reverted plots without inventory volume to 

counterbalance those with inventory volume. In order 

for mathematical additivity to occur, the net change 

assigned to the reverted acres should match the inventory on the reverted acres. In most instances, this would 

certainly overestimate growth on the reverted acres over 

the period. 

One other quirk with this method of handling reversion growth is that for counties where removals exceed 

growth, the net change volume assigned to the reverted 

acreage will be negative. Although cutting does occur on 

reversions, it seems reasonable that it would not be high 

enough to cause reversions to have negative net change 

estimates. Fortunately, this problem is relatively small. 

The impact of the current method of handling reversion growth in the north unit can be approximated by 

determining the difference between the current inventory on the 66 reversions in the unit and the estimated 

net change assigned to the reversions. The current 

inventory for the 66 reversions was 197.7 million cubic 

feet, and the net change volume assigned to these 

reversions totaled 72.0 million cubic feet. This is 125.7 

million cubic feet shy of mathematical additivity. This 

net change estimate translates to an annual change rate 

of 3.7 percent for the period, suggesting that the average 

growth assigned to the reversions was out of proportion 

to the actual inventory on the reversions. This is due in 

part to the hl reversions that had no inventory volume 

but still had an average net change assigned. Therefore, 

predicting a reasonable estimate of reversion growth 

may be preferable to achieving additivity, which would 

result in even higher rates of change on reversions. 

Additivity problems also shotv up with the current 

method of handling Iandcleared plots. In landclearings, 

the initial inventory of the plot is removed from the 

inventory. Since the actual number of Iandcleared acres 

is unknown, the expected number of acres a plot should 

represent (5,760) is used to expand the plot volumes to 

the county. Using 5,760 acres is a fair enough assumption given a large enough sampIe. However, additivity 

problems occur because the expected expansion factor 

seldom matches the initial inventory expansion factor. 

In the north unit, the estimated initial inventory of the 
35 cleared plots was 177.3 million cubic feet, while the 

actual initial inventory was 191.0 million cubic feet. In 

terms of additivity, landclearing volume was underestimated. 

When both landclearing and reversion additivity 

problems are taken into acmunt, the net change for the 

unit is underestimated by 112.1 million cubic feet. When 

the net change estimate is adjusted for this difference, 

the estimated inventory comes within 0.4 percent of the 

actual intrentory . However, beca~se the number of acres 

reverted or landcleard over the period is unknown, the 

effects upon additivity can only be estimated and should 

only serve to reveal two major sources of nonadditivity 

in the Southern FIA net change estimates. 

In conclusion, all forest survey statistics are sample 

estimates and each has an associated sampling error. 

For estimates of forest growth, the variability of the 

estimates can be quite large. With this in mind, as well 

as an understanding of some of the major sources of 

variability and nonadditivity in the growth estimates, 

the growth components provide reasonable and unbiased 

estimates of the unit's growth, removals, and mortality 

while providing a statistically additive estimate of net 

change. 

LITERATURE CITED 

Beers, T. W.; Miller, C. I. 1964. Point sampling: research 

results, theory and applications. Purdue University 

Agricultural Experiment Station. Res. Bull. 786.55 p. 

+ insert. 

Martin, G.L. 1982. A method for estimating ingrowth on 

permanent horizontal points. Forest Science. 28: 

111-1 14. 

Van Deusen, P.C.; Dell, T.R.; and Thomas, C.E. 1986. 

Volume growth estimation from permanent horizontal 

points. Forest Science. 32: 415-422. 

Appendix I .-Definitions 

Current-refers to the second survey or time of death 

for mortality and cut trees. 

Past-refers to the first survey. 

Ground use - 20 = forest 

> 20=nonforest due to land-use change 

Sample kind - 4 or 6zremeasured plots 

Tree class and past twe class- 10 and 20=growing stock 

trees 

3O=rough cull 

4Ozrotten cull 

D.b.h.-must be at least 5.0 inches to be included in 

growing stock growth. Softwoods rnust be at 

least 9.0 inches to be included in sawtimber 

growth, and hardwoods must be at least 11.0 

inches to be included in sawtimber growth. 

