Design and Experiments of a Naturally-Ventilated Radiation Shield for Ground Temperature Measurement

Abstract

Temperature sensors may produce a measurement error of up to 1 °C because of the influence of solar radiation. In order to obtain a relatively minimal temperature error, a new temperature observation system was proposed in this paper for measuring surface air temperatures. Firstly, a radiation shield was designed with two aluminum plates, eight vents, and a multi-layer structure which is able to resist direct solar radiation, reflected radiation, and upwelling long-ware radiation, as well as ensuring the temperature sensor probe could work effectively. Then, the effect of different solar radiation intensities, wind speeds, scattered radiation intensities, long-wave radiation intensities, and underlying surface reflectivity levels on radiation error was calculated through a computational fluid dynamics (CFD) method. The mapping relationship was established between the various influencing factors and the solar radiation error. A back-propagation (BP) network algorithm was used to fit the discrete data obtained from the simulation to obtain the solar radiation error correction equation. Finally, the solar radiation error correction equation was verified. Outdoor experiments were conducted to confirm this system’s measurement accuracy. According to the experimental findings, the root-mean-square error was only 0.095 °C, which is a relatively high degree by which to reduce the temperature error. In addition, the average difference between the corrected value of the temperature observation system and the reference value was barely 0.084 °C.

1. Introduction

Temperature measurement is the basis of meteorology. Temperature changes are closely related to human survival and development, and temperature measurement is one of the foundations of meteorological research. In recent years, along with the gradual warming of the earth’s surface and atmosphere, there have been many research results on ground temperature changes. The temperature data for 1986–2020 showed a significant and continuous upward trend of 0.23 °C/10 years. By the 2020s, surface air temperature under the RCP4.5 and 8.5 scenarios indicated ranges of warming, which were 0.35–0.82 °C and 0.45–0.93 °C, respectively (Fyfe et al. 2013; Stott et al. 2013; Gleisner et al. 2015; Vicente-Serrano et al. 2018) [1,2,3,4]. Zhang et al. (2021) [5] calculated index series over years 1951–2018 for all stations and rural stations, concluding that the global land annual mean temperature and most extreme temperature indices experienced significant urbanization effects statistically. After the mid-1980s, urbanization impacted the temperature substantially in East Asia. Jiang and others (2021) [6] demonstrated that each 10% increase in the urbanization ratio with 10 km² had led to additional annual warming of 0.14 ± 0.11 °C, 0.17 ± 0.08 °C, and 0.30 ± 0.17 °C for daily maximum, mean, and minimum air temperatures in Beijing, respectively, from 1985 to 2017. Accurate temperature measurement has played a vital role in social production. Temperature changes result in a series of chain reactions in agriculture, industry, service industries, etc. Therefore, the improvement of measurement accuracy is extremely important to the study of temperature changes, and it is necessary to increase the accuracy to 0.1 °C, or even 0.05 °C.

Errors in the hardware circuit system and the influence of solar radiation are the main sources of temperature measurement error. Different types of temperature sensors have their advantages, disadvantages, and measurement accuracy. Thermocouple sensors are relatively low-cost. Accuracy is between ±0.5 °C and ±2 °C, over a wide range, while narrower measurement ranges can approach 0.1 °C (Ross-Pinnock et al. 2016). The physical and chemical properties of platinum metal are stable, the material is easy to purify, the accuracy is high, and the reproducibility is good. Therefore, WMO stipulates platinum resistance thermometers as the standard instrument for use between −259.34 °C and 630.74 °C. Current automatic weather stations mainly uses platinum resistance as the temperature sensor material, and the measurement accuracy can reach ±0.01–0.2 °C (Ross-Pinnock et al. 2016) [7]. Thermistors are made of semiconductor materials with a typically non-linear temperature–resistance relationship. Schweiger (2007) [8] proposed that a fast multi-channel precision thermometer could be developed, provided that there was sufficient sensor selection and calibration to observe deviations of less than 0.03 °C in tests performed over a range from −50–10 °C. Therefore, the temperature sensors used in meteorological measurements can achieve a high degree of accuracy.

