Estimation of temporal variation of tritium inventory discharged from the port of Fukushima Dai-ichi Nuclear Power Plant:analysis of the temporal variation and comparison with released tritium inventories from Japan and world major nuclear facilities

ABSTRACT We estimate monthly discharge inventory of tritium from the port of Fukushima Dai-ichi Nuclear Power Plant (1 F) from April 2011 to March 2020, using the Voronoi tessellation based on monitoring inside 1 F port and other techniques utilizing radioactive ratio of tritium to 137Cs in stagnant contaminant water and in discharge amounts. From the estimated results, we find that it dropped immediately after closing the seaside impermeable wall in October 2015 and simultaneously coincided with the sum of input inventories published by TEPCO. By comparing with published data on tritium release inventories in nuclear facilities, we find that the annual discharge inventory from 1 F port in the year 2011 is comparable to the maximum of operating pressurized water reactors in the order. At the national level, the total domestic release inventory significantly decreased after the accident owing to the operational shutdown of most plants. Furthermore, the total Japanese discharge inventory including 1 F are found to be minor compared with those of nuclear reprocessing plants and heavy-water reactors on a worldwide level. From the above results, we suggest that various scenarios can be openly discussed regarding the management of tritium stored inside 1 F with the help of the present estimated data.


Introduction
The accident in Fukushima Dai-ichi Nuclear Power Plant (1 F) operated by Tokyo Electric Power Company Holdings (TEPCO) caused leakage of large amounts of radioactive materials into the environment. Some of leaked radioactive materials were deposited on the ground and sea surface through atmospheric diffusion [1][2][3]. In addition, direct run-offs of contaminated water into the ocean occurred during 1 F accident [4,5]. Among leaked radioactive materials during 1 F accident, caesium isotopes ( 137 Cs and 134 Cs), which made a major part, have a unique property of being strongly fixed to soil clay minerals [6,7]. Therefore, most of the deposited caesium have remained at the top-layer of the soil, and then, such specific character has caused to sustain high air dose rates especially in highly deposited area. Thus, a certain region around 1 F was designated as the restricted area [8].
In 1 F accident, another major radioactive material, tritium (T: abbreviation), was also released into the environment [9][10][11][12][13][14][15][16][17][18][19][20]. Tritium is an isotope of hydrogen ( 3 H), and its main chemical forms are tritiated water (mainly HTO, with a tiny amount of T 2 O) and tritium gas (mainly HT, with a tiny amount of T 2 ) [21,22]. At the beginning of the accident, some of tritium were released into the atmosphere; however, most of it remained inside the reactors. Afterwards, a part of the remaining tritium migrated into the groundwater penetrating into the reactor buildings and cooling water, and main parts of them have been stored inside the tanks constructed inside 1 F site (after removing other radioactive materials) [23]. On the other hand, a part of tritium is regarded to have reached the sea via drainage channel, ground surface, and underground water flows. This paper focuses on the tritium discharged from 1 F port to the open ocean for about 9 years, from the beginning of the accident, April 2011 to March 2020, based on the temporal inventory variation inside 1 F port [24].
While some of the radionuclides released into the atmosphere due to 1 F accident fell into the sea, direct run-off of contaminated water into the ocean also occurred. Then, the concentration of radionuclides on the sea surface along the Fukushima coast temporarily increased at the beginning of the run-off accident, and the collected surface-layer fish also showed high concentration of radioactive caesium [25]. Afterwards, due to seawater flows such as the coastal and ocean currents off the coast of Fukushima, the radionuclides widely dispersed, and their seawater concentration rapidly decreased [26][27][28][29]. These observations are mainly for radioactive caesium isotopes, since the magnitude of their leaked inventories and the impact of their radiation effects are high [30]. On the other hand, there have been relatively few reports on tritium, especially on its initial discharge inventory [9,16,17,19,20]. However, the initial release amount of tritium into the sea should be estimated, because it is also one of the major nuclides released into the environment. Moreover, it should be noted that tritium has a high mobility in the environment due to its chemical properties [21,22] and finally discharges to the ocean without reacting with other substances. Due to their characters, tritium inventory discharged into sea should be continuously estimated from the beginning of the accident.
This paper focuses on tritium flowing into 1 F port and discharging to the open ocean after the accident, and estimates its discharge inventory from 1 F accident to 2020. First, monthly inventory discharged from 1 F port is estimated using the same method as previously reported for 137 Cs based on the monitoring results inside 1 F port [24]. However, since the monitoring of tritium inside the port began in June 2013, which is different from the case of 137 Cs, the tritium discharge inventory from the beginning of the accident to May 2013 is estimated by different methods using the radioactivity ratio (tritium (Bq/L)/ 137 Cs (Bq/ L)) [31] in stagnant water at the beginning of the accident, and the discharge-inventory ratio (determined based on the monitoring results inside the port) of tritium to 137 Cs after June 2013, respectively. Thus, the estimation period reported in this paper is a total of 9 years from April 2011 to March 2020.
After estimating the discharge inventory, an important issue that needs to be analyzed is clarification of the discharge sources. TEPCO has opened the data of tritium monitored separately in drainage water and subdrain etc. purified water on 1 F landside [27]. Thus, it is possible to compare them with the inventory discharged from 1 F port. If the main sources for the discharge inventory can be identified, it means that it becomes possible to effectively launch dischargecontrol measures to suppress the impact on the open sea. This paper estimates each inventory flowing and pouring into 1 F port through drainages, subdrain and groundwater drains (collected and released as subdrain etc. purified water) as well as groundwater bypass released outside of the port and compares their temporal variations with that of the discharging from 1 F port.
As the next important issue, we discuss long-term temporal variations in the tritium release inventory by including the period before 1 F accident. We compare the tritium discharge inventory after 1 F accident estimated in this paper with the release inventory before the accident and those of other normally operating nuclear power plants [32]. Tritium is a radioactive material, which is constantly generated and released even when nuclear reactors operate normally. Since tritium is difficult to separate and manage due to its chemical properties and its environmental impact is much smaller than other radioactive materials, each country has set its own standard and releases it at a concentration below the standard [21]. This paper compares the release inventories of Japan as a whole, before and after 1 F accident. Here, we note that the total domestic release inventory after 1 F accident include the discharged one from 1 F port. This study also compares 1 F and total domestic release inventories with those of major nuclear facilities around the world [21,[33][34][35][36]. So far, there have been few reports on inventory estimation of tritium discharged from 1 F after the accident [9,16,17,19]. Therefore, we have not sufficiently developed scientific discussions on total impacts of released tritium on the environment. In addition, by integrating the present estimations, it is expected that we can fully discuss the issue of the stored treated water [34], which has become a major social problem.
The contents of this paper are as follows: Section 2 explains the estimation method for the tritium inventory inside 1 F port and the inventory discharged from 1 F port to the coast of Fukushima. Since the method and its estimation results for 137 Cs have already been reported in the previous paper of this journal [24], the methodology is briefly described, while the new estimation results on tritium are discussed in detail. Section 3 analyzes main causes of the temporal variations of the estimated discharge inventory, and additionally evaluates the discharge inventory by comparing it with the inflow inventory into 1 F port as estimated separately from the data in drainage water and subdrains etc. purified water reported by TEPCO. Section 4 estimates the discharge inventory before the start of monitoring inside 1 F port (before May 2013). In the section, we use the radioactivity ratio of tritium to 137 Cs in the stagnant water and the ratio of the discharge tritium inventory (shown in Section 2) to the result of 137 Cs (estimated in Ref. [24]) for the estimation of tritium discharge inventory. Then, the estimated discharge inventory over 9 years from immediately after the reactor accident (April 2011) up to March 2020 is finally presented. Section 5 shows the annual discharge inventory after 1 F accident by using the results estimated up to Section 4, and compares it with the release inventory before the accident (during the normal operation). In addition, the annual variation of the release inventory in Japan as a whole (before and after the accident) together with each contribution from other operating nuclear power plant is presented. Furthermore, the release inventories from major nuclear facilities around the world are given as reference information, and the issues of stored treated water are discussed in comparison of them. Finally, Section 6 gives summary and conclusion.

