**1. Introduction**

All bodies in the universe with a temperature greater than zero can emit radiation. After the emission of radiation, the next step is its propagation to a second body through the air or space, where different processes arise: reflection, scattering, absorption, refraction, dispersion, and transmission of radiation [1]. Solar radiation is a term that refers to the energy flow produced by the sun in the form of photons or electromagnetic waves [2], which provides energy to the atmosphere, clouds, and the earth's surface. How energy flows to enter and leave the earth's surface is known as the surface energy balance. This process determines the surface temperature and is closely related to the atmosphere and surface elements (e.g. water, rocks, and vegetation) [3].

Net radiation is a crucial factor in the energy balance of the surface, serving to study characteristics of the earth's surface such as albedo, emissivity, temperature, and humidity, and thermal processes of the soil. Also, it is the leading actor in

processes such as soil and air heating, photosynthesis, evapotranspiration, crops and water resources [4–6]. In an urban environment, net flux regulates climate and heat distribution. Therefore, when these areas grow uncontrollably and impermeable materials replace the earth's surface, the energy balance of the surface is affected, and problems such as heat islands arise [7, 8]. Besides, the heterogeneous nature of urban areas causes the kinetic and thermodynamic properties of the surface to change dramatically if the physical characteristics of the soil are modified. As a result, this causes cities to have unique microclimates [6].

Generally, net radiation is measured from meteorological stations with the help of radiometers. However, these expensive instruments do not effectively represent the net flux variation throughout the territory and do not accurately reflect its effects on the earth's surface [6]. However, other techniques have been developed to measure net radiation effectively. Remote sensing is a science focused on acquiring the electromagnetic energy emitted or reflected by the earth in the form of digital images to obtain information about an object without being in direct contact with it [9]. In addition, data can be continuously produced with high spatial resolutions and at a regional scale [10]. Net radiation retrieval through remote sensing allows its estimation in topographically complex areas. Radiative transfer models, meteorological data, and Digital Elevation Models (DEM) are often necessary to compute net flux [10, 11]. Various technological advances have been made these days by applying remote sensing to estimate net flux with high spatial resolution and precision, trying to reduce dependence on meteorological data [7, 10–14].

The city of San Luis Potosí has experienced gradual and unplanned growth during the last decades, mainly in the city's peripheral areas [15], which in conjunction with the lack of green spaces in the area, has caused an imbalance in the climate, raising temperatures in some parts of the city. A study carried out in the city of San Luis Potosí shows that deforestation worsens the heat island phenomenon; however, as it is only a descriptive methodology of the urban tree canopy [16], it is not thoroughly analyzed why this occurs. Therefore, it is essential to understand how net radiation behaves in the city and what factors affect the urban climate. This work's main objective is to evaluate net radiation behavior in the city of San Luis Potosí through a multi-temporal analysis applying remote sensing. This analysis will serve to determine the net flux influence degree on the urban climate of the area, which is crucial to support decision-making for the improvement of urban planning and the establishment of mitigation measures for heat island phenomena.

#### **2. Remote sensing processes for net radiation computation**

#### **2.1 Study area**

The city of San Luis Potosí is the capital of the San Luis Potosí State, which is part of the 32 states that make up the Mexican Republic, located in the north-central zone of the state between the parallels 22.2214° and 22.0058° North latitude and the meridians �101.0566° and �100.7743° West longitude (**Figure 1**). According to the 2020 Population and Housing Census derived from the National Institute of Statistics and Geography (INEGI) [17], the study area has a population of 1,243,980. The city has an average elevation of 1860 meters above mean sea level and is considered an area with a dry-semi-desert climate. The average level of precipitation is 245 mm. However, this value varies depending on the year. The mean temperature is 16.8°C.

*Evaluation of Net Radiation in San Luis Potosí City – México, with Remote Sensing Processes... DOI: http://dx.doi.org/10.5772/intechopen.110707*

**Figure 1.** *Study area location.*

#### **2.2 Data acquisition**

In order to evaluate energy throughout the San Luis Potosí city, it was necessary to obtain a DEM at a resolution of 30 m from INEGI. Also, satellite images from the Landsat 5 TM and 8 OLI/TIRS sensors were used, with a spatial resolution of 30 m.