Several studies have revealed the relationship between various environmental factors and temperature. The consequence of urbanization is the loss of vegetation, with consequent changes in short-wave radiation, long-wave radiation, and the reflectivity of the underlying surface (Silva and Torres 2021) [9]. Erell (2005) [10] illustrated that, in the presence of a short-wave or long-wave radiant, radiative exchange leads to unacceptable errors in measurement accuracy, and the heating caused by short-wave radiation can be quantified. Moreover, the sun radiates directly to the surface of the temperature sensor, heating the sensor probe and causing the temperature around the probe to be higher than the ambient air. Weather stations usually place a thermometer screen or radiation shield outside the temperature sensor to shield it from direct sunlight. However, aging of the coatings weakens their ability to reflect sunlight, resulting in a 1.63 °C error (Lopardo et al. 2014) [11]. In addition, the poor fluidity in shields forms a microclimate, which reduces the response speed of the internal sensor. On a clear, windless day, at midday, the temperature error can be 2–4 °C (Lin et al. 2005) [12]. Taking into account the effects of seasonal changes, from the study conducted by Mackiewicz (2012) [13], snow surface can seriously elevate radiation errors. The daytime radiation errors can increase by 1 °C when the surface is snow-covered, compared with a non-snow-covered surface. In summary, to improve temperature measurement accuracy, several environmental factors (such as snow, rain, hail, etc.) also need to be considered.

Nakamura and Mahrt (2005) [14] proposed an empirical model to correct temperature measurement errors. They considered the influence of wind speed and short-wave radiation on temperature measurement when building the model, and the root-mean-square error between the measured value and the corrected value after the correction was 0.13 °C. Nevertheless, their model does not consider the influence of scattered radiation or solar radiation. Cheng et al. (2014) [15] analyzed temperature measurement errors between Chinese and imported radiation shields. They proposed an improved correction method for viewing the impact of global solar radiation, wind speed, and air temperature to improve accuracy to 0.26 °C and 0.17 °C, respectively. A new technique using dual temperature sensors with different emissivities could reduce the measurement error to 0.98 °C (Lee et al. 2018) [16]. Kurzeja (2010) [17] researched aspirated radiation shields and pointed out that the root-mean-square error of the measured temperature, without correction, is 0.35 °C. The measurement error of the DTR502B aspirated radiation shield produced by the Finnish company VAISALA is between −0.1 °C and 0.2 °C. The error of the aspirated radiation shield developed by the Huayun company is within ±0.1 °C. Aspirated radiation shields increase wind speed around the sensor, so measurement errors can be minimized. However, an aspirated radiation shield requires higher power to keep the motor running and is expensive; only a few weather stations use it.

As seen in the previous sections, the accuracy of temperature measurement with traditional radiation shields has been previously improved. However, the error range of most radiation shields is still greater than 0.1 °C. Some radiation shields have met the demand, but the price of those is too expensive. Therefore, the traditional radiation shield hasn’t satisfied the requirements of factories. To improve the temperature measurement accuracy and reduce the cost, a new natural ventilation radiation shield was designed. Combined with the algorithm, the error correction equation was established, which was applied to the surface air temperature measurement. Firstly, the sensor structure was optimized by employing a CFD method. Then, the effects of solar radiation intensity, wind speed, scattered radiation, long-wave radiation, and underlying surface reflectivity on radiation error were taken into account to obtain a correction equation. Then, a BP neural network algorithm was used to fit emulated data. Finally, an experimental platform was set up for temperature observation, and the correction equation was used to correct the error and verify the accuracy.