Estimation of the tritium inventory discharging from 1 F port to open ocean using Voronoi tessellation
This section explains the Voronoi tessellation method that makes it possible to estimate the tritium inventory inside 1 F port and calculates the tritium inventory discharged from 1 F port. First, Subsection 2.1 explains the status of tritium monitoring inside 1 F port, and describes briefly the Voronoi tessellation method and the estimation method of the discharge inventory [24]. Subsection 2.2 reports the estimated monthly discharge inventory from June 2013 to March 2020. In order to analyze its temporal variation over 7 years, Subsection 2.3 discusses the variation in relation to the contaminated-water countermeasures and others carried out by the government and TEPCO. Figure 1 exhibits the temporal variations in the tritium concentrations measured inside 1 F port. Tritium monitoring began in June 2013 at multiple fixed points inside the port at an approximate frequency of once a week [37]. Among the monitoring data, Figure 1 shows temporal variations for three typical points as shown in the inset. From Figure 1, it is found that fluctuations of the measured concentrations inside the port are large, but the concentrations tend to be higher at points closer to land and lower at those closer to the port entrance. In the monitoring, the detection limit is set to a certain value, and the measured concentration is reported only when it is more than or just equal to the limit value, while the limit value is only published as the measured one is less than the limit ( Figure 1: the data are plotted only when the measured concentrations were reported). Figure 2 shows the monthly frequency at which the measured value falls below the detection limit (i.e. the number of times when only the detection limit value was reported/the number of measurements) together with the detection limit values. Initially, the detection limit value is set high, while it is found that efforts to reduce the frequency have been made by lowering the detection limit value against the decreasing tendency of the observed concentrations.

Monitoring of tritium inside 1 F port and estimation of discharge inventory using Voronoi tessellation
From these monitoring results, we explain how to estimate the tritium inventory discharging from 1 F port. First, we estimate the tritium inventory inside 1 F port and then multiply it by the daily seawater exchange rate in the port as the following formula [24].

