metrics.qmd

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# Possible metrics {#sec-metrics}

From the map of trenches (@fig-map1) we want to extract some numerical
value that we can assign to an area in order to describe the severity of
trenching. This metric, or variable, need to be

-   simple
-   interpretable
-   updatable
-   area explicit
-   scalable (optional)

It can be based on for example on some variation using the the length or
frequency of trenches. The area of trenches is less suitable, as
trenches are in reality linear elements even though we represent them
here as polygons. The polygons could be turned into line elements, for
example by finding the central lines using ET Geowizards. However, this
is computationally heavy, and we think that the length of the trenches
can be reasonably approximated using half the circumference, minus a
small penalty. The density of trenches is also less suitable as the
individual polygons are somewhat arbitrarily separated.

## Frequency-based metrics {#sec-fbm}

The frequency of trenches can be measured in many ways and at many
different scales. One way is to use the method described for NiN
variable `7TK` [@runehalvorsen2019]. This approach consists of gridding
the entire study region into 10𝖷10 m cells, and then categorizing the
cells as having or not having trenches. The frequency of grid cells with
trenches determines the variable value. There is a worked example of
this in @sec-7TK.

The upper and lower reference values for the variable may be defined
using the natural value of 0% and 100%, respectively. However, the
rescaling of the variable into an indicator should probably follow some
non-linear function, potentially aided by one or more class boundaries,
such as a threshold value representing the value of the variable that
defines the separation distinction good and bad ecosystem condition
[@jakobsson2020] . Expert opinion, possibly aided by real word data or
visual aids such as areal photos of areas with different variable value,
could be used to set this threshold value (as we later did; see
@sec-ref).

A different option for a frequency-based metric include counting the
proportion of mire units (e.g. hydrological units) that are affected by
trenching. This approach require that we know the population of mire
units, or that we have a good, balanced sample of such units, to base
our metric on. We do not have this currently. Secondly, the metric, as
is it described here, becomes quite sensible to errors in the trenching
model, and would probably require setting some (arbitrary) threshold
value for the *severity* of trenching on each mire unit.

## Length based metrics

As describes earlier, the length of trenches, and therefore also the
accumulated length for any given area, may be approximated by using half
the circumference of the trenching polygons (minus some small penalty).
This metric is very simple and easily interpretable. The metric is also
ecologically relevant, as the length of trenches is probably among the
metrices that best explain the impact of trenching on the landscape (in
combination with the depth of the trenches, but this is not something we
have data on currently).

The upper reference value must be defined as 0 m of trenches. The lower
reference value is not obvious, nor the threshold value. These could be
defined using expert opinion, as described for @sec-fbm.

### Area-based metric

The area affected by trenching can perhaps be estimated by adding a
buffer on the trenching polygons. The area affected by trenching as a
proportion of the total mire area is a nice and simple concept for an
indicator. The challenge is how to define the buffer. 10 m buffers have
been used in the past. However, the size of the effect from a trench
decreases non-linearly from the center of the ditch, and the length of
the effect zone will depend a lot on the local typography.

## Scalability

The metric chosen to inform the indicator on trenching should idealy be
scalable, meaning it can be calculated or interpreted at different
scale. The indicator might be useful for regional assessment of wetland
condition, as well as in local or project scale assessment, for example
in association with environmental impact assessments for new building
projects.

I believe the three methods describe above are all scalable and could be
used at local scales as well as regional scale (which is the main focus
here).