The study was developed for the period 1990–2017, and two representative images of the region's rainy and dry seasons per year were needed. **Table 1** describes the characteristics of the sensors used. Landsat 5 TM can record the electromagnetic energy reflected and emitted by the earth's surface in seven different wavelengths (three bands in the visible spectrum, one near infrared, one shortwave infrared and one thermal infrared). While Landsat 8 has two instruments: OLI, composed of nine bands from the visible spectrum to the short-wave infrared, and the TIRS sensor, consisting of two spectral bands in the thermal infrared region [18].

**Table 2** shows the images used by each sensor for path and row 28/45. These images were downloaded from the Earth Explorer page (https://earthexplorer.usgs.g ov/) managed by the US Geological Survey (USGS). For the Landsat 5 TM sensor, ten images acquired in the period 1990–2009 were used, and for Landsat 8, four images were downloaded in the period 2015–2017.

#### **2.3 Preprocessing for Landsat imagery**

The digital number of the satellite images must have a standard and representative scale to calculate the net flux. For this reason, it is necessary to apply a radiometric


#### **Table 1.**

*Landsat 5 TM and Landsat 8 OLI/TIRS spectral bands.*

correction. In this case, the methodology proposed by Chander et al. [19] (Eq. (1)) was used. The process described was developed for the Landsat 5 TM sensor; however, it can also be used for the Landsat 8 sensor, considering that the gain and bias factors are band-specific values and can be found in the image metadata.

$$L\_{\lambda} = \mathbf{G}\_{\text{reccale}} \times \mathbf{Q}\_{\text{cal}} + \mathbf{B}\_{\text{reccale}} \tag{1}$$

where *L<sup>λ</sup>* is the spectral radiance (W/m<sup>2</sup> sr μm); *Qcal* is the digital number of the pixel; and *Grescale* and *Brescale* are band-specific rescaling factors of gains and bias from the sensor. For Landsat 8 OLI/TIRS *Grescale* is RADIANCE\_MULT\_BAND\_x and *Brescale* is RADIANCE\_ADD\_BAND\_x from metadata.

#### **2.4 Net radiation calculation**

For this study, energy retrieval was computed using the processes described by Allen et al. [20]. Net flux is the energy flow from the sun and the earth's surface [14]. It is computed by extracting the incoming short wave and long-wave radiation and the outgoing long-wave radiation (Eq. (2)):

$$R\mathbf{a} = R\mathbf{s}\boldsymbol{\downarrow} - \mathbf{a}R\mathbf{s}\boldsymbol{\downarrow} + RL\boldsymbol{\downarrow} - RL\boldsymbol{\uparrow} - \left(\mathbf{1} - \mathbf{e}\_0\right)RL\boldsymbol{\downarrow} \tag{2}$$

*Evaluation of Net Radiation in San Luis Potosí City – México, with Remote Sensing Processes... DOI: http://dx.doi.org/10.5772/intechopen.110707*


**Table 2.**

*Satellite images used to obtain net radiation.*

where *Rs*↓ is the incident shortwave radiation (W m�<sup>2</sup> ); *α* is the superficial (dimensionless) albedo; *RL*↓ is the incident long-wave radiation (W m�<sup>2</sup> ); *RL*↑ is the reflected long-wave radiation (W m�<sup>2</sup> ); and *ε*<sup>0</sup> is broad band (dimensionless) surface thermal emissivity. The term (1 � *ε*0) *RL*↓ represents the incident long wave fraction reflected from the Earth's surface.

#### *2.4.1 Incident wave radiation*

Defined as the difference between the incident short-wave radiation (W m�<sup>2</sup> ) on the Earth's surface and the short-wave radiation reflected to the atmosphere (Eq. (3)): *Rs*<sup>↓</sup> is one of the essential fluxes to estimate the net radiation, its calculation was carried out from a Digital Elevation Model of the study area:

$$R\_{\uparrow\downarrow} = \frac{G\_{\rm SC} \cos \theta\_{rel} \tau\_{so}}{d^2} \tag{3}$$

where *GSC* is the constant of solar (1367 W m�<sup>2</sup> ), *θrel* is the solar incidence angle, *d*<sup>2</sup> is the relative distance between the earth and the sun (Eq. (9)), and *τs<sup>ω</sup>* is transmissivity of the atmosphere, to determine the level of atmospheric transmissivity present in the study area, we use the function expressed in the Eq. (4). Knowing the transmissivity of the atmosphere is crucial to determine the transmissivity *Rs*↓value. *τs<sup>ω</sup>* for the study area was determined from its atmospheric pressure and the water content in the atmosphere. (Eq. (4)).