Tritiuminventorydischargingfrom1Fport perday
Here, the seawater exchange rate (per day) of 1 F port is set to 0.44 as given by Kanda [28]. The value is also used in this paper as well as the previous paper [24]. It should be noted that since the value is calculated during the decay process of 137 Cs concentration inside the port immediately after the direct run-off of highly contaminated water from Unit 2 intake pit at the beginning of 1 F direct run-off accident, it is considered a value based on actual measurement data. However, afterwards, the northern seawall, etc. has been repaired [38], and the condition inside the port has gradually changed after 1 F accidents. The value of seawater exchange rate is now considered to be decreasing (that is, the closeness inside the port has been improved). Therefore, using the value (0.44) presently means that the estimation becomes somewhat a conservative assessment. On the other hand, if a large amount of fresh water rushes into the port due to heavy rain, the seawater exchange rate may increase temporarily. But, since tritium is different from 137 Cs, whose discharge inventory increases during heavy rain, i.e. most of them then discharge as suspended adsorption components, the tendency to underestimate the tritium discharge inventory is much less than that of 137 Cs. Actually, according to drainage channel monitoring, tritium concentration generally decreases during rainfall [39] due to dilution effects of sources. Moreover, in the case of 137 Cs discharge, it is necessary to consider adsorption effects on the seabed soil inside the port in setting the seawater exchange. However, the effect is estimated to be almost negligible at 1 F port level [28]. From all the above, it is considered to be fully reasonable to use the value for tritium assessments in the target area as seen in Figure 3a.
Next is the estimation method for tritium inventory inside 1 F port. The method is the same as for 137 Cs described in the previous paper. In this subsection, it is briefly described below. For details, the readers should refer to [24]. The tritium monitoring system inside 1 F port (monitoring points and their history) is summarized in Figure 3. As seen in Figure 3(b-d), the monitoring points are indicated by dots [37]. The monitoring of tritium concentration (Bq/L) inside 1 F port began in June 2013, and has continued until the present (December 2020). According to the monitoring system, the Voronoi tessellation [40] (see Figure 3), which takes into account the positional relationships with neighbor monitoring points, is suitable for simply evaluating the inventory inside the port. Voronoi tessellation defines the Voronoi area surrounded by vertical bisectors between adjacent points and divides the target area into multiple Voronoi areas (see Figure 3 (b-d)). The product of the area and average water depth gives the seawater volume of each Voronoi area. Thus, by multiplying the monitoring result (tritium concentration) with each volume, the tritium inventory of seawater in each Voronoi area can be estimated, and by summing all of these amounts, the tritium inventory inside 1 F port can be obtained. Then, the discharge inventory from 1 F port can be estimated by using the formula (1). Here, it is noted that our interest area inside the port is the target area shown in Figure 3a. The reason is that silt fences [37] are installed near the exit of Open Channel (units 1 to 4 Intake Open Channel: a rectangular port area for units 1 to 4 of 1 F to take in/drain seawater as seen in Figure 3(a) and also in Figure 1), and the seawater exchange rate between inside and outside the Open Channel is greatly suppressed. Therefore, only the target area can freely exchange seawater inside the port with one outside at the exchange rate (~0.44) Figure 2. Temporal variation of the monthly frequency when the measurement result was beneath the detection limit whose application periods are displayed along the upper arrows. [28]. In order to estimate the tritium inventory inside the port when the monitoring points are sparse as seen in the monitoring starting period, the monitoring concentration at adjacent points is redistributed as shown by the red arrows in Figure 3 (b-c) (the concentrations at the closest sampling points are mainly reused). Since March 2015, the monitoring has been done at 8 points as shown in Figure 3 (d), and the area inside the port has been covered by almost equal Voronoi area. Thus, it is found that the inventory accuracy inside the port has been improved.

Estimation of monthly tritium discharge inventory from June 2013 to March 2020 by Voronoi tessellation
This subsection shows results of the estimated discharge inventory using the method described in Subsection 2.1. Here, it is noted that when each monitoring value is input to estimate the inventory of each Voronoi area, the value may become less than the detection limit with the frequency as seen in Figure 2. Then, we input both the detection limit value and zero, and estimate the inventory within a certain range given by both values [24]. Since the true value lies between the detection limit and zero, the true discharge inventory is regarded to be within the range. Figure 4 shows the temporal variation in the monthly tritium discharge inventory from 1 F port estimated using the above-stated method (In Table 1, the monthly discharge inventory values during the above-mentioned period is written in black). As seen in Figure 4, the estimation values are composed of the maximum and minimum values, and the difference between the maximum and minimum values at the initial stage of the measurement is very narrow, but it has expanded approximately since the year 2015. This is because the frequency of the measured concentration being less than the detection limit relatively increases owing to tritium concentration inside the port decreasing as seen in Figures 1 and 2.

Analysis of temporal variation factors in tritium discharge inventory estimated by Voronoi tessellation
Now, we analyze temporal variation factors of the estimated discharge inventory over the period of about 7 years as shown in Figure 4. First, it is found that there is a slow decreasing trend as the years goes by, while relatively large fluctuations with repeating rises and drops occur intermittently. Then, the times when the relevant countermeasure works [41] were made in order to improve 1 F port environment are given inside the graph. As an increase event, there was movement of the outlet of K drainage channel from outside to inside of the port using pumps in April 2015 (since the  movement test was conducted from the end of March, it is considered to increase from March [39]), while as a significant decrease event, there was the seaside impermeable wall's closure [42] in October 2015. Due to this closing work, the discharge inventory decreased by about an order of magnitude (at the maximum). Thereafter, one cannot see large variation in the discharge inventory. In the case of tritium, the effect of the closing work was more clearly observed compared to the estimation results of caesium discharge inventory by the same estimation method [24] (see the inset of Figure 4: plots of both temporal variations of tritium and 137 Cs [24]). This difference is considered to be due to the chemical forms of both nuclides, i.e. tritium exists as an isotope of water, while caesium is partly adsorbed into particulate matters. In other words, since the partition of tritium in the particulate (solid phase) component is negligible compared to caesium, it is expected that the concentration in seawater decreases rapidly if contaminated water leakage is suppressed.