2. Design of the Radiation Shield

2.1. Model Construction of the Temperature Sensor

The temperature observation device mainly consists of a naturally-ventilated radiation shield and Pt100 platinum resistance thermometer. Platinum is one of the most stable metal elements in the world. Its resistivity and TCR hardly change under normal working conditions. The noise of DC inside a Pt100 resistor is generally small compared to many other conducting materials. In addition, the temperature sensor designed in this paper is for use in the meteorological profession. The Pt100 is recommended as a temperature sensing element in China’s meteorological platinum resistance temperature transducer professional standard. Three-dimensional schematics of the naturally-ventilated radiation shield and the installation position of the temperature sensor are shown in Figure 1. The radiation shield consists of a temperature sensor probe, a supporting column for the temperature sensor probe, four insulating columns, two aluminum plates, and the resins. Furthermore, this radiation shield adopts a multi-layer structure to obstruct direct solar radiation, reflected radiation, and upwelling long-wave radiation. The upper and lower ends each have an aluminum plate with an outer surface coated with silver, which has high reflectivity and blocks most direct solar radiation. The inner surface of the aluminum plate is painted black to absorb reflected radiation from the ground. The size of the aluminum plate is 180 mm (L) × 180 mm (W) × 1 mm (T). The middle part is made up of two umbrella-shaped annular plates with 50 and 60 mm radii to shield scattered radiation and slanting sunlight. A cylindrical diversion pipe has an aluminum plate at each end with a radius of 40 mm. Eight vents are evenly distributed around the cylindrical diversion pipe to ensure the air around the temperature sensor probe is effectively circulated with the outside air. Below is a reflector in the shape of a truncated cone to reflect sunlight. The aforementioned annular plates, diversion pipe, and reflector are made of white resin with a thickness of 2 mm. The aluminum plate is connected to the middle parts by four support columns with diameters of 3 mm. The temperature sensor probe is installed in the center of the vents.

2.2. CFD Simulation and Result Analysis

On the basis of hydrodynamics and the numerical computation method, computation fluid dynamics (CFD) can help us find the solution to discrete data through the continuity equation, dynamic equation, and energy equation. Under the circumstances of solar radiation and long wave radiation, on the one hand, the absorbed radiation energy is formed between the temperature sensor’s surface and the radiation, and causes an increase in the temperature. On the other hand, natural convection heat transfer and steady heat conduction glue appear when the airflow has skimmed over the temperature sensor’s surface, and causes the temperature to decline, the phenomenon of which is a typical heat balance in fluid mechanics.

Fluent is a piece of CFD software which is used to analyze the relationship between flow distribution, radiation, convection heat transfer, and fluid–structure interaction. Fluent also provides the flexible mesh characteristic. Fluent is able to generate tetrahedrons, hexahedrons, and other meshes for 3D models. The 3D model is divided into tetrahedral meshes by a highly adaptive unstructured meshing technology and a meshing software, ICEM (Huang et al. 2017) [18]. Although the more delicate the meshing, the more accurate the results will be, this also means that the calculation process is more complex and takes longer. It was concluded that a reasonable air domain size is 1200 mm × 1200 mm × 2000 mm, by comparing models with various air domains. The grid size of the air domain is 128 mm. The naturally-ventilated radiation shield is meshed according to the size of each part, with grid sizes from 3–4 mm. The quality of the grids, viewed after gridding, is above 0.3, which meets the simulation requirements. Then, the model is imported into Fluent for numerical calculation (Kumar et al. 2017; Qian et al. 2018) [19,20]. This numerical simulation selects the energy equation, the k-epsilon standard turbulence model, a SIMPLE algorithm, and a solar ray-tracing model to solve the momentum, energy, and turbulence parameters.

The fluid–structure coupling simulation analysis of the temperature sensor is carried out for direct solar radiation, atmospheric convection heat transfer, and internal heat conduction. The flow control equation of external in-compressible air is as follows:

$$\nabla \cdot v=0$$

(1)

$$pv\cdot \nabla v=-\nabla p+\mu {\nabla }^{2}v+\rho g\beta \left(T-T_f\right)$$

(2)

where v is the velocity vector, ρ is the density, p is the pressure, µ is the power, g is the gravity acceleration, and β is the coefficient of thermal expansion for air.

The internal resistance energy equation of the temperature sensor is as follows:

$$\rho C_p\frac{\partial T}{\partial t}=\lambda {\nabla }^{2}T$$

(3)

The boundary condition of the surface heat transfer equation for the temperature sensor is as follows:

$$-\lambda \frac{\partial T}{\partial n}=-q_{dn}+q_{co}$$

(4)

where q is the surface heat flux of the temperature sensor as positive along with the outer normal line, and q_dn, and q_co are the convective heat transfer between direct solar radiation and external air, respectively.

The underlying surface reflectivity and outer surface absorption rate of the natural ventilation radiation shield are 0.2 and 0.8, respectively. The outer surface of the aluminum plate is coated with silver, and the inner surface is blackened, so the inner surface’s absorption rate and the outer surface’s reflectivity are 0.9 and 0.95, respectively. The parameters of the materials involved in the radiation shield and sensors are shown in

Table 1. Material properties of the radiation shield.