$$\tau\_{\rm so} = 0.35 + 0.627 \exp\left[\frac{-0.00146 \, P}{K\_t \cos \theta\_{\rm hor}} - 0.75 \left(\frac{W}{\cos \theta\_{\rm hor}}\right)^{0.4}\right] \tag{4}$$

where *P* is the atmospheric pressure (kPa), *W* is the water content in the atmosphere (mm), and *θhor* is the zenithal solar angle on a horizontal surface. *Kt* corresponds to a turbidity coefficient of 0 < *Kt* < 1.0, in which *Kt* = 1.0 is used in areas with clean air, while *Kt* = 0.5 is used in areas with extreme turbidity, dust, or polluted air. *P* calculating its variation with respect to elevation pixel by pixel using a Digital Elevation Model (DEM) and applying the following formula (Eq. (5)):

$$P = 101.3 \left( \frac{293 - 0.0065 \, z}{293} \right)^{5.26} \tag{5}$$

where 293 is the standard air temperature (K) and *z* is the altitude above sea level (m). *W* (mm) is obtained from near-surface vapor pressure data, which are obtained from meteorological stations within the study area by applying (Eq. (6)). In this work, *e* represents vapors pressure near the surface and was calculated pixel by pixel from the dew point recorded in the study area. This represents an advantage because *W* was not only taken as a constant value of a meteorological station but its special variation throughout the study area was determined.

$$W = \mathbf{0}.\mathbf{1}4e\_a P\_{air} \tag{6}$$

The solar incidence angle is defined as the angle existing between the solar beam and a vertical line perpendicular to the earth's surface. In order to calculate *θrel*, slope and aspect are extracted from the DEM and Eq. (7) is applied:

$$\cos\theta\_{rl} = \begin{aligned} \sin\delta\sin\rho\cos\nu - \sin\delta\cos\rho\sin\kappa\cos\gamma + \cos\delta\cos\rho\cos\kappa\cos\omega \\ + \cos\delta\sin\rho\sin\kappa\cos\gamma\cos\omega + \cos\delta\sin\gamma\sin\kappa\sin\omega \end{aligned} \tag{7}$$

where *δ* is the Earth' declination (positive during summer in the northern hemisphere); *φ* is the pixel latitude; *s* is the slope; *γ* is the surface aspect angle; and *ω* is the hour angle.

#### *2.4.2 Surface albedo*

Surface albedo is the quantity of radiation that is reflected by the earth's surface; it is a biophysical characteristic that regulates net flux. Its value varies according to the land cover, and in some cases, a low albedo value (as it is in the case of urban cover) represents an increase in temperature. It is estimated by using wavelengths capable of reflecting energy (Eq. (8)).

$$\mathfrak{a}\_{s} = \sum\_{b=1}^{n} \left[ \rho\_{s,b} w\_{b} \right] \tag{8}$$

where *Wb* is the weighting coefficient representing the solar radiation fraction on the surface that occurs within the spectral range in a determined band [20]; *n* is the number of bands of the sensor; and *ρs,b* is the surface reflectance of each band, which *Evaluation of Net Radiation in San Luis Potosí City – México, with Remote Sensing Processes... DOI: http://dx.doi.org/10.5772/intechopen.110707*

was calculated using the Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) method, eliminating aerosols' effect, intrinsic radiance introduced into the sensor and reflected in the image. This method includes the MODTRAN radiative transfer code [21].

