© F. Qian et al., Published by EDP Sciences, 2025

1 Introduction

Measurement comparison is the process of comparing, analyzing, and evaluating quantity values that are reproduced by measurement standards for the same quantity value under specified conditions. Besides, conducting measurement comparisons strengthens the management of measurement standards and enables an examination of the accuracy and consistency of measurement values and results issued by each laboratory [1]. The effective comparison of regional measurement institutions to validate and reinforce the technical and managerial competencies of metrological laboratories operating within the region. Internationally, comparison results enable the mutual recognition of metrological capabilities among national institutions worldwide [2]. Participating in measurement comparison is essential for the functioning and administration of metrology institutions. Marine humidity, as a fundamental element in hydrometeorological observation, indicates the possibility of dew, fog, or precipitation when measured. Accordingly, ensuring the accuracy and consistency of marine humidity measurement data is of great significance for marine shipping safety and ecological investigations. To verify the accuracy and consistency of national marine humidity values, comparing the humidity values among three marine metrology laboratories is a pragmatic and efficacious approach [3].

For the purpose of verifying accurate and consistency in the measurement of marine humidity data and the selection of appropriate humidity comparison reference values, this paper thoroughly explores an analysis and provides a description of the comparison methodology. In the preparation stage of organize humidity comparison, the aspects covered include determine the comparison laboratory, unify humidity calibration method, test of characteristic of transfer standard, choose comparison transfer path, clear evaluation criteria, develop and review implementation plans for humidity comparison.

2 Comparison design

2.1 Content of comparison

The content of this comparison is the humidity calibration and measurement capabilities of three marine metrology laboratories, with the aim of validating the accuracy and consistency of humidity measurement data.

2.2 Laboratories and traceability analysis of humidity

The three marine metrology laboratories participate in the humidity comparison, including the Guangzhou Branch of Laboratory A National Marine Measurement Station, the Qingdao Branch of Laboratory B National Marine Measurement Station, and the Shanghai Branch of Laboratory C National Marine Measurement Station. Furthermore, the performance of the metrological standard device of each laboratory is depicted in Table 1.

The humidity value of laboratory A is traced to the precision dew point meter standard device of South China National Centre of Metrology, and ultimately to the humidity standard of the National Institute of Metrology, China. Besides, the humidity values of Laboratory B and Laboratory C are traced to the precision dew point meter standard device of the Shanghai Institute of Measurement and Testing Technology and finally to the humidity standard of the National Institute of Metrology, China. The measurement traceability path is the thin solid line shown in Figure 1. In accordance with the classification of traceability for quantity value proposed by Yuan Zundong and other scholars, it can be categorized into internal reproducibility value, independent traceability value, and non-independent traceability value [4]. Based on the traceability path analysis of the humidity values from each laboratory, it can be concluded that humidity value of each laboratory falls under the category of independent traceability value, and the humidity value reported by these laboratories are mutually independent.

Fig. 1 The measurement traceability path of each laboratory.

2.3 Humidity sensor calibration method

The humidity calibration of the three marine metrology laboratories adopts the method specified in JJF 1076 and the precision dew point hygrometer and the VAISALA humidity sensor are concurrently placed in the humidity verification box or humidity generator for measurement. Then the temperature of humidity verification box or humidity generator is set at 25 °C and the humidity is set at 30%RH to 90%RH in sequence. When the humidity verification box or humidity generator forms a stable and utable and uniform temperature and humidity environment, three sets of humidity data are measured and recorded every 2 min using precision dew point hygrometer and the VAISALA humidity sensor. Hence, the calibration of humidity sensor at each humidity point is realized according to this method [5,6], and the humidity calibration process of each laboratory is shown in Figure 2.

Fig. 2 Schematic diagram of the humidity calibration.

2.4 Transfer standard

This humidity transfer standard employs the impedance-type VAISALA MI70 humidity sensor. To assess the technical condition of the transfer standard and ascertain the uncertainty introduced by the transfer standard due to instability in the transmission process of this comparison, Laboratory A conducted humidity calibration on the transfer standard at both the commencement and the conclusion of the comparison. The humidity correction value of the transfer standard at each calibration point is obtained by equation (1):

$$Y_{ji}=Y_{sji}-Y_{mji}$$(1)

where Y_ji − The humidity correction value of the transfer standard at the i calibration point of laboratory j; Y_sji − The humidity standard value of laboratory j at the i calibration point; Y_mji − Measured value of the transfer standard at the i calibration point by the laboratory j; j − Laboratory code, j = A represents laboratory A, j = B indicates laboratory B, j = C denotes laboratory C; i − The serial number of the calibration point in measurement comparison, for instance, i =1 corresponds to 30%RH,..., i = 7 corresponds to 90%RH.