Material	Density (kg·m −3)	Heat Capacity (J·kg −1·K −1)	Thermal Conductivity (W·m −1·K −1)	Reflectivity
Aluminum	2719	871	202.4	90%
White resin	110	1591	0.2	20%
Copper	9	381	387.6	60%

.

A computer with 8 cores, 6.40 GHz CPU frequency, and 32.0 GB RAM capacity was used for simulation. It took about 8 min to obtain a simulation result; because the simulation time cost is difficult to reduce, it is virtually impossible to correct the radiation error only through the CFD method. A solar radiation intensity of 1000 W/m², wind speed of 2 m/s, altitude of weather station of 0 km, solar elevation angle of 45°, and reflectivity of the grassland of 0.2 were applied as environmental conditions. Using Fluent for calculation, temperature and velocity field simulation results of the radiation shields designed in this paper were obtained. According to the calculation results of Fluent, we can optimize the structure of the radiation shield according to the temperature and wind speed at the location of the sensor, as shown in Figure 2.

From Figure 2a, the ambient temperature of the air domain is 300 K, indicated in blue. The radiation causes warming, with the color becoming progressively redder as the temperature increases. The radiation error at the center of the vent hole is 0.072 K. From Figure 2b, the ambient wind speed in the air domain is 2 m/s, and the wind speed at the center of the vent hole is 1.540 m/s. The radiation error in the center position of the traditional radiation shield is 0.73 K, and the wind speed is 0.63 m/s (Yang et al. 2021) [21]. This model has better radiation protection and ventilation than the traditional radiation shield.

The radiation error at different wind speeds V, solar elevation angle A, solar radiation intensity S, long-wave radiation intensity L, diffuse radiation intensity D, and underlying surface reflectivity R were calculated separately by the control variable method. The range of V, A, S, L, D, and R is 1–8 m/s, 10–90°, 100–1300 W/m², 50–500 W/m², 50–300 W/m², and 0.1–0.9, respectively. We changed only one of the environment variables and left the rest at their default values. The default values and the range of environment variables change as shown in

Table 2. The range of different environmental factors.

Environmental Factors	S (W/m2)	L (W/m2)	D (W/m2)	R	V (m/s)	A (°)
Range	100–1300	50–500	50–300	0.1–0.9	1–8	10–90
Default value	1000	300	200	0.2	2	45

.

A multi-physics field fluid–solid coupled heat transfer analysis was carried out using the CFD method under different environmental conditions. The relationship between different environmental factors and radiation errors was obtained, as shown in Figure 3.

It can be seen from Figure 3a that the radiation error increases with solar radiation intensity. At a wind speed of 1 m/s and solar radiation intensity of 100 W/m², the radiation error is 0.103 °C. At a solar radiation intensity of 1000 W/m², the radiation error is 0.147 °C. The solar radiation intensity causes a significant error, but the temperature rise does not exceed 0.15 °C. This is because the high reflectivity aluminum plate of the radiation shield can better resist the radiation warming caused by direct solar radiation. The radiation shielding structure has a limited ability to block diffuse radiation, and the effect of diffuse radiation intensity on the radiation error is shown in Figure 3b. At a wind speed of 1 m/s and diffuse radiation intensity of 100 W/m², the radiation error is 0.106 °C, and at a diffuse radiation intensity of 300 W/m², the radiation error is 0.191 °C. The aluminum plate below can effectively block long-wave radiation and reflected radiation from the ground, so long-wave radiation and underlying surface reflectivity have less influence on the radiation error, as can be seen in Figure 3c,d. The outer surface of the radiation shield can directly block part of the solar radiation. The blackened inner surface can absorb solar radiation and reduce the reflected radiation, thus reducing the radiation error. Hence, the effect of the solar altitude angle on the radiation error is also on the small side, as shown in Figure 3e. When the wind speed is 1 m/s, and the solar elevation angle is 30°, 50°, 70° or 90°, the radiation error is 0.139 °C, 0.152 °C, 0.159 °C, or 0.162 °C, respectively. However, at 10°, some sunlight hits the sensor directly, causing a radiation rise of 0.139 °C. At 20°, the radiation shield blocks the sunlight relatively well, so the resulting radiation error is reduced to 0.128 °C.

