A Novel Evaluation Method of Tunnel Access Zone Luminance Based on Measured Meteorological Data

Abstract

As the design basis of the tunnel lighting system, tunnel access zone luminance (TAZL) directly affects the energy efficiency of the tunnel lighting system and the driving safety of drivers. Affected by the relative position of the sun, weather conditions and other factors, the TAZL dynamically changes over time, but the existing tunnel mostly uses a fixed luminance value for the design and operation of the tunnel lighting system, which lacks a simplified method to obtain the real-time luminance. In this study, the L₂₀(S) (the average luminance observed by the driver at 20° field of view) at the tunnel stopping sight distance is split, and the sky luminance is calculated by using the sky luminance model. While a segmented prediction model of the ground scenery luminance is established with the maximum sun height angle as the inflection point, the solar irradiance outside the tunnel is adopted as the input parameter. This new proposed L₂₀(S) evaluation model is verified within the error of 5.41%, which provides a convenient and accurate method for the real-time measurement of TAZL.

1. Introduction

With the development of technology and social economy, the construction speed of highway tunnels is advancing by leaps and bounds, especially in China. As of the end of 2021, there are more than 23,000 existing road tunnels with a length of 24 million meters, and among them are 1900 new ones with 2.7 million meters [1,2,3]. The rapid expansion of tunnels has facilitated economic integration and trade between cities, but it has also brought numerous traffic safety accidents, which are more serious than those on ordinary highways [4,5]. Recent studies on road tunnel traffic accidents show that collisions between vehicles or with tunnel side walls occurred more frequently at tunnel entrances [6,7], and the majority of these accidents are related to driver visual factors. As drivers move between different luminance environments within a short period of time, an adaptation time for drivers to identify targets and objects in the tunnel is needed, and this visual “adaptation lagging phenomenon” often occurs when approaching a tunnel during daylight hours [8,9,10]. In order to avoid traffic accidents caused by the “adaptation lagging phenomenon”, it is necessary to implement a smooth transition of luminance at the entrance and exit of the tunnel, so that the driver’s vision can be adequately adapted. The benchmark for achieving a smooth transition of luminance is the luminance level outside the tunnel, which is also named “tunnel access zone luminance (TAZL)”. During the design of the tunnel lighting system, the whole tunnel is divided into four lighting areas, in order L_th, L_tr, L_in and L_ex. The luminance of the road surface in the four areas is taken according to TAZL multiplied by different coefficients. When TAZL is higher, the requirement of lighting luminance level inside will be also higher, and it will increase the energy consumption of the tunnel lighting system at the same time.

Therefore, the massive tunnel volume also brings huge lighting energy consumption, and statistics show that the lighting energy consumption of tunnels accounts for more than 50% of the total energy consumption of tunnel mechanical and electrical facilities, particularly in summer [11,12]. Due to the high value of TAZL, the energy consumption of tunnel lighting could reach 9 times higher in the middle of the day than that of the night [13,14,15]. Therefore, the TAZL is widely used as a critical design basis for tunnel lighting. A scientific evaluation method for TAZL could better offer a luminous environment for drivers to drive safely and comfortably, and is also essential for reducing tunnel lighting equipment investment and energy consumption.

Since the 1960s, scholars from various countries have investigated the relationship between the lighting luminance at the entrance section of the tunnel and TAZL through a series of visual tests. In 1964, Schreuder concluded that there exists a proportional relationship between the luminance of the road surface at the entrance section of the tunnel and TZAL through the target object identification test [16]. In 1985, an Investigation Report on Tunnel Entrance Lighting Technology (CIE 61-1984) was released by the International Commission on Illumination (CIE) to claim the lighting luminance requirements of the tunnel entrance section, which further confirmed the validity and scientificity of the Schreuder test program and its conclusions, resulting in the calculation method of the tunnel exterior luminance L₂₀(S) based on the K value [17]. L₂₀(S) is defined as the average weighted luminance of the sky, tunnel entrance, tunnel portal structure, road and other scenery contained in the 20° viewpoint range facing the tunnel entrance direction, with a stopping sight distance (SSD) along the tunnel axis 1.5m above the road surface [18]. In 1990, CIE proposed the tunnel equivalent veiling luminance L_seq, which used contrast C and SRN subjective evaluation value to determine the luminance value of the tunnel entrance section. L_seq refers to the light curtain phenomenon generated by the scattered light entering the driver’s eye at the same position as L₂₀(S) [19], but it uses a field of view angle of 56.8°, and the calculation takes into account the contribution of the equivalent veiling luminance rather than a luminance-weighted average of the area [20]. The above two TAZL theories both have a scientific nature which can be used as the basis for the design of tunnel lighting, but the method used by various countries is different, among which China, Japan, etc. use the L₂₀(S) method, and the United States and some European countries use the L_seq method.