Comparison with the amount of tritium flowing into the port from 1 F land-site
Section 3 compares the tritium discharge inventory from 1 F port as estimated in Section 2 with the inflow inventory from 1 F land-site into the port, and clarifies major sources of tritium discharging from the port. Subsection 3.1 displays flow-courses of the purified water channels [43] for subdrain and groundwater drains in addition to drainage channels [44] mainly used for water (mainly rainfall) draining on 1 F landsite, and summarize their release destinations (inside/ outside of the port) based on the web information published by TEPCO. Subsection 3.2 estimates the inflow inventory through those channels into the port and compares them with the discharge inventory from 1 F port estimated in Section 2.

Drainage channels and purified water channels on 1 F land-site and the temporal changes of their flowing courses
This subsection shows flow-courses of the drainage channels and the purified water channels for subdrains and groundwater drains according to the web information published by TEPCO [43,44]. Figure 5 is a schematic figure showing the temporal changes of flow-courses of the drainage channels and the purified water channels inside 1 F land-site. The subdrains and groundwater drains correspond to wells pumping up groundwater near the reactor buildings and the bank protection, respectively, as Figure 5(d) schematically shows the well points. Once their pumped water is collected, it is purified and released as subdrain etc. purified water [43] (Note that it is denoted as 'subdrain etc. purified water' by TEPCO).
After 1 F accident, as seen from Figure 5(a-c) (only the flow-courses of drainage channels are displayed), the flow-courses of drainage channels have been changed, and their outlets have also been moved from outside of the port to inside. (The dotted lines indicate the flow-courses whose outlets are located at the outside of the port). Thus, if one assumes that the amount of tritium from 1 F site is always constant, the tritium inventory inside 1 F port should increase with their movements. However, as seen in Figure 4, the discharge inventory from 1 F port shows a decreasing trend. Therefore, the inflow tritium inventory via each drainage channel into 1 F port itself is regarded to decrease. Figure 5(d) shows the flow-course of subdrain etc. purified water, which is found to be always released into the inside of 1 F port. In addition, groundwater wells are located on the hill-side of the buildings in 1 F site, and the pumped water is always released into the outside of the port through the flowcourse called the groundwater bypass [45] as seen in Figure 5(d). Table 2 summarizes the release destinations of these drainage water and subdrain etc. purified water along with their changes with time. The blue color indicates the period when the outlets were located outside of the port, and the red color does the period during when they were set inside of the port. As seen from Table 2, the outlets of the drainage channels have been moved sequentially from the outside of the port to the inside, but those of the groundwater bypass and Unit 5 and 6 drainage channels are always kept at the outside of the port. In order to try to reduce the environmental impacts on the coast as much as possible, the outlets of the drainage water and subdrain etc. purified water generated near the reactor buildings, whose radioactive material concentrations are relatively high, have been moved into inside of the port. By being released into the inside of the port, the radioactive materials can temporarily stay inside the port. Then, one can expect effects of dilution inside the temporarily isolated area, delay of discharge into the coastal environment, and benefits of enabling Start of monitoring estimations and evaluations of the inventory of radioactive materials inside the port due to the temporary retention as reported in [24]. This section clarifies only the tritium inventory flowing into the inside of the port except for a part of exception.

