1 Introduction

In March 2011, the Fukushima nuclear accident in Japan released a large amount of radioactive substances into the ocean, causing significant international impact [1,2,3,4,5]. On August 24, 2023, the Fukushima nuclear power plant initiated a nuclear wastewater discharge plan. The nuclear wastewater was discharged into the sea for 17 days, and a total of about 7800 m3 of nuclear wastewater was discharged. The Fukushima Daiichi Nuclear Power Plant has about 1.34 million tons of nuclear wastewater. In 2023, approximately 31,200 tons of nuclear wastewater will be discharged in four separate releases, directly causing radioactive contamination of the seawater. The γ-ray spectrometry, which does not require complex chemical separation and is simple to operate, is increasingly being used in the monitoring of radionuclides in seawater [6, 7]. At present, the International Atomic Energy Agency (IAEA) Marine Laboratory and Germany, Greece, Ireland [8,9,10,11] mostly use in-situ γ-ray spectrometry to investigate the types, contents and distribution of radionuclides in seawater. Among them, Germany, Greece and Ireland have used seawater in-situ γ-ray spectrometer to establish a marine radioactive monitoring network consisting of several sea or shore monitoring stations and mobile monitoring ships in their respective sea areas. However, most of the detectors used in these countries are NaI(Tl) crystals. The energy resolution of NaI(Tl) crystals is poor, and it is impossible to identify multiple radionuclide contamination at the same time. To enable in-situ radioactive monitoring of China's ocean, we improved a device based on a low-background high-purity germanium (HPGe) γ spectrometer designed for radioactive wastewater monitoring [12], mounting it on a ship to achieve in-situ measurement of radioactivity in seawater.

Assessing the uncertainty of the γ-ray spectrometry is essential for scientifically and reasonably measuring the credibility of its results, and also for improving the quality assurance system of marine environmental radioactivity monitoring and evaluation. Furthermore, uncertainty is an important indicator of the performance of monitoring devices. Analyzing and calculating the uncertainty of monitoring devices is a necessary prerequisite for presenting measurement results and improving the devices. 137Cs is one of the significant artificial radionuclide in seawater [13,14,15]. This paper takes 137Cs as an example, analyzing the uncertainty of the monitoring device in directly measuring the activity concentration of 137Cs in seawater samples. In the next section, we introduce the method, structure and uncertainty source of the developed monitoring device. Section 3 shows the uncertainty calculation process of radioactive measurement for seawater. In Sect. 4, we present the test results of the developed monitoring device.

2 Materials and methods

2.1 Methods

In-situ measurement refers to the method of obtaining radionuclide information by directly measuring the object of interest with a detector. In-situ γ-ray spectrum measurement of seawater involves suspending the γ-ray spectrum detector from a buoy or frame, and directly immersing it in the seawater of the area under investigation for measurement. In-situ γ-ray spectrum measurement of seawater has been extensively researched and applied in many countries [16, 17]. Compared with the laboratory analysis methods, in-situ γ-ray spectrum measurement of seawater offers several advantages: it allows for real-time, continuous monitoring, faster identification of contaminated areas, guidance and optimization for laboratory analysis sampling, application in seafloor geological mapping and mineral exploration, and investigation of radiation around submerged radioactive materials.

Radiochemical analysis method is a common method for monitoring radionuclide, widely used in measuring low-level radioactive samples. For the radiochemical analysis method of 137Cs in seawater, according to China's national standard "Radiochemical analysis of cesium-137 in water and ash of biological samples" [18]: separation of cesium by adsorption with ammonium phosphomolybdate in acidic solution, and the ammonium phosphomolybdate adsorbed with cesium was dissolved in sodium hydroxide solution, and then 137Cs was precipitated with cesium iodobismuthate in citric acid and acetic acid solution and its radioactivity was measured by low background β-ray measuring instrument. Generally, the combined standard relative uncertainty of measuring radionuclide in water samples using radiochemical analysis method is about 8–10%.

2.2 Monitoring device

The designed shipborne radioactive monitoring device consists of a nuclear radiation measurement system, a seawater collection system, and a data processing system (see Fig. 1). The device features high sensitivity, low environmental background, certain anti-contamination and decontamination capabilities, good reliability and stability, stable long-term operation, and ease of maintenance. The nuclear radiation measurement system consists of an HPGe detector, a sampling container (15.4 L), and a lead chamber (Φ55 × 60 cm, 10 cm thick), mainly used to measure the radioactivity in the seawater inside the sampling container and reduce the background counts caused by cosmic rays, natural radionuclides in the environment. The seawater collection system mainly includes a filter, a metering pump, a one-way valve, an accumulator, and a flow controller. The seawater from the monitored area is driven through the filter by the metering pump, then transported to the sampling container. The function of the data processing system is to process the nuclear signals output by the nuclear radiation measurement system, ultimately obtaining the γ-ray spectrum of the monitored samples. When in-situ measurement of seawater in a certain sea area is required, the monitoring device can be installed on a ship and the seawater in the monitoring area can be pumped into the sampling container for measurement through metering pump.

