# Validation of a 3D Local-Scale Adaptive Solar Radiation Model by Using Pyranometer Measurements and a High-Resolution Digital Elevation Model

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Solar Irradiance

- Diffuse Horizontal Irradiance, $DHI$: This is the solar irradiance collected on a horizontal surface from the atmospheric scattering of light, excluding circumsolar radiation.
- Direct Normal Irradiance, $DNI$: It is the component of solar irradiance collected on a surface perpendicular to the Sun’s rays. The horizontal diffuse component, $DHI$, is neglected here. On clear days, this component is much larger than the diffuse component, while on days with high cloud cover, it is practically zero. As it is measured over the Earth’s surface, its values depend highly on atmospheric conditions and the time of the year.
- Global Horizontal Irradiance, $GHI$: This is the sum of all irradiance components collected over a horizontal surface. This includes the direct and diffuse components, as well as the reflected components, which are generally neglected because of their low value. The $GHI$ can be calculated from the following expression:$$GHI=DHI+DNI\xb7sin\alpha $$
- Beam Horizontal Irradiance, $BHI$: It is the direct horizontal component of the irradiance, i.e., the direct irradiance on a plane perpendicular to the vertical of the site. It can be obtained as follows:$$BHI=GHI-DHI$$

#### 2.2. The MAPSol Model

#### 2.2.1. Clear-Sky Beam Irradiance Model

#### 2.2.2. Shadow Detection

- In the absence of self-shadowed triangles (those facing away from the Sun), the entire mesh is illuminated, and no shadows are present.
- Only triangles oriented away from the Sun are capable of casting shadows. These are referred to as potential 1 triangles [31].

#### 2.3. High-Resolution DEM

#### 2.4. Mesh Generation

#### 2.5. Experimental Measurements of Solar Irradiance with Pyranometers

- Indirect conversion detectors: They work by converting the incident photon flux into another type of flux (usually heat), but they can also be a secondary photon flux. Heat flux detectors are widely used and their operation is relatively simple. To convert the photon flux into heat flux, a highly absorbing paint or varnish is applied to the detector, which causes its temperature to rise when the light beam is impinging on it. Knowing the temperature at two points and assuming that the steady state is reached, the intensity of the flux is calculated, which will be proportional to the temperature difference. Figure 5a shows a general scheme of the parts of an indirect heat flux conversion pyranometer. In the upper part there are two domes, the outer dome has the function of avoiding energy exchanges due to convective phenomena; as a whole, the domes act as an integrating sphere. As can be seen, the detector is surrounded by an anti-radiation shield to prevent radiation penetrating from anywhere other than the dome. Figure 5b shows the Pyranometer Kipp and Zonen SMP10, belonging to the Energy Optimization, Thermodynamics and Statistical Physics Group (GTFE), with which the Global Horizontal Irradiance measurements were performed.
- Direct conversion detectors: Again, there are two types. Photoemitter cells are based on the junction of an anode and a cathode, between which there is a large potential difference (in the range of kV), and an avalanche effect is produced. On the other hand, there are detectors based on PN junctions, the photodiodes, where the current generated is proportional to the incident flux. These types of detectors have better sensitivity than avalanche detectors and work with low voltage [49].

**Figure 5.**Heat flux sensing pyranometer: (

**a**) basic scheme (taken from Kipp and Zonen. Instruction Manual SMP Series [50]) and (

**b**) pyranometer belonging to the Group of Energy Optimization, Thermodynamics and Statistical Physics (GTFE) of the University of Salamanca.

## 3. Results

#### 3.1. Experimental Data Acquisition

^{®}Software v. 13.1, Licensed to Universidad de Salamanca”, identifies the files that belong to the same day and extracts the desired information from each of them. Finally, the program generates a new output file where all the information for the same day is merged.

- If $DH{I}_{i}<0\Rightarrow DH{I}_{i}=0$
- If $GH{I}_{i}<0\Rightarrow GH{I}_{i}=0$
- If $(GH{I}_{i}-DH{I}_{i})<0\Rightarrow (GH{I}_{i}-DH{I}_{i})=0$
- If $sin\phantom{\rule{0.166667em}{0ex}}{\alpha}_{i}<0\Rightarrow DN{I}_{i}=0$

#### 3.2. Area Study, High-Resolution DEM and Adapted Mesh

#### 3.3. Simulation with MAPSol

#### 3.4. Comparison of Simulation Results with Experimental Data

- $MAE$: Mean Absolute Error$$MAE=\frac{{\sum}_{i=1}^{n}|{\widehat{GHI}}_{i}-GH{I}_{i}|}{n}$$
- $NMAE$: Normalized Mean Absolute Error$$NMAE=\frac{{\sum}_{i=1}^{n}|{\widehat{GHI}}_{i}-GH{I}_{i}|}{n\times GH{I}_{max}}\xb7100$$
- $RMSE$: Root-Mean-Square Error$$RMSE=\sqrt{\frac{{\sum}_{i=1}^{n}{({\widehat{GHI}}_{i}-GH{I}_{i})}^{2}}{n}}$$
- $NRMSE$: Normalized Root-Mean-Square Error$$NRMSE=\sqrt{\frac{{\sum}_{i=1}^{n}{({\widehat{GHI}}_{i}-GH{I}_{i})}^{2}}{n\times GH{I}_{max}^{2}}}$$
- ${R}^{2}$: Coefficient of determination$${R}^{2}=1-\frac{{\sum}_{i=1}^{n}{({\widehat{GHI}}_{i}-GH{I}_{i})}^{2}}{{\sum}_{i=1}^{n}{({\widehat{GHI}}_{i}-\overline{GHI})}^{2}}$$