Estimation of tritium inventory flowing into 1 F port via inflow of the drainage water and subdrain etc. purified water
This subsection estimates the inflow inventory of each drainage water and subdrain etc. purified water shown in Table 2, and compares them with the estimated discharge inventory from the port shown in Section 2. In each drainage channel, once a week (once a day for caesium isotopes and gross beta) for the concentration of tritium (Bq/L) and once a day for the flow rate (m 3 /sec) are monitored, and their data is all published [27] (Note: the monitoring has started since 16 April 2014). Then, it is possible to estimate the monthly flow inventory by calculating the product between the published concentration and flow rate over a month. In the monthly estimation, we obtain the monthly flow inventory by averaging over about 4-times sampling results per month with averaging everyday flow rate. We regard that the estimated monthly discharge inventory is valid for comparison with the discharge inventory from 1 F port, since the fluctuation of tritium concentration is rather small in the drainage water [27]. Figure 6 shows the temporal variation of the estimated monthly flow inventory into the port via the drainage water and subdrain etc. purified water together with the monthly discharge inventory from 1 F port. The inset of Figure 6 shows breakdown details of the monthly inflow inventory of the whole drainage water and subdrain etc. purified water.
In Figure 6, it is found that the estimation results of the discharge inventory from 1 F port roughly coincides with those of the sum of the drainage water and subdrain etc. purified water flowing into the port after the seaside impermeable wall was closed (October 2015). By concentrating on the features in details, one finds that the coincidence occurs between the inflow inventory and the minimum estimation of the discharge inventory. Here, it is noted that the inflow one does not show such width from the minimum to maximum, since the data is almost beyond the detection limit. Moreover, the inflow is found to be mainly originated from the K drainage channel, whose tritium concentration is relatively high, dominates over the inflow inventory into the port, and rarely falls below the detection limit, i.e. the overestimation is fully suppressed. This result clearly suggests that tritium discharging from 1 F port can be traced after the seaside impermeable wall was closed, that is, the drainage water and subdrain etc. purified water have been the main discharging sources from 1 F port since then. On the other hand, it is found that there were unidentified discharging sources other than drainage water [27] and subdrain etc. purified water [43] before then. In addition, the unknown contribution is found to be about an order of magnitude larger than the sum of the drainage water and the subdrain etc. purified water before the closure. Figure 6. Temporal variation of monthly estimation of tritium discharge inventory from 1 F port and estimated tritium input inventory into 1 F port through all drainages and subdrain etc. purified water with the insert figure for their component decomposition.
As mentioned above, since the large unidentified discharge was regarded to be suppressed by the closure of the seaside impermeable wall [42], it is found that efforts should be made to reduce the tritium concentration of drainage water and subdrain etc. purified water in future in order to further reduce the discharge inventory to the ocean.
Additionally, Figure 6 suggests a stepwise increase in May 2015 in the temporal variation of the release inventory from the drainage channels into 1 F port. This is because the outlet of the K drainage channel, whose radioactive concentration mostly dominates over other drainage ones, was moved to the inside of the port [46] (see the main construction period shown in Table 2). After the event, although monthly fluctuations always appear, the data shows a gradual decreasing trend. On the other hand, the contribution of subdrain etc. purified water increased just after starting the measurement, but the variations were small since 2016, and the release inventory into the port has been maintained almost constant. The groundwater bypass [45], which always releases outside of the port, is also shown as reference information. Its flow inventory is significantly smaller than other flow inventories, and there is almost no temporal variation. This little variation is because it reflects the relatively stable flow of groundwater resulting from rainfall in a large catchment area including the outside area of 1 F site. The groundwater is pumped at the so-called hill side for the reactor buildings and bypassed into the outside of the port.
From the above results, a main reason for the gradual decreasing trend of the discharge inventory from 1 F port after the closure of the seaside impermeable wall is found to be originated from the declining trend of tritium in K drainage channel (the drainage channel collects the drainage water around the reactor buildings, in which the accident occurred: see Figure 5), which mostly contributes to the input inventory into the port. Thus, while further reduction in K drainage is expected as the decommissioning continues, controlling the tritium release of subdrain etc. purified water [47] should be also maintained continuously in future.
At present (March 2020), the amount of groundwater inflow into the reactor buildings has decreased partly due to the installation of the landside impermeable wall [48], but a finite amount of contaminated water is still constantly generated, and the amount of stored treated water containing tritium continues to increase. As a solution to resolve this problem, the release of the stored treated water into the ocean has been discussed [21,49]. Here, we point out that it is now possible to assess release plans considering the environmental impacts more accurately by accounting for the estimated discharge inventory from 1 F port due to the release of drainage water and subdrain etc. purified water in addition to the planned release amount of the stored water. At present, since the unidentified discharge was almost suppressed as described above, we can concentrate only on wellcontrolled release impacts on the environment.

Estimation of tritium discharge inventory from 1 F port just after 1 F accident
Section 4 estimates the discharge inventory before starting the tritium monitoring inside the port, that is, before May 2013. First, Subsection 4.1 classifies the discharging states of 137 Cs from 1 F port into three periods after the accident up to March 2020 based on differences in the decreasing tendencies. Subsection 4.2 estimates the tritium discharge inventory for the classified initial period using the radioactivity ratio of tritium to 137 Cs in the stagnant water inside the buildings at the beginning of the accident [31], and the discharge inventory ratio of tritium to 137 Cs in the following period. As mentioned above, we try to estimate the tritium discharge inventory from 1 F port for about 2 years from April 2011 to May 2013 for the monitoring missing period, in which the tritium monitoring was not carried out inside 1 F port.

Classification of temporal variations in the discharge inventory of 137 Cs from 1 F port after the accident
First, we show a comparison between the estimated results of 137 Cs discharge inventory from 1 F port given by the authors in Ref. [24] and the tritium discharge inventory estimated in this paper in Figure 7. It is found from Figure 7 that 137 Cs monitoring inside the port was carried out from the beginning of the accident (April 2011), while it is necessary to perform estimations of tritium discharge inventory by using different ways from the beginning of the accident up to May 2013, since the tritium monitoring [37] was started at June 2013. Here, one finds that there is a rough correlation between the temporal variations in the discharge inventories of the two nuclides ( 137 Cs and tritium), although there are somewhat deviations with their own fluctuations as seen in Figure 7. Besides, we show a double logarithmic graph of the temporal variations of the estimated discharge inventory of 137 Cs and tritium in the inset of Figure 7. It is found from the inset that the discharge-inventory status can be roughly classified into three periods due to the difference in the decreasing tendency of 137 Cs. The first is the period of about 3 months at the beginning of the accident (referred to as Period I), during which the concentration inside the port rapidly decreased via the exchange of seawater between inside and outside of the port after the accidental direct runoff of rather highly-contaminated water into the port [28]. At the beginning of this period, the ratio of 137 Cs to tritium discharge inventory is considered to follow the radioactivity ratio [31] of stagnant water inside the reactor building [19]. The reason is that it was confirmed that the stagnant water flowed directly into the port [50,51]. The second is the period during which the influences of the direct run-off almost disappeared and the continuous unidentified run-off occurred (referred to as Period II). It is natural to regard that Period II characterized by this unidentified continuous run-off had continued until the seaside impermeable wall was closed [42] (see Section 3). After this period, it is set to Period III, and as shown in Section 3, the tritium discharge inventory from 1 F port roughly matches the tritium amount of drainage water and the subdrain etc. purified water. It is also found from the inset that there is a difference in the decreasing tendency between Periods II and III. As described above, the temporal variations of the discharge inventories of 137 Cs can be classified into three periods, and the tritium discharge inventory of each period can be estimated based on the separately monitored and estimated 137 Cs in the following subsections.