Fig. 1
figure 1

The structure diagram of the shipborne radioactive monitoring device for seawater

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The minimum detectable activity (MDA) is defined as the minimum radioactivity that the detection system can detect within a certain confidence level. At a 95% confidence level, MDA can be represented as [19]:

$${\text{MDA}} = \frac{{4.65 \times \sqrt {N_{{\text{b}}} } }}{\varepsilon \cdot p \cdot t}$$
(1)

where ε is the full energy peak detection efficiency; p is the emission probability of γ photon; t is the live time of the measurement; Nb is the the background count.

To test the detection capability of the shipborne radioactive monitoring device, seawater samples were collected from the southern area of Dalian City (with a sample volume of 100 L). During the measurement, a metering pump was used to circulate seawater in the sampling chamber of the monitoring device and sample collection bucket, with the MDA of the device for 137Cs at different measurement times presented in Table 1. And the performance parameters of the monitoring device obtained according to the measurement results are shown in Table 2.

Table 1 MDA of 137Cs for different measurement time
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Table 2 Parameters of the monitoring device for radioactive seawater
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2.3 Source of uncertainty

As one of the most important artificial radionuclide, 137Cs is an indispensable monitoring item in marine environmental monitoring and evaluation. The shipborne radioactive monitoring device measures 137Cs in seawater directly, hence the decay correction for 137Cs can be ignored. Based on the efficiency calibration of standard source and γ-ray spectrometry, the calculation formula for the activity concentration of 137Cs in seawater is as follows:

$$A_{{{\text{Cs}}}} = \frac{{(n_{{\text{s}}} - n_{{\text{b}}} )A_{0} }}{{(n_{0} - n_{{\text{b}}} )}}$$
(2)

where ACs is the activity concentration of 137Cs in the seawater sample (Bq L–1); ns is the total count rate of the peak area of 137Cs (cps); nb is the background count rate of the instrument (cps); n0 is the total count rate of peak area of the standard source (cps); A0 is the activity concentration of the 137Cs standard source (Bq L–1).

When calibrating the detection efficiency of the instrument, a standard 137Cs solution diluted with seawater is used to prepare the 137Cs standard source. Therefore, the A0 in Eq. 1 is determined by the following formula:

$$A_{0} = \frac{{A_{{\text{s}}} \cdot V_{{\text{s}}} }}{{V_{0} }}$$
(3)

where As is the activity concentration of the 137Cs standard solution (Bq L–1); Vs is the volume of the 137Cs standard solution (L); V0 is the volume of the prepared 137Cs standard source (L).

Substitute Eq. 3 into Eq. 2 can be obtaoned:

$$A_{Cs} = \frac{{(n_{s} - n_{b} )A_{s} V_{s} }}{{(n_{0} - n_{b} )V_{0} }}$$
(4)

From Eq. 4, the relative uncertainty of measuring the activity concentration of 137Cs in seawater by using the shipborne radioactive monitoring device is mainly composed of five uncertainty components: (1) u1 is the relative uncertainty of γ count rate (Ns and Nb) in seawater sample; (2) u2 is the relative uncertainty of activity concentration (As) of 137Cs standard solution; (3) u3 is the relative uncertainty of the sampling volume (Vs) of 137Cs standard solution; (4) u4 is the relative uncertainty of the volume (V0) of 137Cs standard source; (5) u5 is the relative uncertainty of the γ count rate (n0) of 137Cs standard source.

2.4 Uncertainty calculation in direct measurement of seawater

2.4.1 Uncertainty of γ count rate of seawater samples

The uncertainty of count rate under the full energy peak of 137Cs in seawater samples arises not only from the statistical fluctuations of radioactive events but also from various other factors, including those related to the selection of the full-energy peak area of 137Cs and uncertainties introduced by the relative position of the detector [20]. During the measurement process of seawater samples, the sampling container is fixed with the lead chamber, ensuring precise positioning of the seawater sample relative to the detector. This makes the count variation due to geometric positioning significantly less than the statistical fluctuations of the count rate under full energy peak, thus the uncertainties due to different geometric positions can be ignored.

