Assisi supports a a large number of volume calculation options. This study is a discussion of what the options are and how volume is calculated. First an overview...

The volume in trees has historically been calculated using volume tables, volume equations or using tree taper. Assisi uses the terms "Volume Tables" and "Volume Equations" to mean whole tree volume rather than the volume of logs. The term "Log Segmenting" means using taper models to calculate log volumes. The volume of logs is of calculated using a equations, but for organizational purposes, Assisi groups volume calculation methods into these three types.

**Volume Tables**

Volume Tables are tables of tree volume by species, DBH, height and often form class. The values were derived from field studies and were put into this form for convenience before computers were available. The volume in Volume Tables can be board or cubic, merchantable or total height. The tables imply merch standards such as stump height, trim, merch diameters and a unit of volume. Sometimes there are multiple tables available covering a variety of merch options. Height can be expressed as feet or meters or expressed as the number of fixed length logs up to a merch diameter.

Volume Tables are whole tree volumes meaning a single number is looked up that represents the estimated volume from stump to merch or total height. To get the volumes of individual logs, a Volume Distribution table can be used. Volume distributions are the percent of tree volume present in each individual fixed length log. Volume distributions also imply certain merchantability standards such as log length and trim.

*Volume Tables and Volume Distribution tables shown for Norway Spruce in the Calibration **Editor. Settings at top set the tree size range the volumes in the table cover, volume type and log length.*

**Volume Equations**

Volume equations also give the volume of whole trees, but do so through calculating a volume equation. Volume equations were initially made to estimate the volumes found in volume tables and so often carry with them the same merch specifications as volume tables. Later equations began to add terms for the merch specifications themselves such as scaling diameter. Volume distributions can be used with volume equations just like they are used with volume tables.

*Volume Equations shown for Norway Spruce in the Calibration Editor. Equations can be entered and parsed by Assisi or one of the many internal equations can be chosen.*

**Log Segmenting**

The Log Segmenting method of volume calculation uses equations for the volume of individual logs themselves. Log segmenting requires the length and diameters of each log therefore, taper equations are frequently used when using Log Segmenting.

Log segmenting allows more merchandising flexibility because stump, trim and even the lengths of logs can be anything desired. The equations used to calculate the volume of individual logs often assume a certain taper within a log length but the length of the log itself can be anything desired. Board equations often assume certain kerf and saw patterns as well. Cubic equations do not.

When using the Log Segmenting method of volume calculation, there are many ways to specify the length of logs. Log lengths can be a fixed length. They can be variable lengths using market definitions as a guide or they can be called in the field directly. Field measured log lengths allows calling out cull sections and assigning assumed grades as well.

*The Log Scaling settings for Douglas Fir in the Calibration editor. Log Segmenting allows for a large variety of segmenting trees into logs.*

**Taper Equations**

Taper equations are equations to calculate diameters at points along a main tree stem. Taper differs by species, region, age, site and other factors so there are many different kinds of taper equations. Each equation requires a set of measurements such as DBH, total height, merch height, form point height, etc. These are often measured in the field but they can also be estimated using other equations.

*Taper options for White Fir shown in the Calibration Editor. Taper can be mapped to other species, parsed, expressed as a simple code, be composed of log counts or use one of many researched taper equations.*

**Example Log Segmenting**

The process of log segmenting is often described as "walking" up a tree from stump to tip stopping at certain points to delineate individual logs. The diameters of the logs are calculated using the tree's taper function.

For example, say we have a 24" 150' Douglas fir tree. At stump we calculate a diameter and start "walking" up the tree. We stop at the top of the first log which may have been called in the field or has been set to a fixed length of 16'. Once there, we calculate the top diameter and use a log volume equation such as Scribner, international quarter inch or Smalian to calculate the volume of the first log. We then skip a small section called log trim and calculate the diameter of the what will be the bottom of the second log. Again we continue until the top of the second log is reached and calculate volume in the same way. This process continues until we reach a stopping point that is usually the height to a certain minimal diameter called the merch diameter. There are a lot of settings that can fine tune this process but all share these general steps.

*The output of calculating log segments for a 35", 122' White Fir. The chart shows trees with total and merch height measured (green) and estimated (red). The blue highlighted shows the individual logs and trim between then that were estimated given the scaling settings and the taper equation used for White Fir (Walters & Hann, 1986).*

**Example Volume Tables**

The first step in calculating volume via volume tables is looking up the total merch volume in a volume table. Consider a 19" 6 log Black Cherry...

The board volume table for black cherry has the following settings and values:

```
'Volume Table Limits
DBHMin = 4
DBHMax = 40
DBHStep = 1
HeightMin = 8
HeightMax = 80
HeightStep = 8
HeightType = MERCH
HeightsRelativeTo = STUMP
'Trees Outside Volume Table Limits
'true = Truncate DBH and TH to nearest point on table.
'false = Trees outside limits have 0 volume.
IsTruncate = true
```

*Black Cherry Volume Table settings.*

The settings say the table covers DBH from 4 to 40" in 1" steps. Height from 8 to 80 in 8' lengths. The height to use to look up height int he table is the "Merch" height with heights relative to "Stump". Trees with DBH or heights that are beyond the table limits are set to be "Truncated" to the nearest point on the table. IE, larger or smaller trees will get the volume of the nearest size class in the table. What about trees with DBH or height in between table entries? In this case, the volume is linearly interpolated from the nearest 4 points in the table.

Below is the actual values for the Black Cherry volume table. The volume units are international 1/4" MBF units.

*Black Cherry Volume Table values.*

Volume tables sometimes use form class as a lookup variable along with DBH and height. In this case form class is treated like DBH and height in the sense that if the tree's form class is not found directly in the table, the nearest form class in the table will be used. This particular volume table uses a single form class of 82 for all values effectively removing form class as a lookup variable. Ie., 82 will be the "nearest" form class regardless of a tree's actual form class.

For trees with merch height called as the count of fixed length logs rather than in feet directly, we need to convert from the log count (6 in our case) to feet. The log length setting is made in the Log Length Default Length setting for the calibration.

*The length of logs for log called trees is set on the Calibration | Scaling view in the Calibration Editor.*

The units of volume are in international 1/4" MBF units. The units of volume depend on the values entered in the table rather than any calibration settings. Ie., units depend on the source of your volume tables.

For our 19" 6 log tree, with no form class, we find a direct board volume entry at FC82, 19" & 48' of .4004 international 1/4" MBF for this tree. Multiply this value by TPA to get volume per acre represented by this tree.

The second step is distributing this volume to the trees 6 logs. This is done using a Volume Distribution table. A volume distribution table is a list of the percent whole tree volume to assign to individual logs. For a tree with 6 logs, there will be 6 entries with lower logs having higher percentages than upper logs.

There is a single setting for volume distributions that simply says whether to use distributions or not. If true, the whole tree volume looked up above will be distributed to individual logs. If false, volume will be recorded only for the whole tree, not individual logs.

`IsUseVolumeDistributions = True`

*Black Cherry Volume Distribution values.*

We can see from the table for our Black Cherry, log volumes in MBF will be the following with the total of log volume being equal to the whole tree volume: .4004 MBF.

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