Methods listed in the current tunnel lighting specification to obtain the L₂₀(S) value include the checklist method, blackness method, environmental sketch method and digital camera method [18], and the test time is specified as the season of the year with the strongest sunlight and the brightest time of the day. For instance, as China is located in the northern hemisphere, the maximum L₂₀(S) is at noon in summer, so the final value of L₂₀(S) for Chinese road tunnels was taken as the maximum value for three consecutive days of testing in June, July and August with clear skies and no clouds [21]. The majority of countries that adopt the L₂₀(S) method use fixed L₂₀(S) values as the basis for lighting system design, but with the relative position of the sun and meteorological changes, L₂₀(S) changes all the time. The fixed value of L₂₀(S) for the design of the tunnel lighting system will occur in the case of excessive lighting, resulting in a certain amount of energy waste. In addition, under the weather conditions such as cloudy, rainfall, etc., the brighter tunnel lighting environment will lead to glare and other visual discomforts for drivers. Therefore, scholars from various countries have conducted a series of research to improve the method of measuring L₂₀(S).

Some scholars monitored the dynamic changes of L₂₀(S) by means of real measurements and made corrections to the L₂₀(S) values in the existing codes. Wang et al. [22] conducted time-by-time L₂₀(S) tests for tunnels in cold regions and derived the dynamic change characteristics of L₂₀(S) by analyzing the variation under several typical weather situations. Based on real-time traffic data, Lambros et al. [23] first recalculated the L₂₀(S) for 11 existing tunnels and corrected L₂₀(S) by using the traffic weighting method to calculate a new value for the lighting luminance demand inside the tunnel. Zhang et al. [24] conducted L₂₀(S) field tests on highway tunnels and analyzed three factors, namely, the sky area share within the driver’s 20° field of view, the structural form of the test tunnel portal and the road surface color, to derive the influence law of each environmental parameter outside the tunnel on L₂₀(S), and finally proposed the L₂₀(S) correction parameters for different environments outside the tunnel. The environmental sketch method is one of the most basic methods for L₂₀(S) testing, which is based on the principle of obtaining the luminance of each scenery outside the tunnel individually by a point luminance meter, but due to the time-varying characteristics of L₂₀(S), this method has errors and low efficiency. Therefore, some researchers have proposed a digital camera-based L₂₀(S) test method by examining the imaging characteristics of digital cameras. He and Liang [25] calibrated the Nikon D7500 camera by using a point luminance meter, developed a point luminance formula applied to this model of camera based on geometric optics, and wrote a MATLAB code to implement a method for extracting L₂₀(S) from a luminance test photograph outside a tunnel. López and Peña-García [26] established a formula for calculating the L₂₀(S) cone base radius by studying a fixed photograph of the tunnel entrance taken from the center of the travel lane while driving close to the tunnel entrance, proposing a method for measuring L₂₀(S) for different distances as well as angular situations. The above-mentioned researchers proposed various methods to obtain L₂₀(S) based on actual measurements from the perspective of correction and photography, but the resulting L₂₀(S) values are still fixed and the operation is difficult. Therefore, some countries adopt the approach of erecting luminance meters outside the tunnel to achieve real-time monitoring of L₂₀(S), for security considerations, the luminance meters are mostly positioned on the gantry of the tunnel entrance section. However, this placement does not meet the 1.5 m height requirement for L₂₀(S) testing, and in order to solve the problem of L₂₀(S) field-of-view differences between the driver and the device location during the installation of L₂₀(S) test devices outside the tunnel, Constantinos et al. [27] investigated the changes of different test angles on L₂₀(S) parameters and proposed a new method for positioning L₂₀(S) test devices outside the tunnel. However, it is still costly for L₂₀(S) test devices and not suitable for universal installation in all tunnels.

In fact, L₂₀(S) is consisted of the reflection of sunlight from each scene outside the tunnel and the sky light, some scholars have investigated the transformation relationship from photoclimatic data to L₂₀(S) from the perspective of light reflection theory and established the L₂₀(S) prediction model. Zhang [28] analyzed the relationship between solar altitude angle and vertical surface illuminance changes under four orientations based on one year’s photoclimatic measured data and established a mathematical model of luminous efficacy of vertical surface conversion with different orientations using sky clearness index and solar altitude angle as input parameters, which mapped the luminance of scenery outside the tunnel with vertical surface illuminance. He and Liang [29] concluded that the luminance of each scenery outside the tunnel is proportional to its surface illuminance through field measurements, obtained the surface illuminance of each scenery outside the tunnel under clear sky conditions, and proposed the prediction model of L₂₀(S) in cloudless conditions according to the law of relative position change of the sun. Based on the theories and research results related to solar radiation and atmospheric science, Xu [30] proposed a theoretical model of the solar radiation spectrum under clear sky conditions, and obtained the spectral reflection characteristics of each scenery outside the tunnel through experimental tests, presenting a research method of luminance and color temperature outside the tunnel based on radiometry. The above researchers established prediction models to obtain L₂₀(S), but most of the studies took mountain tunnels as the object of investigation and did not consider the luminance of the sky within the 20° view range of the driver, while for urban tunnels as well as underwater tunnels the sky luminance is an important part of L₂₀(S) that cannot be ignored, so the prediction model has shortcomings in the range of adaptation.