The change of humidity correction value of transfer standard through two calibrations before and after of laboratory A is obtained by equation (2):

$$\mathrm{\Delta }{Y}_{Ai}=Y_{Ai}-{Y^{\prime }}_{Ai}$$(2)

where Δ Y_Ai – The change of humidity correction value of transfer standard; Y_Ai – The humidity correction value of transfer standard at i th calibration point by A laboratory before comparison; Y'_Ai – The humidity correction value of transfer standard at i th calibration point by laboratory A after comparison.

The change of humidity correction value follows a distribution characterized by uniformity. By utilizing equation (3), the standard uncertainty due to the instability of transfer standard can be acquired. Referencing Table 2 will provide the obtained standard uncertainty.

$$u_{ei}=\frac{\mathrm{\Delta }{Y}_{Ai}}{\sqrt{3}}$$(3)

where u_ei – The standard uncertainty due to the instability of transfer standard at i th calibration point.

Based on the evaluation of technical status of the transfer standard, the standard uncertainty due to the instability of transfer standard is uniformly determined to be u_ei = 0.5%RH by conservatively taking into account the worst case maximum value of differences between two corrections.

2.5 Comparison transfer path

Circular transmission is employed in this humidity comparison to transfer standard. During the transport, the transfer standard humidity sensor was packed in the Transit cases for added protection and shipped via courier. Besides, the transfer path is the thick and solid line indicated in Figure 3, which is transferred in the order of laboratory A, laboratory B, laboratory C, and back to laboratory A.

Fig. 3 Comparison transfer path.

3 Reference value models and comparison result analysis

This humidity comparison is between equal peers, it is important to choose a reference value for the comparison that is some combination of the measured values of the different participants. Moreover, the results are analyzed and examined in the following four cases by employing the arithmetic mean model, the weighted mean model, the arithmetic mean model calculated using the data from the other two labs, as well as the quantity value measured by the higher-level measurement standard device as the reference value.

3.1 Arithmetic mean model and outlier detection

3.1.1 Arithmetic mean model

Arithmetic mean model in the international key comparison of the CCT-K7 water triple point vessel, due to the large distinctions among laboratories on how to evaluate and correct the uncertainty caused by isotopes, Yan et al. adopted the arithmetic mean method in calculating the reference value of comparison, and eliminated the influence of the uncertainty of numerous laboratories on the weight by adopting arithmetic mean method [7]. When the uncertainty evaluation of the participating laboratories is different significantly, it is fair to use arithmetic mean to calculate the reference value. In this case, each participating laboratory has equal weight, reducing the impact of random factors on the results. The calculation model of arithmetic mean is indicated in equation (4) below:

$$Y_{\text{r}i}=\frac{1}{3}{\displaystyle \sum _{j=A}^{\text{C}}}{Y}_{ji}$$(4)

where Y_ri − reference value of humidity correction of transfer standard at ith calibration point; Y_ji − The humidity correction value of transfer standard at the ith calibration point of laboratory j.

As the calibration outcomes of the three participating laboratories in the comparison are mutually independent, the uncertainty calculation formula corresponding to the reference value Y_ri of each calibration point is illustrated in equation (5):

$$u_{ri}=\frac{1}{3}\sqrt{{\displaystyle \sum _{j=A}^C}{u}_{ji}^2}$$(5)

where u_ji – The standard uncertainty of the measurement results in the laboratory j at i th calibration point; u_ri − The standard uncertainty corresponding to the reference value Y_ri at the i-th calibration point.

3.1.2 Humidity comparison statistics

Since the calibration of the humidity possesses a well-defined mathematical calculation equation (1), the GUM method is used to evaluate the uncertainty of the humidity correction value [8]. To ensure uniformity in comparison, the three marine metrology laboratories involved in this humidity comparison have identified standard uncertainty components in the uncertainty evaluation process. These components include the measurement repeatability of the transfer standard, the measurement of precision dew point hygrometers, and the humidity uniformity and fluctuation of the humidity verification box or humidity generator. The uncertainty evaluation process for humidity correction value in each laboratory is as follows.