#### *2.4.3 Reflected long-wave radiation*

This flux is a surface-driven radiation produced by temperature and emissivity, and to obtain it we used the Stefan-Boltzmann equation (Eq. (9)): The calculation of this variable was used to understand how the land surface of the study area is heated.

$$R\_{L\uparrow} = \mathfrak{e}\_0 \sigma T\_S^4 \tag{9}$$

where *e*<sup>0</sup> is the surface emissivity (dimensionless); *σ* is Stefan Boltzmann constant (5.67 � <sup>10</sup>–8Wm�<sup>2</sup> <sup>K</sup>�<sup>4</sup> ); and *TS* is the temperature of surface (K). The surface emissivity is estimated using the Eq. (10). *e*<sup>0</sup> was obtained from the LAI (Leaf Area Index), which measured the relationship between the total leaf area per unit of land area. *e*<sup>0</sup> allowed us to know the degree of relationship between land cover in the study area and its temperature.

$$
\epsilon\_0 = 0.95 + 0.01 \, LAI \, when \, LAI \le 3; \epsilon\_0 = 0.98 \, when \, LAI > 3 \tag{10}
$$

Surface temperature is a direct indicator of the earth's surface temperature, which can vary due to geological, geophysical, and geochemical parameters of the Earth and atmosphere [22, 23]. This parameter can be calculated by applying the modified Plank equation, which includes atmospheric corrections and surface emissivity (Eq. (11)):

$$T\_S = \frac{K\_2}{\ln\left[\left(\varepsilon\_{NB}\frac{K\_1}{R\_c}\right) + 1\right]}\tag{11}$$

where *εNB* corresponds to the short-wave emissivity of the satellite thermal sensor and *Rc* is the fixed thermal radiance of the surface, which is obtained from the spectral radiance of the thermal bands (Eq. (12)). For Landsat 5 TM, *K*<sup>1</sup> = 607.8 and *K*<sup>2</sup> = 1261 W m�<sup>2</sup> sr�<sup>1</sup> μm�<sup>1</sup> . For thermal 1 band of Landsat 8, constants *K*<sup>1</sup> = 774.89 and *K*<sup>2</sup> = 1321.08 W m�<sup>2</sup> sr�<sup>1</sup> μm�<sup>1</sup> .

$$R\_c = \frac{L\_{t,T} - R\_p}{\tau\_{\rm NB}} - (1 - \varepsilon\_{\rm NB})R\_{sky} \tag{12}$$

where *Lt,T* is the spectral radiance of the thermal bands (Wm�<sup>2</sup> sr�<sup>1</sup> μm�<sup>1</sup> ); *Rp* is the radiance path at length 10.4–12.5 μm Wm�<sup>2</sup> sr�<sup>1</sup> μm�<sup>1</sup> ; *Rsky* is the short-wave thermal radiation in clear sky conditions; and *τNB* is the transmissivity of air in the length range of 10.4–12.5 μm. The Atmospheric Correction Parameter Calculator [24] was used to calculate *Rp*, *τNB* and *Rsky*, which are values that require an atmospheric correction model. These parameters were calculated exclusively for each representative image of the study area, considering its characteristics. These parameters are the following: date of image acquisition, location, atmospheric model of the study area and terrestrial conditions (elevation, average temperature, and atmospheric pressure).

Surface emissivity for the thermal band is calculated through the narrow band transmissivity, and for this work was calculated using band 6 of sensor 5TM and band 10 of sensor 8 TIRS. (Eq. (13)):

$$
\varepsilon\_{\rm NB} = 0.97 + 0.0033 \, LAI, \text{for } LAI \le 3; \\
\varepsilon\_{\rm NB} = 0.8, \text{for } LAI > 3 \tag{13}
$$

Eq. (13) is applied when the Normalized Difference Vegetation Index (NDVI) is greater than zero. NDVI less than zero indicates the presence of water, snow or ice, resulting in *εNB* = 0.985.