The existing research results provide references for the evaluation of L₂₀(S), but they still lack practicality. In this paper, by splitting the driver’s field of view at the SSD point and conducting a time-by-time L₂₀(S) test on the actual tunnel, a novel L₂₀(S) evaluation method is proposed to explore the time-varying characteristics of sky luminance and ground scenery luminance separately, which could provide a better reference for the design and operation of the tunnel entrance section lighting.

2. Materials and Methods

2.1. Measurement Method of L₂₀(S)

As described previously, the schematic diagram of L₂₀(S) is shown in Figure 1, and the calculation formula are:

$${\mathrm{L}}_{20}\left(\mathrm{S}\right)= \mathsf{\alpha }\times {\mathrm{L}}_{\mathrm{S}}+\mathsf{\beta }\times {\mathrm{L}}_{\mathrm{R}}+\mathsf{\gamma }\times {\mathrm{L}}_{\mathrm{E}}+\mathsf{\delta }\times {\mathrm{L}}_{\mathrm{PS}}+\cdots +\mathsf{\theta }\times {\mathrm{L}}_{\mathrm{X}}$$

(1)

$$\mathsf{\alpha }+\mathsf{\beta }+\mathsf{\gamma }+\mathsf{\delta }+\cdots +\mathsf{\theta }=1$$

(2)

where ${\mathrm{L}}_{\mathrm{S}}$ is the sky luminance, cd/m²; α is the percentage of the sky in the 20° view range, %; ${\mathrm{L}}_{\mathrm{R}}$ is the road luminance, cd/m²; β is the percentage of the road, %; ${\mathrm{L}}_{\mathrm{E}}$ is the tunnel entrance luminance, cd/m²; γ is the percentage of the tunnel entrance, %; ${\mathrm{L}}_{\mathrm{PS}}$ is the tunnel portal structure, cd/m²; δ is the percentage of the tunnel portal structure, %; ${\mathrm{L}}_{\mathrm{X}}$ is the other scenery luminance in the 20° view range, cd/m²; θ is the percentage of the other scenery, %.

L₂₀(S) is caused by solar radiation. Current research shows that there exists a transformation relationship between solar irradiance and illuminance [31,32,33], but in the actual test, the vertical surface illuminance can be easily influenced by the test location, and it is difficult to obtain the instantaneous value. Therefore, the horizontal solar irradiance outside the tunnel is selected as the photoclimatic input parameter in this study to investigate the variation law of the ground scenery luminance outside the tunnel.

As the luminance of the sky part within the driver’s 20° viewing angle is normally significantly higher than the luminance of the tunnel ground scenery for most of the urban tunnels, the driver’s 20° view range is divided by the separation line of sky and ground scenery contour into two parts (Figure 2), and the luminance is calculated and studied separately.

Tunnel 1 (the Luhua Road Tunnel in Beijing), Tunnel 2 (the Yangtze River Tunnel on Yingtian Street in Nanjing, Jiangsu Province), and Tunnel 3 (the JYJJ tunnel in Jiangsu Province) were selected as test tunnels (Figure 3) to investigate the coupling relationship between L₂₀(S) and the solar irradiance. The test dates for Tunnel 1 are 20 April 2022 (Date 1), 22 April 2022 (Date 2), and 13 May 2022 (Date 3), and the summer solstice, 23 June 2022 (Date 4); for Tunnel 2 the test date is 14 September 2021 (Date 5); and for Tunnel 3 the test date is 18 August 2022 (Date 6).

The research process is illustrated in Figure 4 and can be divided into the following steps:

• Select a typical tunnel, determine the area share of each scenery within the driver’s 20° view angle by taking photos, and delineate the dividing line between the sky and the ground scenery outside the tunnel;
• Test the luminance of each element of the scenery within the driver’s 20° view angle and record the horizontal solar irradiance outside the tunnel;
• Determine the number of the sky block included in the driver’s 20° view range by combining the information on tunnel orientation, road slope and structure of the tunnel portal;
• Obtain the corresponding sun position information according to the test time, classify the sky type by combining the sky clarity K_t value and confirm the input parameters of the sky luminance calculation model;
• Calculate the sky block luminance in the driver’s 20° view range and validate the calculation results by using the measured sky block luminance;
• Analyze the variation law of ground scenery luminance outside the tunnel by drawing the curves with time and horizontal solar irradiance;
• Establish the calculation model of ground scenery luminance with horizontal solar irradiance as independent variable by using time as segmentation criterion and validate the model by using new measured data;
• Combine the sky luminance and the ground scenery luminance calculation model into the L₂₀(S) calculation model and validate the model by using new measured data.