(1) The standard uncertainty component u_{repeatability} introduced by the measurement repeatability of the transfer standard is evaluated using Type A evaluation method

At the humidity calibration point, the data is obtained from 10 measurements through transfer standard. The standard uncertainty component introduced by measurement repeatability is illustrated in equation (6):

$$u_{\text{repeatability}}=\sqrt{\frac{{\displaystyle \sum _{k=1}^{10}}(Y_{mjik}-Y_{mji}{)}^2}{9\times 3}}$$(6)

where Y_mjik − k-th measured value of the transfer standard at the i calibration point by the laboratory j; Y_mji – Measured value of the transfer standard at the i calibration point by the laboratory j; u_{repeatability} – Standard uncertainty component introduced by the measurement repeatability of the transfer standard.

(2) The standard uncertainty component u_pdph introduced by the measurement of precision dew point hygrometers is evaluated using Type B evaluation method.

The measurement value expanded uncertainty U_pdph of precision dew point hygrometers is obtained from the calibration certificate. The measurement value expanded uncertainty follows a distribution characterized by uniformity. The standard uncertainty component introduced by the measurement of precision dew point hygrometers is illustrated in equation (7):

$$u_{\text{pdph}}=\frac{U_{\text{pdph}}}{\sqrt{3}}$$(7)

where U_pdph – The measurement value expanded uncertainty of precision dew point hygrometers; u_pdph – The measurement value standard uncertainty of precision dew point hygrometers.

(3) The standard uncertainty component u_uniformity introduced by the humidity uniformity of the humidity verification box or humidity generator is evaluated using Type B evaluation method

The humidity uniformity H_uniformity of the humidity verification box or humidity generator is obtained from the calibration certificate. The humidity uniformity follows a distribution characterized by uniformity. The standard uncertainty component introduced by the humidity uniformity is illustrated in Equation (8):

$$u_{\text{uniformity}}=\frac{H_{\text{uniformity}}}{\sqrt{3}}$$(8)

where H_uniformity – The humidity uniformity of the humidity verification box or humidity generator ; u_uniformity – The standard uncertainty component introduced by the humidity uniformity of the humidity verification box or humidity generator.

(4) The standard uncertainty component u_fluctuation introduced by the humidity fluctuation of the humidity verification box or humidity generator is evaluated using Type B evaluation method

The humidity fluctuation H_fluctuation of the humidity verification box or humidity generator is obtained from the calibration certificate. The humidity fluctuation follows a distribution characterized by uniformity. The standard uncertainty component introduced by the humidity fluctuation is illustrated in equation (9):

$$u_{\text{fluctuation}}=\frac{H_{\text{fluctuation}}}{\sqrt{3}}$$(9)

where H_fluctuation – The humidity fluctuation of the humidity verification box or humidity generator ; u_fluctuation – The standard uncertainty component introduced by the humidity fluctuation of the humidity verification box or humidity generator.

The standard uncertainty component is independent of each other, so the combined standard uncertainty of humidity correction value is illustrated in Equation (10):

$$u_{ji}=\sqrt{{u_{\text{repeatability}}}^2+{u_{\text{pdph}}}^2+{u_{\text{uniformity}}}^2+{u_{\text{fluctuation}}}^2}$$(10)

where u_ji – The standard uncertainty of the measurement results in the laboratory j at i th calibration point.

The coverage factor k is set to 2, and the expanded uncertainty is:

$$U_{ji}=2u_{ji}$$

where U_ji – The expanded uncertainty of the measurement results in the laboratory j at i th calibration point.

Furthermore, the humidity correction value and expanded uncertainty data measured by three marine metrology laboratories are illustrated in Table 3.

3.1.3 Outlier detection and reference value calculation

In the calculation of the reference value using the arithmetic mean model, it is essential to identify outliers in the data from the three participating laboratories. Possible outliers listed in Table 3 should be excluded; otherwise, the determination of the reference value for measurement comparison and the assessment of comparison results of each laboratory may be impacted. First, equation (11) is employed to calculate the absolute residual difference between the correction value of each laboratory and the arithmetic mean value of humidity correction.

$$e_{ji}=\left|Y_{ji}{\displaystyle \stackrel{-}{Y_i}}\right|$$(11)

where e_ji – The absolute residual difference between the correction value by laboratory j at i th measurement point and the reference value of the correction value; Y_ji − The humidity correction value of transfer standard at the i th calibration point of laboratory j; ${\overline{Y}}_i$ − Arithmetic mean value of humidity correction of transfer standard from three laboratories at i th calibration point.