Estimation of tritium discharge inventory from 1 F port from the beginning of the accident up to May 2013
First, we estimate the tritium discharge inventory for the initial Period I defined in Subsection 4.1. At Period I, the direct run-offs of the stagnant water inside the reactor building were regarded to occur initially (especially, the influence of the direct run-off from the vicinity of Unit 2 intake pit [50,51] was dominant). Therefore, if the discharge inventory of 137 Cs is given, then that of tritium can be estimated [19] by the concentration ratio of the stagnant water inside the building (tritium concentration/ 137 Cs concentration) [31]. The concentration of each nuclide in the stagnant water in the turbine buildings at the beginning of the accident was reported by Nishihara et al. [31]. According to the literature, the concentration ratio differs depending on the sampling points of the stagnant water (the difference mainly exists among the reactor units and the sampling positions), but we set the concentration ratio of tritium/ 137 Cs to be 0.0126 by using the measured values 137 Cs: 1.9E + 6, and tritium: 2.4E + 4 of Unit 2 seen in Table 7 of Ref. [31] based on the fact that the direct run-off occurred from Unit 2. The choice of the set values allows avoidance of underestimation of the tritium discharge inventory, since it makes the concentration ratio maximum in choosing concentration values inside Unit 2 stagnant water samples. Then, the estimation result of April 2011 is shown in Table 1 (red in Table 1) and shown in Figure 8 (plot with Δ in Figure 8). In Period I (for 3 months), except for the estimation in April (at the beginning of the accident), the method using the concentration ratio of the stagnant water is considered to be less reasonable in terms of the validity, since the direct run-off of stagnant water was suppressed within a few days. However, we keep the above conservative estimate, that is, the same amount as the discharge of the direct run-off is assumed to continue even in May and June (referred to as Period I'). This means that the same amount as discharged in April continued even for other two months (light blue in Table 1 and plotted with ◇ in Figure 8). Since this estimation is unlike the variation in the estimated discharge inventory of 137 Cs, it appears to be much excessive at first glance, but its validity is described in detail below in relation to the estimation in Period II. Here, for the comparison, we note that the tritium discharge inventory at the initial stage of the accident was estimated in some papers [9,16,17,19]. While the amount value is different among the literatures, but it is estimated in the range of 0.05 PBq −1.0 PBq. In these values, the estimations in Refs. [9,16,17] include both the fallout from the atmosphere and the direct run-offs, while Ref. [19] focuses only on the direct run-off and estimates it to be ~0.05 PBq based on the concentration ratio of tritium to 137 Cs in coastal (offshore) monitoring results. Since these estimation results are approximately at the same level as our results (see Table 1: April 2011: 0.024 PBq and Section 5, Table 3: the discharge inventory in year 2011 is 0.14PBq), the validity of the present estimation is considered to be within the literature allowable range.
Next, we try to estimate the tritium discharge inventory during Period II after the influences of direct run-offs disappeared. During this period, it is regarded that the unidentified discharge continued until the closure of the seaside impermeable wall in 2015. In this period, since both tritium and 137 Cs were monitored inside the port for about 2 years from June 2013 until the closure, the discharge-inventory ratio of both nuclides can be estimated. In fact, there seems to be a correlation between the estimated discharge inventories of both nuclides as seen in Figure 7, and the correlation is shown in the inset of Figure 8. Although there are certain variances, the maximum value of the discharge-inventory ratio of tritium to 137 Cs (the ratio shown by the solid line in the inset is 12.8) is used to estimate the discharge inventory of tritium in order to avoid its underestimation. The results are shown in Table 1 (purple characters in  Table 1) and Figure 8 (plot with □ in Figure 8) for Period II.
Here, we discuss the above-mentioned estimation results in Period I and beginning parts in Period II. It is found from Figure 8 that the tritium discharge inventory at the first month just after the accident is much smaller than that of 137 Cs, since the ratio has been estimated to be about 0.0126 (~ 1/79) due to the nuclide concentration ratio [31] in stagnant water. However, the ratio of tritium to 137 Cs is found to significantly increase in the unidentified continuous run-off Period II after the direct run-off was suppressed. From July 2013 to just before the seaside impermeable wall was closed, i.e. during Period II, the ratio was 12.8 to 137 Cs at the maximum as seen  in the inset of Figure 8. Thus, it is found that the ratio increased by about 1000 times from Periods I to the initial period of Period II. Here, it is noted that it is difficult to estimate the time development of the large ratio change until it increases by approximately 1000 times. However, if the maximum ratio measured in Period II is applied to May and June 2011 (Period I'), the estimation results are found to significantly exceed over that at the beginning of the accident (estimated amount in April 2011). Then, such extrapolation is regarded to be clearly unnatural. On the other hand, if the initial discharge estimated on April 2011 continues just for the next 2 months (May and June 2011) as mentioned above, the estimated values of the initial Periods I and II become smoothly continuous, and then the temporal variation is regarded to be rather natural as shown in Figure 8. From the above, although the present estimation in the initial period is conservative, it can be judged to be a rather reasonable and natural estimation.
Next, we discuss the reason why such 1000-times increase in the discharge-inventory ratio occurred from Period I to II. At the time when the direct runoff occurred, the actual run-off [50,51] of stagnant water itself was visually identified. After the suppression measures were rapidly made, the contaminated water flow was considered to be blocked and infiltrated by the bank protection soils and underground structural materials. This indicates that radionuclides in the contaminated water could sufficiently contact with them in the underground area. Thus, it is considered that the discharge amount of 137 Cs, whose adsorption tendency to clay minerals are much stronger [6,7] than tritium, was significantly reduced compared to that of tritium, i.e. a large amount of 137 Cs was considered to be adsorbed on the soils and structural materials around the bank protection area. In addition, the history that various contaminated water treatment systems have step-wisely started their operations since June 2011 is considered to partially contributed to the change of the concentration ratio of tritium to 137 Cs in the discharged water. Thus, the discharge inventory of 137 Cs decreased significantly due to the filtering and adsorbing effects by underground media with operations of water treatment systems, while the tritium discharge inventory remained almost unchanged due to tritium's high mobility in soils and no isolation in the treatment systems on the contaminated water. Therefore, the discharge inventory of tritium is considered to exceed that of 137 Cs during Period I (I') (see Figure 8). In addition, one finds that the situation, i.e. the ratio of tritium discharge inventory is larger than 137 Cs, has continued in period III after the closure of the seaside impermeable wall. This is also because tritium has much higher mobility compared to caesium.
We have so far discussed about 1000-times variation in the discharge ratio considered to occur in Period I and partly Period II. The difference in reactivity of the two nuclides with soil and related materials (as generally described by the difference in solidliquid partition coefficient) is considered to be a main factor behind the occurrence of such large variation on the discharge inventory. However, it is difficult to accurately estimate the detailed temporal variation of the discharge inventory. Then, we judge that while the estimation made in this subsection has a certain uncertainty, it is at least valid as a conservative estimation.