#### *2.4.4 Incident long-wave radiation*

The incoming long-wave radiation is an atmospheric flux from the thermal region of the electromagnetic spectrum (W m�<sup>2</sup> ) and is calculated by the Stefan-Boltzmann equation (Eq. (14)): *RL*<sup>↓</sup> depends on atmospheric emissivity and surface temperature, so it is important that this flux be determined according to the characteristics of the study area.

$$\mathcal{R}\_{\mathcal{L}\downarrow} = \varepsilon\_a \sigma T\_a^4 \tag{14}$$

where *ε<sup>a</sup>* is the effective atmosphere emissivity (dimensionless) and T? is the air temperature near the surface (K). *ε<sup>a</sup>* calculation can be performed using Eq. (15): *ε<sup>a</sup>* depends on *τs<sup>ω</sup>*, therefore in the studio area *τs<sup>ω</sup>* was calculated pixel by pixel to record its spatial variability, allowing *ε<sup>a</sup>* to not just be taken as a constant value.

$$
\varepsilon\_d = 0.85(-\ln \tau\_{sa})^{0.09} \tag{15}
$$

where *τs<sup>ω</sup>* is the broadband atmospheric transmissivity of short-wave radiation derived from Eq. (4). The parameter Ta can be replaced by surface temperature (Ts).

#### **3. Net radiation assessment in the city of San Luis Potosí**

#### **3.1 Dry season**

The net radiation in the dry season in the city of San Luis Potosí was calculated from a representative month (January to May, November and December). **Figure 2** shows the maps with the energy values for 1990–2017. In 1990 there was more incident radiation than reflected radiation, with a maximum value of 695.3 W m�<sup>2</sup> and a minimum value of �61.3 W m�<sup>2</sup> . For this year, most of the study area tends to have high net flux values because, in 1990, the city was not so developed, and there was a more significant presence of vegetation, unlike impermeable materials. In 1995 the maximum value of energy decreased to 523.3 W m�<sup>2</sup> . These values are mainly found in urban coverage, where materials such as pavements and roofing absorb more incident energy. While the minimum radiation values are in the vegetation zones, some of these areas present negative values, which indicate that an energy deficit is being experienced (a slight cooling of the surface).

Further, in 2000 and 2005, it is observed that the city presents average values between 80 and 60 W m�<sup>2</sup> . The lowest values are in areas with vegetation, indicating that most of them are outgoing radiation. In 2009, the highest net flux was

*Evaluation of Net Radiation in San Luis Potosí City – México, with Remote Sensing Processes... DOI: http://dx.doi.org/10.5772/intechopen.110707*

**Figure 2.** *Maps of net radiation in the dry season for 1990-2017.*

concentrated in mountainous regions. Values of approximately 100 W m�<sup>2</sup> can be observed on the city's impervious surfaces, and some minimum values (�30 W m�<sup>2</sup> ) were in farmland areas. In 2015, net flux below 100 W m�<sup>2</sup> was obtained. In 2017 the behavior was very peculiar because the energy recorded was very low, which means there was less incident radiation concerning the outgoing, resulting in a warming of the study area.

#### **3.2 Rainy season**

The energy estimation in the rainy season was performed considering a representative month (June to October) as a sample. **Figure 3** shows the net flux behavior in the rainy season from 1990 to 2017. In 1990 the highest net flux (322.1 W m�<sup>2</sup> ) was in the impervious covers and the lowest (around �84 W m�<sup>2</sup> ) was in vegetation covers. The behavior is very similar to the dry season, although the level of net flux is lower. In 1995, the incident radiation exceeded outgoing radiation. Values of 693.0 W m�<sup>2</sup> were observed on surfaces such as pavements and roofing. In contrast, values close to �57.4 W m�<sup>2</sup> were found in vegetation areas. In 2000, most of the city presented energy of approximately 200 W m�<sup>2</sup> , relief zones had values close to 625.6 W m�<sup>2</sup> , and negative values (�14.9 W m�<sup>2</sup> ) continued to be concentrated in vegetation areas. However, for this year, negative values were lower.

On the other hand, the maps show similar behavior for the years 2005 and 2009. The net flux values are between �94 and 580 W m�<sup>2</sup> . The highest net flux was in some of the city's main avenues and the lowest was in farmland and vegetation areas. In 2015 it was observed that the energy deficit was more significant than in 1995 in the dry season since most of the city's territory registered values close to �100 W m�<sup>2</sup> , which suggests that there was a cooling in surface temperature because the outgoing radiation exceeded the incident radiation. In 2017, the city mainly presented energy close to 30 W m�<sup>2</sup> . During the period 1990–2017, it was observed that generally, in the rainy season, the net flux increases concerning the dry season, which is typical behavior in summer [10]. Also, the results show that in the city's impervious surfaces, the incident radiation is greater than the outgoing radiation, which means that in these areas, the energy cannot be used by processes such as evapotranspiration, causing an increase in temperatures in the city.