Subsequently, the Grubbs criterion critical value G(0.01,3) = 1.155 is adopted to determine outliers. Besides, the ratio of absolute residual of the correction value to the experimental standard deviation of the correction value (e_ji/s)_max are all less than G(0.01,3), and no outliers were determined in the humidity correction values of the three laboratories. All data is applicable for calculating reference values utilizing the arithmetic mean model, as indicated in Table 4.

Based on the humidity correction data of each laboratory given in Table 3, the reference value of humidity correction and standard uncertainty at i th calibration point by equations (4) and (5), as presented in Table 5.

3.1.4 Comparison result based on arithmetic mean model

The comparison result is evaluated utilizing the En value. |En| ≦ 1, then the ratio of difference between the laboratory measurement result and reference value to uncertainty are within the reasonable expected range, and the comparison result is deemed satisfactory. When |En| > 1, the ratio of difference between the laboratory measurement result and reference value to uncertainty exceed reasonable expectations, the comparison result is deemed unsatisfactory, it is imperative to analyze the underlying reasons, and the calculation of the En value is outlined in Equation (12).

$$E_{\text{n}}=\frac{Y_{ji}-Y_{ri}}{k\times u_i}$$(12)

where k − Coverage factor, generally k=2 for 95% confidence; u_i − Standard uncertainty of Y_ji–Y_ri at the i-th calibration point.

When determining the reference value through the arithmetic mean model, the calculation incorporates the quantity values from each laboratory, with each laboratory quantity value being linked to the reference value. So the uncertainty of reference value includes the uncertainty of measured values in each laboratory, the u_ri and u_ji are correlated. To eliminate the correlation between Y_ji and Y_ri, the like terms in the measurement model Δy_ji of Y_ji – Y_ri are merged by using equation (13).

$$\begin{array}{l}\mathrm{\Delta }{y}_{ji}=Y_{ji}-Y_{ri}+\mathrm{\Delta }{Y}_{Ai}\\ \begin{array}{cc}\hfill \mathrm{}\hfill & \hfill =\hfill \end{array}{Y}_{ji}-\frac{1}{3}{\displaystyle \sum _{j=A}^{\text{C}}}{Y}_{ji}+\mathrm{\Delta }{Y}_{Ai}\\ \begin{array}{cc}\hfill \mathrm{}\hfill & \hfill =\hfill \end{array}\frac{2}{3}{Y}_{ji}-\frac{1}{3}{\displaystyle \sum _{\mathrm{}}^{g,h\ne j}}{Y}_{(g,h)i}+\mathrm{\Delta }{Y}_{Ai}\end{array}.$$(13)

In this scenario, the calculation of u_i follows the Equation (14).

$$u_i=\sqrt{{\left(\frac{2}{3}{u}_{ji}\right)}^2+{\left(\frac{1}{3}{u}_{gi}\right)}^2+{\left(\frac{1}{3}{u}_{hi}\right)}^2+u_{ei}^2}.$$(14)

The distribution of En absolute value of each laboratory based on the arithmetic mean model is revealed in Figure 4.

Fig. 4 Absolute values of En in each laboratory when the arithmetic mean is utilized as the reference value.

3.2 Weighted mean model and outlier detection

3.2.1 Weighted mean model

Giancarlo et al. highlighted that if the uncertainty of all laboratories participating in the comparison are sufficiently reliable, the weighted mean method can be employed to calculate the reference value to reflect the fairness of the comparison. During this period, the more independent laboratories are involved in calculating the reference value, the standard uncertainty of the obtained reference value is smaller [9]. Xu et al. also used the weighted mean method to calculate reference values in the measurement and comparison work of a low-temperature radiometer, to evaluate the measurement capability of the light radiation power of laboratory [10]. In this humidity comparison, a standardized approach is employed for the uncertainty evaluation methods across all laboratories, ensuring that the uncertainty results from each laboratory can be regarded as sufficiently reliable. The more independent laboratories participating in the comparison, the smaller standard uncertainty of reference value obtained by the weighted mean model will be. To minimize the standard uncertainty of the reference value and reflect the fairness of the comparison, the reference value is calculated by employing the weighted mean method. The calculation model is demonstrated in equation (15):

$$Y_{ri}^{\text{'}}=\frac{{\displaystyle \sum _{j=A}^C}\frac{Y_{ji}}{u_{ji}^2}}{{\displaystyle \sum _{j=A}^C}\frac{1}{u_{ji}^2}}.$$(15)