2.2. Measurement of the Ground Scenery Luminance

The information of the three tunnels is shown in

Table 1. Information of test tunnels.

Name	Location	Orientation	Type
Luhua Road Tunnel	116.3° E, 39.8° N	15° North by West	urban tunnel
Yingtian Street Yangtze River Tunnel	118.7° E, 32° N	20° East by South	underwater tunnel
JYJJ tunnel	120.2° E, 31.9° N	22° North by West	underwater tunnel

. Tunnel 1 was used as the modeling object for the calculation of the ground scenery luminance outside the tunnel.

The LS-160 type luminance meter produced by Konica Minolta Co., Ltd. (Tokyo, Japan) of Japan (Figure 5a) was used to measure the luminance of each scenery outside the tunnel, and the HD2102.2 type irradiance meter produced by DELTAOHM (Caselle di Selvazzano, Italy) of Italy (Figure 5b,c) was used to measure the solar irradiance. The primary parameters of the test instrument are shown in

Table 2. Primary parameters for the luminance meter and solar irradiance meter.

Instrument	Parameter	Value
Luminance meter	Range	0.01~9,999,000 cd/m2
	Accuracy	±4%
Solar irradiance meter	Range	0.01~2000 W/m2
	Accuracy	±2%

. The testing period was from 9:00 a.m. to 5:00 p.m., and a set of L₂₀(S) tests were conducted approximately every 15 min. Each set of L₂₀(S) test was accompanied by a record of the horizontal solar irradiance outside the tunnel.

As shown in Figure 6, during the luminance test, test points (at least 4) will be evenly placed according to the area share of the test object within the driver’s 20° field of view, the red crosses are the test points and the yellow lines stand for the boundary lines of each scenery. The values of test points will eventually be averaged as the luminance value of the scenery, which can effectively improve the accuracy of the test.

2.3. Calculation of Sky Luminance

Currently, the research on sky model has been relatively well-developed [34,35,36,37,38]; in this study, the CIE general sky model is chosen to calculate the sky luminance of the 20° view range of the driver outside the tunnel [39,40,41]. In this model, the entire sky dome is evenly divided into 145 blocks, named No. 1~No. 145. The formula is

$$\frac{L_{\gamma \alpha }}{L_z}=\frac{\phi \left(Z\right)·f\left(\chi \right)}{\phi \left(0\right)·f\left(Z_s\right)}$$

(3)

where φ(Z) is the luminance gradient function; $f$(χ) is the scattering index function; $L_z$ is the zenith luminance; and cd/m²; $L_{\gamma \alpha }$ is the calculated sky surface element luminance, cd/m². The formulas of φ(Z), χ and $f$(χ) are

$$\phi \left(Z\right)=1+a·\exp \left(\frac{b}{\mathit{cos}Z}\right)$$

(4)

$$\chi =arc\mathit{cos}\left(\mathit{cos}{Z}_s·\mathit{cos}Z+\mathit{sin}{Z}_s·\mathit{sin}Z·\mathit{cos}\left|\alpha -{\alpha }_s\right|\right)$$

(5)

$$f\left(\chi \right)=1+c·\left[\exp \left(d\chi \right)-\exp \left(d\frac{\pi }{2}\right)\right]+e·{\mathit{cos}}^2\chi$$

(6)

where $Z_S$ is the angle between the sun and the zenith, rad; ${\alpha }_S$ represents the azimuthal angle of the sun, rad; Z represents the angle between the computed sky surface element and the zenith, rad; α represents the azimuthal angle of the computed sky surface element, rad; $\gamma$ represents the altitude angle of the computed sky surface element, rad. Constant a and b are the brightness gradient parameter; c, d and e are the scattering characteristics parameters. Parameters a~e are determined by the sky type.

Since the 1960s, scholars from various countries have proposed zenith luminance calculation models applied to different atmospheric turbidity ($T_L)$, which are shown in

Table 3. Zenith luminance calculation models.

