# Association between Land Surface Temperature and Green Volume in Bochum, Germany

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## Abstract

**:**

## 1. Introduction

#### 1.1. The Formation and Properties of Urban Heat Islands

#### 1.2. Green Spaces, Green Area, and Green Volume

^{3}/m

^{2}[32]. GV is a three-dimensional quantity, which necessitates a three-dimensional survey. The derivation of a GV is made possible by using so-called digital terrain models (DTM), which can be derived from laser scanning data such as LiDAR [32]. Thus, GV provides information about the volume of “all plants standing on a green space” [31]. GV is particularly important in urban areas for the natural balance and the well-being of the inhabitants [33]. The greater the volume, the greater the positive impact on the environment [31]. For example, GV improves the climate by balancing the humidity and regulating the temperature [31], which is followed by a decrease in LST [34].

#### 1.3. Problem, Aims, Case Study, and Study Design

#### 1.3.1. Case Study: Bochum, Germany

#### 1.3.2. Research Questions and Study Design

- How does the green volume affect surface heat islands in Bochum?
- a.
- Does the spatial pattern resemble a heat island or a heat archipelago?
- b.
- What is the correlation between LST and GV?
- c.
- What are the contributions of a vertical structure and type of green space on LST?
- c.
- How do SHI distributions across urban districts relate to human populations?

## 2. Materials and Methods

#### 2.1. Remote Sensing Data to Support LST Anlysis

#### 2.2. LST Time-Series Calculation Procedure

_{λ}) [49]:

_{L}and A

_{L}are taken from the metadata, where M

_{L}is the multiplicative rescaling factor (RADIANCE_MULT_BAND_x) and A

_{L}is the additive rescaling factor (RADIANCE_ADD_BAND_x). Both factors are band-specific. Q

_{cal}represents the current value of the pixel or the DN value [49]. Spectral radiance is required to calculate the brightness temperature [50]. For this purpose, the spectral radiance is converted to at-satellite brightness temperature (T) [50]:

_{2}(1321.0789) is divided by the logarithm of the calibration constant K

_{1}(774.8853) divided by the spectral radiance L

_{λ}plus one [51]. The corresponding values of the calibration constants K

_{1}and K

_{2}of band 10 can be taken from the Landsat 8 metadata [50]. However, the calculated temperature data are in Kelvin and must be converted to °C. For this conversion step, the Kelvin value 273.15 must be subtracted from the calculated at-satellite brightness temperature to obtain the corresponding °C value [51].

_{s}is the Boltzmann surface temperature, T

_{b}is the temperature of a blackbody, and ε corresponds to the object-specific emissivity. The object-specific emissivity ε is defined as: “the radiation intensity of an object at a certain temperature and wavelength in relation to the intensity of a black body radiator of the same temperature and wavelength [53]”. It is a measure of the thermal radiation of an object and provides information about how much thermal radiation, for example, a floor surface exchanges with its surroundings [54]. The emissivity is influenced by various factors, such as the water content and depends on an object’s material properties or roughness [53]. According to Boltzmann’s law, an “ideal black body” is assigned an emissivity of ε = 1, where the radiation hitting such a body is completely absorbed [54]. Moreover, a black body has a constant absolute temperature. The specific radiation of a real surface in relation to that of the black body is called the substance-specific emissivity and is less than 1 [55,56]. Since different land cover and object types exist and this diversity is also shown on satellite images, an average emissivity must be chosen to represent the emissivity of all objects.

_{V}corresponds to the emissivity of vegetation areas, ε

_{S}corresponds to the emissivity of open soils, and P

_{V}corresponds to the ratio of vegetation to open soils. The ratio of vegetation to open soils P

_{V}is calculated as [58]:

_{b}, and the object-specific emissivity, ε [52]. For this purpose, the formula of Stefan Boltzmann was applied (Equation (3)). The four LST calculations, each exported in raster format, were combined in the geographic information software ArcGIS Pro using unweighted raster math to produce an average value for Bochum (Figure 4).