## 4. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

WP | Warning points |

DTM | Digital Terrain Model |

DEM | Digital Elevation Model |

DSM | Digital Slope Model |

GHI | Global Horizontal Irradiance |

DHI | Diffuse Horizontal Irradiance |

DNI | Direct Normal Irradiance |

BHI | Beam Horizontal Irradiance |

CSP | Concentrating Solar Power |

GIS | Geographical Information System |

IGN | National Geographic Institute |

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**Figure 2.**Warning points for shading are equidistributed over each triangle (

**left**graph) simply using the centers of the triangles obtained by refining with the 4-T Rivara algorithm (

**right**graph) [32].

**Figure 4.**Schematic of shadow-ring (positioning, taken from Kipp and Zonen. Instructions Manual CM121 Shadow Ring [48]).

**Figure 6.**Spectral range response of a pyranometer of the SMP series manufactured by Kipp and Zonen versus the radiation spectrum at sea level (taken from Kipp and Zonen. Instruction Manual SMP Series [50]).

**Figure 7.**Measurement devices installed on the rooftop of the Trilingüe building of the Faculty of Sciences (40.96062 N, 5.67075 W) of the University of Salamanca (Spain): (

**a**) pyranometer Kipp and Zonen SMP10 and (

**b**) pyranometer SMP10 with shadow ring model Kipp and Zonen CM 121.

**Figure 9.**Sun path chart: Apparent position of the Sun from the Trilingüe building at the University of Salamanca (40.96062° N, 5.670759° W) between 21 December and 21 June [53]. A panoramic photo, taken from pyranometer that register $GHI$, is overlapped aiming to identify shadowing sources.

**Figure 10.**Three-dimensional view of the study area: (

**a**) original point cloud and (

**b**) DEM derived from the point cloud.

**Figure 11.**Adapted thin mesh (1 m) of the complete area (

**c**), zoom of the fine adapted mesh over the Cathedral area (

**b**), and detail of the uniform original mesh over the Cathedral area (

**a**).

**Figure 12.**Three-dimensional reconstruction of the study area by simply projecting the orthophoto onto the fine adapted mesh. The pyranometers described in Section 2.5 are located at the red dot.

**Figure 13.**Mean GHI map for January, April, July and October, computed with MAPSol and coarse adapted mesh. Notice that the calculations assume a clear sky.

**Figure 14.**Annual mean GHI 3D map, computed with MAPSol and coarse adapted mesh. View from the south.

**Figure 15.**Shadow calculated with MAPSol on 4 September 2022 at 7.00 a.m. and coarse adapted mesh (Supplementary Materials). The long shadow of the cathedral tower (blue dotted square) can be seen over the area where the pyranometers are located (red dot).

**Figure 16.**Curves of $GHI$ measured (purple lines) and simulated (green lines) for the selected dates. The effect of the shadow of the cathedral tower at sunrise can be appreciated in the simulated and the measurement data (circled in red in bottom graphics). The accuracy of the irradiance fit calculated with the MAPSol model is very good, as can be seen in all of the graphs. The peak at 9 a.m. in the upper left graphic corresponds to a cloudy interval that affected the pyranometer readings, which cannot be simulated as the model assumes a clear sky.

Feature | First Coverage |
---|---|

Minimum point density | $0.5\phantom{\rule{3.33333pt}{0ex}}{\mathrm{pt}/\mathrm{m}}^{2}$ |

Years of flight | 2009–2015 |

Geodetic reference system | ETRS89 zones 28, 29, 30 and 31 as appropriate |

Altimetric reference system | Orthometric altitudes, reference geoid EGM08 |

RMSE Z | ≤40 cm |

Estimated planimetric accuracy | ≤30 cm |

File size | $2\times 2\phantom{\rule{0.166667em}{0ex}}\mathrm{km}$ |

File format | LAS 1.2 format 3 |

**Table 2.**Main features of the Kipp and Zonen SMP 10 pyranometers [50] used to perform the experimental measurements.

Feature | Value |
---|---|

Spectral range | 285–2800 nm |

Response time | (63%) < 0.7 s |

Response time | (95%) < 2 s |

Non-linearity | <0.2 |

Spectral selectivity | (350–1500 nm) < 3% |

Field of view | $180\xb0$ |

**Table 3.**Experimental and bibliographic values of accumulated energy by irradiance type in $\mathrm{kWh}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{m}}^{-2}{\mathrm{day}}^{-1}$ for each month of the year.

