# Dictionary

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Common terms and concepts used in Swedish forestry and Heureka:

## Volume measures

#### m3sk

Tree stem volume above the felling cut. Includes bark and top of the tree, but not branches.

#### m3fub

Volume of log(s) excluding bark.

#### m3fpb

Volume of log(s) including bark.

#### m3to

Volume of log(s) as given by a cylinder, with diameter = top diameter of the log under bark.

## Mean diameters

#### Dgv - Basal area weighted mean diameter

Basal area weighted mean diameter (cm):

$dgv = \displaystyle \frac{\sum_{i=1}^n{w_i d_i^3}}{\sum_{i=1}^n{w_i d_i^2}}$

where
$n$ = number of tree objects, and
$w_i$ = tree expansion factor for the number of trees that tree object i represents, and

$d_i$ = diameter at breast height for tree object i.
(You can of course also replace $d_i^2$ above with basal area of the tree)

Note: If there are more than one plot in a treatment unit, Heureka first calculates Hgv, Dgv, etc. for each plot, and then uses the plots basal areas and inclusion probabilities to calculate a plot-weighted average for the treatment unit.

#### Dg - Quadratic mean diameter

The diameter that corresponds to the mean basal area of the trees (cm). It is calculated as:

$dg = 100 \cdot \sqrt{\frac{4 G}{\pi N}}$

where
$G$ = sum of basal areas of trees (m2/ha) at breast height, and
$N$ = number of trees per hectar.
The multiplication with 100 is done to convert from m to cm.

## Mean heights

#### Hgv

Basal area weighted mean height (cm):

$hgv = \displaystyle \frac{\sum_{i=1}^n{w_i g_i h_i}}{\sum_{i=1}^n{w_i g_i}}$

where
$n$ = number of tree objects, and
$w_i$ = tree expansion factor for the number of trees that tree object i represents, and
$g_i$ = basal area at breast height for tree object i, and
$h_i$ = height for tree object i

Note: If there are more than one plot on a treatment unit, Heureka first calculates Hgv, Dgv, etc. for each plot, and then uses the plots basal areas and inclusion probabilities to calculate a plot-weighted average for the treatment unit.

## Financial measures

#### Net present value

Sum of discounted revenues minus costs, for an approximately infinite time horizon, and with the real discount rate set by the user. For even-aged management, Heureka approximates an infinite time horizon by assuming that the third forest rotation management regime will be repeated in perpetuity. For uneven-aged management, the last cutting is assumed to be repeated in perpetuity with a cutting time interval equal to the time elapsed between the last two cuttings projected.

For each alternative generated in even-aged management, Heureka generates up to three unique rotations. The reason for not just repeating the second management regime is to allow for the possible chang in growth conditions over time. The climate model, if activated in a simulation, affects site fertility so that a certain rotation will have a different growth potential than the previous one, and consequently the management regime should be adapted to that. The growth of plantations will also be affected by at which time planting is done, since breeding effects is assumed to increase over time. For example, trees planted in twenty years will give higher yields that trees planted today.

The net present value is calculated as

$NPV = \displaystyle \sum_{t=0}^{S} \delta_t R_t + \delta_{S}\cdot SEV$
where
S = Final felling year for the rotation preceeding the last rotation simulated, and
$R_t =$Net revenue in year t, with t = 0 marking year 0 of the planning horizon, and
r = Real discount rate, and
$\delta_t = \displaystyle (1+r)^{-t}=$discount factor for year t, and
SEV = Soil expectation value as given below

#### Soil expectation value

The soil expectation value (SEV) is by definition the net present value for an infinite time horizon when starting from bare land. In Heureka, the soil expecation value refers to the net present value of the last rotation simulated (assumed repeated in perpetuity). If you want to calculate the SEV with Heureka starting from today (year 0), you should use bare land as initial state.

The SEV is calculated as:

$SEV = \displaystyle \alpha\sum_{t=0}^{T} \delta_t R_t$ where
where T = Rotation length for the last forest generation,

α is the discount repeat factor for an eternal series and is calculated as

$\alpha = \displaystyle \frac{1}{1-({1+r})^{-T}}$

#### Terminal value

Heurekas also calculates a result variable called Terminal Value, which has an associated Terminal Value Year. The Terminal Value Year is usually the same as the year after the last planning period. The terminal value represents the part of the net present value that remains after the last planning period. The terminal value is calculated by subtracting the sum of discounted net revenues (that occurs until the last planning period) from the net present value, and the prolonging that value to the last year.