#### 2.3. Green Volume Calculation Procedure

- Use of an NDVI mask to isolate vegetation;
- Development of a normalized digital surface (Oberfläche in German) model (nDOM) that contains heights of all objects between the soil and atmosphere within the NDVI envelope;
- Postprocessing of nDOM to remove outliers or confounding objects;
- Generation of the ‘vegetation nDOM’ as GV.

#### 2.3.1. NDVI Vegetation Mask

#### 2.3.2. Generation of a Normalized Digital Surface Model (nDOM)

#### 2.3.3. DTM and DOM Data Processing

^{3}/m

^{2}, an interpolation to the grids with a ground resolution of one meter was used. At the same time, this resolution considered that a resolution of at least four points per recorded square meter was included [66]. Therefore, the interpolation technique was a triangulation-based natural neighbor interpolation based on test runs with different methods. A DOM and DTM as rasters with a ground resolution of one meter were developed from this process. The nDOM was then calculated with the aforementioned subtraction of the individual raster values from each other.

#### 2.3.4. Postprocessing and Creation of the Vegetation nDOM (GV)

^{3}/m

^{2}for Bochum (Figure 6).

#### 2.4. Statistical Analysis of Heat Island and Green Volume

## 3. Results

#### 3.1. LST Analysis

#### 3.2. Green Volume Distribution

^{3}/m

^{2}across all city quarters, indicating a very high spatial heterogeneity of GV throughout Bochum. The least average GV is observed in Mitte (1.84 m

^{3}/m

^{2}), where the heat island stress is also the greatest. The greatest GV is located southward of Bochum on the hilly vegetated bluffs of the Ruhr River Valley, where lower LST values are observed in Südwest and Süd districts having, on average, 3.08 and 2.83 m

^{3}/m

^{2}, respectively. Although we summarized the GV for the district Wattenscheid, this value is not accurate, since the orthophoto-based NDVI dataset for part of this city had a different angle of reflection than in other tiles (Figure 11).

#### 3.3. Statistical Association of Green Volume and Heat Islands in Bochum

^{3}/m

^{2}. Conversely, when we extracted GV in areas with the lowest observed LST (under 21 °C), the GV was over 15 m

^{3}/m

^{2}. These spatial overlay observations hint at a negative correlation between the GV and the LST and possibly a SHI-inducing breakpoint when the GV is less than 1 m

^{3}/m

^{2}. Indeed, the Pearson’s correlation resulted in a significant (p < 0.05) borderline moderately negative correlation between the GV and LST (r = −0.482), where increases in the GV correlate with a decrease in the LST values and vice versa (Figure 13).

#### 3.4. Contribution of Green Space Typology on LST

## 4. Discussion

^{2}= 0.6031). Weber et al. [34] found an even stronger causal relationship between temperature reduction and GV increases via model simulation (R

^{2}= 0.941), supporting the conclusion that GV could be a stronger indicator for LST reduction than the NDVI. In summary, our study supports the findings from past studies and provides further indicators for the positive effects of GV in reduction of SHIs.

#### 4.1. Drawbacks to the Study

#### 4.2. Future Research Directions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Urban heat island (own representation according to [16]).

**Figure 3.**Flow chart for calculation of LST (own representation after [46]).

**Figure 5.**Ranges of physiological equivalent temperature (PET) for different degrees of human thermal perception and human physiological stress (own representation after [59]).

**Figure 7.**Distribution of heat islands in Bochum (own representation). Boxes (a–c) are shown as insets in Figure 8.

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Schmidt, P.; Lawrence, B.T.
Association between Land Surface Temperature and Green Volume in Bochum, Germany. *Sustainability* **2022**, *14*, 14642.
https://doi.org/10.3390/su142114642

**AMA Style**

Schmidt P, Lawrence BT.
Association between Land Surface Temperature and Green Volume in Bochum, Germany. *Sustainability*. 2022; 14(21):14642.
https://doi.org/10.3390/su142114642

**Chicago/Turabian Style**

Schmidt, Pauline, and Bryce T. Lawrence.
2022. "Association between Land Surface Temperature and Green Volume in Bochum, Germany" *Sustainability* 14, no. 21: 14642.
https://doi.org/10.3390/su142114642