2.3. Radiation Error Correction

The BP (back-propagation) algorithm is the most basic and important among all kinds of neural network algorithms. The BP neural network is a multi-layer neural network with supervised back-propagation training which is composed of the input layer, hidden layer, and output layer. The BP neural network can effectively approximate any nonlinear system. The temperature observation system is complex, and has various influencing factors. Therefore, a BP algorithm is suitable for the temperature observation system to establish the solar radiation error correction equation.

Considering that Fluent cannot calculate all environmental conditions, it is necessary to propose a model that can be applied to all cases. Based on the discrete data obtained from the simulation, 70% of the data were used as training samples, 15% as validation samples, and 15% as test samples. In this model, the number of neurons in the input layer is six, which means six environmental factors, ten neurons in the hidden layer, and one neuron in the output layer, which means radiation error. A three-layer BP neural network algorithm was used to obtain a universal correction, Equation (5).

$$\Delta T_{BP}=purelin\left\{w_2^T\left[\tan sig\left(w_1^{T}x+b_1\right)\right]+b_2\right\}$$

(5)

This equation enables calculation of the radiation error in the current environment from wind speed V, solar elevation angle A, solar radiation S, long-wave radiation L, diffuse radiation intensity D, and underlying surface reflectivity R. Where x is the input and the expression is x = (V D S L E R) ^T, w₁ and b₁ are the weight value and bias term from the input layer to the hidden layer, respectively, and w₂ and b₂ are the weight value and bias term from the hidden layer to the output layer, respectively. This equation can calculate an accurate quantitative value of radiation error ΔT_BP.

$$w_1=\left(\begin{array}{cccccc}-0.34731& -0.06258& 0.23456& 0.11647& 0.39764& 0.10801\\ -1.19507& 0.87389& 1.06133& -0.02869& 0.90530& 0.37652\\ -1.53881& 0.76044& 0.11059& -0.23902& -0.04143& 0.34467\\ 0.53791& -2.20520& 1.92115& 0.67627& 0.55606& -1.87859\\ -0.49806& -4.92025& -1.90616& 0.23396& 0.46964& 1.89548\\ -1.05000& -0.41701& 0.08572& 0.09599& 0.38282& 0.11276\\ 1.04400& 1.92602& -0.13913& 0.03576& 0.16834& -0.10443\\ -4.00819& 0.20744& 0.23804& 0.00421& 0.35032& 0.17451\\ 2.34538& 3.63257& 0.36626& 0.26444& -0.05129& -0.50051\\ -1.30762& -2.12433& 0.40268& 0.16421& -0.01807& -0.09218\end{array}\right)$$

$$b_2=\left(-0.68226\right)$$

$$w_2=\left(\begin{array}{cccccccccc}0.38871& 0.03971& 0.22366& 1.073604& 3.12323& 0.40892& 4.76482& 0.98544& -1.18403& 1.12345\end{array}\right)$$

The accuracy of the radiation error correction equation can be represented by root-mean-square error (RMSE).

$$RMSE=\sqrt{\frac{{\displaystyle {\sum }_{\mathrm{i}=1}^n{(E_c-E_e)}^2}}{n}}$$

(6)

where E_c is the numerical calculation result of CFD, E_e is the calculation of the modified equation ΔT_BP, and n is the number of samples.

The RMSE between the calculated value from Equation (5) and the simulated value by CFD is 0.0005 °C. To show the error distribution of the training model more intuitively, the histogram shown in Figure 4 describes the error of the training sample (70%), the verification sample (15%), and the test sample (15%). It can be seen that errors are distributed within ±0.0015 °C. The correlation between the total sample and this model is 0.99991, as shown in Figure 5, which illustrates that the radiation error correction equation is consistent with the data. Therefore, if this equation corrects the measurement, the error may be reduced to less than 0.1 °C.