Comparison with the tritium release inventory before 1 F accident and those of whole Japan and major world nuclear facilities
In this section, we compare the tritium discharge inventory after 1 F accident estimated in the previous sections with the tritium release inventory during the normal operation before the accident and the release inventory from other operating nuclear power plants in Japan as well as major nuclear facilities around the world [21,[33][34][35][36]. In addition, we show temporal variations of the release inventories of the all-Japan nuclear facilities before and after the Fukushima accident [32], by including the discharge inventory from 1 F port after the accident. First, Subsection 5.1 shows the annual discharge inventory from 1 F port from 2011 to 2019, and compares it with the release inventory in normal operation conditions before the accident. Subsection 5.2 shows the temporal variations in the release inventory of all Japan nuclear facilities before and after the accident as well as the release inventory from each plant in Japan. Finally, we compare the above-stated results with the release inventory in major nuclear facilities around the world [21,[33][34][35][36], and discuss the issue of planned release into the sea of stored and treated water containing tritium [49].

Comparison between the tritium release inventory before 1 F accident and the discharge one from 1 F port after the accident
First, Table 3 shows the annual discharge inventory from 1 F by adding together from the monthly discharge inventories after 1 F accident estimated in the previous sections. In the years 2011-2013, only the Table 4. Annual release inventory of tritium (Bq/year) from Japanese major nuclear facilities including Fukushima Dai-ichi Nuclear Power Plant (highlighted by blue and red colours for those before and after 1 F accident, respectively) in Japan. The first column shows the plant name (company or organization and PWR or BWR) for each nuclear power plant.  maximum estimation value is given in contrast to other years. This is because only the conservative estimation is possible during 2011-2013 as explained in the previous section. Table 4 shows the estimated maximum annual discharge inventory after 1 F accident (written in red) and the annual release inventory in normal operation conditions before the accident [32] (in blue). Table 4 also shows the annual release inventories of other nuclear power plants based on the published data [32]. The inset of Figure 9 shows the temporal variation in the annual release inventory including the discharge one after the accident from 1 F port as shown in Table 4. As mentioned above, by comparing it with the annual release inventory during normal operation conditions before the accident, it is found that the annual release inventory during normal operations and the annual discharge one after the accident from year 2011 to 2015 are almost at the same level, except for the outstanding discharge inventory in the accident year 2011. On the other hand, it indicates that the annual discharge inventory since year 2016 has been reduced to about half of the release inventory during normal operation conditions (see Table 4 and the inset of Figure 9). From the comparison before and after 1 F accident, it is found that the current tritium discharge inventory is less than that during normal operation conditions, i.e. being sufficiently suppressed at present (year 2020). However, the contaminated water is still generated due to the inflow of groundwater into the reactor core, and tritium has been stored in a number of tanks constructed inside 1 F site [23]. One of the reasons why the treated water has been stored is difficulty to separate tritium from contaminated water in reasonable costs. Thus, the mass increase of stored treated water has become a major issue in smoothly proceeding with 1 F decommissioning. The government and TEPCO are now required to take measures to resolve the issue [21,23,49].