Source | AEMET [51] | Experimental Data | Relative Differences (%) | |||
---|---|---|---|---|---|---|

Month | $\mathit{GHI}$ | $\mathit{BHI}$ | $\mathit{GHI}$ | $\mathit{BHI}$ | $\Delta \mathit{GHI}$ | $\Delta \mathit{BHI}$ |

January | 2.08 | 1.18 | 2.31 | 1.47 | 11.06 | 24.58 |

February | 3.09 | 1.89 | 3.09 | 1.97 | 0.00 | 4.23 |

March | 4.49 | 2.82 | 4.74 | 3.08 | 5.57 | 9.22 |

April | 5.56 | 3.50 | 5.19 | 2.89 | 6.65 | 17.43 |

May | 6.44 | 4.08 | 6.90 | 4.65 | 7.14 | 13.97 |

June | 7.60 | 5.45 | 7.33 | 5.13 | 3.55 | 5.87 |

July | 7.82 | 5.96 | 7.82 | 6.17 | 0.00 | 3.52 |

August | 6.84 | 5.05 | 6.95 | 5.48 | 1.61 | 8.51 |

September | 5.27 | 3.71 | 5.21 | 3.75 | 1.14 | 1.08 |

October | 3.43 | 2.14 | 3.53 | 2.32 | 2.92 | 8.41 |

November | 3.38 | 1.28 | 2.26 | 1.27 | 33.14 | 0.78 |

December | 1.78 | 0.96 | 1.53 | 0.67 | 14.04 | 30.21 |

**Table 4.**Annual cumulative values (in kWh · m

^{−2}·yr

^{−1}) and average value per day (in kWh · m

^{−2}·day

^{−1}) of the energy received.

Source | AEMET [51] | Solargis [52] | Measured Records | ||
---|---|---|---|---|---|

Annual | Max. | Min. | Max. | Min. | |

$GHI$ | $1708.2$ | $1733.8$ | 1680 | 1753 | 1733.65 |

$BHI$ | $1146.0$ | $1182.6$ | − | − | 1185.93 |

Daily | Max. | Min. | Max. | Min. | |

$GHI$ | $4.68$ | $4.75$ | $4.6$ | $4.8$ | 4.75 |

$BHI$ | $3.14$ | $3.24$ | − | − | 3.25 |

**Table 5.**Summary of errors, in terms of $MAE$ and $MRSE$ and the corresponding normalized indicators $NMAE$ and $NMRSE$, as well as the coefficient of determination ${R}^{2}$.

Date | $\mathit{MAE}$ | $\mathit{NMAE}$ | $\mathit{MRSE}$ | $\mathit{NMRSE}$ | ${\mathit{R}}^{2}$ |
---|---|---|---|---|---|

15 March 2021 | $9.8632$ | $1.2207$ | $19.5744$ | $0.0242$ | $0.9959$ |

4 August 2022 | $7.1667$ | $0.7465$ | $9.1455$ | $0.0095$ | $0.9994$ |

4 September 2022 | $14.1427$ | $1.5802$ | $18.7152$ | $0.0209$ | $0.9971$ |

11 September 2022 | $7.0888$ | $0.8224$ | $12.0603$ | $0.0140$ | $0.9986$ |

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## Share and Cite

**MDPI and ACS Style**

Rodríguez, E.; García-Ferrero, J.; Sánchez-Aparicio, M.; Iglesias, J.M.; Oliver-Serra, A.; Santos, M.J.; Andrés-Anaya, P.; Cascón, J.M.; Montero García, G.; Medina, A.;
et al. Validation of a 3D Local-Scale Adaptive Solar Radiation Model by Using Pyranometer Measurements and a High-Resolution Digital Elevation Model. *Sensors* **2024**, *24*, 1823.
https://doi.org/10.3390/s24061823

**AMA Style**

Rodríguez E, García-Ferrero J, Sánchez-Aparicio M, Iglesias JM, Oliver-Serra A, Santos MJ, Andrés-Anaya P, Cascón JM, Montero García G, Medina A,
et al. Validation of a 3D Local-Scale Adaptive Solar Radiation Model by Using Pyranometer Measurements and a High-Resolution Digital Elevation Model. *Sensors*. 2024; 24(6):1823.
https://doi.org/10.3390/s24061823

**Chicago/Turabian Style**

Rodríguez, Eduardo, Judit García-Ferrero, María Sánchez-Aparicio, José M. Iglesias, Albert Oliver-Serra, M. Jesús Santos, Paula Andrés-Anaya, J. Manuel Cascón, Gustavo Montero García, Alejandro Medina,
and et al. 2024. "Validation of a 3D Local-Scale Adaptive Solar Radiation Model by Using Pyranometer Measurements and a High-Resolution Digital Elevation Model" *Sensors* 24, no. 6: 1823.
https://doi.org/10.3390/s24061823