3. Observation Experiment and Result Analysis

An air temperature observation platform was set up to verify the reliability of this temperature observation system and the accuracy of the radiation error correction equation. According to the WMO guide to meteorological instruments and observation methods (CIMO Guide), the observed air temperature should represent the free air conditions surrounding it. The station was set up over as large an area as possible, at a height between 1.25 and 2 m above ground level. The sensors should be kept away from local obstructions as much as possible; therefore, a platform was built on the Nanjing University of Information Science and Technology Site (32.12° N, 118.42° E, elevation 22 m). The placement of radiation shields and sensors is shown in Figure 6.

As shown in Figure 6, A is the new radiation shield temperature measurement device designed in this paper. B is an aspirated radiation shield (076B) temperature measurement device designed by the Met One company. C is a traditional radiation shield temperature measurement device. The airflow speed of the suction air in the radiation shield was 3 m/s. The measurements of 076B were selected as the reference values because their radiation error is less than 0.03 °C (Thomas CK and Smoot AR. 2013; Villa DL. 2021) [22,23], so they can be used as a reference. All types of equipment were mounted onto a frame at a height of 1.5 m over a grass surface. The temperature measured in the three radiation shields is called T_A, T_B, and T_C. A wind sentry 03002 and a Pyranometer CMP21 were used to measure wind speed and solar radiation intensity. The observed results of the wind speed and solar radiation intensity measurements are shown in Figure 7.

The temperature measurements T_A, T_B, and T_C over four days were selected. We then calculated the temperature error ΔT_AB between the temperature T_A measured in the new radiation shield and the reference value T_B, as well as the temperature error ΔT_CB between the temperature T_C measured in the new radiation shield and the reference value T_B. The radiation error ΔT_BP was calculated by Equation (5) based on the observed environmental data. The ΔT_BP was then subtracted from T_B to obtain the corrected temperature value T′_A. We calculated the temperature error ΔT′_AB between the correction value T′_A and the reference value T_B. The temperature errors ΔT_AB, ΔT_CB, and ΔT′_AB are shown in Figure 8.

As seen from Figure 8, the temperature error of the radiation shield designed in this paper is significantly lower than that of the traditional radiation shield. The temperature error can be further reduced, after correction, to ±0.1 °C. After calculating the data in Figure 8, it can be seen that the average temperature errors of the traditional radiation shield $\overline{\Delta T_{AB}}$ from May 4 to 7 were 0.585 °C, 0.701 °C, 0.497 °C, and 0.169 °C, respectively. The average temperature errors of the new radiation shield $\overline{\Delta T_{CB}}$ were 0.152 °C, 0.215 °C, 0.113 °C, and 0.054 °C, respectively, and the average temperature errors corrected by the error equation $\overline{\Delta {T^{\prime }}_{AB}}$ were 0.062 °C, 0.093 °C, 0.065 °C, and 0.045 °C, respectively. According to the simulation results in Figure 3, the impact of wind speed on radiation error is undeniable. The radiation error of the new radiation shield can be reduced to 0.03 °C, or lower, when the wind speed is greater than 5 m/s. Therefore, combining Figure 7 and Figure 8, it can be seen that some of the temperature values measured inside the new radiation shield are lower than the reference values for wind speeds greater than 5 m/s. In most environments, the wind speed is within 3 m/s. According to the data in Figure 8, we know that the corrected temperature can reduce the error to ±0.1 °C when the wind speed is greater than 1.5 m/s.

4. Conclusions and Future Work

This paper proposed a natural ventilation radiation shield that can effectively reduce radiation errors. Moreover, outdoor experiments were conducted to verify this system’s measurement accuracy. Based on the experimental results, the following conclusions can be drawn:

(1)

The natural radiation shield was designed with two aluminum plates, eight vents, and a multi-layer structure which is able to resist direct solar radiation, reflected radiation, and upwelling long-wave radiation better than a traditional shield while ensuring that the temperature sensor probe can work effectively.

(2)

The natural ventilation radiation shield proposed in this paper is simpler and lighter in structure compared with the traditional radiation shield, and the radiation error can be reduced to 0.1.

(3)

Using a BP neural network algorithm to establish the error correction equation, the error can be reduced again after the correction of the temperature data inside the radiation shield proposed in this paper. When the wind speed is greater than 1.5 m/s, the error can be reduced to within ±0.1 °C.

The material of the radiation shield designed in this paper is low cost, but oxidation problems will occur, so the choice of outer surface coating needs to be further considered in subsequent research to improve its reflectivity and grow its service life.