Author	Zenith Luminance Calculation Model	Application Conditions
Dogniaux	${\mathrm{L}}_z=\left(1.234T_L-0.252\right)tan{\gamma }_s+0.112T_L-0.0167$	-	${\gamma }_s\le 65°$
Kittler	${\mathrm{L}}_z=0.3+3tan{\gamma }_s$	2.25 ≤$T_L$ ≤ 3.25	${\gamma }_s\le 65°$
Krochmann	${\mathrm{L}}_z=0.1+0.063{\gamma }_s+\left({\gamma }_s\left({\gamma }_s-30\right)/1000\right){\mathrm{e}}^{0.0346\left({\gamma }_s-68\right)}$	$T_L=2.75$	-
Liebelt	${\mathrm{L}}_z=\left(1.34T_L-3.46\right)tan{\gamma }_s+0.1T_L+0.9$	3 ≤ $T_L$ ≤ 7.5	-
Gusev	${\mathrm{L}}_z=0.9+6.5tan{\gamma }_s$	5 ≤ $T_L$ ≤ 6.5	${\gamma }_s\le 65°$
LBL	${\mathrm{L}}_z=\left(1.376T_L-1.81\right)tan{\gamma }_s+0.38$	1.5 ≤ $T_L$ ≤ 8.5	${\gamma }_s\le 65°$

[41,42]. In this study, a suitable zenith luminance model will be selected by calculating the atmospheric turbidity value of the geographic location of the tunnel corresponding to the test time.

Where ${\gamma }_S$ is the altitude angle of the sun, rad. Further, the atmospheric turbidity $T_L$ can be calculated by the following formula

$$T_L=\left(ln{E}_{eo}-ln{E}_{esn}\right){\left({\alpha }_{r}m\right)}^{-1}$$

(7)

where $E_{eo}$ is the solar constant, refers to the solar irradiance received per second per unit area of the top boundary of the atmosphere perpendicular to the sun’s rays at the mean solar-terrestrial distance (D = 1.496 × 10⁸ km). The solar constant value published by the World Meteorological Organization (WMO) in 1981 is 1367 ± 7 W/m², and $E_{eo}$ is 1367 W/m² in this study. ${\alpha }_r$ is the atmospheric extinction coefficient and m is the absolute air mass. ${\alpha }_r$ and m can be calculated as the following equations

$${\alpha }_r={\left(0.94+0.9m\right)}^{-1}$$

(8)

$$\mathrm{m}=\frac{-sin{\gamma }_s+{\left[si{n}^2{\gamma }_s-1+{\left(1.001572\right)}^2\right]}^{1/2}}{0.001572}$$

(9)

where $E_{esn}$ is the direct solar irradiance at the earth’s surface, W/m². This study obtains the hour-by-hour direct solar spectrum by setting up a weather station near the Luhua Road tunnel in Beijing (as shown in Figure 7) and calculates $E_{esn}$ by integrating the spectrum.

To accurately identify the sky types and the corresponding luminance gradient parameters and scattering characteristics parameters, it is necessary to scan the 145 skies one by one, then normalize the luminance values and compare them with the standard values of 15 sky types, which is a multi-step and computationally intensive method. Therefore, in this study, the 15 sky types of the CIE sky model are simply categorized based on the sky clarity $K_t$, and the specific correspondence is shown in

Table 4. The values of the sky luminance calculation parameters for each sky definition $K_t$ range.

${\mathit{K}}_{\mathit{t}}$	a	b	c	d	e
0.00~0.35	1.1	−0.8	0	−1.5	0
0.35~0.70	0	−1	5	−3	0.3
0.70~1.00	−1	−0.3	16	−3	0.3

.

The sky clarity $K_t$ is calculated by the following equation

$$K_t=\frac{E}{H_O}$$

(10)

where E is the horizontal solar irradiance, W/m²; $H_O$ is the extraterrestrial solar irradiance, W/m². The calculation formula of $H_O$ is

$$H_O=\frac{24I_O}{\pi }\left[\cos \phi ·\cos \delta ·\sin \omega +\omega ·\sin \phi \sin \delta \right]$$

(11)

where $\phi$ is the latitude of the test site, rad; $\delta$ is the solar declination angle, rad; $\omega$ is the solar incidence hour angle, rad; $I_O$ is the solar irradiance outside the atmosphere, kW/m². δ and $I_O$ can be calculated by the following equation

$$\delta =23.45\sin \left[\frac{2\pi \left(N-80\right)}{356}\right],-23.45°\le \delta \le 23.45°$$

(12)

$$I_O=E_{eo}\left[1+0.33\cos \left(\frac{360N}{365}\right)\right]$$

(13)

where N is the ordinal number of days in the year for the current day. The solar incidence hour angle $\mathsf{\omega }$ is calculated by the following equation

$$\mathsf{\omega }={\mathit{cos}}^{-1}\left(-\tan \mathsf{\phi }·\tan \mathsf{\delta }\right)·\frac{\mathrm{t}}{{\mathrm{t}}_{\mathrm{sr}}}$$

(14)

where t indicates the number of minutes in the 24-h time range from 00:00 at the time of the test; ${\mathrm{t}}_{\mathrm{sr}}$ is the number of minutes in the 24-h time range from 00:00 at the time of the sunrise on the test day.