Comparison with the release inventories of operating nuclear power plants and major nuclear facilities in Japan and overseas
From , which generally release much more tritium than boiling water reactors. Moreover, heavywater reactors release even more tritium [21]. By paying attention to these releases, it is found that the maximum annual releases during PWR operation and the estimated discharge inventory from 1 F in 2011 are at the same level. Next, focusing on the annual variation of tritium release inventory in Japan as a whole (see Figure 9), it is found that the domestic total release inventory shows the maximum due to the contribution from 1 F in 2011, but it has decreased significantly since 2012. This is mainly due to shutdowns of nuclear power plants in Japan after 1 F accident.
Here, we also show the annual release inventories from the world's major nuclear facilities in Table 5 for comparison [21,[33][34][35][36]. From these data, it is found that there are several nuclear facilities [21] (heavywater reactors and reprocessing plants) that release much larger inventories (in different orders) than that estimated in 1 F at the accident year 2011.
Thus, the impact of 1 F accident is found to be tiny if one compares the tritium discharge inventory into the ocean in 1 F accident with the release inventories from Table 5. Annual release inventory of tritium (Bq/year) in major nuclear facilities in the world and tritium production and release data as reference information.  (2006-2008). The comparison of these release inventories with those of the world's major nuclear facilities shows that Japanese contributions are significantly small. Here, it should be noted that their values in Japanese reprocessing plants are cumulated ones during total operating years as described above, while those in the world's major ones are annual discharge inventories. Currently (2020), the treated water stored in the tanks inside 1 F site has contained approximately 10 15 Bq of tritium, and the further non-stop increase of the stored amount has been a major problem [23] in 1 F decommissioning. In order to smoothly carry out the decommissioning works at 1 F site, its release into the ocean is being discussed as an option [21,49], but as already pointed out, controlled management of the release inventory is strongly required with taking into account the additional discharge inventory from 1 F port to the ocean as presented in this paper. If the release of the stored one into the ocean is conducted, it is necessary to systematically study environmental impacts of the planned releases through various case studies to explore tritium concentration distributions and their temporal variations in advance. Based on the information, it is important to make consensus among the concerned parties before the release. As an example, we can perform scientific analysis and clarification such as comparison among the distributions of seawater tritium concentration before 2011 (1 F and 2 F were normally operating together), those after 1 F accident, and those after the ocean release conduction. As for the monitoring system after the release, it is possible to check the monitoring plan by utilizing various data accumulated until now. Regarding the Fukushima coast, many studies have been made after 1 F accident, and various knowledges such as diffusion and convection of radioactive materials have been piled up. Thus, we can conduct sufficient advanced analysis and exchange various information to enhance the scientific understanding on the coastal environmental impacts by the release. We believe that those activities help to get consensus among the concerned parties and organizations.

Conclusions
In this paper, the tritium discharge inventory from 1 F port to the open sea was estimated from the monitoring results inside the port by using Voronoi tessellation. Since the monitoring of tritium inside the port [37] began in June 2013, the discharge inventory from June 2013 to March 2020 was estimated by the above method. Next, the discharge state from the beginning of the 1 F accident to the present (March 2020) was divided into three periods according to the decreasing trend of 137 Cs discharge inventory [24]. In Period I, immediately after 1 F accident, the tritium discharge inventory was estimated based on the radioactivity ratio of tritium to 137 Cs in the stagnant water [31], and in the subsequent period, Period II, before starting the monitoring, it was calculated by using the estimated discharge-inventory ratio of tritium to 137 Cs obtained from the monitoring results inside 1 F port. Thus, the monthly discharge inventory for 9 years from April 2011 to March 2020 was totally estimated.
From the above estimation results, it was found that the discharge inventory of tritium has a gradual decreasing tendency after 1 F accident, while it has significantly dropped due to the closure of the seaside impermeable wall in 2015 [42]. Before the closure, it was considered that unidentified discharge had continued to occur into 1 F port through the bank protection. Next, the discharge inventory after the closure of the wall was found to coincide approximately with the tritium release inventory calculated from the drainage water and the subdrain etc. purified water. From this fact, i.e. sources of the tritium discharge inventory were recognized, it can be judged that the tritium discharge is partially under control. Next, by comparing the estimated discharge inventory from 1 F port with the released inventory into the sea during the normal operation period before 1 F accident [32], it was found that the discharge inventory other than 2011 (the accident year) is lower than the release inventory during the normal operation, and is sufficiently low compared to the release inventory of other operating major nuclear power plants. Moreover, the discharge inventory of 2011 was found to be at the same level in order as the release inventories in the operating PWR plants. On the other hand, in the nation level, Japan's total release inventory including the estimated tritium discharge inventory from 1 F was found to decrease significantly since 2012. Furthermore, the level of the total domestic release inventory is sufficiently low compared to the world's major nuclear facilities [21,[33][34][35][36] showing particularly high release inventories. In future, further suppression of the discharge inventory from 1 F will be demanded, while it will be necessary to widely discuss the issues of the treated water stored inside 1 F site [23] based on rich scientific information through various comparative studies as described above.

Note
Just after the submission of this paper (March 2021), the Japanese government decided to release the stored treated water of 1F into the sea in April 2021. We believe that the contents of this paper are now of more significance than the submission date.