Tree size-3=sawtimber 

2=pole 

l=sapling 

Tree histories- 1, 11, 12, 15=survivor trees 

3=ongrowt h tree 

2 1,22=mortality trees 

31,32,33,34=cut trees 

35,36,37,38=landclearing trees (21,22 

also included if on a landcleared plot) 

Dista~zce-7.1 feet=limiting distance for minimum size 

(5.0-inch) growing stock growth 

tree. 

12.8 feetzlimiting distance for minimum 

size(9.0-inch) softwood sawtimber 

growth tree. 

15.6 feet=limiting distance for minimum 

size (1 1 .O-inch) hardwood sawtimber growth tree. 

Elapsed time-refers to the intersurvey period (in 

years). 

Rem. exp, factor-refers to the remeasured expansion 

factor-acres represented by one remeasured plot in a county at the time 

of the second survey or 5,760 acres/ 

plot for landclearing plots. 
Appendix 2.-~ississi~~i Growth ~ornponents and Tree Filters for Growing Stock, 1987 

Crowing Stock (in cubic feet) 

Gross growth = survivor growt h + ingrowth + mortality growth + cut growth 

Adjusted gross growth = gross growth - sound to 

cull + cull to sound 

Net growth = adjusted gross growt t-t - mortality 

Yet change = net growth -- cut - landciearing 

Survivor growth = ia + b) 

(a) Sum of [(current volume * current trees/acre - 

past volume * past treelacre) * rem. 

exp. factorielapsed time] 

Filters: ground use = 20 

sample kind = 4 or 6 

tree class = 20 

past tree class = 10 or 20 

d.b.h. and past d.b.h. > = 5.0 inches 

tree histories = 1, 11, 12, 15 

(b) Nongrowth = sum of (current volume * current 

treesiacre " rem. exp. factor/ 

elapsed time) 

Additional filters: tree history = 3 

distance > 7.1 feet 

past d.b.h. > = 5.0 inches 

Ingrowth 

Sum of (current volume * current treeslacre* rem. 

exp. factorielapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

tree class =20 

d.b.h. > = 5.0 inches 

past d.b.h. < 5.0 inches 

tree histories = 1, 11, 12, 15 

Additional filters for ongrowth trees: 

tree history = 3 

distance < = 7.1 feet or past d.b.h. 5.0 

hfortality growth = (a + b) 

(a) Sum of [(current volume - past volume) * past 

trees/acre * rem. exp. factor/elapsed 

time] 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

d. b.h. and past d.b.h. j = 5.0 inches 

tree histories = 21 or 22 

(b) Sum of (current volume * past treeslacre * rem. 

exp. factor,/elapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

d. b.h. = 5.0 inches 

past d.b.h. < 5.0 inches 

tree histories = 21 or 22 

Cut growth = (a + b) 

(a) Sum of [(current volume - past volume) " past 

treeiacre * rem. exp. factor/elapsed time] 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

d. b. h. and past d. b. h. > = 5.0 inches 

tree histories = 31,32,33,34 

(b) Sum of (current volume * past treeslacre * rem. 

exp. factorielapsed timej 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

d.b.h. > = 5.0 inches 

past d.b.h. < 3.0 inches 

tree histories = 31,32,33,34 

Mortality 

Sum of (current volume * past trees/acre * rem. 

exp. factorielapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

d.b.h. and past d.b.h. =- = 5.0 inches 

tree histories = 21 or 22 

Additional filters for mortality ingrowth trees: 

d.b.h. > = 5.0 inches 

past d.b.h. ( 5.0 inches 

Cut 

Sum of (current volume * past trees/acre * rem. 

exp. factorlelapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

d.b.h. and past d.b.h. > = 5.0 inches 

tree histories = 31,32,33,34 

Additional filters for cut ingrowth trees: 

d. b.h. > = 5.0 inches 

past d.b.h. 5.0 inches 

Landclearing 

Sum of (past volume * past trees/acre * rem. exp. 

factor/elapsed time) 

