Height Calibration

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[[::Height Calibration|English]]  • [[::Height Calibration/sv|svenska]]

When importing a stand register to be used as input data the program simulates tree lists with the help of diameter distribution functions. For every tree created the tree height is calculated with height functions (). These functions are based on tree sample data from the National Forest Inventory and covers all regions in Sweden. For specific stands, the actual tree heights will of course differ from those projected. Therefore, it is possible to let the system adjust the calculated heights. The purpose of using a height function is to obtain a realistic height distribution, so that not all trees have the same height.

Calibration is done in two steps, first for each tree species (if species-wise mean height exist in the import file), and then for the for the stand as a whole (if the mean height for the stand is available). The calibration is done separately for each species and tree layer (main layer and over-storey trees).

Calculation of calibration ratios

The calibration ratios are in principle calculated as follows (see about weighting below).

Step 1 - Species-wise as mean height specified in the import file

The calibration ratio for species s and layer k is calculated as

där
H_register (s,k) = Mean height for species s (and layer k) according to the import file.
H_funktion (s,k) = Basal area weighted mean value of the calculated tree heights for trees of species s (and tree layer k).

The calculated tree height are then adjusted (multiplied) with q(s,k). Example: If the calculated mean height for pine is 10 m but the mean height according to the import data is 12 m, the ratio i 12/10 = 1.2, which means that the calculated height of each pine is increased by 20 %.

Step 2 - Calibration at stand level

In this step a similar ratio is calculated as in step 1, but for all trees independent of tree species. It is the adjusted tree height calculated in step 1 that are used to calculate av H_function.

där
H_register(k) = Mean height for layer k for the stand according to the import data.
H_function (k) = Basal are weighted mean height for all created trees (that belong to layer k), adjusted with the factors calculated in step 1.

The height functions are quite robust, while compartment data often contain unreliable tree height estimates. Therefore, there is a built-in restriction for how much the calculated height can be adjusted. By default, the limits are set to max +/- 30 %. This means that the calculated ratios are bounded by the interval [0.7, 1.3]. The limits can be changed by the user in control table Production Model. Example: If the mean height according the import data is 14 m but 10 m according the functions, the ratio is 1.4. Because this is larger than 1.3, the ratio is set to 1.3.

Weighting

The formulas above are somewhat simplified, because there is also an adjustment included that lets a user define the relative importance between the data in the import file and the function values. When simulating the tree list, the user can enter a weighting value [between 0 and 1], in dialog Simulate Tree List.

With weighting, the formula for step 1 is:

and for step 2:

where w = a value between 0 and 1 for how much the imported data should weigh compared to the function values.

Examples:

• A weight of zero (w=0) means that no calibration should be done, and the function values be used as they are.
• w = 1 mean that calibration should be done according to step 1 and 2 above, i.e. the import data should be used for calibration to the largest degree allowed, given the restrictions on the q-values described above.
• w = 0.5 means that import data and function values should have equal weight. If the mean height according to the import data is 12 m and 10 m according the function, the resulting mean height will be 11 m (q = [0.5*12 + (1-0.5)*10]/10 = 11/10 = 1.1). The restriction of the value of q is applied after this weighting, for example: If the mean height according to the import data is 14 m but 10 m according to the function, then ratio q is 1.4 if w = 1. With w = 1 it should be adjusted to 1.3 if the default bounds are used. However, with w = 0.5 the ratio is 1.2 (q = ([0.5*14 + (1-0.5)*10]/10 = 1.2) which is within the allowed range.