Due to the complexity of radioactive components in seawater and varying radioactive backgrounds in different areas (For example, the activity concentration of 238U in coastal seawater of China ranges from 28 to 146 mBq L−1, and the activity concentration of 40 K, the main radioactive contributor in seawater, ranges from 9.4 to 14.2 Bq L−1) [21], it is challenging to obtain the background count under the full energy peak of 137Cs from blank samples using the monitoring device. Instead, it can be read from the γ-ray spectrum of the seawater samples. Therefore, the time for measuring the seawater samples and the background is the same (i.e., ts = tb). The decay of radionuclides follows a statistical distribution, and the relative uncertainty of its net count rate is expressed as:

$$u_{1} = \frac{{\sqrt {\frac{{N_{{\text{s}}} }}{{t_{{\text{s}}}^{{2}} }} + \frac{{N_{{\text{b}}} }}{{t_{{\text{b}}}^{{2}} }}} }}{{\frac{{N_{{\text{s}}} }}{{t_{{\text{s}}} }} - \frac{{N_{{\text{b}}} }}{{t_{{\text{b}}} }}}} = \frac{{\sqrt {N_{{\text{s}}} + N_{{\text{b}}} } }}{{N_{{\text{s}}} - N_{{\text{b}}} }}$$
(5)

where ts and tb are the measurement times for the sample and background, respectively (s); Ns is the total count of the peak area of 137Cs in the sample; Nb is the total count of background in the sample.

2.4.2 Uncertainty of standard source preparation

The 137Cs standard solution, provided by the National Institute of Metrology, China, has an expanded relative uncertainty of 2.5% (k = 2). Therefore, u2 = 2.5%/k = 1.25%.

The relative uncertainty of the sampling volume of 137Cs standard solution includes three uncertainty components: calibration of the volumetric flask, repeatability, and temperature changes. According to the calibration certificate, at 20 °C, the legal tolerance for a 1000 mL single-mark volumetric flask (Class A) is ± 1.0 mL. Calculating by rectangular distribution, the calibration uncertainty u31 = 1.0/\(\sqrt 3\) = 0.58 mL; by repeating the process of filling the volumetric flask with ultrapure water 10 times and weighing on a balance with a sensitivity of 0.1 g, the average volume was 1000.5 mL, with a standard deviation of 1.05 mL, leading to a repeatability-induced standard uncertainty u32 = 1.05 mL; assuming a laboratory temperature variation of (20 ± 4)°C, and with the volumetric expansion coefficient of water being 2.1 × 10–4℃–1, calculating by rectangular distribution, the uncertainty in volume due to differences in calibration and operating temperatures u33 = 1000 × 2.1 × 10–4 × 4/\(\sqrt 3\) = 0.48 mL.

In summary, the relative uncertainty of the sampling volume of 137Cs standard solution is:

$$u_{3} = \sqrt {u_{31}^{2} + u_{32}^{2} + u_{33}^{2} } /V_{s} = 0.{128}\%$$
(6)

The volume of 137Cs standard source we prepared is 50 L, and the seawater is measured 10 times with a 5000 mL graduated cylinder. The uncertainty in the volume of standard source includes uncertainties due to calibration of the graduated cylinder, temperature changes, and repeatability of sampling. According to the calibration certificate of the 5000 mL graduated cylinder, at 20 °C, the capacity tolerance of the cylinder is ± 25 mL. Calculating by rectangular distribution, the relative uncertainty introduced by the calibration of cylinder u41 = 25/(\(\sqrt 3\) × 5000) = 0.289%. Measuring a volume of 5000 mL of distilled water with the cylinder, Weighing with a balance with sensitivity of 0.1 g, and repeating for 10 times, yielded an average volume of 4978.5 mL with a standard deviation of 47.92 mL, resulting in a repeatability-induced relative uncertainty u42 = 0.958%. The relative uncertainty due to temperature changes is referred to as u33, with u43 = 0.0485%.

In summary, the relative uncertainty of the volume of 137Cs standard source is:

$$u_{4} = \sqrt {12u_{41}^{2} + u_{42}^{2} + 12u_{43}^{2} } = {1}.{41}\%$$
(7)

2.4.3 Uncertainty of count rate of standard source

Referring to the quantification of the uncertainties of γ count rate in seawater samples, and considering the sufficiently count of peak area of 137Cs in the standard source, uncertainties arising from peak area selection can be ignored, with the main uncertainty coming from its own statistical fluctuations. For the standard source measurement, the live time is 72,600 s, with a total count of the peak area Ns = 3248 and background count of the peak area Nb = 621.5. The calculation method for u5 is the same as that of u1, calculated using Eq. 5 as u5 = 2.37%.