Given that the measurement value from the three participating laboratories in the comparison are mutually independent, the formula for determining the uncertainty of the reference value for each calibration point is stated as follows equation (16):

$$u_{ri}^{\text{'}}=\sqrt{\frac{1}{{\displaystyle \sum _{j=1}^n}\frac{1}{u_{ji}^2}}}.$$(16)

3.2.2 Outlier detection and reference value calculation

In accordance with the test results of outliers of the humidity correction values of the three laboratories in Section 2.1.2, no outliers were observed, and all data can be calculated using the weighted mean model to derive reference values.

Based on the humidity correction value of each laboratory as provided in Table 3, the correction reference value and standard uncertainty at each calibration point of humidity are acquired through equations (15) and (16), as demonstrated in Table 6.

3.2.3 Comparison results based on weighted mean model

On the condition that calculating reference values by the weighted mean method, the quantity values of each laboratory are likewise involved in the calculation. To eliminate the correlation between Y_ji and Y'_ri, the like terms in the measurement model Δy'_ji of Y_ji – Y'_ri are merged by using equation (17).

$$\begin{array}{l}\mathrm{\Delta }{y}_{ji}^{\text{'}}=Y_{ji}-Y_{ri}^{\text{'}}+\mathrm{\Delta }{Y}_{Ai}\\ \begin{array}{cc}\hfill \mathrm{}\hfill & \hfill =\hfill \end{array}{Y}_{ji}-\frac{{\displaystyle \sum _{j=A}^C}\frac{Y_{ji}}{u_{ji}^2}}{{\displaystyle \sum _{j=A}^C}\frac{1}{u_{ji}^2}}+\mathrm{\Delta }{Y}_{Ai}\\ \begin{array}{cc}\hfill \mathrm{}\hfill & \hfill =\hfill \end{array}(1-\frac{\frac{1}{u_{ji}^2}}{{\displaystyle \sum _{j=A}^C}\frac{1}{u_{ji}^2}})Y_{ji}-\frac{{\displaystyle \sum _{\mathrm{}}^{g,h\ne j}}\frac{Y_{(g,h)i}}{u_{(g,h)i}^2}}{{\displaystyle \sum _{j=A}^C}\frac{1}{u_{ji}^2}}+\mathrm{\Delta }{Y}_{Ai}\end{array}.$$(17)

In this scenario, the calculation of u_i follows the equation (18).

$$u_i=\sqrt{{\left((1-\frac{\frac{1}{u_{ji}^2}}{{\displaystyle \sum _{j=A}^C}\frac{1}{u_{ji}^2}})u_{ji}\right)}^2+{\left(\frac{\frac{1}{u_{gi}^2}}{{\displaystyle \sum _{j=A}^C}\frac{1}{u_{ji}^2}}{u}_{gi}\right)}^2+{\left(\frac{\frac{1}{u_{hi}^2}}{{\displaystyle \sum _{j=A}^C}\frac{1}{u_{ji}^2}}{u}_{hi}\right)}^2+u_{ei}^2}.$$(18)

The distribution of En absolute value of each laboratory based on the weighted mean model can be acquired, as shown in Figure 5.

Fig. 5 Absolute values of En in each laboratory when the weighted mean is utilized as the reference value.

3.3 Arithmetic mean model and outlier detection when the reference value applied to an individual lab is calculated using the data from the other two labs

3.3.1 Arithmetic mean model

Bjkovski et al. introduced that in the process of organizing eight laboratories to conduct temperature comparison, the reference value for the comparison was determined by employing the measured data from three laboratories with CMC qualification through the weighted mean method, thereby enhancing the reliability of reference value [11]. To eliminate the correlation between laboratory quantity values and reference values, Steele et al. proposed an exclusive statistical weighted mean method to calculate reference values, which ensures the independence of reference values and laboratory quantity values [12]. Due to the small number of laboratories in this humidity comparison, the reference value applied to an individual lab in the study is calculated using the arithmetic mean of data from the other two labs, ensuring that the reference value and the laboratory quantity value could be kept independent of each other, making the humidity reference value relatively objective. The calculation model is illustrated in Equation (19) below:

$$Y_{\text{r}ji}=\frac{1}{2}{\displaystyle \sum _{k\ne j}}{Y}_{ki}$$(19)

where: Y_rji − reference value for laboratory j humidity comparison; Y_ki – The humidity correction value of transfer standard at i th calibration point of laboratory k; k − Laboratory code, k≠A indicates excluding the data of laboratory A, k≠B shows excluding the data of laboratory B,k≠C symbolizes excluding the data of laboratory C.