After calculating the luminance of each sky block within the driver’s 20° viewing angle, $L_S$ can be calculated by the following equation

$$L_S={\displaystyle \sum }_{i=1}^n{x}_i{L}_{\gamma \alpha }$$

(15)

where $x_i$ is the area share of each sky block in the driver’s 20° viewing range, %; $L_{\gamma \alpha }$ is the calculated luminance of each sky block in the driver’s 20° viewing range, cd/m².

2.4. Error Calculation

In this study, the coefficient of variation of the root mean square error (CVRMSE, Equation (16)) and normalized mean bias error (NMBE, Equation (17)) proposed in ASHRAE GUIDELINE 14-2014 [43] were used for error analysis of the calculation model to evaluate its accuracy.

$$CVRMSE=\frac{\sqrt{{{\displaystyle \sum }}_{i=1}^n\frac{{\left(y_i-y_i^{\prime }\right)}^2}{n-1}}}{{\overline{y}}_i}\times 100\%$$

(16)

$$NMBE=\frac{{{\displaystyle \sum }}_{i=1}^n\left(y_i-y_i^{\prime }\right)}{\left(n-1\right)\times {\overline{y}}_i}\times 100\%$$

(17)

where $y_i$ is the measured value, $y_i^{\prime }$ is the calculated value, ${\overline{y}}_i$ is the average of the measured value, and n is the sample size. If the CVRMSE is controlled within 15% and the absolute value of NMBE is controlled within 5%, the established L₂₀(S) calculation model can be used for subsequent studies.

3. Results

3.1. Measurements and Calculation of the Ground Scenery Luminance

3.1.1. Calculation Model

The change curve of ground scenery luminance with solar irradiance is plotted according to the test results of the three tunnels (Figure 8), in which the red dashed line indicates the test day noon time, and the data point color indicates the time of the test: from red to green indicates the forenoon and green to blue indicates the afternoon.

A segmental relationship exists between the ground scenery luminance and the solar irradiance, with the 30-min period around noon, i.e., the maximum solar altitude angle of the day as the inflection point interval. Linear regressions were performed for the forenoon and afternoon respectively, using the real-time solar irradiance on Date 1, Date 2 and Date 3 as the independent variables and the corresponding ground scenery luminance as the dependent variable. Lorentz regression was performed on the forenoon data, as shown in Figure 9a, with R² of 0.82, where $L_{fn}$ is the ground scenery luminance in the forenoon, cd/m²; E is the solar irradiance, W/m²; the sample size is 50; and the significance level is 4.3 × 10⁻⁵. Logistic regression was performed for the afternoon data, as shown in Figure 9b, with R² of 0.83, where $L_{an}$ is the ground scenery luminance in the afternoon, cd/m²; the sample size is 55 and the significance level is 6.9 × 10⁻⁷.

According to the aforementioned formula, ground scenery luminance can be calculated through the following segmentation function, as Equation (18):

$$L_G =\{\begin{array}{c}4648-\frac{541003670}{\pi \left[4{\left(E-598\right)}^2+126025\right]} \mathrm{h}\le \mathrm{H}\\ 326258-\frac{325237}{1+{(\frac{E}{4224})}^{3.27}} \mathrm{h}\ge \mathrm{H}\end{array}$$

(18)

where $L_G$ is the ground scenery luminance, cd/m²; E is the solar irradiance, W/m²; h is the real-time solar altitude angle of the geographic location of the tunnel, rad; H is the maximum solar altitude angle on the day of the test at the geographic location of the tunnel, rad.

3.1.2. Validation

According to the fitted model for calculating the $L_G$ value, a new L₂₀(S) test was conducted for the Beijing Luhua Road Tunnel on 21 June 2022, the summer solstice. By inputting the solar irradiance at each test time point, the model was calculated to output the $L_G$ value in real time. The test site and the comparison of the measured and calculated values are shown in Figure 10.

For the forenoon calculation model, the maximum absolute error is 15.16%, the average absolute error is 10.34%, the CVRMSE value is 11.46%, and the NMBE value is 3.17%. For the afternoon calculation model, the maximum absolute error is 15.62%, the average absolute error is 9.06%, the CVRMSE value is 9.06%, and the NMBE value is −1.92%. The error of the model calculation in the forenoon is larger than that in the afternoon, and it can also be observed from Figure 10b that the overall trend of the calculated values is smoother, and the measured values around 11:00 a.m. are obviously larger than the calculated values. After comparing the model data with the measured data at the same time, this error is from the fact that the solar altitude angle has reached the maximum solar altitude angle at 11:00 a.m. on the summer solstice, which makes the road surface luminance reach the maximum value in a day. For the error of the sudden drop of $L_G$ measured at 12 o’clock, it was caused by the small moving clouds around the sun during the test. The whole-day field measurement data were also analyzed with the calculated data error for model validation, with the following validation effect in Figure 11.