2.5 Combined standard relative uncertainty

After completing the sample measurements, an analysis of uncertainties of the measurement results was conducted. Considering all uncertainty components, the equation for the combined standard relative uncertainty is:

$$u = \sqrt {u_{1}^{2} + u_{2}^{2} + u_{3}^{2} + u_{4}^{2} + u_{5}^{2} }$$
(8)

3 Results and discussion

In October 2023, seawater samples were collected from the vicinity of a nuclear power station in northern China, with samples S1 ~ S4 collected near the station and S5 ~ S8 from further away. The obtained seawater samples were directly measured for 137Cs using the monitoring device, with the results and the relative uncertainties calculated according to Eq. 5 listed in Table 3. Using Eq. 8, the combined standard relative uncertainties for each seawater sample were calculated and are listed in Table 4.

Table 3 Measurement results of activity concentration for 137Cs in seawater samples
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Table 4 Comparison of direct measurement results of activity concentration for 137Cs in seawater samples with radiochemical analysis results
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To verify the accuracy of the measurement data, the collected samples were analyzed in the laboratory using radiochemical analysis method. Results obtained from radiochemical analysis method are also included in Table 4. Table 4 shows that samples S1, S2, and S3, due to shorter measurement time (30 min), had larger uncertainties caused by statistical fluctuations, resulting in greater differences from the radiochemical analysis results. S4, S5, and S6, with longer measurement time (180 min), showed good agreement between direct measurement and radiochemical analysis results, but S5 and S6 with low activity concentrations had larger uncertainties caused by statistical fluctuations. For S7 and S8 with lower activity concentrations, longer measurement time was set, the uncertainties were still large, but the differences compared to radiochemical analysis results were smaller. Radiochemical analysis requires sampling, then preparation and analysis in the laboratory, taking a longer time (3 days); the developed shipborne radioactive monitoring device allows for directly measured in the laboratory or sampling site, and a very low MDA can be obtained when the measurement time is long enough.

The shipborne radioactive monitoring device is mainly used for in-situ monitoring and early warning of marine artificial radionuclides. However, if the activity concentration of artificial radionuclides in seawater is lower than the MDA of the monitoring device, the instrument will not be able to accurately measure. Generally, when the nuclear power plant is in normal operation, the activity concentration of artificial radionuclides in the surrounding seawater is very low. China's national standard "Seawater Quality Standard" [22] stipulates that the activity concentration of 137Cs in seawater should not exceed 0.7 Bq L−1. Through the measurement of actual seawater samples, we found that the developed monitoring device can achieve a very low MDA when the measurement time is long enough (measurement for 1 h, MDA for 137Cs is 0.14 Bq L−1). Compared with the monitoring system established in Greece (using NaI(Tl) crystal as detector, energy resolution of 7.6%, measurement for 1 d, MDA for 137Cs is 0.018 Bq L−1), the real-time monitoring network of marine environment established in Germany (using NaI(Tl) crystal as detector, energy resolution of 6.9%, measurement for 30 d, MDA for 137Cs is 0.01 Bq L−1), and the marine radioactive detection device in Ireland (using NaI(Tl) crystal as detector, energy resolution of 7%, measurement for 1 d, MDA for 137Cs is 0.019 Bq L−1), our monitoring device can identify more artificial radionuclides and has higher sensitivity.

4 Conclusions

This paper studies the uncertainty in direct measurement of 137Cs in seawater samples under static measurement conditions using the shipborne radioactive monitoring device, analyzing the sources of uncertainty during the measurement process and calculating the combined standard relative uncertainty. The analysis shows that the main uncertainties affecting the measurement results of the device include the relative uncertainty of the γ count rate of the seawater sample, the relative uncertainty of the γ count rate and volume of the standard source. After identifying the sources of uncertainty, direct measurements and radiochemical analysis were conducted on seawater samples from the vicinity of a nuclear power station in northern China using the device in the laboratory, and the results of these two methods were compared. The results indicate that the monitoring device measured seawater for 1 h, and the MDA of 137Cs was 0.14 Bq L−1; the largest contributor to the uncertainty in the measurements of the shipborne in-situ radioactive monitoring device is the uncertainty caused by statistical fluctuations of the γ count rate of seawater samples. In practical work, according to the specific measurement conditions, measures such as increasing the sampling volume of seawater samples, improving the detection efficiency and prolonging the measurement time can be selectively taken to increase count rate of the peak area of 137Cs, thereby improving the reliability of the measurement results of the monitoring device.

As the test of the monitoring device is carried out in the laboratory, there are still some differences from the actual use, and the influence of environmental temperature, power supply stability and environmental radioactivity background on the measurement results is not considered. Next, we will continue to test the monitoring device, and improve the instrument in terms of data processing and transmission, lead chamber optimization, and electronics design, making it suitable for emergency monitoring in marine nuclear accident.