Given that the measurement value from participating laboratories in the comparison are mutually independent, the formula for calculating the uncertainty of the reference value for each calibration point is outlined in equation (20):

$$u_{rji}=\frac{1}{2}\sqrt{{\displaystyle \sum _{k\ne j}}{u}_{ki}^2}$$(20)

where u_rji − Standard uncertainty of reference value for laboratory j humidity comparison; u_ki –The standard uncertainty of the measurement results at the i calibration point in the laboratory k.

3.3.2 Outlier detection and reference value calculation

Because only two laboratories are participating in reference value calculation after excluding the data from individual laboratory, outlier detection of laboratory data participating in reference value calculation will not be conducted in this case. Based on the humidity correction data of each laboratory given in Table 3, the reference value and standard uncertainty of humidity correction for the comparison in each laboratory are computed and presented in Table 7.

3.3.3 Comparison results based on arithmetic mean of data from the other two labs

When reference value applied to an individual lab in the study is calculated using the arithmetic mean of data from the other two labs., since the reference value is independent of this laboratory quantity value. So u_rji is independent of the u_ji, u_i will calculate according to the following equation (21):

$$u_i=\sqrt{u_{ji}^2+u_{ei}^2+u_{rji}^2}$$(21)

u_i − Standard uncertainty of Y_ji–Y_rji at the i th measurement point; u_ji–The standard uncertainty of the measurement results in the laboratory j at i th calibration point; u_ei − The standard uncertainty due to the instability of transfer standard at i th calibration point; u_rji − Standard uncertainty of reference value for laboratory j humidity comparison. The distribution of En absolute value of each laboratory can be acquired by equations (12) and (21), as shown in Figure 6.

Fig. 6 Absolute values of En in each laboratory when the reference value applied to an individual lab in the study is calculated using the arithmetic mean of data from the other two labs.

3.4 The quantity value measured by the higher-level measurement standard as reference value

3.4.1 The model of reference value in this case

In measurement comparison, the determination of reference value can be more authoritative by employing the quantity value of the pilot laboratory or national measurement standard or higher-level measurement standard as the reference value. Besides, the comparison of gamma-ray emitter conducted by British National Physical Laboratory (NPL) and the regional comparison of national-level hardness tester conducted by BIPM adopted the measurement data of pilot laboratories as reference values to realize the comparison and evaluation of the capabilities of each laboratory [13,14]. In the humidity comparison carried out by NMISA and MIRS/UL-FE/LMK, the reference value obtained by MIRS/UL-FE/LMK via the calibration of the VAISALA temperature and humidity sensor through dewpoint meter is utilized for the comparison in NMISA laboratory [15]. To determine the reference value of the humidity more authoritative, on the condition that the quantity value issued by the higher-level measurement standard is used as reference value, its model is indicated in the following equation (22):

$$Y_{\text{r}i}=Y_{\text{H}i}$$(22)

where Y_Hi − The humidity correction value of the transfer standard measured at the i th calibration point by the higher–level measurement standard.

The uncertainty formula corresponding to the reference value Y_ri of each calibration point is shown in equation (23)

$$u_{\text{r}i}=u_{\text{H}i}$$(23)

where u_Hi − Standard uncertainty of the measurement result of the higher-level measurement standard device at the i calibration point.

Furthermore, the performance of the higher-level measurement standard is depicted in Table 8.

3.4.2 Outlier detection and reference value calculation

When the reference value for the comparison is based on the quantity value issued by the higher-level measurement standard device, outlier detection is unnecessary. The reference value Y_ri and the standard uncertainty u_ri can be obtained according to the calibration certificate of the transfer standard issued by the higher-level measurement standard, as depicted in Table 9.

3.4.3 The comparison results are based on the higher-level measurement standard

When the humidity value provided by higher-level measurement standard is used as the reference value, the reference value is independent of quantity value for each laboratory. The u_i is calculated by equation (21), then En absolute value of each laboratory can be acquired by equation (12), as depicted in Figure 7.

Fig. 7 En absolute values of each laboratory when the quantity value issued by higher-level measurement standard device is used as reference value.

