🔬 Dive into the Background Theory

This section provides a deeper look into the data, mathematics, and methodology behind RegionMatch.

You do not need this section to use the plugin. It is intended for users who want to understand how similarity is computed, how data are prepared, and how configuration choices influence the results.

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1. Mathematical Description of Similarity

This section describes how RegionMatch translates multidimensional regional characteristics into a single similarity score.

1.1 Feature Selection and Weighting

Let \(A\) denote the set of comparison aspects:

• climate

• sociodemography

• orography

• land use

Each aspect \(a \in A\) is associated with a feature vector:

\[X_a \subseteq \mathbb{R}^n\]

Users assign a numeric weight to each aspect:

\[w_a \in \{0,\; 0.5,\; 1\}\]

Weight \(w_a\)	Meaning
1.0	high relevance
0.5	medium relevance
0.0	low relevance

The sum of all weights defines the maximum possible similarity score:

\[S_{\text{max}} = \sum_{a \in A} w_a\]

This implies that the scale of the similarity score depends directly on the selected weights.

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1.2 Distance Calculation

For each aspect \(a\), the distance between the reference region \(x_0 \in \mathbb{R}^n\) and another region \(x_i \in \mathbb{R}^n\) is computed using the standardised Euclidean distance:

\[d_a(x_0, x_i) = \sqrt{ \sum_{j=1}^{n} \frac{(x_{0j} - x_{ij})^2}{\sigma_j^2} }\]

where \(\sigma_j^2\) denotes the variance of feature \(j\) across all regions.

In the implementation, this is computed using:

scipy.spatial.distance.cdist(
    target_features,
    all_features,
    metric="seuclidean",
    V=variances,
)

Standardisation ensures that indicators with large numeric ranges do not dominate the distance calculation.

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1.3 Similarity Score Construction

Raw distances are transformed into similarity values by normalising and inverting the distance range:

\[s_a(x_0, x_i) = 1 - \frac{d_a(x_0, x_i) - d_{\min}}{d_{\max} - d_{\min}}\]

This transformation ensures that:

• values close to 1 indicate high similarity

• values close to 0 indicate low similarity

Each aspect-specific similarity is then weighted according to user-defined relevance:

\[S(x_i) = \sum_{a \in A} w_a \cdot s_a(x_0, x_i)\]

with

\[w_a \in \{0,\; 0.5,\; 1\}\]

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2. Data Basis

RegionMatch relies on a harmonised table that combines administrative, sociodemographic, land use, orographic, and climate information for all German districts (NUTS3 level).

2.1 Overview of Input Data

Data	Unit	Aspect	Source
NUTS_CODE	n.a.	Description	Bundesamt für Kartografie und Geodäsie
NUTS_NAME	n.a.	Description	Bundesamt für Kartografie und Geodäsie
Total area	km²	Sociodemographic	DESTATIS
Total population	n.a.	Sociodemographic	DESTATIS
Population density	1/km²	Sociodemographic	DESTATIS
Population over 65	%	Sociodemographic	Deutschlandatlas
Urban & traffic areas	%	Land use	Deutschlandatlas
Agricultural land	%	Land use	Deutschlandatlas
Forest area	%	Land use	Deutschlandatlas
Orography type	n.a.	Orography	NUKLEUS ensemble
Hot days	days	Climate	NUKLEUS ensemble
Longest dry spell	days	Climate	NUKLEUS ensemble
Heavy precipitation days	days	Climate	NUKLEUS ensemble
Tropical nights	days	Climate	NUKLEUS ensemble

Climate indicators are based on near-surface values, provided as 30-year means for the historical period and as changes relative to the historical period for +2 °C and +3 °C global warming levels.

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3. Climate Indicators

The following climate indicators are used:

Indicator	Abbreviation	Definition
Hot days	TXge30	Days with daily maximum temperature ≥ 30 °C
Tropical nights	TR	Days with daily minimum temperature > 20 °C
Heavy precipitation days	R30mm	Days with precipitation ≥ 30 mm
Longest dry spell	CDD	Longest sequence of days with precipitation < 1 mm

Indicator definitions follow the Climpact standard indices.

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4. Spatial Aggregation of Climate Data

German district geometries are derived from NUTS3 shapefiles provided by the Federal Agency for Cartography and Geodesy (german: Bundesamt für Kartografie und Geodäsie). These geometries are converted to GeoJSON and filtered to include only land districts.

The geometries are then used to spatially aggregate climate model output using regionmask, xarray, and cosine-latitude weighting.

This approach allows efficient computation of district-level climate indicators.

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5. Orography Classification

Orography is provided as elevation (meters above sea level) in the NUKLEUS model data.

Each district is assigned an orography type based on the maximum elevation within its boundaries:

Type	Condition	Code
Lowland	max < 200 m	0
Upland	200–500 m	1
Highlands	500–1500 m	2
High mountains	≥ 1500 m	3

These numeric codes are used directly in the similarity calculation.

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6. Code Structure and Data Updates

6.1 Main Components

• run_plugin.py: Core similarity computation

• utils.py: Visualisation, mapping, and output generation

• prepare_data.py: Input data preparation

6.2 Updating the Data Basis

Data preparation is decoupled from the plugin logic and handled via scripts in data/.

Running the preparation workflow:

• downloads updated sociodemographic and land use data

• computes climate indicators

• determines orography types

• assembles the final input table used by the plugin

This separation ensures reproducibility and easier maintenance.

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