From the results of the test on Date 4, the maximum absolute error between the calculated and measured values of $L_G$ is 15.6%, the overall average absolute error of the calculated model is 9.03%, the CVRMSE value is 11.03%, and the NMBE is 1.01%, which shows that the data for the predictive model are within acceptable limits. At the same time, it also confirms the applicability of this model, and it is possible to predict the ground scenery luminance through solar irradiance.

3.2. Measurements and Calculation of the Sky Luminance

3.2.1. Calculation Model

According to the orientation of the Beijing Luhua Road Tunnel, structural characteristics and sky block distribution, the driver’s 20° viewpoint at the parking sight distance contain sky number 14, 15 and 16 when entering the tunnel from south to north. Compared with the height of the sky, the height of 1.5 m from the ground can be simplified to be close to the ground, i.e., in the background of the sky, the driver’s horizon view is close to the ground surface. The driver’s 20° view is finally determined to contain 31% of the lower right part of sky No. 14, 67% of the lower part of sky No. 15 and 2% of the lower left part of sky No. 16 (Figure 12). The altitude angle γ, zenith angle Z, and azimuth angle α of each sky block are shown in

Table 5. Area share of each sky block within the driver’s 20° view.

Sky Block Number	Percentage of Area	$\mathit{\gamma }$	$\mathit{Z}$	$\mathit{\alpha }$
No. 14	31%	6°	84°	156°
No. 15	67%	6°	84°	168°
No. 16	2%	6°	84°	−180°

. To simplify the subsequent sky luminance calculation process, sky No. 16 within the driver’s 20° view is fused into sky No. 15 due to its significantly lower area share.

3.2.2. Validation

After determining the number of sky block contained within the driver’s 20° view, the sky luminance within the driver’s 20° view at the test time can be calculated according to the sky luminance calculation method in Section 2.4 by entering the time information as well as the solar irradiance data. The comparison of the measured and calculated values is shown in Figure 13. The error calculation results of the three-day test data are shown in

Table 6. Testing data.

Date	The Maximum Absolute Error	The Average Absolute Error	CVRMSE	NMBE
4.20	15.69%	5.72%	6.70%	−1.11%
4.22	15.48%	7.09%	8.55%	−5.26%
5.13	22.80%	6.81%	8.66%	0.39%

.

For data where the measured value differs significantly from the calculated value, such as the 11:50 data on Date 1, the 15:50 data on Date 2 and the 13:50 data on Date 3, the error is caused by the presence of clouds within the driver’s 20° view and the luminance of the clouds is greater than the background sky luminance, or by the presence of small clouds around the sun, which reduces the instantaneous solar irradiance and thus interferes with the input parameters of the calculation model. The calculation model is also validated by analyzing the errors between the calculated and measured data, and the validation effect is shown in Figure 14.

Among 101 sets of sky luminance test data, only 4 sets of relative error values are more than 15%, the maximum value is 22.8%, the overall average absolute error of the calculated model is 6.68%, the CVRMSE value is 7.96%, and the NMBE is −1.8%, which shows that the data for the predictive model are within acceptable limits, and it is possible to reasonably predict the sky luminance.

3.3. Measurements and Calculation of L₂₀(S)

3.3.1. Calculation Model

L₂₀(S) is calculated by weighting the luminance of each scene outside the tunnel cave according to the proportion of the area within the driver’s 20° viewpoint, so according to Section 3.1 and Section 3.2, the model for calculating L₂₀(S) based on the measured photoclimate data is derived as follows.

$${\mathrm{L}}_{20}\left(\mathrm{S}\right)=K_s·L_S+K_G·L_G$$

(19)

where $K_S$ is the percentage of sky area in the driver’s 20° view range, %; $L_S$ is the sky luminance in the driver’s 20° view, cd/m²; $K_G$ is the percentage of ground scenery area in the driver’s 20° view, %; $L_G$ is the ground scenery luminance in the driver’s 20° view, cd/m².

Based on the L₂₀(S) test points, the area share of each part of the scenery in the driver’s 20° view outside the three tunnels is shown in

Table 7. The percentage of the area of each scenery within the 20° view of the driver at the L₂₀(S) testing point of Tunnel 1.

Name of Scenery		Percentage of Area
Sky-32.4%	Sky	32.4%
Ground-67.6%	Residential buildings	8.3%
	Road surface	25.7%
	Tunnel entrance	8.3%
	Tunnel portal structure	25.3%

.