4 Humidity comparison analysis and problems

Through the determination of laboratories, the characteristics analysis of transfer standard, the design of comparison transfer path, the examination of four reference value models, and the statistics of comparison results, a comprehensive overview of the comparison process for marine humidity is presented in detail. Moreover, by utilizing four distinct reference value models, the calibration data of each participating laboratory in the humidity comparison are analyzed and studied. The results demonstrate that the En value of laboratory B is more than 1 when the quantity value issued by the higher-level measurement standard device is taken as the reference value, and the En value of all laboratories do not exceed 1 in other cases. Furthermore, when the uncertainty of calibration results in each laboratory is identical, the arithmetic mean value is considered as the reference value, the weighted mean value is taken as the reference value, and the arithmetic mean value calculated using the data from the other two labs is regarded as the reference value, the three methods exert minimal influence on the En, and the distribution trend of En value remains consistent. In comparison with the evaluation results acquired through the aforementioned three methods, when the measurement value provided by a higher-level measurement standard device serves as the reference value, the En value of laboratory B and laboratory C at each calibration point is generally larger, and the En value of laboratory A at each calibration point is typically smaller. Due to the lack of advantage in uncertainty of humidity correction value of the higher-level measurement standard, the evaluation result may be affected. In the case of different reference value mathematical model, the En value corresponding to the calibration result of each laboratory basically increase further with the increase of humidity. This may be due to the insufficient consideration of the uncertainty component introduced when evaluating the uncertainty of high humidity measurement results, causing a decrease in uncertainty of high humidity measurement results and a increase in En values. Overall, through the humidity comparison conducted by this organization, the humidity calibration capabilities of the three marine metrology research institutions were effectively assessed, confirming the consistency of the marine humidity measurement values across the three laboratories.

Simultaneously, there are likewise some problems in the process of humidity comparison. In the first place, there are merely three laboratories for this humidity comparison, the number of laboratories is relatively small. Second, if the humidity comparison takes a long time, it becomes imperative to contemplate the utilization of additional transfer standards and optimize the transfer path to further diminish the uncertainty due to the instability of the transfer standards. Third, when the humidity value issued by a higher-level measurement standard device is employed as the reference value, the uncertainty of the reference value should be achieved to be less than half to one-third of the uncertainty of the participating laboratory, to ensure that the impact of the uncertainty introduced by the reference value on the evaluation of the result is minimized. Given these problems, we will persist in optimizing and enhancing the humidity comparison in our future work, including inviting more laboratories to participate in the humidity comparison, etc.

5 Conclusion

In this paper, the transfer standard employed the impedance-type VAISALA MI70 humidity sensor is adopted to effectively carry out the measurement comparison between the marine humidity values of three measurement institutions, and the comparison results are analyzed from the reference value model, as well as outlier detection. Moreover, by comparing and analyzing the results, it is determined that there is a commendable consistency between the marine humidity values of the three research institutions, revealed the current technological status of traceability about marine humidity value, which offers assurance for further enhancing the accuracy and reliability of meteorological observation and monitoring values, including humidity. The analysis of different reference value models and comparison results provide a reference for conduct the marine humidity comparison work.

Funding

Project supported by National Marine Date Center, Guangdong–HongKong–Macao Greater Bay Area Branch (No.2024B1212080006).

Conflicts of interest

The authors declare no conflicts of interest.

Data availability statement

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Author contribution statement

Fei Qian: Conceptualization, Methodology, Software, Investigation, Writing - Original draft. Chenhao Gao: Writing - Original draft, Supervision, Writing-review & editing. Yikai Ma: Investigation. Shuqing Li: Investigation. Lei Sun: Investigation.

References

All Tables

All Figures

	Fig. 1 The measurement traceability path of each laboratory.
In the text

	Fig. 2 Schematic diagram of the humidity calibration.
In the text

	Fig. 3 Comparison transfer path.
In the text

	Fig. 4 Absolute values of En in each laboratory when the arithmetic mean is utilized as the reference value.
In the text

	Fig. 5 Absolute values of En in each laboratory when the weighted mean is utilized as the reference value.
In the text

	Fig. 6 Absolute values of En in each laboratory when the reference value applied to an individual lab in the study is calculated using the arithmetic mean of data from the other two labs.
In the text

	Fig. 7 En absolute values of each laboratory when the quantity value issued by higher-level measurement standard device is used as reference value.
In the text