#### **4. Net radiation changes implications**

During the period 1990–2017, it was observed that, in the rainy season, net flux increases compared to the dry season; this is considered a typical behavior in summer [10]. Related to the surface temperature values recorded in the area, it has been found that in the dry seasons, the surface temperature increases, mainly between March to May [25].

On the other hand, in this study, it was found that the city's impermeable materials have the highest values of net flux, meaning that, in these areas, the energy cannot be used for the evapotranspiration processes, causing an increase in the temperature of the city. According to Ovalle et al. [25], it has been verified that the surfaces with coverage without vegetation and urban areas tend to have higher temperatures in the study area. Likewise, the study area has presented climatic changes related to soil cover [25, 26]. Several analyses registered similar behaviors [27–29], where the energy depends on the ground cover. Impermeable surfaces such as asphalt mainly store the incident radiation and reflect less radiation, producing increases or decreases in surface temperature and causing phenomena such as urban heat islands.

*Evaluation of Net Radiation in San Luis Potosí City – México, with Remote Sensing Processes... DOI: http://dx.doi.org/10.5772/intechopen.110707*

**Figure 3.** *Maps of net radiation in the rainy season for 1990-2017.*

In this study, images from the Landsat 5 TM and 8 OLI/TIRS satellites were used because they have a sensor capable of recording wavelengths corresponding to thermal infrared, which is essential in the methodology used to calculate the net

radiation. However, the methodology could be adapted to Sentinel 2 sensors since its images have been found to have greater spatial detail and help estimate net flux in regions with complex terrain. Unlike Landsat sensors, which, due to their temporal resolution, do not allow the analysis of detailed canopy information [30]. Also, the energy analysis in San Luis Potosí city could be complemented with land cover maps to have greater certainty of the effects caused by net radiation.

#### **5. Conclusions**

In this study, an evaluation of the energy in San Luis Potosí city was performed. This multi-temporal analysis is essential to know the net flux behavior throughout the study area and how it affects its climate. In addition, it is a turning point in the energy flow exploration of the soil in the San Luis Potosí city. This analysis can support decision-making on how the city's development is being planned and if it is considering how the urban climate interferes with the population's comfort.

The climate in an urban environment is a multifactorial problem since its variation is due to different causes; the natural soil replaced by impervious surfaces, the reduction of vegetation or the release of greenhouse gases. Therefore, one way to study the climate of a city is through its energy balance. Net radiation is a crucial factor in studying the earth's surface characteristics, such as albedo, emissivity, temperature and humidity and processes. According to the results obtained in this work, the San Luis Potosí city, in the dry season, has low levels of net flux. In the rainy season, there is higher energy. This behavior is typical for winter and summer. However, in both seasons, it was observed that incident radiation predominates over outgoing radiation, which means a problem for the city, which has a significant presence of impervious materials. These surfaces retain energy and emit it in the form of an increased temperature-producing urban heat islands.

This paper proposes to analyze the urban climate of the San Luis Potosí city through net radiation. The methodology includes a multi-temporal analysis to observe the net flux behavior related to its unplanned growth. The method used to estimate the energy was adequate for the study area to produce high-precision maps. Also, the net flux calculation through remote sensing processes was of great help since indicators with a high spatial resolution were generated, showing the net radiation's variability through space and time. However, for future research, determining the city's energy balance and including information on land cover in the study area could improve the urban climate analysis.

#### **Acknowledgements**

The authors of this work thank the United States Geological Survey (USGS) for making this work possible by processing and distributing the satellite images and Centro de Investigación y Estudios de Posgrado, Facultad de Ingeniería, Universidad Autónoma de San Luis Potosí (UASLP) and the Programa educativo de Ingeniería en Geomática. We are also grateful for the cooperation of CIACYT—Laboratorio Nacional de Geoprocesamiento de Información Fitosanitaria (LaNGIF).

*Evaluation of Net Radiation in San Luis Potosí City – México, with Remote Sensing Processes... DOI: http://dx.doi.org/10.5772/intechopen.110707*