Filters: ground use > 20 

past tree class = 10 or 20 

past d.b.h. 7 = 5.0 inches 

tree histories = 21,22,35,36,37,38 

Cull increment 

Sound to cull = sum of (past volume * past treeslacre 

* rem. exp. factor/elapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

tree class =- 20 

past tree class = 10 or 20 

past d.b.h. = 5.0 inches 

tree history = 11 

Cull to sound = sum of (current volume * current 

treesiacre * rem. exp. factorielapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

tree class = 20 

past tree class > 20 

past d.b.h. > = 5.0 inches 

tree history = 11 
Appendix 3--~ississi~~i Growth Components and Tree Filters for Sawtimber, 1987 

Sawtimber fin board feet-International I/? rule) 

Gross growth = survivor growth + ingrowth + mortality growth + cut growth 

Adjusted gross growth= gross growth - sound to cull + 

cull to sound 

Net growth = adjusted gross growth - mortality 

Net change = net growth - cut - landclearing 

Survivor growth = (a + b) 

(a) Sum of [(current volume * current treedacre - 

past volume * past treesiacre) * rem. exp. 

factor/elapsed time] 

Filters: ground use = 20 

sample kind = 4 or 6 

tree class = 20 

tree size and past tree size = 3 

tree histories = 1, 11, 12, 15 

(b) Kongrowth = sum of (current volume * current 

trees/acre * rem. exp. 

factorielapsed time) 

Additional filters: tree history = 3 

softwood-distance 7 12.8 feet and past 

d.b.h. > = 9.0 inches 

hardwood-distance > 15.6 feet and past 

d.5.h > -= 11.0 inches 

lngrowt h 

Sum of (current volume * current trees,/acre * rem. 

exp. factor/elapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

tree class = 20 

tree size = 3 

past tree size < 3 

tree histories = 1, 11, 12, 15 

Additional filters for ongrowt h trees: 

tree history = 3 

softwood-distance < 212.8 feet or past 

d.b.h < 9.0 inches 

hardwood-distance < = 15.6 feet or past 

d.b.h. 4 11.0 inches 

Mortality growth = (a + b) 

(a) Sum of [(current volume - past volume) * past 

treeslacre " rem. exp. factor/elapsed 

time] 

Filters: ground use = 20 

sample kind = 3 or 6 

past tree class = 10 or 20 

tree size and past tree size = 3 

tree histories = 21 or 22 

rb) Sum oft :urrent volume * past treesiacre * rem. 

exp. factor 'elapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

tree size = 3 

past tree size 4 3 

tree histories = 21 or 22 

Cut growth = (a + b) 

(a) Sum of [(current volume - past volume) * past 

treesiacre * rem. exp. factorlelapsed 

time] 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

tree size and past tree size = 3 

tree histories = 31,32,33,34 

tb) Sum of (current volume * past treesiacre * rem. 

exp. factori'elapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

tree size = 3 

past tree size 4 3 

tree histories = 31,32,33,34 

Mortality 

Sum of (current volume * past trees/acre * rern. exp. 

factor/elapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

tree size and past tree size = 3 

tree histories = 21 or 22 

Additional filters for mortality ingrowth trees: 

tree size = 3 

past tree size 3 

Cut 

Sum of (current volume * past treesiacre * rem. 

exp. factor/elapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

past tree class = 10 or 20 

tree size and past tree size = 3 

tree histories = 31,32,33,34 

Additional filters for cut ingrowt h trees: 

tree size = 3 

past tree size < 3 

Landclearing 

Sum of (past volume * past treedacre * rem. 

exp. factor/elapsed time) 

Filters: ground use > 20 

past tree class = 10 or 20 

past tree size = 3 

tree histories = 21,22,35,36,37,38 

Cull increment 

Sound to cull = sum of (past volume * past treesiacre 

* rem. exp. factor/elapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

tree class > 20 

past tree class = 10 or 20 
past tree size = 3 

tree history = 11 

Cull to sound = sum of (current volume * current 

treesiacre * rem. exp. factor/ 

elapsed time) 

Filters: ground use = 20 

sample kind = 4 or 6 

tree class = 20 

past tree class " 20 

past tree size = 3 

tree history = 11