**Appendix A**

**Table A1.** A list of the reviewed models.


233




and long-wave emissivity

*Energies* **2022**, *15*, 4720


### **Appendix B**

This section explains how we developed the map that categorises the districts and areas in Europe. The reasons for the selection of each parameter and their related thresholds are not subjected to further analysis here but rather the process itself for replication. The analysis that was conducted in Section 3 led to the selection of the relevant raster files from the Hotmaps repository. These raster files were:


The first two rasters were relevant for producing the floor space index and the residential gross floor area percentage. To generate the latter, we utilised the raster calculator function in QGIS. We divided the residential gross floor area by the total gross floor area. Using a similar process, the total gross floor area was converted into an approximation of the *FSI* by simply dividing the raster by 10,000, as each pixel equalled one hectare and the pixel's value was expressed in square meters. Section 3 already explained the reasons behind the selection of each threshold; hence, it is not part of this section. This section explains how the rasters were changed to show the thresholds rather than the values. Again, the raster calculator included in QGIS was the tool that was used to generate the typologies of these rasters. Four bands were generated by setting the following conditions on each raster file:

$$\begin{array}{c} (("\mathbb{R}\_{\mathbf{x}}\text{''} > 0) \text{AND}("\mathbb{R}\_{\mathbf{x}}\text{''} \le t \text{1})) \ast p\_{1\mathbf{x}} + (("\mathbb{R}\_{\mathbf{x}}\text{''} > t \text{1}) \text{AND}("\mathbb{R}\_{\mathbf{x}}\text{''} \le t \text{2})) \ast p\_{2\mathbf{x}} + (("\mathbb{R}\_{\mathbf{x}}\text{''} > t \text{2}) \text{AND} \\\ ("\mathbb{R}\_{\mathbf{x}}\text{''} \le t \text{3})) \ast p\_{3\mathbf{x}} + ("\mathbb{R}\_{\mathbf{x}}\text{''} > t \text{3}) \ast p\_{4\mathbf{x}} \end{array} \tag{A1}$$

where *Raster<sup>x</sup>* is the raster subject to be transformed, t1 to t3 are the set thresholds and *p*1.*<sup>x</sup>* to *p*4.*<sup>x</sup>* indicate the prime numbers that were applied to the first to fourth bands of the *x th* layer. Each threshold was defined by a prime number rather than a letter as QGIS does not support strings as a data type. The use of prime numbers allowed for the creation of the final visualisation map. The final visualisation map raster condensed the information from each pixel in the three rasters (i.e., total gross floor area, share of residential gross floor area and final heat demand density) into one raster, as shown in Figure A1. QGIS does not allow the multiplication or addition characters; hence, we used prime numbers to track the original values.

**Figure A1.** The process for blending the three original layers into the visualisation map. The subscript y indicates the band to which pixel belongs.

The prime numbers allowed us to retain the information from all of the layers that made up the map. The product of three prime numbers could only be obtained by multiplying those exact prime numbers. It is important to note that each threshold had a different prime number related to it, as indicated in Table A2.


**Table A2.** The code to transform letter indicators into prime numbers and vice versa.

Let us consider an example in which a pixel on the map (i.e., one hectare) has a final heat demand that is indicated by A, a total gross floor area of B and a percentage of residential GFA of C. The resulting pixel on the visualisation map would have the value of the product of their prime number indicators (in this case, 638). Because this number can only be derived from the multiplication of these three prime numbers, each pixel can be unequivocally identified and categorised.

### **References**