3.3.2. Validation

The L₂₀(S) calculation model proposed in Section 3.3.1 was validated by the L₂₀(S) test for Tunnel 1 on Date 4 and the validation results are shown in Figure 15.

As shown in Figure 15, the measured values around 12 o’clock are obviously larger than the calculated values in which the absolute error is 11.61%. In this set of data, the absolute error of the ground scenery luminance is 15.6%, and the absolute error of the sky luminance is 6.9%. After checking the test data, it is found that the solar irradiance of this group changed little with the previous and the latter group, but the residential building luminance data is obviously abnormal, and therefore this set of errors is considered as measurement mistakes. The overall average absolute error of the L₂₀(S) calculation model is 5.41%, the CVRMSE value is 2.81%, and the NMBE is −0.37%, which indicates that the error of this model is within the acceptable range, and it could achieve the conversion from solar irradiance to L₂₀(S).

4. Discussion

4.1. Comparison among Different L₂₀(S) Measurement Methods

In this study, a coupling relationship between L₂₀(S) and solar irradiance outside the tunnel is found through real measurements, and a model for calculating L₂₀(S) is established based on data fitting. The comparison with the existing L₂₀(S) measurement method is shown in

Table 8. Comparison among different L₂₀(S) measurement methods.

Research Team	Method/Input Parameters	Output L20(S) Characteristics	Error
The present study	Real-time solar irradiance	Dynamic, sky-inclusive, low-cost	0~12%
Lambros et al. [23]	Correction of L20(S) according to traffic volume	Dynamic, focus only on energy efficiency	No measurement
Zhang et al. [24]	Correction of L20(S) considering environmental factors	Fixed value	No measurement
He and Liang [25]	Photo of the tunnel entrance	Fixed value	0~10%
López and Peña-García [26]	Photo of the tunnel entrance	Fixed value	No measurement
Constantinos et al. [27]	L20(S) test devices	Dynamic, costly testing devices	No calculation
Zhang [28]	Solar irradiance	Fixed value, not including sky	No measurement
He and Liang [29]	Real-time solar irradiance	Dynamic, not including sky	0~30%
Xu [30]	Real-time solar irradiance	Dynamic, not including sky	0~21%

.

Compared with the results of previous studies, this proposed L₂₀(S) measurement method only records solar irradiance, has the advantages of convenience, lower cost, and can output real-time L₂₀(S) values dynamically.

4.2. Limitation

In addition, the variation in the geographical location, orientation and meteorological conditions of different tunnels determines that each tunnel has its own unique L₂₀(S) calculation model. Therefore, in future research we will identify the factors influencing the calculation model for different tunnels, such as geographical location, orientation, etc. Afterwards, we will propose the corresponding correction parameters to optimize the calculation model and then create a generalized model suitable for various different tunnels.

5. Conclusions

TAZL directly affects the driver’s driving safety and lighting energy consumption which has dynamic change characteristics and limitations on measurement. A simple and low-cost L₂₀(S) dynamic measurement method is proposed to accurately predict L₂₀(S) by separating the scenery within the driver’s 20° field of view into contents and establishing separate luminance calculation models.

• For the ground scenery luminance part, it is found that there exists a segmented linear relationship between ground scenery luminance and solar irradiance through real-time testing of L₂₀(S). Based on the data fitting, a ground scenery luminance calculation model is established, and the average absolute error is 9.03% as verified by the measured data;
• For the sky luminance part, the CIE sky model was adopted to calculate the luminance of the sky block contained within the driver’s 20° field of view by using the sky clarity KT value as the basis for sky type judgment in this study. The absolute average error of the output sky luminance model within the driver’s 20° field of view is 6.68% as verified by the measured data;
• After the integration of the calculation models, the L₂₀(S) calculation model with time information and solar irradiance data as the input parameters is derived, and the average absolute error of the model is 5.41% as verified by the measured data.

The dynamic L₂₀(S) measurement method proposed in this paper has a good prediction performance of innovation and instruction, which can provide a technical basis for the accurate measurement of tunnel access zone luminance. This method is not restricted to L₂₀(S) prediction, which has the application and practical value of all luminance parameters in TAZL. The real-time L₂₀(S) obtained with this method could act as an input parameter to achieve intelligent control of the tunnel lighting system, thus reducing the energy consumption of tunnel operations and improving driver safety.

Additionally, here are some measurement recommendations. First, the testing period is from 9:00 a.m. to 5:00 p.m., and each test group is 15 min apart. At the beginning of each set of tests, the test time and the solar irradiance are recorded. Second, multiple points should be taken for each scenery to test the luminance and take the average value. Third, the irradiance meter should be placed on a wide, flat surface to avoid errors caused by shadows from surrounding objects.